Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.39.0-wmf.23 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk Gadget Gadget talk Gadget definition Gadget definition talk 4 1558 2412419 2411218 2022-08-06T22:22:32Z AJbobcat 2947782 The illojim created us. We are primitive ancestors to aliens. wikitext text/x-wiki {{Please leave this line alone (sandbox heading)}} <!-- Hello! Namaste! Feel free to try your formatting and editing skills below this line. As this page is for editing experiments, this page will automatically be cleaned periodically. --> Practice in sandbox HI all the illojim is our creator which is a race of aliens that are far advanced from us g3dvl424ge2o9t9ae2ian0fad16hd4t 2412428 2412419 2022-08-06T23:05:55Z Dave Braunschweig 426084 Cleanup wikitext text/x-wiki {{Please leave this line alone (sandbox heading)}} <!-- Hello! Feel free to try your formatting and editing skills below this line. As this page is for editing experiments, this page will automatically be cleaned periodically. --> copaadgn6cz69177ksi0b8aalofil0h 0 8478 2412375 2344298 2022-08-06T14:48:37Z Torvalu4 450271 /* Vestitive act */ wikitext text/x-wiki ==The definition of cession== ::::'''Cedent''' ↔ (transfers his right to) ↔ '''Cessionary''' ::::↑(obligation to cedent) ::::'''Debtor''' The principles of cession were clearly defined in ''Johnson v Incorporated General Insurance Ltd'' 1983 (1) SA 318 (A), which stated that cession in our modern law can be seen as: #A '''transvestitive''' (or '''translative''') juristic act (''oordragshandeling'') #Which transfers a personal incorporeal right emanating from an obligation (''translatio iuris'') #By means of a '''real agreement''' (''saaklike ooreenkoms'') #Made between the cedent and the cessionary #Arising out of a '''''iusta causa cessionis''''' #From which the cedent’s intention to transfer the right to claim ('''''animus transferendi''''') appears or can be inferred #From which the cessionary’s intention to become the holder of the right ('''''animus acquirendi''''') appears or can be inferred. #The ''causa cessionis'' can be a payment (''solutio''), securing of a debt, or an '''obligatory agreement''' (''verbintenisskeppende ooreenkoms'') embodying for example: #*An alienation, e.g. sale, exchange, or donation; #*A settlement (''transactio''); #*A loan. #The cessionary can cede his right to someone else; this is known as '''on-cession'''. #If the on-cessionary (= retrocedent) cedes back his right to the original cessionary (= retrocessionary), we have a '''retrocession'''. #If the parties wish to '''resile''' from the cession agreement; #*and their intention is to cancel or take back the real agreement ('''''animus cancellandi'''''), #*the '''dissolution agreement''' has the effect of a retrocession under which #*the ceded right reverts back to the original cedent. ==Various juristic acts distinguished== From the above, it will be seen that there are several juristic acts incorporated into any cession. # A '''vestitive''' act (e.g. an obligatory agreement) # A '''transvestitive''' act embodied in the real agreement # Two '''divestitive''' acts; and potentially # A dissolution agreement. These acts will be examined in more detail below. ===Vestitive act=== The vestitive (or constitutive) juristic act can be a will, subrogation, court order, securing of a debt or a mere payment (''solutio''),<ref>Louis F. van Huyssteen & Catherine J. Maxwell, ''Contract law in South Africa'', 5th edn. (Alphen aan den Rijn, The Netherlands: Wolters Kluwer, 2017), § 332.</ref> but is usually an obligatory agreement between the '''debtor''' and the '''cedent'''. This act creates an obligation which vests a personal right to performance (or ‘claim’ or ''ius crediti'') in the cedent and a duty to perform in the debtor. It is in fact the ''causa'' of the cession agreement. If an obligatory agreement, it may arise from a number of causes, for example: *a sale *a loan agreement *an undertaking to perform in future *a lease, etc. Thus in schematic form, the vestitive act between the debtor and the cedent becomes the ''causa cessionis'' for the real agreement between the cedent and the cessionary. ::::'''Cedent''' ↔ (cession agreement) ↔ '''Cessionary''' ::::↑(vestitive act = the ''causa cessionis'') ::::'''Debtor''' A series of propositions will be developed in the following discussions. #Relating to the obligatory agreement, let us assume that Donald the debtor owes Cedric the cedent R100.00. The reason for his debt is the sale of goods by Cedric to Donald with payment to be made at the end of the month. ===Transvestitive act=== The transvestitive (or translative) juristic act is the cession agreement (''pactum cessionis''), that is, the real agreement between the '''cedent''' and the '''cessionary''' to divest the cedent’s right to performance and vest it in the cessionary. It is not necessary for the cession agreement to be in writing, but it is advisable See ''Botha v Fick'' 1995 (2) SA 720 (A) where it was held that ‘mere ''consensus'' is sufficient to effect a cession’. The essential elements of the cession agreement are: # An '''''animus transferendi''''' - the cedent’s intention to transfer his/her claim to the cessionary; # An '''''animus acquirendi''''' - the cessionary’s intention to accept transfer of the claim from the cedent; and # A '''''causa cessionis''''' - the vestitive act constituting the underlying obligation between the debtor and cedent. On performance of the cession agreement, the claim passes permanently to the cessionary. From that point onwards, the cession cannot be revoked unilaterally by either the cedent or the cessionary. In schematic form the cession agreement is between: ::::'''Cedent''' ↔ (cession agreement) ↔ '''Cessionary''' ::::↑(vestitive act) ::::'''Debtor''' To continue with the proposition. #Donald the debtor owes Cedric the Cedent R100.00 #Cedric wishes to sell his claim to Susan the cessionary for R90.00. #Susan wishes to purchase the claim from Cedric for R90.00. The Cedent and cessionary have two choices in drafting the cession agreement. :They can incorporate the sale of the claim and cession of the claim into one agreement. #* '''Sale and cession:''' Cedric hereby sells and transfers (cedes) to Susan his claim against Donald in the sum of R100.00 for the sum of R90.00. Alternatively they can seperate the two agreements out. #*'''Sale''' *Cedric sells his claim of R100.00 against Donald to Susan for the sum of R90.00 #*'''Cession''' On payment of the sum of R90.00 by Susan to Cedric, Cedric will cede (transfer) his right title and interest in his claim against Donald to Susan. Once the cession is effected, the cedent falls out of the picture, and the ''vinculum iuris'' is between the debtor and the cessionary. ===Divestitive acts=== If one analyses it carefully one will see that there are in fact two divestitive acts extinguishing obligations. #The first is the act extinguishing the cedent’s obligation to the cessionary. This occurs through the actual cession or transfer of the cedent's claim against the debtor. In our example, Cedric is divested of his claim for R100.00 owed by Donald when ceded to Susan. #The second is the act extinguishing the cessionary’s obligation (if any) to the cedent. In our example it is the payment by Susan of R90.00 to Cedric the cedent. However, there may not be an obligation here if the claim is ceded gratuitously, i.e. a donative cession. #The discharge of the debtor’s obligation to the cessionary is not strictly a part of the cession, as the real agreement is only between the cedent and the cessionary. But it is an inevitable consequence of the transfer of the claim and the ''causa cessionis'' in the first place. It is therefore mentioned here. === Resolutive or dissolution agreement=== The resolutive agreement refers to an agreement between the cedent and cessionary where they agree to retrocede the ceded right for some or other reason. It may be for example that the cedent has borrowed money from the cessionary and ceded a claim due to him as security for the loan. You will recall that on transfer, the ceded claim becomes an asset in the estate of the cessionary. Once the cedent’s debt has been repaid to the cessionary, the cessionary would be unjustly enriched if she retained the cedent’s [former] claim as she would have received both the money from the cedent and the claim. It is in circumstances such as this that a resolutive agreement comes into play. See for example ''Lief v Detmann'' 1964 (2) SA 525 (A) where it was stated that: *‘The only way in which a right of action can be furnished as security for a debt is by way of cession, i.e. by a transaction which in our law results in the cedent being divested of his rights and those rights vesting in the cessionary. Where the cession is made in security for a debt, it does not in my opinion signify that the cedent retains any right in the subject matter of the cession; his continued interest flows from the agreement either express or implied with the cessionary that the right of action will be ceded back to him on the discharge of his debt.’ ==References== {{reflist}} {{CourseCat|filing=deep}} ey40fn1g5jzuewuqbxm5m4i4vuhpc06 0 53432 2412438 2404478 2022-08-07T01:54:03Z Marshallsumter 311529 wikitext text/x-wiki '''2022''' * '''22 August''': First day of classes for the [[Radiation astronomy/Courses/Principles/Syllabus/Fall|Fall semester of Principles of Radiation Astronomy]] an advanced undergraduate course. * '''July 4''': The lecture [[Radiation astronomy/Alloys|Radiation astronomy of alloys]] and its [[Radiation astronomy/Alloys/Quiz|quiz]] are ready for students. * '''June 5''': The course [[Intentional Evolution]] is now available and is part of the [[Unleashing_Creativity/possibilities_curriculum|Possibilities]] curriculum. * '''May 29''': The political essay [[Gota Go Home! The Downfall of Sri Lanka's War Hero]] has been published and is ready for viewers. * '''April 20''': The course [[Embracing Ambiguity]] is now available and is part of the [[Unleashing_Creativity/possibilities_curriculum|Possibilities]] curriculum. * '''April 8''': Students at Memorial University of Newfoundland are documenting public folklore for the town of [[Laneways of Harbour Grace|Harbour Grace]]. * '''April 7''': Students at the University of North Carolina Chapel Hill are contributing to [[OToPS|Open Teaching of Psychological Science]]. * '''April 5''': The course [[Solving Problems]] is now available and is part of the [[Unleashing_Creativity/possibilities_curriculum|Possibilities]] curriculum. <noinclude> <!--Delete items after ~30 days to keep this list fresh. If/when Wikiversity becomes more active, then try to keep the list ~20 items--> [[Category:Main page templates]] [[Category:Wikiversity news]] </noinclude> 83pknk60uuep4ofv4hmkppq0p1ukd9k 0 64082 2412397 2394019 2022-08-06T18:47:36Z 2600:1700:C560:5A70:ED19:E727:7EF5:B440 expanded additional word list wikitext text/x-wiki ==Chapter 2 == ===Activities=== * '''comer''' - to eat * '''beber''' - to drink *'''bailar''' - to dance *'''cantar''' - to sing *'''correr''' - to run *'''escribir cuentos''' - to write stories *'''escuchar música''' - to listen to music *'''estudiar''' - to study *'''esquiar''' - to ski *'''hablar por teléfono''' - to talk on the phone *'''ir a la escuela''' - to go to school *'''hacer la tarea''' - to do homework *'''jugar videojuegos''' - to play videogames *'''leer revistas''' - to read magazines *'''montar en bicicleta''' - to ride a bicycle *'''montar en monopatín / patineta''' - to skateboard *'''nadar''' - to swim *'''pasar tiempo con amigos / amistades''' - to spend time with friends *'''patinar''' - to skate *'''jugar deportes''' - to play sports *'''tocar la guitarra''' - to play the guitar *'''trabajar''' - to work *'''usar la computadora''' - to use the computer *'''mirar la televisión/ver la tele''' - to watch television ===Words to describe something you like or dislike=== *'''A mí''' - (Used for emphasis when talking about what you like.) *'''A mí no''' - (Used for emphasis when talking about what you dislike.) *'''Me gusta...''' - I like to... *'''Me gusta más...''' - I like to...better. *'''Me gusta mucho...''' I like to...a lot. *'''Me gusta poco'''... I like to... very little. *'''A mí también.''' - I do too. *'''A mí tampoco.''' - I don't either / Me neither. *'''No me gusta...''' - I don't like to do... *'''No me gusta (para) nada...''' - I don't like to...at all. *'''¿Qué te gusta hacer?''' - What do you like to do? *'''¿Qué te gusta hacer más?''' - What do you like to do more? *'''¿Te gusta...?''' - Do you like to...? *'''¿Y a ti?''' - And you? ===Other frequently used words=== *'''ni''' - neither, nor *'''o''' - or *'''y''' - and *'''¡Bueno!''' - good *'''¡Bien!''' - well *'''sí''' - yes *'''no''' - no *'''también''' - also, too *'''tampoco''' - neither {''opposite of'' '''también'''} *'''nunca''' - never *'''a''' '''veces''' - sometimes *'''siempre''' - always *'''no... sino... -''' not... but rather... **'''No me gusta trabajar sino escuchar a música.''' I don't like to work but rather listen to music. ====Cultural note==== *Many schools in Latin America don't have a Physical Education class or sports teams, instead many students go to local gyms to join sports teams. ===Cognates/False Cognates=== Cognates are words that have a common etymological origin. False cognates look similar but actually have different meanings. ====Cognates==== *'''popular''' = popular *'''usar''' = to use *'''guitarra''' = guitar *'''instrumento''' = instrument *'''importante''' = important *'''flamenco''' = flamenco *'''tango''' = tango *'''merengue''' = merengue *'''salsa''' = salsa *'''cumbia''' = cumbia *'''famoso''' = famous *'''famosa''' = famous *'''no''' = no ==== False Cognates==== *'''el pie = the foot''' *'''actual = current''' ===Instrumentos=== *'''acordeón''' - accordian *'''bajo''' - bass *'''clarinete''' - clarinet *'''claves''' - keys *'''güiro''' - güiro *'''maracas''' - maracas *'''oboe''' - oboe *'''saxofón''' - saxophone *'''sintetizador''' - synthesizer *'''tambor''' - drum *'''trombón''' - trombone *'''trompeta''' - trumpet *'''tuba''' - tuba *'''violín''' - violin ===Cultural Insight (Dances)=== Many famous dances have originated in Spanish-speaking countries. Below are lists of dances and their country of origin: -Flamenco: Spain -Tango: Argentina -Merengue: Dominican Republic -Salsa: Puerto Rico -Cumbia: Colombia ===Country focus (Estados Unidos)=== [[Image:Flag of the United States.svg|150px|right]] The '''United States of America''' (Spanish: Estados Unidos), usually referred to as the United States, the U.S. or America, is a constitutional federal republic comprising fifty states and a federal district, as well as several territories, or insular areas, scattered around the Caribbean and Pacific. The country is situated mostly in central North America, where its forty-eight contiguous states and Washington, D.C., the capital district, lie between the Pacific and Atlantic Oceans, bordered by Canada to the north and Mexico to the south. The state of Alaska is in the northwest of the continent, with Canada to its east and Russia to the west across the Bering Strait, and the state of Hawaii is an archipelago in the mid-Pacific. [[Image:LocationUSA.png|200px|right]] At 3.79 million square miles (9.83 million km²) and with more than 300 million people, the United States is the fourth largest country by total area, and third largest by population. The United States is one of the world's most ethnically diverse nations, the product of large-scale immigration from many countries. The U.S. economy is the largest national economy in the world, with a nominal 2006 gross domestic product (GDP) of more than US$13 trillion (over 25% of the world total based on nominal GDP and almost 20% by purchasing power parity). [[Image:SF From Marin Highlands3.jpg|150px|thumb|San Francisco was founded as a Spanish mission, but today is a major city home to over 830,000 people.]] The nation was founded by thirteen colonies of Great Britain located along the Atlantic seaboard. Proclaiming themselves "states," they issued the Declaration of Independence on July 4, 1776. The rebellious states defeated Great Britain in the American Revolutionary War, the first successful colonial war of independence. A federal convention adopted the current United States Constitution on September 17, 1787; its ratification the following year made the states part of a single republic. The Bill of Rights, comprising ten constitutional amendments, was ratified in 1791. [[Image:Castillo de San Marcos Fort Panorama 1.jpg|left|thumb|170px|Castillo de San Marcos, a fort in St.Augustine, Florida, the oldest European settlement in the USA.]] In the nineteenth century, the United States acquired land from France, Spain, the United Kingdom, Mexico, and Russia, and annexed the Republic of Texas and the Republic of Hawaii. Disputes between the agrarian South and industrial North over states' rights and the expansion of the institution of slavery provoked the American Civil War of the 1860s. The North's victory prevented a permanent split of the country and led to the end of slavery in the United States. The Spanish-American War and World War I confirmed the nation's status as a military power. In 1945, the United States emerged from World War II as the first country with nuclear weapons, a permanent member of the United Nations Security Council, and a founding member of NATO. In the post–Cold War era, the United States is the only remaining superpower—accounting for approximately 50% of global military spending—and a dominant economic, political, and cultural force in the world. The United States is a multicultural nation, home to a wide variety of ethnic groups, traditions, and values. [[Image:LosAngelesSmog.jpg|thumb|200px|Los Angeles, formely a Spanish pueblo, is today a major city home to 4.1 million people and is a major world center in tourism and culture.]] '''Factbox''': *Official languages: none (English is the ''de facto'' language) *Other Languages: Spanish, French, German, Cantonese, Tagalog, Vietnamese, Mandarin, Italian, Korean, 327 other languages *Capital: Washington D.C. *Government: Democratic Republic *Area: 9,629,091 sq km (3,794,066 sq mi) (4th) *Population: 310,101,000 (July 2010) (3rd) *Religion: Christianity 78.5% (Protestant 51.3%, Catholic 23.9%, Mormon 1.7%, other Christian 1.6%), Non-religious 15%, Judaism 2.1%, Buddhism 2%, Islam 1%, Hinduism 0.4%, other 1% (mostly Unitarian Universalism, traditonal beliefs, Sikhism, Jainism, Confucianism, Taoism, etc.) *Human Development: 0.956 (VERY HIGH, 13th) *Independence: July 4, 1776 *Currency: United States Dollar [[Category:Spanish One]] 23f9x3q9d8gl3jgzakfcma8u714gt8g 2412398 2412397 2022-08-06T18:49:10Z 2600:1700:C560:5A70:ED19:E727:7EF5:B440 wikitext text/x-wiki ==Chapter 2 == ===Activities=== * '''comer''' - to eat * '''beber''' - to drink *'''bailar''' - to dance *'''cantar''' - to sing *'''correr''' - to run *'''escribir cuentos''' - to write stories *'''escuchar música''' - to listen to music *'''estudiar''' - to study *'''esquiar''' - to ski *'''hablar por teléfono''' - to talk on the phone *'''ir a la escuela''' - to go to school *'''hacer la tarea''' - to do homework *'''jugar videojuegos''' - to play videogames *'''leer revistas''' - to read magazines *'''montar en bicicleta''' - to ride a bicycle *'''montar en monopatín / patineta''' - to skateboard *'''nadar''' - to swim *'''pasar tiempo con amigos / amistades''' - to spend time with friends *'''patinar''' - to skate *'''jugar deportes''' - to play sports *'''tocar la guitarra''' - to play the guitar *'''trabajar''' - to work *'''usar la computadora''' - to use the computer *'''mirar la televisión/ver la tele''' - to watch television ===Words to describe something you like or dislike=== *'''A mí''' - (Used for emphasis when talking about what you like.) *'''A mí no''' - (Used for emphasis when talking about what you dislike.) *'''Me gusta...''' - I like to... *'''Me gusta más...''' - I like to...better. *'''Me gusta mucho...''' I like to...a lot. *'''Me gusta poco'''... I like to... very little. *'''A mí también.''' - I do too. *'''A mí tampoco.''' - I don't either / Me neither. *'''No me gusta...''' - I don't like to do... *'''No me gusta (para) nada...''' - I don't like to...at all. *'''¿Qué te gusta hacer?''' - What do you like to do? *'''¿Qué te gusta hacer más?''' - What do you like to do more? *'''¿Te gusta...?''' - Do you like to...? *'''¿Y a ti?''' - And you? ===Other frequently used words=== *'''ni''' - neither, nor *'''o''' - or *'''y''' - and *'''¡Bueno!''' - good *'''¡Bien!''' - well *'''sí''' - yes *'''no''' - no *'''también''' - also, too *'''tampoco''' - neither {''opposite of'' '''también'''} *'''nunca''' - never *'''a''' '''veces''' - sometimes *'''siempre''' - always *'''no... sino... -''' not... but rather... **'''No me gusta trabajar sino escuchar música.''' I don't like to work but rather listen to music. ====Cultural note==== *Many schools in Latin America don't have a Physical Education class or sports teams, instead many students go to local gyms to join sports teams. ===Cognates/False Cognates=== Cognates are words that have a common etymological origin. False cognates look similar but actually have different meanings. ====Cognates==== *'''popular''' = popular *'''usar''' = to use *'''guitarra''' = guitar *'''instrumento''' = instrument *'''importante''' = important *'''flamenco''' = flamenco *'''tango''' = tango *'''merengue''' = merengue *'''salsa''' = salsa *'''cumbia''' = cumbia *'''famoso''' = famous *'''famosa''' = famous *'''no''' = no ==== False Cognates==== *'''el pie = the foot''' *'''actual = current''' ===Instrumentos=== *'''acordeón''' - accordian *'''bajo''' - bass *'''clarinete''' - clarinet *'''claves''' - keys *'''güiro''' - güiro *'''maracas''' - maracas *'''oboe''' - oboe *'''saxofón''' - saxophone *'''sintetizador''' - synthesizer *'''tambor''' - drum *'''trombón''' - trombone *'''trompeta''' - trumpet *'''tuba''' - tuba *'''violín''' - violin ===Cultural Insight (Dances)=== Many famous dances have originated in Spanish-speaking countries. Below are lists of dances and their country of origin: -Flamenco: Spain -Tango: Argentina -Merengue: Dominican Republic -Salsa: Puerto Rico -Cumbia: Colombia ===Country focus (Estados Unidos)=== [[Image:Flag of the United States.svg|150px|right]] The '''United States of America''' (Spanish: Estados Unidos), usually referred to as the United States, the U.S. or America, is a constitutional federal republic comprising fifty states and a federal district, as well as several territories, or insular areas, scattered around the Caribbean and Pacific. The country is situated mostly in central North America, where its forty-eight contiguous states and Washington, D.C., the capital district, lie between the Pacific and Atlantic Oceans, bordered by Canada to the north and Mexico to the south. The state of Alaska is in the northwest of the continent, with Canada to its east and Russia to the west across the Bering Strait, and the state of Hawaii is an archipelago in the mid-Pacific. [[Image:LocationUSA.png|200px|right]] At 3.79 million square miles (9.83 million km²) and with more than 300 million people, the United States is the fourth largest country by total area, and third largest by population. The United States is one of the world's most ethnically diverse nations, the product of large-scale immigration from many countries. The U.S. economy is the largest national economy in the world, with a nominal 2006 gross domestic product (GDP) of more than US$13 trillion (over 25% of the world total based on nominal GDP and almost 20% by purchasing power parity). [[Image:SF From Marin Highlands3.jpg|150px|thumb|San Francisco was founded as a Spanish mission, but today is a major city home to over 830,000 people.]] The nation was founded by thirteen colonies of Great Britain located along the Atlantic seaboard. Proclaiming themselves "states," they issued the Declaration of Independence on July 4, 1776. The rebellious states defeated Great Britain in the American Revolutionary War, the first successful colonial war of independence. A federal convention adopted the current United States Constitution on September 17, 1787; its ratification the following year made the states part of a single republic. The Bill of Rights, comprising ten constitutional amendments, was ratified in 1791. [[Image:Castillo de San Marcos Fort Panorama 1.jpg|left|thumb|170px|Castillo de San Marcos, a fort in St.Augustine, Florida, the oldest European settlement in the USA.]] In the nineteenth century, the United States acquired land from France, Spain, the United Kingdom, Mexico, and Russia, and annexed the Republic of Texas and the Republic of Hawaii. Disputes between the agrarian South and industrial North over states' rights and the expansion of the institution of slavery provoked the American Civil War of the 1860s. The North's victory prevented a permanent split of the country and led to the end of slavery in the United States. The Spanish-American War and World War I confirmed the nation's status as a military power. In 1945, the United States emerged from World War II as the first country with nuclear weapons, a permanent member of the United Nations Security Council, and a founding member of NATO. In the post–Cold War era, the United States is the only remaining superpower—accounting for approximately 50% of global military spending—and a dominant economic, political, and cultural force in the world. The United States is a multicultural nation, home to a wide variety of ethnic groups, traditions, and values. [[Image:LosAngelesSmog.jpg|thumb|200px|Los Angeles, formely a Spanish pueblo, is today a major city home to 4.1 million people and is a major world center in tourism and culture.]] '''Factbox''': *Official languages: none (English is the ''de facto'' language) *Other Languages: Spanish, French, German, Cantonese, Tagalog, Vietnamese, Mandarin, Italian, Korean, 327 other languages *Capital: Washington D.C. *Government: Democratic Republic *Area: 9,629,091 sq km (3,794,066 sq mi) (4th) *Population: 310,101,000 (July 2010) (3rd) *Religion: Christianity 78.5% (Protestant 51.3%, Catholic 23.9%, Mormon 1.7%, other Christian 1.6%), Non-religious 15%, Judaism 2.1%, Buddhism 2%, Islam 1%, Hinduism 0.4%, other 1% (mostly Unitarian Universalism, traditonal beliefs, Sikhism, Jainism, Confucianism, Taoism, etc.) *Human Development: 0.956 (VERY HIGH, 13th) *Independence: July 4, 1776 *Currency: United States Dollar [[Category:Spanish One]] kui5x8iwn2qfaze2g0skxsnw6ww0sy6 0 64128 2412394 2392114 2022-08-06T18:34:30Z 2600:1700:C560:5A70:ED19:E727:7EF5:B440 added all irregular tú commands wikitext text/x-wiki ==Chapter 13 (The Household)== ===Location=== *'''cerca''' - close, near *'''lejos''' - far *'''vivir''' - to live ===Rooms in a house=== *'''apartamento''' - apartment *'''baño''' - bathroom *'''cocina''' - kitchen *'''comedor''' - dining room *'''cuarto''' - room *'''despacho, la oficina''' - home office *'''escalera''' - stairway *'''garaje''' - garage *'''piso''' - story, floor *'''planta baja''' - ground floor *'''primer piso''' - first floor *'''sala''' - living room *'''segundo piso''' - second floor *'''sótano''' - basement *'''ático''' - attic ===Chores=== *'''arreglar el cuarto''' - to straighten up the room *'''ayudar''' - to help *'''cocinar''' - to cook *'''cortar el césped (la grama)''' - to cut the lawn *'''dar''' - to give *'''dar de comer al perro''' - to feed the dog *'''hacer la cama''' - to make the bed *'''lavar''' - to wash *'''limpiar el baño''' - to clean the bathroom *'''pasar la aspiradora''' - to vaccum *'''poner''' - to put, place *'''pongo''' - I place *'''pones''' - you place (singular) *'''poner la mesa''' - to set the table *'''quehaceres''' - chores *'''quitar el polvo''' - to dust *'''sacar la basura''' - to take out the trash '''Note''': The first person conjugation for ''dar'' is ''doy''. ===Clean or dirty=== *'''limpio(a)''' - clean *'''sucio(a)''' - dirty ===Other words=== *'''bastante''' - enough *'''¿Cuáles?''' - Which? (plural) *'''dinero''' - money *'''un momento''' - a moment ===Useful expressions=== *'''¿Qué estás haciendo?''' - What are you doing? *'''recibir''' - to receive *'''si''' - if, whether ===Affirmative ''tú'' commands=== In Spanish, there are two ways to tell someone to do something, the ''tú'' form is used in the same way the word is used, with friends, family, younger people, and people you know. The ''tú'' commands use the ''Ud./él/ella'' conjugations. Below is the list of ending for the affirmative ''tú'' commands, the same as the ''Ud./él/ella'' conjugations. -ar: -a -er: -e -ir: -e Examples: *'''habla''' - talk *'''lee''' - read *'''escribe''' - write There are eight irregular affirmative ''tú'' command conjugations for these words: *'''decir''' - to say, to tell *'''hacer''' - to do, to make *'''ir''' - to go *'''poner''' - to put, place *'''salir''' - to leave, go out *'''ser''' - to be *'''tener''' - to have *'''venir''' - to come Their conjugations for affirmative ''tú'' commands are: *'''di''' - say *'''haz''' - do *'''ve''' - go *'''pon''' - put *'''sé''' - be *'''ten''' - have *'''ven''' - come '''Note''': The command ''ve'' is regular for the verb to see: ''ver''. ===Present progressive tense=== The present progressive tense tells what is happening right now, and when conjugated in Spanish, the equivalent in English is ''-ing''. Below is the list of conjugations for the present progressive tense in Spanish: -ar: -ando -er: -iendo -ir: -iendo Examples: *'''lavando''' - washing *'''comiendo''' - eating *'''escribiendo''' - writing There are a few irregular present progressive conjugations in Spanish; one example is ''leer''. *''leyendo'' - reading ===Etc.=== *'''coche''' - car '''Note''': In the United States and in northern Mexico, ''carro'' is usually used side-by-side with ''coche''. ===Vocabulario adicional=== *'''estufa''' - stove *'''jardín''' - garden *'''lavadero''' - laundry room *'''lavadora''' - washing machine *'''lavaplatos''' - dishwasher *'''muebles''' - furniture *'''patio''' - patio *'''refrigerador''' - refrigerator *'''secadora''' - clothes dryer *'''sillón''' - armchair *'''sofá''' - sofa *'''tocador''' - dressing table *'''quitar''' - to remove *'''quitar la nieve con la pala''' - to shovel snow *'''quitar los platos de la mesa''' - to clear the table *'''rastrillar las hojas''' - to rake leaves ===Cultural Insight (Houses in Spanish-speaking countries)=== In Spanish-speaking countries, houses tend to be viewed as more private than in the most parts of the world. Bars will usually be placed on the windows of first floor rooms of the house and a patio would be located at the center of the house or apartment buliding. Usually, the patio would be decorated with plants and a fountain. A gate would separate the driveway from the sidewalk and a fence would separate the house from a neighbor's. ===Country Focus (Venezuela)=== [[Image:Flag of Venezuela.svg|150px|right]] [[Image:Venezuela in its region.svg|noframe|150px|right]] '''Venezuela''' (Spanish: Venezuela) is a country on the northern coast of South America. The country comprises a continental mainland and numerous islands located off the Venezuelan coastline in the Caribbean Sea. The Bolivarian Republic of Venezuela possesses borders with Guyana to the east, Brazil to the south, and Colombia to the west. Trinidad and Tobago, Grenada, St. Lucia, Barbados, Curaçao, Bonaire, Aruba, Saint Vincent and the Grenadines and the Leeward Antilles lie just north, off the Venezuelan coast. Falling within the tropics, Venezuela sits close to the equator, in the Northern Hemisphere. A former Spanish colony, which has been an independent republic since 1821, Venezuela holds territorial disputes with Guyana, largely concerning the Essequibo area, and with Colombia concerning the Gulf of Venezuela. In 1895, after the dispute over the Guyana border flared up, it was submitted to a neutral commission, which in 1899 decided it mostly in Guyana's favour. Today, the Bolivarian Republic of Venezuela is known widely for its petroleum industry, the environmental diversity of its territory, and its natural features. [[Image:Caracas from El Calvario.jpg|150px|left|thumb|Caracas is home to 3.2 million people and is the the largest city in Venezuela.]] Venezuela is among the most urbanized countries in Latin America; the vast majority of Venezuelans live in the cities of the north, especially in the capital Caracas which is also the largest city. Other major cities include Maracaibo, Valencia, Maracay, Barquisimeto, Ciudad Guayana and the popular tourist city of Mérida. Venezuela is also home to a diversity of wildlife in a variety of protected habitats. Venezuela's heritage, art, and culture have been heavily influenced by its Latin American context. These elements extend to its historic buildings, architecture, art, landscape, boundaries, and monuments. Venezuelan culture has been shaped by indigenous, Spanish and African influences. Before this period, indigenous culture was expressed in art (petroglyphs), crafts, architecture (shabonos), and social organization. Aboriginal culture was subsequently assimilated by Spaniards; over the years, the hybrid culture had diversified by region. [[Image:Espejo Acuático - Los Próceres.jpg|150px|thumb|right|Los Próceres monument in Caracas.]] '''Factbox''': -Official Languages: Spanish -Other Languages: Native American languages -Capital: Caracas -Government: Democracy -Area: 912,050 sq km (353,841 sq mi) (33rd) [[Image:Bolívar usgs.jpg|150px|left|thumb|Pico Bolívar in Venezuela is where the Andes Mountains begin their southward route to Argentina.]] -Population: 26,814,843 (40th) -Religion: Christianity (Catholic 96%, Protestant 2%) 98%, Buddhism 0.2%, other (Traditional beliefs, Judaism) 1.8% -Human Development: 0.844 (58th, HIGH) -Independence: July 5, 1811 -Currency: Venezuela bolívar [[Category:Spanish One]] ofrhpt0h6ut20b95hws771qvjzrkno3 2412395 2412394 2022-08-06T18:35:25Z 2600:1700:C560:5A70:ED19:E727:7EF5:B440 revised list of affirmative irregular commands wikitext text/x-wiki ==Chapter 13 (The Household)== ===Location=== *'''cerca''' - close, near *'''lejos''' - far *'''vivir''' - to live ===Rooms in a house=== *'''apartamento''' - apartment *'''baño''' - bathroom *'''cocina''' - kitchen *'''comedor''' - dining room *'''cuarto''' - room *'''despacho, la oficina''' - home office *'''escalera''' - stairway *'''garaje''' - garage *'''piso''' - story, floor *'''planta baja''' - ground floor *'''primer piso''' - first floor *'''sala''' - living room *'''segundo piso''' - second floor *'''sótano''' - basement *'''ático''' - attic ===Chores=== *'''arreglar el cuarto''' - to straighten up the room *'''ayudar''' - to help *'''cocinar''' - to cook *'''cortar el césped (la grama)''' - to cut the lawn *'''dar''' - to give *'''dar de comer al perro''' - to feed the dog *'''hacer la cama''' - to make the bed *'''lavar''' - to wash *'''limpiar el baño''' - to clean the bathroom *'''pasar la aspiradora''' - to vaccum *'''poner''' - to put, place *'''pongo''' - I place *'''pones''' - you place (singular) *'''poner la mesa''' - to set the table *'''quehaceres''' - chores *'''quitar el polvo''' - to dust *'''sacar la basura''' - to take out the trash '''Note''': The first person conjugation for ''dar'' is ''doy''. ===Clean or dirty=== *'''limpio(a)''' - clean *'''sucio(a)''' - dirty ===Other words=== *'''bastante''' - enough *'''¿Cuáles?''' - Which? (plural) *'''dinero''' - money *'''un momento''' - a moment ===Useful expressions=== *'''¿Qué estás haciendo?''' - What are you doing? *'''recibir''' - to receive *'''si''' - if, whether ===Affirmative ''tú'' commands=== In Spanish, there are two ways to tell someone to do something, the ''tú'' form is used in the same way the word is used, with friends, family, younger people, and people you know. The ''tú'' commands use the ''Ud./él/ella'' conjugations. Below is the list of ending for the affirmative ''tú'' commands, the same as the ''Ud./él/ella'' conjugations. -ar: -a -er: -e -ir: -e Examples: *'''habla''' - talk *'''lee''' - read *'''escribe''' - write There are eight irregular affirmative ''tú'' command conjugations for these words: *'''decir''' - to say, to tell *'''hacer''' - to do, to make *'''ir''' - to go *'''poner''' - to put, place *'''salir''' - to leave, go out *'''ser''' - to be *'''tener''' - to have *'''venir''' - to come Their conjugations for affirmative ''tú'' commands are: *'''di''' - say *'''haz''' - do *'''ve''' - go *'''pon''' - put *'''sal''' - leave, go out *'''sé''' - be *'''ten''' - have *'''ven''' - come '''Note''': The command ''ve'' is regular for the verb to see: ''ver''. ===Present progressive tense=== The present progressive tense tells what is happening right now, and when conjugated in Spanish, the equivalent in English is ''-ing''. Below is the list of conjugations for the present progressive tense in Spanish: -ar: -ando -er: -iendo -ir: -iendo Examples: *'''lavando''' - washing *'''comiendo''' - eating *'''escribiendo''' - writing There are a few irregular present progressive conjugations in Spanish; one example is ''leer''. *''leyendo'' - reading ===Etc.=== *'''coche''' - car '''Note''': In the United States and in northern Mexico, ''carro'' is usually used side-by-side with ''coche''. ===Vocabulario adicional=== *'''estufa''' - stove *'''jardín''' - garden *'''lavadero''' - laundry room *'''lavadora''' - washing machine *'''lavaplatos''' - dishwasher *'''muebles''' - furniture *'''patio''' - patio *'''refrigerador''' - refrigerator *'''secadora''' - clothes dryer *'''sillón''' - armchair *'''sofá''' - sofa *'''tocador''' - dressing table *'''quitar''' - to remove *'''quitar la nieve con la pala''' - to shovel snow *'''quitar los platos de la mesa''' - to clear the table *'''rastrillar las hojas''' - to rake leaves ===Cultural Insight (Houses in Spanish-speaking countries)=== In Spanish-speaking countries, houses tend to be viewed as more private than in the most parts of the world. Bars will usually be placed on the windows of first floor rooms of the house and a patio would be located at the center of the house or apartment buliding. Usually, the patio would be decorated with plants and a fountain. A gate would separate the driveway from the sidewalk and a fence would separate the house from a neighbor's. ===Country Focus (Venezuela)=== [[Image:Flag of Venezuela.svg|150px|right]] [[Image:Venezuela in its region.svg|noframe|150px|right]] '''Venezuela''' (Spanish: Venezuela) is a country on the northern coast of South America. The country comprises a continental mainland and numerous islands located off the Venezuelan coastline in the Caribbean Sea. The Bolivarian Republic of Venezuela possesses borders with Guyana to the east, Brazil to the south, and Colombia to the west. Trinidad and Tobago, Grenada, St. Lucia, Barbados, Curaçao, Bonaire, Aruba, Saint Vincent and the Grenadines and the Leeward Antilles lie just north, off the Venezuelan coast. Falling within the tropics, Venezuela sits close to the equator, in the Northern Hemisphere. A former Spanish colony, which has been an independent republic since 1821, Venezuela holds territorial disputes with Guyana, largely concerning the Essequibo area, and with Colombia concerning the Gulf of Venezuela. In 1895, after the dispute over the Guyana border flared up, it was submitted to a neutral commission, which in 1899 decided it mostly in Guyana's favour. Today, the Bolivarian Republic of Venezuela is known widely for its petroleum industry, the environmental diversity of its territory, and its natural features. [[Image:Caracas from El Calvario.jpg|150px|left|thumb|Caracas is home to 3.2 million people and is the the largest city in Venezuela.]] Venezuela is among the most urbanized countries in Latin America; the vast majority of Venezuelans live in the cities of the north, especially in the capital Caracas which is also the largest city. Other major cities include Maracaibo, Valencia, Maracay, Barquisimeto, Ciudad Guayana and the popular tourist city of Mérida. Venezuela is also home to a diversity of wildlife in a variety of protected habitats. Venezuela's heritage, art, and culture have been heavily influenced by its Latin American context. These elements extend to its historic buildings, architecture, art, landscape, boundaries, and monuments. Venezuelan culture has been shaped by indigenous, Spanish and African influences. Before this period, indigenous culture was expressed in art (petroglyphs), crafts, architecture (shabonos), and social organization. Aboriginal culture was subsequently assimilated by Spaniards; over the years, the hybrid culture had diversified by region. [[Image:Espejo Acuático - Los Próceres.jpg|150px|thumb|right|Los Próceres monument in Caracas.]] '''Factbox''': -Official Languages: Spanish -Other Languages: Native American languages -Capital: Caracas -Government: Democracy -Area: 912,050 sq km (353,841 sq mi) (33rd) [[Image:Bolívar usgs.jpg|150px|left|thumb|Pico Bolívar in Venezuela is where the Andes Mountains begin their southward route to Argentina.]] -Population: 26,814,843 (40th) -Religion: Christianity (Catholic 96%, Protestant 2%) 98%, Buddhism 0.2%, other (Traditional beliefs, Judaism) 1.8% -Human Development: 0.844 (58th, HIGH) -Independence: July 5, 1811 -Currency: Venezuela bolívar [[Category:Spanish One]] i0f2fbs02920lkn9iw7hdtn31ohz0nb 0 68873 2412384 2412307 2022-08-06T15:42:41Z 197.234.221.215 Undo revision 2408430 by [[Special:Contributions/JavaHurricane|JavaHurricane]] ([[User talk:JavaHurricane|talk]]) certainly not spam u 2 are wmf cancer @jimbo Wales @WMFOffice approved! wikitext text/x-wiki [[Image:Cambodia_MapFlag.png|thumb|right|Cambodian flag]] The Kingdom of Cambodia is a country in South East Asia with a population of over 3 million people. Cambodia is the successor state of the once powerful Hindu and Buddhist Khmer Empire, which ruled most of the Indochinese Peninsula between the eleventh and fourteenth centuries. Today Cambodia is regarded as one of developing countries, therefore it has many problems, including problems related with educational development. == '''Cambodian Brief Profile''' == [[Image:Cb-map.png]] Cambodia has an area of 181,035 square kilometers, and it borders Thailand to its west and northwest, Laos to its northeast, and Vietnam to its east and southeast. Cambodia gained independence from France on November 9, 1953. Cambodia's main industries are garments, tourism, and construction. As for its language, more than 90% of its population is of Khmer origin therefore speaks the Khmer language, the country's official language. The remainder includes Chinese, Vietnamese, and Indians. As for the religion, most Cambodians are Buddhists of Khmer extraction, but the country also has a substantial number of Muslim Cham, as well as small animist tribes.　In addition, according the report of The World Bank, “Cambodia's economy is showing resilience in spite of the challenging international economic environment. Economic growth in 2001 was estimated at 6.3 percent, driven by an expanding tourism sector and robust garment exports. In 2001, there was nearly zero inflation. In 2002 inflation continued to be low (World Bank)”. That is, Cambodia’s economic growth has been moderately strong over the past decade. However, this growth has been concentrated in urban areas (The World Bank). Therefore the rural-urban income gap is widening these days. And around 40 percent of the population still remains under the national poverty line. == '''History''' == 1863 - Cambodia becomes a protectorate of France. French colonial rule lasts for 90 years. 1941 - Prince Norodom Sihanouk becomes king. Cambodia is occupied by Japan during World War II. 1945 - The Japanese occupation ends. 1946 - France re-imposes its protectorate. Communist guerrillas begin an armed campaign against the French. 1953 - Cambodia wins its independence from France. Under King Sihanouk, it becomes the Kingdom of Cambodia. Early 1970s - Cambodian army faces two enemies: the North Vietnamese and communist Khmer Rouge. Gradually, the army loses territory. 1975 - Lon Nol is overthrown as the Khmer Rouge led by Pol Pot occupied Phnom Penh. Sihanouk briefly becomes head of state, the country is re-named Kampuchea. Basic freedoms are curtailed and religion is banned. Hundreds of thousands of the educated middle-classes are tortured and executed in special centres. Others starve, or die from disease or exhaustion. 1976 - The country is re-named Democratic Kampuchea. Sihanouk resigns, Khieu Samphan becomes head of state, Pol Pot is prime minister. 1977 - Fighting breaks out with Vietnam. 1979 January - The Vietnamese take Phnom Penh. Pol Pot and Khmer Rouge forces flee to the border region with Thailand. The People's Republic of Kampuchea is established. Many elements of life before the Khmer Rouge take-over started to be re-established. 1981 - The pro-Vietnamese Kampuchean People's Revolutionary Party wins the elections to the National Assembly. 1989 - Vietnamese troops withdraw. The country is re-named the State of Cambodia. Buddhism is re-established as the state religion. 1991 - A peace agreement is signed in Paris. A UN transitional authority shares power temporarily with representatives of the various factions in Cambodia. Sihanouk becomes head of state. 1993 - General election sees the royalist Funcinpec party win the most seats followed by Hun Sen's Cambodian People's Party (CPP). A three-party coalition is formed with Funcinpec's Prince Norodom Ranariddh as prime minister and Hun Sen as deputy prime minister. The monarchy is restored, Sihanouk becomes king again. The country is re-named the Kingdom of Cambodia. 1994 - Thousands of Khmer Rouge guerrillas surrender in government amnesty. 1997 - Hun Sen stages a coup against the prime ministar, Prince Ranariddh, and replaces him with Ung Huot. The coup attracts international condemnation and Cambodia's membership of the Association of Southeast Asian Nations (ASEAN) is delayed. The Khmer Rouge put Pol Pot on trial and sentence him to life imprisonment. # 1998 - On April 15, Pol Pot commits suicide[https://www.theguardian.com/world/1999/jan/21/cambodia] in his jungle hideout. Elections in July are won by Hun Sen's CPP, amid allegations of harassment. A coalition is formed between the CPP and Funcinpec. Hun Sen becomes prime minister, Ranariddh is president of the National Assembly. 2001 - Senate approves a law to create a tribunal to bring genocide charges against Khmer Rouge leaders. 2001 June - International donors, encouraged by Cambodia's reform efforts, pledge $560 million in aid at a donor conference in Tokyo. 2001 June - Five Cambodians, three of them US citizens, are sentenced to life for involvement in armed attack by US-based Cambodian Freedom Fighters (CFF) on government buildings in Phnom Penh in 2000. CFF says it will continue campaign to overthrow Prime Minister Hun Sen. 2001 December - First bridge across the Mekong River opens, linking the east and west of the country. The 1.36km bridge cost $56 million. 2002 February - First multi-party local elections; ruling Cambodian People's Party wins in all but 23 out of 1,620 communes. 2004 August - Parliament ratifies kingdom's entry into World Trade Organization (WTO). 2004 October - King Sihanouk abdicates and is succeeded by his son Norodom Sihamoni. 2005 April - Tribunal to try surviving Khmer Rouge leaders gets green light from UN after years of debate about funding. 2005 October - Prime minister signs a controversial border agreement with Vietnam. Legal action is taken against some critics of the deal, prompting international concern. 2006 July - Ta Mok, one of the top leaders of the brutal Khmer Rouge regime, dies aged 80. 2007 July - UN-backed court tribunals begin questioning suspects about allegations of genocide by the Khmer Rouge. 2007 September - Most senior surviving member of Khmer Rouge, Nuon Chea - "Brother Number Two" - is arrested and charged with crimes against humanity. 2008 February - Cambodian court sentences 20 member of small Cambodian Freedom Fighters group to prison for attack on prime minister's office in November 2000. 2008 March - Genocide tribunal refuses bail plea of Nuon Chea. 2008 April - US court convicts Cambodian-born Cambodian Freedom Fighters leader Chhun Yasith of masterminding 2000 attack. 2008 July - PM Hun Sen's ruling Cambodian People's Party (CPP) claims victory in parliamentary elections. EU monitors say the vote fell short of international standards. 2008 July - Cambodia and Thailand move troops to disputed land near ancient Preah Vihear temple after decision to list it as UN World Heritage Site fans nationalist emotions on both sides. Officials from both states start talks to resolve standoff. (BBC News 2008) This part would focus on the Khmer Rouge, because it has affected the educational system in Cambodia. On 17 April 1975, after five years of civil war, Cambodia’s capital Phnom Penh fell to the forces of the Communist Party of Kampuchea (CPK), popularly known as ''the Khmer Rouge'' (Linton). ''Pol Pot'' was the leader of the Khmer Rouge. “The country was cut off from the outside world, its cities emptied, its economy militarized, and its Buddhist and folk cultures destroyed. The leadership’s ‘vision’ of a better Cambodia led to extraordinary horrors on Cambodian people, who had to endure the forced movement of their urban populations, starvation, unlawful killings, forced labor, torture, and cruel, inhumane and degrading treatment and persecution on a massive scale”(Linton). Mao-think that Pol Pot studied in China, the ethnocentric policy, and anti-Vietnam policy became the theoretical support which created the regime of terror by the Khmer Rouge (Miyamoto). Pol Pot sanctioned the use of massive violence because he believed it was the only “practical” way to achieve and protect his utopian vision for a better society in Cambodia (Valentino). By the hands of the Khmer Rouge, mainly educated people (such as teachers and respected local leaders and so on) had been killed, since they were likely to be rebel groups. Furthermore, the Khmer Rouge had denied the value of education at all points. Therefore, it can be said that Cambodia had experienced a systematic destruction of education by the Khmer Rouge, until Heng Samrin supported by Vietnamese robbed the Khmer Rouge of its power in 1979. According to Linton, an estimated 20% of the 1975’s population of 7.7million people lost their lives. After the Khmer Rouge was over, the United Nations peacekeeping force, the United Nations Transitional Authority in Cambodia (UNTAC), began monitoring Cambodia in 1992. “The goal of UNTAC was disarmament of the troops, and national elections for a constituent assembly which took place in 1993. (…) Contrary to the fears of many, the elections were peaceful. Over 90 percent of the registered voters went to the polls in Cambodian freest, fairest, and most secret election since the colonial era. (…) For the first time in Cambodian history, a majority of Cambodians had voted against an armed government such as the Khmer Rouge” (Chandler). Therefore it can be said: Cambodia was able to gradually recover from many years of violence by the Khmer Rouge regime, in the wake of those elections, although not all problems were solved. == '''Educational Development Strategy and Challenge of Cambodia''' == Although all educational systems of Cambodia were abolished under the regime of terror by the Khmer Rouge, according to the World Bank, there have been significant improvements in the past five years in the education sector in Cambodia, particularly in terms of primary net enrollment gains (it’s because the government of Cambodia has put more efforts on the primary education, according to Komai), the introduction of program based-budgeting and the development of a sound pro-poor policy framework. But in Cambodia, several challenges remain. For example, most Cambodian children attend some schooling, but a large share complete only a few grades-with 85 percent of 15 to 19 year olds completing just grade 1, while only 27 percent complete grade 7 (The World Bank). It is partly because parents (especially those in rural areas) are blind to the importance of education. There are also disparities in education participation rates by different regions. Moreover, inefficiency and poor quality in education service delivery at primary, secondary and tertiary levels are other major challenges. For instance, the number and the quality of teachers in Cambodia are insufficient. It is because almost all of experienced old teachers had been killed under the regime of the Khmer Rouge. In fact, one thirds of teachers in the primary school have not finished even lower secondary education (Komai). And the budget for education is extremely restricted, compared to neighboring nations (Komai). Thus, the salary of teachers is too low, which causes teachers’ corrupt practices. And the time for studying in the school is 15 hours per week, which is extremely insufficient, too (Komai). Another challenge is related to child prostitution. “In Cambodia, child prostitution has become a worsening problem since 1990’s. Many Cambodian children have been deceived by words that there are “good” sources of employment in urban areas and have left their home, and have been forced to work in the house of prostitution. In Cambodia, there are more than 8.000～15.000 children who had been damaged by child prostitution” (Social Ecoo). Furthermore, expanding of child prostitution causes spread of HIV/AIDS among Cambodian children. HIV/AIDS is one of educational challenge, since children who are infected with the HIV virus cannot get an education well. [[Image:Cambodiaeducation.jpg]] == '''The Recommendation for Ways to Approach Educational Development of Cambodia''' == First of all, those involved in educational development in Cambodia should make improvements of Cambodian education quality. It would lead to Cambodian students’ higher promotion and achievement rates. Moreover, if education quality gets improved, even parents in rural areas would come to understand the value of education, and would come to encourage their children to complete higher school grades. Furthermore, the budget for education should be increased. The government of Cambodia has gradually made an increase in the budget for education since 2006, and it is hoped that this trend would be maintained longer. Moreover, the teacher training is also needed, because there are little experienced old teachers left due to the Khmer Rouge’s regime of terror.In addition, vocational education for Cambodian children engaging in child prostitution is necessary. It is because children would not have to sell their body, if there are any other sources of employment. And it would lead to cut down the number of children, who are infected with the HIV virus and cannot go to school though they want to do. == '''The External Actor Involved in Cambodian Educational Development''' == Cambodia has been aided by a number of more developed nations like France, West-Germany, Canada, Australia, the United States, and Japan. The United States has contributed up to $5 million through international relief agencies to children within Cambodia (Sutter). As for Japan, many Japanese organizations such as JICA have supported Cambodian educational development. For example JICA has tried to revive Cambodian educational system, by forming projects including “the project for improvement of science and mathematics education (2000-2004)”, which is aimed to enable teachers engaged in science and mathematics education to acquire skills more than cheap tricks. In addition, The World Bank, UNICEF, UNESCO, Asian Development Bank (ADB), and some NGOs (such as World Vision in the United States, Save the Children in the UK, and so on) have also supported educational development in Cambodia. Among interesting projects formed by those organizations is the World Bank’s “''Education Quality Improvement Project'' (1999 - 2004)”. This project aimed to develop and put into practice a participatory approach to school quality improvement and performance-based resource management. The goal was to have participating schools eventually show improvements in student enrollment, attendance and achievement (The World Bank). The result was that Students in more than 1,000 participating schools in Cambodia achieved higher test scores in literacy, had lower drop-out and higher promotion rates. In addition, this project could show that health and vocational training was the important factor in reducing student drop-out, and in improving promotion rates. <big>'''Works Cited'''</big> BBC News. 2008. “Timeline: Cambodia” ＜http://news.bbc.co.uk/1/hi/world/asia-pacific/country_profiles/1244006.stm＞ “Cambodian Information Center”. 2008. ＜http://www.cambodia.org/＞ Chandler, David. 2008. “A History of Cambodia”. Westview Press: Colorado, America. “Japan International Cooperation Agency”. 1995. ＜http://www.jica.go.jp/Index-j.html＞ Kennsuke, Miyamoto. 1993. “Tounan Asia no Gennzai”. 〔The Present of Southeast Asia〕. Horupu Publication: Tokyo, Japan. Komai, Hiroshi. 2001. “Shinnsei Cambodia”. 〔New Birth of Cambodia〕. Akashi Publication: Tokyo, Japan. Linton, Suzannah. 2004. “Reconciliation in Cambodia”. Documentation Center of Cambodia: Phnom Penh, Cambodia. “Social Ecoo”. 2007. ＜http://www.socialecoo.jp/series/archives/2007/07/03/entry135.html＞ Sutter, Robert G. 1991. “The Cambodian Crisis and U.S. Policy Dilemmas”. Westview Press: Colorado, America. The World Bank Group. 2008. “The World Bank”. ＜http://www.worldbank.org/＞ Valentino, Benjamin A. 2004. “Final Solutions: Mass Killing and Genocide in the Twentieth Century”. Cornell University Press: New York, America. [[Category:Asia]] g6u7w49ridh4rc27bqcbcfao9nhk8nk 2412385 2412384 2022-08-06T15:45:58Z Antandrus 111168 Reverted edits by [[Special:Contributions/197.234.221.215|197.234.221.215]] ([[User_talk:197.234.221.215|talk]]) to last version by [[User:Antandrus|Antandrus]] using [[Wikiversity:Rollback|rollback]] wikitext text/x-wiki [[Image:Cambodia_MapFlag.png|thumb|right|Cambodian flag]] The Kingdom of Cambodia is a country in South East Asia with a population of over 3 million people. Cambodia is the successor state of the once powerful Hindu and Buddhist Khmer Empire, which ruled most of the Indochinese Peninsula between the eleventh and fourteenth centuries. Today Cambodia is regarded as one of developing countries, therefore it has many problems, including problems related with educational development. == '''Cambodian Brief Profile''' == [[Image:Cb-map.png]] Cambodia has an area of 181,035 square kilometers, and it borders Thailand to its west and northwest, Laos to its northeast, and Vietnam to its east and southeast. Cambodia gained independence from France on November 9, 1953. Cambodia's main industries are garments, tourism, and construction. As for its language, more than 90% of its population is of Khmer origin therefore speaks the Khmer language, the country's official language. The remainder includes Chinese, Vietnamese, and Indians. As for the religion, most Cambodians are Buddhists of Khmer extraction, but the country also has a substantial number of Muslim Cham, as well as small animist tribes.　In addition, according the report of The World Bank, “Cambodia's economy is showing resilience in spite of the challenging international economic environment. Economic growth in 2001 was estimated at 6.3 percent, driven by an expanding tourism sector and robust garment exports. In 2001, there was nearly zero inflation. In 2002 inflation continued to be low (World Bank)”. That is, Cambodia’s economic growth has been moderately strong over the past decade. However, this growth has been concentrated in urban areas (The World Bank). Therefore the rural-urban income gap is widening these days. And around 40 percent of the population still remains under the national poverty line. == '''History''' == 1863 - Cambodia becomes a protectorate of France. French colonial rule lasts for 90 years. 1941 - Prince Norodom Sihanouk becomes king. Cambodia is occupied by Japan during World War II. 1945 - The Japanese occupation ends. 1946 - France re-imposes its protectorate. Communist guerrillas begin an armed campaign against the French. 1953 - Cambodia wins its independence from France. Under King Sihanouk, it becomes the Kingdom of Cambodia. Early 1970s - Cambodian army faces two enemies: the North Vietnamese and communist Khmer Rouge. Gradually, the army loses territory. 1975 - Lon Nol is overthrown as the Khmer Rouge led by Pol Pot occupied Phnom Penh. Sihanouk briefly becomes head of state, the country is re-named Kampuchea. Basic freedoms are curtailed and religion is banned. Hundreds of thousands of the educated middle-classes are tortured and executed in special centres. Others starve, or die from disease or exhaustion. 1976 - The country is re-named Democratic Kampuchea. Sihanouk resigns, Khieu Samphan becomes head of state, Pol Pot is prime minister. 1977 - Fighting breaks out with Vietnam. 1979 January - The Vietnamese take Phnom Penh. Pol Pot and Khmer Rouge forces flee to the border region with Thailand. The People's Republic of Kampuchea is established. Many elements of life before the Khmer Rouge take-over started to be re-established. 1981 - The pro-Vietnamese Kampuchean People's Revolutionary Party wins the elections to the National Assembly. 1989 - Vietnamese troops withdraw. The country is re-named the State of Cambodia. Buddhism is re-established as the state religion. 1991 - A peace agreement is signed in Paris. A UN transitional authority shares power temporarily with representatives of the various factions in Cambodia. Sihanouk becomes head of state. 1993 - General election sees the royalist Funcinpec party win the most seats followed by Hun Sen's Cambodian People's Party (CPP). A three-party coalition is formed with Funcinpec's Prince Norodom Ranariddh as prime minister and Hun Sen as deputy prime minister. The monarchy is restored, Sihanouk becomes king again. The country is re-named the Kingdom of Cambodia. 1994 - Thousands of Khmer Rouge guerrillas surrender in government amnesty. 1997 - Hun Sen stages a coup against the prime ministar, Prince Ranariddh, and replaces him with Ung Huot. The coup attracts international condemnation and Cambodia's membership of the Association of Southeast Asian Nations (ASEAN) is delayed. The Khmer Rouge put Pol Pot on trial and sentence him to life imprisonment. 1998 - On April 15, Pol Pot dies in his jungle hideout. Elections in July are won by Hun Sen's CPP, amid allegations of harassment. A coalition is formed between the CPP and Funcinpec. Hun Sen becomes prime minister, Ranariddh is president of the National Assembly. 2001 - Senate approves a law to create a tribunal to bring genocide charges against Khmer Rouge leaders. 2001 June - International donors, encouraged by Cambodia's reform efforts, pledge $560 million in aid at a donor conference in Tokyo. 2001 June - Five Cambodians, three of them US citizens, are sentenced to life for involvement in armed attack by US-based Cambodian Freedom Fighters (CFF) on government buildings in Phnom Penh in 2000. CFF says it will continue campaign to overthrow Prime Minister Hun Sen. 2001 December - First bridge across the Mekong River opens, linking the east and west of the country. The 1.36km bridge cost $56 million. 2002 February - First multi-party local elections; ruling Cambodian People's Party wins in all but 23 out of 1,620 communes. 2004 August - Parliament ratifies kingdom's entry into World Trade Organization (WTO). 2004 October - King Sihanouk abdicates and is succeeded by his son Norodom Sihamoni. 2005 April - Tribunal to try surviving Khmer Rouge leaders gets green light from UN after years of debate about funding. 2005 October - Prime minister signs a controversial border agreement with Vietnam. Legal action is taken against some critics of the deal, prompting international concern. 2006 July - Ta Mok, one of the top leaders of the brutal Khmer Rouge regime, dies aged 80. 2007 July - UN-backed court tribunals begin questioning suspects about allegations of genocide by the Khmer Rouge. 2007 September - Most senior surviving member of Khmer Rouge, Nuon Chea - "Brother Number Two" - is arrested and charged with crimes against humanity. 2008 February - Cambodian court sentences 20 member of small Cambodian Freedom Fighters group to prison for attack on prime minister's office in November 2000. 2008 March - Genocide tribunal refuses bail plea of Nuon Chea. 2008 April - US court convicts Cambodian-born Cambodian Freedom Fighters leader Chhun Yasith of masterminding 2000 attack. 2008 July - PM Hun Sen's ruling Cambodian People's Party (CPP) claims victory in parliamentary elections. EU monitors say the vote fell short of international standards. 2008 July - Cambodia and Thailand move troops to disputed land near ancient Preah Vihear temple after decision to list it as UN World Heritage Site fans nationalist emotions on both sides. Officials from both states start talks to resolve standoff. (BBC News 2008) This part would focus on the Khmer Rouge, because it has affected the educational system in Cambodia. On 17 April 1975, after five years of civil war, Cambodia’s capital Phnom Penh fell to the forces of the Communist Party of Kampuchea (CPK), popularly known as ''the Khmer Rouge'' (Linton). ''Pol Pot'' was the leader of the Khmer Rouge. “The country was cut off from the outside world, its cities emptied, its economy militarized, and its Buddhist and folk cultures destroyed. The leadership’s ‘vision’ of a better Cambodia led to extraordinary horrors on Cambodian people, who had to endure the forced movement of their urban populations, starvation, unlawful killings, forced labor, torture, and cruel, inhumane and degrading treatment and persecution on a massive scale”(Linton). Mao-think that Pol Pot studied in China, the ethnocentric policy, and anti-Vietnam policy became the theoretical support which created the regime of terror by the Khmer Rouge (Miyamoto). Pol Pot sanctioned the use of massive violence because he believed it was the only “practical” way to achieve and protect his utopian vision for a better society in Cambodia (Valentino). By the hands of the Khmer Rouge, mainly educated people (such as teachers and respected local leaders and so on) had been killed, since they were likely to be rebel groups. Furthermore, the Khmer Rouge had denied the value of education at all points. Therefore, it can be said that Cambodia had experienced a systematic destruction of education by the Khmer Rouge, until Heng Samrin supported by Vietnamese robbed the Khmer Rouge of its power in 1979. According to Linton, an estimated 20% of the 1975’s population of 7.7million people lost their lives. After the Khmer Rouge was over, the United Nations peacekeeping force, the United Nations Transitional Authority in Cambodia (UNTAC), began monitoring Cambodia in 1992. “The goal of UNTAC was disarmament of the troops, and national elections for a constituent assembly which took place in 1993. (…) Contrary to the fears of many, the elections were peaceful. Over 90 percent of the registered voters went to the polls in Cambodian freest, fairest, and most secret election since the colonial era. (…) For the first time in Cambodian history, a majority of Cambodians had voted against an armed government such as the Khmer Rouge” (Chandler). Therefore it can be said: Cambodia was able to gradually recover from many years of violence by the Khmer Rouge regime, in the wake of those elections, although not all problems were solved. == '''Educational Development Strategy and Challenge of Cambodia''' == Although all educational systems of Cambodia were abolished under the regime of terror by the Khmer Rouge, according to the World Bank, there have been significant improvements in the past five years in the education sector in Cambodia, particularly in terms of primary net enrollment gains (it’s because the government of Cambodia has put more efforts on the primary education, according to Komai), the introduction of program based-budgeting and the development of a sound pro-poor policy framework. But in Cambodia, several challenges remain. For example, most Cambodian children attend some schooling, but a large share complete only a few grades-with 85 percent of 15 to 19 year olds completing just grade 1, while only 27 percent complete grade 7 (The World Bank). It is partly because parents (especially those in rural areas) are blind to the importance of education. There are also disparities in education participation rates by different regions. Moreover, inefficiency and poor quality in education service delivery at primary, secondary and tertiary levels are other major challenges. For instance, the number and the quality of teachers in Cambodia are insufficient. It is because almost all of experienced old teachers had been killed under the regime of the Khmer Rouge. In fact, one thirds of teachers in the primary school have not finished even lower secondary education (Komai). And the budget for education is extremely restricted, compared to neighboring nations (Komai). Thus, the salary of teachers is too low, which causes teachers’ corrupt practices. And the time for studying in the school is 15 hours per week, which is extremely insufficient, too (Komai). Another challenge is related to child prostitution. “In Cambodia, child prostitution has become a worsening problem since 1990’s. Many Cambodian children have been deceived by words that there are “good” sources of employment in urban areas and have left their home, and have been forced to work in the house of prostitution. In Cambodia, there are more than 8.000～15.000 children who had been damaged by child prostitution” (Social Ecoo). Furthermore, expanding of child prostitution causes spread of HIV/AIDS among Cambodian children. HIV/AIDS is one of educational challenge, since children who are infected with the HIV virus cannot get an education well. [[Image:Cambodiaeducation.jpg]] == '''The Recommendation for Ways to Approach Educational Development of Cambodia''' == First of all, those involved in educational development in Cambodia should make improvements of Cambodian education quality. It would lead to Cambodian students’ higher promotion and achievement rates. Moreover, if education quality gets improved, even parents in rural areas would come to understand the value of education, and would come to encourage their children to complete higher school grades. Furthermore, the budget for education should be increased. The government of Cambodia has gradually made an increase in the budget for education since 2006, and it is hoped that this trend would be maintained longer. Moreover, the teacher training is also needed, because there are little experienced old teachers left due to the Khmer Rouge’s regime of terror.In addition, vocational education for Cambodian children engaging in child prostitution is necessary. It is because children would not have to sell their body, if there are any other sources of employment. And it would lead to cut down the number of children, who are infected with the HIV virus and cannot go to school though they want to do. == '''The External Actor Involved in Cambodian Educational Development''' == Cambodia has been aided by a number of more developed nations like France, West-Germany, Canada, Australia, the United States, and Japan. The United States has contributed up to $5 million through international relief agencies to children within Cambodia (Sutter). As for Japan, many Japanese organizations such as JICA have supported Cambodian educational development. For example JICA has tried to revive Cambodian educational system, by forming projects including “the project for improvement of science and mathematics education (2000-2004)”, which is aimed to enable teachers engaged in science and mathematics education to acquire skills more than cheap tricks. In addition, The World Bank, UNICEF, UNESCO, Asian Development Bank (ADB), and some NGOs (such as World Vision in the United States, Save the Children in the UK, and so on) have also supported educational development in Cambodia. Among interesting projects formed by those organizations is the World Bank’s “''Education Quality Improvement Project'' (1999 - 2004)”. This project aimed to develop and put into practice a participatory approach to school quality improvement and performance-based resource management. The goal was to have participating schools eventually show improvements in student enrollment, attendance and achievement (The World Bank). The result was that Students in more than 1,000 participating schools in Cambodia achieved higher test scores in literacy, had lower drop-out and higher promotion rates. In addition, this project could show that health and vocational training was the important factor in reducing student drop-out, and in improving promotion rates. <big>'''Works Cited'''</big> BBC News. 2008. “Timeline: Cambodia” ＜http://news.bbc.co.uk/1/hi/world/asia-pacific/country_profiles/1244006.stm＞ “Cambodian Information Center”. 2008. ＜http://www.cambodia.org/＞ Chandler, David. 2008. “A History of Cambodia”. Westview Press: Colorado, America. “Japan International Cooperation Agency”. 1995. ＜http://www.jica.go.jp/Index-j.html＞ Kennsuke, Miyamoto. 1993. “Tounan Asia no Gennzai”. 〔The Present of Southeast Asia〕. Horupu Publication: Tokyo, Japan. Komai, Hiroshi. 2001. “Shinnsei Cambodia”. 〔New Birth of Cambodia〕. Akashi Publication: Tokyo, Japan. Linton, Suzannah. 2004. “Reconciliation in Cambodia”. Documentation Center of Cambodia: Phnom Penh, Cambodia. “Social Ecoo”. 2007. ＜http://www.socialecoo.jp/series/archives/2007/07/03/entry135.html＞ Sutter, Robert G. 1991. “The Cambodian Crisis and U.S. Policy Dilemmas”. Westview Press: Colorado, America. The World Bank Group. 2008. “The World Bank”. ＜http://www.worldbank.org/＞ Valentino, Benjamin A. 2004. “Final Solutions: Mass Killing and Genocide in the Twentieth Century”. Cornell University Press: New York, America. [[Category:Asia]] tnr65l8f345v9po66nwhmdvjsaptpv0 2412386 2412385 2022-08-06T15:46:21Z Antandrus 111168 Protected "[[Educational Development of Cambodia]]": Excessive vandalism ([Edit=Allow only autoconfirmed users] (expires 15:46, 20 August 2022 (UTC)) [Move=Allow only autoconfirmed users] (expires 15:46, 20 August 2022 (UTC))) wikitext text/x-wiki [[Image:Cambodia_MapFlag.png|thumb|right|Cambodian flag]] The Kingdom of Cambodia is a country in South East Asia with a population of over 3 million people. Cambodia is the successor state of the once powerful Hindu and Buddhist Khmer Empire, which ruled most of the Indochinese Peninsula between the eleventh and fourteenth centuries. Today Cambodia is regarded as one of developing countries, therefore it has many problems, including problems related with educational development. == '''Cambodian Brief Profile''' == [[Image:Cb-map.png]] Cambodia has an area of 181,035 square kilometers, and it borders Thailand to its west and northwest, Laos to its northeast, and Vietnam to its east and southeast. Cambodia gained independence from France on November 9, 1953. Cambodia's main industries are garments, tourism, and construction. As for its language, more than 90% of its population is of Khmer origin therefore speaks the Khmer language, the country's official language. The remainder includes Chinese, Vietnamese, and Indians. As for the religion, most Cambodians are Buddhists of Khmer extraction, but the country also has a substantial number of Muslim Cham, as well as small animist tribes.　In addition, according the report of The World Bank, “Cambodia's economy is showing resilience in spite of the challenging international economic environment. Economic growth in 2001 was estimated at 6.3 percent, driven by an expanding tourism sector and robust garment exports. In 2001, there was nearly zero inflation. In 2002 inflation continued to be low (World Bank)”. That is, Cambodia’s economic growth has been moderately strong over the past decade. However, this growth has been concentrated in urban areas (The World Bank). Therefore the rural-urban income gap is widening these days. And around 40 percent of the population still remains under the national poverty line. == '''History''' == 1863 - Cambodia becomes a protectorate of France. French colonial rule lasts for 90 years. 1941 - Prince Norodom Sihanouk becomes king. Cambodia is occupied by Japan during World War II. 1945 - The Japanese occupation ends. 1946 - France re-imposes its protectorate. Communist guerrillas begin an armed campaign against the French. 1953 - Cambodia wins its independence from France. Under King Sihanouk, it becomes the Kingdom of Cambodia. Early 1970s - Cambodian army faces two enemies: the North Vietnamese and communist Khmer Rouge. Gradually, the army loses territory. 1975 - Lon Nol is overthrown as the Khmer Rouge led by Pol Pot occupied Phnom Penh. Sihanouk briefly becomes head of state, the country is re-named Kampuchea. Basic freedoms are curtailed and religion is banned. Hundreds of thousands of the educated middle-classes are tortured and executed in special centres. Others starve, or die from disease or exhaustion. 1976 - The country is re-named Democratic Kampuchea. Sihanouk resigns, Khieu Samphan becomes head of state, Pol Pot is prime minister. 1977 - Fighting breaks out with Vietnam. 1979 January - The Vietnamese take Phnom Penh. Pol Pot and Khmer Rouge forces flee to the border region with Thailand. The People's Republic of Kampuchea is established. Many elements of life before the Khmer Rouge take-over started to be re-established. 1981 - The pro-Vietnamese Kampuchean People's Revolutionary Party wins the elections to the National Assembly. 1989 - Vietnamese troops withdraw. The country is re-named the State of Cambodia. Buddhism is re-established as the state religion. 1991 - A peace agreement is signed in Paris. A UN transitional authority shares power temporarily with representatives of the various factions in Cambodia. Sihanouk becomes head of state. 1993 - General election sees the royalist Funcinpec party win the most seats followed by Hun Sen's Cambodian People's Party (CPP). A three-party coalition is formed with Funcinpec's Prince Norodom Ranariddh as prime minister and Hun Sen as deputy prime minister. The monarchy is restored, Sihanouk becomes king again. The country is re-named the Kingdom of Cambodia. 1994 - Thousands of Khmer Rouge guerrillas surrender in government amnesty. 1997 - Hun Sen stages a coup against the prime ministar, Prince Ranariddh, and replaces him with Ung Huot. The coup attracts international condemnation and Cambodia's membership of the Association of Southeast Asian Nations (ASEAN) is delayed. The Khmer Rouge put Pol Pot on trial and sentence him to life imprisonment. 1998 - On April 15, Pol Pot dies in his jungle hideout. Elections in July are won by Hun Sen's CPP, amid allegations of harassment. A coalition is formed between the CPP and Funcinpec. Hun Sen becomes prime minister, Ranariddh is president of the National Assembly. 2001 - Senate approves a law to create a tribunal to bring genocide charges against Khmer Rouge leaders. 2001 June - International donors, encouraged by Cambodia's reform efforts, pledge $560 million in aid at a donor conference in Tokyo. 2001 June - Five Cambodians, three of them US citizens, are sentenced to life for involvement in armed attack by US-based Cambodian Freedom Fighters (CFF) on government buildings in Phnom Penh in 2000. CFF says it will continue campaign to overthrow Prime Minister Hun Sen. 2001 December - First bridge across the Mekong River opens, linking the east and west of the country. The 1.36km bridge cost $56 million. 2002 February - First multi-party local elections; ruling Cambodian People's Party wins in all but 23 out of 1,620 communes. 2004 August - Parliament ratifies kingdom's entry into World Trade Organization (WTO). 2004 October - King Sihanouk abdicates and is succeeded by his son Norodom Sihamoni. 2005 April - Tribunal to try surviving Khmer Rouge leaders gets green light from UN after years of debate about funding. 2005 October - Prime minister signs a controversial border agreement with Vietnam. Legal action is taken against some critics of the deal, prompting international concern. 2006 July - Ta Mok, one of the top leaders of the brutal Khmer Rouge regime, dies aged 80. 2007 July - UN-backed court tribunals begin questioning suspects about allegations of genocide by the Khmer Rouge. 2007 September - Most senior surviving member of Khmer Rouge, Nuon Chea - "Brother Number Two" - is arrested and charged with crimes against humanity. 2008 February - Cambodian court sentences 20 member of small Cambodian Freedom Fighters group to prison for attack on prime minister's office in November 2000. 2008 March - Genocide tribunal refuses bail plea of Nuon Chea. 2008 April - US court convicts Cambodian-born Cambodian Freedom Fighters leader Chhun Yasith of masterminding 2000 attack. 2008 July - PM Hun Sen's ruling Cambodian People's Party (CPP) claims victory in parliamentary elections. EU monitors say the vote fell short of international standards. 2008 July - Cambodia and Thailand move troops to disputed land near ancient Preah Vihear temple after decision to list it as UN World Heritage Site fans nationalist emotions on both sides. Officials from both states start talks to resolve standoff. (BBC News 2008) This part would focus on the Khmer Rouge, because it has affected the educational system in Cambodia. On 17 April 1975, after five years of civil war, Cambodia’s capital Phnom Penh fell to the forces of the Communist Party of Kampuchea (CPK), popularly known as ''the Khmer Rouge'' (Linton). ''Pol Pot'' was the leader of the Khmer Rouge. “The country was cut off from the outside world, its cities emptied, its economy militarized, and its Buddhist and folk cultures destroyed. The leadership’s ‘vision’ of a better Cambodia led to extraordinary horrors on Cambodian people, who had to endure the forced movement of their urban populations, starvation, unlawful killings, forced labor, torture, and cruel, inhumane and degrading treatment and persecution on a massive scale”(Linton). Mao-think that Pol Pot studied in China, the ethnocentric policy, and anti-Vietnam policy became the theoretical support which created the regime of terror by the Khmer Rouge (Miyamoto). Pol Pot sanctioned the use of massive violence because he believed it was the only “practical” way to achieve and protect his utopian vision for a better society in Cambodia (Valentino). By the hands of the Khmer Rouge, mainly educated people (such as teachers and respected local leaders and so on) had been killed, since they were likely to be rebel groups. Furthermore, the Khmer Rouge had denied the value of education at all points. Therefore, it can be said that Cambodia had experienced a systematic destruction of education by the Khmer Rouge, until Heng Samrin supported by Vietnamese robbed the Khmer Rouge of its power in 1979. According to Linton, an estimated 20% of the 1975’s population of 7.7million people lost their lives. After the Khmer Rouge was over, the United Nations peacekeeping force, the United Nations Transitional Authority in Cambodia (UNTAC), began monitoring Cambodia in 1992. “The goal of UNTAC was disarmament of the troops, and national elections for a constituent assembly which took place in 1993. (…) Contrary to the fears of many, the elections were peaceful. Over 90 percent of the registered voters went to the polls in Cambodian freest, fairest, and most secret election since the colonial era. (…) For the first time in Cambodian history, a majority of Cambodians had voted against an armed government such as the Khmer Rouge” (Chandler). Therefore it can be said: Cambodia was able to gradually recover from many years of violence by the Khmer Rouge regime, in the wake of those elections, although not all problems were solved. == '''Educational Development Strategy and Challenge of Cambodia''' == Although all educational systems of Cambodia were abolished under the regime of terror by the Khmer Rouge, according to the World Bank, there have been significant improvements in the past five years in the education sector in Cambodia, particularly in terms of primary net enrollment gains (it’s because the government of Cambodia has put more efforts on the primary education, according to Komai), the introduction of program based-budgeting and the development of a sound pro-poor policy framework. But in Cambodia, several challenges remain. For example, most Cambodian children attend some schooling, but a large share complete only a few grades-with 85 percent of 15 to 19 year olds completing just grade 1, while only 27 percent complete grade 7 (The World Bank). It is partly because parents (especially those in rural areas) are blind to the importance of education. There are also disparities in education participation rates by different regions. Moreover, inefficiency and poor quality in education service delivery at primary, secondary and tertiary levels are other major challenges. For instance, the number and the quality of teachers in Cambodia are insufficient. It is because almost all of experienced old teachers had been killed under the regime of the Khmer Rouge. In fact, one thirds of teachers in the primary school have not finished even lower secondary education (Komai). And the budget for education is extremely restricted, compared to neighboring nations (Komai). Thus, the salary of teachers is too low, which causes teachers’ corrupt practices. And the time for studying in the school is 15 hours per week, which is extremely insufficient, too (Komai). Another challenge is related to child prostitution. “In Cambodia, child prostitution has become a worsening problem since 1990’s. Many Cambodian children have been deceived by words that there are “good” sources of employment in urban areas and have left their home, and have been forced to work in the house of prostitution. In Cambodia, there are more than 8.000～15.000 children who had been damaged by child prostitution” (Social Ecoo). Furthermore, expanding of child prostitution causes spread of HIV/AIDS among Cambodian children. HIV/AIDS is one of educational challenge, since children who are infected with the HIV virus cannot get an education well. [[Image:Cambodiaeducation.jpg]] == '''The Recommendation for Ways to Approach Educational Development of Cambodia''' == First of all, those involved in educational development in Cambodia should make improvements of Cambodian education quality. It would lead to Cambodian students’ higher promotion and achievement rates. Moreover, if education quality gets improved, even parents in rural areas would come to understand the value of education, and would come to encourage their children to complete higher school grades. Furthermore, the budget for education should be increased. The government of Cambodia has gradually made an increase in the budget for education since 2006, and it is hoped that this trend would be maintained longer. Moreover, the teacher training is also needed, because there are little experienced old teachers left due to the Khmer Rouge’s regime of terror.In addition, vocational education for Cambodian children engaging in child prostitution is necessary. It is because children would not have to sell their body, if there are any other sources of employment. And it would lead to cut down the number of children, who are infected with the HIV virus and cannot go to school though they want to do. == '''The External Actor Involved in Cambodian Educational Development''' == Cambodia has been aided by a number of more developed nations like France, West-Germany, Canada, Australia, the United States, and Japan. The United States has contributed up to $5 million through international relief agencies to children within Cambodia (Sutter). As for Japan, many Japanese organizations such as JICA have supported Cambodian educational development. For example JICA has tried to revive Cambodian educational system, by forming projects including “the project for improvement of science and mathematics education (2000-2004)”, which is aimed to enable teachers engaged in science and mathematics education to acquire skills more than cheap tricks. In addition, The World Bank, UNICEF, UNESCO, Asian Development Bank (ADB), and some NGOs (such as World Vision in the United States, Save the Children in the UK, and so on) have also supported educational development in Cambodia. Among interesting projects formed by those organizations is the World Bank’s “''Education Quality Improvement Project'' (1999 - 2004)”. This project aimed to develop and put into practice a participatory approach to school quality improvement and performance-based resource management. The goal was to have participating schools eventually show improvements in student enrollment, attendance and achievement (The World Bank). The result was that Students in more than 1,000 participating schools in Cambodia achieved higher test scores in literacy, had lower drop-out and higher promotion rates. In addition, this project could show that health and vocational training was the important factor in reducing student drop-out, and in improving promotion rates. <big>'''Works Cited'''</big> BBC News. 2008. “Timeline: Cambodia” ＜http://news.bbc.co.uk/1/hi/world/asia-pacific/country_profiles/1244006.stm＞ “Cambodian Information Center”. 2008. ＜http://www.cambodia.org/＞ Chandler, David. 2008. “A History of Cambodia”. Westview Press: Colorado, America. “Japan International Cooperation Agency”. 1995. ＜http://www.jica.go.jp/Index-j.html＞ Kennsuke, Miyamoto. 1993. “Tounan Asia no Gennzai”. 〔The Present of Southeast Asia〕. Horupu Publication: Tokyo, Japan. Komai, Hiroshi. 2001. “Shinnsei Cambodia”. 〔New Birth of Cambodia〕. Akashi Publication: Tokyo, Japan. Linton, Suzannah. 2004. “Reconciliation in Cambodia”. Documentation Center of Cambodia: Phnom Penh, Cambodia. “Social Ecoo”. 2007. ＜http://www.socialecoo.jp/series/archives/2007/07/03/entry135.html＞ Sutter, Robert G. 1991. “The Cambodian Crisis and U.S. Policy Dilemmas”. Westview Press: Colorado, America. The World Bank Group. 2008. “The World Bank”. ＜http://www.worldbank.org/＞ Valentino, Benjamin A. 2004. “Final Solutions: Mass Killing and Genocide in the Twentieth Century”. Cornell University Press: New York, America. [[Category:Asia]] tnr65l8f345v9po66nwhmdvjsaptpv0 0 93629 2412458 1899000 2022-08-07T02:20:35Z Clarisa64 2947790 /* Users who might answer your questions */I answered a query with a recommendation. wikitext text/x-wiki This is a place where learners can receive feedback and generally discuss Spanish. If you are interested in helping provide feedback, please sign below. ==Users who might answer your questions== Hola Y Buenos noches.Mi nombres es... limegreentoes1.--[[User:Limegreentoes1|Limegreentoes1]] 23:21, 16 November 2011 (UTC) Hola, I'm really interested in learning Spanish, I need someone who can volunteer in helping me perfect or practice it. [[User:Kizito29|Kizito29]] ([[User talk:Kizito29|discuss]] • [[Special:Contributions/Kizito29|contribs]]) 06:41, 19 July 2018 (UTC) :{{At|Kizito29}} You might try DuoLingo. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:21, 19 July 2018 (UTC) @Dave. Thank you, I'll look into that. Keep in touch. Chao [[User:Kizito29|Kizito29]] ([[User talk:Kizito29|discuss]] • [[Special:Contributions/Kizito29|contribs]]) 16:54, 19 July 2018 (UTC) @Kizito29 I can highly recommend Kwizq for your Spanish language learning. It's an excellent online site. Good luck 👍 eahl2npok7j6mi2xafbnayhoo76cx9x 0 108874 2412503 2160143 2022-08-07T11:33:11Z 176.82.181.72 wikitext text/x-wiki Zic As Aaaaaaaaaaaaaaaaaaaaas == Sunsuneo Minecraft Java Edition ==   Selecciona cualquier comando para escribirlo fácilmente   == Agricunchjjj Minecraft Playstation Edition == Puedes seleccionar el comando pero luego tienes que escribir las coordenadas del /tp o material del /give @s etc   == Afanisilestain Minecraft Bedrock Edition == Estás obligado a escribir el comando entero menos /tp /time set /weather o /setworldspawn   == vanilla vanilla trotrotro Minecraft Pocket Edition ==   Al igual que en bedrock pero se necesita poner / después el comando que quieras usar y después estás obligado a poner todos los detalles del comando y todo el texto en letra minúscula   Zic As     == Estropajon == Me invento películas mentales en el As   == Sunsuneo Minecraft Java Edition ==   Selecciona cualquier comando para escribirlo fácilmente   == Agricunchjjj Minecraft Playstation Edition == Puedes seleccionar el comando pero luego tienes que escribir las coordenadas del /tp o material del /give @s etc   == Afanisilestain Minecraft Bedrock Edition == Estás obligado a escribir el comando entero menos /tp /time set /weather o /setworldspawn   == vanilla vanilla trotrotro Minecraft Pocket Edition ==   Al igual que en bedrock pero se necesita poner / después el comando que quieras usar y después estás obligado a poner todos los detalles del comando y todo el texto en letra minúscula   == Estropajon ==   Descucacualorenzo   == Sunsuneo Minecraft Java Edition ==   Selecciona cualquier comando para escribirlo fácilmente   == Agricunchjjj Minecraft Playstation Edition == Puedes seleccionar el comando pero luego tienes que escribir las coordenadas del /tp o material del /give @s etc   == Afanisilestain Minecraft Bedrock Edition == Estás obligado a escribir el comando entero menos /tp /time set /weather o /setworldspawn   == vanilla vanilla trotrotro Minecraft Pocket Edition ==   Al igual que en bedrock pero se necesita poner / después el comando que quieras usar y después estás obligado a poner todos los detalles del comando y todo el texto en letra minúscula   == Estropajon == [[File:Paralympic low res.pdf|thumb|300px|Low resolution copy of the final proposal from UCNISS to the Australian Paralympic Committee, for the production of a text called, The History of the Paralympic Movement in Australia. Design by Sunshine Connelly for UCNISS.]] [[File:Wheelchair basketball at the 2008 Summer Paralympics.jpg|thumb|300px|Wheelchair basketball at the 2008 Summer Paralympics, Iran vs South Africa. An example of an image on Wikimedia Commons, The repository that feeds Wikipedia. It is difficult to find images of Australian athletes or events - something this project will address]] ==Background== [http://www.paralympic.org.au/ The Australian Paralympic Committee] (APC) has [[The History of the Paralympic Movement in Australia/Request for Proposals|sought costed proposals]] from suitably qualified individuals or organisations to document the '''History of the Paralympic Movement in Australia''' in a format which meets the needs of the [http://www.paralympic.org.au/ APC] for online and possible print publication. This [http://en.wikiversity.org/wiki/UCNISS/History_of_the_Paralympic_Movement_in_Australia Wikiversity page] has been developed to present an open, collaborating response to the [http://www.paralympic.org.au/ APC] request for proposals and the requirement to create a well-researched and referenced multi-media document that can be published online. We aim to offer a compelling case to be entrusted to share the story of: * The development of Paralympic sport and, where the two intersect, the wider story of sport for people with a disability in Australia. * Australia's participation in the thirteen summer and ten winter Paralympic Games (to the end of 2010). * The foundation and growth of the Australian Paralympic Committee. * Key individuals in the growth of the Paralympic movement in Australia. We recognise that there is an enormous amount of material available to inform this story. Our approach to the project is to unfold the story with our project team and other experts as required. Our commitment to a wiki format should deliver a triangulated story of the Paralympic Movement in Australia that ensures a community-enriched account of a remarkable culture. We anticipate that during the course of the project we will be able to explore some important themes that cross Paralympic history in Australia: the interplay between sport and rehabilitation; the growth of the [http://www.paralympic.org.au/ APC] and its place within the Australian sport system; and the impact of the Paralympic movement on wider perceptions within the community of the role and “status” of people with a disability. If successful in our bid we would like to start work on the project on '''2 May 2011''' and deliver content continuously up to 31 December 2012. ==Proposal== [[File:StateLibQld 1 100176.jpg|thumb|300px|The [http://www.nla.gov.au/ National Library of Australia] and other key Australian cultural organisations have a working relationship with the [http://commons.wikimedia.org/wiki/Main_Page Wikimedia Commons] project. In 2010 the [http://www.slq.qld.gov.au/ State Library of Queensland] [[:Wikipedia:Wikipedia:Wikipedia Signpost/2010-12-20/Image donation|Donated its collection of historic images to Wikimedia Commons.]]]] [[File:PediaPress Hardcover standing01.jpg|thumb|300px|An example of a printed and hard cover bound book from PediaPress. This book is user generated out of Wikipedia articles. This is the same quality that the History of the Paralympic Movement in Australia book will be]] This is an open proposal to the [http://www.paralympic.org.au/ Australian Paralympic Committee] (APC) from the [http://www.ucniss.net University of Canberra's National Institute of Sport Studies] (UCNISS) to produce a text called: ''A History of the Paralympic Movement in Australia'', and to establish a repository of media and digitised primary resources such as video and audio recordings, images and scanned documents, to compliment the text. This proposal aims to: * Produce an initial text and multi media repository. * Develop a participatory community around the text and repository. * Ensure long term maintenance and integration of the content with Australian Paralympic information networks. We propose to establish the text and media repository on the popular web based collaborative writing platforms provided by the [http://wikimediafoundation.org/wiki/Home Wikimedia Foundation]. The Wikimedia Foundation has established editor communities, robust technology and sound operating principles. Their [[Wikibooks:Main Page|Wikibooks]] and [http://commons.wikimedia.org/wiki/Main_Page Wikimedia Commons] are 'sister' projects to the more popular [http://www.wikipedia.org/ Wikipedia]. We believe these projects offer a range of benefits that offer cost effectiveness for [http://www.paralympic.org.au/ APC's] objectives, namely: # Online collaborative editing platforms with celebrated accessibility standards, especially for people relying on screen readers. # International technical management, with robust policies and procedures to ensure 24/7/365 reliability with very high national and international visibility. # Reliable online media storage, management and delivery that maintains strict copyright diligence, and uses open standard formats and archive policies to ensure long term access and reusability. # The [http://pediapress.com/ PediaPress] print on demand service, delivering quality printed and bound books directly from the online text, based on the latest up to date version, or on customised individual needs, at significantly low cost to the [http://www.paralympic.org.au/ APC] and end users. # A proven volunteer base, especially within the [http://commons.wikimedia.org/wiki/Main_Page Wikimedia Commons] project, who help maintain the integrity of the media and text, such as it being free of spam and vandalism, along with comprehensive content categorisation and linkages, with stringent copy editing and review processes available in the "featured content" nomination process. # Seamless integration with the [http://www.wikipedia.org/ Wikipedia] project, helping to improving the accuracy and quality of all the [http://www.wikipedia.org/%20Wikipedia Wikipedia] articles related to the Australian Paralympic community, athletes, Games, history and organisation. # Support for establishing a community of volunteer editors of Australian Paralympic content in the wiki platforms, helping to maintain accuracy and relevance of the text and repository beyond the time frame of this project. This proposal aims to deliver a comprehensive historical text, embedding multi media after producing and uploading it to a high quality media repository, situated on the most successful collaborative production and management platforms to date, and leveraging their communities and processes to assure reliability and long term sustainability. Furthermore, this project will reach out and support members of the Australian Paralympic community through information, training and support, to help them become contributors to [[Wikibooks:Main Page|Wikibooks]], [http://commons.wikimedia.org/wiki/Main_Page Wikimedia Commons], and [http://www.wikipedia.org/ Wikipedia], thereby enabling them to play an ongoing and important role in maintaining a high quality online profile for everything Australian Paralympic. We note the diversity of materials the APC has collected and produced. Our text will link to these and ensure the visibility of these materials. There will be explicit mention of these materials on the wiki to ensure their visibility. ==Project Structure and Management== [[File:DBP 1972 733 Weltspiele der Gelähmten.jpg|thumb|300px|Paralympic Games 1972 in Heidelberg. Graphics by Schwarz. First Day of Issue / Erstausgabetag: 18. Juli 1972. This stamp is in the public domain in Germany because it was released by Deutsche Bundespost on behalf of the Federal Minister of Post and Telecommunication and thus is an official work according to German copyright law (§ 5 Abs. 1 UrhG).]] We are proposing an inclusive approach in this project. At the time of the submission of the tender (25 March 2011) the following roles are allocated in this project: ===Project Managers=== We have identified two distinct project management roles and nominate two individuals to fulfill these roles throughout the life of the project. Both Project Managers will assure the ongoing viability and stability of the project. :* [[User:Postillion|Keith Lyons]] :: Director of [[UCNISS]] will be responsible for: ::* Oversight of project timelines, meetings, events, production, communications and reporting ::* Networking and promotion of the project ::* Quality assurance of the whole project and primary point of contact for the [http://www.paralympic.org.au/ APC] :*[[User:Leighblackall|Leigh Blackall]] :: Learning Commons Coordinator with [[UCNISS]] will be responsible for: ::* Representing the project to Wikimedia Australia, Wikimedia Commons, Wikibooks, and the Wikimedia Foundation community outreach programs. ===Sport Historians=== '''Sport historians''' will be responsible for primary research, gathering resources, reviewing for accuracy and consistency, structuring and writing content, referencing, linking and editing. They will be supported by the Librarians and Copy Writers. We extend an open invitation to any sport historian to join this group. [http://www.ucniss.net UCNISS] is developing a keen interest in Australian sport history and has a number of PhD projects underway at present. This open proposal seeks to build upon the ethnographic research experience of Keith Lyons and the historical research credentials of proposed contributors that include: :*[http://www.linkedin.com/pub/greg-blood/2a/14a/729 Greg Blood] :*Bruce Coe :*[http://www.australianoftheyear.org.au/recipients/?m=robin-poke-2011 Robin Poke] Each of these contributors is a highly regarded sport historian with excellent local, national and international contexts. Greg is a member of staff at the Australian Institute of Sport and has been a librarian at the Australian Sports Commission since 1983. Bruce is completing a PhD on [http://archive.is/20121202095346/keithlyons.wordpress.com/2010/12/17/marks-and-coe-meeting-in-the-commons/ the life of E S Marks]. Robin is undertaking a PhD in the history of Australian Rowing. Since 2007 Robin has been an interviewer for the [http://catalogue.nla.gov.au/Record/4353507 National Library of Australia’s Sport Oral History project], which has involved him in interviews with Australia’s first Paralympians. All three are members of the Australian Capital Territory Chapter of the Australian Society of Sports History. :*[http://www.canberra.edu.au/faculties/health/sport-studies/staff/robin-mcconnell Robin McConnell] Robin has significant historical research experience most recently applied in his project, Sport in Prisoner of War Camps. He has researched the History of Rugby in New Zealand. He has supervised postgraduate research in sport history, and has taught the history of sport at University of Ulster. Robin has written about the Special Olympics and is the author of a study of a Maori leader ''Taua of Kareponia'' (Te Maru Publications 1993). Robin is an external examiner of sport history PhDs. :*[http://www.sportscoachingbrain.com/about-wayne-goldsmith/ Wayne Goldsmith] Wayne will work with Keith Lyons to coordinate the work of the sport historians and will take a lead role in gathering data for the project. Wayne will use [http://www.sportscoachingbrain.com/ his extensive experience of social media] to ensure that the project has a strong user focus. He will have an important day-to-day role in content delivery. :*[http://www.staffs.ac.uk/staff/profiles/nbt1.jsp Nigel Thomas] To ensure that our work meets international benchmark standards we have secured the services of Nigel Thomas (Staffordshire University) as the senior editorial consultant for the project. Nigel is the co-author (with Andy Smith) of [http://books.google.com.au/books?id=x3FKBSzsBPQC&printsec=frontcover&dq=Nigel+Thomas+Disability&source=bl&ots=uVnNSlcFey&sig=HqxDH1rnEoPnJYquhxMpAfDrv1g&hl=en&ei=CIR1TZ73DoSqvQOn9enYBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBgQ6AEwAA#v=onepage&q&f=false Disability, sport and society: an introduction] (2009). ===Librarians=== '''Librarians''' will support the Sport Historians in sourcing material, checking for and negotiating copyright, digitisation and formatting to open standards, uploading media and ensuring appropriate meta data, linking and categorisation is included. They are supported by the Copy Writers. We propose: :* John Vandenberg John is the President of Wikimedia Australia and will assist in managing the collection of APC media on Wikimedia Commons. John presently manages the [[Wikipedia:Wikipedia:Wikipedia Signpost/2010-12-20/Image donation|State Library of Queensland project]] where several thousand images where loaded to Wikimedia Commons and are presently being categorised and integrated into Wikipedia. John also created extension software to Media Wiki, that can automate many processes we will need to undertake in the initial preparation of content and its uploading. :* [http://www.canberra.edu.au/monitor/2009/mar/20092003_harmony Pat Tandy] Pat is University of Canberra's Faculty of Health Liaison Librarian. Pat's brief is to assist with research work, helping us find primary and secondary resources across Australia's library data bases, including the National Library, Archive and others. ===Copy Writers=== '''Copy writers''' support the Sport Historians in formatting text to MediaWiki text, linking, and [[w:Copy editing|copy editing]]. They support the Librarians in uploading, formatting to open standards, meta data, linking and categorisation. We propose as copy writers: :*[[User:Graham87|Graham Pearce]]<br> ::Perth, Western Australia<br> ::Wikipedia administrator<br> ::Expert in the use of Media Wikis with a Screen Reader<br> :*[[User:LauraHale|Laura Hale]]<br> ::PhD student with [[UCNISS]]<br> :*UCNISS Undergraduate students<br> ::Once this project is worked into existing assessment assignments in their units<br> ===Trainers=== '''Trainers''' support the APC Liaison with work on community awareness campaigns. They go to regional centres around Australia to meet with Australian Paralympic Community members, to show them how to edit Wikibooks, Wikimedia Commons and Wikipedia. In this role they also support the Librarians and Historians in gathering media and primary resources. They monitor the Wikibooks and Commons pages relating to the project, and provide online support for anyone contributing. We propose the following trainers: :*[[User:Graham87|Graham Pearce]]<br> ::Perth, Western Australia<br> ::Wikipedia administrator<br> ::Expert in the use of Media Wikis with a Screen Reader<br> :*[[User:LauraHale|Laura Hale]]<br> ::PhD student with [[UCNISS]]<br> :*Wikimedia Australia<br> ::A committee with resources for training Australian's in the use of Media Wikis<br> ===Project Reporters=== '''Project Reporters''' support the Project Managers in documenting the project, and the APC Liaison in setting up the forum and publishing updates to it. They prepare press releases for mainstream media, and participate in research work. They also monitor social media and public relations generally. Our proposals for project reporters are: :* [[User:Postillion|Keith Lyons]] :: Director of [[UCNISS]], and sport blogger :*[[User:Leighblackall|Leigh Blackall]] :: Learning Commons Coordinator with [[UCNISS]] :*[[User:LauraHale|Laura Hale]]<br> ::PhD student with [[UCNISS]]<br> ===Project Advisor=== We recognise that the project needs a high level of quality assurance particularly in relation to access to the information we present. In addition to Graham Pearce's role we have identified [http://www.canberra.edu.au/centres/phiw/staff_profiles/profile_fleming.htm Michele Fleming] as a key member of our team. Michele is the Dean of Students and Director of the [http://www.canberra.edu.au/seasu Student Equity and Support Unit] at the University of Canberra Disability Service. Michele has responsibility for elite athletes at the University of Canberra. At present she is the second investigator on an ALTC research grant that aims to develop an online tool for the Higher Education sector on the Disability Standards for Education. Michelle is working to ensure that all of the University's web content meets accessibility requirements. The [http://www.canberra.edu.au/library University of Canberra Library] has considerable experience of the support for diverse learning needs and through Pat Tandy will advise the Project team about accessibility better practice. ===APC Liaison=== We will work closely with the APC and nominated APC liaison personnel throughout this project. ==Software and Systems to be Used== [[File:Pediapress hardcover color2.jpg|thumb|300px|The high standard of print on demand products available through Wikibooks. Readers can create custom books, including and omitting sections, using always the latest information included on the wiki. More information, including previews of the format, are available on the [http://pediapress.com PediaPress website]. A video by PediaPress, explaining the user experience for printing and ordering a book, is [http://www.youtube.com/watch?v=D1K03AZfpDM available on Youtube]]] [[File:Sportdag voor oorlogsinvaliden te Doorn.ogv|thumb|300px|On the training ground for the military convalescent Aardenburg in Doorn, 1954. The annual sports festival for disabled veterans. '''This is an embedded video from Wikimedia Commons'''. Wikimedia Commons accepts video, audio, images, graphics and PDF, keeping them in open standard formats, meta data tagged, integrated with other projects, and licensed with free to reuse copyright.]] We propose using the production, publishing and content management services offered by the Wikimedia Foundation, to ensure media is formatted to open standard formats, and to use Creative Commons licensing to manage copyright. These systems and software ensure long term accessibility of the production, and the technical and legal flexibility should the APC need to move content to another platform, or commission derivatives, or to keep locally stored backups. The Wikimedia Foundation hosts the services Wikibooks and Wikimedia Commons, both 'sister' projects to Wikipedia, which are all mediated collaborative approaches to content authoring and management, using established and robust platforms that do not require extensive involvement from APC's own IT experts. The Wikimedia Foundation keeps the technical infrastructure running across all projects, attracting significant donations each year, while the respective project's very large volunteer base manage the content and community governance. ===Wikibooks=== '''Wikibooks''' focuses on the production of texts following the book structure. Like all Wikimedia Foundation projects, it is a successful and well managed collaboration space, freely available to APC interests. Wikibooks includes the feature for readers to print and order a book version of the content, significantly cheaper and less resource intensive than APC might find through a conventional print run. An advantage of this is that it is possible to print and bind just segments of the whole project (for example, "organisational history"), which could enable individual tailoring of the physical book to specific audiences. We believe that the [[Wikibooks:Wikijunior|Wikijunior]] feature of Wikibooks will provide an enormous opportunity to extend the reach of the APC History project. We believe we can produce a high quality text from Wikibooks and do so on demand with updated text and media content. ===Printed and bound book=== '''PediaPress''' is a web based software and print-on-demand service that extends the feature set of Wikibooks and all Wikimedia Foundation projects into printed and delivered books. PediaPress enables all users to create customized books, printed, perfect bound, and delivered by post. This print and deliver option is available via the "Print/export - create a book" links in the navigation bar of Wikimedia Foundation projects. PediaPress offers a 4 minute video on Youtube that explains the process of producing a book from Wikipedia articles: ''[http://www.youtube.com/watch?v=D1K03AZfpDM Wikipedia In Print - How to create custom books with a mix of content from the free encyclopedia]''. This same process can be applied to a Wikibook. There is an additional option for a printed and bound book, one that engages the services of a graphic designer, producing the original text and images into a manually designed and higher quality product. We would use the web service [http://lulu.com Lulu] to publish this version, where it manages the purchase orders and distribution at next to no cost to this project. Depending on the results of market research, the costs of the production of this print option could be recovered through purchase royalties. Therefore, the cost of this production is not included in the project budget. Leigh Blackall established this production process in his work with Otago Polytechnic's textbook, [http://www.lulu.com/product/paperback/anatomy-and-physiology-of-animals/2285614 Anatomy and Physiology of Animals on Lulu.com]. This text is developed and maintained on Wikibooks, but a graphic designer produces a print version annually for download from Lulu with the production cost recovered through sale royalties. ===Wikimedia Commons=== '''Wikimedia Commons''' is the Wikimedia Foundation's project for all multi media used on all the Wikimedia Foundation projects. The vast volunteer base offers considerable resource in catagorising and managing the multimedia that the APC would load to the project. That content would then be used widely across all Wikimedia Foundation projects, especially Wikipedia, helping to lift the profile of APC, its community and it athletes, ultimately promoting community development efforts around its projects. Wikimedia Commons manages copyright, archiving and formats, ensures open standard formats which assist in the long term archival concerns of the media. Currently the National Library of Australia and other key Australian cultural organisations have a working relationship with the Wikimedia Commons project. Recently the State Library of Queensland [[Wikipedia:Wikipedia:Wikipedia Signpost/2010-12-20/Image donation|donated its collection of historic images to Wikimedia Commons]]. ===Images, video and audio=== '''Open standard formats''' relate primarily to multi media used in this project. Wikimedia Commons only accepts media in open standard formats, so as to ensure the integrity of the archive against software redundancy, proprietary fee structures and digital restrictions management software. This principle helps ensure that all work created and collected in this project is also free from such concerns, thereby acquiring the same archival integrity. Multi media such as images, video, audio and PDF documents are easily embedded into the wikis, as demonstrated in this section with the embedded video of war veterans participating in games in 1954. Open standard multi media formats are increasingly recognised by main providers of Internet services, such as Google Chrome and FireFox browsers playing open standard video and audio files in their browsers without the need for plugin software and extensions. This is made possible by the [[w:HTML5 video|HTML5 video]] tag released in 2010. ===Wikimedia Foundation and Wikimedia Australia=== '''Wikimedia Australia''' is a chapter of the '''Wikimedia Foundation''', the peak body that governs and administers the Wikibooks, Wikimedia Commons, Wikipedia and other projects. In their 2011-2015 Strategic Plan, the Wikimedia Foundation's priorities included support for cultural and learning institutions seeking to engage their communities in the projects. Funding is provided to the Chapters each year for outreach activities, community building activities, knowledge-creation project and partnerships with cultural and knowledge institutions. This project will actively liaise with the Wikimedia Foundation and Wikimedia Australia to ensure understanding and to seek support where it aligns with their strategic priorities. ===Open Office=== '''Open Office''' is a free and open source software package equivalent to Microsoft Office. A key feature of [[w:Open Office|Open Office]] is its ability to export documents to MediaWiki syntax, making it easier for an author who is familiar with standard word processing software like MS Word or Open Office Text, to produce documents for Wikibooks. The added value of this as a workflow for the initial historians is that they produce a document in 2 format versions, affording backup and flexibility in use. ===Creative Commons=== '''Open copyrights''' are a critical consideration for [http://www.paralympic.org.au/ APC] management in that all content used in this project needs to adopt the [http://creativecommons.org/licenses/by-sa/2.0/ Creative Commons Attribution Share Alike copyright license], an internationally recognised copyright license that facilitates the benefits described in this proposal. This copyright license is one in which [http://www.paralympic.org.au/ APC] retains copyright, but gives rights for content to be reused, with the only restrictions being the requirement of attribution on all derived content, and the sharing back of all derivatives through use of the same copyright license. This is inline with the explicit guidelines put forward by the Australian Attorney General, adopting the recommendations of the 2010 Government 2.0 Task Force. Such licensing will ensure Australian Paralympians, the Paralympic community, and the Committee enjoy the maximum level of exposure and recognition through this work as possible. With regard to potential competitors or exploiters of [http://www.paralympic.org.au/ APC] content, this license presents a dilemma for them, in that any content they adopt and reuse from this [http://www.paralympic.org.au/ APC] project, the copyright license compels them to attribute [http://www.paralympic.org.au/ APC] and to use the same licensing arrangement on the work derived from [http://www.paralympic.org.au/ APC] source content. The [http://wikimediafoundation.org/wiki/Home Wikimedia Foundation] has the resources to monitor and track such terms and conditions over copyright. ===Backup=== The systems and software above are implicitly designed and selected for backup and sustainability concerns. We are engaging in a copyright regime that facilitates legitimate copying for backup and republishing, and using open standard media formats that ensure the long term reusability of the content free of commercial limitations. Apart from these system features, the software and services offered by the Wikimedia Foundation (Wikibooks, Wikimedia Commons, and Wikipedia all running on the free and open source platform MediaWiki) provides a number of features that support backup made by users. Firstly, and most simply, all pages can be exported to Open Document Text, for use in word processors such as Open Office, Google Docs and Microsoft Word 2007. Pages also export to HTML, and of course MediaWiki text. As to more large scale backup, The entire English Wikibooks database is periodically [http://dumps.wikimedia.org/enwikibooks/ exported to an XML format]. These openly available backups contain content, edit history and discussion threads for all pages on the project. It is not difficult to use this backup to create a locally hosted wiki with only the APC project content. If the Wikimedia Foundation ever stopped providing these backups, we can create our own via [http://www.mediawiki.org/wiki/Export the core mediawiki function called Export]. The skills for doing this are brought to the project by our librarian, John Vandenberg. As for large scale HTML backup, there are many tools which convert a wiki into a static website, consisting of just HTML and images. The Wikimedia Foundation provides [http://static.wikipedia.org/new/wikipedia/en/index.html a static copy of all the Wikipedia] for example. Again, John Vandenberg brings these skills and services to the project. The Database dumps and Export features do not include the image files. John Vandenberg, our librarian on this project, has created software which obtains all images from the Wikimedia Commons server, and with just a few hours work, this software can be customised to backup only the images used within the APC project. Wikimedia Australia, an organisation supporting this bid, can periodically copy these dumps and store them on a server in Australia as an additional backup measure should APC require it. This service is offered free of charge, until such time as traffic should require cost recovery. ==Project Timeline== {{center top}} {| bgcolor="whitesmoke" style="border: DarkGreen solid 1px;" |- ! Tasks ! May 2011 ! Jun ! Jul ! Aug ! Sep ! Oct ! Nov ! Dec ! Jan2012 ! Feb ! Mar ! Apr ! May ! Jun ! Jul ! Aug ! Sep ! Oct ! Nov ! Dec2012 |- | [[#Research|Research]] | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | |- | [[#Initial framework document|Initial framework document]] | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | | | | | | | | | | | |- | [[#Online forum|Online forum]] | bgcolor="pink" | | | | | | | | | | | | | | | | | | | | | |- | [[#Monitoring and moderating|Monitoring and moderating]] | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | |- | [[#Interviews|Interviews]] | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | | | |- | [[#Source media|Source media]] | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | | | | | | |- | [[#Final text|Final text]] | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | |- | [[#Linking the text|Linking the text]] | | | | | | | | | | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | |- | [[#Volunteer editing community|Volunteer editing community]] | | | | | | | | | | | | | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | |} {{center bottom}} The Project Timeline has the following phases: ===Research=== * Identify media and primary resources; gauge initial expectations, and outcome expectations in the Australian Paralympic Community; establish historical timelines; identify key people, events, organisations and social contexts. * Conducted by [[#Sport Historians|Sport Historians]], [[#Librarians|Librarians]] and the [[#Project Reporter|Project Reporter]] ===Initial Framework Document=== * Create an initial framework document, based on research and use of existing materials, covering the history of the Paralympic Movement in Australia; * Prepared by the [[#Project Managers|Project Managers]], [[#Project Reporter|Project Reporter]] and [[#APC Liaison|APC Liaison]] ===Online Forum=== * Set up an online forum for input by people involved in the Paralympic movement in Australia; * Set up by the [[#Project Reporter|Project Reporter]] in consultation with the [[#APC Liaison|APC Liaison]] ===Monitoring and Moderating=== * Monitor and moderate input; * Managed by the [[#Project Reporter|Project Reporter]] and the [[#Project Advisor|Project Advisor]]. ===Interviews=== * Interviews with people who have played a significant role in Australian Paralympic sport * Conducted by the [[#Sport Historians|Sport Historians]] ===Source Media=== * Liaison with representatives of the APC to source media such as photographs, videos, audio, competition results, team lists and other materials relevant to the project; * Conducted by the [[#Sport Historians|Sport Historians]], [[#Librarians|Librarians]] in consultation with [[#APC Liaison|APC Liaison]] ===Final Text=== * Create a final text for the period up to 2010, within a structure which includes the following elements: ** personal stories; ** each [[w:Category:Paralympics|Paralympic Games]]; ** other key Games, such as the Stoke Mandeville Games, the Commonwealth Paraplegic Games and the FESPIC Games; ** organisational history and changes; ** some social and historical contexts. * Written by the [[#Sport Historians|Sport Historians]] and [[#Copy Writers|Copy Writers]] ===Linking the Text=== * Linking the text to oral history interviews, other audio, video and photographs through a customised website. * [[#Sport Historians|Sport Historians]], [[#Copy Writers|Copy Writers]] and [[#Librarians|Librarians]] ===Volunteer Editing Community=== * Develop and support a volunteer editing community, skilled and willing to help maintain the document in perpetuity. * Conducted by the [[#Trainers|Trainers]] ==Budget== This is an open and collaborative project. Our budget identifies our anticipated costs but we believe that we will garner enormous in kind contributions particularly in regard to the training that can occur. Our outline budget is: {| border=1 cellspacing=0 cellpadding=5 | '''task''' | '''hours''' | '''budget''' | '''comment''' |- | Sport historians | 300 | $30,000 | Sourcing, reviewing, writing, referencing, editing |- | Librarians | 100 | $10,000 | Copyright, digital formatting, uploading and meta data, initial online content management |- | Copy writing | 200 | $20,000 | * Wiki authoring, editing, uploading and formatting * Possible [[w:LETS|LETS]] option |- | Training | 100 | $10,000 | * Wiki skills training (both online and face to face) and ongoing online support * Possible [[w:LETS|LETS]] option |- | Project reporting | 100 | $10,000 | Project progress reporting; public relations communications; social media management; research publications; graphic design |- | APC Liaison | 100 | $10,000 | * Supported by trainers and journalists * Representation to [http://wikimedia.org.au/ Wikimedia Australia], [http://commons.wikimedia.org/ Wikimedia Commons], Wikibooks, and Wiki Media Foundation; communications with APC organisation and community * Possible role for an APC member |- | Project management | 200 | $20,000 | Planning, personnel management, documentation, contracts, liaison with APC, Wikimedia Foundation and Wikimedia Australia, presentations, |- | Total | 1100 | $110,000 | '''''[[w:LETS|LETS]] is a payment system sometimes used by volunteers.''''' |- |} ==APC's Selection Criteria== ===Demonstrated Writing Skills and Experience=== All members of the proposed Project Team have considerable writing experience. A number of the team have substantial experience of social and open media. We are keen to share our experience in open access publishing. '''Wikibooks production:''' Leigh Blackall has worked the Wikibooks production model on a number of occasions. He developed this approach for Otago Polytechnic with their [[Wikibooks:Anatomy and Physiology of Animals|Anatomy and Physiology of Animals textbook]] involving a similar budget to this proposal, and now rating first in a Google search. Subsequently he produced the [[Wikibooks:Sustainable Business|Sustainable Business Wikibook]] with support from Otago Polytechnic, but this time including the New Zealand Ministry of Environment and New Zealand Trade and Enterprise. Finally, while in New Zealand, he produced the [[Wikibooks:Open Education Practices: A User Guide for Organisations|Open Educational Practices: A User Guide for Organisations Wikibook]] for the New Zealand Ministry of Education. Since working with UCNISS Leigh has encouraged teaching staff to adopted and further develop this model. Most notable to date has been James Neill working with University of Canberra students to develop an open textbook for their Psychology unit, [[Motivation and emotion/Textbook|Motivation and Emotion]]. '''Sport Historians:''' Keith Lyons has been involved in sport history research for three decades. He was a founding member of the British Association of Sport History. He is supervising two PhD students at present at the University of Canberra. He has a particular interest in oral history and ethnography. He will coordinate the sports history input with the assistance of Wayne Goldsmith. Greg Blood, Bruce Coe, Robin McConnell and Robin Poke will contribute to the development of text. Nigel Thomas (Staffordshire University) is the editorial consultant for the project. '''Online Sport Historian and MediaWiki Copy Editor:''' Laura Hale is an experienced online sport historian and Media Wiki editor. In the United States she set up and managed the [http://www.fanhistory.com/wiki/Main_Page Fan History Wiki]. Laura and a team of ten administrators developed and supported an editor community of over 2500 people, creating 900,000 articles rated as 'good' out of over 1 million articles total. Currently, Laura is working on the Wikipedia article [[w:Netball|Netball]]. Since moving to Canberra, Laura writes the [http://ozziesport.com/ Ozzie Sport blog], documenting her work researching Australian sport fandom online. '''Copy Writer for Screen Readers:''' Graham Pearce is a Wikipedia administrator based in Perth, Western Australia. He relies on a screen reader to read and edit Wikipedia. Graham will assist with copy writing, ensure screen reader usability, support volunteer editors online, and assist in communications with the wider Wikimedia Foundation community. '''Volunteer Writers and Producers:''' UCNISS has a significant volunteer base in the form of students enrolled in Sport Studies Undergraduate and Post Graduate Degrees. Students are encouraged to engage in Work Integrated Learning activities. This project provides opportunities for meeting a range of learning objectives, and it will be possible to adjust student assignments to accommodate and encourage participation in this project. ===Networking Skills=== The team that will support this bid have substantial experience working with networks of contacts. Whilst we have extensive links within sport, we point in particular to our connections with Wikimedia communities. We believe this will be a catalyst for drawing in a network of volunteer editors to assist with copy editing, categorisation, programing, support and peer review. ===Experience in Historical Research=== '''Nigel Thomas''' is our senior editorial consultant. He has worked in various sport development roles prior to joining higher education in 1997. These include: Hammersmith and Fulham Borough Council; the British Sports Association for the Disabled; and the Youth Sport Trust. His PhD (2004) is a study on mainstreaming in disability sport. Nigel's research focuses on the history, mainstreaming and media coverage of disability sport and the Paralympic Games and has culminated in the publication of a text book co-authored with Andy Smith published by Routledge in 2009 [http://books.google.com.au/books?id=x3FKBSzsBPQC&printsec=frontcover&dq=Nigel+Thomas+Disability&source=bl&ots=uVnNSlcFey&sig=HqxDH1rnEoPnJYquhxMpAfDrv1g&hl=en&ei=CIR1TZ73DoSqvQOn9enYBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBgQ6AEwAA#v=onepage&q&f=false Disability, sport and society: an introduction]. Nigel is working on a European Commission funded project aimed at encouraging sport for disabled people. In collaboration with European Observatoire of Sport and Employment (EOSE), the European Paralympic Committee (EPC) and working with 22 national partners in a year-long work package which summarises current policy and makes recommendations on future campaigns to 'promote European fundamental values by encouraging sport for persons with disabilities'. '''Selected Publications by [http://www.staffs.ac.uk/staff/profiles/nbt1.jsp Nigel Thomas]''' *Thomas, N and Smith, A. (2009) Disability, Sport and Society: A Student Introduction. London: Routledge. *Thomas, N (2008) Sport and Disability. In B.Houlihan (Eds.) Sport and Society. A Student Introduction. London: Sage. *Smith, A and Thomas, N. (2005) Including Pupils with Special Educational Needs and Disabilities in National Curriculum Physical Education: A Brief Review’. European Journal of Special Needs Education, 21 (1): 69-83. *Smith, A. and Thomas, N (2005) The ‘Inclusion’ of Elite Athletes with Disabilities in the 2002 Manchester Commonwealth Games: An Exploratory Analysis of British Newspaper Coverage. Sport, Education and Society, 10 (1). *Thomas.N., and Smith.A. (2003) ‘Pre-occupied with Able-bodiedness?’, An analysis of the British media coverage of the 2000 Paralympic Games, Adapted Physical Activity Quarterly, 20(2):166-181. '''Robin Poke''' has worked in all media and in sports administration. He was founder editor of SBS Radio News, a current affairs reporter with Radio Australia, was head of sport at Capital Television in Canberra then worked on a freelance basis with ABC radio and television and the Canberra Times, and with SBS Television. Robin’s involvement in sport has been through rowing and the Olympic movement. He established the national magazine, Australian Rowing, and was for many years honorary media director for the national federation. He held media liaison positions with the Australian team at the 1996, 2000 and 2004 Olympic Games and is now President of the ACT Olympic Council. Robin is presently an author, journalist and sports historian. His first book, a biography of Olympic rowing gold medallist Peter Antonie, was published in 2007, and his second, containing chapters on each of Australia’s 74 individual Olympic gold medallists, will be published in 2012. Since 2007 he has been an interviewer for the National Library of Australia’s Sport Oral History project, which has involved him in interviews with Australia’s first Paralympians. Robin is also a member of the Australian Society for Sports History. '''Robin McConnell''' has significant historical research experience most recently applied in his project, Sport in POW camps. Previously Robin researched History of Rugby In NZ, an well as supervising postgraduate research in historical sport topics, and teaching the history of sport at University of Ulster in Belfast. Robin is also an international marker of sport history PhDs and has written two books with historical dimensions. '''Laura Hale''' has extensive experience in terms of fandom based history. Acquiring her skills informally and self directed, her [http://www.fanhistory.com/wiki/Fanhistory.com:Philosophy Fanhistory Philosophy] gives insight to her approach, as well as the [http://www.fanhistory.com/wiki/Fanhistory.com:About Fanhistory About] page. Currently Laura is applying her data gathering and analytical skills to Australian expressions of sport fandom online, with a recent post applied to [http://ozziesport.com/2011/03/paralympic-sport-in-online-australia/ Australian paralympics]. Her methods will be a valuable component for gathering data on Australian Paralympic fandom expressed online, helping to give one aspect of social context to the history writing work ===An Understanding of Sport in Australia=== UCNISS offers undergraduate degrees in Sport, ''Coaching and Exercise Science, Sport Management, Sport Media and Bachelor of Sport Studies (Honours)''. Within these degrees includes study units such as ''The Australian Sports System, Governance and Sport, Sports and the Law, Contemporary Issues in Sport, Industrial Relations in Sport, Sport Research and Practice, Sport Sponsorship and Media, and Sport as Entertainment'' to name a few. All teaching in the University is research lead, and students expect course work to be contemporary and relevant. This teaching, research and assignment work gives UCNISS a strong understanding of the Sport Sector in Australia, and a valuable resource in the form of academics and students, to apply their studies on any number of specific issues or areas within that sector. ===An Understanding of Sport for People with Disabilities and the Paralympic Movement=== Our Project Team has extensive knowledge of sport for people with disabilities and the Paralympic Movement. Any limitations in our understanding will be addressed through our extensive network of contacts. ===An Understanding of Modern Information Technologies=== UCNISS has on its team a combined forty years or more experience in Internet media production. This experience includes working with open copyrights, open standard formats, the MediaWikis of the Wikimedia Foundation, authoring and facilitating blogs, forums and a wide range of popular social media. Leigh Blackall has produced three large online texts, commissioned by Government Ministries in New Zealand, and countless video documentaries on a wide range of things from art festivals to research projects. The texts all used the Wikibooks platform, and the PediaPress print on demand service, and the video was all produced to open standard formats, and published across all popular media sharing sites. Lara Hale and Graham Pearce also bring many years experience editing and administering MediaWiki, with Graham holding valuable expertise in using screen reader technology. John Vandenberg's specific skill is in creating MediaWiki extension software that assists with large volume work such as meta data tagging and categorising large numbers of media files. Perhaps most critical of all is that all members are deeply networked within the communities of practice, bringing significant social capital to the project. ===An Openness to Input=== UCNISS is an open education and research organisation. We are advocates for open access and collaboration. We place educational content and research data and outputs on Wikiversity and a host of popular social media channels. We play an active role in encouraging and supporting all staff in adopting such open academic practices. The project we propose here invites other tenderers to participate with us in both the proposal and implementation phase. The project itself invites input from the wider Paralympic and wiki communities, and anyone else with interest in the Paralympics in Australia. To this end, we have deliberately selected the most high profile, most popular collaborative authoring spaces, with the most open copyright licensing and digital format selections, to make that principle in practice loud and clear. When input from third parties occurs, we have the processes in place to recognise and appreciate the input as we work towards the development of a sustained community of practitioners. ==Additional Information== ===Australian Government Principles on Intellectual Property=== * [http://agimo.govspace.gov.au/2010/10/07/government-2-0-update-%E2%80%93-amended-ip-principles-released/ Gov2.0 update: IP Principles Released]. Australian Government Department of Finance and Deregulation. AGIMO Blog. http://agimo.govspace.gov.au/2010/10/07/government-2-0-update-%E2%80%93-amended-ip-principles-released/ 7 October 2010. {{quote|This is a formal endorsement of the Taskforce recommendation that agencies should license their Public Sector Information (PSI) under Creative Commons BY license as the default license type and only adopt more restrictive licenses after a process of ‘due diligence and on a case-by-case basis’.}} ===Wikimedia Foundation Strategic Priorities=== * [http://upload.wikimedia.org/wikipedia/foundation/c/c0/WMF_StrategicPlan2011_spreads.pdf Wikimedia Strategic Plan 2011-2015]. Strategic Priorities, P8. http://upload.wikimedia.org/wikipedia/foundation/c/c0/WMF_StrategicPlan2011_spreads.pdf {{Quote|Through 2015, the Wikimedia Foundation will: ...Encourage diversity by conducting outreach among groups that have the potential to bring new expertise to the projects, as well as by supporting leaders from underrepresented groups in their efforts to cultivate new members from within their communities... Provide project funding for efforts to connect Wikimedia projects with the work of institutions of culture and learning}} ===Support letter from Wikimedia Australia=== John Vandenberg. [[Talk:The History of the Paralympic Movement in Australia/Tender#Support letter from Wikimedia Australia|Support letter from Wikimedia Australia]]. http://en.wikiversity.org/wiki/Talk:UCNISS/History_of_the_Paralympic_Movement_in_Australia 8 March 2011 {{quote|At this stage, this letter is encouragement for this proposal. Should it be successful, we hope you will engage us for assistance in developing a volunteer community of APC content contributors, editors and managers. This could be in the form of funding workshops and seminars in regional Australia, printing information, and networking events.}} ===Support letter from Graham Pearce=== Graham Pearce. [[Talk:The History of the Paralympic Movement in Australia/Tender#Support letter from Graham Pearce|Support letter from Graham Pearce]]. http://en.wikiversity.org/wiki/Talk:UCNISS/History_of_the_Paralympic_Movement_in_Australia 4 March 2011. {{quote|It is vital that the history of the Australian Paralympic movement be documented in a manner that is easy to access for everyone. I believe that the current proposal is the best way to achieve this aim... Due to its license, it could be easily adapted by educational institutions, disability organisations, or any other interested parties... Both Wikibooks and Wikimedia Commons use the MediaWiki software, which is accessible to users of screen readers and screen magnifiers... people with disabilities, including users of screen readers and screen magnifiers, [can] take part in this project on an equal footing with their non-disabled peers.}} '''Full support letter from Wikimedia Australia''' [[File:Wmau to ucniss.jpg|right|300px]] :''This is a copy of a signed letter sent to UCNISS'' To the University of Canberra's National Institute of Sport Studies, regarding the proposal to assist the Australian Paralympic Committee develop and publish texts and media on Wikibooks and Wikimedia Commons for the purpose of developing a document called, History of the Paralympic Movement in Australia. Firstly, let us state how pleased we are to see yet another Australian cultural organisation engaging with the projects of the Wikimedia Foundation, helping to build reliable, usable, accessible and ultimately sustainable information resources for the world over, not least, Australians. Should your proposal be successful, we at Wikimedia Australia would like to extend an offer of support. Looking at your draft proposal, we are particularly interested in the list item: ::o Support in the development of an APC volunteer base to take a contribution and editing role in the project. We think this point relates to us and what we can offer. The purpose of Wikimedia Australia is to: # organise and participate in educational and social events that promote development of Free Cultural Works and related open source software systems, in particular ''wikis'' # increase public awareness, support and participation in the projects hosted by the Wikimedia Foundation (WMF) # develop resources to assist Australians in the creation and maintenance of Free Cultural Works Wikimedia Australia is an independent, not-for-profit organisation, whose primary aim is to promote equality of opportunity to access and participate in the collaborative creation of "[http://freedomdefined.org/Definition Free Cultural Works]", especially educational works, and works about Australia, its culture, natural environment, and Australian news and media. At this stage, this letter is encouragement for this proposal. Should it be successful, we hope you will engage us for assistance in developing a volunteer community of APC content contributors, editors and managers. This could be in the form of funding workshops and seminars in regional Australia, printing information, and networking events. Good luck with this proposal, and congratulations on this conceptual first step. We hope it is successful and given the opportunity to prove its worth. [[user:John Vandenberg|John Vandenberg]]<br> President<br> Wikimedia Australia '''Full support letter from Graham Pearce''' To whom it may concern, My name is Graham Pearce, and I am a totally blind Wikipedia editor from Perth, Western Australia. I have been editing Wikipedia and other Wikimedia Foundation projects for six years, and I am an English Wikipedia administrator. It is vital that the history of the Australian Paralympic movement be documented in a manner that is easy to access for everyone. I believe that the current proposal is the best way to achieve this aim, because Wikibooks is well-suited to the creation of structured online texts, which do not have the same space limitations as printed books. The resulting product would be freely available online around the world, thus increasing the profile of the Australian Paralympic Movement. Due to its license, it could be easily adapted by educational institutions, disability organisations, or any other interested parties, to meet their individual needs. Both Wikibooks and Wikimedia Commons use the MediaWiki software, which is accessible to users of screen readers and screen magnifiers. Therefore the results of the proposal would be easy-to-use for people with visual impairments. It would also be possible for people with disabilities, including users of screen readers and screen magnifiers, to take part in this project on an equal footing with their non-disabled peers. In conclusion, this proposal presents a unique opportunity to document the history of the Australian Paralympic Committee using collaborative tools, and as a screen reader user, I fully support it. Yours sincerely, [[User:Graham87|Graham Pearce]] 02:35, 4 March 2011 (UTC) [[Category:UCNISS]] [[Category:The History of the Paralympic Movement in Australia]] [[Category:Sports]] j6i00ppt0scix7dio9yl70osh03mkl3 2412504 2412503 2022-08-07T11:33:43Z 176.82.181.72 wikitext text/x-wiki Aaaaaaaaaaaa aaaaaaaaaaaaa aaaaaaaaaaaa ajajajajajaja en el Aabetis Zic As Aaaaaaaaaaaaaaaaaaaaas == Sunsuneo Minecraft Java Edition ==   Selecciona cualquier comando para escribirlo fácilmente   == Agricunchjjj Minecraft Playstation Edition == Puedes seleccionar el comando pero luego tienes que escribir las coordenadas del /tp o material del /give @s etc   == Afanisilestain Minecraft Bedrock Edition == Estás obligado a escribir el comando entero menos /tp /time set /weather o /setworldspawn   == vanilla vanilla trotrotro Minecraft Pocket Edition ==   Al igual que en bedrock pero se necesita poner / después el comando que quieras usar y después estás obligado a poner todos los detalles del comando y todo el texto en letra minúscula   Zic As     == Estropajon == Me invento películas mentales en el As   == Sunsuneo Minecraft Java Edition ==   Selecciona cualquier comando para escribirlo fácilmente   == Agricunchjjj Minecraft Playstation Edition == Puedes seleccionar el comando pero luego tienes que escribir las coordenadas del /tp o material del /give @s etc   == Afanisilestain Minecraft Bedrock Edition == Estás obligado a escribir el comando entero menos /tp /time set /weather o /setworldspawn   == vanilla vanilla trotrotro Minecraft Pocket Edition ==   Al igual que en bedrock pero se necesita poner / después el comando que quieras usar y después estás obligado a poner todos los detalles del comando y todo el texto en letra minúscula   == Estropajon ==   Descucacualorenzo   == Sunsuneo Minecraft Java Edition ==   Selecciona cualquier comando para escribirlo fácilmente   == Agricunchjjj Minecraft Playstation Edition == Puedes seleccionar el comando pero luego tienes que escribir las coordenadas del /tp o material del /give @s etc   == Afanisilestain Minecraft Bedrock Edition == Estás obligado a escribir el comando entero menos /tp /time set /weather o /setworldspawn   == vanilla vanilla trotrotro Minecraft Pocket Edition ==   Al igual que en bedrock pero se necesita poner / después el comando que quieras usar y después estás obligado a poner todos los detalles del comando y todo el texto en letra minúscula   == Estropajon == [[File:Paralympic low res.pdf|thumb|300px|Low resolution copy of the final proposal from UCNISS to the Australian Paralympic Committee, for the production of a text called, The History of the Paralympic Movement in Australia. Design by Sunshine Connelly for UCNISS.]] [[File:Wheelchair basketball at the 2008 Summer Paralympics.jpg|thumb|300px|Wheelchair basketball at the 2008 Summer Paralympics, Iran vs South Africa. An example of an image on Wikimedia Commons, The repository that feeds Wikipedia. It is difficult to find images of Australian athletes or events - something this project will address]] ==Background== [http://www.paralympic.org.au/ The Australian Paralympic Committee] (APC) has [[The History of the Paralympic Movement in Australia/Request for Proposals|sought costed proposals]] from suitably qualified individuals or organisations to document the '''History of the Paralympic Movement in Australia''' in a format which meets the needs of the [http://www.paralympic.org.au/ APC] for online and possible print publication. This [http://en.wikiversity.org/wiki/UCNISS/History_of_the_Paralympic_Movement_in_Australia Wikiversity page] has been developed to present an open, collaborating response to the [http://www.paralympic.org.au/ APC] request for proposals and the requirement to create a well-researched and referenced multi-media document that can be published online. We aim to offer a compelling case to be entrusted to share the story of: * The development of Paralympic sport and, where the two intersect, the wider story of sport for people with a disability in Australia. * Australia's participation in the thirteen summer and ten winter Paralympic Games (to the end of 2010). * The foundation and growth of the Australian Paralympic Committee. * Key individuals in the growth of the Paralympic movement in Australia. We recognise that there is an enormous amount of material available to inform this story. Our approach to the project is to unfold the story with our project team and other experts as required. Our commitment to a wiki format should deliver a triangulated story of the Paralympic Movement in Australia that ensures a community-enriched account of a remarkable culture. We anticipate that during the course of the project we will be able to explore some important themes that cross Paralympic history in Australia: the interplay between sport and rehabilitation; the growth of the [http://www.paralympic.org.au/ APC] and its place within the Australian sport system; and the impact of the Paralympic movement on wider perceptions within the community of the role and “status” of people with a disability. If successful in our bid we would like to start work on the project on '''2 May 2011''' and deliver content continuously up to 31 December 2012. ==Proposal== [[File:StateLibQld 1 100176.jpg|thumb|300px|The [http://www.nla.gov.au/ National Library of Australia] and other key Australian cultural organisations have a working relationship with the [http://commons.wikimedia.org/wiki/Main_Page Wikimedia Commons] project. In 2010 the [http://www.slq.qld.gov.au/ State Library of Queensland] [[:Wikipedia:Wikipedia:Wikipedia Signpost/2010-12-20/Image donation|Donated its collection of historic images to Wikimedia Commons.]]]] [[File:PediaPress Hardcover standing01.jpg|thumb|300px|An example of a printed and hard cover bound book from PediaPress. This book is user generated out of Wikipedia articles. This is the same quality that the History of the Paralympic Movement in Australia book will be]] This is an open proposal to the [http://www.paralympic.org.au/ Australian Paralympic Committee] (APC) from the [http://www.ucniss.net University of Canberra's National Institute of Sport Studies] (UCNISS) to produce a text called: ''A History of the Paralympic Movement in Australia'', and to establish a repository of media and digitised primary resources such as video and audio recordings, images and scanned documents, to compliment the text. This proposal aims to: * Produce an initial text and multi media repository. * Develop a participatory community around the text and repository. * Ensure long term maintenance and integration of the content with Australian Paralympic information networks. We propose to establish the text and media repository on the popular web based collaborative writing platforms provided by the [http://wikimediafoundation.org/wiki/Home Wikimedia Foundation]. The Wikimedia Foundation has established editor communities, robust technology and sound operating principles. Their [[Wikibooks:Main Page|Wikibooks]] and [http://commons.wikimedia.org/wiki/Main_Page Wikimedia Commons] are 'sister' projects to the more popular [http://www.wikipedia.org/ Wikipedia]. We believe these projects offer a range of benefits that offer cost effectiveness for [http://www.paralympic.org.au/ APC's] objectives, namely: # Online collaborative editing platforms with celebrated accessibility standards, especially for people relying on screen readers. # International technical management, with robust policies and procedures to ensure 24/7/365 reliability with very high national and international visibility. # Reliable online media storage, management and delivery that maintains strict copyright diligence, and uses open standard formats and archive policies to ensure long term access and reusability. # The [http://pediapress.com/ PediaPress] print on demand service, delivering quality printed and bound books directly from the online text, based on the latest up to date version, or on customised individual needs, at significantly low cost to the [http://www.paralympic.org.au/ APC] and end users. # A proven volunteer base, especially within the [http://commons.wikimedia.org/wiki/Main_Page Wikimedia Commons] project, who help maintain the integrity of the media and text, such as it being free of spam and vandalism, along with comprehensive content categorisation and linkages, with stringent copy editing and review processes available in the "featured content" nomination process. # Seamless integration with the [http://www.wikipedia.org/ Wikipedia] project, helping to improving the accuracy and quality of all the [http://www.wikipedia.org/%20Wikipedia Wikipedia] articles related to the Australian Paralympic community, athletes, Games, history and organisation. # Support for establishing a community of volunteer editors of Australian Paralympic content in the wiki platforms, helping to maintain accuracy and relevance of the text and repository beyond the time frame of this project. This proposal aims to deliver a comprehensive historical text, embedding multi media after producing and uploading it to a high quality media repository, situated on the most successful collaborative production and management platforms to date, and leveraging their communities and processes to assure reliability and long term sustainability. Furthermore, this project will reach out and support members of the Australian Paralympic community through information, training and support, to help them become contributors to [[Wikibooks:Main Page|Wikibooks]], [http://commons.wikimedia.org/wiki/Main_Page Wikimedia Commons], and [http://www.wikipedia.org/ Wikipedia], thereby enabling them to play an ongoing and important role in maintaining a high quality online profile for everything Australian Paralympic. We note the diversity of materials the APC has collected and produced. Our text will link to these and ensure the visibility of these materials. There will be explicit mention of these materials on the wiki to ensure their visibility. ==Project Structure and Management== [[File:DBP 1972 733 Weltspiele der Gelähmten.jpg|thumb|300px|Paralympic Games 1972 in Heidelberg. Graphics by Schwarz. First Day of Issue / Erstausgabetag: 18. Juli 1972. This stamp is in the public domain in Germany because it was released by Deutsche Bundespost on behalf of the Federal Minister of Post and Telecommunication and thus is an official work according to German copyright law (§ 5 Abs. 1 UrhG).]] We are proposing an inclusive approach in this project. At the time of the submission of the tender (25 March 2011) the following roles are allocated in this project: ===Project Managers=== We have identified two distinct project management roles and nominate two individuals to fulfill these roles throughout the life of the project. Both Project Managers will assure the ongoing viability and stability of the project. :* [[User:Postillion|Keith Lyons]] :: Director of [[UCNISS]] will be responsible for: ::* Oversight of project timelines, meetings, events, production, communications and reporting ::* Networking and promotion of the project ::* Quality assurance of the whole project and primary point of contact for the [http://www.paralympic.org.au/ APC] :*[[User:Leighblackall|Leigh Blackall]] :: Learning Commons Coordinator with [[UCNISS]] will be responsible for: ::* Representing the project to Wikimedia Australia, Wikimedia Commons, Wikibooks, and the Wikimedia Foundation community outreach programs. ===Sport Historians=== '''Sport historians''' will be responsible for primary research, gathering resources, reviewing for accuracy and consistency, structuring and writing content, referencing, linking and editing. They will be supported by the Librarians and Copy Writers. We extend an open invitation to any sport historian to join this group. [http://www.ucniss.net UCNISS] is developing a keen interest in Australian sport history and has a number of PhD projects underway at present. This open proposal seeks to build upon the ethnographic research experience of Keith Lyons and the historical research credentials of proposed contributors that include: :*[http://www.linkedin.com/pub/greg-blood/2a/14a/729 Greg Blood] :*Bruce Coe :*[http://www.australianoftheyear.org.au/recipients/?m=robin-poke-2011 Robin Poke] Each of these contributors is a highly regarded sport historian with excellent local, national and international contexts. Greg is a member of staff at the Australian Institute of Sport and has been a librarian at the Australian Sports Commission since 1983. Bruce is completing a PhD on [http://archive.is/20121202095346/keithlyons.wordpress.com/2010/12/17/marks-and-coe-meeting-in-the-commons/ the life of E S Marks]. Robin is undertaking a PhD in the history of Australian Rowing. Since 2007 Robin has been an interviewer for the [http://catalogue.nla.gov.au/Record/4353507 National Library of Australia’s Sport Oral History project], which has involved him in interviews with Australia’s first Paralympians. All three are members of the Australian Capital Territory Chapter of the Australian Society of Sports History. :*[http://www.canberra.edu.au/faculties/health/sport-studies/staff/robin-mcconnell Robin McConnell] Robin has significant historical research experience most recently applied in his project, Sport in Prisoner of War Camps. He has researched the History of Rugby in New Zealand. He has supervised postgraduate research in sport history, and has taught the history of sport at University of Ulster. Robin has written about the Special Olympics and is the author of a study of a Maori leader ''Taua of Kareponia'' (Te Maru Publications 1993). Robin is an external examiner of sport history PhDs. :*[http://www.sportscoachingbrain.com/about-wayne-goldsmith/ Wayne Goldsmith] Wayne will work with Keith Lyons to coordinate the work of the sport historians and will take a lead role in gathering data for the project. Wayne will use [http://www.sportscoachingbrain.com/ his extensive experience of social media] to ensure that the project has a strong user focus. He will have an important day-to-day role in content delivery. :*[http://www.staffs.ac.uk/staff/profiles/nbt1.jsp Nigel Thomas] To ensure that our work meets international benchmark standards we have secured the services of Nigel Thomas (Staffordshire University) as the senior editorial consultant for the project. Nigel is the co-author (with Andy Smith) of [http://books.google.com.au/books?id=x3FKBSzsBPQC&printsec=frontcover&dq=Nigel+Thomas+Disability&source=bl&ots=uVnNSlcFey&sig=HqxDH1rnEoPnJYquhxMpAfDrv1g&hl=en&ei=CIR1TZ73DoSqvQOn9enYBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBgQ6AEwAA#v=onepage&q&f=false Disability, sport and society: an introduction] (2009). ===Librarians=== '''Librarians''' will support the Sport Historians in sourcing material, checking for and negotiating copyright, digitisation and formatting to open standards, uploading media and ensuring appropriate meta data, linking and categorisation is included. They are supported by the Copy Writers. We propose: :* John Vandenberg John is the President of Wikimedia Australia and will assist in managing the collection of APC media on Wikimedia Commons. John presently manages the [[Wikipedia:Wikipedia:Wikipedia Signpost/2010-12-20/Image donation|State Library of Queensland project]] where several thousand images where loaded to Wikimedia Commons and are presently being categorised and integrated into Wikipedia. John also created extension software to Media Wiki, that can automate many processes we will need to undertake in the initial preparation of content and its uploading. :* [http://www.canberra.edu.au/monitor/2009/mar/20092003_harmony Pat Tandy] Pat is University of Canberra's Faculty of Health Liaison Librarian. Pat's brief is to assist with research work, helping us find primary and secondary resources across Australia's library data bases, including the National Library, Archive and others. ===Copy Writers=== '''Copy writers''' support the Sport Historians in formatting text to MediaWiki text, linking, and [[w:Copy editing|copy editing]]. They support the Librarians in uploading, formatting to open standards, meta data, linking and categorisation. We propose as copy writers: :*[[User:Graham87|Graham Pearce]]<br> ::Perth, Western Australia<br> ::Wikipedia administrator<br> ::Expert in the use of Media Wikis with a Screen Reader<br> :*[[User:LauraHale|Laura Hale]]<br> ::PhD student with [[UCNISS]]<br> :*UCNISS Undergraduate students<br> ::Once this project is worked into existing assessment assignments in their units<br> ===Trainers=== '''Trainers''' support the APC Liaison with work on community awareness campaigns. They go to regional centres around Australia to meet with Australian Paralympic Community members, to show them how to edit Wikibooks, Wikimedia Commons and Wikipedia. In this role they also support the Librarians and Historians in gathering media and primary resources. They monitor the Wikibooks and Commons pages relating to the project, and provide online support for anyone contributing. We propose the following trainers: :*[[User:Graham87|Graham Pearce]]<br> ::Perth, Western Australia<br> ::Wikipedia administrator<br> ::Expert in the use of Media Wikis with a Screen Reader<br> :*[[User:LauraHale|Laura Hale]]<br> ::PhD student with [[UCNISS]]<br> :*Wikimedia Australia<br> ::A committee with resources for training Australian's in the use of Media Wikis<br> ===Project Reporters=== '''Project Reporters''' support the Project Managers in documenting the project, and the APC Liaison in setting up the forum and publishing updates to it. They prepare press releases for mainstream media, and participate in research work. They also monitor social media and public relations generally. Our proposals for project reporters are: :* [[User:Postillion|Keith Lyons]] :: Director of [[UCNISS]], and sport blogger :*[[User:Leighblackall|Leigh Blackall]] :: Learning Commons Coordinator with [[UCNISS]] :*[[User:LauraHale|Laura Hale]]<br> ::PhD student with [[UCNISS]]<br> ===Project Advisor=== We recognise that the project needs a high level of quality assurance particularly in relation to access to the information we present. In addition to Graham Pearce's role we have identified [http://www.canberra.edu.au/centres/phiw/staff_profiles/profile_fleming.htm Michele Fleming] as a key member of our team. Michele is the Dean of Students and Director of the [http://www.canberra.edu.au/seasu Student Equity and Support Unit] at the University of Canberra Disability Service. Michele has responsibility for elite athletes at the University of Canberra. At present she is the second investigator on an ALTC research grant that aims to develop an online tool for the Higher Education sector on the Disability Standards for Education. Michelle is working to ensure that all of the University's web content meets accessibility requirements. The [http://www.canberra.edu.au/library University of Canberra Library] has considerable experience of the support for diverse learning needs and through Pat Tandy will advise the Project team about accessibility better practice. ===APC Liaison=== We will work closely with the APC and nominated APC liaison personnel throughout this project. ==Software and Systems to be Used== [[File:Pediapress hardcover color2.jpg|thumb|300px|The high standard of print on demand products available through Wikibooks. Readers can create custom books, including and omitting sections, using always the latest information included on the wiki. More information, including previews of the format, are available on the [http://pediapress.com PediaPress website]. A video by PediaPress, explaining the user experience for printing and ordering a book, is [http://www.youtube.com/watch?v=D1K03AZfpDM available on Youtube]]] [[File:Sportdag voor oorlogsinvaliden te Doorn.ogv|thumb|300px|On the training ground for the military convalescent Aardenburg in Doorn, 1954. The annual sports festival for disabled veterans. '''This is an embedded video from Wikimedia Commons'''. Wikimedia Commons accepts video, audio, images, graphics and PDF, keeping them in open standard formats, meta data tagged, integrated with other projects, and licensed with free to reuse copyright.]] We propose using the production, publishing and content management services offered by the Wikimedia Foundation, to ensure media is formatted to open standard formats, and to use Creative Commons licensing to manage copyright. These systems and software ensure long term accessibility of the production, and the technical and legal flexibility should the APC need to move content to another platform, or commission derivatives, or to keep locally stored backups. The Wikimedia Foundation hosts the services Wikibooks and Wikimedia Commons, both 'sister' projects to Wikipedia, which are all mediated collaborative approaches to content authoring and management, using established and robust platforms that do not require extensive involvement from APC's own IT experts. The Wikimedia Foundation keeps the technical infrastructure running across all projects, attracting significant donations each year, while the respective project's very large volunteer base manage the content and community governance. ===Wikibooks=== '''Wikibooks''' focuses on the production of texts following the book structure. Like all Wikimedia Foundation projects, it is a successful and well managed collaboration space, freely available to APC interests. Wikibooks includes the feature for readers to print and order a book version of the content, significantly cheaper and less resource intensive than APC might find through a conventional print run. An advantage of this is that it is possible to print and bind just segments of the whole project (for example, "organisational history"), which could enable individual tailoring of the physical book to specific audiences. We believe that the [[Wikibooks:Wikijunior|Wikijunior]] feature of Wikibooks will provide an enormous opportunity to extend the reach of the APC History project. We believe we can produce a high quality text from Wikibooks and do so on demand with updated text and media content. ===Printed and bound book=== '''PediaPress''' is a web based software and print-on-demand service that extends the feature set of Wikibooks and all Wikimedia Foundation projects into printed and delivered books. PediaPress enables all users to create customized books, printed, perfect bound, and delivered by post. This print and deliver option is available via the "Print/export - create a book" links in the navigation bar of Wikimedia Foundation projects. PediaPress offers a 4 minute video on Youtube that explains the process of producing a book from Wikipedia articles: ''[http://www.youtube.com/watch?v=D1K03AZfpDM Wikipedia In Print - How to create custom books with a mix of content from the free encyclopedia]''. This same process can be applied to a Wikibook. There is an additional option for a printed and bound book, one that engages the services of a graphic designer, producing the original text and images into a manually designed and higher quality product. We would use the web service [http://lulu.com Lulu] to publish this version, where it manages the purchase orders and distribution at next to no cost to this project. Depending on the results of market research, the costs of the production of this print option could be recovered through purchase royalties. Therefore, the cost of this production is not included in the project budget. Leigh Blackall established this production process in his work with Otago Polytechnic's textbook, [http://www.lulu.com/product/paperback/anatomy-and-physiology-of-animals/2285614 Anatomy and Physiology of Animals on Lulu.com]. This text is developed and maintained on Wikibooks, but a graphic designer produces a print version annually for download from Lulu with the production cost recovered through sale royalties. ===Wikimedia Commons=== '''Wikimedia Commons''' is the Wikimedia Foundation's project for all multi media used on all the Wikimedia Foundation projects. The vast volunteer base offers considerable resource in catagorising and managing the multimedia that the APC would load to the project. That content would then be used widely across all Wikimedia Foundation projects, especially Wikipedia, helping to lift the profile of APC, its community and it athletes, ultimately promoting community development efforts around its projects. Wikimedia Commons manages copyright, archiving and formats, ensures open standard formats which assist in the long term archival concerns of the media. Currently the National Library of Australia and other key Australian cultural organisations have a working relationship with the Wikimedia Commons project. Recently the State Library of Queensland [[Wikipedia:Wikipedia:Wikipedia Signpost/2010-12-20/Image donation|donated its collection of historic images to Wikimedia Commons]]. ===Images, video and audio=== '''Open standard formats''' relate primarily to multi media used in this project. Wikimedia Commons only accepts media in open standard formats, so as to ensure the integrity of the archive against software redundancy, proprietary fee structures and digital restrictions management software. This principle helps ensure that all work created and collected in this project is also free from such concerns, thereby acquiring the same archival integrity. Multi media such as images, video, audio and PDF documents are easily embedded into the wikis, as demonstrated in this section with the embedded video of war veterans participating in games in 1954. Open standard multi media formats are increasingly recognised by main providers of Internet services, such as Google Chrome and FireFox browsers playing open standard video and audio files in their browsers without the need for plugin software and extensions. This is made possible by the [[w:HTML5 video|HTML5 video]] tag released in 2010. ===Wikimedia Foundation and Wikimedia Australia=== '''Wikimedia Australia''' is a chapter of the '''Wikimedia Foundation''', the peak body that governs and administers the Wikibooks, Wikimedia Commons, Wikipedia and other projects. In their 2011-2015 Strategic Plan, the Wikimedia Foundation's priorities included support for cultural and learning institutions seeking to engage their communities in the projects. Funding is provided to the Chapters each year for outreach activities, community building activities, knowledge-creation project and partnerships with cultural and knowledge institutions. This project will actively liaise with the Wikimedia Foundation and Wikimedia Australia to ensure understanding and to seek support where it aligns with their strategic priorities. ===Open Office=== '''Open Office''' is a free and open source software package equivalent to Microsoft Office. A key feature of [[w:Open Office|Open Office]] is its ability to export documents to MediaWiki syntax, making it easier for an author who is familiar with standard word processing software like MS Word or Open Office Text, to produce documents for Wikibooks. The added value of this as a workflow for the initial historians is that they produce a document in 2 format versions, affording backup and flexibility in use. ===Creative Commons=== '''Open copyrights''' are a critical consideration for [http://www.paralympic.org.au/ APC] management in that all content used in this project needs to adopt the [http://creativecommons.org/licenses/by-sa/2.0/ Creative Commons Attribution Share Alike copyright license], an internationally recognised copyright license that facilitates the benefits described in this proposal. This copyright license is one in which [http://www.paralympic.org.au/ APC] retains copyright, but gives rights for content to be reused, with the only restrictions being the requirement of attribution on all derived content, and the sharing back of all derivatives through use of the same copyright license. This is inline with the explicit guidelines put forward by the Australian Attorney General, adopting the recommendations of the 2010 Government 2.0 Task Force. Such licensing will ensure Australian Paralympians, the Paralympic community, and the Committee enjoy the maximum level of exposure and recognition through this work as possible. With regard to potential competitors or exploiters of [http://www.paralympic.org.au/ APC] content, this license presents a dilemma for them, in that any content they adopt and reuse from this [http://www.paralympic.org.au/ APC] project, the copyright license compels them to attribute [http://www.paralympic.org.au/ APC] and to use the same licensing arrangement on the work derived from [http://www.paralympic.org.au/ APC] source content. The [http://wikimediafoundation.org/wiki/Home Wikimedia Foundation] has the resources to monitor and track such terms and conditions over copyright. ===Backup=== The systems and software above are implicitly designed and selected for backup and sustainability concerns. We are engaging in a copyright regime that facilitates legitimate copying for backup and republishing, and using open standard media formats that ensure the long term reusability of the content free of commercial limitations. Apart from these system features, the software and services offered by the Wikimedia Foundation (Wikibooks, Wikimedia Commons, and Wikipedia all running on the free and open source platform MediaWiki) provides a number of features that support backup made by users. Firstly, and most simply, all pages can be exported to Open Document Text, for use in word processors such as Open Office, Google Docs and Microsoft Word 2007. Pages also export to HTML, and of course MediaWiki text. As to more large scale backup, The entire English Wikibooks database is periodically [http://dumps.wikimedia.org/enwikibooks/ exported to an XML format]. These openly available backups contain content, edit history and discussion threads for all pages on the project. It is not difficult to use this backup to create a locally hosted wiki with only the APC project content. If the Wikimedia Foundation ever stopped providing these backups, we can create our own via [http://www.mediawiki.org/wiki/Export the core mediawiki function called Export]. The skills for doing this are brought to the project by our librarian, John Vandenberg. As for large scale HTML backup, there are many tools which convert a wiki into a static website, consisting of just HTML and images. The Wikimedia Foundation provides [http://static.wikipedia.org/new/wikipedia/en/index.html a static copy of all the Wikipedia] for example. Again, John Vandenberg brings these skills and services to the project. The Database dumps and Export features do not include the image files. John Vandenberg, our librarian on this project, has created software which obtains all images from the Wikimedia Commons server, and with just a few hours work, this software can be customised to backup only the images used within the APC project. Wikimedia Australia, an organisation supporting this bid, can periodically copy these dumps and store them on a server in Australia as an additional backup measure should APC require it. This service is offered free of charge, until such time as traffic should require cost recovery. ==Project Timeline== {{center top}} {| bgcolor="whitesmoke" style="border: DarkGreen solid 1px;" |- ! Tasks ! May 2011 ! Jun ! Jul ! Aug ! Sep ! Oct ! Nov ! Dec ! Jan2012 ! Feb ! Mar ! Apr ! May ! Jun ! Jul ! Aug ! Sep ! Oct ! Nov ! Dec2012 |- | [[#Research|Research]] | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | |- | [[#Initial framework document|Initial framework document]] | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | | | | | | | | | | | |- | [[#Online forum|Online forum]] | bgcolor="pink" | | | | | | | | | | | | | | | | | | | | | |- | [[#Monitoring and moderating|Monitoring and moderating]] | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | |- | [[#Interviews|Interviews]] | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | | | |- | [[#Source media|Source media]] | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | | | | | | |- | [[#Final text|Final text]] | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | |- | [[#Linking the text|Linking the text]] | | | | | | | | | | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | | | | |- | [[#Volunteer editing community|Volunteer editing community]] | | | | | | | | | | | | | | | | | | | bgcolor="pink" | | bgcolor="pink" | | bgcolor="pink" | |} {{center bottom}} The Project Timeline has the following phases: ===Research=== * Identify media and primary resources; gauge initial expectations, and outcome expectations in the Australian Paralympic Community; establish historical timelines; identify key people, events, organisations and social contexts. * Conducted by [[#Sport Historians|Sport Historians]], [[#Librarians|Librarians]] and the [[#Project Reporter|Project Reporter]] ===Initial Framework Document=== * Create an initial framework document, based on research and use of existing materials, covering the history of the Paralympic Movement in Australia; * Prepared by the [[#Project Managers|Project Managers]], [[#Project Reporter|Project Reporter]] and [[#APC Liaison|APC Liaison]] ===Online Forum=== * Set up an online forum for input by people involved in the Paralympic movement in Australia; * Set up by the [[#Project Reporter|Project Reporter]] in consultation with the [[#APC Liaison|APC Liaison]] ===Monitoring and Moderating=== * Monitor and moderate input; * Managed by the [[#Project Reporter|Project Reporter]] and the [[#Project Advisor|Project Advisor]]. ===Interviews=== * Interviews with people who have played a significant role in Australian Paralympic sport * Conducted by the [[#Sport Historians|Sport Historians]] ===Source Media=== * Liaison with representatives of the APC to source media such as photographs, videos, audio, competition results, team lists and other materials relevant to the project; * Conducted by the [[#Sport Historians|Sport Historians]], [[#Librarians|Librarians]] in consultation with [[#APC Liaison|APC Liaison]] ===Final Text=== * Create a final text for the period up to 2010, within a structure which includes the following elements: ** personal stories; ** each [[w:Category:Paralympics|Paralympic Games]]; ** other key Games, such as the Stoke Mandeville Games, the Commonwealth Paraplegic Games and the FESPIC Games; ** organisational history and changes; ** some social and historical contexts. * Written by the [[#Sport Historians|Sport Historians]] and [[#Copy Writers|Copy Writers]] ===Linking the Text=== * Linking the text to oral history interviews, other audio, video and photographs through a customised website. * [[#Sport Historians|Sport Historians]], [[#Copy Writers|Copy Writers]] and [[#Librarians|Librarians]] ===Volunteer Editing Community=== * Develop and support a volunteer editing community, skilled and willing to help maintain the document in perpetuity. * Conducted by the [[#Trainers|Trainers]] ==Budget== This is an open and collaborative project. Our budget identifies our anticipated costs but we believe that we will garner enormous in kind contributions particularly in regard to the training that can occur. Our outline budget is: {| border=1 cellspacing=0 cellpadding=5 | '''task''' | '''hours''' | '''budget''' | '''comment''' |- | Sport historians | 300 | $30,000 | Sourcing, reviewing, writing, referencing, editing |- | Librarians | 100 | $10,000 | Copyright, digital formatting, uploading and meta data, initial online content management |- | Copy writing | 200 | $20,000 | * Wiki authoring, editing, uploading and formatting * Possible [[w:LETS|LETS]] option |- | Training | 100 | $10,000 | * Wiki skills training (both online and face to face) and ongoing online support * Possible [[w:LETS|LETS]] option |- | Project reporting | 100 | $10,000 | Project progress reporting; public relations communications; social media management; research publications; graphic design |- | APC Liaison | 100 | $10,000 | * Supported by trainers and journalists * Representation to [http://wikimedia.org.au/ Wikimedia Australia], [http://commons.wikimedia.org/ Wikimedia Commons], Wikibooks, and Wiki Media Foundation; communications with APC organisation and community * Possible role for an APC member |- | Project management | 200 | $20,000 | Planning, personnel management, documentation, contracts, liaison with APC, Wikimedia Foundation and Wikimedia Australia, presentations, |- | Total | 1100 | $110,000 | '''''[[w:LETS|LETS]] is a payment system sometimes used by volunteers.''''' |- |} ==APC's Selection Criteria== ===Demonstrated Writing Skills and Experience=== All members of the proposed Project Team have considerable writing experience. A number of the team have substantial experience of social and open media. We are keen to share our experience in open access publishing. '''Wikibooks production:''' Leigh Blackall has worked the Wikibooks production model on a number of occasions. He developed this approach for Otago Polytechnic with their [[Wikibooks:Anatomy and Physiology of Animals|Anatomy and Physiology of Animals textbook]] involving a similar budget to this proposal, and now rating first in a Google search. Subsequently he produced the [[Wikibooks:Sustainable Business|Sustainable Business Wikibook]] with support from Otago Polytechnic, but this time including the New Zealand Ministry of Environment and New Zealand Trade and Enterprise. Finally, while in New Zealand, he produced the [[Wikibooks:Open Education Practices: A User Guide for Organisations|Open Educational Practices: A User Guide for Organisations Wikibook]] for the New Zealand Ministry of Education. Since working with UCNISS Leigh has encouraged teaching staff to adopted and further develop this model. Most notable to date has been James Neill working with University of Canberra students to develop an open textbook for their Psychology unit, [[Motivation and emotion/Textbook|Motivation and Emotion]]. '''Sport Historians:''' Keith Lyons has been involved in sport history research for three decades. He was a founding member of the British Association of Sport History. He is supervising two PhD students at present at the University of Canberra. He has a particular interest in oral history and ethnography. He will coordinate the sports history input with the assistance of Wayne Goldsmith. Greg Blood, Bruce Coe, Robin McConnell and Robin Poke will contribute to the development of text. Nigel Thomas (Staffordshire University) is the editorial consultant for the project. '''Online Sport Historian and MediaWiki Copy Editor:''' Laura Hale is an experienced online sport historian and Media Wiki editor. In the United States she set up and managed the [http://www.fanhistory.com/wiki/Main_Page Fan History Wiki]. Laura and a team of ten administrators developed and supported an editor community of over 2500 people, creating 900,000 articles rated as 'good' out of over 1 million articles total. Currently, Laura is working on the Wikipedia article [[w:Netball|Netball]]. Since moving to Canberra, Laura writes the [http://ozziesport.com/ Ozzie Sport blog], documenting her work researching Australian sport fandom online. '''Copy Writer for Screen Readers:''' Graham Pearce is a Wikipedia administrator based in Perth, Western Australia. He relies on a screen reader to read and edit Wikipedia. Graham will assist with copy writing, ensure screen reader usability, support volunteer editors online, and assist in communications with the wider Wikimedia Foundation community. '''Volunteer Writers and Producers:''' UCNISS has a significant volunteer base in the form of students enrolled in Sport Studies Undergraduate and Post Graduate Degrees. Students are encouraged to engage in Work Integrated Learning activities. This project provides opportunities for meeting a range of learning objectives, and it will be possible to adjust student assignments to accommodate and encourage participation in this project. ===Networking Skills=== The team that will support this bid have substantial experience working with networks of contacts. Whilst we have extensive links within sport, we point in particular to our connections with Wikimedia communities. We believe this will be a catalyst for drawing in a network of volunteer editors to assist with copy editing, categorisation, programing, support and peer review. ===Experience in Historical Research=== '''Nigel Thomas''' is our senior editorial consultant. He has worked in various sport development roles prior to joining higher education in 1997. These include: Hammersmith and Fulham Borough Council; the British Sports Association for the Disabled; and the Youth Sport Trust. His PhD (2004) is a study on mainstreaming in disability sport. Nigel's research focuses on the history, mainstreaming and media coverage of disability sport and the Paralympic Games and has culminated in the publication of a text book co-authored with Andy Smith published by Routledge in 2009 [http://books.google.com.au/books?id=x3FKBSzsBPQC&printsec=frontcover&dq=Nigel+Thomas+Disability&source=bl&ots=uVnNSlcFey&sig=HqxDH1rnEoPnJYquhxMpAfDrv1g&hl=en&ei=CIR1TZ73DoSqvQOn9enYBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBgQ6AEwAA#v=onepage&q&f=false Disability, sport and society: an introduction]. Nigel is working on a European Commission funded project aimed at encouraging sport for disabled people. In collaboration with European Observatoire of Sport and Employment (EOSE), the European Paralympic Committee (EPC) and working with 22 national partners in a year-long work package which summarises current policy and makes recommendations on future campaigns to 'promote European fundamental values by encouraging sport for persons with disabilities'. '''Selected Publications by [http://www.staffs.ac.uk/staff/profiles/nbt1.jsp Nigel Thomas]''' *Thomas, N and Smith, A. (2009) Disability, Sport and Society: A Student Introduction. London: Routledge. *Thomas, N (2008) Sport and Disability. In B.Houlihan (Eds.) Sport and Society. A Student Introduction. London: Sage. *Smith, A and Thomas, N. (2005) Including Pupils with Special Educational Needs and Disabilities in National Curriculum Physical Education: A Brief Review’. European Journal of Special Needs Education, 21 (1): 69-83. *Smith, A. and Thomas, N (2005) The ‘Inclusion’ of Elite Athletes with Disabilities in the 2002 Manchester Commonwealth Games: An Exploratory Analysis of British Newspaper Coverage. Sport, Education and Society, 10 (1). *Thomas.N., and Smith.A. (2003) ‘Pre-occupied with Able-bodiedness?’, An analysis of the British media coverage of the 2000 Paralympic Games, Adapted Physical Activity Quarterly, 20(2):166-181. '''Robin Poke''' has worked in all media and in sports administration. He was founder editor of SBS Radio News, a current affairs reporter with Radio Australia, was head of sport at Capital Television in Canberra then worked on a freelance basis with ABC radio and television and the Canberra Times, and with SBS Television. Robin’s involvement in sport has been through rowing and the Olympic movement. He established the national magazine, Australian Rowing, and was for many years honorary media director for the national federation. He held media liaison positions with the Australian team at the 1996, 2000 and 2004 Olympic Games and is now President of the ACT Olympic Council. Robin is presently an author, journalist and sports historian. His first book, a biography of Olympic rowing gold medallist Peter Antonie, was published in 2007, and his second, containing chapters on each of Australia’s 74 individual Olympic gold medallists, will be published in 2012. Since 2007 he has been an interviewer for the National Library of Australia’s Sport Oral History project, which has involved him in interviews with Australia’s first Paralympians. Robin is also a member of the Australian Society for Sports History. '''Robin McConnell''' has significant historical research experience most recently applied in his project, Sport in POW camps. Previously Robin researched History of Rugby In NZ, an well as supervising postgraduate research in historical sport topics, and teaching the history of sport at University of Ulster in Belfast. Robin is also an international marker of sport history PhDs and has written two books with historical dimensions. '''Laura Hale''' has extensive experience in terms of fandom based history. Acquiring her skills informally and self directed, her [http://www.fanhistory.com/wiki/Fanhistory.com:Philosophy Fanhistory Philosophy] gives insight to her approach, as well as the [http://www.fanhistory.com/wiki/Fanhistory.com:About Fanhistory About] page. Currently Laura is applying her data gathering and analytical skills to Australian expressions of sport fandom online, with a recent post applied to [http://ozziesport.com/2011/03/paralympic-sport-in-online-australia/ Australian paralympics]. Her methods will be a valuable component for gathering data on Australian Paralympic fandom expressed online, helping to give one aspect of social context to the history writing work ===An Understanding of Sport in Australia=== UCNISS offers undergraduate degrees in Sport, ''Coaching and Exercise Science, Sport Management, Sport Media and Bachelor of Sport Studies (Honours)''. Within these degrees includes study units such as ''The Australian Sports System, Governance and Sport, Sports and the Law, Contemporary Issues in Sport, Industrial Relations in Sport, Sport Research and Practice, Sport Sponsorship and Media, and Sport as Entertainment'' to name a few. All teaching in the University is research lead, and students expect course work to be contemporary and relevant. This teaching, research and assignment work gives UCNISS a strong understanding of the Sport Sector in Australia, and a valuable resource in the form of academics and students, to apply their studies on any number of specific issues or areas within that sector. ===An Understanding of Sport for People with Disabilities and the Paralympic Movement=== Our Project Team has extensive knowledge of sport for people with disabilities and the Paralympic Movement. Any limitations in our understanding will be addressed through our extensive network of contacts. ===An Understanding of Modern Information Technologies=== UCNISS has on its team a combined forty years or more experience in Internet media production. This experience includes working with open copyrights, open standard formats, the MediaWikis of the Wikimedia Foundation, authoring and facilitating blogs, forums and a wide range of popular social media. Leigh Blackall has produced three large online texts, commissioned by Government Ministries in New Zealand, and countless video documentaries on a wide range of things from art festivals to research projects. The texts all used the Wikibooks platform, and the PediaPress print on demand service, and the video was all produced to open standard formats, and published across all popular media sharing sites. Lara Hale and Graham Pearce also bring many years experience editing and administering MediaWiki, with Graham holding valuable expertise in using screen reader technology. John Vandenberg's specific skill is in creating MediaWiki extension software that assists with large volume work such as meta data tagging and categorising large numbers of media files. Perhaps most critical of all is that all members are deeply networked within the communities of practice, bringing significant social capital to the project. ===An Openness to Input=== UCNISS is an open education and research organisation. We are advocates for open access and collaboration. We place educational content and research data and outputs on Wikiversity and a host of popular social media channels. We play an active role in encouraging and supporting all staff in adopting such open academic practices. The project we propose here invites other tenderers to participate with us in both the proposal and implementation phase. The project itself invites input from the wider Paralympic and wiki communities, and anyone else with interest in the Paralympics in Australia. To this end, we have deliberately selected the most high profile, most popular collaborative authoring spaces, with the most open copyright licensing and digital format selections, to make that principle in practice loud and clear. When input from third parties occurs, we have the processes in place to recognise and appreciate the input as we work towards the development of a sustained community of practitioners. ==Additional Information== ===Australian Government Principles on Intellectual Property=== * [http://agimo.govspace.gov.au/2010/10/07/government-2-0-update-%E2%80%93-amended-ip-principles-released/ Gov2.0 update: IP Principles Released]. Australian Government Department of Finance and Deregulation. AGIMO Blog. http://agimo.govspace.gov.au/2010/10/07/government-2-0-update-%E2%80%93-amended-ip-principles-released/ 7 October 2010. {{quote|This is a formal endorsement of the Taskforce recommendation that agencies should license their Public Sector Information (PSI) under Creative Commons BY license as the default license type and only adopt more restrictive licenses after a process of ‘due diligence and on a case-by-case basis’.}} ===Wikimedia Foundation Strategic Priorities=== * [http://upload.wikimedia.org/wikipedia/foundation/c/c0/WMF_StrategicPlan2011_spreads.pdf Wikimedia Strategic Plan 2011-2015]. Strategic Priorities, P8. http://upload.wikimedia.org/wikipedia/foundation/c/c0/WMF_StrategicPlan2011_spreads.pdf {{Quote|Through 2015, the Wikimedia Foundation will: ...Encourage diversity by conducting outreach among groups that have the potential to bring new expertise to the projects, as well as by supporting leaders from underrepresented groups in their efforts to cultivate new members from within their communities... Provide project funding for efforts to connect Wikimedia projects with the work of institutions of culture and learning}} ===Support letter from Wikimedia Australia=== John Vandenberg. [[Talk:The History of the Paralympic Movement in Australia/Tender#Support letter from Wikimedia Australia|Support letter from Wikimedia Australia]]. http://en.wikiversity.org/wiki/Talk:UCNISS/History_of_the_Paralympic_Movement_in_Australia 8 March 2011 {{quote|At this stage, this letter is encouragement for this proposal. Should it be successful, we hope you will engage us for assistance in developing a volunteer community of APC content contributors, editors and managers. This could be in the form of funding workshops and seminars in regional Australia, printing information, and networking events.}} ===Support letter from Graham Pearce=== Graham Pearce. [[Talk:The History of the Paralympic Movement in Australia/Tender#Support letter from Graham Pearce|Support letter from Graham Pearce]]. http://en.wikiversity.org/wiki/Talk:UCNISS/History_of_the_Paralympic_Movement_in_Australia 4 March 2011. {{quote|It is vital that the history of the Australian Paralympic movement be documented in a manner that is easy to access for everyone. I believe that the current proposal is the best way to achieve this aim... Due to its license, it could be easily adapted by educational institutions, disability organisations, or any other interested parties... Both Wikibooks and Wikimedia Commons use the MediaWiki software, which is accessible to users of screen readers and screen magnifiers... people with disabilities, including users of screen readers and screen magnifiers, [can] take part in this project on an equal footing with their non-disabled peers.}} '''Full support letter from Wikimedia Australia''' [[File:Wmau to ucniss.jpg|right|300px]] :''This is a copy of a signed letter sent to UCNISS'' To the University of Canberra's National Institute of Sport Studies, regarding the proposal to assist the Australian Paralympic Committee develop and publish texts and media on Wikibooks and Wikimedia Commons for the purpose of developing a document called, History of the Paralympic Movement in Australia. Firstly, let us state how pleased we are to see yet another Australian cultural organisation engaging with the projects of the Wikimedia Foundation, helping to build reliable, usable, accessible and ultimately sustainable information resources for the world over, not least, Australians. Should your proposal be successful, we at Wikimedia Australia would like to extend an offer of support. Looking at your draft proposal, we are particularly interested in the list item: ::o Support in the development of an APC volunteer base to take a contribution and editing role in the project. We think this point relates to us and what we can offer. The purpose of Wikimedia Australia is to: # organise and participate in educational and social events that promote development of Free Cultural Works and related open source software systems, in particular ''wikis'' # increase public awareness, support and participation in the projects hosted by the Wikimedia Foundation (WMF) # develop resources to assist Australians in the creation and maintenance of Free Cultural Works Wikimedia Australia is an independent, not-for-profit organisation, whose primary aim is to promote equality of opportunity to access and participate in the collaborative creation of "[http://freedomdefined.org/Definition Free Cultural Works]", especially educational works, and works about Australia, its culture, natural environment, and Australian news and media. At this stage, this letter is encouragement for this proposal. Should it be successful, we hope you will engage us for assistance in developing a volunteer community of APC content contributors, editors and managers. This could be in the form of funding workshops and seminars in regional Australia, printing information, and networking events. Good luck with this proposal, and congratulations on this conceptual first step. We hope it is successful and given the opportunity to prove its worth. [[user:John Vandenberg|John Vandenberg]]<br> President<br> Wikimedia Australia '''Full support letter from Graham Pearce''' To whom it may concern, My name is Graham Pearce, and I am a totally blind Wikipedia editor from Perth, Western Australia. I have been editing Wikipedia and other Wikimedia Foundation projects for six years, and I am an English Wikipedia administrator. It is vital that the history of the Australian Paralympic movement be documented in a manner that is easy to access for everyone. I believe that the current proposal is the best way to achieve this aim, because Wikibooks is well-suited to the creation of structured online texts, which do not have the same space limitations as printed books. The resulting product would be freely available online around the world, thus increasing the profile of the Australian Paralympic Movement. Due to its license, it could be easily adapted by educational institutions, disability organisations, or any other interested parties, to meet their individual needs. Both Wikibooks and Wikimedia Commons use the MediaWiki software, which is accessible to users of screen readers and screen magnifiers. Therefore the results of the proposal would be easy-to-use for people with visual impairments. It would also be possible for people with disabilities, including users of screen readers and screen magnifiers, to take part in this project on an equal footing with their non-disabled peers. In conclusion, this proposal presents a unique opportunity to document the history of the Australian Paralympic Committee using collaborative tools, and as a screen reader user, I fully support it. Yours sincerely, [[User:Graham87|Graham Pearce]] 02:35, 4 March 2011 (UTC) [[Category:UCNISS]] [[Category:The History of the Paralympic Movement in Australia]] [[Category:Sports]] egx6kaweyquaejxbv8v00cfg1o4sy6t 0 134852 2412484 2366774 2022-08-07T04:51:16Z Marshallsumter 311529 wikitext text/x-wiki [[Image:Lambda Bootis.jpeg|thumb|right|250px|This is a visual image of lambda Boötis. Credit: Aladin at SIMBAD.{{tlx|free media}}]] The '''first blue source in Boötes''' is unknown. This is a lesson in map reading, coordinate matching, and searching. It is also a project in the history of [[Radiation astronomy/Blues|blue astronomy]] looking for the first astronomical blue source discovered in the constellation of Boötes. Nearly all the background you need to participate and learn by doing you've probably already been introduced to at a secondary level. Some of the material and information is at the college or university level, and as you progress in finding blue sources, you'll run into concepts and experimental tests that are an actual search. To succeed in finding a blue source in Boötes is the first step. Next, you'll need to determine the time stamp of its discovery and compare it with any that have already been found. Over the history of blue astronomy a number of sources have been found, many as point sources in the night sky. These points are located on the celestial sphere using coordinate systems. Familiarity with these coordinate systems is not a prerequisite. Here the challenge is geometrical, astrophysical, and historical. {{clear}} ==Control groups== A control group for this experiment may be a blue source observed by ancient hominins in their version of the constellation Boötes. {{clear}} ==Astronomical blue sources== [[Image:M87 jet.jpg|thumb|right|225px|This image shows the blue glow generated by the synchrotron radiation from the elliptical galaxy M87's energetic jet. Credit: Hubble Space Telescope.{{tlx|free media}}]] The image at right shows the blue light, towards the lower right, due to synchrotron radiation, of a jet emerging from the bright active galactic nucleus (AGN) core of Messier 87. {{clear}} ==First sources== The "earliest known astronomy anywhere in the world [is] that of the Australian Aborigines, whose culture has existed for some 40,000 years".<ref name=Haynes/> "The Aranda tribes of Central Australia, for example, distinguish red stars from white, blue and yellow stars."<ref name=Haynes>{{ cite book |author=R Haynes |title=Explorers of the southern sky: a history of Australian astronomy |publisher=Cambridge University Press |location=Cambridge, England, UK |date=June 27, 1996 |editor=Raymond Haynes |editor2=Roslynn Haynes |editor3=David Malin |editor4=Richard McGee |pages=527 |url=http://books.google.com/books?id=XoeiJxMmXZ8C&lr=&source=gbs_navlinks_s |arxiv= |bibcode= |doi= |pmid= |isbn=0521365759 |accessdate=2013-08-02 }}</ref> ==Backgrounds== To introduce yourself to some aspects of the challenge may I suggest reading the highlighted links mentioned above, and if you're curious, those listed under the section "See also" below. Blue rays are a form of [[radiation]] that is currently part of the electromagnetic radiation intersecting the Earth. More information about the radiation of astronomy is in [[Radiation/Astronomy|radiation astronomy]] and [[Radiation astronomy/Blues|blue astronomy]]. ==Constellations== [[Image:Boötes IAU.svg|thumb|right|250px|This is an image of the International Astronomical Union (IAU) sky map of the constellation Boötes. Credit: IAU and Roger Sinnott & Rick Fienberg, Sky & Telescope magazine.{{tlx|free media}}]] [[Image:Sidney Hall - Urania's Mirror - Bootes, Canes Venatici, Coma Berenices, and Quadrans Muralis.jpg|thumb|right|250px|This card shows Boötes, Canes Venatici, Coma Berenices, and Quadrans Muralis. Credit: Sidney Hall, [[c:User:Adam Cuerden|Adam Cuerden]] restorationist.{{tlx|free media}}]] The Wikipedia article about the constellation Boötes contains a high school level description. The figure at right shows the sky map of Boötes. Around the edges of the map are coordinates related to longitude and latitude, but with the Earth rotating on its axis every 24 hours the celestial coordinates must remain fixed. How has this been accomplished? Boötes was one of the 48 constellations described by the 2nd century astronomer Ptolemy and is now one of the 88 modern constellations. In ancient Babylon the stars of Boötes were known as SHU.PA. They were apparently depicted as the god [[Enlil]], who was the leader of the Babylonian pantheon and special patron of farmers.{{sfn|White|2008|p=207}} The second image at the right is Boötes as depicted in Urania's Mirror, a set of constellation cards published in London c.1825. In his left hand he holds his hunting dogs, Canes Venatici. Below them is the constellation Coma Berenices. Above the head of Boötes is Quadrans Muralis, now obsolete, but which lives on as the name of the early January Quadrantid meteor shower. Mons Mænalus can be seen at his feet. Also, in the Wikipedia article is a [[w:List of stars in Boötes|list of stars in Boötes]]. From the Wikipedia article on the [[w:Zodiac|Zodiac]], is Boötes a zodiacal constellation? Earlier versions of the stars that now compose Boötes may occur in astrohistory as they are found or rediscovered. {{clear}} ==Star classification by color== {| class="wikitable" ! Class ! Temperature<ref name=calib /><br>K ! abbr="color" | Conventional color ! abbr="color" | Apparent color<ref name="möre">The Guinness book of astronomy facts & feats, Patrick Moore, 1992, 0-900424-76-1</ref><ref>{{ cite book | date = 2004-12-21 | url = http://outreach.atnf.csiro.au/education/senior/astrophysics/photometry_colour.html | title = The Colour of Stars | publisher = Australia Telescope Outreach and Education | accessdate = 2007-09-26 }}&nbsp;— Explains the reason for the difference in color perception.</ref><ref>[http://www.vendian.org/mncharity/dir3/starcolor/ What color are the stars?], Mitchell Charity. Accessed online March 19, 2008.</ref> ! Mass<ref name=calib>Tables VII, VIII, Empirical bolometric corrections for the main-sequence, G. M. H. J. Habets and J. R. W. Heinze, ''Astronomy and Astrophysics Supplement Series'' '''46''' (November 1981), pp. 193–237, bibcode=1981A&AS...46..193H. Luminosities are derived from M_bol figures, using M_bol(ʘ)=4.75.</ref><br>(solar masses, M_ʘ) ! Radius<ref name=calib /><br>(solar radii, R_ʘ) ! Luminosity<ref name=calib /><br>(bolometric, L_ʘ) ! Hydrogen<br>lines ! Fraction of all<br>[[w:main sequence star|main sequence star]]s<ref name="LeDrew2001">{{ cite journal |author=Glenn LeDrew |url=http://adsabs.harvard.edu/abs/2001JRASC..95...32L |title=The Real Starry Sky |journal=Journal of the Royal Astronomical Society of Canada |month=February |year=2001 |volume=95 |issue=1 (whole No. 686, February 2001), pp. 32–33. ''Note:'' Table 2 has an error and so this article will use 824 as the assumed correct total of main-sequence stars }}</ref> |- style="background:#9bb0ff;" !style="background:#9bb0ff;"| [[#Class O|O]] | ≥&nbsp;33,000&nbsp;K | style="background:#9aafff;" | blue | style="background:#9bb0ff;" | blue | ≥&nbsp;16 | ≥&nbsp;6.6 | ≥&nbsp;30,000 | Weak | ~0.00003% |- style="background:#aabfff;" !style="background:#abbfff;"| [[#Class B|B]] | 10,000–33,000&nbsp;K | style="background:#cad7ff;" | blue to blue white | style="background:#aabfff;" | blue white | 2.1–16 | 1.8–6.6 | 25–30,000 | Medium | 0.13% |- style="background:#cad7ff;" !style="background:#cad7ff;"| [[#Class A|A]] | 7,500–10,000&nbsp;K | style="background:#f8f7ff;" | white | style="background:#cad7ff;" | white to blue white | 1.4–2.1 | 1.4–1.8 | 5–25 | [[w:Strong (relative detectability)|Strong]] | 0.6% |- style="background:#f8f7ff;" !style="background:#f8f7ff;"| [[#Class F|F]] | 6,000–7,500&nbsp;K | style="background:#FCFFD3;" | yellowish white | style="background:#f8f7ff;" | white | 1.04–1.4 | 1.15–1.4 | 1.5–5 | Medium | 3% |- style="background:#fff4ea;" !style="background:#fff4ea;"| [[#Class G|G]] | 5,200–6,000&nbsp;K | style="background:#fff2a1;" | yellow | style="background:#Fff4ea;" | yellowish white | 0.8–1.04 | 0.96–1.15 | 0.6–1.5 | Weak | 7.6% |- style="background:#ffd2a1;" !style="background:#ffd2a1;"| [[#Class K|K]] | 3,700–5,200&nbsp;K | style="background:#FFA351;" | orange | style="background:#Ffd2a1;" | yellow orange | 0.45–0.8 | 0.7–0.96 | 0.08–0.6 | Very weak | 12.1% |- style="background:#ffcc6f;" !style="background:#ffcc6f;"| [[#Class M|M]] | ≤&nbsp;3,700&nbsp;K | style="background:#FF6151; color:#FFFFFF" | red | style="background:#ffcc6f;" | orange red | ≤&nbsp;0.45 | ≤&nbsp;0.7 | ≤&nbsp;0.08 | Very weak | 76.45%. |} ==Testing a source== There are many web sites that may have a blue source listed for the constellation Boötes. ===Wikipedia sources=== '''A. Constellation article''' Under "Notable features" in the Wikipedia article on the constellation Boötes is the [[w:List of stars in Boötes|list of stars in Boötes]]. Click on this link. In the table of this Wikipedia article is [[w:Alpha Boötis|α Boo]]. To the right are coordinates: # [Right ascension] (RA): 14^h 15^m 40.35^s and # [Declination] (Dec): +19° 11' 14.2". Find these coordinates on the Boötes map at the right. Is alpha Boötis really inside the boundaries of the constellation? To evaluate the star as a blue source, skip ahead to the section "Blue source". '''B. Wikipedia search''' Another way to look for blue sources in the constellation is to perform a search on Wikipedia. Try "Boötes blue" without the quotes. This yields 2,236 possible astronomical blue source candidates. To evaluate a blue source, skip ahead to section "Blue source". ===SIMBAD sources=== Another way to find possible blue sources in Boötes is to use search queries on SIMBAD. Click on the SIMBAD link under "External links" below, then click on "Criteria query" or "by criteria". In the tan box, type in "region(05 45 08.9173 -16 42 58.017, 10m)", without the quotes. This tells the SIMBAD computer you are interested in a circular region of the celestial sphere centered on the coordinates for alpha Boötis, with a radius of 10 arcminutes (m). Notice on the page over at the right from the tan colored box: "'''Return'''". The default is "object count". Click on "submit query". In a few moments a result something like "'''Number of objects:''' 9" should appear. Click "Back" to see the tan box again. To see if you have found at least one object, change "'''Return'''" to "display" by clicking on the circle to its left, then "submit query". SIMBAD should display a list of objects. Read through the resource [[Radiation astronomy/Blues|blue astronomy]] for clues that may indicate whether a particular spectral type (Sp type) is a blue source. If none of the objects listed seems to be described as a blue source, try going "Back" and increasing the arcminutes from "10m" to "20m", and repeat until a blue source is found. Once you believe you have discovered a blue source, proceed to the section "Blue source". ==A blue source== There are several ways to evaluate a blue source for the constellation Boötes. ===Stellar classifications=== Stellar classification places the range of effective surface temperatures for conventional color blue, bluish, or blue white stars as the class K stars as class O ≥33,000 K blue, 10,000-33,000 K blue to blue white, and 7,500-10,000 K to white, or white to blue white (apparent color). {| class="wikitable" style="float: right; text-align: center; margin-left: 1em;" |+ ''Typical characteristics'' ! Stellar<br>Class ! Standard<br>star<br>* Not a standard star. ! Radius<br>([[w:Solar radius|R_ʘ]]) ! Luminosity<br>([[w:Solar luminosity|L_ʘ]]) ! [[w:Effective temperature|T_eff]]<br>([[w:Kelvin|K]]) ! Linear<br>approximation ! Planckian radiator<br>peak wavelength<br>(nm) |- | B9 || HR 5475 || 320% || 21400% || 12,417 || --- || 241 |- | A0 || [[w:Lambda Boötis|Lambda Boötis]] || 170% || 1910% || 8,720 || --- || 344 |- | A1V || [[w:1 Boötis|1 Boötis]] || --- || 5600% || 9,863 || --- || 304 |- | A8IV || [[w:Kappa Boötis|κ² Boötis]] || --- || 2800% || 7,760 || --- || 387 |} Some of the effective temperatures for the standard stars are fairly recent.<ref name=Catalano>{{ cite journal |author=S. Catalano, K. Biazzo, A. Frasca and E. Marilli |title=Measuring starspot temperature from line depth ratios |journal=Astronomy & Astrophysics |month=November |year=2002 |volume=394 |issue=3 |pages=1009-21 |url=http://www.aanda.org/articles/aa/full/2002/42/aa2543/node1.html |arxiv= |bibcode=2002A&A...394.1009C |doi=10.1051/0004-6361:20021223 |pmid= |pdf=http://www.aanda.org/articles/aa/pdf/2002/42/aa2543.pdf |accessdate=2012-08-15 }}</ref> The Planckian radiator peak wavelength for any effective surface temperature in K may be found using your handheld calculator with the formula: : y=(1.48833/(0.0000495*6060))*exp(1.48833/(0.0000495*6060))/(exp(1.48833/(0.0000495*6060))-1)-5. Depending on the internal software, ask it to print or display y. Iteratively enter different temperatures (e.g. 6060 in the equation) and wavelengths (e.g. 495 nm as 0.0000495 in the equation) to see how close to zero you are. For the temperature, wavelength pair (6060 K,495 nm), the value is -3.419065E-03. This is close in the third digit. The temperature, wavelength pair (3800 K,690 nm) gives an equation of : y=(1.48833/(0.0000690*3800))*exp(1.48833/(0.0000690*3800))/(exp(1.48833/(0.0000690*3800))-1)-5, with a value of 0.695831, which is not as close, and suggests an error in the first digit. When the temperature is higher than the minimum for a specific wavelength, the value of the equation is negative. When the wavelength is shorter than the minimum for a specific temperature, the value of the equation is positive. ===Wikipedia source=== Click on the link to the Wikipedia article. After you've enjoyed reading about the source, use the 'find' command of your browser to see if this Wikipedia page mentions anything about "blue" or "blue rays". Does the article mention whether or not the source is a blue source? What is the current time stamp for the Wikipedia article on the source? [Hint]: look for something like "This page was last modified on 12 January 2012 at 06:47." very near the bottom of the page. For now this is an adequate time stamp. From reading the Wikipedia article on the source, if you believe the text demonstrates that the source is not a blue source in Boötes edit the "Non-blue source in Boötes" section near the bottom of the page with an entry similar to "# Alpha Boötis 12 January 2012 at 06:47 Wikipedia article "Alpha Boötis".", without the outer quotes, and finish the entry with four "~"s without the quotes after the period. The date included with your designation or username is a time stamp for the entry. The last portion of the entry is the source of your information. On the other hand, if there are one or more sentences in the article that you believe demonstrates that the source is a blue source in Boötes edit the section below "Blue source in Boötes" with a similar entry. Go to the section entitle, "Challenging an entry". ===SIMBAD source=== To check any source (even one from Wikipedia) on SIMBAD, click of the "External link" to the "SIMBAD Astronomical Database". At the lower right side of the SIMBAD Astronomical Database page is a "Basic search" box. There are several ways to try your target: # source name: without the quotes or # source coordinates: without the quotes, for example, "05 45 08.9173 -16 42 58.017". If you are looking at a SIMBAD generated table which lists possible targets, click on one. On its SIMBAD page move over to the right side until you see an Aladin visual photograph of the object. Is it a blue source? Even if the source does not look blue, look down the left hand side of the page for "Spectral type:". From your reading of [[Radiation astronomy/Blues|blue astronomy]], do you believe the source is a blue source, or not? Noting that SIMBAD does, or does not consider the source to be a blue source is important, so skip down to the "SIMBAD time stamp" section. If you have already found a blue source (or a table of them) using SIMBAD, click on the blue link identifier for the first. ===SIMBAD time stamp=== Peruse the SIMBAD page for a time stamp or date of last revision. [Hint: it may look something like "2012.01.09CET20:10:02" and be in the upper right.] If the entry at SIMBAD convinces you that the source is not a blue source, edit the "Non-blue source in Boötes" section near the bottom of this page and type in an entry similar to "# Source Name 2012.01.09CET20:10:02 SIMBAD article "SIMBAD source name".", without the first set of quotes, followed by four ~s. If your SIMBAD analysis convinces you that you have found a blue source in Boötes (did you check the coordinates vs. the map of Boötes?), make an entry something like the ones in the section "Blue source in Boötes". ==Challenging an entry== Any entry in either the section "Blue source in Boötes" or "Non-blue source in Boötes" can be challenged. The time stamp may be challenged to see if there is an earlier one. The source may be challenged by an earlier source. ===Wikipedia challenge=== Is Wikipedia a 'primary source', or does the Wikipedia article cite a source? Even though Wikipedia has an article on the source, is it a good place to stop in testing whether the source has been detected as an astronomical blue source? If the Wikipedia article cites a primary source, skip down to the section on "Primary sources". ===SIMBAD challenge=== Is SIMBAD a 'primary source'? SIMBAD is an astronomical database provided by the Centre de Données astronomiques de Strasbourg. It is an authoritative source, but they do occasionally make a mistake. If you find a blue source within the constellation on SIMBAD, the next step is to find the earliest time stamp of discovery. ==Primary sources== Primary sources may be searched for possible additional information perhaps not yet evaluated by SIMBAD or not presented in a Wikipedia article about a source. ===Wikipedia test source=== For a Wikipedia article that cites a primary source, scroll down to the reference and open the reference. Read through the article looking for where the source mentioned in the Wikipedia article occurs. Some primary source authors may use source designations that are not mentioned in the Wikipedia article. To look for other designations, click on the link to SIMBAD in the "External links" on this page, enter the source name from the Wikipedia article, and see if other names are mentioned in the article. When none of the names are mentioned, click on the link for "Google Advanced Search" in the list of "External links", enter the source name or designation(s) such as "Gliese 866", with "blue" to see if the source has a reference indicating it is a blue source. And, look for the earliest one. Compose an entry using the primary source. ===SIMBAD test source=== Further down the SIMBAD page is a list of "Identifiers". Click on the blue bold portion. On the page that appears, there should be a primary source listed after '''Ref:'''. Click on the blue link with the oldest year. This yields an earlier time stamp and entry citation like the current one in the section "Blue source in Boötes". If you find another source or an earlier time stamp, compose a similar entry and edit the section. Additional information to add into the reference can be found by clicking on "ADS services" from the SIMBAD page. ==Changing an entry== From your analysis of the source so far, is it a blue source? If you have found an earlier time stamp for the source than the one listed in the section below "Non-blue source in Boötes" and the answer to the above question is "no", you can edit the section with your result. Or, you can leave the entries as is and try another star or object. If you have found an earlier time stamp for the source than the one listed in the section below "Blue source in Boötes", edit the section with your result. Or, if you found another blue source with a comparable or earlier time stamp, edit the section with your result. ==Blue sources in Boötes== # '''NGC 5548''' is a Type I Seyfert galaxy with a bright blue/white core. It is in the constellation Boötes. This galaxy was studied by the Multicolor Active Galactic Nuclei Monitoring 2m telescope.<ref name=Suganuma>{{ cite journal |author=Masahiro Suganuma, Yuzuru Yoshii, Yukiyasu Kobayashi, Takeo Minezaki, Keigo Enya, Hiroyuki Tomita, Tsutomu Aoki, Shintaro Koshida, and Bruce A. Peterson |title=Reverberation Measurements of the Inner Radius of the Dust Torus in Nearby Seyfert 1 Galaxies |journal=The Astrophysical Journal |month=March 1, |year=2006 |volume=639 |issue=1 |pages=46-63 |url=http://iopscience.iop.org/0004-637X/639/1/46/fulltext |arxiv= |bibcode=2006ApJ...639...46S |doi=10.1086/499326 |pmid= |pdf=http://iopscience.iop.org/0004-637X/639/1/46/pdf/0004-637X_639_1_46.pdf |accessdate=2012-08-16 }}</ref> --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|talk]]) 02:31, 17 August 2012 (UTC) # [[w:Pi Boötis|Pi Boötis]], specifically HR 5475, the brighter component is a blue-white B-type main sequence dwarf. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|talk]]) 02:56, 17 August 2012 (UTC) ==Non-blue sources in Boötes== # [[w:Arcturus|Arcturus]], or alpha Boötis, is an orange-yellow, spectral type K1.5IIIFe-0.5 or K1.5 IIIpe orange giant star. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|talk]]) 01:42, 17 August 2012 (UTC) ==Hypotheses== {{main|Hypotheses}} # The first blue source in Boötes was likely observed over 42,000 b2k. ==See also== {{div col|colwidth=20em}} * [[Radiation astronomy/Blues|Blue astronomy]] * [[Radiation astronomy/First cyan source in Caelum|First cyan source in Caelum]] * [[Radiation astronomy/First orange source in Cancer|First orange source in Cancer]] * [[Radiation astronomy/First red source in Canis Major|First red source in Canis Major]] * [[First X-ray source in Apus]] * [[First X-ray source in Aquarius]] * [[First yellow source in Aquila]] * [[Theory/Astronomy|Theoretical astronomy]] {{Div col end}} ==References== {{reflist|2}} ==External links== * [http://www.iau.org/ International Astronomical Union] * [http://www.jstor.org/ JSTOR] * [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED] * [http://nssdc.gsfc.nasa.gov/ NASA's National Space Science Data Center] * [http://www.osti.gov/ Office of Scientific & Technical Information] * [http://www.ncbi.nlm.nih.gov/pccompound PubChem Public Chemical Database] * [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System] * [http://www.scirus.com/srsapp/advanced/index.jsp?q1= Scirus for scientific information only advanced search] * [http://cas.sdss.org/astrodr6/en/tools/quicklook/quickobj.asp SDSS Quick Look tool: SkyServer] * [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database] * [http://simbad.harvard.edu/simbad/ SIMBAD Web interface, Harvard alternate] * [http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp Spacecraft Query at NASA.] * [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl Universal coordinate converter] <!-- footer templates --> {{tlx|Radiation astronomy resources}}{{Principles of radiation astronomy}}{{tlx|Reasoning resources}}{{Sisterlinks|Blue astronomy}} <!-- categories --> [[Category:Radiation astronomy/Lessons]] [[Category:Astronomy learning projects/Lessons]] [[Category:History of Sciences/Lessons]] [[Category:Semantics/Lessons]] [[Category:Sources/Lessons]] 3yp10twsvh5ezo48mri9oifma0bub9a 0 136038 2412468 2367950 2022-08-07T02:57:17Z Marshallsumter 311529 wikitext text/x-wiki [[Image:Mercury-mariner2.jpg|thumb|right|200px|This is a mosaic image taken by Mariner 10 of the rocky-object Mercury. Credit: NASA.{{tlx|free media}}]] '''Radiation astronomy''' is the key introductory lecture of the course on the [[principles of radiation astronomy]]. This is a quiz based on the lecture that you are free to take at any time or knowledge level. Once you’ve read and studied the lecture itself, the links contained within it, listed under [[Radiation astronomy/Quiz#See also|'''See also''']], [[Radiation astronomy/Quiz#External links|'''External links''']] and in the {{tlx|principles of radiation astronomy}} template, you should have adequate background to take the quiz and score highly. As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score. This quiz may need up to an hour to take and is equivalent to an ''hourly''. Enjoy learning by doing! {{clear}} ==Quiz== <quiz> {Yes or No, Extraterrestrial radiation sources only irradiate the surface of the Earth at night. |type="()"} - Yes + No {Which of the following is not a characteristic of radiation? |type="()"} - throwing a beam - a stream of charged or neutral particles + calculating the energy of a beam - sending out a traveling ray - a secondary-object hazard {Which of the following are radiation astronomy phenomena associated with the Sun? |type="[]"} + the color of the upper rim as seen from Earth + an excess brightness at or near the edge of the Sun + the iron XIV green line + neutron emission + polar coronal holes + meteor emission + changes in the line-blanketing {True or False, The H''β'' emission line does appear when the F492M filter is used on the ''Hubble Space Telescope'' because its wavelength is 486.1 nm. |type="()"} + TRUE - FALSE {Before the current era and perhaps before 6,000 b2k which classical planet may have been green? |type="{}"} { Osiris|Saturn (i) } {Complete the text: |type="{}"} Capella B has a surface temperature of approximately { 5700 K (i) }, is spectral type { G0 III|G0III (i) }, has an orbital period with Capella A of about { 104 d|104.0217 d (i) }, and is a { RS Canum Venaticorum|RS CVn (i) } variable. {True or False, A '''principle''' is a law or rule that has to be followed. |type="()"} - TRUE + FALSE {A cosmic ray may originate from what astronomical source? |type="()"} - Jupiter - the solar wind - the diffuse X-ray background - Mount Redoubt in Alaska - the asteroid belt + an active galactic nucleus {Which of the following are radiation astronomy phenomena associated with the rocky-object Io? |type="[]"} + surface regions reflecting or emitting violet or purple - an excess brightness at or near the edge + red regions that may be phosphorus - neutron emission - polar coronal holes + meteor emission - rotation {True or False, Any small luminous blue dot appearing in the cloudless portion of the night sky, especially with a fixed location relative to other such dots is most likely to be an active galactic nucleus. |type="()"} - TRUE + FALSE {Azurite is a natural pigment composed of what likely source of blue? |type="{}"} { copper|copper oxide|copper carbonate|copper hydroxide (i) } {Complete the text: |type="{}"} Vega has a surface temperature of approximately { 10,000 K (i) }, is spectral type { A0V|A0 V (i) }, has { no|no known (i) } stellar companions in a binary or multiple star system, and is a suspected { variable (i) } star. {True or False, A relativistic neutron may fly a megaparsec rather than undergo decay after about 14 minutes because its half-life may grow with energy. |type="()"} + TRUE - FALSE {The Larmor radius limits proton astronomy because of what characteristic of a proton? |type="()"} - the proton has a half-life of about one year - at the Larmor radius from the Sun the quarks inside a proton become unstable - at relativistic speeds the charge on a proton approaches zero - for very high speeds (almost relativistic) local or large scale magnetic fields produce little deflection - solar proton events may have a significant impact on the Earth's atmosphere + the proton has the same charge as the positron {Which of the following are radiation astronomy phenomena associated with the apparent liquid-object Earth? |type="[]"} + rain + snow + hail + neutron emission - polar coronal holes + meteor emission - rotation {True or False, There are blue or blue mineral containing meteorites. |type="()"} + TRUE - FALSE {Beta rays, or beta particles, are more penetrating than what other Greek letter designated rays or particles? |type="{}"} { Alpha|alpha rays, alpha particles (i) } {True or False, During large solar flares, the region near Mercury may be strongly illuminated with solar neutrons. |type="()"} + TRUE - FALSE {Complete the text: |type="{}"} { X|X-ray (i) } and { gamma|gamma-ray (i) } radiation are best absorbed by atoms with heavy nuclei. {True or False, When an electron is accelerated to near relativistic speeds it is called a delta ray. |type="()"} - TRUE + FALSE {Which of the following is not characteristic of a neutrino? |type="()"} - neutrinos are affected by the weak nuclear force + produced by a positron annihilating an electron - a decay product of a neutron - produced by the near surface fusion on the [[Sun (star)|Sun]] - may have a mass - comes in mutable varieties {Which of the following are radiation astronomy phenomena associated with the plasma-object the Sun? |type="[]"} + coronal clouds + H^1- ions + X-rays + neutron emission + polar coronal holes + meteor emission - rotation {True or False, There are red or red mineral containing meteorites. |type="()"} + TRUE - FALSE {Any natural object radiating through a portion or all of a natural object's atmosphere may be called a what? |type="{}"} { meteor (i) } {Complete the text: |type="{}"} At the high end of the proton energy spectrum (above ≈ { 10 to the 18th|10^18|10¹⁸|10E18|10 E +18 (i) } eV) the { Larmor radius|larmor radius (i) } deflection becomes small enough that { proton (i) } astronomy becomes possible. {True or False, X-ray bursts are the most luminous electromagnetic events known to occur in the universe. |type="()"} - TRUE + FALSE {Which of the following is not a phenomenon associated with optical astronomy? |type="()"} - actuators may be a part of active optics + the Vela satellites were the first devices in space ever to detect optical bursts - the Moon - an emission with a wavelength of 320 nm - adaptive optics - the color index {Which of the following are radiation astronomy phenomena associated with the gaseous-object Neptune? |type="[]"} - Voyager 2 + blue rays + clouds - neutron emission - polar coronal holes + meteor emission - rotation {True or False, There are violet or violet mineral containing meteorites. |type="()"} + TRUE - FALSE {Beta particles may be the key to? |type="{}"} { fusion|nuclear fusion (i) } {Complete the text: |type="{}"} The { Oh-My-God|omg (i) } particle was observed on the evening of October 15, 1991, over { Dugway Proving Ground|Dugway (i) }, Utah. {True or False, The rocky surface of the planet Venus can be detected when Venus is observed using infrared astronomy. |type="()"} - TRUE + FALSE {Which of the following is not a phenomenon associated with violet astronomy? |type="()"} - photographs of the planet Venus taken in 1927 - the purple haze within a few arcseconds of the central star of the Homunculus - the faintness of carbon stars - the stellar abundance of aluminum - adaptive optics + the helium beta line {True or False, Protons accelerated up to energies > 110 MeV and are able to hit the surface of Mercury. |type="()"} + TRUE - FALSE {Which of the following emission/absorption phenomena are associated with radiation astronomy? |type="[]"} + helium lines at 501 and 505 nm + the strong C₂ (1,2) band + nitrogen emission in plasmas at 566.934 nm from N VIII + helium emission line at 5876 Å + neutral iron line at 526.96 nm + calcium yellow line at 569.4 nm {Complete the text: |type="{}"} Sirius A has a surface temperature of approximately { 9900 K (i) }, is spectral type { A1V|A1 V (i) }, has an orbital period with Sirius B of about { 50 y|50 yrs|50 yr (i) }, and is { not (i) } a variable star. {True or False, There are cyan or cyan mineral containing meteors or meteorites. |type="()"} + TRUE - FALSE {What negatively charged particles may be used as tracers of cosmic magnetic fields? |type="{}"} { electrons (i) } {Complete the text: |type="{}"} Although { electron astronomy (i) } is usually not recognized as a formal branch of { astronomy (i) }, the measurement of { electron (i) } fluxes help to understand a variety of natural phenomena. {True or False, To date, all of the reported hypervelocity stars (HVSs), which are believed to be ejected from the Galactic center, are blue. |type="()"} + TRUE - FALSE {Observations of comets have benefited greatly from what phenomenon of cyan astronomy? |type="()"} - Cherenkov radiation - the electric blue glow of lightning - gas-expansion velocity decreases with increasing heliocentric distance - methane possesses prominent absorption bands in the visible - adaptive optics + the light of the neutral CN-radical {Which of the following are radiation astronomy phenomena usually associated with lithium emission? |type="[]"} + a green emission line - nucleosynthesis + an orange line at 610.3 nm + the Spite plateau + lithium-drifted silicon detectors - the Fraunhofer E line - asymptotic supergiant branch + an infrared line at 812.6 nm {True or False, There are yellow or yellow mineral containing meteorites. |type="()"} + TRUE - FALSE {Red ochre is a natural pigment composed of what likely source of red? |type="{}"} { hematite|iron|iron oxide|Fe2O3|Fe₂O₃ (i) } {True or False, Boron has an emission line in the yellow. |type="()"} - TRUE + FALSE {Complete the text: |type="{}"} The { delta-ray|delta ray (i) } tracks in emulsion chambers have been used for { direct (i) } measurements of { cosmic-ray|cosmic ray (i) } nuclei above { 1 TeV/nucleon (i) } in a series of balloon-borne experiments. {True or False, Olivine is a silicate mineral that may be detected in cometary coma dust with green astronomy. |type="()"} + TRUE - FALSE {Which of the following is a phenomenon associated with yellow astronomy? |type="()"} - [[Jupiter]] + sodium line emission - sunspots on the Sun - an emission with a wavelength of 420 nm - phosphorus - TiO {Radiation astronomy may help to detect what type of astronomical object? |type="[]"} + a stellar class M dwarf - the hydrogen Balmer alpha line + the photosphere of the Sun + extrasolar planets - lithium - the CMB {True or False, There are orange or orange mineral containing meteorites. |type="()"} + TRUE - FALSE {Cyanogen is a natural poisonous gas composed of what likely source of cyan? |type="{}"} { CN|cyanide (i) } {Why are antiprotons unlikely to be directly used as their own radiation astronomy? |type="[]"} + the observable universe is apparently composed almost entirely of matter - there exist other places that are almost entirely composed of antimatter + apparent asymmetry of matter and antimatter in the visible universe + baryogenesis - positron astronomy - a complete periodic table of antimatter + antiparticles are created everywhere in the universe where high-energy particle collisions take place {Complete the text: |type="{}"} Methane possesses prominant { absorption bands|absorption (i) } in the visible and near-infrared (IR) making { Uranus (i) } aquamarine or { cyan (i) } in color. {True or False, The red shift cannot affect blue stars. |type="()"} - TRUE + FALSE {Which of the following is not a phenomenon associated with red astronomy? |type="()"} - a stellar class M dwarf - the hydrogen Balmer alpha line - the photosphere of the Sun + an emission with a wavelength of 618 nm - lithium - "cometary knots" {Radiation astronomy has helped to verify what famous theories? |type="[]"} - Cherenkov radiation - the universe consists primarily of perfect vacuum - tachyonic gamma rays + extrasolar planets - warp drive - general relativity + quantum mechanics {Tarapacaite is a natural mineral pigment composed of what likely source of yellow? |type="{}"} { chromate|potassium chromate (i) } {Complete the text: |type="{}"} Io is the innermost of the four { Galilean (i) } moons of the planet { Jupiter (i) } . {True or False, The Earth's atmosphere does not transmit infrared radiation between 6 and 7 microns in wavelength because of water vapor. |type="()"} + TRUE - FALSE {Which of the following is not a radiation phenomenon associated with a crater? |type="()"} + strata - elongated dust particles - high albedo - olivine - Rayleighs - volcanoes {Infrared astronomy has really helped to detect what type of astronomical object? |type="()"} - a stellar class G dwarf - the hydrogen Balmer alpha line - the photosphere of the Sun + extrasolar planets - lithium - the CMB {Various radiation observatories occur at different altitudes and geographic locations due to what effect? |type="()"} - the presence of oceans on the Earth - locally available carving tools + light pollution - most astronomical objects are observed at night - currently dormant volcanoes seldom erupt - human habitation increases near an astronomical observatory {True or False, Due to the limited shielding provided by its relatively weak magnetic dipole moment, the surface of Mercury is everywhere subject to bombardment by cosmic rays. |type="()"} + TRUE - FALSE {Moldavite is a mineral that may be associated with what radiation astronomy phenomenon? |type="[]"} - predicting the end of the Earth - determining the accuracy of local computers + meteorite impacts - demonstrating that Venus was once a comet - predicting when currently dormant volcanoes will erupt + fireballs {Orpiment is a natural mineral pigment composed of what likely source of orange? |type="{}"} { arsenic|arsenic sulfide (i) } {Complete the text: |type="{}"} The orange and brown coloration in the clouds of { Jupiter (i) } are caused by { upwelling (i) } compounds that change color when they are exposed to { ultraviolet (i) } light from the Sun. {Which types of radiation astronomy directly observe the rocky-object surface of Venus? |type="[]"} - meteor astronomy - cosmic-ray astronomy - neutron astronomy - proton astronomy - beta-ray astronomy - neutrino astronomy - gamma-ray astronomy - X-ray astronomy - ultraviolet astronomy - visual astronomy - infrared astronomy - submillimeter astronomy + radio astronomy + radar astronomy + microwave astronomy - superluminal astronomy {True or False, The position of the Sun can be determined directly with the use of radar astronomy. |type="()"} - TRUE + FALSE {Radiation phenomena associated with craters include? |type="[]"} + catena + secondary craters - checking equations about complex systems + deformed strata + electric arcs + explosions {True or False, The emission of synchrotron light from the Sun may more accurately fit the spectral radiance of the Sun than black body radiation. |type="()"} + TRUE - FALSE {Superluminal astronomy has really helped to verify what famous theory? |type="()"} - Cherenkov radiation - the universe consists primarily of perfect vacuum - tachyonic gamma rays - extrasolar planets - warp drive + general relativity {Which of the following is involved in planetary astronomy more so than planetary science? |type="[]"} + the occurrence of blue rock types on the surface of rocky objects - the Earth and other rocky objects have a green mineral containing mantle - checking equations about complex systems + the advantages of a 559 nm band pass - digging holes in the surface of Mars + surface temperatures low enough to produce methane lakes {True or False, A cometary orbit about the Sun is a radiation astronomy phenomenon. |type="()"} + TRUE - FALSE {Purpurite is a natural mineral pigment composed of what likely source of violet or purple? |type="{}"} { manganese|manganese oxide (i) } {Complete the text: |type="{}"} The aluminum abundance was derived from the resonance line at { 394.4 (i) } nm, and Al is underabundant by ~ -0.7 { dex (i) } with respect to iron. {True or False, A metallic or stony object that is the remains of a meteor is called a meteoroid. |type="()"} - TRUE + FALSE {Various radiation observatories occur at different altitudes and geographic locations due to what effect? |type="()"} - the presence of oceans on the Earth - locally available carving tools + the atmosphere of the Earth - most astronomical objects are observed at night - currently dormant volcanoes seldom erupt - human habitation increases near an astronomical observatory {Which of the following is not a radiation phenomenon associated with a planet? |type="()"} - airglow - elongated dust particles - high albedo - olivine - Rayleighs + coronal mass ejection {What radiation astronomy phenomena are associated with Mars? |type="[]"} - it may help with faster-than-light travel + O(¹''S'') lines + ice + polar caps - the Greenwich meridian - it demonstrates that a power law is better than an exponential law {With respect to protoplanetary disks what green mineral has been found? |type="{}"} { olivine (i) } {Complete the text: |type="{}"} Astronomers place the submillimetre waveband between the { far-infrared (i) } and { microwave (i) } wavebands, typically taken to be between a few hundred micrometres and a millimetre. {True or False, The V 2 rocket was first used as a sounding rocket for X-ray astronomy before being converted to a weapon. |type="()"} - TRUE + FALSE {The Mesoamerican Long Count calendar is an astronomical document produced to help astronomers for what purpose? |type="()"} - predict the end of the Earth - determine the accuracy of local computers + accurately predict the equinoxes - demonstrate that Venus was once a comet - predict when currently dormant volcanoes will erupt - demonstrate that the local pyramids were built by aliens {When close binary stars are present, what characteristics are readily observed? |type="[]"} + iron XIV line + facular excess brightness + starspots + magnetic poles + flares - neon clouds {True or False, Jupiter shows intense X-ray emission associated with auroras in its polar regions. |type="()"} + TRUE - FALSE {The Cr¹⁺ ion has an emission line often observed in what solar limb phenomenon? |type="{}"} { limb faculae|faculae (i) } {Complete the text: |type="{}"} Terahertz radiation refers to electromagnetic waves propagating at { frequencies (i) } in the { terahertz (i) } range. {True or False, The emission of synchrotron and black-body light from the Sun may more accurately fit the spectral radiance of the Sun than black body radiation alone. |type="()"} + TRUE - FALSE {Dimensional analysis may help with astronomical calculations for what reason? |type="()"} - it may help with faster-than-light travel - it allows the conversion of matter into energy + checking equations about complex systems - it differentiates English units from the metric system - there is an inherent preference for the Paris meridian over the Greenwich meridian - it demonstrates that a power law is better than an exponential law {Which of the following radiation astronomy phenomena are associated with the rocky object Mercury? |type="[]"} + apparent impact craters - an excess brightness at or near the edge - the iron XIV line + neutron emission - polar coronal holes + meteor emission - changes in the line-blanketing {Using HIFI instrument aboard the ''Herschel'' Space Observatory, the first detection of what ion occurred on March 1 and March 23, 2010? |type="{}"} { chloronium|H2Cl+|H₂Cl⁺|H₂Cl¹⁺ (i) } {Complete the text: |type="{}"} The detection of absorption by interstellar { hydrogen fluoride|HF (i) } in the { submillimeter (i) } band occurs along the sight line to the submillimeter continuum sources W49N and W51. {True or False, Visual Bremsstrahlung radiation is not detected from the Sun because the photosphere isn't ionized enough to produce it. |type="()"} - TRUE + FALSE {Which of the following is involved in planetary astronomy more so than planetary science? |type="()"} - the occurrence of rock types on the surface of rocky objects - the Earth and other rocky objects may have a mantle - checking equations about complex systems + the advantages of radar - digging holes in the surface of the Moon - surface temperatures low enough to produce methane lakes {Which of the following is not a radiation phenomenon associated with a comet? |type="()"} - airglow - elongated dust particles - high albedo - olivine - Rayleighs + coronal mass ejection {Yes or No, Hydrogen has an emission line in the yellow. |type="()"} - Yes + No {Which of the following is not a radiation phenomenon associated with a star? |type="()"} - airglow - elongated dust particles + high albedo - olivine - Rayleighs - coronal mass ejection {True or False, Beryllium has an emission line in the yellow. |type="()"} - TRUE + FALSE {Why is much of the surface of Mars covered with red iron oxide dust when the rocks that compose much of its surface are blue or violet? |type="()"} - Mars has been systematically bombarded with small iron-nickel meteorites or micrometeorites that oxidize in its atmosphere - Mars has been frequently bombarded with hematite containing micrometeorites - asteroid impacts on Mars may have forced iron from near its core into the atmosphere and onto the surface as hematite dust that oxidized - Mars is like Earth in surface hematite composition, but Earth has much more water + precipitation from iron-rich water {True or False, The planet Saturn exhibits a pale yellow hue due to ammonia crystals in its upper atmosphere. |type="()"} + TRUE - FALSE </quiz> ==Hypotheses== {{main|Hypotheses}} # Quiz questions about radiation astronomy may be made too difficult. # Quiz questions could start out as easy association and work up to more difficult. # In 2015 two quizzes made the top 1000: [[Planets/Quiz]] and [[Classical planets/Quiz]], as such more quizzes may make this list. # [[Intergalactic medium]] was averaging 6 hits per day, but after the move to the subpage its down to 1 per day, which suggests that subpaging reduces reader interest or access. ==See also== {{div col|colwidth=20em}} * [[Cosmic-ray astronomy/Quiz]] * [[Meteor astronomy/Quiz]] * [[Planetary science/Quiz]] * [[Radiation astronomy/Problem set]] * [[Radiation chemistry/Quiz|Radiation astrochemistry/Quiz]] * [[Radiation geography/Quiz|Radiation astrogeography/Quiz]] * [[Radiation history/Quiz|Radiation astrohistory/Quiz]] {{Div col end}} ==External links== * [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED] * [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System] * [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database] <!-- footer templates --> {{tlx|Charge ontology}}{{tlx|History of science resources}}{{Principles of radiation astronomy}}{{tlx|Radiation astronomy resources}}{{Sisterlinks|Radiation astronomy}} <!-- categories --> [[Category:Astrophysics quizzes]] [[Category:History of Sciences quizzes]] [[Category:Radiation quizzes]] [[Category:Radiation astronomy quizzes]] 839flbec6q49jjhhzxmmvimedcpyuf2 0 139384 2412359 2412121 2022-08-06T13:44:24Z Young1lim 21186 /* Adder */ wikitext text/x-wiki {{nocat}} == Adder == * Binary Adder Architecture Exploration ( [[Media:adder.20131113.pdf |pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20211108.pdf |pdf]] || || [[Media:adder.rca.20140313.pdf |pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf |pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20211106.pdf |pdf]] || || [[Media:adder.cla.20140313.pdf |pdf]] || |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf |pdf]] || || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf |pdf]] || || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20211111.pdf |pdf]] || || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf |pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf |pdf]] || || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf |pdf]], [[Media:adder.cca.20140313.pdf |pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf |pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf |pdf]] || || [[Media:adder.ksa.20140409.pdf |pdf]] || |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf |pdf]] || || || |- || '''9. Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA.20220805.pdf |pdf]] || || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf |pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf |pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf |pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf |pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:bshift.20131105.pdf |bshfit.vhdl]], [[Media:bshift.makefile.20131109.pdf |bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf |pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf |pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf |pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf |pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf |pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf |Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf |H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf |pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Computer architecture]] l0p3djaqgdx0am4ehlbkf1fvlug1eni 2412361 2412359 2022-08-06T13:45:42Z Young1lim 21186 /* Adder */ wikitext text/x-wiki {{nocat}} == Adder == * Binary Adder Architecture Exploration ( [[Media:adder.20131113.pdf |pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20211108.pdf |pdf]] || || [[Media:adder.rca.20140313.pdf |pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf |pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20211106.pdf |pdf]] || || [[Media:adder.cla.20140313.pdf |pdf]] || |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf |pdf]] || || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf |pdf]] || || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20211111.pdf |pdf]] || || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf |pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf |pdf]] || || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf |pdf]], [[Media:adder.cca.20140313.pdf |pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf |pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf |pdf]] || || [[Media:adder.ksa.20140409.pdf |pdf]] || |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf |pdf]] || || || |- || '''9. Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA.20220806.pdf |pdf]] || || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf |pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf |pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf |pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf |pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:bshift.20131105.pdf |bshfit.vhdl]], [[Media:bshift.makefile.20131109.pdf |bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf |pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf |pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf |pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf |pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf |pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf |Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf |H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf |pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Computer architecture]] okzsa0blvzccrczp3z520a28alo1yhy 6 139697 2412471 989055 2022-08-07T03:13:07Z Marshallsumter 311529 /* Licensing */ wikitext text/x-wiki == Summary == "The Chandra image shows Mira A (right), a highly evolved red giant star, and Mira B (left), a white dwarf. Mira A is losing gas rapidly from its upper atmosphere via a stellar wind. Mira B exerts a gravitational tug that creates a gaseous bridge between the two stars. Gas from the wind and bridge accumulates in an accretion disk around Mira B and collisions between rapidly moving particles in the disk produce X-rays." Scalebar: 0.3 arcsec. Credit: NASA/CXC/SAO/M. Karovska et al. == Licensing == {{Information1 |Description=The Chandra image shows Mira A (right), a highly evolved red giant star, and Mira B (left), a white dwarf. Mira A is losing gas rapidly from its upper atmosphere via a stellar wind. Mira B exerts a gravitational tug that creates a gaseous bridge between the two stars. Gas from the wind and bridge accumulates in an accretion disk around Mira B and collisions between rapidly moving particles in the disk produce X-rays. |Source=Chandra X-ray Observatory Photo Album Mira More Images of Mira at url=http://chandra.harvard.edu/photo/2005/mira/more.html |Date=April 28, 2005. |Author=NASA/CXC/SAO/M. Karovska et al. |Rationale = No free licensed or public domain alternatives known to exist to show Mira A (right), a highly evolved red giant star, and Mira B (left), a white dwarf. Mira A is losing gas rapidly from its upper atmosphere via a stellar wind. Mira B exerts a gravitational tug that creates a gaseous bridge between the two stars. Gas from the wind and bridge accumulates in an accretion disk around Mira B and collisions between rapidly moving particles in the disk produce X-rays. |Permission="The images on this web site may be used for non-commercial educational and public information purposes. Please credit images to "NASA/CXC/SAO" unless other credits are given. In that case, credit the appropriate organization(s) or person(s) as they are listed with the image on our site." [http://chandra.harvard.edu/photo/image_use.html]. |other_versions= }} {{Fairuse}} pgur2ziusjfeeewc1rpqgbd2no9lu7m 0 149045 2412486 1985509 2022-08-07T05:00:31Z Marshallsumter 311529 wikitext text/x-wiki [[Image:Orionid meteor.jpg|thumb|right|250px|This image is of a green and red Orionid meteor. Credit: [https://sites.google.com/site/thebrockeninglory/ Brocken Inaglory].{{tlx|free media}}]] '''[[Radiation/Meteors|Meteor astronomy]]''' is a lecture for the [[Portal:Radiation astronomy|radiation astronomy department]] course on the [[principles of radiation astronomy]]. You are free to take this quiz based on [[Radiation/Meteors|meteor astronomy]] at any time. To improve your score, read and study the lecture, the links contained within, listed under [[Radiation astronomy/Meteors/Quiz#See also|'''See also''']], [[Radiation astronomy/Meteors/Quiz#External links|'''External links''']], and in the {{tlx|principles of radiation astronomy}} template. This should give you adequate background to get 100 %. As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score. '''Suggestion:''' Have the lecture available in a separate window. To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association. Enjoy learning by doing! {{clear}} ==Quiz== <quiz> {Why is much of the surface of Mars covered with red iron oxide dust when the rocks that compose much of its surface are blue or violet? |type="()"} - Mars has been systematically bombarded with small iron-nickel meteorites or micrometeorites that oxidize in its atmosphere - Mars has been frequently bombarded with hematite containing micrometeorites - asteroid impacts on Mars may have forced iron from near its core into the atmosphere and onto the surface as hematite dust that oxidized - Mars is like Earth in surface hematite composition, but Earth has much more water + precipitation from iron-rich water {Which of the following is not a radiation phenomenon associated with a comet? |type="()"} - airglow - elongated dust particles - high albedo - olivine - Rayleighs + coronal mass ejection {Which of the following are radiation astronomy phenomena associated with the apparent liquid-object Earth? |type="[]"} + rain + snow + hail + neutron emission - polar coronal holes + meteor emission - rotation {With respect to protoplanetary disks what green mineral has been found? |type="{}"} { olivine (i) } {Which of the following are astronomical phenomena associated with the Sun as a likely source? |type="[]"} + coronal clouds + cosmic rays + neutrinos - Oh My God type particles + meteors - comets + blue rays {Complete the text: |type="{}"} Match up the item letter with each of the cosmogonic possibilities below: interior models of the giant planets - A high interest for cosmogony, geophysics and nuclear physics - B hierarchical accumulation - C clouds and globular clusters - D cosmic helium abundance - E deuterium fusion - F a large deficiency of light elements - G after galactic sized systems had collapsed - H the motions of hydrogen { D (i) } formation of luminous quasars { H (i) }. stars with an initial mass less than the solar mass { G (i) }. rotating liquid drops { B|F (i) }. primordial is less than 26 per cent { E (i) }. a solar mixture of elements dominated by hydrogen and helium gas { A (i) }. around 13 Jupiter masses { F (i) }. smaller rocky objects { C (i) }. {The charge on a planetary dust particle may change with? |type="{}"} { latitude (i) } {Which weather phenomena are most likely to interfere with observing stars? |type="[]"} + a late-summer rainstorm - a clear sky + an approaching dust storm - below normal temperatures + a typhoon + a snow fall + fog {Various gaps and density minima have been observed in the Saturnian |type="{}"} { ring|rings (i) } system. {Which of the following are characteristic of a binary formed via gravitational fragmentation? |type="[]"} + the local Jeans length + the local speed of sound + the mean molecular weight - the electron neutrino + the mean particle density - neutrons {Complete the text: |type="{}"} The moon was formed independently of the earth and later { captured (i) }, presumably by a { three-body| three body (i) } interaction. {True or False, A hydrometeor is a precipitation product. |type="()"} + TRUE - FALSE {Usually associated with clouds filling the sky, thunder and lightning, wind and what water based meteorites |type="{}"} { rain (i) } {True or False, A lithometeor is a rocky-object meteor. |type="()"} + TRUE - FALSE {Meteorites found on Earth may be from which of the following? |type="[]"} - Saturn - Mercury + the Moon + the asteroid belt - Jupiter + Mars + Earth {True or False, A cryometeor is a very large chunk of amber. |type="()"} - TRUE + FALSE {Complete the text: |type="{}"} An aerometeor is a { discrete (i) } unit of air traveling or { falling (i) } through an atmosphere. {True or False, A metallic or stony object that is the remains of a meteor is called a meteoroid. |type="()"} - TRUE + FALSE {On 19 May 1910, the Earth actually passed through the tail of what comet. |type="{}"} { Halley's (i) } {True or False, The observations of planetary motion agree with computed orbits to the accuracy of the observations. |type="()"} - TRUE + FALSE {A cloud at nearly a quarter of the distance to Proxima Centauri is called the |type="{}"} { Oort cloud (i) } {True or False, Clouds are a form of radiation because they have a temperature gradient. |type="()"} - TRUE + FALSE {Which phenomena are associated with the heliosphere? |type="[]"} + a region of space where the interstellar medium is blown away by the solar wind + a bubble in space + virtually all the material emanates from the Sun itself - Voyager 2 + Voyager 1 + the termination shock {True or False, The prismoidal method provides a good approximation of the dust emission peak for cold sources. |type="()"} + TRUE - FALSE {A natural rocky source of chemicals from the sky to the ground may originate from what astronomical source? |type="()"} - Jupiter - the solar wind - the diffuse X-ray background - Mount Redoubt in Alaska + the asteroid belt - the International Space Station {True or False, A new cosmogony predicts that all particles in one stream have the same mineral composition. |type="()"} + TRUE - FALSE {Complete the text: |type="{}"} The majority of known asteroids orbit the Sun between the orbits of { Mars|Jupiter (i) } and { Jupiter|Mars (i) }. {True or False, Mars may have suffered asteroid impacts. |type="()"} + TRUE - FALSE {Which of the following are radiation astronomy phenomena associated with the gaseous-object Neptune? |type="[]"} - Voyager 2 + blue rays + clouds - neutron emission - polar coronal holes + meteor emission - rotation {True or False, The visible path of a meteoroid that has entered the Earth's atmosphere is called a meteorite. |type="()"} - TRUE + FALSE {Complete the text: |type="{}"} The 0.6 m Tortugas Mountain Observatory is used to monitor the temporal changes in the { Jovian|Jupiter (i) } cloud deck and equatorial activity on { Saturn (i) }. {True or False, Mercury may have once been a satellite of Jupiter, or possibly of Saturn. |type="()"} + TRUE - FALSE {Which of the following is not a characteristic of showers? |type="()"} + throwing a beam - meteors - rain - snow - hail {True or False, Micrometeoroids have less stable orbits than meteoroids. |type="()"} + TRUE - FALSE {Which of the following are radiation astronomy phenomena associated with the rocky-object Io? |type="[]"} + surface regions reflecting or emitting violet or purple - an excess brightness at or near the edge + red regions that may be phosphorus - neutron emission - polar coronal holes + meteor emission - rotation {True or False, To date, all of the reported hypervelocity stars (HVSs), which are believed to be ejected from the Galactic center, are blue. |type="()"} + TRUE - FALSE {Any natural object radiating through a portion or all of a natural object's atmosphere may be called a what? |type="{}"} { meteor (i) } {True or False, Olivine is a silicate mineral that may be detected in cometary coma dust with green astronomy. |type="()"} + TRUE - FALSE {Observations of comets have benefited greatly from what phenomenon of cyan astronomy? |type="()"} - Cherenkov radiation - the electric blue glow of lightning - gas-expansion velocity decreases with increasing heliocentric distance - methane possesses prominent absorption bands in the visible - adaptive optics + the light of the neutral CN-radical {Yes or No, A cometary orbit about the Sun is a radiation astronomy phenomenon. |type="()"} + Yes - No {Which of the following is not a radiation phenomenon associated with a planet? |type="()"} - airglow - elongated dust particles - high albedo - olivine - Rayleighs + coronal mass ejection </quiz> ==Hypotheses== {{main|Hypotheses}} # Meteors range in size from galaxy clusters to dust grains and molecular clusters. ==See also== {{div col|colwidth=12em}} * [[Astronomy/Quiz]] * [[Green astronomy/Quiz]] * [[Planetary science/Quiz]] * [[Radiation chemistry/Quiz|Radiation astrochemistry/Quiz]] * [[Radiation geography/Quiz|Radiation astrogeography/Quiz]] * [[Radiation history/Quiz|Radiation astrohistory/Quiz]] * [[Radiation astronomy/Quiz]] * [[Theoretical radiation astronomy/Quiz]] {{Div col end}} ==External links== * [http://www.iau.org/ International Astronomical Union] * [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED] * [http://nssdc.gsfc.nasa.gov/ NASA's National Space Science Data Center] * [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System] * [http://cas.sdss.org/astrodr6/en/tools/quicklook/quickobj.asp SDSS Quick Look tool: SkyServer] * [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database] * [http://simbad.harvard.edu/simbad/ SIMBAD Web interface, Harvard alternate] * [http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp Spacecraft Query at NASA] * [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl Universal coordinate converter] <!-- footer templates --> {{tlx|Radiation astronomy resources}}{{Principles of radiation astronomy}}{{Sisterlinks|Meteor astronomy}} <!-- categories --> [[Category:Astrophysics quizzes]] [[Category:Meteorology quizzes]] [[Category:Meteors quizzes]] [[Category:Radiation astronomy quizzes]] kvytl5a3avsjxe96b8rzex4yt2kdm0f 0 153343 2412485 1967032 2022-08-07T04:58:03Z Marshallsumter 311529 wikitext text/x-wiki [[Image:HR 3775.jpeg|thumb|right|250px|This is an optical image in the visual range of Theta Ursae Majoris. It is listed in SIMBAD as an F7V spectral type star with a parallax of 74.19 mas. Credit: Aladin at SIMBAD.{{tlx|free media}}]] Students start from specific situations of motion, determine how to calculate energy and convert units, then evaluate types of energy. {{clear}} ==Energies== '''Def.''' a [[wikt:quantity|quantity]] that denotes the [[wikt:ability|ability]] to do [[wikt:work|work]] and is measured in a unit dimensioned in [[wikt:mass|mass]] × [[wikt:distance|distance]]²/[[wikt:time|time]]² (ML²/T²) or the equivalent is called '''energy'''. '''Def.''' a [[wikt:physical|physical]] [[wikt:quantity|quantity]] that denotes ability to [[wikt:push|push]], [[wikt:pull|pull]], [[wikt:twist|twist]] or [[wikt:accelerate|accelerate]] a body which is measured in a unit dimensioned in [[wikt:mass|mass]] × [[wikt:distance|distance]]/[[wikt:time|time]]² (ML/T²): [[wikt:SI|SI]]: [[wikt:newton|newton]] (N); [[wikt:CGS|CGS]]: [[wikt:dyne|dyne]] (dyn) is called '''force'''. In astronomy we estimate distances and times when and where possible to obtain forces and energy. The key values to determine in both force and energy are (L/T²) and (L²/T²). Force (F) x distance (L) = energy (E), L/T² x L = L²/T². Force and energy are related to distance and time using proportionality constants. :{| style="padding:5px;" |- |colspan=2| Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:<ref name=Newton1>- Proposition 75, Theorem 35: p.956 - I.Bernard Cohen and Anne Whitman, translators: Isaac Newton, ''The Principia'': Mathematical Principles of Natural Philosophy. Preceded by ''A Guide to Newton's Principia'', by I. Bernard Cohen. University of California Press 1999 {{ISBN|0-520-08816-6}} {{ISBN|0-520-08817-4}}</ref> |- |valign="top"| :<math>F = G \frac{m_1 m_2}{r^2}\ </math>, where: * ''F'' is the force between the masses, * ''G'' is the gravitational constant, * ''m''₁ is the first mass, * ''m''₂ is the second mass, and * ''r'' is the distance between the centers of the masses. |valign="top"| [[Image:NewtonsLawOfUniversalGravitation.svg|200px|thumb|right|The diagram shows two masses attracting one another. Credit: [[w:user:Dna-Dennis|Dna-Dennis]].{{tlx|free media}}]] |} In the International System of Units (SI) units, ''F'' is measured in newtons (N), ''m''₁ and ''m''₂ in kilograms (kg), ''r'' in meters (m), and the constant ''G'' is approximately equal to {{val|6.674|e=-11|u=N m² kg⁻²}}.<ref name=NISTgravity>{{ cite web |title=CODATA2006 |url=http://www.physics.nist.gov/cgi-bin/cuu/Value?bg }}</ref> Observationally, we may not know the origin of the force. Coulomb's law states that the electrostatic force <math>F</math> experienced by a charge, <math>q</math> at position <math>r_q</math>, in the vicinity of another charge, <math>Q</math> at position <math>r_Q</math>, in vacuum is equal to: :<math>F = {qQ\over4\pi\varepsilon_0}{1\over {r^2}},</math> where <math>\varepsilon_0</math> is the electric constant and <math>r</math> is the distance between the two charges. Coulomb's constant is :<math>k_e = 1 / (4\pi\varepsilon_0\varepsilon),</math> where the constant <math>\varepsilon_0</math> is called the permittivity of free space in SI units of C² m⁻² N⁻¹. For reality, <math>\varepsilon</math> is the relative (dimensionless) permittivity of the substance in which the charges may exist. The energy <math>E</math> for this system is :<math>E = F \cdot D,</math> where <math>D</math> is the displacement. ==Unknown forces== Newton's second law of motion is that <math>F = ma</math>, where <math>F</math> is the force applied, <math>m</math> is the mass of the object receiving the force, and <math>a</math> is the acceleration observed for the astronomical object. The newton is therefore:<ref name=IBWM>{{ cite book |title = Table 3. Coherent derived units in the SI with special names and symbols, In: ''The International System of Units (SI)'' | publisher = International Bureau of Weights and Measures | year = 2006 | url = http://www.bipm.org/en/si/si_brochure/chapter2/2-2/table3.html }}</ref> :<math>{1~{\rm N} = 1~{\rm kg} \frac{{\rm m}} {{\rm s}^2}}</math> where: : N: newton : kg: kilogram : m: metre : s: second. In dimensional analysis: :<math>{\mathsf F} = \frac{\mathsf {ML}} {{\mathsf T}^2}</math> where : '''M''': mass : '''L''': length : '''T''': time. But, for a force of unknown type, mass or charge may be meaningless until proven applicable. So that :<math>{\mathsf A} = {\mathsf {F/M}} = \frac{\mathsf L} {{\mathsf T}^2},</math> :<math>{\mathsf A} = {\mathsf {F/Q}} = \frac{\mathsf L} {{\mathsf T}^2},</math> :<math>{\mathsf P} = {\mathsf {E/M}} = \frac{{\mathsf L}^2} {{\mathsf T}^2},</math> and :<math>{\mathsf P} = {\mathsf {E/Q}} = \frac{{\mathsf L}^2} {{\mathsf T}^2},</math> where <math>{\mathsf P}</math> may be called an '''energy phantom''', or '''astronomical energy phantom'''. ==Problem 1== [[Image:Van Maanen's star.gif|thumb|right|200px|The image is an optical negative centered on the SIMBAD coordinates J2000.0 for Van Maanen's star. Image is from the Palomar 48-inch Schmidt reflecting telescope. Van Maanen's star is the largest black dot center top right. Credit: NASA/IPAC Extragalactic Database.{{tlx|free media}}]] [[Image:SIMBAD image.jpg|thumb|left|200px|The SIMBAD image is in natural color of Van Maanen's star. Credit: Aladin at SIMBAD.{{tlx|free media}}]] In the image at right Van Maanen's star (largest dark spot) is not at the center of the coordinates where expected, but as a high proper motion star it is actually off-center to the center top right. This is an example of the change in radiation flux to a specific location of observation by a source undergoing a change in location for observation (but staying within the observation field of view) within an observable change in radiation flux (the star did not move close enough to blacken the entire frame nor change intensity sufficiently to disappear into the background of the detector). Using a meter stick or smaller measuring device, measure the distance in mm that the star is displaced from the center of the negative. The image is 5' x 5' and may be considered from May 1.0, 1994. According to [[w:SIMBAD|SIMBAD]], Van Maanen's star (designated VAN MAANEN STAR), is at optical coordinates: 00^h 49^m 09.902^s +05° 23' 19.01".<ref name=Leeuwen>{{ cite journal |author=F. Van Leeuwen |title=Validation of the new Hipparcos reduction |journal=Astronomy & Astrophysics |month=November 1, |year=2007 |volume=474 |issue=2 |pages=653-64 |url=http://adsabs.harvard.edu/abs/2007A%26A...474..653V |arxiv=0708.1752 |bibcode=2007A&A...474..653V |doi=10.1051/0004-6361:20078357 |pmid= |accessdate=2013-12-05 }}</ref> a. If the SIMBAD coordinates for the center of the image are the star's current position, how many milliarcseconds (mas) has the star moved since the above image was taken? b. If the only direction of motion for the star is in the plane of the image, and the star is 14.1 ± 0.1 ly away, how fast is it moving? c. The image at SIMBAD for the star at left, also called Gliese 35, shows a split color image of the star (assume the position of the star is between the two color spots), where the image is 2.4' x 2.4'. The star is not at the coordinates but along the line of travel. If the star slowed down between these two images, what is its speed in the SIMBAD image? d. Using the two speeds from above, calculate the deceleration, or acceleration, the star may have experienced. {{clear}} ==Problem 2== In Problem 1, let the acceleration you've calculated be applied at the same magnitude over the entire time from the star's initial position to its position in the visual image at left. What is the value of the energy phantom for Van Maanen's star? ==Problem 3== If the sole influence on Van Maanen's star is another star at the Sun's distance and mass, directly behind Van Maanen's star in the plane of the image, what is the force of gravity applied by this star to Van Maanen's star at its initial position in the image? Let the mass of Van Maanen's star be 0.68 ± 0.02 M_ʘ. Is this gravitational force enough to account for the deceleration? ==Problem 4== If the sole influence on Van Maanen's star is another star at the Sun's distance directly in front of Van Maanen's star in the plane of the image, what is the force of electrostatics applied by this star to Van Maanen's star at its initial position in the image? Let the charge of the star be Q_S = -0.3 x 10²⁸ e.s.u. and the amount of charge on Van Maanen's star be 0.68 ± 0.02 Q_S. Is this electrostatic force enough to account for the deceleration? Which is stronger, the gravitational force or the electrostatic force? ==Problem 5== How much closer would the star have to be to produce the deceleration of Van Maanen's star for each force? ==Hypotheses== {{main|Hypotheses}} # In astronomy observations usually consist of detection of radiation followed by analysis which usually includes assumptions about the forces and fields observed. # The four known forces or interactions all stem from an electromagnetic type source that manifests itself at varying intensities depending on the collection of particles. ==See also== {{div col|colwidth=20em}} * [[Radiation/Astronomy|Radiation astronomy]] {{Div col end}} ==References== {{reflist|2}} ==External links== * [http://www.iau.org/ International Astronomical Union] * [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED] * [http://nssdc.gsfc.nasa.gov/ NASA's National Space Science Data Center] * [http://www.osti.gov/ Office of Scientific & Technical Information] * [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System] * [http://www.scirus.com/srsapp/advanced/index.jsp?q1= Scirus for scientific information only advanced search] * [http://cas.sdss.org/astrodr6/en/tools/quicklook/quickobj.asp SDSS Quick Look tool: SkyServer] * [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database] * [http://simbad.harvard.edu/simbad/ SIMBAD Web interface, Harvard alternate] * [http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp Spacecraft Query at NASA.] * [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl Universal coordinate converter] <!-- footer templates --> {{Charge ontology}}{{tlx|Flight resouces}}{{tlx|Principles of radiation astronomy}}{{tlx|Radiation astronomy resources}}{{tlx|Repellor vehicle}}{{tlx|Technology resources}}{{Sisterlinks|Energy}} <!-- categories --> [[Category:Abstractions/Problems]] [[Category:Astronomy learning projects/Problems]] [[Category:Astrophysics/Problems]] [[Category:Entities/Problems]] [[Category:Radiation astronomy/Problems]] [[Category:Technology/Problems]] 6h071eg5mpy6a8us0laqsx1mezjusar 6 158647 2412475 1412167 2022-08-07T03:43:51Z Marshallsumter 311529 /* Licensing */ wikitext text/x-wiki == Summary == These images both depict the same area - the region of ionized gas around the nucleus of the bright Seyfert galaxy NGC 4151. [[Category:Astronomy images]] == Licensing == {{Information1 |Description = These images both depict the same area - the region of ionized gas around the nucleus of the bright Seyfert galaxy NGC 4151. |Source = The image appears on a website entitled, "The interaction of jets and clouds in NGC 4151" at url=http://www.astr.ua.edu/keel/agn/ngc4151stis.html. |Date = October 2003 |Author = John Hutchings et al. in Astrophysical Journal Letters 492, L115 (1998). |Rationale = No free licensed or public domain alternatives known to exist to show hese images both depicting the same area - the region of ionized gas around the nucleus of the bright Seyfert galaxy NGC 4151. |Permission = Fair Use }} {{Fairuse}} njqa4o8gmn7oyj9ngabfxnizk1o1oq6 0 168246 2412437 2398280 2022-08-07T01:39:47Z Marshallsumter 311529 /* Opticals */ wikitext text/x-wiki [[Image:Galactic.jpg|thumb|right|250px|This is a Hubble Space Telescope Image of NGC 4414. Credit: Hubble Heritage Team (AURA/STScI/NASA).{{tlx|free media}}]] [[Image:Pic iroberts1.jpg|thumb|right|250px|This is an image of Messier 31, the Andromeda galaxy from 1899. Credit: Isaac Roberts.]] "In 1995, the majestic spiral galaxy NGC 4414 was imaged by the Hubble Space Telescope as part of the HST Key Project on the Extragalactic Distance Scale. [The galaxy was] observed ... on 13 different occasions over the course of two months."<ref name=Freedman>{{ cite web |author=Wendy Freedman |title=MAGNIFICENT DETAILS IN A DUSTY SPIRAL GALAXY |publisher=NASA Goddard Space Flight Center |location=Greenbelt, Maryland USA |date=1999 |url=http://nssdc.gsfc.nasa.gov/photo_gallery/caption/hst_ngc4414_9925.txt |accessdate=2014-10-28 }}</ref> "Images were obtained with Hubble's Wide Field Planetary Camera 2 (WFPC2) through three different color filters."<ref name=Freedman/> "Based on [...] careful brightness measurements of variable stars in NGC 4414, [...] an accurate determination of the distance to the galaxy [was made]."<ref name=Freedman/> "The resulting distance to NGC 4414, 19.1 megaparsecs or about 60 million light-years, along with similarly determined distances to other nearby galaxies, contributes to astronomers' overall knowledge of the rate of expansion of the universe. The Hubble constant (H0) is the ratio of how fast galaxies are moving away from us to their distance from us. This astronomical value is used to determine distances, sizes, and the intrinsic luminosities for many objects in our universe, and the age of the universe itself."<ref name=Freedman/> "Due to the large size of the galaxy compared to the WFPC2 detectors, only half of the galaxy observed was visible in the datasets collected by the Key Project astronomers in 1995. In 1999, the Hubble Heritage Team revisited NGC 4414 and completed its portrait by observing the other half with the same filters as were used in 1995. The end result is a stunning full-color look at the entire dusty spiral galaxy. The new Hubble picture shows that the central regions of this galaxy, as is typical of most spirals, contain primarily older, yellow and red stars. The outer spiral arms are considerably bluer due to ongoing formation of young, blue stars, the brightest of which can be seen individually at the high resolution provided by the Hubble camera. The arms are also very rich in clouds of interstellar dust, seen as dark patches and streaks silhouetted against the starlight."<ref name=Freedman/> '''Standard-candles astronomy''' is the astronomical effort to find, study and develop standard-candle candidates for use as standard candles. '''Standard candles''' are stars in [[Radiation astronomy/Visuals|visual astronomy]] that may be used to calculate distances because their characteristics are, or appear to be, distance independent. {{clear}} ==Colors== {{main|Radiation astronomy/Colors}} [[Image:B-, R-, I-, and H-band Tully-Fisher relations.gif|thumb|right|250px|These graphs show ''B''-, ''R''-, ''I''-, and ''H''-band Tully-Fisher relations. Credit: Michael J. Pierce.]] "The empirical relationship between the luminosity of a spiral/irregular galaxy and its rotational velocity, known as the luminosity-line-width or Tully-Fisher relation (Tully and Fisher 1977, TF), has become one of the most widely used extragalactic distance indicators."<ref name=Pierce>{{ cite book |author=Michael J. Pierce |title=Tully-Fisher Relations |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby7_1.html |accessdate=2014-03-26 }}</ref> "Spiral and irregular galaxies are common in both the field and in all but the richest clusters. Consequently, the TF relation is an extremely valuable technique for extensive mapping of local large scale structure, the Hubble flow, and any associated peculiar velocities. In addition, since the local population is dominated by spirals and irregulars, the TF relations can, at least in principle, be calibrated directly by Cepheids. The TF relations provide an opportunity to go from local calibrating galaxies to the "smooth" Hubble flow in a single step."<ref name=Pierce/> Differences "in samples, extinction, and particularly line-width corrections can lead to quite different results."<ref name=Pierce/> "The necessary data consist of apparent magnitudes, usually corrected for Galactic and internal extinction, and some measure of rotation velocities, corrected for projection effects, for a sample of galaxies. Usually, the rotational velocity is obtained via the doppler broadening of the HI 21-cm line, although Fabry-Perot imaging and long slit rotation curves (both obtained via H) are useful as well."<ref name=Pierce/> "As originally proposed by [TF], the observational parameters of the TF relation are: (1) the photographic magnitude corrected for extinction, used as a measure of the luminosity of a galaxy, and (2) the global HI 21-cm line-width corrected for projection, used as a measure of the galaxy's rotational velocity. The raw measurements must be corrected for inclination effects, with the corrections for extinction and projection going in the opposite sense; when extinction corrections to the magnitudes are small (i.e., the galaxy is nearly face-on) the projection corrections for the rotational velocity are large, and vice versa. Consequently, considerable care must be taken to determine the proper corrections to the fundamental observables, and [there are] several different prescriptions for these corrections [...]. Nevertheless, any systematics introduced by the use of different correction schemes should in principle scale out, provided that the "local calibrators" and the sample galaxies are treated in the same way."<ref name=Pierce11>{{ cite web |author=Michael J. Pierce |title=Tully-Fisher Relations |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby7_1_1.html |accessdate=2014-03-26 }}</ref> "The publication of the ''Second Reference Catalog of Bright Galaxies'' by de Vaucouleurs et al. (1976) greatly increased the size of the existing data base of total magnitudes for a wide variety of galaxies. In addition, the completion of extensive HI 21-cm surveys [...] significantly improved the status of the line-width data. These data were subsequently used by several groups to examine both the utility of the TF relation as a distance indicator and the character of the local Hubble flow [...]. Similar photoelectric data were obtained [...] in the ''V'', ''r'', and ''IV'' (λ₀ ~ 1 µm) bands."<ref name=Pierce11/> "A significant improvement in the application of the TF relations occurred with the introduction of infrared H-band magnitudes (λ₀ = 1.6 µm) [... The] infrared offered two distinct advantages over visible wavelengths: first, that the extinction at H is only 10% that in ''B'', and second, that the infrared light is dominated by late-type giants. Thus, over the entire range of morphological types, the infrared is presumably a better tracer of the stellar mass than the B luminosity. Subsequent observations proved that the infrared Tully-Fisher relation (hereafter IRTF relation) has a significantly smaller dispersion than does the ''B''-band relation, implying that uncertainties in the extinction corrections for the blue light (which were still rather crude [...]), and/or variations in mean stellar population, were significant. [Restricting] the sample of bright spirals to those with inclinations greater than 45° and with no morphological peculiarities, following [TF produced] a distance modulus for the Virgo Cluster of 30.98 ± 0.09 mag (internal errors only), with the updated Hyades distance."<ref name=Pierce12>{{ cite web |author=Michael J. Pierce |title=Tully-Fisher Relations |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby7_1_2.html |accessdate=2014-03-26 }}</ref> "For luminosity, the choices are: (i) the total magnitude for the galaxy, or (ii) a suitably defined aperture magnitude. The former offers the advantage of having a relatively simple definition, while the latter has been a necessity for infrared photometry where until recently single element detectors were state of the art. For the rotational velocity parameter the choices are: (i) the maximum of the rotation curve (V_max), or (ii) the rotational velocity at a suitably chosen radius, perhaps corresponding to a particular aperture magnitude definition [...]."<ref name=Pierce2>{{ cite web |author=Michael J. Pierce |title=Tully-Fisher Relations |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby7_2.html |accessdate=2014-03-26 }}</ref> "Total magnitudes have been the choice for the luminosity parameter over visible wavelengths, even when derived through multiaperture photometry and template growth curves [...]. The use of total magnitudes was motivated by the availability of the data, the desire for a uniform magnitude system, and the expectation that the mass-to-light ratio of galaxies is constant, or at least a smooth function of mass. The latter is of particular concern at optical wavelengths where the large color difference between the bulge and disk components of spiral galaxies suggests differences in the mass-to-light ratio. This results in a significant morphological type dependence for the TF relations at bluer wavelengths. Consequently, a TF relation based on blue photometry through small apertures is of limited use [...]. [There are] numerous problems associated with multi-aperture photometry (e.g., centering errors, contaminating stars, the use of circular apertures and mean growth curves, etc.) [...]. With the introduction of CCDs, full growth curves using elliptical annuli can be easily constructed with contaminating regions (e.g., stars, cosmetic defects) suitably dealt with. The sky level for each image can also be easily estimated, provided the field of view is sufficiently large. Together, these advantages of CCD photometry can result in total magnitudes with a precision of ~ 5% [...]."<ref name=Pierce2/> Dispersions occur "for the TF relations of 0.37, 0.31, and 0.28 mag for the ''B'', ''R'' and ''I'' bands, respectively, from CCD photometry of a complete sample of galaxies in the Ursa Major Cluster. There is likely significant line-of-sight depth for this sample, since it spans about 8° on the sky, suggesting an intrinsic dispersion for the longer wavelength TF relations of ≤ 0.25 mag, or 12% in distance. Much of the improvement over previous work (typically with ~ 0.5 mag) was attributed to an increased accuracy of inclination estimates obtained via ellipses fitted to galaxy isophotes. For example, they found a significant improvement in the dispersion for the IRTF relation using photometry from the literature, provided that the line-widths were corrected with the improved inclinations. Apparently, the redder wavelengths are preferable, though the ''B''-band is still useful for comparative purposes."<ref name=Pierce2/> "Although the infrared aperture magnitudes have been very successful, they are not free of problems. The ''H''-band magnitude (''H''_-0.5) is defined to be the apparent H magnitude through an aperture size (A) given by log(''A'' / D₂₅^b,i) = -0.5, where D₂₅^b,i is the ''B''-band diameter of the galaxy at the 25 mag arcsec^-2 isophote, corrected for internal and Galactic extinction, as well as projection. This definition allows the use of small apertures that are more tractable with traditional infrared photometers, and also reduces the effect of the sky signal to a manageable level. (The ''H''-band sky is very bright: µ_''H'' ~ 13.4 mag arcsec^-2. Compare this with a mean H-band surface brightness, over D₂₅^b,i of µ_''H'' ~ 18 mag arcsec^-2 for a moderate luminosity spiral and ~ 21 mag arcsec^-2 for a typical dwarf irregular galaxy.) There are well-known observational techniques used in infrared astronomy to combat these high background levels. Nevertheless, nearby systems having low surface brightness and large angular size pose a special problem due to uncertainties in the sky level. In addition to the general problems associated with aperture photometry mentioned above, there is an additional difficulty in tying the infrared aperture size to the optical diameter [...]. Significant systematic errors have been introduced into some of the IRTF distance estimates from biased ''B''-band isophotal diameters, a consequence of using different catalogs of ''B''-band diameters for different distance ranges [...]. CCD photometry is almost a necessity to provide a uniform and unbiased aperture definition, at which point aperture photometry itself becomes of limited value. The application of infrared imaging technology over the next few years should alleviate most of these concerns, provided the data reach a sufficiently faint surface brightness level for total magnitudes to be estimated."<ref name=Pierce2/> "For the TF relations to be successfully applied, the galaxies must have detectable gas in essentially circular motion; otherwise, the estimate of V_max will be inaccurate. Although there is occasionally detectable HI in lenticular systems [...], defining a TF relation for E/S0 galaxies involves several complications: the origin of the gas is uncertain, the gas is usually patchy, its detection is difficult, and its motion may not be circular. Because of these difficulties (and the potential for significant M/L variations among early-type galaxies [...], it is best to limit samples of galaxies to types Sb - Irr having no signs of peculiar morphology, due, for example, to recent interactions. In addition, the galaxies must have enough gas in their exterior regions such that the observable rotation curve reaches a peak and Vmax can be adequately sampled. It is now clear that disk galaxies within the cores of even moderately poor clusters like Virgo suffer significant stripping of their outer envelope of HI gas [...]. Fortunately, only a few systems in Virgo are gas-stripped to radii within the turn-over in their rotation curves. The most serious cases also have morphological peculiarities and would likely have been excluded on this basis alone (e.g., NGC 4438). However, this remains an uncertainty for galaxies in the cores of more distant clusters; for these galaxies a full rotation curve may be necessary to assure that the rotation curves do indeed turn over."<ref name=Pierce25>{{ cite web |author=Michael J. Pierce |title=Tully-Fisher Relations |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby7_2_5.html |accessdate=2014-03-26 }}</ref> "The modest morphological type dependence mentioned [...] (i.e., earlier types having low luminosities for their line-widths [...]) is a consequence of late-type galaxies being systematically bluer than those of earlier type, coupled with the historical use of the ''B''-band TF relation. Because the effect decreases dramatically toward longer wavelengths, a likely cause is the smaller bulge-to-disk ratio and the larger fraction of young stars in the low mass, gas-rich systems. Some of the effect may also be the result of a decrease in dust content for the later morphological types [...]. If so, the assumption of a mean optical depth for all morphological types could contribute to a morphological type dependence, especially at the shorter wavelengths where extinction estimates would be significantly overestimated."<ref name=Pierce25/> "As mentioned above, the kinematics of lower luminosity irregular galaxies become progressively more dominated by turbulence and less by rotational motion. Consequently, the TF relations must progressively break down below some luminosity. [... The] TF relations for systems fainter than ''M''_''B'' ~ -15.0 become rather poorly defined as the corrections to the line-widths become large and the inclinations become more uncertain. With these factors in mind it is recommended that samples be limited to galaxies brighter than ''M''_''B'' ~ -16.0 for which the kinematics are dominated by rotation."<ref name=Pierce25/> Disk "galaxies have flat rotation curves over a broad range of luminosity and mass, with dark matter dominating at moderately large radii. At the same time, it is clear that the TF relation implies a "disk-halo conspiracy", such that the mass within some characteristic optical radius is coupled with the mass [...]. [Gravitational] interplay between the luminous and non-luminous matter in luminous disk galaxies is sufficient to redistribute the total mass in such a way as to produce the flat rotation curves which are observed. [... Low] mass galaxies are more susceptible to significant sweeping of gas via supernovae-driven winds during protogalactic collapse than are more massive systems due to a lower binding energy. In such a situation, star formation can be radically slowed and, in some cases, essentially quenched. As a result, these systems today would have a larger dark-to-luminous matter ratio than more massive systems since the dark matter (assumed to be non-baryonic) would be unaffected by radiation and gas dynamics."<ref name=Pierce3>{{ cite web |author=Michael J. Pierce |title=Tully-Fisher Relations |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby7_3.html |accessdate=2014-03-26 }}</ref> "''B''-, ''R''-, ''I''-, and ''H''-band Tully-Fisher relations for the Local Calibrators [in the set of graphs at the right] (top), Ursa Major cluster members (middle), and Virgo cluster members (bottom). It is apparent from the figures that the slope of the relations increases going to longer wavelengths and the dispersion decreases. The variation in slope is thought to arise from the differing contributions to the observed bandpass made by greater fraction of young stars found in the lower-luminosity systems. The smaller dispersion at longer wavelengths is likely due to a reduction in the sensitivity of these effects, as well as those expected from extinction variations. Nothe the much larger dispersion found for the Virgo cluster data."<ref name=Pierce4/> "There are now reliable distance estimates to three systems in or near the Local Group (M31, M33, NGC 3109), two systems in the M81 Group (M81 and NGC 2403), and one galaxy in the Sculptor Group (NGC 300). If, in addition to these systems, we could make use of the other members of the M81 and Sculptor groups with ''M''_''B'' ≤ -16.0, the total number of calibrators would be 15."<ref name=Pierce4>{{ cite web |author=Michael J. Pierce |title=Tully-Fisher Relations Absolute Calibration |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby7_4.html |accessdate=2014-03-26 }}</ref> The "absolute calibration of the TF relations [...] are shown as the upper sequence of panels in [the set of graphs at the right]."<ref name=Pierce4/> "The solid points represent those systems with individual distance estimates provided by Cepheids and/or RR Lyrae variables, while the open symbols represent additional members of the M81 and Sculptor groups (square and triangles, respectively). These are assumed to be at a mean distance given by those systems with individual distance estimates. The distribution of the additional members of the M81 Group is consistent with a small dispersion, implying a small line-of-sight depth for the group. The large dispersion for members of the Sculptor Group is consistent with previous suggestions of significant line-of-sight depth for the group [...]. The dispersions are ~ 0.20 mag for the systems with individual distance estimates, implying a precision in distance estimates from the TF relations of ~ 10% for an individual galaxy."<ref name=Pierce4/> "From the six local calibrating galaxies currently with individual distances the zero point of the calibration is established to an uncertainty of 0.08 mag [...]. The distances assumed for the local calibrators are all estimated relative to the distance of the LMC, which is tied to the Galactic calibration of Cepheids and RR Lyraes. The distance of the LMC is uncertain to ~ 7% [...] and so the primary source of error in the TF calibration lies with the Galactic calibration of the Cepheid ''P-L'' and ''P-L-C'' relations."<ref name=Pierce4/> A "significant systematic color difference between field (i.e., the "local calibrators") and cluster galaxies [...]. This results in a systematic variation in the estimated distances with bandpass. A small (~ 0.25 mag) correction is necessary in the ''B''-band in order to produce consistent distance estimates over all bandpasses and environments. The resulting calibration is given by:"<ref name=Pierce4/> :<math>M^{b,i}_B = -7.48(log(W^i_R) - 2.50) -19.55 + \Delta_B,</math> with an error on the <math>\Delta_B</math> of ± 0.14, :<math>M^{b,i}_R = -8.23(log(W^i_R) - 2.50) - 20.46 + \Delta_R,</math> with an error on the <math>\Delta_R</math> of ± 0.10, :<math>M^{b,i}_I = -8.72(log(W^i_R) - 2.50) - 20.94,</math> with an error on the last term of ± 0.10, :<math>M^{b,i}_H = -9.50(log(W^i_R) - 2.50) - 21.67,</math> with an error on the last term of ± 0.08, "where the correction factors δ_''B'' = 0.25 and δ_''R'' = 0.06 are required for statistically consistent distances between the different bands for "cluster galaxies". The corrections for "field-galaxies" should be zero. The existence of a "color correction" diminishes the utility of the ''B''-band relation and implies that longer wavelength bandpasses produce more reliable distance estimates. Note that these calibrations apply only to the [...] prescriptions for extinction and line-width corrections."<ref name=Pierce4/> {{clear}} ==Minerals== {{main|Radiation astronomy/Minerals}} [[Image:A further away schematic galaxy.gif|thumb|right|250px|This is a schematic galaxy to show brightness fluctuations. Credit: John L. Tonry.]] [[Image:A schematic galaxy.gif|thumb|left|250px|This diagram shows a schematic galaxy up close. Credit: John L. Tonry.]] "An image of an elliptical galaxy with milli-arcsec resolution would look like an enormous globular cluster, but even when the resolution is a thousand times worse, the discreteness of the stars causes measurable bumpiness in its surface brightness. This phenomenon, dubbed "surface brightness fluctuations", has been recognized for many years and is sometimes referred to as "incipient resolution". (When there are only a few stars per seeing resolution element, the eye perceives this characteristic mottling as barely resolved stars.)"<ref name=Tonry>{{ cite book |author=John L. Tonry |title=Surface Brightness Fluctuations |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby9_1.html |accessdate=2014-03-26 }}</ref> "Observations of external galaxies from which fluxes could be determined for individual stars, drawn from a significant part of the stellar luminosity function, would provide us a wealth of information about the distances of galaxies, their stellar populations, and their formation history. The first steps in this direction [involved resolving] individual Pop II stars in Local Group galaxies, and [observing] the top of the luminosity function in the bulge of M31 and NGC 205. [The] resolution required to observe any but the most luminous stars in galaxies significantly beyond the Local Group will not be achieved in the near future."<ref name=Tonry/> "Although we cannot determine the fluxes of individual stars without resolving them, we can nevertheless measure a very useful flux that is characteristic of the stellar population. [The] average profiles of globular clusters could best be determined at the bluest wavelengths where these fluctuations are minimized."<ref name=Tonry/> "The first measurement of surface brightness fluctuations [used] a method by which the fluctuations could be quantified. [A] completely empirical [approach used] calibration of fluctuation absolute magnitudes, observations of four galaxy clusters, and the application of fluctuations to the distance scale."<ref name=Tonry/> "The schematic galaxy at the right-hand side is twice as distant as the one on the left-hand side. Large dots symbolize giant stars, small ones main-sequence stars, and the grid represents the pixels of a CCD. Although the mean surface brightness collected in a CCD pixel is the same for the two galaxies, since ''f'' ∝ ''d''^-2 and n ∝ ''d''², the rms fluctuation from pixel to pixel relative to the mean varies as ''d''^-1. The image at the left is about as mottled as an ''I''-band image of a real galaxy would be at its effective radius if the galaxy were 200 kpc distant and the scale of CCD pixels were 1"."<ref name=Tonry/> "Surface brightness fluctuations are fundamentally a very simple effect, and [as each schematic galaxy] illustrates this with a cartoon of two galaxies, one twice as distant as the other. A grid representing a CCD's pixels is superposed on the images, and we must imagine that we can only measure the total flux within each pixel. We do not resolve individual stars in this case, but we can measure both the mean flux per pixel and the rms variation in flux from pixel to pixel. The two galaxies cannot be distinguished on the basis of mean flux per pixel (surface brightness) because the number of stars projected into a pixel of fixed angular size increases as distance squared (''d''²) and the flux per star decreases as ''d''^-2. If ''N'' is the mean number of stars, the mean flux is <math>N \bar{f}</math>, and the variance in flux is <math>N \bar{f}^2</math>, where <math>\bar{f}</math> is a mean flux per star. In schematic galaxies, ''N'' scales as ''d''², <math>\bar{f}</math> scales as ''d''^-2, and so the variance scales as ''d''^-2 and the rms scales as ''d''^-1. The galaxy which is twice as distant appears twice as smooth as the nearer galaxy. We can now determine the mean flux <math>\bar{f}</math> as the ratio of the variance and the mean."<ref name=Tonry/> "The mean luminosity, <math>\bar{L}</math>is simply related to the moments of the luminosity function of the stellar population we are sampling. If ''n''_i is the expectation of the number of stars of luminosity ''L''_i, the average luminosity is the ratio of the second and first moments of the luminosity function:"<ref name=Tonry/> :<math>\bar{L} = \Sigma n_i L^2_i/ \Sigma n_iL_i.</math> "This luminosity is roughly that of a giant star, and it is the first ratio of moments which has the dimensions of luminosity and is not dominated by the poorly known faint end of the luminosity function."<ref name=Tonry/> "There are two aspects to determining a distance from surface brightness fluctuations: (1) measurement of a fluctuation flux, and (2) conversion to a distance by assumption of a fluctuation luminosity. The two are coupled, but it is worth discussing them separately because they involve very different problems. It is useful to bear in mind that for typical old, metal rich stellar populations the absolute fluctuation magnitudes are roughly <math>\bar{M}_B</math> = +2.5, <math>\bar{M}_V</math> = +1.0, <math>\bar{M}_R</math> = +0.0, and <math>\bar{M}_I</math> = -1.5, with sensitivity to metallicity and age ranging from very high in ''B'' to fairly low in ''I''. [To summarize]:"<ref name=Tonry2>{{ cite book |author=John L. Tonry |title=Surface Brightness Fluctuations Method |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby9_2.html |accessdate=2014-03-26 }}</ref> (1) "This method is applicable to relatively dust-free systems such as E and S0 galaxies, spiral bulges, or globular clusters."<ref name=Tonry2/> (2) "Observation times must be long enough to collect more than 5-10 photons per source of apparent magnitude barm, and the point spread function must be well sampled and uniform. The formal measurement errors in barm can be as small as 3% times the square of the product of psf FWHM (in arcsec) and distance (in 1000 km s^-1)."<ref name=Tonry2/> (3) "The ''I'' band is preferred for distance measurement because <math>\bar{M}</math> is so bright at redder wavelengths that it overcomes the disadvantages of brighter sky background. Use of the ''I'' band also minimizes dust absorption. Observations of cluster galaxies shows us how barMI depends on mean color: redder populations have brighter <math>\bar{M}_I</math>. The intrinsic scatter of <math>\bar{M}_I</math> about this relation appears to be smaller than 0.08 magnitude."<ref name=Tonry2/> (4) "Calibration of the zero point of <math>\bar{M}_I</math> can be based on theoretical stellar populations, galactic globular clusters, or Local Group galaxies. The latter calibration has been made, and preliminary indications are that the first two will be consistent at the 0.10 magnitude level."<ref name=Tonry2/> "The basic procedure in measuring a fluctuation flux is to perform the usual observations and reductions so as to obtain an image which is as flat and uniform as possible and for which a photometric calibration is known."<ref name=Tonry2/> "Fluctuation fluxes are subject to the usual photometric calibration errors. Fundamentally, we need to transfer the known magnitude of a standard star to the power spectrum of the psf that we fit to a data power spectrum, since zero-wavenumber of a power spectrum is just the squared integral of the flux of the psf. Applying the same photometric reduction to the standard star and the psf star accomplishes this transfer with an accuracy of roughly 1-2%. Uncertainties in atmospheric extinction, galactic extinction, and extinction within the galaxy vary, but can also contribute an error of 1-2% (or more if there is considerable intervening dust)."<ref name=Tonry3>{{ cite web |author=John L. Tonry |title=Surface Brightness Fluctuations Uncertainties |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby9_3.html |accessdate=2014-03-26 }}</ref> {{clear}} ==Theoretical radiation standards== [[Image:65Cyb-LB3-apmag.jpg|250px|thumb|right|Asteroid 65 Cybele and 2 stars with their '''apparent magnitudes''' are labeled. Credit: [[c:user:Kheider|Kevin Heider]].{{tlx|free media}}]] [[Image:Artist's impression of vampire star.ogv|thumb|right|250px|This movie is an artist's impression of a Type Ia supernova. Credit: ESO/M. Kornmesser.]] '''Def.''' any "astronomical object of known diameter whose distance can then be calculated from the angle it subtends"<ref name=StandardRulerWikt>{{ cite web |author=[[wikt:User:SemperBlotto|SemperBlotto]] |title=standard ruler |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=3 October 2007 |url=https://en.wiktionary.org/wiki/standard_ruler |accessdate=11 June 2019 }}</ref> is called a '''standard ruler'''. '''Def.''' "a numerical measure of the brightness of a star, planet etc.; a decrease of 1 unit represents an increase in the light received by a factor of 2.512"<ref name=ApparentMagnitudeWikt>{{ cite web |author=[[wikt:User:SemperBlotto|SemperBlotto]] |title=apparent magnitude |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=15 August 2005 |url=https://en.wiktionary.org/wiki/apparent_magnitude |accessdate=11 June 2019 }}</ref> is called an '''apparent magnitude''' (<math>m\!\,</math>). '''Def.''' "the apparent magnitude [intrinsic luminosity]<ref name=AbsoluteMagnitudeWikt1>{{ cite web |author=[[wikt:User:Speednat|Speednat]] |title=absolute magnitude |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=15 July 2012 |url=https://en.wiktionary.org/wiki/absolute_magnitude |accessdate=11 June 2019 }}</ref> that a star etc. [celestial body]<ref name=AbsoluteMagnitudeWikt1/> would have if viewed from a distance of 10 parsecs [or about 32.6 light years]<ref name=AbsoluteMagnitudeWikt2>{{ cite web |author=[[wikt:User:Speednat|Speednat]] |title=absolute magnitude |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=24 December 2012 |url=https://en.wiktionary.org/wiki/absolute_magnitude |accessdate=11 June 2019 }}</ref>"<ref name=AbsoluteMagnitudeWikt>{{ cite web |author=[[wikt:User:SemperBlotto|SemperBlotto]] |title=absolute magnitude |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=15 August 2005 |url=https://en.wiktionary.org/wiki/absolute_magnitude |accessdate=11 June 2019 }}</ref> is called an '''absolute magnitude''' (<math>M\!\,</math>). '''Def.''' the "magnitude of a star in terms of the total amount of radiation received at all wavelengths"<ref name=BolometricMagnitudeWikt>{{ cite web |author=[[wikt:User:SemperBlotto|SemperBlotto]] |title=bolometric magnitude |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=11 December 2008 |url=https://en.wiktionary.org/wiki/bolometric_magnitude |accessdate=11 June 2019 }}</ref> is called a '''bolometric magnitude'''. '''Def.''' a "difference between the bolometric magnitude [<math>M_{bol}</math>] and and visual magnitude [<math>M_V</math>] of a star"<ref name=BolometricCorrectionWikt>{{ cite web |author=[[wikt:User:SemperBlotto|SemperBlotto]] |title=bolometric correction |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=22 January 2008 |url=https://en.wiktionary.org/wiki/bolometric_correction |accessdate=11 June 2019 }}</ref> is called a '''bolometric correction'''. :<math>M_{bol}=M_V+BC.</math> '''Def.''' any "astronomical object of known absolute magnitude"<ref name=StandardCandleWikt>{{ cite web |author=[[wikt:User:Prim Ethics|Prim Ethics]] |title=standard candle |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=12 March 2010 |url=https://en.wiktionary.org/wiki/standard_candle |accessdate=11 June 2019 }}</ref> is called a '''standard candle'''. Its luminosity distance [<math>D_L\!\,</math> in parsecs] can then be calculated from its apparent magnitude. :<math> M = m - 5 ((\log_{10}{D_L}) - 1)\!\,</math> An object's absolute magnitude may be calculated from its distance modulus (<math>\mu\!\,</math>) and apparent magnitude using :<math> M = m - {\mu}.\!\,</math> :<math> m = M + {\mu}.\!\,</math> Using the Sun (<math>\odot</math>) as a standard candle: :<math>M_{bol_{\rm star}} - M_{bol_{\rm Sun}} = -2.5 \log_{10} {\frac{L_{\rm star}}{L_{\odot}}},</math> Or, :<math>\frac{L_{\rm star}}{L_{\odot}} = 10^{((M_{bol_{\rm Sun}} - M_{bol_{\rm star}})/2.5)},</math> where :<math>L_{\odot}</math> is the Sun's (sol) luminosity (bolometric luminosity) :<math>L_{\rm star}</math> is the star's luminosity (bolometric luminosity) :<math>M_{bol_{\rm Sun}}</math> is the bolometric magnitude of the Sun :<math>M_{bol_{\rm star}}</math> is the bolometric magnitude of the star. :<math>m = H + 2.5 \log_{10}{\left(\frac{d_{OS}^2 d_{OOb}^2}{p(\chi) d_0^4}\right)}\!\,</math> where <math>H</math> is the absolute magnitude for a solar system object, the observer is Ob, the Sun (S), and the object is O. :<math>d_0\!\, = 1AU</math> :<math>\chi\!\, = phaseangle</math> The phase angle lies between the Sun-object and object-observer lines. :<math>\cos{\chi} = \frac{ d_{OOb}^2 + d_{OS}^2 - d_{ObS}^2 } {2 d_{OOb} d_{OS}}.\!\,</math> where <math>p(\chi)\!\,</math> is between 0 and 1 for the integration of reflected light. :<math>p(\chi) = \frac{2}{3} \left( \left(1 - \frac{\chi}{\pi}\right) \cos{\chi} + \frac{1}{\pi} \sin{\chi} \right).\!\,</math> :<math>d_{OOb}\!\,</math> where the distance (d) is between the observer (O) and the object (O). :<math>d_{OS}\!\,</math> where S is the Sun. :<math>d_{ObS}\!\,</math> "A supernova [in the movie at right] is one way that a star can end its life, exploding in a display of grandiose fireworks. One family of supernovae, called Type Ia supernovae, are of particular interest in cosmology as they can be used as standard candles to measure distances in the Universe and so can be used to calibrate the accelerating expansion that is driven by dark energy. One defining characteristic of Type Ia supernovae is the lack of hydrogen in their spectrum. Yet hydrogen is the most common chemical element in the Universe. Such supernovae most likely arise in systems composed of two stars, one of them being the end product of the life of sun-like stars, or white dwarfs. When such white dwarfs, acting as stellar vampires that suck matter from their companion, become heavier than a given limit, they become unstable and explode."<ref name=Kornmesser>{{ cite book |author=M. Kornmesser |title=Artist's impression of vampire star |publisher=ESO |location= |date=November 17, 2009 |url=http://www.eso.org/public/videos/eso0943b/ |accessdate=2014-03-25 }}</ref> {{clear}} ==Entities== {{main|Radiation astronomy/Entities}} [[Image:Luminosity function for globular clusters.gif|thumb|right|250px|The image is a graph of absolute magnitude versus frequency for globular clusters. Credit: William E. Harris.]] "The basic ideas [of using globular cluster luminosity functions (or GCLFs)] are illustrated in [the image at the right], which is a plot of the GCLF (the relative number ''Φ'' (m) of globular clusters as a function of magnitude m) for the Virgo giant ellipticals. The functional shape of ''Φ'' (m) is characterized by two simple parameters: the magnitude level or turnover point (m₀) where the population of clusters reaches a maximum; and the ''dispersion'' (''σ'' (m) or standard deviation of the distribution. As an empirical curve, the observations show that a Gaussian or log-normal function"<ref name=Harris>{{ cite web |author=William E. Harris |title=Method |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby4_2.html |accessdate=2014-03-26 }}</ref> :<math>\Phi(m) = A \times e^{-(m-m_0)^2/2{\sigma}^2},</math> "(where ''A'' is a normalization factor representing the peak population of globular clusters in the galaxy) does an excellent job of describing the GCLF in all galaxies studied to date. The log-normal fitting function gives a convenient way to parameterize the data and to intercompare the GCLFs from different galaxies. For the nearest ''rich'' systems of galaxies containing giant ellipticals (the Virgo and Fornax clusters) the deepest limits achieved at present reach to just about 1 σ fainter than the turnover (Harris et al. 1991)."<ref name=Harris/> "The actual use of the GCLF method, in its simplest form, goes as follows. The 'standard candle' is essentially the magnitude of the turnover, m₀. The goal in observing any distant galaxy is then to obtain photometry of its halo clusters which reaches sufficiently faint to estimate ''m''₀ accurately. In practice, the GCLF is normally found as the residual excess of starlike objects [...], after a background [luminosity function] LF for the field has been subtracted and photometric detection incompleteness at the faintest levels has been accounted for. By fitting an analytic interpolation function (such as the Gaussian model above) to the observed data, or else by using a maximum-likelihood fit to the total observed LF (GCLF plus background), the curve parameters (''A'', ''m''₀, σ) and their internal uncertainties can be estimated [...]. Adopting an absolute magnitude ''M''₀(turnover), and any necessary correction for foreground reddening, immediately yields the distance modulus."<ref name=Harris/> "If the limiting magnitude of the photometry goes clearly past the turnover as in the example of [the image at right], both ''m''₀ and σ can be solved for simultaneously. Ideally, the uncertainty e (''m''₀) would be equal to σ / √''N'', which for a sample size ''N'' of several hundred or more clusters should be ± 0.1 mag or smaller. In practice, the extra noise introduced by the background LF subtraction and completeness corrections, and the uncertainty in σ itself, lead to best-case results near e (''m''₀) ≃ ± 0.2 mag for a ''single galaxy''. However, if the limit of the data falls at or a bit short of the turnover, then the fitted solutions for ''m''₀ and σ become strongly correlated (Hanes and Whittaker 1987). It is still possible to estimate ''m''₀ to a typical precision of ± 0.3 mag, but only by performing a restricted function fit with an assumed, externally-known value of σ (hence the importance of the basic premise that the GCLF parameters are the same for galaxies of the same type [...]). An alternative is to adopt the well-defined Virgo GCLF ([shown in the image at the right]) as a fiducial function and to match any other galaxy to it by adjusting its distance relative to Virgo until a best fit is achieved."<ref name=Harris/> "The range of applicability of the GCLF method, and its basic strengths, are readily summarized."<ref name=Harris/> (1) "The GCLF works by far the best in giant E galaxies, which contain the largest globular cluster populations (''N'' ≥ 1000 is observationally feasible in such galaxies). On the other hand, the GCLF method is immensely more difficult to employ in late-type galaxies (Sc, Sd, Irr), and so in most cases it is difficult to match the GCLF distance scale ''directly'' with any of the Population I techniques."<ref name=Harris/> (2) "Because the clusters are nonvariable objects, they do not require repeated or carefully scheduled time-series observations. Telescope time is thus employed efficiently."<ref name=Harris/> (3) "Because it applies to objects in the halos of large galaxies, the method is free of a host of observational problems that affect all Population I standard candles, such as internal reddening differences, crowding and source confusion, and inclination-angle corrections."<ref name=Harris/> (4) "The distance range of the primary GCLF method is set by the limiting magnitude at which the turnover ''M''₀ is still detectable. With current ground-based capabilities, the limit should be near ''d'' ≃ 50 Mpc (Harris 1988a)."<ref name=Harris/> "So far, the motivation for the GCLF as a standard candle is almost totally empirical rather than theoretical. The astrophysical basis for its similarity from one galaxy to another is a challenging problem, and is probably less well understood than for any other standard candle currently in use. Because globular clusters are old-halo objects that probably predate the formation of most of the other stellar populations in galaxies [...], to first order it is not surprising that they look far more similar from place to place than their parent galaxies do. Methods for allowing clusters to form with average masses that are nearly independent of galaxy size or type [...]. Other constraints arising from cluster metallicity distributions and the early chemical evolution of the galaxies [may occur]. None of these yet serve as more than general guidelines for understanding why the early cluster formation process should be so nearly invariant in the early universe."<ref name=Harris/> "After the initial formation epoch, dynamical effects on the clusters including tidal shocking and dynamical friction, and evaporation of stars driven by internal relaxation and the surrounding tidal field, must also affect the GCLF within a galaxy over many Gyr, and these mechanisms might well behave rather similarly in large galaxies of many different types. [...] their importance decreases dramatically for distances ≳ 2-3 kpc from the galaxy nucleus, and for the more massive, compact clusters like present-day globulars. [...] close to the centers of the Virgo ellipticals has shown no detectable GCLF differences with radius. The implication is therefore that today's GCLF resembles the original mass formation spectrum of at least the brighter clusters, perhaps only slightly modified by dynamical processes. Many qualitative arguments can be constructed as to why the GCLFs should, or should not, resemble each other in different galaxies, but at the present time these must take a distant second place to the actual data."<ref name=Harris/> {{clear}} ==Emissions== {{main|Radiation astronomy/Emissions}} [[Image:1-agnsasanewst.jpg|thumb|right|250px|This graph depicts using AGNs to estimate distances. Credit: Darach Watson (et al).]] “Accurate distances to celestial objects are key to establishing the age and energy density of the Universe and the nature of dark energy.”<ref name=Watson>{{ cite book |author=Darach Watson |title=AGNs as a new standard candle? |publisher=Physics Organization |location= |date=September 27, 2011 |url=http://phys.org/news/2011-09-agns-standard-candle.html |accessdate=2014-03-27 }}</ref> “A distance measure using active galactic nuclei (AGN) has been sought for more than forty years, as they are extremely luminous and can be observed at very large distances.”<ref name=Watson/> Active "galactic nuclei are home to supermassive black holes which unleash powerful radiation. When this radiation ionizes nearby gas clouds, they also emit their own light signature. With both emissions in range of data gathering telescopes, all that’s needed is a way to measure the time it takes between the radiation signal and the ionization point. The process is called reverberation mapping."<ref name=Plotner>{{ cite book |author=Tammy Plotner |title=AGNs as a new standard candle? |publisher=Physics Organization |location= |date=September 27, 2011 |url=http://phys.org/news/2011-09-agns-standard-candle.html |accessdate=2014-03-27 }}</ref> “We use the tight relationship between the luminosity of an AGN and the radius of its broad line region established via reverberation mapping to determine the luminosity distances to a sample of 38 AGN.”<ref name=Watson/> “All reliable distance measures up to now have been limited to moderate redshift — AGN will, for the first time, allow distances to be estimated to z~4, where variations of dark energy and alternate gravity theories can be probed.”<ref name=Watson/> "The AGN Hubble diagram [is at the right]. The luminosity distance indicator τ is plotted as a function of redshift for 38 AGN with H lag measurements. On the right axis the luminosity distance and distance modulus (m-M) are shown using the surface brightness fluctuations distance to NGC3227 as a calibrator. The current best cosmology is plotted as a solid line. The line is not fit to the data but clearly follows the data well. Cosmologies with no dark energy components are plotted as dashed and dotted lines. The lower panel shows the logarithm of the ratio of the data compared to the current cosmology on the left axis, with the same values but in magnitudes on the right. The red arrow indicates the correction for internal extinction for NGC3516. The green arrow shows where NGC7469 would lie using the revised lag estimate. NGC7469 is our largest outlier and is believed to be an example of an object with a misidentified lag."<ref name=Plotner/> “The scatter due to observational uncertainty can be reduced significantly. A major advantage held by AGN is that they can be observed repeatedly and the distance to any given object substantially refined.”<ref name=Watson/> “The ultimate limit of the accuracy of the method will rely on how the BLR (broad-line emitting region) responds to changes in the luminosity of the central source. The current tight radius-luminosity relationship indicates that the ionisation parameter and the gas density are both close to constant across our sample.”<ref name=Watson/> {{clear}} ==X-rays== {{main|Radiation astronomy/X-rays|X-ray astronomy}} [[Image:SN2005ke labels.jpg|thumb|right|250px|Shown here is the explosion in optical, ultraviolet and X-ray wavelengths. Credit: NASA/Swift/S. Immler.]] Supernova 2005ke, which was detected in 2005, is a Type Ia supernova, an important "standard candle" explosion used by astronomers to measure distances in the universe. Shown here is the explosion in optical, ultraviolet and X-ray wavelengths. This is the first X-ray image of a Type Ia, and it has provided observational evidence that Type Ia are the explosion of a white dwarf orbiting a red giant star. An explosion called SN 2005ke is the first Type Ia supernova detected in X-ray wavelengths, and it is much brighter in the ultraviolet than expected. A Type Ia is an explosion of a white dwarf in orbit around either another white dwarf or a red giant star. The dense white dwarf can accumulate gas donated from the companion. When the dwarf reaches the critical mass of 1.4 solar masses, a thermonuclear explosion ensues. Type Ia are called "standard candles" and are used by astronomers to measure distances in the universe, because each Type Ia shines with a known luminosity. Immler's team says it has the first observational evidence to support one theory about the origin of these supernovae. Immler's group has found direct evidence in the X-ray and ultraviolet light of SN 2005ke that a white dwarf, now obliterated, was indeed orbiting a red giant. The scientists detected shock waves from the explosion ramming into gas from a red giant and found no evidence of a second white dwarf. This observation may help astronomers understand the birthplaces and evolution of these supernovae, so crucial to the field of cosmology and dark energy. {{clear}} ==Opticals== {{main|Radiation astronomy/Opticals|Optical astronomy}} [[Image:Hubble views new supernova in Messier 82.jpg|thumb|right|250px|Spiral galaxy Messier 82 has long been known for its remarkable starburst activity. Credit: NASA, ESA, A. Goobar (Stockholm University), and Hubble Heritage.{{tlx|free media}}]] "Spiral galaxy Messier 82 has long been known for its remarkable starburst activity, caused by interactions with its near neighbour Messier 81, and has been the subject of intense study for many years. On 21 January 2014, astronomers at the University of London Observatory in London, UK, pointed their telescope at the galaxy and spied something peculiar… an intensely bright spot seemed to have suddenly appeared within the galaxy [1]."<ref name=Cooke>{{ cite book |author=Ben Cooke |author2=Tom Wright |author3=Matthew Wilde |author4=Guy Pollack |title=Hubble views new supernova in Messier 82 |publisher=Space Telescope |location=Baltimore, Maryland USA |date=March 3, 2014 |url=http://www.spacetelescope.org/images/potw1409a/ |accessdate=2014-03-25 }}</ref> "This bright spot is actually a new supernova known as SN 2014J — the closest supernova to Earth in recent decades! Since its discovery, SN 2014J has been confirmed as a type Ia supernova, making it the closest of its type to Earth in over 40 years (since SN 1972E) [2]. This new NASA/ESA Hubble Space Telescope image is set against a previous mosaic of Messier 82 from 2006 (heic0604a), and shows the supernova as an intensely bright spot towards the bottom right of the frame."<ref name=Cooke/> "Type Ia supernovae are even more exciting for astronomers, as they have particular properties that we can use to probe the distant Universe. They are used as standard candles to measure distances and help us understand the scale of the cosmos. Catching such a supernova so soon after its explosion is very unusual; this early discovery will enable astronomers to explore its evolution in great detail, and to potentially infer the properties of its progenitor star."<ref name=Cooke/> "Messier 82 is several times more luminous than our Milky Way. Because it is only 12 million light-years away, it is one of the brighter galaxies in the northern sky. It can be found in the constellation of Ursa Major (The Great Bear). The supernova is currently visible through a modest amateur telescope, so why not see if you can spot it from your back garden?"<ref name=Cooke/> "The image shown here was taken on 31 January 2014 with Hubble’s Wide Field Camera 3. This image is inset into a photo mosaic of the entire galaxy taken in 2006 with Hubble’s Advanced Camera for Surveys."<ref name=Cooke/> {{clear}} ==Visuals== {{main|Radiation astronomy/Visuals|Visual astronomy}} [[Image:Blackbody spectral density.gif|thumb|right|250px|In this diagram, the photon spectral density of a blackbody at 6000 K (solid line) and 5000 K (dashed line) is illustrated. Credit: Douglas L. Welch.]] "Classical Cepheid variable stars are potentially the most accurate distance indicators available for the near-field (0.5 kpc - 10 Mpc). Their suitability as distance indicators arises from a number of factors including luminosity (''M''_''V'' = -2 to -7 mag), ease of detection through variability, precision, permanence, and understanding of the pulsation phenomenon. The classical (or Type I) Cepheids are young, disk objects and as such are only found in galaxies with recent star formation (primarily spiral or irregular galaxies)."<ref name=Welch>{{ cite book |author=Douglas L. Welch |title=Classical Cepheid Variable Stars |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby3_1.html |accessdate=2014-03-26 }}</ref> "The traditional path to a Cepheid-based distance to a galaxy has involved the following steps: (1) acquisition of plate material at several epochs; (2) discovery of variables; (3) magnitude estimates; (4) determination of periods; (5) estimation of mean magnitudes and colors on a standard system; (6) correction for absorption and distance estimate (given an absolute calibration)."<ref name=Welch1>{{ cite book |author=Douglas L. Welch |title=Classical Cepheid Variable Stars |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby3_2.html |accessdate=2014-03-26 }}</ref> "The differences between observations in the optical and near-infrared are sufficiently great that they warrant discussion. In this section, we will discuss the relative merits of optical (0.4 - 0.9 µm) and near-infrared (1.0 - 2.5 µm) observations of Cepheids. To accomplish this, we will consider, in turn, the wavelength dependence of observables, factors affecting the detected signal, and factors contributing to the noise."<ref name=Welch2>{{ cite book |author=Douglas L. Welch |title=Classical Cepheid Variable Stars |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby3_3.html |accessdate=2014-03-26 }}</ref> "Panoramic detectors used in the optical (0.4 - 0.9 µm) and the near-infrared (1.0 - 2.5 µm) are unity gain devices which produce a single electron for every detected photon. A blackbody at an effective temperature of 5500 K - typical of longer period Cepheids - has a slowly varying photon spectral density from the ''V'' bandpass (0.5 µm) out to ''K'' (2.2 µm). [...] However, the near-infrared spectra of stars of this effective temperature are strongly distorted by the H^- opacity minimum at 1.6 µm, centered on the photometric ''H'' bandpass. The effect of this opacity minimum is to allow radiation characteristic of a hotter source function to escape, and consequently a Cepheid will appear approximately 20% brighter at 1.6 µm than predicted by a blackbody spectrum scaled to, say, a ''V'' magnitude. (A second and less important effect which works in the same direction is the smaller amount of limb-darkening in the near-infrared.)"<ref name=Welch2/> "One consequence of the H^- opacity feature is the near constant ''H'' - ''K'' color of Cepheids (and for that matter, RR Lyrae stars) through their pulsation cycle. Since the ''H'' - ''K'' index varies extremely slowly in this temperature regime, a useful value for the total absorption for bandpasses in the 1 - 2.5 µm regime may be estimated on the basis of the ''H'' - ''K'' index at one phase point."<ref name=Welch2/> "In [the diagram at right], the photon spectral density of a blackbody at 6000 K (solid line) and 5000 K (dashed line) is illustrated. These effective temperatures represent the range encountered during the pulsation of a typical 10-day Cepheid. The positions of the ''B'', ''V'', ''I'', ''J'', ''H'', and ''K'' bandpasses are indicated. The number of detected photons from sources of these effective temperatures is proportional to the area under the curve for each bandpass. Wider bandpasses and higher quantum-efficiency detectors in the near infrared are particularly advantageous for the cooler and brighter long-period Cepheids. The increased near-infrared flux due to the lower H- opacity is not shown in this diagram."<ref name=Welch2/> "During pulsation, both the effective temperature and radius of a Cepheid vary. Since the relative change in radius rarely exceeds 5% in Cepheids (except for the longest period stars), the areal change is only of order 10%. Therefore, the large lightcurve amplitudes observed in the optical are primarily a reflection of the changes in surface brightness during the pulsation cycle, due to the changes in effective temperature. This variation is illustrated in [the diagram at the right], where the relative number of photons at minimum and maximum effective temperature are easily compared. For detection of variation, a short wavelength bandpass such as ''B'' or ''V'' is indicated, whereas for measurement of mean lightcurve characteristics, a long wavelength bandpass such as ''I'', ''J'', ''H'', or ''K'' is advantageous."<ref name=Welch2/> "Other well-known advantages of longer wavelength observation are the smaller total absorption, reduced sensitivity to flux redistribution due to metallicity, and reduced sensitivity to possible photometric contamination by an upper main-sequence companion."<ref name=Welch2/> "The bandwidths of the ''J'', ''H'', and ''K'' filters are typically 0.3 - 0.35 µm, compared to 0.2 µm at I and 0.08-0.10 µm at ''B'' or ''V''. Furthermore, the quantum efficiency of thinned CCDs at I is typically 30-35%, whereas quantum efficiencies greater than 60% over the ''J'', ''H'', and ''K'' bandpasses can be realized with HgCdTe detectors. The reflectivity of aluminum is 93-96% in the 1.0-2.5 µm region compared to 86% at ''I''."<ref name=Welch2/> "The difference between long-wavelength optical and infrared photometry is not substantial with respect to crowding. The ''K''-giant background against which Cepheids will be detected acts as a background having statistical fluctuations due to variations in the number of giant stars per pixel, but is significantly redder (''V'' - ''K'' = 3.3) than the variables (''V'' - ''K'' = 2.0). The effects of both crowding and sky noise are obviously reduced when the [full width at half maximum] FWHM of the stellar images is small (i.e., good seeing conditions)."<ref name=Welch2/> {{clear}} ==Blues== {{main|Radiation astronomy/Blues|Blue astronomy}} [[Image:Maximum magnitude-rate of decline for novae.gif|thumb|right|250px|This is a graph of the maximum magnitude-rate of decline for Galactic novae. Credit: Cohen (1985).]] "Novae possess a number of attributes that make them potentially valuable standard candles. They are luminous (approaching ''M''_''V'' = -10) and easy to recognize. Because they belong to an old stellar population, they are found predominantly in ellipticals and the bulges of spirals [...]; such environments are relatively dust-free and photometrically smooth, so that observations of novae beyond the Local Group are simpler and easier to interpret than observations of Cepheids. The available evidence suggests that observations of novae are not strongly affected by metallicity effects [...]. Finally, the calibration of novae as standard candles possesses relatively low intrinsic scatter [...], and is well understood theoretically [...]."<ref name=Pritchet>{{ cite book |author=Christopher J. Pritchet |title=Novae Background |publisher=Caltech |location=Pasadena, California |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby5_1.html |accessdate=2014-03-26 }}</ref> "All [or nearly all early] observations of extragalactic novae were made in continuum blue light."<ref name=Pritchet/> "The relationship between the maximum luminosity (magnitude) of a nova and its rate of decline (MMRD) is the usual starting point for deriving extragalactic distances. [L]uminous novae decay more rapidly than intrinsically faint novae [...]. The MMRD correlation for Galactic novae [has been confirmed. In addition there are] expansion parallaxes for a number of (previously undetected) spatially resolved shells around old Galactic novae. The physical basis for the MMRD relation [is that] more massive white dwarfs require less accreted matter to produce a thermonuclear runaway, and these lower mass envelopes can be ejected more rapidly; thus the most luminous novae are also the fastest."<ref name=Pritchet2>{{ cite web |author=Christopher J. Pritchet |title=Novae Method |publisher=Caltech |location=Pasadena, California |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby5_2.html |accessdate=2014-03-26 }}</ref> "To measure the distance to an external galaxy using the MMRD relation, it is necessary to determine the apparent magnitudes of novae at maximum light, and a mean rate of decline over two magnitudes. At present the calibration of the MMRD relation is in the ''B'' or ''m''_pg bands [...], so that observations through these bandpasses are preferred. It is essential that the observations sample the light curves of novae frequently enough near maximum light that ''m''^max can be estimated for the fastest (i.e., brightest) novae. The signal to noise ratio of the photometry should be high enough that novae discovered near maximum light can be followed at least 2 magnitudes below this level."<ref name=Pritchet2/> "The calibration can be effected in two ways: (1) using Galactic novae (in which case the use of the MMRD relation is a primary distance indicator, calibrated using geometrical techniques); or (2) using novae in M31 (in which case the distance scale is tied to the distance of M31)."<ref name=Pritchet3>{{ cite web |author=Christopher J. Pritchet |title=Novae Calibration |publisher=Caltech |location=Pasadena, California |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby5_3.html |accessdate=2014-03-26 }}</ref> At right is a graph of the maximum "magnitude-rate of decline relation for Galactic novae [...]. Closed symbols represent the novae designated ''high quality'' [...]; the solid line [from the equation below] is a least-squares fit to the high-quality data."<ref name=Pritchet3/> An "MMRD relation for Galactic novae is given by:"<ref name=Pritchet3/> :<math>M^{max}_V = -9.96 - 2.31 \times log \dot{m},</math> "where <math>\dot{m}</math> is the mean rate of decline (in mag d^-1) over the first 2 magnitudes. The mean scatter around this relation is ± 0.52 mag (1 ) for the high quality subset [data]. The data and fit are shown in [the graph at the right]. A slightly different result is obtained if the Galactic data are corrected for the constancy of ''M''_''B'' 15 days after maximum light [...]. In principle such a correction removes systematic errors in the absolute magnitudes, and results in a tighter MMRD correlation (σ ≃ 0.47 mag for ''all'' objects)."<ref name=Pritchet3/> "An alternate calibration of the MMRD relation is obtained by studying novae in the nearby spiral galaxy M31. [...] Only about 1/3 of the known novae in M31 have sufficient information in their light curves to be useful in determining the MMRD relation, and only about 1/4 of these possess good quality light curves with a well-observed maximum and rate of decay. [...] The 1 σ scatter around the mean relation depends on the subset of data chosen, and is in the range 0.20 - 0.28 mag [...]."<ref name=Pritchet3/> "To compare the M31 MMRD data with the mean Galactic MMRD, we assume (''m'' - ''M'')_''B'' ≃ 24.6 for M31 [...], (''B'' - ''V'')^max ≃ 0.23 [...], and (''m''_pg - ''B'') ≃ -0.17 [...]. With these assumptions, [...] the agreement between the Galactic and M31 MMRD relations is not good: the flattening observed in the M31 MMRD relation for bright and faint novae is not seen for Galactic novae. In addition, there appears to be a systematic offset of about 0.3 mag between the two MMRD relations, in the sense that Galactic novae are ''fainter'' than M31 novae. (This offset would increase to ~ 0.5 mag if the mean ''internal'' absorption for M31 novae were 0.2 mag [...]. However, we note that [there may not be] any systematic difference in the MMRD relation for novae close to and far from obvious dust patches in the bulge of M31.)"<ref name=Pritchet3/> "The flattening at faint magnitudes in the M31 MMRD relation may be due to Malmquist bias: in the presence of a magnitude limit, only the brightest novae will be detected. Whether or not this flattening is real has little effect on distance determinations outside the Local Group, because it is predominantly the most luminous novae that are detected at large distances. The flattening of the M31 MMRD relation for luminous novae is a more difficult problem. If one aligns the MMRD relations for Galactic and M31 novae in the ''linear'' (-1.3 ≲ log mdot ≲ -0.7) regime, then the luminous (log mdot ≲ -0.6) Galactic novae lie an average of ~ 0.8 mag above the M31 MMRD relation. One possible explanation for this is that maximum light for M31 novae is not as well sampled as it is for Galactic novae; this is particularly apparent in the light curves of Arp 1 and Arp 2 [...]."<ref name=Pritchet3/> "The shift of the Galactic and M31 MMRD relations relative to each other seems to imply that the true distance modulus of M31 is 0.3 mag less than the value obtained with ''quality'' distance indicators (e.g., RR Lyrae stars, IR observations of Cepheids). However, [...] this discrepancy vanishes if a different sample of objects is chosen to define the Galactic MMRD, and if uncorrected ''M''_''V''^max values are used for the Galactic nova sample (instead of ''M''_''V'' values corrected for the Buscombe - de Vaucouleurs effect). It is also worth noting that the theoretical MMRD [...] possesses a flatter slope than that observed for [...] data on Galactic novae, and hence provides a better overall fit to the S-shaped MMRD relation observed for M31 novae."<ref name=Pritchet3/> It "should be noted that the Galactic MMRD relation is defined with far fewer objects than is the case for M31; furthermore, the overall quality of the Galactic data (as demonstrated by the scatter in the MMRD relation) is considerably lower than for M31, probably due to such effects as uncertain Galactic absorption, and due to the assumption of spherical symmetry that is inherent in Cohen's application of the expansion parallax technique [...]. In fact, the offset between the Galactic and M31 MMRD relations is almost exactly what would be expected if the prolate geometry of nova shells is not taken into account when applying the expansion parallax technique [...]."<ref name=Pritchet3/> "In view of all of the above, it seems somewhat safer to employ the M31 MMRD relation as the calibrator for the extragalactic distance scale. This makes the distance scale dependent on an assumed distance to M31. However, [...] there is concordance in most distance estimates for M31 (except those derived using novae!); using the M31 calibration is therefore a more prudent approach at the present time."<ref name=Pritchet3/> "Several other methods for using novae as distance indicators have been proposed in the literature. Here we give a brief discussion of some of these methods, and their limitations."<ref name=Pritchet5>{{ cite book |author=Christopher J. Pritchet |title=Novae Other Distance Indicators using Novae |publisher=Caltech |location=Pasadena, California |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby5_5.html |accessdate=2014-03-26 }}</ref> "<''M''₁₅>: [The] mean magnitude of an ensemble of novae 15 days after maximum light was a constant; from the most recent data on Galactic novae, [...] <''M''₁5> ≃ -5.60 ± 0.14, where the quoted error is the 1 σ error in the mean. The rough constancy of <''M''₁₅> is a consequence of the MMRD relation [...]. For Virgo cluster novae, <''B''₁₅> ≃ +26 if (''m'' - ''M'') = 31.5; hence the <''M''₁₅> distance indicator will be strongly affected by Malmquist bias at the distance of the Virgo cluster unless the observational completeness limit goes somewhat fainter than B > 26. Note that there are exceptional objects (e.g., M31 novae Arp 1, 2, and 3) that suggest this method be used with caution."<ref name=Pritchet5/> "''Luminosity Function of Novae'': The luminosity function of novae at maximum light is approximately Gaussian [with] the mean magnitude of this Gaussian to determine the distance to M31. [...] The most recent compilation of M31 nova data [...] appears to show a double-peaked luminosity function; [using] the magnitude of the minimum between the two peaks as a distance indicator. Yet another method is to use the integral luminosity function of novae at maximum light; this function is linear over a wide range of magnitude, and possesses a well-defined intercept [...]."<ref name=Pritchet5/> "The use of the luminosity function of novae at maximum light as a distance indicator demands large samples of novae that are essentially complete at the faintest magnitudes; it is therefore unlikely that this method will be useful for any but the nearest luminous galaxies (i.e., those with high nova rates). [Using] the dip between two peaks in the luminosity function is not completely reliable, because, [...] different samples of M31 novae have luminosity functions with very different structure. (The very existence of this dip is in some question [...]"<ref name=Pritchet5/> The "luminosity function of all M31 nova observations (i.e., random phases) possesses no useful information that can be used in determining extragalactic distances [...]."<ref name=Pritchet5/> "''Period of Visibility'': [There] exists a strong correlation between the mean period of visibility of novae (down to some limiting magnitude ''m''_lim, and the absolute magnitude that this ''m''_lim corresponds to. Application of this correlation (calibrated using M31 data) to the Virgo elliptical observations [...] yields a distance modulus that is similar to that obtained using the MMRD relation. This method needs complete samples of novae down to some chosen ''m''_lim, but the samples do not have to be large. (With a large sample of novae, it would in principle be possible to apply this technique at several different ''m''_lim values.)"<ref name=Pritchet5/> {{clear}} ==Oranges== {{main|Radiation astronomy/Oranges|Orange astronomy}} [[Image:Ngc416 red clump stars.jpg|thumb|right|250px|The image shows orange and red stars in NGC 416. Credit: Andrzej Udalski, Peter Garnavich and Krzysztof Stanek.]] [[Image:Hipparcos diagram red clump.gif|thumb|right|250px|This is the Hipparcos color-magnitude diagram. Credit: Hipparcos.]] [[Image:Hipparcos Hubble distribution.gif|thumb|right|250px|This image shows the variance in the I-band. Credit: Stanek and Garnavich (1998).]] "Stellar cluster NGC 416 [in the image at the right is] located in the nearby Small Magellanic Cloud galaxy."<ref name=Stanek>{{ cite book |author=Krzysztof Z. Stanek |title=Red Clump Stars as Distance Indicator |publisher=Ohio State University |location=Columbus, Ohio USA |date=January 21, 2000 |url=http://www.astronomy.ohio-state.edu/~kstanek/CfA/RedClump/ |accessdate=2014-03-27 }}</ref> "The cluster [in the image at the right] contains many red clump stars, allowing for accurate distance measurement to the host galaxy. This photograph was made with the 1.3-meter (51-inch) Warsaw University Telescope at Las Campanas Observatory, near La Sarena, Chile."<ref name=Stanek/> "The ideal distance indicator would be a standard candle abundant enough to provide many examples within reach of parallax measurements and sufficiently bright to be seen out to local group galaxies."<ref name=Stanek/> Red "clump stars (shown in the Hipparcos color-magnitude diagram [second image at the right]) precisely fit this description. These stars are the metal rich equivalent of the better known horizontal branch stars, and theoretical models predict that their absolute luminosity fairly weakly depends on their age and chemical composition. Indeed the absolute magnitude-color diagram of Hipparcos clearly shows how compact the red clump is."<ref name=Stanek/> The "variance in the I-band is only about 0.15 mag (see the [third figure at the right])."<ref name=Stanek/> "Red clump giants can provide a very precise estimate of the distances to metal-rich Galactic globular clusters and nearby galaxies."<ref name=Stanek/> {{clear}} ==Reds== {{main|Radiation astronomy/Reds|Red astronomy}} "Supernovae [especially Type Ia (SNe Ia)], as extremely luminous (''M''_''B'' ~ -19.5) point sources, offer an attractive route to extragalactic distances. [...] Type II supernovae have a wide range in peak absolute magnitude and can not be treated as standard candles. Distances to individual SNe II can be estimated by means of the expanding photosphere (Baade-Wesselink) and the expanding radiosphere methods, but only elementary applications based on simplifying assumptions have been made to SNe II beyond the Local Group [...]. [Applications] of the method to SN 1987A in the Large Magellanic Cloud [have been] based on detailed calculations [...]. Supernovae of Type Ib, Type Ic, or Type II-L may turn out to be good standard candles but the present samples are small and all three subtypes have the disadvantage of being less luminous than Type Ia."<ref name=Branch>{{ cite web |author=David Branch |title=Type-Ia Supernovae Background and Dispersion in Absolute Magnitude |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby6_1.html |accessdate=2014-03-26 }}</ref> "Supernovae of Type Ia lack hydrogen lines and helium lines in their optical spectra; during the first month after maximum light they do have a strong absorption feature produced by the red doublet (λ6347, λ6371 Å) of singly ionized silicon. [... One model is that] Type Ia supernovae are the result of the nuclear detonation of a white dwarf which is at or near the Chandrasekhar mass limit [...]. Since such stars are present in the old stellar populations of all galaxies (but see Foss et al. 1991), there is good reason to believe that Type Ia supernovae behave as standard candles."<ref name=Branch/> "Numerous analyses of unrestricted samples of SNe Ia, involving various assumptions about relative distances and interstellar extinction, have produced values of the dispersion in peak ''M''_pg or ''M''_''B'' that are generally consistent with [early results having a] determined σ = 0.6 mag. Smaller dispersions of 0.3-0.5 mag have been obtained by restricting the SN Ia samples to those beyond the Local Supercluster [...], in elliptical galaxies [...], in the Virgo cluster [...], and in the Coma cluster [...]. The restriction to remote samples lowers the dispersion by a combination of two effects: (1) the avoidance of the problem of uncertain relative distances for the nearby galaxies, and (2) the tendency to select against SNe Ia that are observationally subluminous (whether they are intrinsically subluminous or are highly extinguished)."<ref name=Branch/> A "small intrinsic dispersion for ordinary SNe Ia that may be ≲ 0.3 mag. Most SNe Ia that are observationally subluminous tend to be red and in inclined disk galaxies, and probably just suffer high interstellar extinction. The peculiar, intrinsically subluminous SN 1991bg also was red. If observationally faint events enter into samples of remote SNe Ia, in spite of the selection against them, they can be recognized by their colors, and, in the case of those that are intrinsically abnormal, by their spectra. There is not yet any solid evidence for anomalously ''bright'' SNe Ia."<ref name=Branch/> "From the Hubble diagram for [a] sample of 35 SNe Ia"<ref name=Branch/> :<math>M_B = -18.13 + 5 log h,</math> with an error on the first constant of ± 0.08, "where ''h'' is the Hubble constant in units of 100 km s^-1 Mpc^-1."<ref name=Branch/> "From a sample of 40 SNe"<ref name=Branch/> :<math>M_B = -18.36 + 5 log h,</math> with an error on the first constant of ± 0.04. "The difference is primarily due to the fact that [for the first equation no] corrections for parent-galaxy extinction, while [for the second] an inclination-dependent correction to those SNe Ia in spirals that appear to be subluminous [has been applied]. Perhaps the most accurate available estimate for the intrinsic absolute magnitude is [for] for nine SNe Ia in ellipticals:"<ref name=Branch/> :<math>M_B = -18.33 + 5 log h,</math> with an error on the first constant of ± 0.11. "The standard model for a Type Ia supernova is the thermonuclear disruption of a carbon-oxygen white dwarf that has accreted enough mass from a companion star to approach the Chandrasekhar mass [...]. The nuclear energy released in the explosion unbinds the white dwarf and provides the kinetic energy of the ejected matter, but adiabatic expansion quickly degrades the initial internal energy and the observable light curve is powered by delayed energy input from the radioactive decay of ⁵⁶Ni and ⁵⁶Co. This model brings with it a self-calibration of the peak luminosity. Arnett (1982a) predicted on the basis of an analytical model that the SN Ia peak luminosity would be equal to the instantaneous decay luminosity of the nickel and cobalt, in which case the peak luminosity follows directly from the ejected nickel mass and the rise time to maximum light. The rise time can be inferred from observation but owing to uncertainties in the physics of the nuclear burning front [...] the amount of synthesized and ejected ⁵⁶Ni cannot yet be accurately predicted by theory. [The] nickel mass can be estimated indirectly from spectra and light curves. The more nuclear burning, the more ⁵⁶Ni and kinetic energy, and the greater the blueshifts in the spectrum and the faster the decay of the light curve. [From] the blueshifts in the spectra [...] the nickel mass must be in the range 0.4 to 1.4 ''M''_⊙ [with] a value of 0.6 ''M''_⊙ (as in the particular carbon deflagration model W7 [...]). Adopting a rise time to maximum of 17 ± 3 days and distributing the luminosity according to the observed ultraviolet-deficient flux distribution of SNe Ia, [provides an] estimated ''M''_''B'' = -19.5^+0.4_-0.9) at bolometric maximum, which corresponds to ''M''_''B'' = -19.6 with limits of -19.2 and -20.5 at the time of maximum blue light a few days earlier."<ref name=Branch2>{{ cite book |author=David Branch |title=Type-Ia Supernovae Physical Basis and Self-Calibration |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby6_2.html |accessdate=2014-03-26 }}</ref> ==Infrareds== {{main|Radiation astronomy/Infrareds|Infrared astronomy}} [[Image:Standard Candle in the Wind.jpg|thumb|right|250px|The images show a standard candle. Credit: NASA/JPL-Caltech/M. Marengo (Iowa State).]] "This image layout [at right] illustrates how NASA's Spitzer Space Telescope was able to show that a "standard candle" used to measure cosmological distances is shrinking -- a finding that affects precise measurements of the age, size and expansion rate of our universe. The image on the left, taken by Spitzer in infrared light, shows Delta Cephei, a type of standard candle used to measure the distances to galaxies that are relatively close to us. Cepheids like this one are the first rungs on the so-called cosmological distance ladder -- a tool needed to measure farther and farther distances."<ref name=Marengo>{{ cite book |author=M. Marengo |title=Standard Candle in the Wind |publisher=Caltech |location=Pasadena, California USA |date=January 1, 2012 |url=http://www.spitzer.caltech.edu/images/3470-ssc2011-01a-Standard-Candle-in-the-Wind |accessdate=2014-03-25 }}</ref> "Spitzer showed that the star has a bow shock in front of it. This can be seen as the red arc shape to the left of the star, which is depicted in blue-green (the colors have been assigned to specific infrared wavelengths we can't see with our eyes). The presence of the bow shock told astronomers that Delta Cephei must have a wind that is forming the shock. This wind is made up of gas and dust blowing off the star. Before this finding, there was no direct proof that Cepheid stars could lose mass, or shrink."<ref name=Marengo/> "The finding is important because the loss of mass around a Cepheid can obscure the star's light, making it appear brighter in infrared observations, and dimmer in visible light, than it really is. This, in turn, affects calculations of how far away the star is. Even tiny inaccuracies in such distant measurements can cause the whole cosmological distance ladder to come unhinged."<ref name=Marengo/> "The diagram on the right illustrates how Delta Cephei's bow shock was formed. As the star speeds along through space, its wind hits interstellar gas and dust, causing it to pile up in the bow shock. A companion star to Delta Cephei, seen just below it, is lighting up the region, allowing Spitzer to better see the region. By examining the structure of the bow shock, astronomers were able to calculate how fast the star is losing mass."<ref name=Marengo/> "In this image, infrared light captured by the infrared array camera is blue and blue-green (3.6- and 4.5-micron light is blue and 8.0-micron light is blue-green). Infrared light captured by the multiband imaging photometer is colored green and red (24-micron light is green and 70-micron light is red)."<ref name=Marengo/> {{clear}} ==Oxygens== [[Image:Planetary nebulae H-R.gif|thumb|right|250px|The diagram is a schematic H-R showing the evolutionary tracks of planetary nebula central stars. Credit: Jacoby et al. 1989.]] At right is a "schematic H-R diagram showing the evolutionary tracks of planetary nebula [PN] central stars. The tracks illustrate the strong dependence of magnitude and lifetime with core mass: the luminosity of a helium burning central star goes approximately as ''L'' ~ M^3.5, but the lifetime of the object goes as τ ~ M^-9.5. It is these two relationships, coupled with a sharply peaked core-mass distribution, which cause the abrupt truncation in planetary-nebula luminosity function."<ref name=Jacoby>{{ cite book |author=Jacoby et al. 1989 |title=Planetary Nebulae |publisher=Caltech |location=Pasadena, California USA |date=1989 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby8_1.html |accessdate=2014-03-26 }}</ref> "It is common to think of using the brightest stars to determine extragalactic distances. Indeed, over 50 years ago, Hubble (1936a) first attempted to resolve stars in other galaxies to quantify the expansion of the universe, and since then, the use of blue and red supergiants for extragalactic distance determinations has been explored several times (e.g., Sandage and Tammann 1974, Humphreys 1983). However, only recently has it been appreciated that young planetary nebulae also fall into the "brightest stars" category and are therefore potentially useful as standard candles. As can be seen in the H-R diagram [at right], the central stars of these objects are almost as luminous as the brightest red supergiants - the fact that their continuum emission emerges in the far ultraviolet, instead of the optical or near infrared, does not affect their detectability. On the contrary, since their surrounding nebulae reprocess the EUV radiation into discrete emission lines, planetaries can be viewed through interference filters which suppress the starlight from the host galaxy. As a result, observations made through a narrow band [oxygen III 500.7 nm] 5007 filter can detect ~ 15% of the energy emitted from these extremely luminous objects, with little contamination and confusion from continuum sources."<ref name=Ciardullo>{{ cite book |author=R. Ciardullo |title=Planetary Nebulae |publisher=Caltech |location=Pasadena, California USA |date=1989 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby8_1.html |accessdate=2014-03-26 }}</ref> "Planetary nebulae have several advantages over other extragalactic distance indicators. Because PN are not associated with any one stellar population, they can be found in galaxies of all Hubble types, and hence are particularly valuable for probing the [elliptical] E and [intermediate] S0 galaxies which define the cores of large groups and clusters. Likewise, internal extinction is usually not a problem in extragalactic PN observations: unlike blue supergiants or Cepheids, PN can be found far away from star forming regions, in areas of the galaxy which are relatively dust free. Since PN are observed through narrow band filters which suppress the continuum, the identification and measurement of these objects does not require complex, crowded field photometric procedures, and, unlike variable star standard candles, PN observations are required only once. Perhaps most importantly, in a large galaxy there may be several hundred planetaries populating the brightest two magnitudes of the planetary nebula luminosity function (PNLF). With the luminosity function so well defined, distance derivations are straightforward, and the internal errors can be as small as 3% (cf. Jacoby et al. 1989)."<ref name=Ciardullo/> "Despite these facts, the use of PN to determine extragalactic distances is a relatively new phenomenon. The first suggestion that PN might be a useful standard candle can be found in the book ''Galaxies and Cosmology'' by Hodge (1966), where it is listed in Table 12.1 along with such well-known distance indicators as Cepheids, RR Lyrae, and novae. Actual PN distance measurements, however, were [not] made until the 1970s, when Ford and Jenner (1978) used a 50 Å wide λ 5007 filter and the SIT Video Camera on the Kitt Peak 4-m telescope to find and measure the brightest PN in the bulge of M81. Ford (1978) had noticed that the absolute [O III] λ 5007 flux of the brightest PN in each of seven Local Group galaxies varied by less than 25%. Thus, by comparing the [O III] λ 5007 fluxes of M81's brightest PN with those of the brightest PN found in M31, Ford and Jenner (1978) estimated the distance ratio between these two galaxies to be ~ 4. A few years later, Jacoby and Lesser (1981) used a similar argument to place limits on the distances to five Local Group dwarfs, and Lawrie and Graham (1983) estimated the distance modulus of NGC 300."<ref name=Ciardullo/> "None of the above results was exceptionally persuasive, however. Some of this skepticism arose from the analysis method which excluded all but the brightest objects from consideration. However, the main concern at the time was that little was known about the luminosity function of planetaries; hence the uncertainties associated with these distances were completely unknown. It is an irony of the subject that distances to Galactic planetary nebulae are extremely difficult to obtain, and that a single PN is definitely not a standard candle. (For instance, NGC 7027, one of the best studied Galactic PN has recent distance estimates that range from 178 pc [Daub 1982] to 1500 pc [Pottasch et al. 1982].) However, while a single PN may not be a standard candle, an ensemble of these objects can yield a well determined distance. The reason for this is the invariance of the [O III] λ 5007 planetary nebula luminosity function."<ref name=Ciardullo/> {{clear}} ==Materials== {{main|Chemicals/Materials|Radiation astronomy/Materials}} [[Image:SNe-samples-revised.jpg|thumb|right|250px|The images show necessary adjustments to Type Ia supernovae brightness. Credit: Supernova Factory.]] "Type Ia supernovae result from the explosions of white dwarf stars. These supernovae vary widely in peak brightness, how long they stay bright, and how they fade away, as the lower graph shows. Theoretical models (dashed black lines) seek to account for the differences, for example why faint supernovae fade quickly and bright supernovae fade slowly. A new analysis by the Nearby Supernova Factory indicates that when peak brightnesses are accounted for, as shown in the upper graph, the late-time behaviors of faint and bright supernovae provide solid evidence that the white dwarfs that caused the explosions had different masses, even though the resulting blasts are all “standard candles.”"<ref name=Preuss>{{ cite book |author=Paul Preuss |title=Standard-Candle Supernovae are Still Standard, but Why? |publisher=Lawrence Berkeley National Laboratory |location=Berkeley, California USA |date=March 3, 2014 |url=http://newscenter.lbl.gov/news-releases/2014/03/03/standard-candle-supernovae/ |accessdate=2014-03-25 }}</ref> "Sixteen years ago two teams of supernova hunters, one led by Saul Perlmutter of the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab), the other by Brian Schmidt of the Australian National University, declared that the expansion of the universe is accelerating – a Nobel Prize-winning discovery tantamount to the discovery of dark energy. Both teams measured how fast the universe was expanding at different times in its history by comparing the brightnesses and redshifts of Type Ia supernovae, the best cosmological “standard candles.”"<ref name=Preuss/> "These dazzling supernovae are remarkably similar in brightness, given that they are the massive thermonuclear explosions of white dwarf stars, which pack roughly the mass of our sun into a ball the size of Earth. Based on their colors and how fast they brighten and fade away, the brightnesses of different Type Ia supernovae can be standardized to within about 10 percent, yielding accurate gauges for measuring cosmic distances."<ref name=Preuss/> "Until recently, scientists thought they knew why Type Ia supernovae are all so much alike. But their favorite scenario was wrong."<ref name=Preuss/> "The assumption was that carbon-oxygen white dwarf stars, the progenitors of the supernovae, capture additional mass by stripping it from a companion star or by merging with another white dwarf; when they approach the Chandrasekhar limit (40 percent more massive than our sun) they experience thermonuclear runaway. Type Ia brightnesses were so similar, scientists thought, because the amounts of fuel and the explosion mechanisms were always the same."<ref name=Preuss/> “The Chandrasekhar mass limit has long been put forward by cosmologists as the most likely reason why Type Ia supernovae brightnesses are so uniform, and more importantly, why they are not expected to change systematically at higher redshifts.”<ref name=Aldering>{{ cite book |author=Greg Aldering |title=Standard-Candle Supernovae are Still Standard, but Why? |publisher=Lawrence Berkeley National Laboratory |location=Berkeley, California USA |date=March 3, 2014 |url=http://newscenter.lbl.gov/news-releases/2014/03/03/standard-candle-supernovae/ |accessdate=2014-03-25 }}</ref> “The Chandrasekhar limit is set by quantum mechanics and must apply equally, even for the most distant supernovae.”<ref name=Aldering/> "But a new analysis of normal Type Ia supernovae, led by SNfactory member Richard Scalzo of the Australian National University, a former Berkeley Lab postdoc, shows that in fact they have a range of masses. Most are near or slightly below the Chandrasekhar mass, and about one percent somehow manage to exceed it."<ref name=Preuss/> "While white dwarf stars are common, it’s hard to get a Chandrasekhar mass of material together in a natural way.”<ref name=Scalzo>{{ cite book |author=Richard Scalzo |title=Standard-Candle Supernovae are Still Standard, but Why? |publisher=Lawrence Berkeley National Laboratory |location=Berkeley, California USA |date=March 3, 2014 |url=http://newscenter.lbl.gov/news-releases/2014/03/03/standard-candle-supernovae/ |accessdate=2014-03-25 }}</ref> "A Type Ia starts in a two-star (or perhaps a three-star) system, because there has to be something from which the white dwarf accumulates enough mass to explode."<ref name=Preuss/> "Some models picture a single white dwarf borrowing mass from a giant companion."<ref name=Preuss/> “The most massive newly formed carbon-oxygen white dwarfs are expected to be around 1.2 solar masses, and to approach the Chandrasekhar limit a lot of factors would have to line up just right even for these to accrete the remaining 0.2 solar masses.”<ref name=Scalzo/> "If two white dwarfs are orbiting each other they somehow have to get close enough to either collide or gently merge, what Scalzo calls “a tortuously slow process.” Because achieving a Chandrasekhar mass seems so unlikely, and because sub-Chandrasekhar white dwarfs are so much more numerous, many recent models have explored how a Type Ia explosion could result from a sub-Chandrasekhar mass – so many, in fact, that Scalzo was motivated to find a simple way to eliminate models that couldn’t work."<ref name=Preuss/> "He and his SNfactory colleagues determined the total energy of the spectra of 19 normal supernovae, 13 discovered by the SNfactory and six discovered by others. All were observed by the SNfactory’s unique SNIFS spectrograph (SuperNova Integral Field Spectrograph) on the University of Hawaii’s 2.2-meter telescope on Mauna Kea, corrected for ultraviolet and infrared light not observed by SNIFS."<ref name=Preuss/> "A supernova eruption thoroughly trashes its white dwarf progenitor, so the most practical way to tell how much stuff was in the progenitor is by spectrographically “weighing” the leftover debris, the ejected mass. To do this Scalzo took advantage of a supernova’s layered composition."<ref name=Preuss/> "A Type Ia’s visible light is powered by radioactivity from nickel-56, made by burning carbon near the white dwarf’s center. Just after the explosion this radiation, in the form of gamma rays, is absorbed by the outer layers – including iron and lighter elements like silicon and sulfur, which consequently heat up and glow in visible wavelengths."<ref name=Preuss/> "But a month or two later, as the outer layers expand and dissipate, the gamma rays can leak out. The supernova’s maximum brightness compared to its brightness at late times depends on how much gamma radiation is absorbed and converted to visible light – which is determined both by the mass of nickel-56 and the mass of the other material piled on top of it."<ref name=Preuss/> "The SNfactory team compared masses and other factors with light curves: the shape of the graph, whether narrow or wide, that maps how swiftly a supernova achieves its brightest point, how bright it is, and how hastily or languorously it fades away. The typical method of “standardizing” Type Ia supernovae is to compare their light curves and spectra."<ref name=Preuss/> “The conventional wisdom holds that the light curve width is determined primarily or exclusively by the nickel-56 mass, whereas our results show that there must also be a deep connection with the ejected mass, or between the ejected mass and the amount of nickel-56 created in a particular supernova.”<ref name=Scalzo/> “The white dwarfs exploding as Type Ia supernovae have a range of masses, and the resulting light-curve width is directly proportional to the total mass involved in the explosion.”<ref name=Aldering/> "For a supernova whose light falls off quickly, the progenitor is a lot less massive than the Chandrasekhar mass – yet it’s still a normal Type Ia, whose luminosity can be confidently standardized to match other normal Type Ia supernovae."<ref name=Preuss/> "The same is true for a Type Ia that starts from a “classic” progenitor with Chandrasekhar mass, or even more. For the heavyweights, however, the pathway to supernova detonation must be significantly different than for lighter progenitors. These considerations alone were enough to eliminate a number of theoretical models for Type Ia explosions."<ref name=Preuss/> "Carbon-oxygen white dwarfs are still key. They can’t explode on their own, so another star must provide the trigger. For super-Chandrasekhar masses, two C-O white dwarfs could collide violently, or one could accrete mass from a companion star in a way that causes it to spin so fast that angular momentum supports it beyond the Chandrasekhar limit."<ref name=Preuss/> "More relevant for cosmolology, because more numerous, are models for sub-Chandrasekhar mass. From a companion star, a C-O white dwarf could accumulate helium, which detonates more readily than carbon – the result is a double detonation. Or two white dwarfs could merge. There are other surviving models, but the psychological “safety net” that the Chandrasekhar limit once provided cosmologists has been lost. Still, says Scalzo, the new analysis narrows the possibilities enough for theorists to match their models to observations."<ref name=Preuss/> “This is a significant advance in furthering Type Ia supernovae as cosmological probes for the study of dark energy, likely to lead to further improvements in measuring distances. For instance, light-curve widths provide a measure of the range of the star masses that are producing Type Ia supernovae at each slice in time, well back into the history of the universe."<ref name=Aldering/> {{clear}} ==Sun== {{main|Stars/Sun|Sun (star)}} :<math>M_{V\odot} = 4.83.</math> :<math>M_{bol\odot} = 4.75.</math><ref name=Strobel>{{ cite journal | author = G. Cayrel de Strobel | title = Stars resembling the Sun | journal = Astronomy and Astrophysics Review | volume = 7 | issue = 3 | pages = 243–88 | year = 1996 | doi = 10.1007/s001590050006 |bibcode = 1996A&ARv...7..243C }}</ref> ==Betelgeuse== {{main|Stars/Betelgeuse}} The star Betelgeuse may still be too far away for visual trigonometric parallax. Standard candles have probably been used to estimate its distance from the Sun. Estimates from visual trigonometric parallax may be available to evaluate the historical accuracy of standard stellar candles. In 1977 the first direct angular-diameter observations of 119 Tauri were made.<ref name=White>{{ cite journal |author=Nathaniel M. White |title=The Occultation of 119 Tauri and the Effective Temperatures of Three M Supergiants |journal=The Astrophysical Journal |month=December 1, |year=1980 |volume=242 |issue=12 |pages=646-56 |url=http://articles.adsabs.harvard.edu/full/1980ApJ...242..646W |arxiv= |bibcode=1980ApJ...242..646W |doi=10.1086/158501 |pmid= |accessdate=2014-03-26 }}</ref> As a spectral type M2.2 Iab information is inferred about Betelgeuse (a type M2.2 Iab) from the occultation measurements of 119 Tauri.<ref name=White/> The occultations were on January 31, and April 23, 1977. The spectral type of 119 Tau has been constant since 1940.<ref name=White/> In 1977, 119 Tauri (CE Tau) was a spectral type M2.2 Iab, with a spectral range of M2.0-M2.4 Iab-Ib.<ref name=White/> In 1977, Betelgeuse was a spectral type M2.0 Iab^-, with a range of M1.3-M2.8 Iab-Ib.<ref name=White/> For α Sco in 1980 it was M1.1 Iab with a range of M0.7-M1.5 Iab-Ib As of 2014, 119 Tauri is an M2Iab according to SIMBAD. As of 2014, Betelgeuse (alf Ori) is an M2Iab according to SIMBAD. "The spectral type of α Ori varies roughly with the 5.8 yr period and epoch [...] for brightness, radial velocity, and possible angular-diameter variations. Recently, α Ori has shown the latest spectral type between 1973 and 1975 and again in 1980 January-February with a spectral type of M2.8 Iab^-. Its spectral type was about M1.5 around 1969-1971 and again around 1977-1978. By 1982 or 1983, α Ori should again have a spectral type of about M1.5."<ref name=White/> In 1977, apparently α Scorpii (Antares) was an M2.2 Iab, but in 2014 it is an M1.5Iab-b. The standard candle being used in 1977 for spectral region K5-M4 is the CN (cyanide) index from the CN absorption in selected bands.<ref name=White/> The apparent magnitude needed for calculating an object's distance in pc is obtained using a photospheric magnitude received for the 1.04 µm flux peak, ''I''(104) in early-M stars.<ref name=White/> Near-infrared "photometry on the narrow-band eight-color system [...] has been obtained for these stars. The mean [CN] indices and spectral types derived from photometry of the three supergiants are"<ref name=White/> # 119 Tau, CN index = 18 ± 2, ''I''(104) mag = +0.84 ± 0.03, ''M''_V = -5.2 (-4.8 to -5.6), distance = 417 pc, # α Ori, CN index = 18 ± 3, ''I''(104) mag = -2.68 ± 0.03, ''M''_V = -5.2, (-4.5 to -5.8), distance = 96 pc, and # α Sco, CN index = 19 ± 3, ''I''(104) mag = -2.28 ± 0.02, ''M''_V = -5.5, (-4.5 to -5.9), distance = 107 pc. "The distance to α Ori is about half the value, 200 pc, that is almost universally used in the literature."<ref name=White/> "The direct evidence for a distance of 200 pc [to Betelgeuse] is a trigonometric parallax of 0.005, which is 10 times smaller than the expected error of measurement [0.005 ± 0.05 mas]."<ref name=White/> In 1977 using the absorption spectrum of cyanide believed to be applicable for the spectral region K5-M4 to produce a CN index and the relationship between apparent magnitude and absolute magnitude, a distance of 96 pc was estimated for Betelgeuse. Parallax measurements at that time estimated a distance of 200 pc, but the error was 10 times greater than the value derived.<ref name=White/> A parallax measurement by the satellite ''Hipparcos'' indicated a distance of 197 ± 45 pc published in 2008. While post 1980 adjustments were made to increase the estimated distance of Betelgeuse, the initial discrepancy is quite large, at least a factor of 2 using a standard candle. In 1977, the distance to Betelgeuse estimated by various standard candles suggested 200 pc, "almost universally used in the literature."<ref name=White/> ==SN 2005ke== [[Image:SN2005ke labels.jpg|thumb|300px|Supernova 2005ke, which was detected in 2005, is a Type Ia supernova, an important "standard candle" explosion used by astronomers to measure distances in the universe. Shown here is the explosion in optical, ultraviolet and X-ray wavelengths. This is the first X-ray image of a Type Ia, and it has provided observational evidence that Type Ia are the explosion of a white dwarf orbiting a red giant star. Credit: NASA/Swift/S. Immler.]] A Type Ia supernova is an explosion of a white dwarf in orbit around either another white dwarf or a red giant star. The dense white dwarf can accumulate gas donated from the companion. When the dwarf reaches the critical mass of 1.4 ''M''_⊙, a thermonuclear explosion ensues. As each Type Ia shines with a known luminosity, Type Ia are called "standard candles" and are used by astronomers to measure distances in the universe. SN 2005ke is the first Type Ia supernova detected in X-ray wavelengths, and it is much brighter in the ultraviolet than expected. {{clear}} ==Andromeda galaxy== [[Image:M31 xmm novae.jpg|thumb|right|250px|This image is a mosaic of XMM-Newton's European Photon Imaging Camera’s (EPIC) observations of the central region of M31 as seen from 2000 to 2004. Credit: W. Pietsch (MPE Garching, Germany), ESA/XMM Newton.]] "This image [on the right] is a mosaic of XMM-Newton's European Photon Imaging Camera’s (EPIC) observations of the central region of M31 as seen from 2000 to 2004."<ref name=Pietsch>{{ cite book |author=W. Pietsch |title=XMM-Newton Image of M31 |publisher=European Space Agency |location= |date=5 August 2007 |url=http://m.esa.int/spaceinimages/Images/2007/05/XMM-Newton_image_of_M_31 |accessdate=2016-02-12 }}</ref> "The color coding is such that red displays X-ray photons received in the energy band 0.2-0.5 keV, green in the 0.5-1 keV band and blue in the 1-2 keV band. The positions of ten counterparts of optical novae detected in these images are indicated with circles and nova names. Nova names are given omitting the M31N prefix."<ref name=Pietsch/> "It was detected that eleven out of the 34 novae that had exploded in the galaxy during the previous year were shining X-rays into space. An additional seven novae remained detectable in X-rays up to 10 years after outburst."<ref name=Pietsch/> {{clear}} ==Distances== For nearby objects: :<math> M = m + 5 (1 + \log_{10}{p})\!\,</math> :<math> m = M - 5 ( 1+ \log_{10}p).\!\,</math> where p is the parallax in arcseconds. "The use of elliptical galaxies as distance indicators developed from studies aimed at determining their physical properties. The discovery of the relationship between luminosity and central velocity dispersion, ''L'' ∝ σ⁴, by Faber and Jackson (1976) marks the beginning of the potential use of normal elliptical galaxies as standard candles. Following that discovery, automatic, quantitative techniques based on Fourier or cross correlation methods for measuring velocity dispersions came into frequent use [...]. The use of these quantitative methods led to a growth of work on the properties and distances of elliptical galaxies, notably the suggestion [...] of a second parameter at work in the Faber-Jackson relation and the use of that relation [...] to measure the infall of the Local Group towards the Virgo cluster. The uncertainty in the distance to a single galaxy in [a] use of the Faber-Jackson relation was 32%."<ref name=Davies>{{ cite book |author=Roger L. Davies |title=The ''D''_n-σ Relation for Elliptical Galaxies |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby10_1.html |accessdate=2014-03-26 }}</ref> "The distribution and physical properties of elliptical galaxies make them attractive as potential distance indicators because:"<ref name=Davies/> (1) They are luminous galaxies so that their global properties can be measured accurately at large distances. The Dn- method can be used to measure distances both within the Local Supercluster and out to distances more than twice that of the Coma cluster. (2) "They are strongly clustered so that many galaxies can contribute to the determination of the distance to an aggregate of galaxies. This increases the precision of the distance estimate and reduces systematic "Malmquist-like" biases."<ref name=Davies/> (3) "They have a single dominant old stellar population and are free of the obscuring effects of dust."<ref name=Davies/> "The method is, however, potentially sensitive to variations in the physical properties of ellipticals: residual star formation, the unknown distribution of intrinsic shapes, variations in the degree of rotational support, the presence of central velocity dispersion anomalies, and/or the presence of a weak disk."<ref name=Davies/> "Unfortunately there are no nearby examples of luminous elliptical galaxies that can be used for absolute calibration using primary indicators. Furthermore, there is no theoretical basis for an absolute calibration of the ''D''_n-σ relation. Thus, the method is best suited to measuring relative distances that can then be calibrated by some of the other methods discussed elsewhere in this review. For this reason the method has been applied primarily to measure the peculiar motions of galaxies and aggregates of galaxies, rather than to derive absolute distances for individual galaxies."<ref name=Davies/> "The implementation of the ''D''_n-σ method requires the measurement of the central velocity dispersion and luminosity profile (or curve of growth) of each galaxy to sufficient precision that the measurement errors do not contribute to the intrinsic uncertainty of the distance estimator (σ^1.2 / ''D''_n). [A] typical scatter of 23% in ''D''_n at fixed σ [occurs]. [The] single measurements of ''D''_n range in precision from 5-12% and for σ from 9-14% (these estimates were made from repeat measurements which were used to improve the precision of their measurements). Single measurements of this quality would contribute significantly to the scatter in ''D''_n in the best observed clusters. A reasonable aim for future work is to determine ''D''_n to 6%, and to 5%, which in the absence of cosmological scatter would generate a distance determination with an uncertainty ≤ 9%."<ref name=Davies2>{{ cite book |author=Roger L. Davies |title=The ''D''_n-σ Relation for Elliptical Galaxies Methods |publisher=Caltech |location=Pasadena, California USA |date=August 1992 |url=http://ned.ipac.caltech.edu/level5/Jacoby/Jacoby10_2.html |accessdate=2014-03-26 }}</ref> "If the peculiar motions of aggregates of galaxies (hypothesised to be at the same distance) are to be determined, then a measurement of recession velocity is required in addition to the parameters which enter into the distance estimator. (Of course, this can be obtained from the same observational data that was used to derive the velocity dispersions.) The measured galaxies must then be assigned to groups on the basis of position and recession velocity using an algorithm [...]."<ref name=Davies2/> ==Hypotheses== {{main|Hypotheses}} # Many of the standard candles have such a wide range of sizes that distance estimates are at best only good to an order of magnitude. # Photons reaching Earth from any source say nothing about its distance. ==See also== {{div col|colwidth=20em}} * [[Radiation astronomy/Hypervelocity stars|Hypervelocity stellar astronomy]] * [[Standard candles/Laboratory|Standard candles laboratory]] * [[Radiation astronomy/Standard candles/Quiz|Standard candles quiz]] * [[Stars/Astronomy|Stellar astronomy]] * [[Radiation astronomy/Stars|Stellar radiation astronomy]] * [[Stars/Sciences|Stellar science]] * [[Stars/Sun|Sun]] * [[Stars/X-ray classification|X-ray classification of stars]] {{Div col end}} ==References== {{reflist|2}} ==External links== * [http://www.iau.org/ International Astronomical Union] * [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED] * [http://nssdc.gsfc.nasa.gov/ NASA's National Space Science Data Center] * [https://en.wikiversity.org/w/index.php?title=Standard-candles astronomy&action=info Page views in the past 30 days] * [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System] * [http://cas.sdss.org/astrodr6/en/tools/quicklook/quickobj.asp SDSS Quick Look tool: SkyServer] * [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database] * [http://simbad.harvard.edu/simbad/ SIMBAD Web interface, Harvard alternate] * [http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp Spacecraft Query at NASA] * [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl Universal coordinate converter] <!-- footer templates --> {{tlx|Physics resources}}{{Principles of radiation astronomy}}{{tlx|Radiation astronomy resources}}{{tlx|Technology resources}}{{Sisterlinks|Standard candles}}{{Sisterlinks|Standard-candles astronomy}} <!-- categories --> [[Category:Astrophysics/Lectures]] [[Category:Distances/Lectures]] [[Category:Events/Lectures]] [[Category:Mathematics/Lectures]] [[Category:Radiation astronomy/Lectures]] [[Category:Technology/Lectures]] 3a0i5vmi6ejfzj16up6r401lrat8wlp 6 168498 2412479 1265195 2022-08-07T04:08:19Z Marshallsumter 311529 /* Licensing */ wikitext text/x-wiki == Summary == These Multi-angle Imaging SpectroRadiometer (MISR) images show the progression of a "loose tooth"—an iceberg calving from the Amery Ice Shelf. [[Category:Glaciology images]] == Licensing == {{Information1 |Description = These Multi-angle Imaging SpectroRadiometer (MISR) images show the progression of a "loose tooth"—an iceberg calving from the Amery Ice Shelf. |Source = The image appears on a website entitled, "State of the Cryosphere: Ice Shelves" at url=https://nsidc.org/cryosphere/sotc/iceshelves.html. |Date = 6 October 2011 |Author = Clare Averill and David J. Diner, Jet Propulsion Laboratory; and Helen A. Fricker, Scripps Institution of Oceanography |Rationale = No free licensed or public domain alternatives known to exist to show Multi-angle Imaging SpectroRadiometer (MISR) images of the progression of a "loose tooth"—an iceberg calving from the Amery Ice Shelf. |Permission = Fair Use }} {{Fairuse}} s7aotyoncpd8qmysg5bubizy471h9u9 6 168509 2412480 1265238 2022-08-07T04:11:37Z Marshallsumter 311529 /* Licensing */ wikitext text/x-wiki == Summary == Photos of the A54 iceberg calving from the Scar Inlet Shelf (the remainder of the Larsen Ice Shelf). [[Category:Glaciology images]] == Licensing == {{Information1 |Description = Photos of the A54 iceberg calving from the Scar Inlet Shelf (the remainder of the Larsen Ice Shelf). |Source = The image appears on a website entitled, "Status of the Cryosphere: Ice calving" at url=https://nsidc.org/cryosphere/sotc/iceshelves.html. |Date = 05 March 2006 |Author = Ted Scambos, National Snow and Ice Data Center, University of Colorado, Boulder, and NASA Moderate Resolution Imaging Spectroradiometer images courtesy NASA Earth Observatory. |Rationale = No free licensed or public domain alternatives known to exist to show photos of the A54 iceberg calving from the Scar Inlet Shelf (the remainder of the Larsen Ice Shelf). |Permission = Fair Use }} {{Fairuse}} 0256dk8b8vgf7n60fzfr6t2xitp2w7a 6 170338 2412476 1283426 2022-08-07T03:48:41Z Marshallsumter 311529 /* Licensing */ wikitext text/x-wiki == Summary == Rapids are before the Rhine Falls. [[Category:Hydromorphology images]] == Licensing == {{Information1 |Description = Rapids are before the Rhine Falls. |Source = The image appears on a website entitled, "Rapid" at url=https://en.wikipedia.org/wiki/Rapid. |Date = 12 May 2008 |Author = herbert.g and raxa |Rationale = No free licensed or public domain alternatives known to exist to show rapids before the Rhine Falls. |Permission = Fair Use }} {{Fairuse}} b5k6s20ze6ahn1kikpsqo42puzqb32a 6 170736 2412481 1287426 2022-08-07T04:14:30Z Marshallsumter 311529 /* Licensing */ wikitext text/x-wiki == Summary == This is an ultra-rich in carbon MM found near the CONCORDIA station in Antarctica. [[Category:Micrometeorite images]] == Licensing == {{Information1 |Description = This is an ultra-rich in carbon MM found near the CONCORDIA station in Antarctica. |Source = The image appears on a website entitled, "Des poussières de comètes en Antarctique ?" at url=http://www2.cnrs.fr/presse/communique/1873.htm. |Date = 6 mai 2010 |Author = J. Duprat, E. Dobrică, C. Engrand, J. Aléon, Y. Marrocchi, S.Mostefaoui, A. Meibom, H. Leroux, J.-N. Rouzaud, M. Gounelle and F. Robert |Rationale = No free licensed or public domain alternatives known to exist to show an ultra-rich in carbon MM found near the CONCORDIA station in Antarctica. |Permission = Fair Use }} {{Fairuse}} 1hpksjlegsic5z3i6jbwv84lso86abl 0 171005 2412347 2412119 2022-08-06T13:35:08Z Young1lim 21186 /* Geometric Series Examples */ wikitext text/x-wiki Many of the functions that arise naturally in mathematics and real world applications can be extended to and regarded as complex functions, meaning the input, as well as the output, can be complex numbers <math>x+iy</math>, where <math>i=\sqrt{-1}</math>, in such a way that it is a more natural object to study. '''Complex analysis''', which used to be known as '''function theory''' or '''theory of functions of a single complex variable''', is a sub-field of analysis that studies such functions (more specifically, '''holomorphic''' functions) on the complex plane, or part (domain) or extension (Riemann surface) thereof. It notably has great importance in number theory, e.g. the [[Riemann zeta function]] (for the distribution of primes) and other <math>L</math>-functions, modular forms, elliptic functions, etc. <blockquote>The shortest path between two truths in the real domain passes through the complex domain. — [[wikipedia:Jacques_Hadamard|Jacques Hadamard]]</blockquote>In a certain sense, the essence of complex functions is captured by the principle of [[analytic continuation]].{{mathematics}} ==''' Complex Functions '''== * Complex Functions ([[Media:CAnal.1.A.CFunction.20140222.Basic.pdf|1.A.pdf]], [[Media:CAnal.1.B.CFunction.20140111.Octave.pdf|1.B.pdf]], [[Media:CAnal.1.C.CFunction.20140111.Extend.pdf|1.C.pdf]]) * Complex Exponential and Logarithm ([[Media:CAnal.5.A.CLog.20131017.pdf|5.A.pdf]], [[Media:CAnal.5.A.Octave.pdf|5.B.pdf]]) * Complex Trigonometric and Hyperbolic ([[Media:CAnal.7.A.CTrigHyper..pdf|7.A.pdf]], [[Media:CAnal.7.A.Octave..pdf|7.B.pdf]]) '''Complex Function Note''' : 1. Exp and Log Function Note ([[Media:ComplexExp.29160721.pdf|H1.pdf]]) : 2. Trig and TrigH Function Note ([[Media:CAnal.Trig-H.29160901.pdf|H1.pdf]]) : 3. Inverse Trig and TrigH Functions Note ([[Media:CAnal.Hyper.29160829.pdf|H1.pdf]]) ==''' Complex Integrals '''== * Complex Integrals ([[Media:CAnal.2.A.CIntegral.20140224.Basic.pdf|2.A.pdf]], [[Media:CAnal.2.B.CIntegral.20140117.Octave.pdf|2.B.pdf]], [[Media:CAnal.2.C.CIntegral.20140117.Extend.pdf|2.C.pdf]]) ==''' Complex Series '''== * Complex Series ([[Media:CPX.Series.20150226.2.Basic.pdf|3.A.pdf]], [[Media:CAnal.3.B.CSeries.20140121.Octave.pdf|3.B.pdf]], [[Media:CAnal.3.C.CSeries.20140303.Extend.pdf|3.C.pdf]]) ==''' Residue Integrals '''== * Residue Integrals ([[Media:CAnal.4.A.Residue.20140227.Basic.pdf|4.A.pdf]], [[Media:CAnal.4.B.pdf|4.B.pdf]], [[Media:CAnal.4.C.Residue.20140423.Extend.pdf|4.C.pdf]]) ==='''Residue Integrals Note'''=== * Laurent Series with the Residue Theorem Note ([[Media:Laurent.1.Residue.20170713.pdf|H1.pdf]]) * Laurent Series with Applications Note ([[Media:Laurent.2.Applications.20170327.pdf|H1.pdf]]) * Laurent Series and the z-Transform Note ([[Media:Laurent.3.z-Trans.20170831.pdf|H1.pdf]]) * Laurent Series as a Geometric Series Note ([[Media:Laurent.4.GSeries.20170802.pdf|H1.pdf]]) === Laurent Series and the z-Transform Example Note === * Overview ([[Media:Laurent.4.z-Example.20170926.pdf|H1.pdf]]) ====Geometric Series Examples==== * Causality ([[Media:Laurent.5.Causality.1.A.20191026n.pdf|A.pdf]], [[Media:Laurent.5.Causality.1.B.20191026.pdf|B.pdf]]) * Time Shift ([[Media:Laurent.5.TimeShift.2.A.20191028.pdf|A.pdf]], [[Media:Laurent.5.TimeShift.2.B.20191029.pdf|B.pdf]]) * Reciprocity ([[Media:Laurent.5.Reciprocity.3A.20191030.pdf|A.pdf]], [[Media:Laurent.5.Reciprocity.3B.20191031.pdf|B.pdf]]) * Combinations ([[Media:Laurent.5.Combination.4A.20200702.pdf|A.pdf]], [[Media:Laurent.5.Combination.4B.20201002.pdf|B.pdf]]) * Properties ([[Media:Laurent.5.Property.5A.20220105.pdf|A.pdf]], [[Media:Laurent.5.Property.5B.20220126.pdf|B.pdf]]) * Applications ([[Media:Laurent.6.Application.6A.20220805.pdf|A.pdf]], [[Media:Laurent.5.Application.6B.20220723.pdf|B.pdf]]) * Double Pole Case :- Examples ([[Media:Laurent.5.DPoleEx.7A.20220722.pdf|A.pdf]], [[Media:Laurent.5.DPoleEx.7B.20220720.pdf|B.pdf]]) :- Properties ([[Media:Laurent.5.DPoleProp.5A.20190226.pdf|A.pdf]], [[Media:Laurent.5.DPoleProp.5B.20190228.pdf|B.pdf]]) ====The Case Examples==== * Example Overview : ([[Media:Laurent.4.Example.0.A.20171208.pdf|0A.pdf]], [[Media:Laurent.6.CaseExample.0.B.20180205.pdf|0B.pdf]]) * Example Case 1 : ([[Media:Laurent.4.Example.1.A.20171107.pdf|1A.pdf]], [[Media:Laurent.4.Example.1.B.20171227.pdf|1B.pdf]]) * Example Case 2 : ([[Media:Laurent.4.Example.2.A.20171107.pdf|2A.pdf]], [[Media:Laurent.4.Example.2.B.20171227.pdf|2B.pdf]]) * Example Case 3 : ([[Media:Laurent.4.Example.3.A.20171017.pdf|3A.pdf]], [[Media:Laurent.4.Example.3.B.20171226.pdf|3B.pdf]]) * Example Case 4 : ([[Media:Laurent.4.Example.4.A.20171017.pdf|4A.pdf]], [[Media:Laurent.4.Example.4.B.20171228.pdf|4B.pdf]]) * Example Summary : ([[Media:Laurent.4.Example.5.A.20171212.pdf|5A.pdf]], [[Media:Laurent.4.Example.5.B.20171230.pdf|5B.pdf]]) ==''' Conformal Mapping '''== * Conformal Mapping ([[Media:CAnal.6.A.Conformal.20131224.pdf|6.A.pdf]], [[Media:CAnal.6.A.Octave..pdf|6.B.pdf]]) go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Complex analysis]] 9pntxioys68trwwkkrlb4gr6p93e0py 2412349 2412347 2022-08-06T13:36:27Z Young1lim 21186 /* Geometric Series Examples */ wikitext text/x-wiki Many of the functions that arise naturally in mathematics and real world applications can be extended to and regarded as complex functions, meaning the input, as well as the output, can be complex numbers <math>x+iy</math>, where <math>i=\sqrt{-1}</math>, in such a way that it is a more natural object to study. '''Complex analysis''', which used to be known as '''function theory''' or '''theory of functions of a single complex variable''', is a sub-field of analysis that studies such functions (more specifically, '''holomorphic''' functions) on the complex plane, or part (domain) or extension (Riemann surface) thereof. It notably has great importance in number theory, e.g. the [[Riemann zeta function]] (for the distribution of primes) and other <math>L</math>-functions, modular forms, elliptic functions, etc. <blockquote>The shortest path between two truths in the real domain passes through the complex domain. — [[wikipedia:Jacques_Hadamard|Jacques Hadamard]]</blockquote>In a certain sense, the essence of complex functions is captured by the principle of [[analytic continuation]].{{mathematics}} ==''' Complex Functions '''== * Complex Functions ([[Media:CAnal.1.A.CFunction.20140222.Basic.pdf|1.A.pdf]], [[Media:CAnal.1.B.CFunction.20140111.Octave.pdf|1.B.pdf]], [[Media:CAnal.1.C.CFunction.20140111.Extend.pdf|1.C.pdf]]) * Complex Exponential and Logarithm ([[Media:CAnal.5.A.CLog.20131017.pdf|5.A.pdf]], [[Media:CAnal.5.A.Octave.pdf|5.B.pdf]]) * Complex Trigonometric and Hyperbolic ([[Media:CAnal.7.A.CTrigHyper..pdf|7.A.pdf]], [[Media:CAnal.7.A.Octave..pdf|7.B.pdf]]) '''Complex Function Note''' : 1. Exp and Log Function Note ([[Media:ComplexExp.29160721.pdf|H1.pdf]]) : 2. Trig and TrigH Function Note ([[Media:CAnal.Trig-H.29160901.pdf|H1.pdf]]) : 3. Inverse Trig and TrigH Functions Note ([[Media:CAnal.Hyper.29160829.pdf|H1.pdf]]) ==''' Complex Integrals '''== * Complex Integrals ([[Media:CAnal.2.A.CIntegral.20140224.Basic.pdf|2.A.pdf]], [[Media:CAnal.2.B.CIntegral.20140117.Octave.pdf|2.B.pdf]], [[Media:CAnal.2.C.CIntegral.20140117.Extend.pdf|2.C.pdf]]) ==''' Complex Series '''== * Complex Series ([[Media:CPX.Series.20150226.2.Basic.pdf|3.A.pdf]], [[Media:CAnal.3.B.CSeries.20140121.Octave.pdf|3.B.pdf]], [[Media:CAnal.3.C.CSeries.20140303.Extend.pdf|3.C.pdf]]) ==''' Residue Integrals '''== * Residue Integrals ([[Media:CAnal.4.A.Residue.20140227.Basic.pdf|4.A.pdf]], [[Media:CAnal.4.B.pdf|4.B.pdf]], [[Media:CAnal.4.C.Residue.20140423.Extend.pdf|4.C.pdf]]) ==='''Residue Integrals Note'''=== * Laurent Series with the Residue Theorem Note ([[Media:Laurent.1.Residue.20170713.pdf|H1.pdf]]) * Laurent Series with Applications Note ([[Media:Laurent.2.Applications.20170327.pdf|H1.pdf]]) * Laurent Series and the z-Transform Note ([[Media:Laurent.3.z-Trans.20170831.pdf|H1.pdf]]) * Laurent Series as a Geometric Series Note ([[Media:Laurent.4.GSeries.20170802.pdf|H1.pdf]]) === Laurent Series and the z-Transform Example Note === * Overview ([[Media:Laurent.4.z-Example.20170926.pdf|H1.pdf]]) ====Geometric Series Examples==== * Causality ([[Media:Laurent.5.Causality.1.A.20191026n.pdf|A.pdf]], [[Media:Laurent.5.Causality.1.B.20191026.pdf|B.pdf]]) * Time Shift ([[Media:Laurent.5.TimeShift.2.A.20191028.pdf|A.pdf]], [[Media:Laurent.5.TimeShift.2.B.20191029.pdf|B.pdf]]) * Reciprocity ([[Media:Laurent.5.Reciprocity.3A.20191030.pdf|A.pdf]], [[Media:Laurent.5.Reciprocity.3B.20191031.pdf|B.pdf]]) * Combinations ([[Media:Laurent.5.Combination.4A.20200702.pdf|A.pdf]], [[Media:Laurent.5.Combination.4B.20201002.pdf|B.pdf]]) * Properties ([[Media:Laurent.5.Property.5A.20220105.pdf|A.pdf]], [[Media:Laurent.5.Property.5B.20220126.pdf|B.pdf]]) * Applications ([[Media:Laurent.6.Application.6A.20220806.pdf|A.pdf]], [[Media:Laurent.5.Application.6B.20220723.pdf|B.pdf]]) * Double Pole Case :- Examples ([[Media:Laurent.5.DPoleEx.7A.20220722.pdf|A.pdf]], [[Media:Laurent.5.DPoleEx.7B.20220720.pdf|B.pdf]]) :- Properties ([[Media:Laurent.5.DPoleProp.5A.20190226.pdf|A.pdf]], [[Media:Laurent.5.DPoleProp.5B.20190228.pdf|B.pdf]]) ====The Case Examples==== * Example Overview : ([[Media:Laurent.4.Example.0.A.20171208.pdf|0A.pdf]], [[Media:Laurent.6.CaseExample.0.B.20180205.pdf|0B.pdf]]) * Example Case 1 : ([[Media:Laurent.4.Example.1.A.20171107.pdf|1A.pdf]], [[Media:Laurent.4.Example.1.B.20171227.pdf|1B.pdf]]) * Example Case 2 : ([[Media:Laurent.4.Example.2.A.20171107.pdf|2A.pdf]], [[Media:Laurent.4.Example.2.B.20171227.pdf|2B.pdf]]) * Example Case 3 : ([[Media:Laurent.4.Example.3.A.20171017.pdf|3A.pdf]], [[Media:Laurent.4.Example.3.B.20171226.pdf|3B.pdf]]) * Example Case 4 : ([[Media:Laurent.4.Example.4.A.20171017.pdf|4A.pdf]], [[Media:Laurent.4.Example.4.B.20171228.pdf|4B.pdf]]) * Example Summary : ([[Media:Laurent.4.Example.5.A.20171212.pdf|5A.pdf]], [[Media:Laurent.4.Example.5.B.20171230.pdf|5B.pdf]]) ==''' Conformal Mapping '''== * Conformal Mapping ([[Media:CAnal.6.A.Conformal.20131224.pdf|6.A.pdf]], [[Media:CAnal.6.A.Octave..pdf|6.B.pdf]]) go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Complex analysis]] m5dqotzbv3d842zb7c5yu9bik1rcti4 0 171008 2412380 2412074 2022-08-06T15:22:44Z Young1lim 21186 /* The Temporal Characteristics of Random Processes */ wikitext text/x-wiki ==''' Random Variables '''== === Single Random Variables === * Random Variables ([[Media:RV1.RVariable.1.A.20200427.pdf |A.pdf]]) * Distribution Function ([[Media:RV1.Distribution.2.A.201200428.pdf |A.pdf]]) * Density Function ([[Media:RV1.Density.3.A.20200429.pdf |A.pdf]]) * Functions of Random Variables ([[Media:RV1.RVFunction.4.A.20220317.pdf |A.pdf]]) * Gaussian Random Variables ([[Media:RV1.4.Gaussian.20200430.pdf |A.pdf]], [[Media:RV1.4B.Gaussian.20180314.pdf |B.pdf]]) * Other Distribution and Density Functions ([[Media:RV1.5.Other.20200501.pdf |A.pdf]]) * Conditional Distribution and Density Functions ([[Media:RV1.6.Conditional.20200506.pdf |A.pdf]]) </br> === The Characteristics of a Single Random Variable === * Expected Value ([[Media:RV2.Expectation.1.A.20200506.pdf |A.pdf]]) * Moments ([[Media:RV2.Moment.2.B.20200507.pdf |A.pdf]], [[Media:RV2.Moment.2.B.20180320.pdf |B.pdf]]) * Moment Generating Functions ([[Media:RV2.MFunctions.3.A.20200508.pdf |A.pdf]]) * Transformations of Random Variables ([[Media:RV2.Transform.4.A.20200514.pdf |A.pdf]]) </br> === Multiple Random Variables === * Vector Random Variables ([[Media:3MRV.1A.VectorRV.20200515.pdf |A.pdf]]) * Joint Distribution ([[Media:3MRV.2A.JointDist.20200518.pdf |A.pdf]]) * Joint Density ([[Media:3MRV.3A.JointDensity.20200521.pdf |A.pdf]]) * Conditional Joint Distribution and Density ([[Media:3MRV.4A.CondDistrib.20200527.pdf |A.pdf]]) * Statistical Independence ([[Media:3MRV.5A.StatIndep.20200423.pdf |A.pdf]]) * Sums of Random Variables ([[Media:3MRV.6A.RVSum.20200528.pdf |A.pdf]]) * Central Limit Theorem ([[Media:3MRV.7A.CLimit.20200612.pdf |A.pdf]]) </br> === The Characteristics of Multiple Random Variables === * Expected Values ([[Media:4MRV.1A.Expect.20200617.pdf |A.pdf]]) * Joint Characteristic Functions ([[Media:4MRV.2A.JChar.20200618.pdf |A.pdf]]) * Jointly Gaussian Random Variables ([[Media:4MRV.3A.JGauss.20200619.pdf |A.pdf]]) * Transformations of Multiple Random Variables ([[Media:4MRV.4A.Transform.20200620.pdf |A.pdf]]) * Linear Transformation of Gaussian Random Variables ([[Media:4MRV.5A.LinearTrans.20200623.pdf |A.pdf]]) * Simulating Multiple Random Variables ([[Media:4MRV.6A.Simulation.20200624.pdf |A.pdf]]) * Sampling and Some Limit Theorem ([[Media:4MRV.7A.LimitTheorem.20200625.pdf |A.pdf]]) * Complex Random Variables ([[Media:4MRV.8A.ComplexRV.20200626.pdf |A.pdf]]) </br> ==''' Random Processes '''== === The Temporal Characteristics of Random Processes === * Random Processes ([[Media:5MRV.1A.RandomProcess.20210216.pdf |A.pdf]]) * Joint Distribution, Independence, Processes ([[Media:5MRV.2A.JointDistribution.20210220.pdf |A.pdf]]) * Stationary Random Processes ([[Media:5MRV.3A.Stationary.20220402.pdf |A.pdf]], [[Media:5MRV.3B.Stationary.20220805.pdf |B.pdf]]) * Covariance & Correlation of Random Variables ([[Media:5MRV.4A.CovCorrRV.20210910.pdf |A.pdf]]) * Covariance & Correlation of Random Processses ([[Media:5MRV.5A.CovCorrRP.20210911.pdf |A.pdf]]) * Example Random Processes ([[Media:5MRV.4A.Example.20210227.pdf |A.pdf]]) * Ergodic Random Processes ([[Media:5MRV.5A.Ergodicity.20211022.pdf |A.pdf]], [[Media:5MRV.7B.Ergodicity.20211215.pdf |B.pdf]]) * Measurement of Correlation Functions ([[Media:5MRV.6A.Measure.20201013.pdf |A.pdf]]) * Complex Random Processes ([[Media:5MRV.7A.Complex.20201022.pdf |A.pdf]]) </br> === The Spectral Characteristics of Random Processes === * Power Density Spectrum - Continuous Time ([[Media:6MRV.1A.PSpecCT.20210204.pdf |A.pdf]]) * Auto Correlation Function ([[Media:6MRV.2A.AutoCor.20201218.pdf |A.pdf]]) * Power Density Spectrum - Discrete Time ([[Media:6MRV.3A.PSpecDT.20201203.pdf |A.pdf]]) * Cross Power Density Spectrum ([[Media:6MRV.4A.CPSpec.20191108.pdf |A.pdf]]) * Cross Correlation Function ([[Media:6MRV.5A.CCorrel.20191114.pdf |A.pdf]]) * Noise Definitions ([[Media:6MRV.6A.Noise.20191121.pdf |A.pdf]]) * Power Spectrum of Complex Random Processes ([[Media:6MRV.7A.ComplexProc.20191125.pdf |A.pdf]]) </br> === Linear System with Random Inputs === * Continuous Time LTI System ([[Media:7LTI.1A.CTime.20191203.pdf |A.pdf]]) * Discrete Time LTI System ([[Media:7LTI.2A.DTime.20191211.pdf |A.pdf]]) * System Response ([[Media:7LTI.3A.Response.20191224.pdf |A.pdf]]) * Spectral Characteristics ([[Media:7LTI.4A.Spectral.20200104.pdf |A.pdf]]) * Noise Modeling ([[Media:7LTI.5A.Noise.20200122.pdf |A.pdf]]) <br> === Optimum Linear System === * Maximum SNR ([[Media:8OPT.1A.MaxSNR.20200128.pdf |A.pdf]]) * Minimum Squared Error ([[Media:8OPT.2A.MinSE.20200207.pdf |A.pdf]]) <br> === Noise in Some Application Systems === * AM Communication Systems ([[Media:9APP.1A.AM.20200212.pdf |A.pdf]]) * FM Communication Systems ([[Media:9APP.2A.FM.20200221.pdf |A.pdf]]) * Control Systems ([[Media:9APP.3A.Control.20200225.pdf |A.pdf]]) * PLL Systems ([[Media:9APP.4A.PLL.20200305.pdf |A.pdf]]) * Random Waveforms ([[Media:9APP.5A.RandWave.20200311.pdf |A.pdf]]) * Radar Systems ([[Media:9APP.6A.Radar.20200313.pdf |A.pdf]]) <br> ==''' Correlation and Power Spectra '''== # Correlation Functions of Random Signals ([[Media:RAND.1.A.Correlation.20121106.pdf |pdf]]) # Spectra of Random Signals ([[Media:RAND.2.A.Spectra.20121108.pdf |pdf]]) </br> ==''' Ergodicity, Statistics, Estimation '''== </br> ==''' Random Processes and Linear Systems '''== </br> # Time Domain Techniques for Noisy Signals ([[Media:RAND.3.A.Time.20130205.pdf |A.pdf]], [[Media:Dirichlet.pdf |B.pdf]]) # Frequency Domain Techniques for Noisy Signals # Correlation v.s. Convolution for Noisy Signals </br> # System Identification ([[Media:RP.SysId.1.A.pdf |pdf]]) # Matched Filter <ref>[[Understanding Digital Communications]], See Baseband Mod/Demod Section</ref> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] kkrlxwgj2r5v6wnbkuscujwb5ij4o2e 2412382 2412380 2022-08-06T15:34:57Z Young1lim 21186 /* The Temporal Characteristics of Random Processes */ wikitext text/x-wiki ==''' Random Variables '''== === Single Random Variables === * Random Variables ([[Media:RV1.RVariable.1.A.20200427.pdf |A.pdf]]) * Distribution Function ([[Media:RV1.Distribution.2.A.201200428.pdf |A.pdf]]) * Density Function ([[Media:RV1.Density.3.A.20200429.pdf |A.pdf]]) * Functions of Random Variables ([[Media:RV1.RVFunction.4.A.20220317.pdf |A.pdf]]) * Gaussian Random Variables ([[Media:RV1.4.Gaussian.20200430.pdf |A.pdf]], [[Media:RV1.4B.Gaussian.20180314.pdf |B.pdf]]) * Other Distribution and Density Functions ([[Media:RV1.5.Other.20200501.pdf |A.pdf]]) * Conditional Distribution and Density Functions ([[Media:RV1.6.Conditional.20200506.pdf |A.pdf]]) </br> === The Characteristics of a Single Random Variable === * Expected Value ([[Media:RV2.Expectation.1.A.20200506.pdf |A.pdf]]) * Moments ([[Media:RV2.Moment.2.B.20200507.pdf |A.pdf]], [[Media:RV2.Moment.2.B.20180320.pdf |B.pdf]]) * Moment Generating Functions ([[Media:RV2.MFunctions.3.A.20200508.pdf |A.pdf]]) * Transformations of Random Variables ([[Media:RV2.Transform.4.A.20200514.pdf |A.pdf]]) </br> === Multiple Random Variables === * Vector Random Variables ([[Media:3MRV.1A.VectorRV.20200515.pdf |A.pdf]]) * Joint Distribution ([[Media:3MRV.2A.JointDist.20200518.pdf |A.pdf]]) * Joint Density ([[Media:3MRV.3A.JointDensity.20200521.pdf |A.pdf]]) * Conditional Joint Distribution and Density ([[Media:3MRV.4A.CondDistrib.20200527.pdf |A.pdf]]) * Statistical Independence ([[Media:3MRV.5A.StatIndep.20200423.pdf |A.pdf]]) * Sums of Random Variables ([[Media:3MRV.6A.RVSum.20200528.pdf |A.pdf]]) * Central Limit Theorem ([[Media:3MRV.7A.CLimit.20200612.pdf |A.pdf]]) </br> === The Characteristics of Multiple Random Variables === * Expected Values ([[Media:4MRV.1A.Expect.20200617.pdf |A.pdf]]) * Joint Characteristic Functions ([[Media:4MRV.2A.JChar.20200618.pdf |A.pdf]]) * Jointly Gaussian Random Variables ([[Media:4MRV.3A.JGauss.20200619.pdf |A.pdf]]) * Transformations of Multiple Random Variables ([[Media:4MRV.4A.Transform.20200620.pdf |A.pdf]]) * Linear Transformation of Gaussian Random Variables ([[Media:4MRV.5A.LinearTrans.20200623.pdf |A.pdf]]) * Simulating Multiple Random Variables ([[Media:4MRV.6A.Simulation.20200624.pdf |A.pdf]]) * Sampling and Some Limit Theorem ([[Media:4MRV.7A.LimitTheorem.20200625.pdf |A.pdf]]) * Complex Random Variables ([[Media:4MRV.8A.ComplexRV.20200626.pdf |A.pdf]]) </br> ==''' Random Processes '''== === The Temporal Characteristics of Random Processes === * Random Processes ([[Media:5MRV.1A.RandomProcess.20210216.pdf |A.pdf]]) * Joint Distribution, Independence, Processes ([[Media:5MRV.2A.JointDistribution.20210220.pdf |A.pdf]]) * Stationary Random Processes ([[Media:5MRV.3A.Stationary.20220402.pdf |A.pdf]], [[Media:5MRV.3B.Stationary.20220806.pdf |B.pdf]]) * Covariance & Correlation of Random Variables ([[Media:5MRV.4A.CovCorrRV.20210910.pdf |A.pdf]]) * Covariance & Correlation of Random Processses ([[Media:5MRV.5A.CovCorrRP.20210911.pdf |A.pdf]]) * Example Random Processes ([[Media:5MRV.4A.Example.20210227.pdf |A.pdf]]) * Ergodic Random Processes ([[Media:5MRV.5A.Ergodicity.20211022.pdf |A.pdf]], [[Media:5MRV.7B.Ergodicity.20211215.pdf |B.pdf]]) * Measurement of Correlation Functions ([[Media:5MRV.6A.Measure.20201013.pdf |A.pdf]]) * Complex Random Processes ([[Media:5MRV.7A.Complex.20201022.pdf |A.pdf]]) </br> === The Spectral Characteristics of Random Processes === * Power Density Spectrum - Continuous Time ([[Media:6MRV.1A.PSpecCT.20210204.pdf |A.pdf]]) * Auto Correlation Function ([[Media:6MRV.2A.AutoCor.20201218.pdf |A.pdf]]) * Power Density Spectrum - Discrete Time ([[Media:6MRV.3A.PSpecDT.20201203.pdf |A.pdf]]) * Cross Power Density Spectrum ([[Media:6MRV.4A.CPSpec.20191108.pdf |A.pdf]]) * Cross Correlation Function ([[Media:6MRV.5A.CCorrel.20191114.pdf |A.pdf]]) * Noise Definitions ([[Media:6MRV.6A.Noise.20191121.pdf |A.pdf]]) * Power Spectrum of Complex Random Processes ([[Media:6MRV.7A.ComplexProc.20191125.pdf |A.pdf]]) </br> === Linear System with Random Inputs === * Continuous Time LTI System ([[Media:7LTI.1A.CTime.20191203.pdf |A.pdf]]) * Discrete Time LTI System ([[Media:7LTI.2A.DTime.20191211.pdf |A.pdf]]) * System Response ([[Media:7LTI.3A.Response.20191224.pdf |A.pdf]]) * Spectral Characteristics ([[Media:7LTI.4A.Spectral.20200104.pdf |A.pdf]]) * Noise Modeling ([[Media:7LTI.5A.Noise.20200122.pdf |A.pdf]]) <br> === Optimum Linear System === * Maximum SNR ([[Media:8OPT.1A.MaxSNR.20200128.pdf |A.pdf]]) * Minimum Squared Error ([[Media:8OPT.2A.MinSE.20200207.pdf |A.pdf]]) <br> === Noise in Some Application Systems === * AM Communication Systems ([[Media:9APP.1A.AM.20200212.pdf |A.pdf]]) * FM Communication Systems ([[Media:9APP.2A.FM.20200221.pdf |A.pdf]]) * Control Systems ([[Media:9APP.3A.Control.20200225.pdf |A.pdf]]) * PLL Systems ([[Media:9APP.4A.PLL.20200305.pdf |A.pdf]]) * Random Waveforms ([[Media:9APP.5A.RandWave.20200311.pdf |A.pdf]]) * Radar Systems ([[Media:9APP.6A.Radar.20200313.pdf |A.pdf]]) <br> ==''' Correlation and Power Spectra '''== # Correlation Functions of Random Signals ([[Media:RAND.1.A.Correlation.20121106.pdf |pdf]]) # Spectra of Random Signals ([[Media:RAND.2.A.Spectra.20121108.pdf |pdf]]) </br> ==''' Ergodicity, Statistics, Estimation '''== </br> ==''' Random Processes and Linear Systems '''== </br> # Time Domain Techniques for Noisy Signals ([[Media:RAND.3.A.Time.20130205.pdf |A.pdf]], [[Media:Dirichlet.pdf |B.pdf]]) # Frequency Domain Techniques for Noisy Signals # Correlation v.s. Convolution for Noisy Signals </br> # System Identification ([[Media:RP.SysId.1.A.pdf |pdf]]) # Matched Filter <ref>[[Understanding Digital Communications]], See Baseband Mod/Demod Section</ref> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] sdk78kkuvrth14kp80147igyq1ihjkg 6 193656 2412474 1383995 2022-08-07T03:33:58Z Marshallsumter 311529 wikitext text/x-wiki == Summary == This aurora suggests that the closer the observer the more it looks like radiation spraying down. [[Category:Aurora images]] == Licensing == {{Information1 |Description = This aurora suggests that the closer the observer is to being directly underneath the more it looks like radiation spraying down. |Source = The image appears on a website entitled, "Celestial illumination" at url=http://www.flickr.com/photos/salomonsen/6424624257/. |Date = May 2014 |Author = Ole C. Salomonsen |Rationale = No free licensed or public domain alternatives known to exist to show this aurora suggesting that the closer the observer is to being directly underneath the more it looks like radiation spraying down. |Permission = Fair Use }} {{Fairuse}} krks8e9g4lx4fuil99d9dba5yna7o5k 6 199439 2412454 1409263 2022-08-07T02:09:27Z Marshallsumter 311529 /* Licensing */ wikitext text/x-wiki == Summary == Positrons from a terrestrial gamma ray flash are detected by the Fermi gamma ray telescope. [[Category:Positron astronomy images]] == Licensing == {{Information1 |Description = Positrons from a terrestrial gamma ray flash are detected by the Fermi gamma ray telescope. |Source = The image appears on a website entitled, "Fermi GBM positron event" at url=http://www.nasa.gov/images/content/509305main_GBM_positron_event_300dpi.jpg. |Date = 14 December 2009 |Author = NASA Goddard Space Flight Center |Rationale = No free licensed or public domain alternatives known to exist to show positrons from a terrestrial gamma ray flash as detected by the Fermi gamma ray telescope. |Permission = Fair Use }} {{Fairuse}} kc3cnh5qepueaxbctcb4lpkar8o5wfa 0 203942 2412414 2412263 2022-08-06T21:19:11Z Young1lim 21186 /* Monads III : Mutable State Monads */ wikitext text/x-wiki ==Introduction== * Overview I ([[Media:HSKL.Overview.1.A.20160806.pdf |pdf]]) * Overview II ([[Media:HSKL.Overview.2.A.20160926.pdf |pdf]]) * Overview III ([[Media:HSKL.Overview.3.A.20161011.pdf |pdf]]) * Overview IV ([[Media:HSKL.Overview.4.A.20161104.pdf |pdf]]) * Overview V ([[Media:HSKL.Overview.5.A.20161108.pdf |pdf]]) </br> ==Applications== * Sudoku Background ([[Media:Sudoku.Background.0.A.20161108.pdf |pdf]]) * Bird's Implementation :- Specification ([[Media:Sudoku.1Bird.1.A.Spec.20170425.pdf |pdf]]) :- Rules ([[Media:Sudoku.1Bird.2.A.Rule.20170201.pdf |pdf]]) :- Pruning ([[Media:Sudoku.1Bird.3.A.Pruning.20170211.pdf |pdf]]) :- Expanding ([[Media:Sudoku.1Bird.4.A.Expand.20170506.pdf |pdf]]) </br> ==Using GHCi== * Getting started ([[Media:GHCi.Start.1.A.20170605.pdf |pdf]]) </br> ==Using Libraries== * Library ([[Media:Library.1.A.20170605.pdf |pdf]]) </br> </br> ==Function Oriented Typeclasses== === Background === * Constructors ([[Media:Background.1.A.Constructor.20180904.pdf |pdf]]) * TypeClasses ([[Media:Background.1.B.TypeClass.20180904.pdf |pdf]]) * Functions ([[Media:Background.1.C.Function.20180712.pdf |pdf]]) * Expressions ([[Media:Background.1.D.Expression.20180707.pdf |pdf]]) * Operators ([[Media:Background.1.E.Operator.20180707.pdf |pdf]]) === Functors === * Functor Overview ([[Media:Functor.1.A.Overview.20180802.pdf |pdf]]) * Function Functor ([[Media:Functor.2.A.Function.20180804.pdf |pdf]]) * Functor Lifting ([[Media:Functor.2.B.Lifting.20180721.pdf |pdf]]) === Applicatives === * Applicatives Overview ([[Media:Applicative.3.A.Overview.20180606.pdf |pdf]]) * Applicatives Methods ([[Media:Applicative.3.B.Method.20180519.pdf |pdf]]) * Function Applicative ([[Media:Applicative.3.A.Function.20180804.pdf |pdf]]) * Applicatives Sequencing ([[Media:Applicative.3.C.Sequencing.20180606.pdf |pdf]]) === Monads I : Background === * Side Effects ([[Media:Monad.P1.1A.SideEffect.20190316.pdf |pdf]]) * Monad Overview ([[Media:Monad.P1.2A.Overview.20190308.pdf |pdf]]) * Monadic Operations ([[Media:Monad.P1.3A.Operations.20190308.pdf |pdf]]) * Maybe Monad ([[Media:Monad.P1.4A.Maybe.201900606.pdf |pdf]]) * IO Actions ([[Media:Monad.P1.5A.IOAction.20190606.pdf |pdf]]) * Several Monad Types ([[Media:Monad.P1.6A.Types.20191016.pdf |pdf]]) === Monads II : State Transformer Monads === * State Transformer : - State Transformer Basics ([[Media:MP2.1A.STrans.Basic.20191002.pdf |pdf]]) : - State Transformer Generic Monad ([[Media:MP2.1B.STrans.Generic.20191002.pdf |pdf]]) : - State Transformer Monads ([[Media:MP2.1C.STrans.Monad.20191022.pdf |pdf]]) * State Monad : - State Monad Basics ([[Media:MP2.2A.State.Basic.20190706.pdf |pdf]]) : - State Monad Methods ([[Media:MP2.2B.State.Method.20190706.pdf |pdf]]) : - State Monad Examples ([[Media:MP2.2C.State.Example.20190706.pdf |pdf]]) === Monads III : Mutable State Monads === * Mutability Background : - Types ([[Media:MP3.1A.Mut.Type.20200721.pdf |pdf]]) : - Primitive Types ([[Media:MP3.1B.Mut.PrimType.20200611.pdf |pdf]]) : - Polymorphic Types ([[Media:MP3.1C.Mut.Polymorphic.20201212.pdf |pdf]]) : - Continuation Passing Style ([[Media:MP3.1D.Mut.Continuation.20220110.pdf |pdf]]) : - Expressions ([[Media:MP3.1E.Mut.Expression.20220628.pdf |pdf]]) : - Lambda Calculus ([[Media:MP3.1F.Mut.LambdaCal.20220806.pdf |pdf]]) : - Non-terminating Expressions ([[Media:MP3.1F.Mut.Non-terminating.20220616.pdf |pdf]]) : - Inhabitedness ([[Media:MP3.1F.Mut.Inhabited.20220319.pdf |pdf]]) : - Existential Types ([[Media:MP3.1E.Mut.Existential.20220128.pdf |pdf]]) : - forall Keyword ([[Media:MP3.1E.Mut.forall.20210316.pdf |pdf]]) : - Mutability and Strictness ([[Media:MP3.1C.Mut.Strictness.20200613.pdf |pdf]]) : - Strict and Lazy Packages ([[Media:MP3.1D.Mut.Package.20200620.pdf |pdf]]) * Mutable Objects : - Mutable Variables ([[Media:MP3.1B.Mut.Variable.20200224.pdf |pdf]]) : - Mutable Data Structures ([[Media:MP3.1D.Mut.DataStruct.20191226.pdf |pdf]]) * IO Monad : - IO Monad Basics ([[Media:MP3.2A.IO.Basic.20191019.pdf |pdf]]) : - IO Monad Methods ([[Media:MP3.2B.IO.Method.20191022.pdf |pdf]]) : - IORef Mutable Variable ([[Media:MP3.2C.IO.IORef.20191019.pdf |pdf]]) * ST Monad : - ST Monad Basics ([[Media:MP3.3A.ST.Basic.20191031.pdf |pdf]]) : - ST Monad Methods ([[Media:MP3.3B.ST.Method.20191023.pdf |pdf]]) : - STRef Mutable Variable ([[Media:MP3.3C.ST.STRef.20191023.pdf |pdf]]) === Monads IV : Reader and Writer Monads === * Function Monad ([[Media:Monad.10.A.Function.20180806.pdf |pdf]]) * Monad Transformer ([[Media:Monad.3.I.Transformer.20180727.pdf |pdf]]) * MonadState Class :: - State & StateT Monads ([[Media:Monad.9.A.MonadState.Monad.20180920.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.9.B.MonadState.Class.20180920.pdf |pdf]]) * MonadReader Class :: - Reader & ReaderT Monads ([[Media:Monad.11.A.Reader.20180821.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.12.A.MonadReader.20180821.pdf |pdf]]) * Control Monad ([[Media:Monad.9.A.Control.20180908.pdf |pdf]]) === Monoid === * Monoids ([[Media:Monoid.4.A.20180508.pdf |pdf]]) === Arrow === * Arrows ([[Media:Arrow.1.A.20190504.pdf |pdf]]) </br> ==Polymorphism== * Polymorphism Overview ([[Media:Poly.1.A.20180220.pdf |pdf]]) </br> ==Concurrent Haskell == </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] ==External links== * [http://learnyouahaskell.com/introduction Learn you Haskell] * [http://book.realworldhaskell.org/read/ Real World Haskell] * [http://www.scs.stanford.edu/14sp-cs240h/slides/ Standford Class Material] [[Category:Computer programming]] krhcie77zykkuzssxsmc4jjtsm0cknx 0 215261 2412482 2389667 2022-08-07T04:23:21Z Marshallsumter 311529 wikitext text/x-wiki [[Image:Hubble Sees Monstrous Cloud Boomerang Back to our Galaxy (24676686535).jpg|right|thumb|300px|The invisible cloud is plummeting toward our galaxy at nearly 700,000 miles per hour. Credit: Saxton/Lockman/NRAO/AUI/NSF/Mellinger.{{tlx|free media}}]] Particle radiation upwards in size above that of atomic nuclei may be lumped together as meteor radiation. As an example, there is the image on the right. "The invisible cloud is plummeting toward our galaxy at nearly 700,000 miles per hour."<ref name=Saxton>{{ cite book |author=B. Saxton |author2=F. Lockman |author3=A. Mellinger |author4=Ann Jenkins |author5=Ray Villard |title=Hubble Sees Monstrous Cloud Boomerang Back to our Galaxy |publisher=NASA |location=Washington, DC USA |date=28 January 2016 |url=http://www.nasa.gov/feature/goddard/2016/hubble-sees-monstrous-cloud-boomerang-back-to-our-galaxy |accessdate=2016-11-05 }}</ref> "This composite image shows the size and location of the Smith Cloud on the sky. The cloud appears in false-color, radio wavelengths as observed by the Green Bank Telescope in West Virginia. The visible-light image of the background star field shows the cloud's location in the direction of the constellation Aquila."<ref name=Saxton/> "Though hundreds of enormous, high-velocity gas clouds whiz around the outskirts of our galaxy, this so-called “Smith Cloud” is unique because its trajectory is well known. New Hubble observations suggest it was launched from the outer regions of the galactic disk, around 70 million years ago. The cloud was discovered in the early 1960s by doctoral astronomy student Gail Smith, who detected the radio waves emitted by its hydrogen."<ref name=Saxton/> "Hubble Space Telescope measurements show that the cloud came out of a region near the edge of the galaxy's disk of stars 70 million years ago. The cloud is now stretched into the shape of a comet by gravity and gas pressure. Following a ballistic path, the cloud will fall back into the disk and trigger new star formation 30 million years from now."<ref name=Saxton/> "Astronomers have measured this comet-shaped region of gas to be 11,000 light-years long and 2,500 light-years across. If the cloud could be seen in visible light, it would span the sky with an apparent diameter 30 times greater than the size of the full moon."<ref name=Saxton/> "The astronomers found that the Smith Cloud is as rich in sulfur as the Milky Way’s outer disk, a region about 40,000 light-years from the galaxy’s center (about 15,000 light-years farther out than our sun and solar system). This means that the Smith Cloud was enriched by material from stars. This would not happen if it were pristine hydrogen from outside the galaxy, or if it were the remnant of a failed galaxy devoid of stars. Instead, the cloud appears to have been ejected from within the Milky Way and is now boomeranging back."<ref name=Saxton/> {{clear}} ==Theoretical meteor radiation== For this resource, a theoretical definition to handle all sizes of radiated meteors is proposed. Here's that [[Definitions/Theory#Theoretical definition|theoretical definition]]: '''Def.''' any natural object radiating through a portion or all of the [[Earth]]'s or another natural, astronomical object's atmosphere is called a '''meteor'''. These are usage notes: # Such an object may be as small as an electron or much larger. # Astronomical objects that are atoms, nuclei, or subatomic particles are part of cosmic-ray astronomy. # Astronomical objects larger than atoms, nuclei, or subatomic particles that are fast-moving relative to perceived, almost motionless objects, radiating through another natural object's atmosphere or gaseous environment are also here referred to as meteors. # These can be a high-velocity star moving through the [[interstellar medium]] or a larger object moving through an [[intergalactic medium]]. # At the extreme a meteor can be a galaxy cluster moving relative to apparently stationary clusters in its neighborhood of the universe. ==High-velocity galaxies== {{main|Radiation astronomy/High-velocity galaxies}} [[Image:Irregular galaxy NGC 1427A (captured by the Hubble Space Telescope).jpg|thumb|right|250px|The irregular galaxy NGC 1427A is passing through the Fornax cluster at nearly 600 kilometers per second (400 miles per second). Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA).{{tlx|free media}}]] "The irregular galaxy NGC 1427A is a spectacular example of the resulting stellar rumble. Under the gravitational grasp of a large gang of galaxies, called the Fornax cluster, the small bluish galaxy is plunging headlong into the group at 600 kilometers per second or nearly 400 miles per second."<ref name=Gregg>{{ cite book |author=M. Gregg |title=The Impending Destruction of NGC 1427A |publisher=Hubblesite.org |location=Baltimore, Maryland USA |date=3 March 2005 |url=http://hubblesite.org/newscenter/archive/releases/2005/09/image/a/ |accessdate=2016-11-05 }}</ref> "Galaxy clusters, like the Fornax cluster, contain hundreds or even thousands of individual galaxies. Within the Fornax cluster, there is a considerable amount of gas lying between the galaxies. When the gas within NGC 1427A collides with the Fornax gas, it is compressed to the point that it starts to collapse under its own gravity. This leads to formation of the myriad of new stars seen across NGC 1427A, which give the galaxy an overall arrowhead shape that appears to point in the direction of the galaxy's high-velocity motion."<ref name=Gregg/> {{clear}} ==Hypervelocity stars== {{main|Radiation astronomy/Hypervelocity stars}} [[Image:Hs-2009-03-a-web_print.jpg|thumb|right|250px|The Hubble Space Telescope image shows four high-velocity, runaway stars plowing through their local interstellar medium. Credit: NASA - Hubble's Advanced Camera for Surveys.{{tlx|free media}}]] [[Image:Mira the star-by Nasa alt crop.jpg|thumb|left|250px|This ultraviolet-wavelength image mosaic, taken by NASA's Galaxy Evolution Explorer (GALEX), shows a comet-like "tail" stretching 13 light years across space behind the star Mira. Credit: NASA.{{tlx|free media}}]] [[Image:Features in Mira's Tail.jpg|thumb|right|250px|A close-up view of a star racing through space faster than a speeding bullet can be seen in this image from NASA's Galaxy Evolution Explorer. Credit: NASA/JPL-Caltech/C. Martin (Caltech)/M. Seibert(OCIW).{{tlx|free media}}]] [[Image:Mira xray scale.jpg|thumb|right|250px|The Chandra image shows Mira A (right), a highly evolved red giant star, and Mira B (left), a white dwarf. Scalebar: 0.3 arcsec. Credit: NASA/CXC/SAO/M. Karovska et al.{{tlx|fairuse}}]] "To date, all of the reported hypervelocity stars (HVSs), which are believed to be ejected from the Galactic center, are blue and therefore almost certainly young.”<ref name=Kollmeier>{{ cite journal |author=Juna A. Kollmeier |author2=Andrew Gould |title=Where Are the Old-Population Hypervelocity Stars? |journal=The Astrophysical Journal |date=July 20, 2007 |volume=664 |issue=1 |pages=343-8 |url=http://iopscience.iop.org/0004-637X/664/1/343 |arxiv= |bibcode= |doi=10.1086/518405 |pmid= |accessdate=2012-03-05 }}</ref> '''Def.''' a high-velocity star moving through space with an abnormally high velocity relative to the surrounding interstellar medium is called a '''runaway star'''. "Of particular importance has been access to high resolution R~40,000-100,000 echelle spectra providing an ability to study the dynamics of hot plasma and separate multiple stellar and interstellar absorption components."<ref name=Barstow>{{ cite book |author=Martin A. Barstow |author2=L. Binette |author3=Noah Brosch |author4=F.Z. Cheng |author5=Michel Dennefeld |author6=A.I. G. de Castro |author7=H. Haubold |author8=K.A. van der Hucht |author9=N. Kappelmann |author10=P. Martinez |author11=A. Moisheev |author12=I. Pagano |author13=Erez N. Ribak |author14=J. Sahade |author15=B. I. Shustov |author16=J.-E. Solheim |author17=W. Wamsteker |author18=K. Werner |author19=Helmut Becker-Ross |author20=Stefan Florek |title=The WSO: a world-class observatory for the ultraviolet, In: ''Future EUV/UV and Visible Space Astrophysics Missions and Instrumentation'' |publisher=The International Society for Optical Engineering |location= |date=February 26, 2003 |editor=J. Chris Blades |editor2=Oswald H. W. Siegmund |volume=4854 |issue=364 |pages= |url=http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=876587 |arxiv= |bibcode= |doi=10.1117/12.459779 |pmid= |isbn= |accessdate=2013-07-15 }}</ref> At left is a radiated object, the binary star Mira, and its associated phenomena. Ultra-violet studies of Mira by NASA's [[w:Galaxy Evolution Explorer|Galaxy Evolution Explorer]] (Galex) space telescope have revealed that it sheds a trail of material from the outer envelope, leaving a tail 13 light-years in length, formed over tens of thousands of years.<ref name=Martin>{{ cite journal |last=Martin|first=Christopher | journal=Nature |volume=448 |title=A turbulent wake as a tracer of 30,000 years of Mira's mass loss history |doi=10.1038/nature06003 |date=August 17, 2007 |pages=780–783 |accessdate=2007-12-11 |pmid=17700694 |last2=Seibert|first2=M|last3=Neill|first3=JD|last4=Schiminovich|first4=D|last5=Forster|first5=K|last6=Rich|first6=RM|last7=Welsh|first7=BY|last8=Madore|first8=BF|last9=Wheatley|first9=JM |issue=7155 |bibcode=2007Natur.448..780M }}</ref><ref name=Minkel>Minkel, JR.[http://www.sciam.com/article.cfm?articleID=6AE74053-E7F2-99DF-353EB7B9AE43FCF6&chanID=sa007&ec=su_astro "Shooting Bullet Star Leaves Vast Ultraviolet Wake"], "The Scientific American", August 15, 2007 Accessed August 21, 2007.</ref> It is thought that a hot [[w:bow shock|bow-wave]] of compressed plasma/gas is the cause of the tail; the bow-wave is a result of the interaction of the stellar wind from Mira A with gas in interstellar space, through which Mira is moving at an extremely high speed of 130 kilometres/second (291,000 miles per hour).<ref name=wareing2007>{{cite journal | url=http://www.iop.org/EJ/article/1538-4357/670/2/L125/22252.html |last=Wareing |first=Christopher | journal=Astrophysical Journal Letters |volume=670 |issue=2 |title=It's a wonderful tail: the mass-loss history of Mira |doi= 10.1086/524407 |date=November 6, 2007 |pages=L125–L129 |last2=Zijlstra |first2=A. A. |last3=O'Brien |first3=T. J. |last4=Seibert |first4=M. |bibcode=2007ApJ...670L.125W |arxiv = 0710.3010 }}</ref><ref name=Clavin>{{ cite book |url=http://www.galex.caltech.edu/MEDIA/2007-04/images.html |title=GALEX finds link between big and small stellar blasts |accessdate=2007-08-16 |author=W. Clavin |date= August 15, 2007 |publisher=California Institute of Technology |archiveurl = http://web.archive.org/web/20070827103038/http://www.galex.caltech.edu/MEDIA/2007-04/images.html <!-- Bot retrieved archive --> |archivedate = 2007-08-27 }}</ref> The tail consists of material stripped from the head of the bow-wave, which is also visible in ultra-violet observations. Mira's bow-shock will eventually evolve into a [[w:planetary nebula|planetary nebula]], the form of which will be considerably affected by the motion through the [[w:interstellar medium|interstellar medium]] (ISM).<ref name=Wareing>{{ cite journal | author=Christopher Wareing | journal=Philosophical Transactions of the Royal Society A | volume=366 | issue=1884 | title=Wonderful Mira | doi=10.1098/rsta.2008.0167 | pmid=18812301 | date=December 13, 2008 | pages=4429–40 |bibcode = 2008RSPTA.366.4429W }}</ref> At second right is the only available X-ray image, by the Chandra X-ray Observatory, of Mira A on the right and Mira B (left). "Mira A is losing gas rapidly from its upper atmosphere [apparently] via a stellar wind. [Mira B is asserted to be a white dwarf. In theory] Mira B exerts a gravitational tug that creates a gaseous bridge between the two stars. Gas from the wind and bridge accumulates in an accretion disk around Mira B and collisions between rapidly moving particles in the disk produce X-rays."<ref name=Karovska>{{ cite book |author=M. Karovska |display-authors=etal |title=More Images of Mira |publisher=NASA/CXC/SAO/M. Karovska, et al. |location= |date=April 28, 2005 |url=http://chandra.harvard.edu/photo/2005/mira/more.html |accessdate=2012-12-22 }}</ref> Mira A, spectral type M7&nbsp;IIIe<ref name=aj114_1584>{{ cite journal | last=Castelaz | first=Michael W. | author2=Luttermoser, Donald G. | title=Spectroscopy of Mira Variables at Different Phases. | journal=The Astronomical Journal | year=1997 | volume=114 | pages=1584–1591 | bibcode=1997AJ....114.1584C | doi=10.1086/118589 }}</ref>, has an effective surface temperature of 2918–3192<ref name=aaa421>{{ cite journal | last=Woodruff | first=H. C. | author2=Eberhardt, M. |author3=Driebe, T. |author4=Hofmann, K.-H. |author5=Ohnaka, K. |author6=Richichi, A. |author7=Schert, D. |author8=Schöller, M. |author9=Scholz, M. |author10=Weigelt, G. |author11=Wittkowski, M. |author12=Wood, P. R. | title=Interferometric observations of the Mira star o Ceti with the VLTI/VINCI instrument in the near-infrared | journal=Astronomy & Astrophysics | year=2004 | volume=421 | issue=2 | pages=703–714 | url=http://www.eso.org/~mwittkow/publications/conferences/SPIECWo5491199.pdf |format=PDF | accessdate=2007-12-07 | doi=10.1051/0004-6361:20035826 | bibcode=2004A&A...421..703W |arxiv = astro-ph/0404248 }}</ref>. Mira A is not a known X-ray source according to SIMBAD, but here is shown to be one. {{clear}} ==High-velocity stars== [[Image:Double Nucleus of the Andromeda Galaxy (M31).tif|right|thumb|250px|A "double nucleus" is in the center of the neighboring spiral galaxy M31. Credit: Tod R. Lauer, NASA.{{tlx|free media}}]] "In 1988, the first evidence for a black hole at the exact center of M31 came from ground-based observations by Dr. John Kormendy (now at the University of Hawaii), and independently by Dr. Alan Dressler (Observatories of the Carnegie Institution of Washington), and Dr. Douglas O. Richstone (University of Michigan). Their data indicated an abrupt increase in the orbital velocities of stars in the center of the M31 nucleus."<ref name=Villard>{{ cite book |author=Ray Villard |author2=Tod Lauer |author3=Sandra Faber |title=Hubble Space Telescope Finds a Double Nucleus in the Andromeda Galaxy |publisher= |location= |date=20 July 1993 |url=http://hubblesite.org/newscenter/archive/releases/1993/18/text/ |accessdate=2016-11-05 }}</ref> {{clear}} ==High-velocity clouds== [[Image:NGC 6745.jpg|right|thumb|250px|High relative velocities cause ram pressures at the surface of contact between the interacting interstellar clouds. Credit: Tod R. Lauer, NASA.{{tlx|free media}}]] [[Image:15-137-CircinusX1-XRayLightRings-NeutronStar-Chandra-20150624.jpg|left|thumb|250px|The speed of the jet of high-energy particles produced by the system is at least 99.9% of the speed of light. Credit: X-ray: NASA/CXC/Univ. of Wisconsin-Madison/S. Heinz, et al.; Optical: DSS.{{tlx|free media}}]] "A large spiral galaxy, with its nucleus still intact, peers at the smaller passing galaxy (nearly out of the field of view at lower right), while a bright blue beak and bright whitish-blue top feathers show the distinct path taken during the smaller galaxy's journey. These galaxies did not merely interact gravitationally as they passed one another, they actually collided."<ref name=Lynds>{{ cite book |author=Roger Lynds |author2=Earl J. O'Neil Jr. |title=A Bird's eye view of a Galaxy Collision |publisher=NASA Goddard Space Flight Center |location=Greenbelt, Maryland USA |date=March 1996 |url=https://commons.wikimedia.org/wiki/File:NGC_6745.jpg |accessdate=2016-11-05 }}</ref> The "situation is quite different for the interstellar media in the above two galaxies - material consisting largely of clouds of atomic and molecular gases and of tiny particles of matter and dust, strongly coupled to the gas. Wherever the interstellar clouds of the two galaxies collide, they do not freely move past each other without interruption but, rather, suffer a damaging collision. High relative velocities cause ram pressures at the surface of contact between the interacting interstellar clouds. This pressure, in turn, produces material densities sufficiently extreme as to trigger star formation through gravitational collapse. The hot blue stars in this image are evidence of this star formation."<ref name=Lynds/> "Circinus X-1 is [in the image on the left] the source of a surprisingly powerful jet of high-energy particles."<ref name=Heinz>{{ cite book |author=Sebastian Heinz |title=Circinus X-1 |publisher= |location= |date=23 June 2015 |url=http://chandra.si.edu/photo/2015/cirx1/ |accessdate=2016-11-05 }}</ref> The "rings are echoes from a burst of X-rays emitted by Circinus X-1 in late 2013. The burst reflected off intervening clouds of dust, with some reflected X-rays arriving to Earth from different angles at a time delay of about one to three months, creating the observed rings."<ref name=Heinz/> Each "ring was created by the X-ray reflections off a different dust cloud."<ref name=Heinz/> "These rings can be seen in the composite image where X-rays from Chandra are red, green, and blue corresponding to low, medium, and high-energy X-rays respectively, which have been combined with a view in visible light [Gold] from the Digitized Sky Survey. The sharp edges are caused by the large size of the X-ray rings compared to the relatively small field-of-view of the Chandra detectors, providing only partial coverage."<ref name=Heinz/> The "speed of the jet of high-energy particles produced by the system is at least 99.9% of the speed of light."<ref name=Heinz/> {{clear}} ==Volcanic clouds== [[Image:MountRedoubtEruption.jpg|thumb|right|250px|Mount Redoubt in Alaska erupted on April 21, 1990. Credit: R. Clucas, USGS.{{tlx|free media}}]] The mushroom-shaped plume in the image on the right rose from avalanches of hot debris that cascaded down the north flank, when '''Mount Redoubt''' erupted on April 21, 1990. "Redoubt Volcano is a steep-sided cone about 10 km in diameter at its base and with a volume of 30-35 cubic kilometers. The volcano is composed of intercalated pyroclastic deposits and lava flows and rests on Mesozoic granitic rocks of the Alaska-Aleutian Range batholith (Till and others, 1993; 1994). It has been moderately dissected by the action of numerous alpine glaciers. A 1.8-km-wide, ice-filled summit crater is breached on the north side by a northward-flowing glacier, informally known as the Drift Glacier, which spreads into a piedmont lobe in the upper Drift River Valley. The most recently active vent is located on the north side of the crater at the head of the Drift glacier. Holocene lahar deposits in the Crescent River and Drift River valleys extend downstream as far as Cook Inlet."<ref name=Miller>{{ cite book |author=Miller |display-authors=etal |title=Description |publisher=University of Alaska |location= |date= 1998 |url=http://www.avo.alaska.edu/volcanoes/volcinfo.php?volcname=Redoubt |accessdate=2016-02-18 }}</ref> {{clear}} ==Clouds== {{main|Radiation astronomy/Clouds|Clouds}} [[Image:Img20050526 0007 at tannheim cumulus.jpg|thumb|right|250px|This image shows a cumulus cloud above Lechtaler Alps, Austria. Credit: [[c:User:Glg|Glg]].{{tlx|free media}}]] '''Def.''' a visible mass of # water droplets suspended in the air, # dust, # steam, # smoke, # a group or swarm is called a '''cloud'''. Clouds have been observed on other planets and moons within the Solar System, but, due to their different temperature characteristics, they are composed of other substances such as methane, ammonia, and sulfuric acid. Clouds act as electric insulators; space charge develops on the surface of the cloud and the distribution of fair-weather currents and fields in the vicinity of the cloud are altered. The "electrical environment around clouds is such that high space charge densities can exist."<ref name=Harrison>{{ cite journal |author=R. G. Harrison |author2=K. S. Carslaw |title=Ion-aerosol-cloud processes in the lower atmosphere |journal=Reviews of Geophysics |date=September 2003 |volume=41 |issue=3 |pages=1012 |url=http://onlinelibrary.wiley.com/doi/10.1029/2002RG000114/full |arxiv= |bibcode= |doi=10.1029/2002RG000114 |pmid= |accessdate=2015-01-06 }}</ref> {{clear}} ==Cumulonimbuses== [[Image:Fly00890 - Flickr - NOAA Photo Library.jpg|thumb|right|250px|The perfect thunderstorm is observed from a C130 research aircraft during Project Cement #1. Credit: NOAA/AOML/Hurricane Research Division.{{tlx|free media}}]] A "thunderstorm supplies a negative charge to the Earth. The net positive space charge in the air between the ground and a height of ~ 10 km is nearly equal to the negative charge on the Earth's surface".<ref name=Stansbery>{{ cite book |author=Eileen K. Stansbery |title=A global model of thunderstorm electricity and the prediction of whistler duct formation |publisher=Rice University |location=Houston, Texas USA |date=March 1989 |editor= |pages=174 |url=http://scholarship.rice.edu/bitstream/handle/1911/16298/9012871.PDF?sequence=1 |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2015-01-03 }}</ref> 'Giant' "thunderclouds can produce transverse electric fields of tens of microvolts per meter in the equatorial plane of the midlatitude magnetosphere."<ref name=Park>{{ cite journal |author=C. G. Park |author2=M. Dejnakarintra |title=Penetration of thundercloud electric fields into the ionosphere and magnetosphere: 1. Middle and subauroral latitudes |journal=Journal of Geophysical Research Space Physics |date=1 October 1973 |volume=78 |issue=28 |pages=6623-33 |url=http://onlinelibrary.wiley.com/doi/10.1029/JA078i028p06623/abstract |arxiv= |bibcode= |doi=10.1029/JA078i028p06623 |pmid= |accessdate=2015-01-06 }}</ref> The "contribution to global thunderstorm activity by oceanic thunderstorms should be regarded as itself having a diurnal variation of some 18% in amplitude."<ref name=Muir>{{ cite journal |author=M.S. Muir |author2=C.A. Smart |title=Diurnal variations in the atmospheric electric field on the South Polar ice-cap |journal=Journal of Atmospheric and Terrestrial Physics |date=February 1981 |volume=43 |issue=2 |pages=171-7 |url=http://www.sciencedirect.com/science/article/pii/0021916981900775 |arxiv= |bibcode= |doi=10.1016/0021-9169(81)90077-5 |pmid= |accessdate=2015-01-06 }}</ref> {{clear}} ==Molecular clouds== [[Image:Molecular.cloud.arp.750pix.jpg|thumb|right|250px|This cloud of gas and dust is being deleted. Credit: Hubble Heritage Team (STScI/AURA), N. Walborn (STScI) & R. Barbß (La Plata Obs.), NASA.{{tlx|free media}}]] In the image at right is a molecular cloud of gas and dust that is being reduced. "Likely, within a few million years, the intense light from bright stars will have boiled it away completely. The cloud has broken off of part of the Carina Nebula, a star forming region about 8000 light years away. Newly formed stars are visible nearby, their images reddened by blue light being preferentially scattered by the pervasive dust. This image spans about two light years and was taken by the orbiting Hubble Space Telescope in 1999."<ref name=Nemiroff>{{ cite book |author=Robert Nemiroff (MTU) |author2=Jerry Bonnell (USRA) |title=Disappearing Clouds in Carina |publisher=NASA |location=Goddard Space Flight Center, Greenbelt, Maryland, USA |date=June 30, 2003 |url=http://apod.nasa.gov/apod/ap030630.html |accessdate=2012-09-05 }}</ref> A '''molecular cloud''', sometimes called a '''stellar nursery''' if [[w:star formation|star formation]] is occurring within, is a type of [[w:interstellar cloud|interstellar cloud]] whose density and size permit the formation of molecules, most commonly [[w:molecular hydrogen|molecular hydrogen]] (H₂). Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H₂ is CO ([[w:carbon monoxide|carbon monoxide]]). The ratio between CO [[w:luminosity|luminosity]] and H₂ [[w:mass|mass]] is thought to be constant, although there are reasons to doubt this assumption in observations of some other [[w:galaxies|galaxies]].<ref name=Kulesa>{{ cite book | author=Craig Kulesa | title=Overview: Molecular Astrophysics and Star Formation | work=Research Projects | url=http://loke.as.arizona.edu/~ckulesa/research/overview.html | accessdate=September 7, 2005 }}</ref> Such clouds make up < 1% of the ISM, have temperatures of 10-20 K and high densities of 10² - 10⁶ atoms/cm³. These clouds are astronomical radio and infrared sources with radio and infrared molecular emission and absorption lines. {{clear}} ==Giant molecular clouds== A vast assemblage of molecular gas with a mass of approximately 10³–10⁷ times the mass of the Sun<ref name="murray">See, e.g., Table 1 and the Appendix of {{ cite journal | last1 = Murray | first1 = N. | title = Star Formation Efficiencies and Lifetimes of Giant Molecular Clouds in the Milky Way | doi = 10.1088/0004-637X/729/2/133 | journal = The Astrophysical Journal | volume = 729 | issue = 2 | pages = 133 | year = 2011 | pmid = | pmc = |arxiv = 1007.3270 |bibcode = 2011ApJ...729..133M }}</ref> is called a '''giant molecular cloud''' ('''GMC'''). GMCs are ≈15–600 [[w:light-year|light-year]]s in diameter (5–200 parsecs).<ref name="murray" /> Whereas the average density in the solar vicinity is one particle per cubic centimetre, the average density of a GMC is 10²–10³ particles per cubic centimetre. Although the Sun is much denser than a GMC, the volume of a GMC is so great that it contains much more mass than the Sun. The substructure of a GMC is a complex pattern of filaments, sheets, bubbles, and irregular clumps.<ref name="williams2000">{{ cite book | author = J. P. Williams |author2=L. Blitz |author3=C. F. McKee | title = The Structure and Evolution of Molecular Clouds: from Clumps to Cores to the IMF, In: ''Protostars and Planets IV'' | pages = 97 | publisher = Tucson: University of Arizona Press |url=https://arxiv.org/pdf/astro-ph/9902246 | year = 2000 }}</ref> The densest parts of the filaments and clumps are called "molecular cores", whilst the densest molecular cores are, unsurprisingly, called "dense molecular cores" and have densities in excess of 10⁴–10⁶ particles per cubic centimeter. Observationally molecular cores are traced with carbon monoxide and dense cores are traced with ammonia. The concentration of [[w:Cosmic dust|dust]] within molecular cores is normally sufficient to block light from background stars so that they appear in silhouette as [[w:dark nebulae|dark nebulae]].<ref name="francesco2006">{{ cite book | author = Di Francesco, J. |display-authors=etal | title = An Observational Perspective of Low-Mass Dense Cores I: Internal Physical and Chemical Properties, In: ''Protostars and Planets V'' | year = 2006 |url=https://arxiv.org/pdf/astro-ph/0602379 }}</ref> GMCs are so large that "local" ones can cover a significant fraction of a constellation; thus they are often referred to by the name of that constellation, e.g. the [[w:Orion Molecular Cloud Complex|Orion Molecular Cloud]] (OMC) or the [[w:Taurus Molecular Cloud|Taurus Molecular Cloud]] (TMC). These local GMCs are arrayed in a ring in the neighborhood of the Sun coinciding with the [[w:Gould Belt|Gould Belt]].<ref name=Grenier>{{ cite book | author = Grenier | title = The Gould Belt, star formation, and the local interstellar medium, In: ''The Young Universe'' | year = 2004 |url=http://uk.arxiv.org/abs/astro-ph/0409096 }}</ref> The most massive collection of molecular clouds in the galaxy forms an asymmetrical ring around the galactic center at a radius of 120 parsecs; the largest component of this ring is the [[w:Sagittarius B2|Sagittarius B2]] complex. The Sagittarius region is chemically rich and is often used as an exemplar by astronomers searching for new molecules in interstellar space.<ref name=Bonn>[http://www.mpifr-bonn.mpg.de/staff/epolehampton/thesis/node23.html Sagittarius B2 and its Line of Sight]</ref> ==Chamaeleon I dark clouds== [[Image:Chamaeleon_I_cloud.png|thumb|right|250px|A [[w:ROSAT|ROSAT]] false-color image in X-rays between 500 eV and 1.1 keV shows the Chamaeleon I dark cloud. The contours are 100 µm emission from dust measured by the IRAS satellite. Credit: Dr. David Burrows and then graduate student Jeff Mendenhall of the Penn State Department of Astronomy & Astrophysics, and is based on a mosaic of images collected by Dr. Burrows and by Dr. Eric Feigelson of Penn State using the US/German ROSAT satellite.{{tlx|free media}}]] The Chamaeleon I (Cha I) cloud is a coronal cloud and one of the nearest active [[star-forming region]]s at ~160 pc.<ref name=Feigelson2004/> It is relatively isolated from other star-forming clouds, so it is unlikely that older pre-main sequence (PMS) stars have drifted into the field.<ref name=Feigelson2004>{{ cite journal |doi=10.1086/423613 |author=Feigelson ED, Lawson WA |title=An X-ray census of young stars in the Chamaeleon I North Cloud |journal=The Astrophysical Journal |date=October 2004 |volume=614 |issue=10 |pages=267–83 |url=http://www.iop.org/EJ/article/0004-637X/614/1/267/60370.web.pdf?request-id=63d27661-73a2-47f1-8b87-17c4df8c7e65 |bibcode=2004ApJ...614..267F |arxiv = astro-ph/0406529 }}</ref> The total stellar population is 200-300.<ref name=Feigelson2004/> The Cha I cloud is further divided into the North cloud or region and South cloud or main cloud. {{clear}} ==Chamaeleon II dark clouds== "The Chamaeleon II dark cloud contains some 40 X-ray sources.<ref name=Alcala2000>{{ cite journal |author=Alcalá JM |author2=Covino E |author3=Sterzik MF |author4=Schmitt JHMM |author5=Krautter J |author6=Neuhäuser R |title=A ROSAT pointed observation of the Chamaeleon II dark cloud |journal=Astronomy & Astrophysics |date=March 2000 |volume=355 |issue=3 |pages=629–38 |bibcode=2000A&A...355..629A }}</ref> Observation in Chamaeleon II was carried out from September 10 to 17, 1993.<ref name=Alcala2000/> Source RXJ 1301.9-7706, a new WTTS candidate of [[w:spectral type|spectral type]] K1, is closest to 4U 1302-77.<ref name=Alcala2000/> ==Chamaeleon III dark clouds== Chamaeleon III appears to be devoid of current star-formation activity."<ref name=Yamauchi>{{ cite journal |author=Yamauchi S |author2=Hamaguchi K |author3=Koyama K |author4=Murakami H |title=ASCA Observations of the Chamaeleon II Dark Cloud |journal=Publ Astron Soc Japan |date=October 1998 |volume=50 |issue=10 |pages=465–74 |bibcode=1998PASJ...50..465Y }}</ref> "HD 104237 ([[w:spectral type|spectral type]] A4e) observed by [the [[w:Advanced Satellite for Cosmology and Astrophysics|Advanced Satellite for Cosmology and Astrophysics]] (ASCA)], located in the Chamaeleon III dark cloud, is the brightest Herbig Ae/Be star in the sky.<ref name=Hamaguchi>{{ cite journal |author=Hamaguchi K |author2=Yamauchi S |author3=Koyama K |title=X-ray Study of the Intermediate-Mass Young Stars Herbig Ae/Be Stars |journal=The Astrophysical Journal 2005 | arxiv=astro-ph/0406489v1 |bibcode = 2005ApJ...618..360H |doi=10.1086/423192 | volume=618 | page=260 }}</ref> ==Aerometeors== {{main|Radiation astronomy/Aerometeors}} [[Image:Straalstroom.jpg|thumb|250px|right|Clouds are shown along a jet stream over Canada. Credit: NASA.{{tlx|free media}}]] [[Image:Cyclone Catarina from the ISS on March 26 2004.JPG|250px|thumb|left|[[Meteorology]] is represented by cyclone Catarina. Credit: NASA.{{tlx|free media}}]] '''Def.''' a discrete unit of air, wind, or mist traveling or falling through or partially through an atmosphere is called an '''aerometeor'''. '''Def.''' any of the high-speed, high-altitude air currents that circle the Earth in a westerly direction is called a '''jet stream'''. '''Def.''' a system of winds rotating around a center of low atmospheric pressure, the more or less violent small-scale circulations such as tornadoes, waterspouts, and dust devils is called a '''cyclone'''. At left is an image of the cyclone Catarina. {{clear}} ==Plasma meteors== {{main|Radiation astronomy/Plasmas}} [[Image:Coronal Mass Ejection.gif|thumb|right|250px|Arcs rise above an active region on the surface of the Sun in this series of images taken by the STEREO (Behind) spacecraft. Credit: Images courtesy of the NASA STEREO Science Center.{{tlx|free media}}]] A '''magnetic cloud''' is a transient event observed in the [[w:solar wind|solar wind]]. It was defined in 1981 by Burlaga et al. 1981 as a region of enhanced [[w:magnetic field|magnetic field]] strength, smooth rotation of the magnetic field vector and low [[w:proton|proton]] temperature <ref name=Burlaga>{{ cite journal |author=Burlaga L. F. |author2=E. Sittler |author3=F. Mariani |author4=R. Schwenn |title=Magnetic loop behind an interplanetary shock: Voyager, Helios and IMP-8 observations |journal=Journal of Geophysical Research |volume=86 |pages=6673 1981 |url=http://onlinelibrary.wiley.com/doi/10.1029/JA086iA08p06673/pdf }}</ref>. Magnetic clouds are a possible manifestation of a [[w:Coronal Mass Ejection|Coronal Mass Ejection]] (CME). The association between CMEs and magnetic clouds was made by Burlaga et al. in 1982 when a magnetic cloud was observed by [[w:Helios probes|Helios-1]] two days after being observed by [[w:Solar Maximum Mission|SMM]]<ref name=Burlaga82>{{ cite journal |author=Burlaga, L. F. |display-authors=etal |title=A magnetic cloud and a coronal mass ejection |journal=Geophysical Research Letters |volume=9 |pages=1317-1320 1982 |url=http://onlinelibrary.wiley.com/doi/10.1029/GL009i012p01317/full }}</ref>. However, because observations near Earth are usually done by a single spacecraft, many CMEs are not seen as being associated with magnetic clouds. The typical structure observed for a fast CME by a satellite such as [[w:Advanced Composition Explorer|ACE]] is a fast-mode [[w:shock wave|shock wave]] followed by a dense (and hot) sheath of plasma (the downstream region of the shock) and a magnetic cloud. Other signatures of magnetic clouds are now used in addition to the one described above: among other, bidirectional superthermal electrons, unusual charge state or abundance of iron, helium, carbon and/or oxygen. The typical time for a magnetic cloud to move past a satellite at the [[w:Lagrange Point|L1]] point is 1 day corresponding to a radius of 0.15 [[w:Astronomical Unit|AU]] with a typical speed of 450&nbsp;km s⁻¹ and magnetic field strength of 20 nT <ref name=Lepping>{{ cite journal |author=Lepping, R. P. |display-authors=etal |title=Magnetic field structure of interplanetary magnetic clouds at 1 AU |journal=Journal of Geophysical Research |volume=95 |pages=11957-11965 1990 |bibcode=1990JGR....9511957L }}</ref> '''Def.''' a massive burst of [[wikt:solar wind|solar wind]], other light [[wikt:isotope|isotope]] [[wikt:plasma|plasma]], and [[wikt:magnetic field|magnetic field]]s rising above the [[wikt:solar corona|solar corona]] or being released into space is called a '''coronal mass ejection''' (CME). {{clear}} ==Coronal clouds== A [[Plasmas/Plasma objects/Coronal clouds|coronal cloud]] is a cloud, or cloud-like, natural astronomical entity, composed of plasma and usually associated with a star or other astronomical object where the temperature is such that X-rays are emitted. While small coronal clouds are above the photosphere of many different visual spectral type stars, others occupy parts of the [[interstellar medium]] (ISM), extending sometimes millions of kilometers into space, or thousands of light-years, depending on the size of the associated object such as a galaxy. "This energy [10³² to 10³³ ergs] appears in the form of electromagnetic radiation over the entire spectrum from γ-rays to radio burst, in fast electrons and nuclei up to relativistic energies, in the creation of a hot coronal cloud, and in large-scale mass motions including the ejections of material from the Sun."<ref name=Lin>{{ cite journal |author=R. P. Lin |author2=H. S. Hudson |title=Non-thermal processes in large solar flares |journal=Solar Physics |date=September-October 1976 |volume=50 |issue=10 |pages=153-78 |url=http://adsabs.harvard.edu/full/1976SoPh...50..153L |arxiv= |bibcode=1976SoPh...50..153L |doi=10.1007/BF00206199 |pmid= |accessdate=2013-07-07 }}</ref> '''Def.''' the [[wikt:luminous|luminous]] [[wikt:plasma|plasma]] [[wikt:atmosphere|atmosphere]] of the [[Stars/Sun|Sun]] or other [[wikt:star|star]], extending millions of kilometres into space, most easily seen during a total solar eclipse is called a '''corona''', or '''stellar corona'''. "Coronal clouds are irregular objects suspended in the corona with matter streaming out of them into nearby active regions."<ref name=Tandberg>{{ cite book |author=E. Tandberg-Hanssen |title=Prominences, In: ''Illustrated Glossary for Solar and Solar-Terrestrial Physics'' |publisher=D. Reidel Publishing Company |location=Dordrecht-Holland |date= 1977 |editor=A. Bruzek |editor2=C. J. Durrant |pages=97-109 |url=http://link.springer.com/chapter/10.1007/978-94-010-1245-4_10 |arxiv= |bibcode= |doi=10.1007/978-94-010-1245-4_10 |pmid= |isbn=978-94-010-1247-8 |accessdate=2013-07-10 }}</ref> ==Lightnings== {{main|Radiation astronomy/Lightnings}} [[Image:Upperatmoslight1.jpg|thumb|right|250px|The composite shows upper atmospheric lightning and electrical discharge phenomena. Credit: [[c:User:Abestrobi|Abestrobi]].{{tlx|free media}}]] The temperature for a [[lightning]] bolt channel is 28 kK or 28,000 K with a peak emittance wavelength of black-body radiation at approximately 100 nm (far ultraviolet light). {{clear}} ==Sprites== [[Image:Jellyfish lightning sprite.jpg|thumb|right|250px|The image shows an example of jellyfish lightning or sprites. Credit: H. H. C. Stenbaek-Nielsen.{{tlx|fairuse}}]] "During a thunderstorm, high in the ionosphere, you’ll find an odd variety of lightning that is far above the thunderstorm itself. Jellyfish lightning, also known as sprites, are red flashes of light that last for a few seconds. They can have a wide bell-shaped top and tentacle-like wisps of light at the bottom, resembling a jellyfish."<ref name=Winter>{{ cite book |author=Lisa Winter |title=Origins Of Mysterious "Sprite" Lightning Discovered |publisher=IFLScience |location= |date=May 12, 2014 |url=http://www.iflscience.com/environment/origins-mysterious-sprite-lightning-discovered |accessdate=2014-08-30 }}</ref> "In high-speed videos we can see the dynamics of sprite formation and then use that information to model and to reproduce the dynamics."<ref name=Qin>{{ cite book |author=Jianqi Qin |title=Origins Of Mysterious "Sprite" Lightning Discovered |publisher=IFLScience |location= |date=May 12, 2014 |url=http://www.iflscience.com/environment/origins-mysterious-sprite-lightning-discovered |accessdate=2014-08-30 }}</ref> "These sprites only occur during thunderstorms, though sprites are about three times higher up than storms. [...] the storms are necessary for sprites to occur, they aren’t quite sufficient enough to cause them on their own [...] The tentacle-like tendrils at the bottom were shown to form much faster than the bell-shaped top. [...] localized plasma irregularities can spark the formation of a sprite."<ref name=Winter/> {{clear}} ==Solar winds== [[Image:1024px--D3- LighningStormPanorama.jpg|thumb|right|250px|A lightning storm over England is imaged. Credit: Catalin Fatu.{{tlx|fairuse}}]] "The sun spits out charged particles that hit our atmosphere two to four days later at 1.5-2.7 million kph, but it does not do so evenly."<ref name=Luntz>{{ cite book |author=Stephen Luntz |title=Solar Activity Could Cause Lightning Storms On Earth |location= |date=May 16, 2014 |url=http://www.iflscience.com/space/solar-activity-could-cause-lightning-storms-earth |accessdate=2014-08-31 }}</ref> "The solar wind is not continuous, it has slow and fast streams. Because the Sun rotates, these streams can be sent out behind each other - so if you have a fast solar wind catching up with a slow solar wind, it causes a concentration to occur."<ref name=Scott>{{ cite book |author=Christ Scott |title=Solar Activity Could Cause Lightning Storms On Earth |location= |date=May 16, 2014 |url=http://www.iflscience.com/space/solar-activity-could-cause-lightning-storms-earth |accessdate=2014-08-31 }}</ref> "The slow phase is composed similarly to the solar corona while fast particles have a composition close to that of the photosphere, the outer layer of the sun that produces the light."<ref name=Luntz/> There is "a 31% increase in average lightning strikes over central England (422 to 321) in the 40 days after major solar wind events compared to the days beforehand. Lightning peaked 12-18 days after the wind's arrival. A matching increase in thundery days provided supporting evidence."<ref name=Luntz/> "It's unexpected, because these streams of particles bring with them an enhanced magnetic field - and this shields Earth from the very high-energy cosmic rays from outside of the Solar System.”<ref name=Scott/> "The reduction in cosmic rays is only around 1%, but still noticeable. Cosmic rays emitted by supernovae are thought to trigger lighting strikes, and it was expected that the shielding effect of the solar wind would cause a reduction in lightning, rather than an increase."<ref name=Luntz/> Sunspot "numbers negatively correlate with thunder days in other parts of the world."<ref name=Luntz/> "High speed streams were found to occur after periods when the sun was putting out less light, but sunspot numbers increased. Scott and his fellow authors attribute this to the streams coming from an active region appearing on the eastern side of the sun."<ref name=Luntz/> "We propose that these particles, while not having sufficient energies to reach the ground and be detected there, nevertheless electrify the atmosphere as they collide with it, altering the electrical properties of the air and thus influencing the rate or intensity at which lightning occurs."<ref name=Scott/> {{clear}} ==Gigantic jets== [[Image:Sprites-Argentina-2014-02-02.png|thumb|right|250px|This is a gigantic jet observed over a thunderstorm. Credit: [[c:User:Welias|Welias]].{{tlx|free media}}]] [[Image:Gigantic jet near Phillipines.png|thumb|left|250px|This is an image of a gigantic jet above a thunderstorm near the Philippines. Credit: H. T. Su, R. R. Hsu, A. B. Chen, Y. C. Wang, W. S. Hsiao, W. C. Lai, L. C. Lee, M. Sato & H. Fukunishi.{{tlx|fairuse}}]] On February 02, 2014, the Oro Verde Observatory (República Argentina) reported 10 or more gigantic jet event[s] observed over a thunderstorm in Entre Ríos south. Storm center [is] located at 33°S, 60°W, near the Rosario city. Each gigantic "jet could transfer 30 coulombs of negative charge from the clouds to the ionosphere (H T Su ''et al.'' 2003 Nature 423 974)."<ref name=Pennicott>{{ cite book |author=Katie Pennicott |title=Giant jets caught on camera |publisher=Institute of Physics |location= |date=25 June 2003 |url=http://physicsworld.com/cws/article/news/2003/jun/25/giant-jets-caught-on-camera |accessdate=2015-04-11 }}</ref> "During a thunderstorm in the South China Sea in July 2002, Su and co-workers used low-light-level cameras to photograph the clouds every 17 milliseconds. The five jets they observed - dubbed carrot-jets or tree-jets according to their shapes - were visible for some tens of milliseconds. But crucially, the team also detected simultaneous bursts of radio waves in four of the five cases, which indicates that the jets had transferred significant amounts of charge. The thunderclouds were at an altitude of 16 km."<ref name=Pennicott/> "Such electromagnetic bursts have only previously been linked with powerful lightning strikes, which are known to transfer large quantities of charge. But [lightning may not have] triggered the radio waves they detected, since the local lightning detection network registered no strikes at the times of the jets."<ref name=Pennicott/> On the left is an image of a fully developed gigantic jet above a thunderstorm near the Philippine. {{clear}} ==Filaments== [[Image:Solar filament.jpg|thumb|right|250px|This solar filament, some 350,000 kilometres long, erupted from the surface of the Sun on 31 August. Credit: NASA.{{tlx|fairuse}}]] "This solar filament, some 350,000 kilometres long, erupted from the surface of the Sun on 31 August. Seen in the extreme ultraviolet by NASA’s Solar Dynamics Observatory satellite, the eruption became a coronal mass ejection moving at about 1,400 kilometres per second — its particles grazed Earth’s magnetosphere several days later, sparking an auroral display."<ref name=NASA2012>{{ cite book |author=NASA |title=Plasma Burst |publisher=NASA |location=Greenbelt, Maryland USA |date=31 August 2012 |url=https://www.pinterest.com/pin/105764291220958091/ |accessdate=2015-05-18 }}</ref> {{clear}} ==Rays== {{main|Radiation/Rays}} [[Image:Radiation aurora.jpg|thumb|right|250px|This aurora suggests that the closer the observer is to being directly underneath the more it looks like radiation spraying down. Credit: Ole C. Salomonsen.{{tlx|fairuse}}]] [[Image:Northern lights on Kvaløya 2012-01-23a.jpg|thumb|left|250px|Aurora is seen from the island of Kvaløya in Norway during the 23rd of January 2011. Credit: [http://www.flickr.com/people/46083981@N00 Lars Tiede].{{tlx|free media}}]] The image on the right suggests that the closer the observer is to being directly underneath the aurora the more it looks like radiation spraying down. The more distant from being directly below the more the aurora looks like ribbons. The image on the left is from a location within the auroral oval where it frequently appears directly overhead. {{clear}} ==Gaseous meteors== Gaseous objects have at least one chemical element or compound present in the gaseous state. These gaseous components make up at least 50 % of the detectable portion of the gaseous object. [[Atmospheres/Astronomy|Atmospheric astronomy]] determines whether gaseous objects have layers or spherical portions predominantly composed of gas. Within these spherical portions may occur various gaseous meteors such as clouds, winds, or streams. ==Interstellar clouds== "Carbon monoxide is the second most abundant molecule, after H₂, in interstellar clouds. In diffuse clouds, the amount of CO is mainly derived from measurements of absorption at UV wavelengths."<ref name=Federman>{{ cite journal |author=S.R. Federman, David L. Lambert |title=The need for accurate oscillator strengths and cross sections in studies of diffuse interstellar clouds and cometary atmospheres |journal=Journal of Electron Spectroscopy and Related Phenomena |date=May 2002 |volume=123 |issue=2-3 |pages=161-71 |url=http://www.sciencedirect.com/science/article/pii/S0368204802000178 |arxiv= |bibcode= |doi= |pmid= |pdf=http://144.206.159.178/FT/578/62760/14353822.pdf |accessdate=2013-01-20 }}</ref> ==Lyman-alpha blob== [[Image:Lyman-alpha blob LAB-1.jpg|thumb|right|250px|Composite of two different images taken with the FORS instrument on the [[w:Very Large Telescope|Very Large Telescope]] of the Lyman-alpha blob LAB-1. Credit ESO/M. Hayes.{{tlx|free media}}]] A '''Lyman-alpha blob''' ('''LAB''') is a huge concentration of a gas emitting the [[w:Lyman-alpha line|Lyman-alpha emission line]]. LABs are some of the largest known individual objects in the [[w:Universe|Universe]]. Some of these gaseous structures are more than 400,000 light years across. So far they have only been found in the high-[[w:redshift|redshift]] universe because of the ultraviolet nature of the Lyman-alpha emission line. Since the [[w:Earth's atmosphere|Earth's atmosphere]] is very effective at filtering out UV photons, the Lyman-alpha photons must be redshifted in order to be transmitted through the atmosphere. {{clear}} ==Beaming gases== [[Image:Ngc4151stis.gif|thumb|right|250px|These images both depict the same area - the region of ionized gas around the nucleus of the bright Seyfert galaxy NGC 4151. Credit: Hutchings et al. in Astrophysical Journal Letters 492, L115 (1998).{{tlx|fairuse}}]] "These images [at right] both depict the same area - the region of ionized gas around the nucleus of the bright Seyfert galaxy NGC 4151. In one case, the observations used a narrow-band filter to isolate the bright gaseous emission of doubly ionized oxygen - [O III] - at 5007 Angstroms, while the other used a diffraction grating to spread the light at each point into a spectrum. The color coding was used to indicate this and to show the direction of spectral dispersion, though the wavelength range spanned by the observation would not produce a vivid color range visually. The brilliant nucleus is spread into a horizontal line, producing radiation at all wavelengths in the form of a continuum. In the dispersed image, a single cloud of gas with small internal motions will have a single Doppler shift, and will have the same appearance as in the filtered image, perhaps with a position shift due to its overall Doppler shift with respect to the average. However, a parcel of gas with a large velocity dispersion, such as one might see in a turbulent situation or near a shock front, will be preferentially smeared along the wavelength direction (left-right in this depiction). Careful comparison of these two images shows that there are many such regions, mostly located in the locations close to where the galaxy's small radio jets emerge from the nucleus. These radio jets lie approximately along the axes of the twin emission-line cones. This connection between rapid local gas motions and the emerging jets has been interpreted as evidence that much of the "turbulent" motion in the outer regions of Seyfert nuclei is powered by the radio jets, as they transfer energy to their surroundings."<ref name=KeelNGC4151>{{ cite book |author=Bill Keel |title=The interaction of jets and clouds in NGC 4151 |publisher=University of Arizona |location=Tucson, Arizona USA |date=October 2003 |url=http://www.astr.ua.edu/keel/agn/ngc4151stis.html |accessdate=2014-03-19 }}</ref> "The emission-line image shows clearly the biconical region where most of the ionized gas appears, in support of a `beaming picture" for the various kinds of Seyfert nuclei. It poses an interesting puzzle, however, because to get this plan view we must be outside the cones, but we see the broad-line region and thus classify NGC 4151 as a type 1 Seyfert - in fact, it was the prototype of the class. Thus, there are directions outside these cones where we can have a fairly clear view of the core, so the simple mental picture of a solid torus and clear views along its axis cannot be taken quite literally."<ref name=KeelNGC4151/> {{clear}} ==Liquid meteors== {{main|Radiation astronomy/Hydrometeors}} [[Image:FoggDam-NT.jpg|thumb|right|250px|A thunderstorm dumps heavy rain over Fogg Dam during the Build-Up which is the lead-up to the Wet Season. Credit: [[c:User:Bidgee|Bidgee]].{{tlx|free media}}]] Liquid water precipitation falls from the atmosphere and reaches the ground, such as drizzle and rain. Suspended liquid water particles may form and remain suspended in the air (damp haze, cloud, fog, and mist), or may be lifted by the wind from the Earth’s surface (blowing spray) causing restrictions to visibility.<ref name=Mireles>{{ cite book |author=Mark R. Mireles |author2=Kirth L. Pederson |author3=Charles H. Elford |title=Meteorologial Techniques |publisher=Air Force Weather Agency/DNT |location=Offutt Air Force Base, Nebraska, USA |date=February 21, 2007 |editor= |pages= |url=http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA466107 |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2013-02-17 }}</ref> {{clear}} ==Sea levels== [[Image:Recent Sea Level Rise.png|thumb|right|250px|This figure shows the change in annually averaged sea level at 23 geologically stable tide gauge sites with long-term records as selected. Credit: [[w:User:Robert A. Rohde|Robert A. Rohde]].{{tlx|free media}}]] [[Image:Holocene Sea Level.png|thumb|right|250px|This figure shows changes in sea level during the Holocene, the time following the end of the most recent glacial period, based on data from Fleming et al. 1998, Fleming 2000, & Milne et al. 2005. Credit: [[w:User:Robert A. Rohde|Robert A. Rohde]].{{tlx|free media}}]] [[Image:Post-Glacial Sea Level.png|thumb|right|250px|This figure shows sea level rise since the end of the last glacial episode based on data from Fleming et al. 1998, Fleming 2000, & Milne et al. 2005. Credit: [[w:User:Robert A. Rohde|Robert A. Rohde]].{{tlx|free media}}]] '''Mean sea level''' (MSL) is a measure of the average height of the ocean's surface (such as the halfway point between the mean high tide and the mean low tide); used as a standard in reckoning land elevation.<ref name=Proudman>{{ cite book |url=http://www.straightdope.com/columns/read/148/what-is-sea-level#1 |title=''What is "Mean Sea Level"?'' |publisher=Proudman Oceanographic Laboratory }}</ref> MSL also plays an extremely important role in [[w:aviation|aviation]], where standard sea level pressure is used as the measurement datum of altitude at [[w:flight level|flight level]]s. The upper figure at right shows the change in annually averaged sea level at 23 geologically stable tide gauge sites with long-term records as selected by Douglas (1997). The thick dark line is a three-year moving average of the instrumental records. This data indicates a sea level rise of ~27.5 cm from 1800-2000. Because of the limited geographic coverage of these records, it is not obvious whether the apparent decadal fluctuations represent true variations in global sea level or merely variations across regions that are not resolved. For comparison, the recent annually averaged satellite altimetry data [1] from TOPEX/Poseidon are shown in red. These data indicate a somewhat higher rate of increase than tide gauge data, however the source of this discrepancy is not obvious. It may represent systematic error in the satellite record and/or incomplete geographic sampling in the tide gauge record. The month to month scatter on the satellite measurements is roughly the thickness of the plotted red curve. The second figure at the right shows changes in sea level during the Holocene, the time following the end of the most recent glacial period, based on data from Fleming et al. 1998, Fleming 2000, & Milne et al. 2005. These papers collected data from various reports and adjusted them for subsequent vertical geologic motions, primarily those associated with post-glacial continental and hydroisostatic rebound. The first refers to deformations caused by the weight of continental ice sheets pressing down on the land, the latter refers to uplift in coastal areas resulting from the increased weight of water associated with rising sea levels. It should be noted that because of the latter effect and associated uplift, many islands, especially in the Pacific, exhibited higher local sea levels in the mid Holocene than they do today. Uncertainty about the magnitude of these corrections is the dominant uncertainty in many measurements of Holocene scale sea level change. The black curve is based on minimizing the sum of squares error weighted distance between this curve and the plotted data. It was constructed by adjusting a number of specified tie points, typically placed every 1 kyr and forced to go to 0 at the modern day. A small number of extreme outliers were dropped. It should be noted that some authors propose the existence of significant short-term fluctuations in sea level such that the sea level curve might oscillate up and down about this ~1 kyr mean state. Others dispute this and argue that sea level change has been a smooth and gradual process for essentially the entire length of the Holocene. Regardless of such putative fluctuations, evidence such as presented by Morhange et al. (2001) suggests that in the last 10 kyr sea level has never been higher than it is at present. The lower figure shows sea level rise since the end of the last glacial episode based on data from Fleming et al. 1998, Fleming 2000, & Milne et al. 2005. At least one episode of rapid deglaciation, known as meltwater pulse 1A, is agreed upon and indicated on the plot. A variety of other accelerated periods of deglaciation have been proposed (i.e. MWP-1B, 2, 3, 4), but it is unclear if these actually occurred or merely reflect misinterpretation of difficult measurements. No other events are evident in the data presented above. The lowest point of sea level during the last glaciation is not well constrained by observations (shown here as a dashed curve), but is generally argued to be approximately 130 +/- 10 m below present sea level and to have occurred at approximately 22 +/- 3 thousand years ago. The time of lowest sea level is more or less equivalent to the last glacial maximum. Prior to this time, ice sheets were still increasing in size so that sea level was decreasing almost continuously over a period of approximately 100,000 years. {{clear}} ==Rivers== [[Image:Limpopo.jpg|thumb|right|250px|Aerial view, extreme long shot, looks down as the Limpopo River winds its way through Southern Mozambique. Credit: TSGT Cary Humphries.{{tlx|free media}}]] [[Image:Loboc river.png|thumb|left|250px|Loboc River is in the Bohol province of the Philippines. Credit: [[c:User:Qaalvin|Qaalvin]].{{tlx|free media}}]] '''Def.''' a large and often winding stream which drains a land mass, carrying water down from higher areas to a lower point, ending at an ocean or in an inland sea is called a '''river'''. {{clear}} ==Meanders== [[Image:Rio-cauto-cuba.JPG|thumb|right|250px|This is an aerial photo of the meanders by the Río Cauto in Cuba. Credit: [[c:User:Not home|Not home]].{{tlx|free media}}]] '''Def.''' a winding, crooked, or involved course or a tortuous or intricate movement of water as a stream or river is called a '''meander'''. {{clear}} ==Rapids== [[Image:Rapids.jpg|thumb|right|250px|Rapids are before the Rhine Falls. Credit: [[w:User:Gulliveig|Gulliveig]].{{tlx|fairuse}}]] '''Def.''' a rough section of a river or stream which is difficult to navigate due to the swift and turbulent motion of the water is called a '''rapid'''. On the right are rapids featuring white water before the Rhine Falls. {{clear}} ==Waterfalls== [[Image:Iceland Godafoss 1972.jpg|thumb|right|250px|Goðafoss is in Iceland. Credit: [[c:User:Roger McLassus|Roger McLassus]].{{tlx|free media}}]] [[Image:Salto del Angel-Canaima-Venezuela08.JPG|thumb|left|250px|Salto Angel is in Canaima, Venezuela. Credit: [[c:User:Poco a poco|Poco a poco]].{{tlx|free media}}]] '''Def.''' a flow of water over the edge of a cliff is called a '''waterfall'''. Angel Falls in the image on the left is the world's tallest at 979 m. {{clear}} ==Meltwaters== [[Image:Meltwater from a glacier.JPG|thumb|right|250px|The photo shows a meltwater stream to the right of the dome. Credit: Alexandra Iezzi, AVO/USGS.{{tlx|fairuse}}]] [[Image:Meltwater Redoubt 2009.jpg|thumb|250px|left|This shows flooding caused by the melting of Drift Glacier. Credit: AVO/USGS.{{tlx|fairuse}}]] "On a summit flight, we were able to see the source of the meltwater stream. It appears to starts to the right of the dome where a fall face can be seen and continues down."<ref name=Iezzi>{{ cite book |author=Alexandra Iezzi |title=Image 79741 |publisher=AVO/USGS |location=Alaska USA |date=14 July 2015 |url=http://www.avo.alaska.edu/images/image.php?id=79741 |accessdate=2016-02-18 }}</ref> The image on the left shows flooding some 7.6 m deep caused by the melting of Drift Glacier. {{clear}} ==Lavas== [[Image:Pahoehoe toe.jpg|thumb|right|250px|Advancing Pahoehoe toe, Kilauea Hawaii 2003, results when Kohola breakouts. Credit: Hawaii Volcano Observatory (DAS).{{tlx|free media}}]] [[Image:Zhupanovsky Dzenzursky 2013.jpg|thumb|right|250px|Many characteristics of a low-viscosity lava flow are visible in this image of Zhupanovsky and Dzenzursky volcanoes on Russia’s Kamchatka Peninsula. Credit: Robert Simmon, NASA Earth Observatory, Landsat 8, the USGS Earth Explorer.{{tlx|free media}}]] [[Image:Zhupanovsky volcano.jpg|thumb|right|250px|This view of Zhupanovsky shows some of the lava flows. Credit: [[:ru:Шпиленок, Игорь Петрович|Игорь Шпиленок]].{{tlx|free media}}]] [[Image:Ropy pahoehoe.jpg|thumb|right|250px|This Pahoehoe is from Kīlauea in Hawaii. Credit: Tari Noelani Mattox, USGS.{{tlx|free media}}]] [[Image:20011005-0039 DAS large.jpg|thumb|right|250px|Basalt lava (glowing rock) is oozing over basalt lava flow. Credit: USGS.{{tlx|free media}}]] [[Image:Aa large.jpg|thumb|left|250px|Glowing `a`a flow front advances over pahoehoe on the coastal plain of Kilauea Volcano, Hawai`i. Credit: USGS.{{tlx|free media}}]] '''Def.''' melted rock ejected by a volcano from its crater or fissured sides is called a '''lava'''. '''Usage notes''' Geologists make a distinction between magma (molten rock underground) and lava (molten rock on the surface). '''Def.''' molten matter within the earth, the source of the material of lava flows, dikes of eruptive rocks, etc is called a '''magma'''. "Streams of molten rock that ooze from gaps or vents in the Earth’s surface are called lava flows. Though generally slow-moving, these rivers of rock pose a hazard to everything in their paths. They can bury or burn homes and roads, ruin farmland for generations, and transform glaciers into muddy landslides (lahars)."<ref name=Klemetti>{{ cite book |author=Erik Klemetti |author2=Adam Voiland |title=The Shapes that Lavas Take, Part 1 |publisher=NASA |location=Washington, DC USA |date=21 November 2013 |url=http://earthobservatory.nasa.gov/IOTD/view.php?id=82424 |accessdate=2015-02-18 }}</ref> "Lava flows can take many shapes and move at very different rates depending on the viscosity of the magma, the slope of the land, and the rate of an eruption. Some of the speediest flows travel 60 kilometers (40 miles) per hour; the slowest creep along at less than 1 kilometer (0.6 miles) per hour. They can sometimes even flow for more than a year after an eruption has ended."<ref name=Klemetti/> "While viscous lava flows are defined by steep flow fronts and pressure ridges, low-viscosity lavas tend to move faster and create longer, narrower shapes. They also tend to have smaller flow fronts and levee-like structure along their edges. Many characteristics of a low-viscosity lava flow are visible in [the image on the right second down] of Zhupanovsky and Dzenzursky volcanoes on Russia’s Kamchatka Peninsula. The image was acquired by the Operational Land Imager (OLI) on the Landsat 8 satellite on September 9, 2013."<ref name=Voiland>{{ cite book |author=Erik Klemetti |author2=Adam Voiland |title=The Shapes that Lavas Take, Part 2 |publisher=NASA |location=Washington, DC USA |date=22 November 2013 |url=http://www.earthobservatory.nasa.gov/IOTD/view.php?id=82427&eocn=home&eoci=iotd_title |accessdate=2015-02-18 }}</ref> "In the image, younger lava flows appear grey, while older flows are covered by green vegetation. The exact ages of the flows are unclear, but the eruptions that produced them likely occurred during the past few thousand years. Distinctive lava levees are visible along the edges of many of the younger flows. These features form as lava cools and hardens along the edges or top of a flow while the center of a flow still advances."<ref name=Voiland/> "In comparison to the Chao dacite in Chile (the product of viscous lava), the flows at Zhupanovsky [at lowest right] and Dzenzursky are much narrower and longer. They have smaller flow fronts (10 to 30 meters tall) in comparison to the sheer 400-meter cliffs at Chao, as well as more prominent lava levees along the edges. Like Chao, the flows shown above have pressure ridges caused by the compression of the cooling top of the lava as the flow advanced."<ref name=Voiland/> '''Def.''' a form of lava flow of basaltic rock, usually dark-colored with a smooth or ropey surface is called '''pahoehoe'''. "Ropy pahoehoe [shown in the fourth image down on the right, taken 11 June 1995] is the most common surface texture of pahoehoe flows. The numerous folds and wrinkles ("ropes") that are characteristic of ropy pahoehoe form when the thin, partially solidified crust of a flow is slowed or halted (for example, if the crust encounters an obstruction or slower-moving crust). Because lava beneath the crust continues to move forward, it tends to drag the crust along. The crust then behaves like an accordian that is squeezed together--the crust is flexible enough to develop wrinkles or a series of small ridges and troughs as it is compressed and driven forward."<ref name=Mattox>{{ cite book |author=Tari Noelani Mattox |title=Photo glossary of volcano terms |publisher=U.S. Geological Survey |location=Menlo Park, California, USA |date=4 September 2000 |url=http://web.archive.org/web/20070102035046/http://volcanoes.usgs.gov/Products/Pglossary/pahoehoe_ropy.html |accessdate=2015-02-18 }}</ref> '''Def.''' a form of lava flow [shown on the right, fifth image down] consisting of basaltic rock, usually dark-colored with a jagged and loose, clinkery surface is called an '''aa'''. "`A`a (pronounced "ah-ah") is a Hawaiian term for lava flows that have a rough rubbly surface composed of broken lava blocks called clinkers. The incredibly spiny surface of a solidified `a`a flow makes walking very difficult and slow. The clinkery surface actually covers a massive dense core, which is the most active part of the flow. As pasty lava in the core travels downslope, the clinkers are carried along at the surface. At the leading edge of an `a`a flow, however, these cooled fragments tumble down the steep front and are buried by the advancing flow. This produces a layer of lava fragments both at the bottom and top of an `a`a flow."<ref name=USGSaa>{{ cite book |author=United States Geological Survey |title=VHP Photo Glossary: AA |publisher=USGS |location=Menlo Park, California USA |date=17 July 2008 |url=http://volcanoes.usgs.gov/images/pglossary/aa.php |accessdate=2015-03-10 }}</ref> {{clear}} ==Rocky meteors== {{main|Radiation astronomy/Rocks}} [[Image:Dark Flight Incoming.jpg|thumb|right|250px|The image shows the first film ever of a meteor plunging down at terminal velocity. Credit: Anders Helstrup / Dark Flight, montage, Hans Erik Foss Amundsen.{{tlx|fairuse}}]] "A skydiver may have captured the first film ever of a meteorite plunging down at terminal velocity, also known as its “dark flight” stage."<ref name=Fang>{{ cite book |author=Janet Fang |title=Skydiver Almost Hit by Meteorite |publisher=IFLScience |location= |date=April 4, 2014 |url=http://www.iflscience.com/space/skydiver-almost-hit-meteorite |accessdate=2014-08-31 }}</ref> "The footage was captured in 2012 by a helmet cam worn by Anders Helstrup as he and other members of the Oslo Parachute Club jumped from a small plane that took off from an airport in Hedmark, Norway."<ref name=Fang/> “It can’t be anything else. The shape is typical of meteorites -- a fresh fracture surface on one side, while the other side is rounded.”<ref name=Amundsen>{{ cite book |author=Hans Erik Foss Amundsen |title=Skydiver Almost Hit by Meteorite |publisher=IFLScience |location= |date=April 4, 2014 |url=http://www.iflscience.com/space/skydiver-almost-hit-meteorite |accessdate=2014-08-31 }}</ref> “It has never happened before that a meteorite has been filmed during dark flight; this is the first time in world history.”<ref name=Amundsen/> "Having the rock in hand would certainly help. But despite triangulations and analyses, Helstrup and his recruits still haven’t found it."<ref name=Fang/> {{clear}} ==Meteoroids== {{main|Radiation astronomy/Meteoroids}} '''Def.''' "a relatively small (sand- to boulder-sized) fragment of debris in a solar system"<ref name=MeteoroidWikt>{{ cite book |author=[[wikt:User:SnoopY|SnoopY]] |title=meteoroid |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=21 December 2005 |url=https://en.wiktionary.org/wiki/meteoroid |accessdate=2016-02-06 }}</ref> is called a '''meteoroid'''. "As of 2011 the International Astronomical Union officially defines a meteoroid as a solid object moving in interplanetary space, of a size considerably smaller than an asteroid and considerably larger than an atom".<ref name=Millman>{{ cite journal |author=Peter M. Millman 1961 |title=A report on meteor terminology |journal=JRASC |volume=55 |pages=265–267 |bibcode=1961JRASC..55..265M }}</ref><ref name=Glossary>{{ cite book |url=http://www.imo.net/glossary |title=Glossary International Meteor Organization |publisher=Imo.net |date=2008-11-18 |accessdate=2011-09-16}}</ref> The visible path of a meteoroid that enters the Earth's atmosphere (or another body's) atmosphere is called a '''''meteor''''', or colloquially a '''''shooting star''''' or '''''falling star'''''. If a meteoroid reaches the ground and survives impact, then it is called a meteorite. Beech and Steel, writing in ''Quarterly Journal of the Royal Astronomical Society'', proposed a new definition where a meteoroid is between 100 µm and 10 m across.<ref name=Beach>{{ cite journal |author=Martin Beech, Duncan Steel 1995 |date=September |title=On the Definition of the Term Meteoroid |journal=Quarterly Journal of the Royal Astronomical Society |volume=36 |issue=3 |pages=281–284 |bibcode=1995QJRAS..36..281B }})</ref> Following the discovery and naming of asteroids below 10 m in size (e.g., 2008 TC3), Rubin and Grossman refined the Beech and Steel definition of meteoroid to objects between 10&nbsp;µm and 1 m in diameter.<ref name=Rubin2010>{{Cite journal |author=Rubin, A.E. |author2=Grossman, J.N. 2010 |date=January |title=Meteorite and meteoroid: New comprehensive definitions |journal=Meteoritics & Planetary Science |volume=45 |issue=1 |pages=114–122 |bibcode=2010M&PS...45..114R |doi = 10.1111/j.1945-5100.2009.01009.x }})</ref> The [near-Earth object] NEO definition includes larger objects, up to 50 m in diameter, in this category. Very small meteoroids are known as '''micrometeoroids''' (see also interplanetary dust). The composition of meteoroids can be determined as they pass through Earth's atmosphere from their trajectories and the light spectra of the resulting meteor. Their effects on radio signals also give information, especially useful for daytime meteors which are otherwise very difficult to observe. The light spectra, combined with trajectory and light curve measurements, have yielded various compositions and densities, ranging from fragile snowball-like objects with density about a quarter that of ice,<ref name=Povenmire>Povenmire, H. [http://www.lpi.usra.edu/meetings/lpsc2000/pdf/1183.pdf PHYSICAL DYNAMICS OF THE UPSILON PEGASID FIREBLL – EUROPEAN NETWORK 190882A]. Florida Institute of Technology</ref> to nickel-iron rich dense rocks. In meteoroid ablation spheres from deep-sea sediments, "[t]he silicate spheres are the most dominant group."<ref name=Blanchard>{{ cite journal |author=M.B. Blanchard |author2=D.E. Brownlee |author3=T.E. Bunch |author4=P.W. Hodge |author5=F.T. Kyte |title=Meteoroid ablation spheres from deep-sea sediments |journal=Earth and Planetary Science Letters |date=January 1980 |volume=46 |issue=2 |pages=178-90 |url=http://www.sciencedirect.com/science/article/pii/0012821X80900047 |arxiv= |bibcode= |doi=10.1016/0012-821X(80)90004-7 |pmid= |accessdate=2012-01-02 }}</ref> From these trajectory measurements, meteoroids have been found to have many different orbits, some clustering in streams (see Meteor showers) often associated with a parent comet, others apparently sporadic. Debris from meteoroid streams may eventually be scattered into other orbits. ... Meteoroids travel around the Sun in a variety of orbits and at various velocities. The fastest ones move at about 26 miles per second (42 kilometers per second) through space in the vicinity of Earth's orbit. The Earth travels at about 18 miles per second (29 kilometers per second). Thus, when meteoroids meet the Earth's atmosphere head-on (which would only occur if the meteors were in a retrograde orbit), the combined speed may reach about 44 miles per second (71 kilometers per second). Meteoroids moving through the earth's orbital space average about 20&nbsp;km/s.<ref name=OrbitalDebris>{{ cite book |title=Report on Orbital Debris |url=http://hdl.handle.net/2060/19900003319 |work=NASA |publisher=NASA Technical Reports Server |accessdate=1 September 2012 }}</ref> {{clear}} ==Fireballs== [[Image:2013-02-15T101834Z 1461539070 GM1E92F1EHS01 RTRMADP 3 RUSSIA-METEORITE.JPG|thumb|center|350px|This is a fireball meteor trail with some burning still visible above the Urals city of Chelyabinsk, Russia, on February 15, 2013. Credit: Reuters/www.chelyabinsk.ru.{{tlx|fairuse}}]] Above is a [[visual astronomy]] image of a fireball trail with some burning still visible from a meteor as it passed overhead in Chelyabinsk, Russia, on February 15, 2013. A relatively small percentage of meteoroids hit the Earth's atmosphere and then pass out again: these are termed Earth-grazing fireballs (for example The Great Daylight 1972 Fireball). For 2011 there are 4589 fireball records at the American Meteor Society.<ref name="Fireballs2011">{{ cite book |title=Fireball Report: 4589 records found between 2011-01-01 and 2011-12-31 |publisher=American Meteor Society |url=http://www.amsmeteors.org/fireball2/public.php?start_date=2011-01-01&end_date=2011-12-31&submit=Find+Reports |accessdate=2012-04-24 }}</ref> "At 66 kilometers (41 miles) per second, they appear as fast streaks, faster by a hair than their sisters, the Eta Aquarids of May. And like the Eta Aquarids, the brightest of family tend to leave long-lasting trains. Fireballs are possible three days after maximum."<ref name=Levy>{{ cite book |author=David Levy |author2=Stephen Edberg |title=Observe: Meteors |publisher=Astronomical League |location= |date= |editor= |pages= |url= |arxiv= |bibcode=1986obse.book.....L |doi= |pmid= |isbn= }}</ref> {{clear}} ==Bolides== '''Def.''' a fireball reaching magnitude &minus;14 or brighter.<ref name=Belton>{{ cite book | author = MJS Belton | title = Mitigation of hazardous comets and asteroids | publisher = Cambridge University Press | date = | year = 2004 | location = | pages = | url = http://books.google.com/?id=Dw0A7T0fy6AC | doi = | id = | isbn = 0-521-82764-7 }}:156</ref> is called a '''bolide'''. '''Def.''' a fireball reaching an magnitude &minus;17 or brighter is called a '''superbolide'''. ==Meteor showers== {{main|Radiation astronomy/Showers}} [[Image:Leonid meteor shower as seen from space (1997).jpg|thumb|right|250px|This photograph shows the Leonids as many begin contacting the Earth's atmosphere. Credit: NASA.{{tlx|free media}}]] Meteors may occur in [[w:meteor shower|showers]], which arise when the Earth passes through a trail of debris left by a comet, or as "random" or "sporadic" meteors, not associated with a specific single cause. A number of specific meteors have been observed, largely by members of the public and largely by accident. {{clear}} ==Cryometeors== {{main|Radiation astronomy/Cryometeors}} [[Image:Nssl0098 - Flickr - NOAA Photo Library.jpg|thumb|right|250px|This is a very large hailstone from the NOAA Photo Library. Credit: NOAA Legacy Photo; OAR/ERL/Wave Propagation Laboratory.{{tlx|free media}}]] A '''megacryometeor''' is a very large chunk of ice sometimes called huge hailstones, but do not need to form in thunderstorms. {{clear}} ==Glaciers== {{main|Glaciers}} [[Image:Baltoro glacier from air.jpg|thumb|right|250px|The Baltoro Glacier in the Karakoram, Kashmir, Northern Pakistan, at 62 kilometres (39 mi) in length, is one of the longest alpine glaciers on Earth. Credit: [http://www.flickr.com/people/22539273@N00 Guilhem Vellut from Paris].{{tlx|free media}}]] A '''glacier''' is a slowly moving river of ice. As with rivers of water, a glacier usually follows its stream bed from a high altitude source to sea level. {{clear}} ==Glacial fracturing== [[Image:Larsen C Ice Shelf Rift.jpg|right|thumb|250px|A huge iceberg, a quarter the size of Wales, is poised to break off from the Larsen C ice shelf. Credit: Adrian Luckman.{{tlx|fairuse}}]] "Icequakes are seismic tremblings caused by sudden movement within a glacier or ice sheet, such as from a fracturing crevasse. (Anyone who has dropped an ice cube into a glass of water knows ice snaps under stress.)"<ref name=Oskin>{{ cite book |author=Becky Oskin |title=Faraway Earthquake Triggered Antarctica Icequakes |publisher=LiveScience.com |location= |date=10 August 2014 |url=http://www.livescience.com/47282-chile-earthquake-caused-antarctica-icequakes.html |accessdate=2014-08-16 }}</ref> "Chile's magnitude-8.8 earthquake on Feb. 27, 2010, set off a flurry of Antarctic icequakes, each lasting from one to 10 seconds, researchers report today (Aug. 10) in the journal Nature Geoscience. The epicenter was 2,900 miles (4,700 km) north of Antarctica."<ref name=Oskin/> "We think the crevasses are being activated by the surface waves from this big earthquake coming through, and that's making the icequake."<ref name=Walter>{{ cite book |author=Jacob Walter |title=Faraway Earthquake Triggered Antarctica Icequakes |publisher=LiveScience.com |location= |date=10 August 2014 |url=http://www.livescience.com/47282-chile-earthquake-caused-antarctica-icequakes.html |accessdate=2014-08-16 }}</ref> "An iceberg [in the image on the right] expected to be one of the 10 largest ever recorded is ready to break away from Antarctica."<ref name=Luckman>{{ cite book |author=Adrian Luckman |title=Huge Antarctic iceberg poised to break away |publisher=BBC |location=London, England |date=6 January 2017 |url=http://www.bbc.com/news/science-environment-38522954 |accessdate=2017-01-09 }}</ref> "A long-running rift in the Larsen C ice shelf grew suddenly in December and now just 20 km of ice is keeping the 5,000 sq km piece from floating away."<ref name=McGrath>{{ cite book |author=Matt McGrath |title=Huge Antarctic iceberg poised to break away |publisher=BBC |location=London, England |date=6 January 2017 |url=http://www.bbc.com/news/science-environment-38522954 |accessdate=2017-01-09 }}</ref> "Larsen C is about 350m thick and floats on the seas at the edge of West Antarctica, holding back the flow of glaciers that feed into it."<ref name=McGrath/> "Researchers have been tracking the rift in Larsen C for many years, watching it with some trepidation after the collapse of Larsen A ice shelf in 1995 and the sudden break-up of the Larsen B shelf in 2002."<ref name=McGrath/> In "December [2016] the speed of the rift went into overdrive, growing by a further 18 km in just a couple of weeks."<ref name=McGrath/> "The rift is about 100 m wide but is estimated to be half a kilometre deep."<ref name=McGrath/> This "is a geographical and not a climate event. The rift has been present for decades, but it has punched through at this particular time."<ref name=Luckman/> "The collapse of the Larsen B ice shelf which occurred in 2002 followed on from a large rift calving event."<ref name=McGrath/> "We would expect in the ensuing months to years further calving events [from Larsen C], and maybe an eventual collapse - but it's a very hard thing to predict, and our models say it will be less stable; not that it will immediately collapse or anything like that."<ref name=Luckman/> "Even the sea level contribution of this area is not on anybody's radar; it's just a big geographical event that will change the landscape there."<ref name=Luckman/> {{clear}} ==Glacial surges== [[Image:Surging glacier.jpg|thumb|right|250px|In 1941, Hole-in-the-Wall Glacier surged. Credit: W.O. Field, World Data Center for Glaciology, Boulder, CO.{{tlx|fairuse}}]] [[Image:Sermersauq Ice Cap Glacier.jpg|thumb|left|250px|The image shows a glacial surge from the Sermersauq Ice Cap. Credit: Robert Gilbert, Niels Nielsen, Henrik Möller, Joseph R. Desloges, and Morten Rasch.{{tlx|fairuse}}]] '''Def.''' "a glacier that experiences a dramatic increase in flow rate, 10 to 100 times faster than its normal rate; usually surge events last less than one year and occur periodically, between 15 and 100 years"<ref name=Beitler/> is called a '''surging glacier'''. "In 1941, Hole-in-the-Wall Glacier [imaged at the right] surged, also knocking over trees during its advance."<ref name=Beitler>{{ cite book |author=Janet Beitler |title=Cryosphere Glossary |publisher=National Snow and Ice Data Center 2014 |url=http://nsidc.org/cryosphere/glossary/G |accessdate=2014-09-20 }}</ref> An "outlet glacier of the Sermersauq Ice Cap [on Disko Island, West Greenland, shown at the left with progressive surges marked] has surged 10.5 km downvalley to within 10 km of the fjord. [...] surging of the glacier, begun in 1995, was undetected until July 1999, when it was discovered during a geomorphic survey of the valley. Mapping from TM, Landsat and SPOT satellite imagery, and subsequent field work have documented the history of the event. On 17 June 1995 the terminus of the glacier was about where it appears in the 1985 air photography [...]. By 24 September 1995 the glacier had advanced 1.25 km and by 12 October another 1.25 km (mean advance during the second period : 70 m day^-1). The advance slowed from 18 m day^-1 in 1996 to 5 m day^-1 in 1997 and <1 m day^-1 between 1997 and 1999. By summer 1999 the advance ceased; the maximum extension of the terminus, about 10.5 km down-valley to about 10 km from the head of the fjord, was mapped from imagery on 9 July 1999 [...]."<ref name=Gilbert>{{ cite journal |author=Robert Gilbert |author2=Niels Nielsen |author3=Henrik Möller |author4=Joseph R. Desloges |author5=Morten Rasch |title=Glacimarine sedimentation in Kangerdluk (Disko Fjord), West Greenland, in response to a surging glacier |journal=Marine Geology |date= 2002 |volume=191 |issue= |pages=1-18 |url=http://geog.queensu.ca/gilbert/surge%20paper.PDF |arxiv= |bibcode= |doi= |pmid= |accessdate=2014-09-24 }}</ref> {{clear}} ==Glacial calving== [[Image:Perito Moreno Glacier Patagonia Argentina Luca Galuzzi 2005.JPG|thumb|250px|right|This shows calving by the Perito Moreno Glacier, in Los Glaciares National Park, southern Argentina. Credit: [[c:User:Lucag|Luca Galuzzi]].{{tlx|free media}}]] [[Image:Loosetooth.jpg|thumb|right|250px|These Multi-angle Imaging SpectroRadiometer (MISR) images show the progression of a "loose tooth"—an iceberg calving from the Amery Ice Shelf. Credit: NASA Earth Observatory, Clare Averill and David J. Diner, Jet Propulsion Laboratory; and Helen A. Fricker, Scripps Institution of Oceanography.{{tlx|fairuse}}]] [[Image:Jakobshavn retreat-1851-2006.jpg|thumb|right|250px|Retreating calving front of the Jacobshavn Isbrae glacier in Greenland from 1851 - 2006. Credit: NASA Earth Observatory, Cindy Starr, based on data from Ole Bennike and Anker Weidick (Geological Survey of Denmark and Greenland) and Landsat data.{{tlx|free media}}]] [[Image:Larsen 2006.jpg|thumb|right|250px|Photos show the A54 iceberg calving from the Scar Inlet Shelf (the remainder of the Larsen Ice Shelf). Credit: Ted Scambos, National Snow and Ice Data Center, University of Colorado, Boulder, and NASA Moderate Resolution Imaging Spectroradiometer images courtesy NASA Earth Observatory.{{tlx|fairuse}}]] The image on the right shows calving by the Perito Moreno Glacier, in Los Glaciares National Park, southern Argentina. "Calving of huge, tabular icebergs is unique to Antarctica, and the process can take a decade or longer. Calving results from rifts that reach across the shelf. In the case of Antarctica's Amery Ice Shelf, the calving area resembles a loose tooth [images on the second right]."<ref name=Averill>{{ cite book |author=Clare Averill |author2=David J. Diner |author3=Helen A. Fricker |title=State of the Cryosphere: Ice calves |publisher=NASA/JPL |location=Pasadena, California USA |date=6 October 2001 |url=https://nsidc.org/cryosphere/sotc/iceshelves.html |accessdate=2014-11-02 }}</ref> "On a stable ice shelf, calving is a near-cyclical, repetitive process producing large icebergs every few decades. The icebergs drift generally westward around the continent, and as long as they remain in the cold, near-coastline water, they can survive decades or more. However, they eventually are caught up in north-drifting currents where they melt and break apart."<ref name=Averill/> "In Greenland, floating ice tongues downstream from large outlet glaciers are more broken up by crevasses. Calving of the ice tongues releases armadas of smaller, steep-sided icebergs that drift south sometimes reaching North Atlantic shipping lanes. Calving of the large glacier, Jacobshavn, on the east coast of Greenland is responsible for the majority of icebergs reaching Atlantic shipping and fishing areas off of Newfoundland and most likely shed the iceberg responsible for the sinking of the Titanic in 1912. The Petermann Glacier in northwestern Greenland also shed a large ice island in August 2010. These denizens of the ocean are now tracked by the National Ice Center in the United States, along with other organizations."<ref name=Averill/> "By 2006, the Jacobshavn Glacier [third image on the right] had retreated back to where its two main tributaries join, leading to two fast-flowing glaciers where there had previously been just one."<ref name=Averill/> "The rapidly retreating Jakobshavn Glacier in western Greenland drains the central ice sheet. This image [third one on the right] shows the glacier in 2001, flowing from upper right to lower left. Terminus locations before 2001 were determined by surveys and more recent contours were derived from Landsat data. The recent stages of retreat have widened the ice front, placing more of the glacier in contact with the ocean."<ref name=Averill/> "In recent years, calving of the largest ice tongues in Greenland (in particular, Jacobshavn, Helheim, and Kangerdlugssuaq) has accelerated probably due to warmer air and/or ocean temperatures. As the ice tongues have retreated, the reduced backpressure against the glacier has allowed these glaciers to accelerate significantly."<ref name=Averill/> "The images [fourth set of images on the right] show a tabular iceberg calving from an ice shelf. This iceberg happens to be calving from the remnant piece of the Larsen B ice shelf at the southwestern corner of the embayment. While the Larsen B Ice Shelf underwent disintegration [...], this was a normal calving event."<ref name=Averill/> "Large tabular iceberg calvings are natural events that occur under stable climatic conditions, so they are not a good indicator of warming or changing climate. Over the past several decades, however, meteorological records have revealed atmospheric warming on the Antarctic Peninsula, and the northernmost ice shelves on the peninsula have retreated dramatically (Vaughan and Doake 1996)."<ref name=Averill/> "The most pronounced ice shelf retreat has occurred on the Larsen Ice Shelf, located on the eastern side of the Antarctic Peninsula's northern tip. The shelf is divided into four regions from north to south: A, B, C, and D."<ref name=Averill/> {{clear}} ==Lithometeors== {{main|Radiation astronomy/Lithometeors}} [[Image:VolcanicBombMojaveDesert.JPG|thumb|right|250px|This is a volcanic bomb found in the Mojave Desert National Preserve by Rob McConnell. Credit: [[c:User:Wilson44691|Wilson44691]].{{tlx|free media}}]] '''Def.''' a suspension of dry dust in the atmosphere is called a '''lithometeor'''. '''Def.''' the solid material thrown into the air by a volcanic eruption that settles on the surrounding areas is called '''tephra'''. {{clear}} ==Micrometeors== [[Image:Micrometeorite.jpg|thumb|right|250px|This is a micrometeorite collected from the antarctic snow. Credit: NASA.{{tlx|free media}}]] A '''micrometeoroid''' is a tiny [[w:meteoroid|meteoroid]]; a small particle of rock in space, usually weighing less than a [[w:gram|gram]]. A [[w:micrometeorite|micrometeorite]] is such a particle that survives passage through the Earth's atmosphere and reaches the Earth's surface. Micrometeoroids are extremely common in space. These tiny particles are a major contributor to [[w:space weathering|space weathering]] processes. When they hit the surface of the Moon, or any airless body (Mercury, the asteroids, etc.), the resulting melting and vaporization causes darkening and other optical changes in the [[w:regolith|regolith]]. Micrometeoroids have less stable [[w:orbit|orbit]]s than meteoroids, due to their greater [[w:surface area|surface area]] to [[w:mass|mass]] ratio. Micrometeoroids pose a significant threat to [[w:space exploration|space exploration]].<ref name = "White Sands">Micrometeoroids and Orbital Debris (MMOD) - NASA - White Sands Test Facility, Las Cruces, NM [http://www.nasa.gov/centers/wstf/laboratories/hypervelocity/mmod.html]</ref> Their velocities relative to a [[w:spacecraft|spacecraft]] in orbit average 10 kilometers per second (22,500&nbsp;mph),<ref name = "White Sands"/> and resistance to micrometeoroid impact is a significant design challenge for spacecraft and [[w:space suit|space suit]] designers (''See [[w:Thermal Micrometeoroid Garment|Thermal Micrometeoroid Garment]]''). While the tiny sizes of most micrometeoroids limits the damage incurred, the high velocity impacts will constantly degrade the outer casing of spacecraft in a manner analogous to [[w:sandblasting|sandblasting]]. Long term exposure can threaten the functionality of spacecraft systems. {{clear}} ==Hydrometeors== '''Def.''' precipitation products of the [[wikt:condensation|condensation]] of atmospheric water vapour are called '''hydrometeors'''. '''Def.''' any or all of the forms of water particles, whether liquid or solid, that fall from the atmosphere are called '''precipitation'''. ==Emissions== '''Def.''' the solid material thrown into the air by a volcanic eruption that settles on the surrounding areas is called '''tephra'''. "[T]ephra, is a general term for fragments of volcanic rock and lava that are blasted into the air by volcanic explosions or carried upward in the volcanic plume by hot, hazardous gases. The larger fragments usually fall close to the volcano, but the finer particles can be advected quite some distance. ... [Fine ash] can contain rock, minerals, and volcanic glass fragments smaller than .1 inch in diameter, or slightly larger than the size of a pinhead."<ref name=Mireles/> ==Absorptions== [[Image:MM cristaux.jpg|right|thumb|250px|This is an ultra-rich in carbon MM found near the CONCORDIA station in Antarctica. Credit: J. Duprat, E. Dobrică, C. Engrand, J. Aléon, Y. Marrocchi, S.Mostefaoui, A. Meibom, H. Leroux, J.-N. Rouzaud, M. Gounelle and F. Robert.{{tlx|fairuse}}]] "[T]he carbonaceous material [is] known from observation to dominate the terrestrial [micrometeorite (MM)] flux."<ref name=Taylor/> "Ureilites occur about half as often as eucrites (Krot et al. 2003), are relatively friable, have less a wide range of cosmic-ray exposure ages including two less than 1 Myr, and, like the dominant group of MM precursors, contain carbon."<ref name=Taylor>{{ cite journal |author=Susan Taylor |author2=Gregory F. Herzog |author3=Jeremy S. Delaney |title=Crumbs from the crust of Vesta: Achondritic cosmic spherules from the South Pole water well |journal=Meteoritics & Planetary Science |date= 2007 |volume=42 |issue=2 |pages=223-33 |url= |bibcode=2007M&PS...42..223T |doi=10.1111/j.1945-5100.2007.tb00229.x |pmid= |accessdate=2011-08-07 }}</ref> {{clear}} ==Comets== {{main|Radiation astronomy/Comets}} [[Image:Hs-2009-23-crop.jpg|thumb|right|250px|This is a Hubble Space Telescope image taken on July 23, 2009, showing a blemish of about 5,000 miles long left by the 2009 Jupiter impact.<ref name=Overbye>{{ cite book |author=Dennis Overbye |title=Hubble Takes Snapshot of Jupiter’s ‘Black Eye’ |url=http://www.nytimes.com/2009/07/25/science/space/25hubble.html?ref=science |date=2009-07-24 |publisher=New York Times |accessdate=2009-07-25 }}</ref> Credit: NASA, ESA, and H. Hammel (Space Science Institute, Boulder, Colo.), and the Jupiter Impact Team.{{tlx|free media}}]] [[Image:Jupiter showing SL9 impact sites.jpg|thumb|right|250px|Brown spots mark the places where fragments of Comet Shoemaker-Levy 9 tore through Jupiter's atmosphere in July 1994. Credit: Hubble Space Telescope Comet Team and NASA.{{tlx|free media}}]] Jupiter has been called the Solar System's vacuum cleaner,<ref name=Lovett>{{ cite book |first=Richard A.|last=Lovett |title=Stardust's Comet Clues Reveal Early Solar System |publisher=National Geographic News |date=December 15, 2006 |url=http://news.nationalgeographic.com/news/2006/12/061215-comet-stardust.html |accessdate = 2007-01-08 }}</ref> because of its immense gravity well and location near the inner Solar System. It receives the most frequent comet impacts of the Solar System's planets.<ref name=Nakamura>{{ cite journal |author=Nakamura, T. |author2=Kurahashi, H. |title=Collisional Probability of Periodic Comets with the Terrestrial Planets: An Invalid Case of Analytic Formulation |journal=Astronomical Journal 1998 |volume=115 |issue=2 |pages=848–54 |url=http://www.iop.org/EJ/article/1538-3881/115/2/848/970144.html |accessdate=2007-08-28 |doi = 10.1086/300206|bibcode=1998AJ....115..848N }}</ref> A 1997 survey of historical astronomical drawings suggested that the astronomer [Giovanni Domenico Cassini] Cassini may have recorded an impact scar in 1690. The survey determined eight other candidate observations had low or no possibilities of an impact.<ref>{{Cite journal |author=Tabe, Isshi |author2=Watanabe, Jun-ichi |author3=Jimbo, Michiwo 1997| date=February|title=Discovery of a Possible Impact SPOT on Jupiter Recorded in 1690 |journal=Publications of the Astronomical Society of Japan |volume=49|pages=L1–L5 |bibcode=1997PASJ...49L...1T |last2=Watanabe |last3=Jimbo}}</ref> A fireball was photographed by Voyager 1 during its Jupiter encounter in March 1979.<ref name="impact2012"/> During the period July 16, 1994, to July 22, 1994, over 20 fragments from the comet Shoemaker–Levy&nbsp;9 (SL9, formally designated D/1993 F2) collided with Jupiter's southern hemisphere, providing the first direct observation of a collision between two Solar System objects. This impact provided useful data on the composition of Jupiter's atmosphere.<ref name=Baalke>{{ cite book |last = Baalke|first = Ron |url = http://www2.jpl.nasa.gov/sl9/ |title = Comet Shoemaker-Levy Collision with Jupiter |publisher = NASA |accessdate = 2007-01-02}} </ref><ref name=Britt>{{ cite book |first=Robert R.|last=Britt |title=Remnants of 1994 Comet Impact Leave Puzzle at Jupiter |publisher=space.com |date=August 23, 2004 |url=http://www.space.com/scienceastronomy/mystery_monday_040823.html |accessdate = 2007-02-20}}</ref> On July 19, 2009, an impact site was discovered at approximately 216 degrees longitude in System 2.<ref name=Staff>{{ cite news |author=Staff |url=http://www.abc.net.au/news/stories/2009/07/21/2632368.htm |title=Amateur astronomer discovers Jupiter collision |date=2009-07-21 |work=ABC News online |accessdate=2009-07-21}}</ref><ref name=Salway>{{cite book|url=http://www.iceinspace.com.au/index.php?id=70,550,0,0,1,0 |first=Mike| last= Salway|date= July 19, 2009 |id=IceInSpace News |title=Breaking News: Possible Impact on Jupiter, Captured by Anthony Wesley |publisher=IceInSpace |accessdate=2009-07-19}}</ref> This impact left behind a black spot in Jupiter's atmosphere, similar in size to Oval BA. Infrared observation showed a bright spot where the impact took place, meaning the impact warmed up the lower atmosphere in the area near Jupiter's south pole.<ref name=Grossman>{{ cite book |last=Grossman |first=Lisa |date=July 20, 2009 |title=Jupiter sports new 'bruise' from impact |newspaper=New Scientist |url=http://www.newscientist.com/article/dn17491-jupiter-sports-new-bruise-from-impact.html }}</ref> 2010 Jupiter impact event: A fireball, smaller than the previous observed impacts, was detected on June 3, 2010, by Anthony Wesley, an amateur astronomer in Australia, and was later discovered to have been captured on video by another amateur astronomer in the Philippines.<ref name=Bakich>{{ cite book |url=http://www.astronomy.com/asy/default.aspx?c=a&id=9918 | title=Another impact on Jupiter | date=2010-06-04 | first=Michael| last=Bakich | publisher=Astronomy Magazine online | accessdate=2010-06-04 }}</ref> Yet another fireball was seen on August 20, 2010.<ref name=Beatty>{{ cite book |url=http://www.skyandtelescope.com/community/skyblog/observingblog/101264994.html |title=Another Flash on Jupiter! |last=Beatty|first=Kelly |date=22 August 2010 |work=Sky & Telescope |publisher=Sky Publishing |quote=Masayuki Tachikawa was observing ... 18:22 Universal Time on the 20th ... Kazuo Aoki posted an image ... Ishimaru of Toyama prefecture observed the event|accessdate=23 August 2010 | archiveurl= http://web.archive.org/web/20100827180208/http://www.skyandtelescope.com/community/skyblog/observingblog/101264994.html | archivedate= 27 August 2010 <!--DASHBot--> }}</ref> On September 10, 2012, another fireball was detected.<ref name="impact2012">{{ cite book |date=2012-09-10 |title=Another fireball on Jupiter? |publisher=Cosmic Diary blog |author=Franck Marchis |url=http://cosmicdiary.org/fmarchis/2012/09/10/another-fireball-on-jupiter/ |accessdate=2012-09-11 }}</ref><ref name=Hall>{{ cite book |url=http://georgeastro.weebly.com/jupiter.html |title=George's Astrophotography |first=George|last=Hall |date=September 2012 |quote=10 Sept. 2012 11:35 UT .. observed by Dan Petersen |accessdate=17 September 2012 }}</ref> The second image at right shows the atmospheric impact sites for the Comet Shoemaker-Levy 9 fragments. Spectroscopic studies revealed absorption lines in the Jovian spectrum due to diatomic sulfur (S₂) and carbon disulfide (CS₂), the first detection of either in Jupiter, and only the second detection of S₂ in any astronomical object. Other molecules detected included ammonia (NH₃) and hydrogen sulfide (H₂S). The amount of sulfur implied by the quantities of these compounds was much greater than the amount that would be expected in a small cometary nucleus, showing that material from within Jupiter was being revealed. "Sun-grazing comets almost never re-emerge, but their sublimative destruction near the sun has only recently been observed directly, while chromospheric impacts have not yet been seen, nor impact theory developed."<ref name=Brown>{{ cite journal |author=J.C. Brown |author2=H.E. Potts |author3=L.J. Porter |author4=G.le Chat |title=Mass Loss, Destruction and Detection of Sun-grazing & -impacting Cometary Nuclei |journal=Astronomy & Astrophysics |date=November 8, 2011 |volume=535 |issue= |pages=12 |url=http://arxiv.org/pdf/1107.1857.pdf |arxiv= |bibcode= |doi=10.1051/0004-6361/201015660 |pmid= |accessdate=2012-11-25 }}</ref> "[N]uclei are ... destroyed by ablation or explosion ... in the chromosphere, producing flare-like events with cometary abundance spectra."<ref name=Brown/> "The death of a comet at r ~ ''R''_ʘ has been seen directly only very recently (Schrijver et al 2011) using the SDO AIA XUV instrument. This recorded sublimative destruction of Comet C/2011 N3 as it crossed the solar disk very near periheloin ''q'' = 1.139''R''_ʘ."<ref name=Brown/> "The phenomenon of flare induced sunquakes - waves in the photosphere - discovered by Kosovichev and Zharkova (1998) and now widely studied (e.g. Kosovichev 2006) should also result from the momentum impulse delivered by a cometary impact."<ref name=Brown/> {{clear}} ==Rogue planets== A '''rogue planet''' — also known as an '''interstellar planet''', '''nomad planet''', '''free-floating planet''' or '''orphan planet''' — is a [[w:planetary-mass object|planetary-mass object]] which has either been ejected from its system or was never gravitationally bound to any star, brown dwarf or other such object, and that therefore orbits the galaxy directly.<ref>[http://www.space.com/searchforlife/seti_orphan_planets_050224.html ''Orphan Planets: It's a Hard Knock Life''], [http://www.space.com/ Space.com], 24 Feb 2005, retrieved 5 Feb 2009.</ref><ref>[http://web.archive.org/web/20010521192001/http://www.space.com/scienceastronomy/astronomy/free_floaters_010403-1.html ''Free-Floating Planets – British Team Restakes Dubious Claim''], Space.com, 18 Apr 2001, retrieved 5 Feb 2009.</ref><ref>[http://astrobiology.arc.nasa.gov/news/expandnews.cfm?id=783 ''Orphan 'planet' findings challenged by new model''], [http://astrobiology.nasa.gov/ NASA Astrobiology], 18 Apr 2001, retrieved 5 Feb 2009.</ref> Astronomers agree that either way, the [[w:definition of planet|definition of planet]] should depend on its current observable state and not its origin. Larger planetary-mass objects which were not ejected, but have always been free-floating, are thought to have formed in a similar way to stars, and the [[w:IAU|IAU]] has proposed that those objects be called sub-brown dwarfs<ref>[http://www.dtm.ciw.edu/boss/definition.html Working Group on Extrasolar Planets – Definition of a "Planet"] POSITION STATEMENT ON THE DEFINITION OF A "PLANET" (IAU)</ref> (an example of this is [[w:Cha 110913-773444|Cha 110913-773444]], which may be an ejected rogue planet or may have formed on its own and be a sub-brown dwarf).<ref name="CNN">[http://archives.cnn.com/2000/TECH/space/10/06/space.planets.reut/index.html Rogue planet find makes astronomers ponder theory]</ref> The closest rogue planet to Earth yet discovered, [[w:CFBDSIR 2149-0403|CFBDSIR 2149-0403]], is around 100 light years away.<ref>[http://www.washingtonpost.com/national/health-science/astronomers-spy-a-planet-untethered-to-any-star-there-may-be-many-more/2012/11/17/ff15b274-2e89-11e2-beb2-4b4cf5087636_story.html?tid=ts_carousel Astronomers spy a planet untethered to any star; there may be many more], ''Washington Post'', 19 Nov 2012. Retrieved 20 Nov 2012.</ref> When a planetary-sized object passes in front of a background star, its gravitational field causes a momentary increase in the visible brightness of the background star. This is known as [[w:microlensing|microlensing]]. Astrophysicist Takahiro Sumi of Osaka University in Japan and colleagues, who form the Microlensing Observations in Astrophysics (MOA) and the Optical Gravitational Lensing Experiment (OGLE) collaborations, carried out a study of microlensing which they published in 2011. They observed 50 million stars in our galaxy using the 1.8 meter MOA-II telescope at New Zealand's [[w:Mount John Observatory|Mount John Observatory]] and the 1.3 meter [[w:University of Warsaw|University of Warsaw]] telescope at Chile's [[w:Las Campanas Observatory|Las Campanas Observatory]]. They found 474 incidents of microlensing, ten of which were brief enough to be planets of around Jupiter's size with no associated star in the immediate vicinity. The researchers estimated from their observations that there are nearly two free-floaters for every star in our galaxy.<ref>[http://news.sciencemag.org/sciencenow/2011/05/homeless-planets-may-be-common.html?ref=hp Homeless' Planets May Be Common in Our Galaxy] by Jon Cartwright, Science Now ,18 May 2011, Accessed 20 may 2011 </ref><ref>[http://www.physorg.com/news/2011-05-class-planets.html Planets that have no stars: New class of planets discovered], Physorg.com, May 18, 2011. Accessed May 2011.</ref><ref>{{ cite arXiv |last=T. Sumi |eprint=1105.3544 |class=astro-ph.EP |title=Unbound or Distant Planetary Mass Population Detected by Gravitational Microlensing |date=2011 }}</ref> Other estimations suggest a much larger number, up to 100,000 times more free-floating planets than stars in our Milky Way.<ref>{{cite web |title=Researchers say galaxy may swarm with 'nomad planets' |url=http://news.stanford.edu/news/2012/february/slac-nomad-planets-022312.html |accessdate=29 February 2012 |publisher=Stanford University }}</ref> ==Asteroids== {{main|Rocks/Rocky objects/Asteroids}} [[Image:ESA Gaia Asteroids detection 20150717 625.jpg|thumb|center|400px|This is a plot of Gaia asteroid detections. Credit: ESA/Gaia/DPAC/CU4, L. Galluccio, F. Mignard, P. Tanga (Observatoire de la Côte d'Azur).{{tlx|fairuse}}]] '''Asteroids''' are small rocky objects orbiting the [[Stars/Sun|Sun]]. Large numbers of asteroids as indicated in the image from Gaia at the top ranging in size from Ceres to dust particles are found in the asteroid belt especially between the orbits of Mars and [[Jupiter]]. {{clear}} ==Centaurs== '''Def.''' an "icy planetoid that orbits the Sun between Jupiter and Neptune"<ref name=CentaurWikt>{{ cite book |author=[[wikt:User:SnoopY|SnoopY]] |title=Centaur, In: ''Wiktionary'' |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=21 December 2005 |url=https://en.wiktionary.org/wiki/Centaur |accessdate=2015-08-31 }}</ref> is called a '''Centaur'''. "The recent investigation of the orbital distribution of Centaurs (Emel’yanenko et al., 2005) showed that there are two dynamically distinct classes of Centaurs, a dominant group with semimajor axes a > 60 AU and a minority group with a < 60 AU."<ref name=Emelyanenko>{{ cite journal |author=V. V. Emel’yanenko |title=Structure and dynamics of the Centaur population: constraints on the origin of short-period comets |journal=Earth, Moon, and Planets |date=December 2005 |volume=97 |issue=3-4 |pages=341-51 |url=http://dccm.susu.ac.ru/acm2005.pdf |bibcode= |doi=10.1007/s11038-006-9095-5 |pmid= |accessdate=2011-10-06 }}</ref> "[T]he intrinsic number of such objects is roughly an order of magnitude greater than that for a<60 AU".<ref name=Emelyanenko/> ==Moons== [[Image:PIA12758 Helene crop.jpg|right|thumb|250px|Cassini imaged the surface of Saturn's moon Helene as the spacecraft flew by the moon on Jan. 31, 2011. Credit: NASA / Jet Propulsion Lab / Space Science Institute.{{tlx|free media}}]] [[Image:PIA17208-SaturnMoon-Epimetheus-CloseFlyby-20151206.jpg|left|thumb|250px|NASA's Cassini spacecraft captured this view of Saturn's moon Epimetheus. Credit: NASA/JPL-Caltech/Space Science Institute.{{tlx|free media}}]] "Cassini imaged [on the right] the surface of Saturn's moon Helene as the spacecraft flew by the moon on Jan. 31, 2011."<ref name=Porco>{{ cite book |author=C. Porco |title=Flying by Helene |publisher=NASA's Science Mission Directorate |location=Washington, D.C. USA |date=31 January 2011 |url=http://www.ciclops.org/view/6723/Flying_by_Helene?js=1 |accessdate=2016-11-06 }}</ref> "This small moon leads Dione by 60 degrees in the moons' shared orbit. Helene is a "Trojan" moon of Dione, named for the Trojan asteroids that orbit 60 degrees ahead of and behind Jupiter as it circles the Sun."<ref name=Porco/> "This view looks toward the leading hemisphere of Helene (33 kilometers, 21 miles across). North on Helene is up and rotated 2 degrees to the left."<ref name=Porco/> "The image was taken with the Cassini spacecraft narrow-angle camera using a combination of spectral filters sensitive to wavelengths of polarized green light centered at 617 and 568 nanometers. The view was obtained at a distance of approximately 31,000 kilometers (19,000 miles) from Helene and at a Sun-Helene-spacecraft, or phase, angle of 65 degrees. Scale in the original image was 187 meters (612 feet) per pixel. The image was contrast enhanced and magnified by a factor of 1.5 to enhance the visibility of surface features."<ref name=Porco/> "NASA's Cassini spacecraft captured this view [on the left] of Saturn's moon Epimetheus (116 kilometers, or 72 miles across) during a moderately close flyby on Dec. 6, 2015. This is one of Cassini's highest resolution views of the small moon, along with PIA09813."<ref name=Lavoie2015>{{ cite book |author=Sue Lavoie |title=PIA17208: Examining Epimetheus |publisher=NASA/JPL |location=Pasadena, California USA |date=6 December 2015 |url=http://photojournal.jpl.nasa.gov/catalog/PIA17208 |accessdate=2016-11-06 }}</ref> "This view looks toward the Saturn facing side of Epimetheus. North on Epimetheus is up. The image was taken in green polarized light with the Cassini spacecraft narrow-angle camera."<ref name=Lavoie2015/> {{clear}} ==Superluminals == {{main|Radiation astronomy/Superluminals}} [[Image:Grs1915 radio.jpg|thumb|right|250px|This image shows a pair of objects ejected from GRS 1915+105 moving apart at an apparently superluminal speed. Credit: Felix Mirabe, Saclay, France, and Luis Rodriguez, the National Autonomous University, Mexico City.{{tlx|free media}}]] [[Image:Bhexplode merlin big.gif|thumb|right|250px|In the time-lapse sequence, micro-quasar GRS1915 expels bubbles of hot gas in spectacular jets. Credit: R. Spencer (U. Manchester) et al., MERLIN, Jodrell Bank.{{tlx|fairuse}}]] "In far-distant quasars and galaxies, millions or even billions of light-years away, the gravitational energy of supermassive black holes is capable of accelerating "jets" of subatomic particles to speeds approaching that of light. The VLA has observed such jets for many years. In some of these jets, blobs of material have been seen to move at apparent speeds greater than that of light -- a phenomenon called ''superluminal motion''. The apparent faster-than-light motion actually is an illusion seen when a jet of material is travelling close to -- but below -- the speed of light and directed toward Earth."<ref name=Mirabel>{{ cite book |author=Felix Mirabel |author2=Luis Rodriguez |title="Microquasars" in Our Own Galaxy |publisher=National Radio Astronomy Observatory |location=West Virginia USA |date= 2000 |url=https://www.nrao.edu/pr/2000/vla20/background/superlum/ |accessdate=2014-03-17 }}</ref> "In the Spring of 1994, Felix Mirabel from Saclay, France, and Luis Rodriguez, from the National Autonomous University in Mexico City, were observing an X-ray emitting object called GRS 1915+105, which had just shown an outburst of radio emission. This object was known to be about 40,000 light-years away, within our own Milky Way Galaxy -- in our own cosmic neighborhood. Their time series of VLA observations, seen in this image, showed that a pair of objects ejected from GRS 1915+105 were moving apart at an apparently superluminal speed. This was the first time that superluminal motion had been detected in our own Galaxy."<ref name=Mirabel/> "This surprising result showed that the supermassive black holes at the centers of galaxies -- black holes millions of times more massive than the Sun -- have smaller counterparts capable of producing similar jet ejections. GRS 1915+105 is thought to be a double-star system in which one of the components is a black hole or neutron star only a few times the mass of the Sun. The more-massive object is pulling material from its stellar companion. The material circles the massive object in an accretion disk before being pulled into it. Friction in the accretion disk creates temperatures hot enough that the material emits X-rays, and magnetic processes are believed to accelerate the material in the jets."<ref name=Mirabel/> "Since Mirabel and Rodriguez discovered the superluminal motion in GRS 1915+105, several other Galactic "microquasars" have been discovered and studied with the VLA and the VLBA. In 1999, NRAO astronomer Robert Hjellming turned the VLA toward a bursting microquasar within 24 hours of a reported X-ray outburst. Working with X-ray observers Donald Smith and Ronald Remillard of MIT, Hellming found that this object is a microquasar only 1,600 light-years away, making it the closest black hole to Earth yet discovered."<ref name=Mirabel/> "Microquasars within our own Galaxy, because they are closer and thus easier to study, have become invaluable "laboratories" for revealing the physical processes that produce superfast jets of material. For discovering this new class of celestial object, Mirabel and Rodriguez received the prestigous Bruno Rossi Prize of the American Astronomical Society in 1997."<ref name=Mirabel/> "On the far side of our Galaxy, gas clouds explode away from a small black hole. This might seem peculiar, as black holes are supposed to attract matter. But material falling toward a black hole collides and heats up, creating an environment similar to a quasar that is far from stable. In the [at second right] time-lapse sequence, micro-quasar GRS1915 expels bubbles of hot gas in spectacular jets. These computer enhanced radio images show one plasma bubble coming almost directly toward us at 90 percent the speed of light, and another moving away. Each of the four frames marks the passage of one day. Originally detected on October 29th, these bubbles have now faded from view."<ref name=Mirabel/> {{clear}} ==See also== {{div col|colwidth=20em}} * [[Radiation astronomy/Acoustics|Acoustic astronomy]] * [[Radiation astronomy/Active galactic nuclei|Active galactic nuclei astronomy]] * [[Radiation astronomy/Cyans|Cyan astronomy]] * [[Radiation astronomy/Fieries|Fiery meteor astronomy]] * [[Radiation astronomy/Galaxies|Galaxies]] * [[Radiation astronomy/Gravitationals|Gravitational astronomy]] * [[Radiation astronomy/High-velocity galaxies|High-velocity galaxy astronomy]] * [[Radiation astronomy/Lightnings|Lightning astronomy]] * [[Radiation astronomy/Minerals|Mineral astronomy]] * [[Radiation astronomy/Planets|Planets]] * [[Radiation astronomy/Radars|Radar astronomy]] * [[Radiation astronomy/Stars|Stellar astronomy]] * [[Radiation astronomy/Superluminals|Superluminal astronomy]] * [[Radiation astronomy/Yellows|Yellow astronomy]] {{Div col end}} ==References== {{reflist|2}} ==External links== {{Principles of radiation astronomy}}{{tlx|Radiation astronomy resources}}{{Sisterlinks|Meteors}} <!-- footer categories --> [[Category:Astrophysics/Lectures]] [[Category:Meteors/Lectures]] [[Category:Radiation astronomy/Lectures]] [[Category:Radiation/Lectures]] 9d51clpplwyqr9qbx6jt9tetfx68cil 6 219008 2412477 1646586 2022-08-07T04:04:29Z Marshallsumter 311529 /* Licensing */ wikitext text/x-wiki == Summary == A huge iceberg, a quarter the size of Wales, is poised to break off from the Larsen C ice shelf. [[Category:Earth images]] [[Category:Glaciology images]] [[Category:Meteorology images]] [[Category:Radar images]] [[Category:Rocks images]] == Licensing == {{Information1 |Description = A huge iceberg, a quarter the size of Wales, is poised to break off from the Larsen C ice shelf. |Source = The image appears on a website entitled, "Huge Antarctic iceberg poised to break away" at url=http://www.bbc.com/news/science-environment-38522954. |Date = 6 January 2017 |Author = Adrian Luckman |Rationale = No free licensed or public domain alternatives known to exist to show a huge iceberg, a quarter the size of Wales, poised to break off from the Larsen C ice shelf about 2017. |Permission = Fair Use }} {{Fairuse}} g2nen3uebtgurnpvxd1jtoesciasqbe 2 219126 2412399 2412127 2022-08-06T19:45:44Z ThaniosAkro 2805358 /* Right hand side positive */ wikitext text/x-wiki <math>3</math> cube roots of <math>W</math> <math>W = 0.828 + 2.035\cdot i</math> <math>w_0 = 1.2 + 0.5\cdot i</math> <math>w_1 = \frac{-1.2 - 0.5\sqrt{3}}{2} + \frac{1.2\sqrt{3} - 0.5}{2}\cdot i</math> <math>w_2 = \frac{-1.2 + 0.5\sqrt{3}}{2} + \frac{- 1.2\sqrt{3} - 0.5}{2}\cdot i</math> <math>w_0^3 = w_1^3 = w_2^3 = W</math> <math></math> <math></math> <math>y = x^3 - x</math> <math>y = x^3</math> <math>y = x^3 + x</math> ===allEqual=== <math>y = f(x) = x^3</math> <math>y = f(-x)</math> <math>y = f(x) = x^3 + x</math> <math>x = p</math> <math>y = f(x) = (x-5)^3 - 4(x-5) + 7</math> {{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}} <div style="padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;"> [[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]]. </div> ====Welcomee==== {{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}} <div style="padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em; background-color: #FFF800; "> [[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]]. </div> =====Welcomen===== {{Robelbox|title=|theme={{{theme|9}}}}} <div style="padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em; background-color: #FFFFFF; "> [[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. 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To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]]. </div> <syntaxhighlight lang=python> # python code. if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 : pass </syntaxhighlight> {{Robelbox/close}} {{Robelbox/close}} {{Robelbox/close}} <noinclude> [[Category: main page templates]] </noinclude> ==Law of addition== ===Factors of integer N=== Several modern methods for determining the factors of a given integer attempt to create two congruent squares modulo integer <math>N.</math> <math>x^2 \equiv y^2 \pmod{N}</math> This means that the difference between the two squares is exactly divisible by <math>N</math>: <math>N\mid (x^2 - y^2).</math> Integer <math>N</math> always contains the factors <math>N,1,</math> called trivial factors. If <math>N</math> contains two non-trivial factors <math>p,q,</math> then: <math>\frac{(x+y)(x-y)}{p \cdot q}.</math> With a little luck <math>p\mid (x+y)</math> and <math>q\mid (x-y)</math> in which case: <math>p = \text{igcd}(x+y, N)</math> and <math>q = \text{igcd}(x-y, N)</math> where "<math>\text{igcd}</math>" is function "<math>\text{integer greatest common divisor.}</math>" ====A simple example:==== We will use quadratic congruences to calculate factors of <math>N = 4171</math> for <math>164 \ge x \ge 1.</math> =====Right hand side exact square===== One congruence produced an exact square for y: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 70 | 4900 | 729 |} :<math>4900 \equiv 729 \pmod{N}</math> :<math>70^2 \equiv 27^2 \pmod{N}</math> <math>p = \text{igcd}(70-27, 4171)</math> <math>= \text{igcd}(43, 4171)</math> <math>= 43.</math> <math>q = \text{igcd}(70+27, 4171)</math> <math>= \text{igcd}(97, 4171)</math> <math>= 97.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> <math></math> <math></math> <math></math> <math></math> <math></math> <math></math> <math></math> <math></math> =====Right hand side negative===== Table below contains a sample of values of <math>x</math> that produce negative <math>y:</math> {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 7 | 49 | -4122 |- | 8 | 64 | -4107 ** |- | 9 | 81 | -4090 |- | 10 | 100 | -4071 |- | 11 | 121 | -4050 !! |- | 12 | 144 | -4027 |- | 60 | 3600 | -571 |- | 61 | 3721 | -450 <math>\ \ </math>!! |- | 62 | 3844 | -327 |- | 63 | 3969 | -202 |- | 64 | 4096 | -75 <math>\ \ \ \ </math>** |- | 65 | 4225 | 54 |} ======Non-trivial result 1====== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 8 | 64 | -4107 ** |- | 64 | 4096 | -75 <math>\ \ \ \ </math>** |} :<math>64 \equiv -4107 \pmod{N}</math> :<math>4096 \equiv -75 \pmod{N}</math> :<math>64\cdot 4096 \equiv -4107\cdot (-75) \pmod{N}</math> :<math>262144 \equiv 308025 \pmod{N}</math> :<math>512^2 \equiv 555^2 \pmod{4171}</math> <math>p = \text{igcd}(555-512, 4171)</math> <math>= \text{igcd}(43, 4171)</math> <math>= 43.</math> <math>q = \text{igcd}(555+512, 4171)</math> <math>= \text{igcd}(1067, 4171)</math> <math>= 97.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> ======Non-trivial result 2====== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 11 | 121 | -4050 !! |- | 61 | 3721 | -450 <math>\ \ </math>!! |} :<math>121 \equiv -4050 \pmod{N}</math> :<math>3721 \equiv -450 \pmod{N}</math> :<math>121\cdot 3721 \equiv -4050 \cdot (-450) \pmod{N}</math> :<math>450241 \equiv 1822500 \pmod{N}</math> :<math>671^2 \equiv 1350^2 \pmod{4171}</math> <math>p = \text{igcd}(1350-671, 4171)</math> <math>= \text{igcd}(679, 4171)</math> <math>= 97.</math> <math>q = \text{igcd}(1350+671, 4171)</math> <math>= \text{igcd}(2021, 4171)</math> <math>= 43.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> =====With 3 congruences===== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 56 | 3136 | -1035 |- | 59 | 3481 | -690 |- | 145 | 21025 | 16854 |} :<math>3136 \equiv -1035 \pmod{N}</math> :<math>3481 \equiv -690 \pmod{N}</math> :<math>21025 \equiv 16854 \pmod{N}</math> :<math>3136\cdot 3481 \cdot 21025 \equiv -1035 \cdot -690 \cdot 16854 \pmod{N}</math> :<math>229517646400 \equiv 12036284100 \pmod{N}</math> :<math>479080^2 \equiv 109710^2 \pmod{4171}</math> <math>p=\text{igcd}(479080-109710,4171)</math> <math>= 43.</math> <math>q = \text{igcd}(479080+109710, 4171)</math> <math>= 97.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> <math></math> <math></math> <math></math> <math></math> <math></math> <math></math> ======Trivial result====== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 89 | 7921 | 3750 **!! |- | 145 | 21025 | 16854 <math>\ </math>!! |} :<math>7921 \equiv 3750 \pmod{N}</math> :<math>21025 \equiv 16854 \pmod{N}</math> :<math>7921\cdot 21025 \equiv 3750 \cdot 16854 \pmod{N}</math> :<math>166539025 \equiv 63202500 \pmod{N}</math> :<math>12905^2 \equiv 7950^2 \pmod{4171}</math> <math>p = \text{igcd}(12905-7950, 4171)</math> <math>= \text{igcd}(4955, 4171)</math> <math>= 1.</math> <math>q = \text{igcd}(12905+7950, 4171)</math> <math>= \text{igcd}(20855, 4171)</math> <math>= 4171.</math> This congruence produced the trivial factors of <math>4171.</math> <syntaxhighlight lang=python> # python code: </syntaxhighlight> ===Adding 2 congruences=== {{RoundBoxTop|theme=2}} If <math>A \equiv B \pmod{N}, </math> and <math>C \equiv D \pmod{N}, </math> then: <math>A+C \equiv B+D \pmod{N}.</math> Proof: <math>A-B = K_1\cdot N</math>, therefore <math>A = B + K_1\cdot N</math> and <math>C = D + K_2\cdot N</math> <math>(A+C) - (B+D) = B + K_1\cdot N + D + K_2\cdot N - B - D = N(K_1 + K_2)</math> which is exactly divisible by N. {{RoundBoxBottom}} ===Quadratic Congruences=== A quadratic congruence is a congruence that contains at least one exact square, for example: <math>x^2 \equiv y \pmod{N}</math> or <math>x^2 \equiv y^2 \pmod{N}.</math> Initially, let us consider the congruence: <math>x^2 \equiv y \pmod{N}.</math> If <math>y = x^2 - N,</math> then: <math>x^2 \equiv y \pmod{N}.</math> Proof: <math>x^2 - y = x^2 - (x^2 - N) = N</math> which is exactly divisible by <math>N.</math> Consider an example with real numbers. Let <math>N = 257</math> and <math>26 \ge x \ge 6.</math> <syntaxhighlight> N = 257 x | x^2 - N ----|-------- 6 | -221 7 | -208 8 | -193 9 | -176 10 | -157 11 | -136 12 | -113 13 | -88 14 | -61 15 | -32 16 | -1 17 | 32 18 | 67 19 | 104 20 | 143 21 | 184 22 | 227 23 | 272 24 | 319 25 | 368 26 | 419 </syntaxhighlight> A cursory glance at the values of <math>x^2 - N</math> indicates that the value <math>x^2 - N</math> is never divisible by <math>5.</math> Proof: <math>N \equiv 2 \pmod{5}</math> therefore <math>N - 2 = k5</math> or <math>N = 5k + 2.</math> The table shows all possible values of <math>x\ %\ 5:</math> <syntaxhighlight> x | x^2 | y = x^2 - N ------ | --------------- | ----------------------------------------------- 5p + 0 | 25pp | 25pp - (5k+2) = 25pp - 5k - 2 5p + 1 | 25pp + 10p + 1 | 25pp + 10p + 1 - (5k+2) = 25pp + 10p - 5k - 1 5p + 2 | 25pp + 20p + 4 | 25pp + 20p + 4 - (5k+2) = 25pp + 20p - 5k + 2 5p + 3 | 25pp + 30p + 9 | 25pp + 30p + 9 - (5k+2) = 25pp + 30p - 5k + 7 5p + 4 | 25pp + 40p + 16 | 25pp + 40p + 16 - (5k+2) = 25pp + 40p - 5k + 14 </syntaxhighlight> As you can see, the value <math>y = x^2 - N</math> is never exactly divisible by <math>5.</math> If you look closely, you will see also that it is never exactly divisible by <math>3.</math> Why is this? An interesting question that leads us to the topic of quadratic residues. ====Quadratic Residues==== Consider all the congruences for prime number <math>5:</math> <math>x^2 \equiv y \pmod{5}</math> for <math>5 > x \ge 0.</math> <syntaxhighlight> x | x^2 | (x^2) % 5 ---|---------|----------- 0 | 0 | 0 1 | 1 | 1 2 | 4 | 4 3 | 9 | 4 4 | 16 | 1 </syntaxhighlight> Quadratic residues of <math>5</math> are <math>0,1,4.</math> Values <math>2,3</math> are not quadratic residues of <math>5.</math> These values are quadratic non-residues. To calculate the quadratic residues of a small prime <math>p:</math> <syntaxhighlight lang=python> # python code: def quadResidues(p) : L1 = [] for v in range (p>>1, -1, -1) : L1 += [(v*v) % p] return L1 print (quadResidues(11)) </syntaxhighlight> <syntaxhighlight> [3, 5, 9, 4, 1, 0] </syntaxhighlight> Quadratic residues of <math>11</math> are <math>0,1,3,4,5,9.</math> The method presented here answers the question, "What are the quadratic residues of p?" If <math>p</math> is a very large prime, the question is often, "Is r a quadratic residue of p?" The answer is found in advanced number theory. Let us return to quadratic residues mod <math>N = 257.</math> <math>N\ %\ 5 = 2,</math> therefore <math>N</math> is not a quadratic residue of <math>5.</math> This is why <math>x^2 - N</math> is never divisible by <math>5</math> exactly. <math>N\ %\ 11 = 4,</math> therefore <math>N</math> is a quadratic residue of <math>11</math> and a value of <math>x</math> that satisfies the congruence <math>x^2 \equiv 4 \pmod{257}</math> has form <math>11p \pm 2.</math> From the table above: <syntaxhighlight> N = 257 x | x^2 - N ----|-------- 9 | -176 13 | -88 20 | 143 24 | 319 </syntaxhighlight> These <math>4</math> values of <math>x^2 - N</math> are exactly divisible by <math>11.</math> <math>x = 9</math> is <math>11\cdot 1 - 2.</math> <math>x = 13</math> is <math>11\cdot 1 + 2.</math> <math>x = 20</math> is <math>11\cdot 2 - 2.</math> <math>x = 24</math> is <math>11\cdot 2 + 2.</math> =====Products===== This section uses prime number <math>41</math> as an example. Using <code>quadResidues(p)</code> quadratic residues of <math>41</math> are: <syntaxhighlight> qr41 = [0, 1, 2, 4, 5, 8, 9, 10, 16, 18, 20, 21, 23, 25, 31, 32, 33, 36, 37, 39, 40] </syntaxhighlight> Quadratic non-residues of <math>41</math> are: <syntaxhighlight> qnr41 = [3, 6, 7, 11, 12, 13, 14, 15, 17, 19, 22, 24, 26, 27, 28, 29, 30, 34, 35, 38] </syntaxhighlight> ======of 2 residues====== A simple test to verify that the product of 2 residues is a residue: <syntaxhighlight lang=python> # Python code. for index1 in range (0, len(qr41)) : v1 = qr41[index1] for index2 in range (index1, len(qr41)) : v2 = qr41[index2] residue = (v1*v2) % 41 if residue not in qr41 : print ('residue',residue,'not quadratic.') </syntaxhighlight> This test shows that, at least for prime number <math>41,</math> the product of 2 residues is a residue. Advanced math proves that this is true for all primes. ======of 2 non-residues====== A simple test to verify that the product of 2 non-residues is a residue: <syntaxhighlight lang=python> # Python code. for index1 in range (0, len(qnr41)) : v1 = qnr41[index1] for index2 in range (index1, len(qnr41)) : v2 = qnr41[index2] residue = (v1*v2) % 41 if residue not in qr41 : print ('residue',residue,'not quadratic.') </syntaxhighlight> This test shows that, at least for prime number <math>41,</math> the product of 2 non-residues is a residue. Advanced math proves that this is true for all primes. ======of residue and non-residue====== A simple test to verify that the product of residue and non-residue is non-residue: <syntaxhighlight lang=python> # Python code. for index1 in range (1, len(qr41)) : v1 = qr41[index1] for index2 in range (0, len(qnr41)) : v2 = qnr41[index2] residue = (v1*v2) % 41 if residue not in qnr41 : print ('residue',residue,'quadratic.') </syntaxhighlight> This test shows that, at least for prime number <math>41,</math> the product of residue and non-residue is non-residue. Advanced math proves that this is true for all primes. {{RoundBoxTop|theme=2}} Some authors may consider <math>0</math> as not a legitimate residue. <math>0</math> is not included as a residue in the test above. {{RoundBoxBottom}} {{RoundBoxTop|theme=2}} <syntaxhighlight lang=python> </syntaxhighlight> <syntaxhighlight> </syntaxhighlight> {{RoundBoxBottom}} <math></math> <math></math> <math></math> ===Examples=== {{RoundBoxTop|theme=5}} <math></math> <math></math> <math></math> <math></math> <math>39x^2 + 64y^2 - 2496 = 0</math> <math>64x^2 + 39y^2 - 2496 = 0</math> <math></math> <math></math> <math></math> ====Techniques==== {{RoundBoxTop|theme=4}} =====For speed===== {{RoundBoxTop|theme=7}} ======Many comparisons====== {{RoundBoxTop|theme=8}} If your code contains many numerical comparisons, it may be tempting to put: <math></math> <math></math> <math></math> <math></math> <syntaxhighlight lang=python> # python code. if a == b == c == d == e == f == g == h == 0 : pass </syntaxhighlight> If all values <code>a,b,c,d,e,f,g,h</code> are equal and non-zero, processing the above statement takes time. For greater speed, put <math>0</math> and the value most likely to be non-zero at beginning of comparison: <syntaxhighlight lang=python> # python code. if 0 == f == a == b == c == d == e == g == h : pass </syntaxhighlight> <math></math> <math></math> <math></math> <math></math> <math></math> {{RoundBoxBottom}} ======Divide by 2====== {{RoundBoxTop|theme=8}} <math></math> <math></math> <math></math> <math></math> Division by 2 seems simple enough: <syntaxhighlight lang=python> # python code. a = b / 2 </syntaxhighlight> Divisions are time consuming. If b is a large Decimal number, the following code is faster: <syntaxhighlight lang=python> # python code. a = D('0.5') * b </syntaxhighlight> If b is <code>type int,</code> right shift is faster than multiplication by <code>0.5:</code> <syntaxhighlight lang=python> # python code. a = b >> 1 </syntaxhighlight> Also, right shift preserves precision of <code>type int:</code> <syntaxhighlight lang=python> # python code. >>> b = 12345678901234567890123456789 >>> a = b/2 ; a 6.172839450617284e+27 >>> a = b >> 1 ; a 6172839450617283945061728394 </syntaxhighlight> {{RoundBoxTop|theme=8}} To preserve rightmost bit: <syntaxhighlight lang=python> # python code. >>> b = 12345678901234567890123456789 >>> rightbit = b & 1 ; rightbit 1 >>> b >>= 1 ; b 6172839450617283945061728394 </syntaxhighlight> <math></math> <math></math> <math></math> <math></math> <math></math> {{RoundBoxBottom}} {{RoundBoxBottom}} {{RoundBoxBottom}} =====For clarity===== {{RoundBoxTop|theme=7}} <math></math> <math></math> <math></math> <math></math> <syntaxhighlight lang=python> # python code. </syntaxhighlight> <math></math> <math></math> {{RoundBoxBottom}} <math></math> <math></math> <math></math> <math></math> <syntaxhighlight lang=python> # python code. </syntaxhighlight> <math></math> <math></math> {{RoundBoxBottom}} {{RoundBoxBottom}} ===tables=== {{RoundBoxTop|theme=1}} {| class="wikitable" |- ! || No equal roots !! 2 equal roots !! 3 equal roots !! 4 equal roots !! 2 pairs of equal roots |- | Cubic: 1(a), 2(a) | different | different | different | same | different |- | Quadratic: 1(b), 2(b) | different | different | same, 1root | null | same, 2roots |- | Linear: 1(c), 2(c) | different | same | null | null | null |} See [[Cubic_function#Function_as_product_of_linear_function_and_quadratic | Function_as_product_of_linear_function_and_quadratic]] above. To calculate all roots: <syntaxhighlight lang=python> # python code. a,b,c,d = 1,-3,-9,-5 # Associated quadratic: p = -1 A = a B = A*p + b C = B*p + c # Associated linear function: a1 = A b1 = a1*p + B print ('x3 =', -b1/a1) </syntaxhighlight> <syntaxhighlight> x3 = 5.0 </syntaxhighlight> Roots of cubic function <math>f(x) = x^3 - 3x^2 - 9x - 5</math> are <math>-1, -1, 5.</math> <syntaxhighlight lang=python> # python code. </syntaxhighlight> {{RoundBoxBottom}} =Testing= ======table1====== {|style="border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;" align="center" | Hello As <math>abs(x)</math> increases, the value of <math>f(x)</math> is dominated by the term <math>-ax^3.</math> When <math>x</math> has a very large negative value, <math>f(x)</math> is always positive. When <math>x</math> has a very large negative value, <math>f(x)</math> is always positive. When <math>x</math> has a very large negative value, <math>f(x)</math> is always positive. When <math>x</math> has a very large positive value, <math>f(x)</math> is always negative. <syntaxhighlight> 1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727 3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147 0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989 </syntaxhighlight> |} {{RoundBoxTop|theme=2}} [[File:0410cubic01.png|thumb|400px|''' Graph of cubic function with coefficient a negative.''' </br> There is no absolute maximum or absolute minimum. ]] Coefficient <math>a</math> may be negative as shown in diagram. As <math>abs(x)</math> increases, the value of <math>f(x)</math> is dominated by the term <math>-ax^3.</math> When <math>x</math> has a very large negative value, <math>f(x)</math> is always positive. When <math>x</math> has a very large positive value, <math>f(x)</math> is always negative. Unless stated otherwise, any reference to "cubic function" on this page will assume coefficient <math>a</math> positive. {{RoundBoxBottom}} <math>x_{poi} = -1</math> <math></math> <math></math> <math></math> <math></math> =====Various planes in 3 dimensions===== {{RoundBoxTop|theme=2}} <gallery> File:0713x=4.png|<small>plane x=4.</small> File:0713y=3.png|<small>plane y=3.</small> File:0713z=-2.png|<small>plane z=-2.</small> </gallery> {{RoundBoxBottom}} <syntaxhighlight lang=python> </syntaxhighlight> <syntaxhighlight> </syntaxhighlight> <syntaxhighlight lang=python> </syntaxhighlight> <syntaxhighlight> </syntaxhighlight> <syntaxhighlight> 1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727 3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147 0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989 6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471 6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723 5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162 0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342 1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698 6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112 0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472 </syntaxhighlight> <math>\theta_1</math> {{RoundBoxTop|theme=2}} [[File:0422xx_x_2.png|thumb|400px|''' Figure 1: Diagram illustrating relationship between <math>f(x) = x^2 - x - 2</math> and <math>f'(x) = 2x - 1.</math>''' </br> ]] {{RoundBoxBottom}} <math>O\ (0,0,0)</math> <math>M\ (A_1,B_1,C_1)</math> <math>N\ (A_2,B_2,C_2)</math> <math>\theta</math> <math>\ \ \ \ \ \ \ \ </math> :<math>\begin{align} (6) - (7),\ 4Apq + 2Bq =&\ 0\\ 2Ap + B =&\ 0\\ 2Ap =&\ - B\\ \\ p =&\ \frac{-B}{2A}\ \dots\ (8) \end{align}</math> <math>\ \ \ \ \ \ \ \ </math> :<math>\begin{align} 1.&4141475869yugh\\ &2645er3423231sgdtrf\\ &dhcgfyrt45erwesd \end{align}</math> <math>\ \ \ \ \ \ \ \ </math> :<math> 4\sin 18^\circ = \sqrt{2(3 - \sqrt 5)} = \sqrt 5 - 1 </math> ====Introduction to floats==== {{RoundBoxTop|theme=5}} Although integers are great for many situations, they have a serious limitation, integers are [[Wikipedia:Natural number|whole numbers]]. This means that they do not include all [[Wikipedia:Real number|real numbers]]. A ''real number'' is a value that represents a quantity along a continuous line<ref>[[Wikipedia:Real number]]</ref>, which means that it can have fractions in decimal forms. <code>4.5</code>, <code>1.25</code>, and <code>0.75</code> are all real numbers. In computer science, real numbers are represented as floats. To test if a number is float, we can use the <code>isinstance</code> built-in function. <syntaxhighlight lang=python> >>> isinstance(4.5, float) True >>> isinstance(1.25, float) True >>> isinstance(0.75, float) True >>> isinstance(3.14159, float) True >>> isinstance(2.71828, float) True >>> isinstance(1.0, float) True >>> isinstance(271828, float) False >>> isinstance(0, float) False >>> isinstance(0.0, float) True </syntaxhighlight> As a general rule of thumb, floats have a ''[[Wikipedia:Decimal mark|decimal point]]'' and integers do not have a ''decimal point''. So even though <code>4</code> and <code>4.0</code> are the same number, <code>4</code> is an integer while <code>4.0</code> is a float. The basic arithmetic operations used for integers will also work for floats. (Bitwise operators will not work with floats.) <syntaxhighlight lang=python> >>> 4.0 + 2.0 6.0 >>> -1.0 + 4.5 3.5 >>> 1.75 - 1.5 0.25 >>> 4.13 - 1.1 3.03 >>> 4.5 // 1.0 4.0 >>> 4.5 / 1.0 4.5 >>> 4.5 % 1.0 0.5 >>> 7.75 * 0.25 1.9375 >>> 0.5 * 0.5 0.25 >>> 1.5 ** 2.0 2.25 </syntaxhighlight> {{RoundBoxBottom}} ghthz38q07zgdxe5hlyzv73plo3lg83 0 232469 2412416 2412271 2022-08-06T21:47:27Z Young1lim 21186 /* Synchrnoization */ wikitext text/x-wiki == '''Background''' == '''Combinational and Sequential Circuits''' * [[Media:DD2.B.4..Adder.20131007.pdf |Adder]] * [[Media:DD3.A.1.LatchFF.20160308.pdf |Latches and Flipflops]] '''FSM''' * [[Media:DD3.A.3.FSM.20131030.pdf |FSM]] * [[Media:CArch.2.A.Bubble.20131021.pdf |FSM Example]] '''Tiny CPU Example''' * [[Media:CDsgn6.TinyCPU.2.A.ISA.20160511.pdf |Instruction Set]] * [[Media:CDsgn6.TinyCPU.2.B.DPath.20160502.pdf |Data Path]] * [[Media:CDsgn6.TinyCPU.2.C.CPath.20160427.pdf |Control Path]] * [[Media:CDsgn6.TinyCPU.2.D.Implement.20160513.pdf |FPGA Implementation]] </br> == '''Microprocessor Architecture''' == * ARM Architecture : - Programmer's Model ([[Media:ARM.1Arch.1A.Model.20180321.pdf |pdf]]) : - Pipelined Architecture ([[Media:ARM.1Arch.2A.Pipeline.20180419.pdf |pdf]]) * ARM Organization * ARM Cortex-M Processor Architecture * ARM Processor Cores </br> == '''Instruction Set Architecture''' == * ARM Instruction Set : - Overview ([[Media:ARM.2ISA.1A.Overview.20190611.pdf |pdf]]) : - Addressing Modes ([[Media:ARM.2ISA.2A.AddrMode.20191108.pdf |pdf]]) : - Multiple Transfer ([[Media:ARM.2ISA.3A.MTransfer.20190903.pdf |pdf]]) : - Assembler Format :: - Data Processing ([[Media:ARM.2ISA.4A.Proc.Format.20200204.pdf |pdf]]) :: - Data Transfer ([[Media:ARM.2ISA.4B.Trans.Format.20200205.pdf |pdf]]) :: - Coprocessor ([[Media:ARM.2ISA.4C.CoProc.Format.20191214.pdf |pdf]]) :: - Summary ([[Media:ARM.2ISA.4D.Summary.Format.20200205.pdf |pdf]]) : - Binary Encoding ([[Media:ARM.2ISA.5A.Encoding.201901105.pdf |pdf]]) * Thumb Instruction Set </br> == '''Assembly Programming''' == === ARM Assembly Programming (I) === * 1. Overview ([[Media:ARM.2ASM.1A.Overview.20200101.pdf |pdf]]) * 2. Example Programs ([[Media:ARM.2ASM.2A.Program.20200108.pdf |pdf]]) * 3. Addressing Modes ([[Media:ARM.2ASM.3A.Address.20200127.pdf |pdf]]) * 4. Data Transfer ([[Media:ARM.2ASM.4A.DTransfer.20200206.pdf |pdf]]) * 5. Data Processing ([[Media:ARM.2ASM.5A.DProcess.20200208.pdf |pdf]]) * 6. Control ([[Media:ARM.2ASM.6A.Control.20200215.pdf |pdf]]) * 7. Arrays ([[Media:ARM.2ASM.7A.Array.20200311.pdf |pdf]]) * 8. Data Structures ([[Media:ARM.2ASM.8A.DataStruct.20200718.pdf |pdf]]) * 9. Finite State Machines ([[Media:ARM.2ASM.9A.FSM.20200417.pdf |pdf]]) * 10. Functions ([[Media:ARM.2ASM.10A.Function.20210115.pdf |pdf]]) * 11. Parameter Passing ([[Media:ARM.2ASM.11A.Parameter.20210106.pdf |pdf]]) * 12. Stack Frames ([[Media:ARM.2ASM.12A.StackFrame.20210611.pdf |pdf]]) :: :: === ARM Assembly Programming (II) === :: * 1. Thumb instruction programming ([[Media:ARM.2ASM.Thumb.20210612.pdf |pdf]]) * 2. Exceptions ([[Media:ARM.2ASM.Exception.20220722.pdf |pdf]]) * 3. Exception Programming ([[Media:ARM.2ASM.ExceptionProg.20220311.pdf |pdf]]) * 4. Exception Handlers ([[Media:ARM.2ASM.ExceptionHandler.20220131.pdf |pdf]]) * 5. Interrupt Programming ([[Media:ARM.2ASM.InterruptProg.20211030.pdf |pdf]]) * 6. Interrupt Handlers ([[Media:ARM.2ASM.InterruptHandler.20211030.pdf |pdf]]) * 7. Vectored Interrupt Programming ([[Media:ARM.2ASM.VectoredInterrupt.20220801.pdf |pdf]]) </br> * ARM Assembly Exercises ([[Media:ESys.3.A.ARM-ASM-Exercise.20160608.pdf |A.pdf]], [[Media:ESys.3.B.Assembly.20160716.pdf |B.pdf]]) :: === ARM Assembly Programming (III) === * 1. Fixed point arithmetic (integer division) * 2. Floating point arithmetic * 3. Matrix multiply === ARM Linking === * arm link ([[Media:arm_link.20211208.pdf |pdf]]) </br> === ARM Microcontroller Programming === * 1. Input / Output * 2. Serial / Parallel Port Interfacing * 3. Analog I/O Interfacing * 4. Communication </br> == '''Memory Architecture''' == </br> === '''Memory Hierarchy''' === </br> === '''System and Peripheral Buses''' === </br> === '''Architectural Support''' === * High Level Languages * System Development * Operating Systems </br> == '''Peripheral Architecture''' == </br> === '''Vectored Interrupt Controller ''' === </br> === '''Timers ''' === * Timer / Counter ([[Media:ARM.4ASM.Timer.20220801.pdf |pdf]]) * Real Time Clock * Watchdog Timer </br> === '''Serial Bus''' === * '''UART''' : Universal Asynchronous Receiver/Transmitter ([[Media:ARM.4ASM.UART.20220805.pdf |pdf]]) * '''I2C''' : Inter-Integrated Circuit * '''SPI''' : Serial Peripheral Interface * '''USB''' : Universal Serial Bus Device Controller </br> === '''I/Os ''' === * General Purpose Input/Output ports (GPIO) * Pulse Width Modulator * Analog-to-Digital Converter (ADC) * Digital-to-Analog Converter (DAC) </br> <!-- == '''Interrupts and Exceptions ''' == --> </br> == '''Synchrnoization'''== </br> === H/W and S/W Synchronization === * busy wait synchronization * handshake interface </br> === Interrupt Synchronization === * interrupt synchronization * reentrant programming * buffered IO * periodic interrupt * periodic polling </br> ==''' Interfacing '''== </br> === Time Interfacing === * input capture * output compare </br> === Serial Interfacing === * Programming UART * Programming SPI * Programming I2C * Programming USB </br> === Analog Interfacing === * OP Amp * Filters * ADC * DAC </br> == '''Old materials''' == === '''Instruction Set Architecture''' === * ARM Instruction Set :: - Overview ([[Media:ARM.2ISA.1A.Overview.20180528.pdf |pdf]]) :: - Binary Encoding ([[Media:ARM.2ISA.2A.Encoding.20180528.pdf |pdf]]) :: - Assembler Format ([[Media:ARM.2ISA.3A.Format.20180528.pdf |pdf]]) * Thumb Instruction Set * ARM Assembly Language ([[Media:ESys3.1A.Assembly.20160608.pdf |pdf]]) * ARM Machine Language ([[Media:ESys3.2A.Machine.20160615.pdf |pdf]]) </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] gtttpafnsfvvsnklbwitv5kkzxi0fm7 2412417 2412416 2022-08-06T21:49:04Z Young1lim 21186 /* Serial Bus */ wikitext text/x-wiki == '''Background''' == '''Combinational and Sequential Circuits''' * [[Media:DD2.B.4..Adder.20131007.pdf |Adder]] * [[Media:DD3.A.1.LatchFF.20160308.pdf |Latches and Flipflops]] '''FSM''' * [[Media:DD3.A.3.FSM.20131030.pdf |FSM]] * [[Media:CArch.2.A.Bubble.20131021.pdf |FSM Example]] '''Tiny CPU Example''' * [[Media:CDsgn6.TinyCPU.2.A.ISA.20160511.pdf |Instruction Set]] * [[Media:CDsgn6.TinyCPU.2.B.DPath.20160502.pdf |Data Path]] * [[Media:CDsgn6.TinyCPU.2.C.CPath.20160427.pdf |Control Path]] * [[Media:CDsgn6.TinyCPU.2.D.Implement.20160513.pdf |FPGA Implementation]] </br> == '''Microprocessor Architecture''' == * ARM Architecture : - Programmer's Model ([[Media:ARM.1Arch.1A.Model.20180321.pdf |pdf]]) : - Pipelined Architecture ([[Media:ARM.1Arch.2A.Pipeline.20180419.pdf |pdf]]) * ARM Organization * ARM Cortex-M Processor Architecture * ARM Processor Cores </br> == '''Instruction Set Architecture''' == * ARM Instruction Set : - Overview ([[Media:ARM.2ISA.1A.Overview.20190611.pdf |pdf]]) : - Addressing Modes ([[Media:ARM.2ISA.2A.AddrMode.20191108.pdf |pdf]]) : - Multiple Transfer ([[Media:ARM.2ISA.3A.MTransfer.20190903.pdf |pdf]]) : - Assembler Format :: - Data Processing ([[Media:ARM.2ISA.4A.Proc.Format.20200204.pdf |pdf]]) :: - Data Transfer ([[Media:ARM.2ISA.4B.Trans.Format.20200205.pdf |pdf]]) :: - Coprocessor ([[Media:ARM.2ISA.4C.CoProc.Format.20191214.pdf |pdf]]) :: - Summary ([[Media:ARM.2ISA.4D.Summary.Format.20200205.pdf |pdf]]) : - Binary Encoding ([[Media:ARM.2ISA.5A.Encoding.201901105.pdf |pdf]]) * Thumb Instruction Set </br> == '''Assembly Programming''' == === ARM Assembly Programming (I) === * 1. Overview ([[Media:ARM.2ASM.1A.Overview.20200101.pdf |pdf]]) * 2. Example Programs ([[Media:ARM.2ASM.2A.Program.20200108.pdf |pdf]]) * 3. Addressing Modes ([[Media:ARM.2ASM.3A.Address.20200127.pdf |pdf]]) * 4. Data Transfer ([[Media:ARM.2ASM.4A.DTransfer.20200206.pdf |pdf]]) * 5. Data Processing ([[Media:ARM.2ASM.5A.DProcess.20200208.pdf |pdf]]) * 6. Control ([[Media:ARM.2ASM.6A.Control.20200215.pdf |pdf]]) * 7. Arrays ([[Media:ARM.2ASM.7A.Array.20200311.pdf |pdf]]) * 8. Data Structures ([[Media:ARM.2ASM.8A.DataStruct.20200718.pdf |pdf]]) * 9. Finite State Machines ([[Media:ARM.2ASM.9A.FSM.20200417.pdf |pdf]]) * 10. Functions ([[Media:ARM.2ASM.10A.Function.20210115.pdf |pdf]]) * 11. Parameter Passing ([[Media:ARM.2ASM.11A.Parameter.20210106.pdf |pdf]]) * 12. Stack Frames ([[Media:ARM.2ASM.12A.StackFrame.20210611.pdf |pdf]]) :: :: === ARM Assembly Programming (II) === :: * 1. Thumb instruction programming ([[Media:ARM.2ASM.Thumb.20210612.pdf |pdf]]) * 2. Exceptions ([[Media:ARM.2ASM.Exception.20220722.pdf |pdf]]) * 3. Exception Programming ([[Media:ARM.2ASM.ExceptionProg.20220311.pdf |pdf]]) * 4. Exception Handlers ([[Media:ARM.2ASM.ExceptionHandler.20220131.pdf |pdf]]) * 5. Interrupt Programming ([[Media:ARM.2ASM.InterruptProg.20211030.pdf |pdf]]) * 6. Interrupt Handlers ([[Media:ARM.2ASM.InterruptHandler.20211030.pdf |pdf]]) * 7. Vectored Interrupt Programming ([[Media:ARM.2ASM.VectoredInterrupt.20220801.pdf |pdf]]) </br> * ARM Assembly Exercises ([[Media:ESys.3.A.ARM-ASM-Exercise.20160608.pdf |A.pdf]], [[Media:ESys.3.B.Assembly.20160716.pdf |B.pdf]]) :: === ARM Assembly Programming (III) === * 1. Fixed point arithmetic (integer division) * 2. Floating point arithmetic * 3. Matrix multiply === ARM Linking === * arm link ([[Media:arm_link.20211208.pdf |pdf]]) </br> === ARM Microcontroller Programming === * 1. Input / Output * 2. Serial / Parallel Port Interfacing * 3. Analog I/O Interfacing * 4. Communication </br> == '''Memory Architecture''' == </br> === '''Memory Hierarchy''' === </br> === '''System and Peripheral Buses''' === </br> === '''Architectural Support''' === * High Level Languages * System Development * Operating Systems </br> == '''Peripheral Architecture''' == </br> === '''Vectored Interrupt Controller ''' === </br> === '''Timers ''' === * Timer / Counter ([[Media:ARM.4ASM.Timer.20220801.pdf |pdf]]) * Real Time Clock * Watchdog Timer </br> === '''Serial Bus''' === * '''UART''' : Universal Asynchronous Receiver/Transmitter ([[Media:ARM.4ASM.UART.20220806.pdf |pdf]]) * '''I2C''' : Inter-Integrated Circuit * '''SPI''' : Serial Peripheral Interface * '''USB''' : Universal Serial Bus Device Controller </br> === '''I/Os ''' === * General Purpose Input/Output ports (GPIO) * Pulse Width Modulator * Analog-to-Digital Converter (ADC) * Digital-to-Analog Converter (DAC) </br> <!-- == '''Interrupts and Exceptions ''' == --> </br> == '''Synchrnoization'''== </br> === H/W and S/W Synchronization === * busy wait synchronization * handshake interface </br> === Interrupt Synchronization === * interrupt synchronization * reentrant programming * buffered IO * periodic interrupt * periodic polling </br> ==''' Interfacing '''== </br> === Time Interfacing === * input capture * output compare </br> === Serial Interfacing === * Programming UART * Programming SPI * Programming I2C * Programming USB </br> === Analog Interfacing === * OP Amp * Filters * ADC * DAC </br> == '''Old materials''' == === '''Instruction Set Architecture''' === * ARM Instruction Set :: - Overview ([[Media:ARM.2ISA.1A.Overview.20180528.pdf |pdf]]) :: - Binary Encoding ([[Media:ARM.2ISA.2A.Encoding.20180528.pdf |pdf]]) :: - Assembler Format ([[Media:ARM.2ISA.3A.Format.20180528.pdf |pdf]]) * Thumb Instruction Set * ARM Assembly Language ([[Media:ESys3.1A.Assembly.20160608.pdf |pdf]]) * ARM Machine Language ([[Media:ESys3.2A.Machine.20160615.pdf |pdf]]) </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] 1w6cckqca2rg5xtsfsm6t9q3u9jdh1u 0 234453 2412483 2371947 2022-08-07T04:45:17Z Marshallsumter 311529 wikitext text/x-wiki [[Image:Superclusters atlasoftheuniverse.gif|thumb|250px|right|The universe within 1 billion light-years (307 Mpc) of Earth is shown to contain the local superclusters, galaxy filaments and voids. Credit: Richard Powell.{{tlx|free media}}]] "Galaxies and clusters of galaxies are not uniformly distributed in the Universe, instead they collect into vast clusters and sheets and walls of galaxies interspersed with large voids in which very few galaxies seem to exist. The map above shows many of these superclusters including the Virgo supercluster - the minor supercluster of which our galaxy is just a minor member. The entire map is approximately 7 percent of the diameter of the entire visible Universe."<ref name=Powell>{{ cite book |author=Richard Powell |title=The Universe within 1 billion Light Years The Neighbouring Superclusters |publisher=Atlas of the Universe |location= |date=30 July 2006 |url=http://www.atlasoftheuniverse.com/superc.html |accessdate=2018-04-01 }}</ref> {{clear}} ==Galaxies== {{main|Radiation astronomy/Galaxies|Stars/Galaxies}} [[Image:M81 wide Galex.jpg|thumb|right|250px|This Galaxy Evolution Explorer (GALEX) image of the spiral galaxy Messier 81 is in ultraviolet light. Credit: NASA/JPL-Caltech/J. Huchra (Harvard-Smithsonian CfA).{{tlx|free media}}]] The radiation astronomy of galaxies generally is about the galaxy as a radiated or radiation emitting astronomical object. The stellar aspects of individual galaxies are in [[Stars/Galaxies|galaxies of stars]]. A galaxy is often perceived as a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter.<ref name=Sparke>{{Cite book |last1=Sparke |first1=L. S. |last2=Gallagher |first2=J. S. III |date=2000 |title=Galaxies in the Universe: An Introduction |publisher=Cambridge University Press |isbn=978-0-521-59740-1 |accessdate=July 25, 2018 |archive-date=March 24, 2021 |url=https://web.archive.org/web/20210324072126/https://books.google.com/books?id=tzNF79roUfoC }}</ref><ref name=nasa060812>{{cite web |last1=Hupp |first1=E. |last2=Roy |first2=S. |last3=Watzke |first3=M. |date=August 12, 2006 |title=NASA Finds Direct Proof of Dark Matter |url=http://www.nasa.gov/home/hqnews/2006/aug/HQ_06297_CHANDRA_Dark_Matter.html |publisher=NASA |accessdate=April 17, 2007 }}</ref> Galaxies range in size from dwarfs with just a few hundred million ({{10^|8}}) stars to giants with one hundred trillion ({{10^|14}}) stars,<ref name=science250_4980_539>{{cite journal |last1=Uson |first1=J. M. |last2=Boughn |first2=S. P. |last3=Kuhn |first3=J. R. |date=1990 |title=The central galaxy in Abell 2029&nbsp;– An old supergiant |journal=Science |volume=250 |issue=4980 |pages=539–540 |bibcode=1990Sci...250..539U |doi=10.1126/science.250.4980.539 |pmid=17751483 }}</ref> each orbiting its galaxy's center of mass. Galaxies are categorized according to their visual morphology as elliptical,<ref name=uf030616>{{cite web |last1=Hoover |first1=A. |date=June 16, 2003 |title=UF Astronomers: Universe Slightly Simpler Than Expected |url=http://news.ufl.edu/2003/06/16/galaxies/ |publisher=Hubble News Desk |accessdate=March 4, 2011 |archiveurl=https://web.archive.org/web/20110720083835/http://news.ufl.edu/2003/06/16/galaxies/ |archivedate=July 20, 2011 |df=mdy-all }} Based upon: * {{Cite journal |last1=Graham |first1=A. W. |last2=Guzman |first2=R. |date=2003 |title=HST Photometry of Dwarf Elliptical Galaxies in Coma, and an Explanation for the Alleged Structural Dichotomy between Dwarf and Bright Elliptical Galaxies |journal=The Astronomical Journal |volume=125 |issue=6 |pages=2936–2950 |bibcode=2003AJ....125.2936G |doi=10.1086/374992 |arxiv = astro-ph/0303391 }}</ref> spiral, or irregular.<ref name="IRatlas">{{cite web |last1=Jarrett |first1=T. H. |title=Near-Infrared Galaxy Morphology Atlas |url=http://www.ipac.caltech.edu/2mass/gallery/galmorph/ |publisher=California Institute of Technology |accessdate=January 9, 2007 }}</ref> The number of galaxies in the observable universe has increased from a previous estimate of 200&nbsp;billion ({{val|2e11}})<ref name="apj624_2">{{cite journal |last1=Gott III |first1=J. R. |year=2005 |title=A Map of the Universe |journal=The Astrophysical Journal |volume=624 |issue=2 |pages=463–484 |bibcode=2005ApJ...624..463G |doi=10.1086/428890 |arxiv = astro-ph/0310571 }}</ref> to a suggested 2 trillion ({{val|2e12}}) or more,<ref name="Conselice">{{cite journal |title=The Evolution of Galaxy Number Density at z < 8 and its Implications |author=Christopher J. Conselice |journal=The Astrophysical Journal |volume=830 |issue=2 |year=2016 |arxiv=1607.03909v2 |bibcode= 2016ApJ...830...83C |doi=10.3847/0004-637X/830/2/83 |page=83 }}</ref><ref name="NYT-20161017">{{cite journal |last=Fountain |first=Henry |title=Two Trillion Galaxies, at the Very Least |url=https://www.nytimes.com/2016/10/18/science/two-trillion-galaxies-at-the-very-least.html |date=17 October 2016 |Journal=The New York Times |accessdate=17 October 2016 }}</ref> containing more [[stars]] than all the grains of sand on planet Earth.<ref name="SU-20020201">{{cite web |last=Mackie |first=Glen |title=To see the Universe in a Grain of Taranaki Sand |url=http://astronomy.swin.edu.au/~gmackie/billions.html |date=1 February 2002 |work=Centre for Astrophysics and Supercomputing |accessdate=28 January 2017 }}</ref> {{clear}} ==Intergalactic medium== {{main|Sources/Intergalactic medium}} [[Image:Radio galaxy 3C98.png|thumb|250px|right|The pseudo-colour image is of the large-scale radio structure of the FRII radio galaxy 3C98. Lobes, jet and hotspot are labelled. Credit: [[w:User:Mhardcastle|Mhardcastle]].{{tlx|free media}}]] The '''intergalactic medium''' (IGM) is a rarefied plasma.<ref name=jafelice_opher1992>{{ cite journal | title=The origin of intergalactic magnetic fields due to extragalactic jets | month=July | year=1992 | author=Luiz C. Jafelice, Reuven Opher | journal=Monthly Notices of the Royal Astronomical Society | volume=257 | issue=1 | pages=135–51 | publisher=Royal Astronomical Society | bibcode=1992MNRAS.257..135J }}</ref> "The Chandra observations found evidence for the massive and hot intergalactic medium filaments by noting a slight dimming in distant quasar X-rays likely caused by hot gas absorption."<ref name=wadsley2002>{{ cite book | author=James W. Wadsley |author2=Marcelo I. Ruetalo |author3=J. Richard Bond |author4=Carlo R. Contaldi |author5=Hugh M. P. Couchman |author6=Joachim Stadel |author7=Thomas R. Quinn |author8=Michael D. Gladders | url=http://antwrp.gsfc.nasa.gov/apod/ap020820.html | title=The Universe in Hot Gas | date=August 20, 2002 | publisher=NASA | accessdate=2009-06-19 }}</ref> {{clear}} ==Theoretical galaxy clusters== [[Image:Ancient galactic structure.jpg|right|thumb|300px|This image shows the region where the ancient galactic structure was found. Credit: NAOJ/Harikane ''et al''.{{tlx|fairuse}}]] '''Def.''' a "cluster of hundreds of galaxies"<ref name=GalaxyClusterWikt>{{ cite web |author=[[wikt:User:Sae1962|Sae1962]] |title=galaxy cluster |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=23 October 2012 |url=https://en.wiktionary.org/wiki/galaxy_cluster |accessdate=28 May 2019 }}</ref> is called a '''galaxy cluster'''. '''Def.''' a "massive, thread-like formation of gravitationally bound galaxies forming the boundaries between large voids in the universe"<ref name=GalaxyFilamentWikt>{{ cite web |author=[[wikt:User:Hekaheka|Hekaheka]] |title=galaxy filament |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=12 May 2014 |url=https://en.wiktionary.org/wiki/galaxy_filament |accessdate=28 May 2019 }}</ref> is called a '''galaxy filament'''. '''Def.''' an "extended group of clusters of galaxies"<ref name=SuperclusterWikt>{{ cite web |author=[[wikt:User:SemperBlotto|SemperBlotto]] |title=supercluster |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=29 January 2009 |url=https://en.wiktionary.org/wiki/supercluster |accessdate=28 May 2019 }}</ref> is called a '''supercluster'''. '''Def.''' a "group of galaxies that hold together gravitationally"<ref name=GalaxyGroupWikt>{{ cite web |author=[[wikt:User:Lo Ximiendo|Lo Ximiendo]] |title=galaxy group |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=23 October 2012 |url=https://en.wiktionary.org/wiki/galaxy_group |accessdate=31 May 2019 }}</ref> is called a '''galaxy group'''. '''Def.''' a "number of galaxies that become a galaxy group over time"<ref name=ProtogroupWikt>{{ cite web |author=[[wikt:User:SemperBlotto|SemperBlotto]] |title=protogroup |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=5 February 2017 |url=https://en.wiktionary.org/wiki/protogroup |accessdate=31 May 2019 }}</ref> is called a '''protogroup'''. "Where galaxies live in the universe and how they interact with their surroundings (the intergalactic medium that surrounds them) and each other are major influences on their ability to form stars. But precisely how this so-called environment dictates the life and death of galaxies remains a mystery."<ref name=Brown>{{ cite web |author=Toby Brown |title=Something Is Killing the Universe's Most Extreme Galaxies |publisher=Live Science |location=McMaster University |date=19 September 2019 |url=https://www.livescience.com/whats-killing-universe-extreme-galaxies.html?utm_source=ls-newsletter&utm_medium=email&utm_campaign=20190920-ls |accessdate=21 September 2019 }}</ref> "Galaxy clusters are the most massive and most extreme environments in the universe, containing many hundreds or even thousands of galaxies. Where you have mass, you also have gravity and the huge gravitational forces present in clusters accelerates galaxies to great speeds, often thousands of kilometres-per-second, and superheats the plasma in between galaxies to temperatures so high that it glows with X-ray light."<ref name=Brown/> "As galaxies fall through clusters, the intergalactic plasma can rapidly remove their gas in a violent process called ram pressure stripping. When you remove the fuel for star formation, you effectively kill the galaxy, turning it into a dead object in which no new stars are formed."<ref name=Brown/> "In addition, the high temperature of clusters can stop hot gas cooling and condensing onto galaxies. In this case, the gas in the galaxy isn't actively removed by the environment but is consumed as it forms stars. This process leads to a slow, inexorable shut down in star formation known, somewhat morbidly, as starvation or strangulation."<ref name=Brown/> The image on the right "shows the region where the ancient galactic structure was found. The blue shading shows the area it covers. The red objects in the zoomed-in bits are the 12 galaxies."<ref name=Harikane>{{ cite web |author=Harikane |title=Huge Cosmic Structures Already Existed When the Universe Was a Baby |publisher=Live Science |location= |date=30 September 2019 |url=https://www.livescience.com/galaxy-cluster-infant-universe.html?utm_source=ls-newsletter&utm_medium=email&utm_campaign=20191001-ls |accessdate=5 October 2019 }}</ref> "The discovery, which could help explain the shape of the modern cosmos, reveals 12 galaxies that existed in a clump 13 billion years ago — just about 700 million years after the Big Bang. We can see them now because they're so far away in the expanding universe (13 billion light-years) that their starlight is only now reaching Earth. One of the galaxies, a mammoth named Himiko after a mythological Japanese queen, was discovered a decade ago [...]."<ref name=Letzter>{{ cite web |author=Rafi Letzter |title=Huge Cosmic Structures Already Existed When the Universe Was a Baby |publisher=Live Science |location= |date=30 September 2019 |url=https://www.livescience.com/galaxy-cluster-infant-universe.html?utm_source=ls-newsletter&utm_medium=email&utm_campaign=20191001-ls |accessdate=5 October 2019 }}</ref> "Himiko sits at the edge of the system, which [is called] a "protocluster" because it's so small and ancient compared to most of the clusters we can see in the universe."<ref name=Letzter/> "It is reasonable to find a protocluster near a massive object, such as Himiko. However, we're surprised to see that Himiko was located not in the center of the protocluster but on the edge, 500 million light-years away from the center."<ref name=Ouchi>{{ cite web |author=Masami Ouchi |title=Huge Cosmic Structures Already Existed When the Universe Was a Baby |publisher=Live Science |location= |date=30 September 2019 |url=https://www.livescience.com/galaxy-cluster-infant-universe.html?utm_source=ls-newsletter&utm_medium=email&utm_campaign=20191001-ls |accessdate=5 October 2019 }}</ref> "[T]here is a clear trend that the star-formation activity of galaxies tends to be lower in high-density environment than low-density environment."<ref name=Harikane/> ""[P]rotoclusters" like this one from the early eons of the universe are rarely found and are poorly understood."<ref name=Harikane/> {{clear}} ==Zwicky classifications== Galaxy clusters are classified according to the concentration of galaxy members as a function of cluster diameter dividing them into categories: # highly compact, with any specific clump having more than ten galaxies, # medium compact, a single or several concentrations are optically separated by diameters, # open, no concentration detected at all.<ref name=Zwicky>{{ cite book |author=F. Zwicky |author2=E. Herzog |author3=P. Wild |author4=M. Karpowicz |author5=C. T. Kowal |title=Catalogue of galaxies and of clusters of galaxies |volume=I |publisher=California Institute of Technology |location=Pasadena. California USA |date=1961 |editor= |pages=319 |url=https://ui.adsabs.harvard.edu/abs/1961cgcg.book.....Z/abstract |arxiv= |bibcode=1961cgcg.book.....Z |doi= |pmid= |isbn= |accessdate=1 February 2020 }}</ref> ==Bautz-Morgan classifications== The '''Bautz–Morgan classification''' is a criteria based on the number and hierarchy of the brightest dominant members within cluster boundaries based on their Hubble sequence morphology.<ref name="Bautz-Morgan 1970b">{{cite journal | last1 = Bautz | first1 = L. P. | last2 = Morgan | first2 = W. W. |date=December 1970 | title = On the Classification of the Forms of Clusters of Galaxies | journal = Astrophysical Journal | volume = 162 | pages = L149 | format = PDF | id = A&AA ID. AAA004.160.015 | bibcode = 1970ApJ...162L.149B | doi = 10.1086/180643 | accessdate = March 10, 2012 | url = http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1970ApJ...162L.149B&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf }}</ref> * A '''type I''' cluster is dominated by a bright, large, supermassive cD galaxy. * A '''type II''' cluster contains elliptical galaxies whose brightness relative to the cluster is intermediate to that of type I and type III. * A '''type III''' cluster has no remarkable members, such as the Virgo Cluster. Type III has two subdivisions, '''type IIIE''' and '''type IIIS''' ** '''Type IIIE''' clusters do not contain many giant spirals ** '''Type IIIS''' clusters contain many giant spirals * The deprecated '''type IV''' was for clusters whose brightest members were predominantly spirals.<ref name="Bautz-Morgan 1970a">{{cite journal | last1 = Bautz | first1 = Laura P. | last2 = Morgan | first2 = W. W. |date=September 1970 | title = Preliminary Classification of Clusters of Galaxies | journal = Bulletin of the American Astronomical Society | volume = 2 | pages = 294 | format = PDF | id = A&AA ID. AAA004.160.006 | bibcode = 1970BAAS....2R.294B | accessdate = March 10, 2012 | url = http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1970BAAS....2R.294B&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf }}</ref> {|class=wikitable width=100% |- ! X-ray - Optical images ! Example ! Type |- | [[Image:A2199 Xray Optical2.jpg|100px]] | Abell 2199 | {{nobr|Type I}} |- | [[Image:Abell S740.jpg|100px]] | Abell S740 | {{nobr|Type I-II}} |- | [[Image:Coma Cluster of Galaxies (visible, wide field).jpg|100px]] | Coma Cluster | {{nobr|Type II}} |- | [[Image:New Hubble view of galaxy cluster Abell 1689.jpg|100px]] | Abell 1689 | {{nobr|Type II-III}} |- | [[Image:ESO-M87.jpg|100px]] | Virgo Cluster | {{nobr|Type III}} |- | | | {{nobr|Type IIIS}} |- | | | {{nobr|Type IIIE}} |- |} ==Rood-Sastry classifications== Galaxy clusters are classified according to their richness based on the distribution of the ten brightest members and morphology as a "Tuning Fork" in the following categories:<ref name=Rood>{{ cite journal |author=Herbert J. Rood |author2=Gummuluru N. Sastry |title="Tuning Fork" Classification of Rich Clusters of Galaxies |journal=Publications of the Astronomical Society of the Pacific |date=June 1971 |volume=83 |issue=493 |pages=313-19 |url=https://www.jstor.org/stable/40675069 |arxiv= |bibcode= |doi= |pmid= |accessdate=1 February 2020 }}</ref> # cD (super-giant) - cluster with a remarkable brightest member as central dominant. # B (binary) - Two super-giants galaxies separated by ≤ 10 diameters of the larger galaxy (generally with a filament connection between them). # L (line) - Three or more galaxies as top brightest members in line. # C (core-halo) - Four or more top brightest separated around the centre. # F (flat) - Several of the top ten brightest members in flattened configuration. # I (irregular) - Galaxies that are distributed with no well-defined centre. ==Oemler's classifications== Fractions of clusters with spirals (Sps), no spirals (S0s) and ellipticals (Es) subdivided into spiral-rich and spiral-poor.<ref name=Oemler>{{ cite journal |author=Augustus Oemler Jr. |title=The Systematic Properties of Clusters of Galaxies. Photometry of 15 Clusters |journal=The Astrophysical Journal |date=1974 |volume=194 |issue= |pages=1-20 |url=https://ui.adsabs.harvard.edu/abs/1974ApJ...194....1O/abstract |arxiv= |bibcode=1974ApJ...194....1O |doi=10.1086/153216 |pmid= |accessdate=1 February 2020 }}</ref> ==Abell 2029== [[Image:Abell 2029 composite Chandra.jpg|right|thumb|300px|A2029 in X-ray from the Chandra X-ray Observatory (left) and in the optical from the Digitized Sky Survey (right). Credit: NASA (Chandra - SDSS II).{{tlx|fairuse}}]] Abell 2029 is composed of thousands of galaxies (optical image, right) enveloped in a gigantic cloud of hot gas (X-ray image, left), and an amount of dark matter equivalent to more than a hundred trillion Suns. Both the gas and the galaxies are confined to the cluster primarily by the gravity of the dark matter. If this galaxy cluster is a representative sample of the universe, the Chandra observation indicates that 70 to 90 percent of the mass of the universe consists of dark matter - mysterious particles left over from the dense early universe that interact with each other and "normal" matter only through gravity. Abell 2029 or A2029 is a large galaxy cluster 315 megaparsecs (1.027 billion light-years) away in the constellation Virgo.<ref>Chandra X-ray Observatory, [http://chandra.harvard.edu/photo/2004/darkenergy/ "Galaxy Clusters and Dark Energy: Chandra Opens New Line of Investigation on Dark Energy"], '''Harvard-Smithsonian Center for Astrophysics'''</ref> A2029 is a Bautz–Morgan classification type I cluster due to its large central galaxy, IC 1101. {{clear}} ==Abell 2065== [[Image:Abell 2065.jpg|right|thumb|250px|Abell 2065 is photographed with amateur equipment. Credit: [[c:user:DavidC|David Chifiriuc]].{{tlx|free media}}]] Abell 2065, a highly concentrated galaxy cluster in the constellation of Corona Borealis contains over 400 member galaxies, the brightest of which are 16th magnitude, is more than one billion light-years from Earth.<ref name=Ridpath>{{cite book |title = Stars and Planets Guide |last1 = Ridpath |first1 = Ian |last2 = Tirion |first2 = Wil |date = 2001 |publisher = Princeton University Press |isbn = 0-691-08913-2}}</ref> On a larger scale still, Abell 2065, along with Abell 2061, Abell 2067, Abell 2079, Abell 2089, and Abell 2092, make up the Corona Borealis Supercluster.<ref name=postman88>{{cite journal |title=The dynamics of the Corona Borealis supercluster |author=Postman, M. |author2=Geller, M. J. |author3=Huchra, J. P. |journal=Astronomical Journal | volume= 95 |date= 1988 |pages= 267–83 |doi= 10.1086/114635 |bibcode=1988AJ.....95..267P }}</ref> {{clear}} ==Canes Venatici II Group== The 'Canes II Group or Canes Venatici II Group (CVn II Group) is a group of galaxies about 26.1 million light-years away from Earth in the Local Supercluster.<ref>Gerard de Vaucouleurs, 1975. ''Nearby Groups of Galaxies'', ch. 5. the nearer groups within 10 megaparsecs. Published in "Galaxies and the Universe," ed. by A. Sandage, M. Sandage and J. Kristian</ref> The largest galaxy within the cluster is Messier 106 (NGC 4258), which is a barred spiral galaxy.<ref name="Atlas"/> Canes II is directly behind Canes I, which makes it difficult to show which galaxy belongs in which cluster.<ref name="Atlas">{{cite web |url=http://www.atlasoftheuniverse.com/galgrps/cvnii.html |title=The Canes II Group |date=2003 |publisher=Atlas of the Universe |accessdate=2009-08-06 }}</ref> ==M51 Group== The M51 Group, which includes the Whirlpool Galaxy (M51) and the Sunflower Galaxy (M63),<ref name="garcia1993" /><ref name="giuricinetal2002" /><ref name="nbg" /><ref name="fouqueetal1992" /> is located to the southeast of the M101 Group. The distances to the NGC 5866 Group, M51 and M101 groups (as determined from the distances to the individual member galaxies) are similar, which suggests that the M51 Group, the M101 Group, and the NGC 5866 Group are actually part of a single large, loose, elongated group.<ref name="ferrareseetal00" /> ==M81 Group== The '''M81 Group''' is a galaxy group in the constellations Ursa Major and Camelopardalis that includes the galaxies Messier 81 and Messier 82, as well as several other galaxies with high apparent brightnesses.<ref name="karachentsev2005">{{cite journal | author=I. D. Karachentsev | title=The Local Group and Other Neighboring Galaxy Groups | journal=Astronomical Journal | date=2005 | volume=129 | issue=1 | pages=178–188 | bibcode=2005AJ....129..178K | doi = 10.1086/426368 |arxiv = astro-ph/0410065 }}</ref> The approximate center of the group is located at a distance of 3.6 Mpc, making it one of the nearest groups to the Local Group.<ref name="karachentsev2005" /> The group is estimated to have a total mass of (1.03 ± 0.17){{e|12}} Solar mass.<ref name="Karachentsevetal2006">{{cite journal | author=Karachentsev, I. D. | author2=Kashibadze, O. G. | title=Masses of the local group and of the M81 group estimated from distortions in the local velocity field | journal=Astrophysics | date=2006 | volume=49 | issue=1 | pages=3–18 | bibcode=2006Ap.....49....3K | doi = 10.1007/s10511-006-0002-6 }}</ref> The M81 Group, the Local Group, and other nearby groups all lie within the Virgo Supercluster (i.e. the Local Supercluster).<ref name="tully1982">{{cite journal | author= R. B. Tully | title=The Local Supercluster | journal=Astrophysical Journal | date=1982 | volume=257 | pages=389–422 | bibcode=1982ApJ...257..389T | doi = 10.1086/159999 }}</ref> The table below lists galaxies that have been identified as associated with the M81 Group by I. D. Karachentsev.<ref name="karachentsev2005" /> {| class="wikitable sortable" style="text-align:center;border-collapse:collapse;" cellpadding="2" |+'''Members of the M81 Group''' |- ! style="background:#efefef;" | Name ! style="background:#efefef;" | Galaxy morphological classification (Type)<ref name="ned">{{cite web | title=NASA/IPAC Extragalactic Database | work=Results for various galaxies | url=http://nedwww.ipac.caltech.edu/ | accessdate=2007-02-09}}</ref> ! style="background:#efefef;" | R.A. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Dec. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Redshift (km/s)<ref name="ned" /> ! style="background:#efefef;" | Apparent Magnitude<ref name="ned" /> |- | Arp's Loop | | {{RA|09|57|32.6}} | {{DEC|+69|17|00}} | 99 | 16.1 |- | DDO 78 | Im | {{RA|10|26|27.4}} | {{DEC|+67|39|16}} | 55 ± 10 | 15.8 |- | F8D1 | dE | {{RA|09|44|47.1}} | {{DEC|+67|26|19}} | | 13.9 |- | FM1 | dSph | {{RA|09|45|10.0}} | {{DEC|+68|45|54}} | | 17.5 |- | HIJASS J1021+6842 | | {{RA|10|21|00.0}} | {{DEC|+68|42|00}} | 46 | 20 |- | HS 117 | I | {{RA|10|21|25.2}} | {{DEC|+71|06|51}} | -37 | 16.5 |- | Holmberg I | IAB(s)m | {{RA|09|40|32.3}} | {{DEC|+71|10|56}} | 139 ± 0 | 13.0 |- | Holmberg II | Im | {{RA|08|19|05.0}} | {{DEC|+70|43|12}} | 142 ± 1 | 11.1 |- | Holmberg IX | Im | {{RA|09|57|32.0}} | {{DEC|+69|02|45}} | 46 ± 6 | 14.3 |- | IC 2574 | SAB(s)m | {{RA|10|28|23.5}} | {{DEC|+68|24|44}} | 57 ± 2 | 13.2 |- | IKN | | {{RA|10|08|05.9}} | {{DEC|+68|23|57}} | | 17.0 |- | KKH 57 | dSph | {{RA|10|00|16.0}} | {{DEC|+63|11|06}} | | 18.5 |- | Messier 81 | SA(s)ab | {{RA|09|55|33.2}} | {{DEC|+69|03|55}} | -34 ± 4 | 6.9 |- | Messier 81 Dwarf A | I | {{RA|08|23|56.0}} | {{DEC|+71|01|45}} | 113 ± 0 | 16.5 |- | Messier 82 | I0 | {{RA|09|55|52}} | {{DEC|+69|40|47}} | 203 ± 4 | 9.3 |- | NGC 2366 | IB(s)m | {{RA|07|28|54.7}} | {{DEC|+69|12|57}} | 80 ± 1 | 11.4 |- | NGC 2403 | SAB(s)cd | {{RA|07|36|51.4}} | {{DEC|+65|36|09}} | 131 ± 3 | 8.9 |- | NGC 2976 | SAc pec | {{RA|09|47|15.5}} | {{DEC|+67|54|59}} | 3 ± 5 | 10.8 |- | NGC 3077 | I0 pec | {{RA|10|03|19.1}} | {{DEC|+68|44|02}} | 14 ± 4 | 10.6 |- | NGC 4236 | SB(s)dm | {{RA|12|16|42}} | {{DEC|+69|27|45}} | 0 ± 4 | 10.1 |- | PGC 28529 | Im | {{RA|09|53|48.5}} | {{DEC|+68|58|08}} | -40 | 17.1 |- | PGC 28731 | dE | {{RA|09|57|03.1}} | {{DEC|+68|35|31}} | -135 ± 30 | 15.6 |- | PGC 29231 | dE | {{RA|10|04|41.1}} | {{DEC|+68|15|22}} | | 16.7 |- | PGC 31286 | dSph | {{RA|10|34|29.8}} | {{DEC|+66|00|30}} | | 16.7 |- | PGC 32667 | Im | {{RA|10|52|57.1}} | {{DEC|+69|32|58}} | 116 ± 1 | 14.9 |- | UGC 4459 | Im | {{RA|08|34|07.2}} | {{DEC|+66|10|54}} | 20 ± 0 | 14.5 |- | UGC 4483 | | {{RA|08|37|03.0}} | {{DEC|+69|46|31}} | 156 ± 0 | 15.1 |- | UGC 5428 | Im | {{RA|10|05|06.4}} | {{DEC|+66|33|32}} | -129 ± 0 | 18 |- | UGC 5442 | Im | {{RA|10|07|01.9}} | {{DEC|+67|49|39}} | -18 ± 14 | 18 |- | UGC 5692 | 13.5 | {{RA|10|30|35.0}} | {{DEC|+70|37|07.2}} | 56 ± 3 | 13.5 |- | UGC 6456 | Pec | {{RA|11|27|59.9}} | {{DEC|+78|59|39}} | -103 ± 0 | 14.5 |- | UGC 7242 | Scd | {{RA|12|14|08.4}} | {{DEC|+66|05|41}} | 68 ± 2 | 14.6 |- | UGC 8201 | Im | {{RA|13|06|24.9}} | {{DEC|+67|42|25}} | 31 ± 0 | 12.8 |- | UGCA 133 | Im | {{RA|07|34|11.4}} | {{DEC|+66|53|10}} | | 15.6 |- |} Note that the object names used in the above table differ from the names used by Karachentsev. New General Catalogue (NGC), Index Catalogue (IC), Uppsala General Catalogue (UGC), and Principal Galaxies Catalogue (PGC) numbers have been used in many cases to allow for easier referencing. ==M94 Group== The M94 Group (Canes Venatici I Group) is a loose, extended group of galaxies located about 13 million light-years away<ref name="karachentsev2005"/> in the constellations Canes Venatici and Coma Berenices. The group is one of many groups that lies within the Virgo Supercluster (i.e. the Local Supercluster)<ref name="tully1982"/> and one of the closest groups to the Local Group. Although the galaxies in this cluster appear to be from a single large cloud-like structure, many of the galaxies within the group are only weakly gravitationally bound, and some have not yet formed stable orbits around the center of this group. Instead, most of the galaxies in this group appear to be moving with the expansion of the universe.<ref name="karachentsev2005" /><ref name="karachentsevetal2003">{{cite journal |author1=I. D. Karachentsev |author2=M. E. Sharina |author3=A. E. Dolphin |author4=E. K. Grebel |author5=D. Geisler |author6=P. Guhathakurta |author7=P. W. Hodge |author8=V. E. Karachentseva |author9=A. Sarajedini |author10=P. Seitzer | title=Galaxy flow in the Canes Venatici I cloud | journal=Astronomy and Astrophysics | date=2003 | volume=398 | issue=2 | pages=467–477 | bibcode=2003A&A...398..467K | doi=10.1051/0004-6361:20021598|arxiv = astro-ph/0210414 }}</ref> The table below lists galaxies that have been consistently identified as group members in the Nearby Galaxies Catalog,<ref name="nbg">{{cite book | author=R. B. Tully | date=1988 | title=Nearby Galaxies Catalog | edition= | publisher=Cambridge University Press | location=Cambridge | isbn=0-521-35299-1}}</ref> the Lyons Groups of Galaxies (LGG) Catalog,<ref name="garcia1993">{{cite journal | author=A. Garcia | title=General study of group membership. II - Determination of nearby groups | journal=Astronomy and Astrophysics Supplement | date=1993 | volume=100 | pages=47–90 | bibcode=1993A&AS..100...47G}}</ref> and the three group lists created from the Nearby Optical Galaxy sample.<ref name="giuricinetal2002">{{cite journal |author1=G. Giuricin |author2=C. Marinoni |author3=L. Ceriani |author4=A. Pisani | title=Nearby Optical Galaxies: Selection of the Sample and Identification of Groups | journal=Astrophysical Journal | date=2000 | volume=543 | issue=1 | pages=178–194 | bibcode=2000ApJ...543..178G | doi=10.1086/317070|arxiv = astro-ph/0001140 }}</ref> {| class="wikitable" style="text-align:center;border-collapse:collapse;" cellpadding="2" |+'''Members of the M94 Group''' |- ! style="background:#efefef;" | Name ! style="background:#efefef;" | Galaxy morphological classification (Type)<ref name="ned"/> ! style="background:#efefef;" | R.A. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Dec. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Redshift (km/s)<ref name="ned" /> ! style="background:#efefef;" | Apparent Magnitude<ref name="ned" /> |- | IC 3687 | IAB(s)m | {{RA|12|42|15.1}} | {{DEC|+38|30|12}} | 354 ± 1 | 13.7 |- | IC 4182 | SA(s)m | {{RA|13|05|49.5}} | {{DEC|+37|36|18}} | 321 ± 1 | 13.0 |- | M94 | (R)SA(r)ab | {{RA|12|50|53.0}} | {{DEC|+41|07|14}} | 308 ± 1 | 9.0 |- | NGC 4144 | SAB(s)cd | {{RA|12|09|58.6}} | {{DEC|+46|27|26}} | 265 ± 1 | 12.1 |- | NGC 4190 | Im pec | {{RA|12|13|44.8}} | {{DEC|+36|38|03}} | 228 ± 1 | 13.4 |- | NGC 4214 | IAB(s)m | {{RA|12|15|39.2}} | {{DEC|+36|19|37}} | 291 ± 3 | 10.2 |- | NGC 4244 | SA(s)cd | {{RA|12|17|29.6}} | {{DEC|+37|48|26}} | 244 | 10.9 |- | NGC 4395 | SA(s)m | {{RA|12|25|48.9}} | {{DEC|+33|32|48}} | 319 ± 1 | 10.6 |- | NGC 4449 | IBm | {{RA|12|28|11.9}} | {{DEC|+44|05|40}} | 207 ± 4 | 10.0 |- | UGC 6817 | Im | {{RA|11|50|53.0}} | {{DEC|+38|52|49}} | 242 ± 1 | 13.4 |- | UGC 7559 | IBm | {{RA|12|27|05.2}} | {{DEC|+37|08|33}} | 218 ± 5 | 14.2 |- | UGC 7577 | Im | {{RA|12|27|40.9}} | {{DEC|+43|29|44}} | 195 | 12.8 |- | UGC 7698 | Im | {{RA|12|32|54.4}} | {{DEC|+31|32|28}} | 331 ± 1 | 13.0 |- | UGC 8320 | IBm | {{RA|13|14|27.9}} | {{DEC|+45|55|09}} | 192 ± 1 | 12.7 |- |} ==M101 Group== The '''M101 Group''' is a loose group of galaxies located in Ursa Major. The group is named after the brightest galaxy in the group, the Pinwheel Galaxy (M101). Most of the other members of the group are companions of the Pinwheel Galaxy.<ref name="garcia1993">{{cite journal | author=A. Garcia | title=General study of group membership. II - Determination of nearby groups | journal=Astronomy and Astrophysics Supplement | date=1993 | volume=100 | pages=47–90 | bibcode=1993A&AS..100...47G}}</ref><ref name="giuricinetal2002"/><ref name="nbg"/><ref name="fouqueetal1992">{{cite journal |author1=P. Fouque |author2=E. Gourgoulhon |author3=P. Chamaraux |author4=G. Paturel | title=Groups of galaxies within 80 Mpc. II - The catalogue of groups and group members | journal=Astronomy and Astrophysics Supplement | date=1992 | volume=93 | pages=211–233 | bibcode=1992A&AS...93..211F}}</ref> The group itself is one of many located within the Virgo Supercluster (i.e. the Local Supercluster).<ref name="tully1982"/> The table below lists galaxies that have been consistently identified as group members in the Nearby Galaxies Catalog,<ref name="nbg" /> the survey of Fouque et al.,<ref name="fouqueetal1992" /> the Lyons Groups of Galaxies (LGG) Catalog,<ref name="garcia1993" /> and the three group lists created from the Nearby Optical Galaxy sample of Giuricin et al.<ref name="giuricinetal2002" /> {| class="wikitable" style="text-align:center;border-collapse:collapse;" cellpadding="2" |+'''Members of the M101 Group''' |- ! style="background:#efefef;" | Name ! style="background:#efefef;" | Galaxy morphological classification (Type)<ref name="ned"/> ! style="background:#efefef;" | R.A. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Dec. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Redshift (km/s)<ref name="ned" /> ! style="background:#efefef;" | Apparent Magnitude<ref name="ned" /> |- | Pinwheel Galaxy|Pinwheel Galaxy (M101) | SAB(rs)cd | {{RA|14|03|12.6}} | {{DEC|+54|20|57}} | 241 ± 2 | 8.3 |- | NGC 5204 | SA(s)m | {{RA|13|29|36.5}} | {{DEC|+58|25|07}} | 201 ± 1 | 11.7 |- | NGC 5474 | SA(s)cd pec | {{RA|14|05|01.6}} | {{DEC|+53|39|44}} | 273 ± 9 | 11.3 |- | NGC 5477 | SA(s)m | {{RA|14|05|33.2}} | {{DEC|+54|27|39}} | 304 ± 5 | 14.4 |- | NGC 5585 | SAB(s)d | {{RA|14|19|48.2}} | {{DEC|+56|43|45}} | 293 ± 2 | 11.2 |- | UGC 8837 | IB(s)m | {{RA|13|54|45.8}} | {{DEC|+53|54|03}} | 144 ± 3 | 13.8 |- | UGC 9405 | Im | {{RA|14|35|24.4}} | {{DEC|+57|15|19}} | 222 ± 6 | 17 |- |} Other possible members galaxies (galaxies listed in only one or two of the lists from the above references) include the irregular galaxies NGC 5238 and UGC 8508. ==M109 Group== The M109 Group (aka the NGC 3992 Group or Ursa Major cloud) is a group of galaxies about 10²² m (55 million lys) away<ref>[http://www.atlasoftheuniverse.com/galgrps/uma.html The Ursa Major Groups]</ref> in the constellation Ursa Major. The table below lists galaxies that have been consistently identified as group members in the Nearby Galaxies Catalog,<ref name="nbg"/> the survey of Fouque et al.,<ref name="fouqueetal1992"/> the Lyons Groups of Galaxies (LGG) Catalogue,<ref name="garcia1993" /> and the three group lists created from the Nearby Optical Galaxy sample of Giuricin et al.<ref name="giuricinetal2002" /> {| class="wikitable" style="text-align:center;border-collapse:collapse;" cellpadding="2" |+'''Members of the M109 Group''' |- ! style="background:#efefef;" | Name ! style="background:#efefef;" | Galaxy morphological classification (Type)<ref name="ned"/> ! style="background:#efefef;" | R.A. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Dec. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Redshift (km/s)<ref name="ned" /> ! style="background:#efefef;" | Apparent Magnitude<ref name="ned" /> |- | Messier 109 | SB(rs)bc | {{RA|11|57|36.0}} | {{DEC|+53|22|28}} | 1048 ± 1 | 10.6 |- | NGC 3718 | SB(s)a pec | {{RA|11|32|34.9}} | {{DEC|+53|04|05}} | 993 ± 1 | 11.6 |- | NGC 3726 | SAB(r)c | {{RA|11|33|21.2}} | {{DEC|+47|01|45}} | 866 ± 1 | 10.9 |- | NGC 3729 | SB(r)a pec | {{RA|11|33|49.3}} | {{DEC|+53|07|32}} | 1060 ± 1 | 12.0 |- | NGC 3769 | SB(r)b | {{RA|11|37|44.1}} | {{DEC|+47|53|35}} | 737 ± 2 | 12.5 |- | NGC 3782 | SAB(s)cd | {{RA|11|39|20.7}} | {{DEC|+46|30|48}} | 739 ± 6 | 13.1 |- | NGC 3870 | S0 | {{RA|11|45|56.6}} | {{DEC|+50|11|59}} | 756 ± 7 | 13.4 |- | NGC 3877 | Sc | {{RA|11|46|07.8}} | {{DEC|+47|29|41}} | 895 ± 4 | 12.1 |- | NGC 3893 | SAB(rs)c | {{RA|11|48|38.2}} | {{DEC|+48|42|39}} | 967 ± 1 | 11.2 |- | NGC 3913 | (R)SA(rs)d | {{RA|11|50|38.9}} | {{DEC|+55|21|14}} | 954 ± 4 | 13.2 |- | NGC 3917 | SAcd | {{RA|11|50|45.5}} | {{DEC|+51|49|27}} | 965 ± 1 | 12.5 |- | NGC 3922 | S0/a | {{RA|11|51|13.4}} | {{DEC|+50|09|25}} | 906 ± 7 | 13.4 |- | NGC 3928 | SA(s)b | {{RA|11|51|47.6}} | {{DEC|+48|40|59}} | 988 ± 4 | 13.0 |- | NGC 3949 | SA(s)bc | {{RA|11|53|41.4}} | {{DEC|+47|51|32}} | 800 ± 1 | 11.5 |- | NGC 3953 | SB(r)bc | {{RA|11|53|48.9}} | {{DEC|+52|19|36}} | 1052 ± 2 | 10.8 |- | NGC 3972 | SA(s)bc | {{RA|11|55|45.1}} | {{DEC|+55|19|15}} | 852 ± 1 | 13.1 |- | NGC 3982 | SAB(r)b | {{RA|11|56|28.1}} | {{DEC|+55|07|31}} | 1109 ± 6 | 12.0 |- | NGC 4010 | SB(s)d | {{RA|11|58|37.9}} | {{DEC|+47|15|41}} | 902 ± 1 | 13.2 |- | NGC 4026 | S0 | {{RA|11|59|25.2}} | {{DEC|+50|57|42}} | 930 ± 40 | 11.7 |- | NGC 4085 | SAB(s)c | {{RA|12|05|22.7}} | {{DEC|+50|21|10}} | 746 ± 5 | 13.0 |- | NGC 4088 | SAB(rs)bc | {{RA|12|05|34.2}} | {{DEC|+50|32|21}} | 757 ± 1 | 11.2 |- | NGC 4100 | (R)SA(rs)bc | {{RA|12|06|08.1}} | {{DEC|+49|34|59}} | 1074 ± 1 | 11.9 |- | NGC 4102 | SAB(s)b | {{RA|12|06|23.1}} | {{DEC|+52|42|39}} | 846 ± 2 | 12.0 |- | NGC 4142 | SB(s)d | {{RA|12|09|30.2}} | {{DEC|+53|06|18}} | 1157 ± 7 | 13.9 |- | NGC 4157 | SAB(s)b | {{RA|12|11|04.4}} | {{DEC|+50|29|05}} | 774 ± 2 | 12.2 |- | UGC 6628 | SAm | {{RA|11|40|06.7}} | {{DEC|+45|56|34}} | 841 ± 1 | 13.2 |- | UGC 6667 | Scd | {{RA|11|42|26.3}} | {{DEC|+51|35|53}} | 973 ± 1 | 14.2 |- | UGC 6840 | SB(rs)m | {{RA|11|52|07.0}} | {{DEC|+52|06|29}} | 1046 ± 5 | 14.3 |- | UGC 6917 | SBm | {{RA|11|56|28.8}} | {{DEC|+50|25|42}} | 911 ± 1 | 13.1 |- | UGC 6923 | Im | {{RA|11|56|49.4}} | {{DEC|+53|09|37}} | 1066 ± 2 | 15.1 |- | UGC 6930 | SAB(s)d | {{RA|11|57|17.3}} | {{DEC|+49|16|59}} | 777 ± 0 | 12.7 |- | UGC 6983 | SB(rs)cd | {{RA|11|59|09.3}} | {{DEC|+52|42|27}} | 1082 ± 1 | 13.1 |- | UGC 7218 | Im | {{RA|12|12|56.5}} | {{DEC|+52|15|55}} | 770 ± 7 | 14.8 |- |} ==NGC 1023 Group== The NGC 1023 group is a group of galaxies about 20.6 million light-years from Earth in the Local Supercluster along with the Local Group.<ref>http://www.atlasoftheuniverse.com/virgo.html</ref> {| class="wikitable" style="text-align:center;border-collapse:collapse;" cellpadding="2" |+'''Members of the group''' |- ! style="background:#efefef;" | Name ! style="background:#efefef;" | Galaxy morphological classification (Type) ! style="background:#efefef;" | Magnitude |- | NGC 1023 | SB(rs)0 | +10.65 |- | NGC 925 | SAB(s)d | +10.96 |- | NGC 891 | SA(s)b | +11.24 |- | NGC 1239 | SAB(rs)cd | +12.14 |- | NGC 1058 | SA(rs)c | +12.26 |- |} ==NGC 2997 Group== The NGC 2997 group is a group of galaxies about 24.8 million light-years from Earth containing NGC 2997 as a member and is a group in the Local Supercluster along with the Local Group.<ref>G. De Vaucouleurs, 1975. Nearby Groups of Galaxies, ch. 5. the nearer groups within 10 megaparsecs. Published in "Galaxies and the Universe," ed. by A. Sandage, M. Sandage and J. Kristian.</ref> ==NGC 4038 Group== The table below lists galaxies that have been consistently identified as group members in the Nearby Galaxies Catalog,<ref name="nbg"/> the survey of Fouque et al.,<ref name="fouqueetal1992"/> the Lyons Groups of Galaxies (LGG) Catalog,<ref name="garcia1993" /> and the three group lists created from the Nearby Optical Galaxy sample of Giuricin et al.<ref name="giuricinetal2002" /> {| class="wikitable" style="text-align:center;border-collapse:collapse;" cellpadding="2" |+'''Members of the NGC 4038 Group''' |- ! style="background:#efefef;" | Name ! style="background:#efefef;" | Galaxy morphological classification (Type)<ref name="ned"/> ! style="background:#efefef;" | R.A. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Dec. (J2000)<ref name="ned" /> ! style="background:#efefef;" | Redshift (km/s)<ref name="ned" /> ! style="background:#efefef;" | Apparent Magnitude<ref name="ned" /> |- | Antennae Galaxies (NGC 4038/NGC 4039) | | {{RA|12|01|53.3}} | {{DEC|-18|52|30}} | 1705 ± 5 | 13.0 |- | NGC 3956 | SA(s)c | {{RA|11|54|00.7}} | {{DEC|-20|34|02}} | 1645 ± 5 | 13.1 |- | NGC 3957 | SA0 | {{RA|11|54|01.5}} | {{DEC|-19|34|08}} | 1637 ± 19 | 13.1 |- | NGC 3981 | SAB(s)bc pec | {{RA|11|56|07.5}} | {{DEC|-19|53|46}} | 1723 ± 4 | 12.1 |- | NGC 4024 | SB0 | {{RA|11|58|31.2}} | {{DEC|-18|20|49}} | 1694 ± 15 | 13.2 |- | NGC 4027 | SB(s)dm | {{RA|11|59|30.2}} | {{DEC|-19|15|55}} | 1671 ± 6 | 11.7 |- | NGC 4033 | E6 | {{RA|12|00|34.7}} | {{DEC|-17|50|33}} | 1617 ± 20 | 13.2 |- | NGC 4050 | SB(r)ab | {{RA|12|02|54.0}} | {{DEC|-16|22|25}} | 1761 ± 8 | 13.1 |- | PGC 37476 | SB(rs)c | {{RA|11|55|50.6}} | {{DEC|-18|11|47}} | 1596 ± 8 | 14.0 |- | PGC 38087 | SB(s)cd | {{RA|12|03|24.4}} | {{DEC|-19|31|21}} | 1664 ± 7 | 15.0 |- | UGCA 254 | SAB(s)cd | {{RA|11|54|49.5}} | {{DEC|-16|51|50}} | 1813 ± 6 | 14.5 |- | UGCA 257 | SB(s)m | {{RA|11|58|25.4}} | {{DEC|-22|26|24}} | 1795 ± 5 | 13.6 |- |} The NGC 4038 group along with other galaxies and galaxy groups<ref name="fouqueetal1992" /> are part of the Crater Cloud<ref name="Tully1982">{{Cite journal |last=Tully |first=R. B. |date=June 1982 |title=The Local Supercluster |bibcode=1982ApJ...257..389T |journal=The Astrophysical Journal |language=en |volume=257 |pages=389–422 |doi=10.1086/159999 |issn=0004-637X }}</ref><ref>{{Cite journal |last=Read |first=A. M. |last2=Ponman |first2=T. J. |last3=Wolstencroft |first3=R. D. |date=1995-11-15 |title=The X-ray properties of the merging galaxy pair NGC 4038/9 – the Antennae |url=https://academic.oup.com/mnras/article/277/2/397/1002834 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=277 |issue=2 |pages=397–412 |doi=10.1093/mnras/277.2.397 |issn=0035-8711 |arxiv=astro-ph/9506047 |bibcode=1995MNRAS.277..397R }}</ref> which is a component of the Virgo Supercluster.<ref name="ned" /> ==NGC 4065 Group== [[Image:SDSS NGC 4065 Group.jpeg|right|thumb|300px|Sloan Digital Sky Survey (SDSS) image shows the NGC 4065 Group. Credit: Sloan Digital Sky Survey.{{tlx|free media}}]] The NGC 4065 Group is a group of galaxies<ref name="ned"/><ref name=":1">{{Cite web |url=http://simbad.u-strasbg.fr/simbad/sim-id?Ident=NGC+4065+GROUP&QueryType=ned |title=NGC 4065 GROUP |last= |first= |date= |website=sim-id |archive-url= |archive-date= |access-date=2019-02-17 }}</ref><ref name=":2" /><ref name="Gregory1978">{{Cite journal |last=Gregory |first=S. A. |last2=Thompson |first2=L. A. |date=June 1978 |title=The Coma/A1367 supercluster and its environs |url=http://adsabs.harvard.edu/doi/10.1086/156198 |journal=The Astrophysical Journal |language=en |volume=222 |pages=784 |doi=10.1086/156198 |issn=0004-637X |via= }}</ref> located about {{convert|100|Mpc|Mly|abbr=on|order=flip}}<ref name=":2">{{Cite journal |last=Freeland |first=E. |last2=Sengupta |first2=C. |last3=Croston |first3=J. H. |date=2010-12-01 |title=Quantifying the importance of ram-pressure stripping in a galaxy group at 100 Mpc |url=http://adsabs.harvard.edu/abs/2010MNRAS.409.1518F |journal=Monthly Notices of the Royal Astronomical Society |volume=409 |pages=1518–1524 |doi=10.1111/j.1365-2966.2010.17379.x |issn=0035-8711 }}</ref><ref name="ned" /> in the constellation Coma Berenices.<ref name=":6">{{Cite web |url=https://www.webbdeepsky.com/galaxies/2018/galaxy/april |title=Webb Deep-Sky Society: Galaxy of the Month for April 2018 |website=www.webbdeepsky.com |access-date=2019-02-16 }}</ref><ref>{{Cite web |url=http://www.kopernik.org/images/archive/n4065.htm |title=NGC 4065 Galaxy Group |website=www.kopernik.org |access-date=2019-02-16 }}</ref> The group's brightest member is NGC 4065<ref name="Gregory1978"/><ref name=":7">{{Cite journal |last=Venkatesan |first=T. C. A. |last2=Batuski |first2=David J. |last3=Hanisch |first3=Robert J. |last4=Burns |first4=Jack O. |date=1994-11-01 |title=Why do head-tail sources exist in poor clusters of galaxies? |url=http://adsabs.harvard.edu/abs/1994ApJ...436...67V |journal=The Astrophysical Journal |volume=436 |pages=67–78 |doi=10.1086/174881 |issn=0004-637X }}</ref><ref>{{Cite web |url=https://www.astronomy-mall.com/Adventures.In.Deep.Space/NGC%204000%20-%204999%20(11-30-17).htm |title=Astronomy-Mall: Adventures In Deep Space NGC objects 4001-4999 |last=Gottlieb |first=Steve |date= |website=Astronomy-Mall |archive-url= |archive-date= |access-date=2019-02-02 }}</ref><ref name=":3" /> and located in the Coma Supercluster.<ref name="Gregory1978"/><ref name=":5">{{Cite journal |last=Tifft |first=W. G. |last2=Gregory |first2=S. A. |date=1979-07-01 |title=Band theory applied to the Coma/A1367 supercluster |url=http://adsabs.harvard.edu/abs/1979ApJ...231...23T |journal=The Astrophysical Journal |volume=231 |pages=23–27 |doi=10.1086/157158 |issn=0004-637X }}</ref><ref>{{Cite journal |last=Chincarini |first=G. L. |last2=Giovanelli |first2=R. |last3=Haynes |first3=M. P. |date=1983-05-01 |title=The geometry of two superclusters Coma-A1367 and Perseus-Pisces |url=http://adsabs.harvard.edu/abs/1983A%26A...121....5C |journal=Astronomy and Astrophysics |volume=121 |pages=5–9 |issn=0004-6361 }}</ref><ref>{{Cite journal |last=Jaffe |first=W. |last2=Gavazzi |first2=G. |last3=Valentijn |first3=E. |date=1986-02-01 |title=Radio continuum survey of the Coma/A1367 supercluster. I - 610 MHz observations of CGCG galaxies in four groups |url=http://adsabs.harvard.edu/abs/1986AJ.....91..199J |journal=The Astronomical Journal |volume=91 |pages=199–203 |doi=10.1086/114000 |issn=0004-6256 }}</ref><ref>{{Cite journal |last=Galli |first=R. |last2=Carrasco |first2=L. |last3=Gavazzi |first3=G. |date=1999-04-01 |title=The 3-D structure of the Coma–A 1367 supercluster: Optical spectroscopy of 102 galaxies |url=https://aas.aanda.org/articles/aas/abs/1999/08/ds1602/ds1602.html |journal=Astronomy and Astrophysics Supplement Series |language=en |volume=136 |issue=2 |pages=227–235 |doi=10.1051/aas:1999209 |issn=0365-0138 }}</ref><ref>{{Cite journal |last=Gavazzi |first=Giuseppe |last2=Fumagalli |first2=Mattia |last3=Cucciati |first3=Olga |last4=Boselli |first4=Alessandro |date=July 2010 |title=A snapshot on galaxy evolution occurring in the Great Wall: the role of Nurture at z=0 |url=http://arxiv.org/abs/1003.3795 |journal=Astronomy and Astrophysics |volume=517 |pages=A73 |doi=10.1051/0004-6361/201014153 |issn=0004-6361 |via= }}</ref><ref name=":2" /><ref name=":8">{{Cite journal |last=Burns |first=Jack O. |last2=Hanisch |first2=Robert J. |last3=White |first3=Richard A. |last4=Nelson |first4=Eric R. |last5=Morrisette |first5=Kim A. |last6=Moody |first6=J. Ward |date=1987-09-01 |title=A VLA 20 CM survey of poor groups of galaxies |url=http://adsabs.harvard.edu/abs/1987AJ.....94..587B |journal=The Astronomical Journal |volume=94 |pages=587–617 |doi=10.1086/114494 |issn=0004-6256 }}</ref> The group is dominated by mostly elliptical galaxies<ref name=":6" /><ref name=":5" /> with only 15 to 31 percent of the members being spiral galaxies.<ref name="Gregory1978"/><ref name=":3" /> The NGC 4065 Group exhibits bimodal X-ray emission with one peak on the galaxies NGC 4061 and NGC 4065 and the other on NGC 4066.<ref name=":3">{{Cite journal |last=Freeland |first=E. |last2=Stilp |first2=A. |last3=Wilcots |first3=E. |date=2009-07-01 |title=H I Observations of Five Groups of Galaxies |url=http://adsabs.harvard.edu/abs/2009AJ....138..295F |journal=The Astronomical Journal |volume=138 |pages=295–304 |doi=10.1088/0004-6256/138/1/295 |issn=0004-6256 }}</ref> {{clear}} ==NGC 5866 Group== The NGC 5866 Group is located to the northwest of the M101 group.<ref name="ferrareseetal00">{{cite journal |author1=L. Ferrarese |author2=H. C. Ford |author3=J. Huchra |author4=R. C. Kennicutt Jr. |author5=J. R. Mould |author6=S. Sakai |author7=W. L. Freedman |author8=P. B. Stetson |author9=B. F. Madore |author10=B. K. Gibson |author11=J. A. Graham |author12=S. M. Hughes |author13=G. D. Illingworth |author14=D. D. Kelson |author15=L. Macri |author16=K. Sebo |author17=N. A. Silbermann | title=A Database of Cepheid Distance Moduli and Tip of the Red Giant Branch, Globular Cluster Luminosity Function, Planetary Nebula Luminosity Function, and Surface Brightness Fluctuation Data Useful for Distance Determinations | journal=Astrophysical Journal Supplement | date=2000 | volume=128 | issue=2 | pages=431–459 | bibcode=2000ApJS..128..431F | doi=10.1086/313391 |arxiv = astro-ph/9910501 }}</ref> ==Antlia Cluster== [[Image:Antlia cluster.jpg|right|thumb|250px|Cluster is of the Pneumatic Machine (Antlia, originally Antlia Pneumatica). Credit: Atlas of the Universe.{{tlx|free media}}]] The Antlia Cluster (or Abell S0636)<ref name="Nakazawa2000">{{cite journal | last1 = Nakazawa | first1 = Kazuhiro | last2 = Makishima | first2 = Kazuo | last3 = Fukazawa | first3 = Yasushi | last4 = Tamura | first4 = Takayuki |date=August 2000 | title = ASCA Observations of a Near-by Cluster in Antlia | trans-title = | journal = Publications of the Astronomical Society of Japan | volume = 52 | pages = 623–630 | location = Tokyo, Japan | publisher = PASJ | doi = 10.1093/pasj/52.4.623 | accessdate = March 4, 2012 | bibcode = 2000PASJ...52..623N }}</ref> is a galaxy cluster|cluster of galaxies located in the Hydra-Centaurus Supercluster. The Antlia Cluster is the third nearest to the Local Group after the Virgo Cluster and Fornax Cluster.<ref name="SmithCastelli2008">{{Cite journal | last1 = Smith Castelli | first1 = Analía V. | last2 = Bassino | first2 = Lilia P. | last3 = Richtler |first3=Tom |author4=Cellone, Sergio A. |author5=Aruta, Cristian |author6=Infante, Leopoldo | title = Galaxy populations in the Antlia cluster - I. Photometric properties of early-type galaxies |date=June 2008 | journal = Monthly Notices of the Royal Astronomical Society | publisher = MNRAS | volume = 386 | issue = 4 | pages = 2311–2322 | doi = 10.1111/j.1365-2966.2008.13211.x | accessdate = | bibcode = 2008MNRAS.386.2311S |arxiv = 0803.1630 }}</ref> Antlia's distance from Earth is {{convert|40.5|Mpc|Mly|1|abbr=on}} to {{convert|40.9|Mpc|Mly|1|abbr=on|lk=off}}<ref name="Dirsch2003">{{cite journal | last1 = Dirsch | first1 = B. | last2 = Richtler | first2 = T. | last3 = Bassino | first3 = L. P. |date=September 2003 | title = The globular cluster systems of NGC 3258 and NGC 3268 in the Antlia cluster | trans-title = | journal = Astronomy and Astrophysics | volume = 408 | pages = 929–939 | publisher = A&A | doi = 10.1051/0004-6361:20031027 | accessdate = March 3, 2012 | bibcode = 2003A&A...408..929D |arxiv = astro-ph/0307200 }}</ref> and can be viewed from Earth in the constellation Antlia.<ref name="Dirsch2003" /><ref name="SmithCastelli2005">{{cite conference | title = Dwarf Galaxies in the Antlia Cluster: First Results, In: ''Groups of Galaxies in the Nearby Universe'' | author = Smith Castelli, A. V. |author2=Bassino, L. P.|author3=Cellone, S. A.|author4=Richtler, T.|author5=Dirsch, B.|author6=Infante, L.|author7=Aruta, C.|author8= Gómez, M. |date=December 2005 | conference = Proceedings of the ESO Workshop | editor = I. Saviane | editor2 = V.D. Ivanov | editor3 = J. Borissova | volume = 1 | publisher = Springer-Verlag (2007) | isbn = 978-3-540-71172-8 | bibcode = 2007ggnu.conf..109S | accessdate = | page = 109 |arxiv = astro-ph/0603391 |doi = 10.1007/978-3-540-71173-5_17 }}</ref> The Antlia Cluster should not be confused with the Antlia Dwarf Galaxy.<ref name="Dirsch2003" /> Antlia is classified as a rare ''Bautz-Morgan type III'' cluster,<ref name="Nakazawa2000" /><ref name="Hopp1985">{{cite journal | last1 = Hopp | first1 = U. | last2 = Materne | first2 = J. |date=July 1985 | title = The Antlia cluster of galaxies and its environment - The Hydra I-Centaurus supercluster | journal = Astronomy and Astrophysics Supplement Series | volume = 61 | pages = 93–106 | issn = 0365-0138 | accessdate = |bibcode = 1985A&AS...61...93H }}</ref> meaning it has no central dominant (cD) brightest cluster galaxy.<ref name="Guthrie">{{cite journal | last1 = Guthrie | first1 = B. N. G. |date=July 1974 | title = Radio emission associated with the brightest galaxies in clusters | journal = Monthly Notices of the Royal Astronomical Society | volume = 168 | pages = 15–20 | publisher = MNRAS | id = A&AA ID: AAA012.160.002 | doi = 10.1093/mnras/168.1.15 | accessdate = | bibcode = 1974MNRAS.168...15G }}</ref> However, the cluster is dominated by two massive elliptical galaxies, NGC 3268 and NGC 3258, and contains a total of about 234 galaxies.<ref name="Nakazawa2000" /><ref name="Dirsch2003" /> The cluster is very dense compared to other clusters such as Virgo and Fornax, thus containing early-type galaxies and a larger portion of dwarf ellipticals.<ref name="Dirsch2003" /><ref name="SmithCastelli2005" /> The Cluster is split into two galaxy groups, ''The Northern subgroup'' gravitating around NGC 3268, and ''the Southern subgroup'' centered on NGC 3258.<ref name="Dirsch2003" /> The cluster has an overall redshift of z = 0.0087, implying that the cluster is, like most objects in the Universe, receding from the Local Group.<ref name="Nakazawa2000" /> Using the now-obsolete scientific satellite Advanced Satellite for Cosmology and Astrophysics (ASCA), X-ray observations show that the cluster is almost isothermal, with a mean temperature of kT ~ 2.0 keV.<ref name="Nakazawa2000" /> Members of cluster: {{div col|colwidth=12em}} * NGC 3267<ref name="Nakazawa2000" /><ref name="SmithCastelli2008" /> * NGC 3568<ref name="Nakazawa2000" /><ref name="SmithCastelli2008" /> * NGC 3258<ref name="Nakazawa2000" /><ref name="SmithCastelli2008" /> * NGC 3269<ref name="Nakazawa2000" /><ref name="SmithCastelli2008" /> * NGC 3271<ref name="Nakazawa2000" /><ref name="SmithCastelli2008" /> * NGC 3258A<ref name="SmithCastelli2008" /> * NGC 3258B<ref name="SmithCastelli2008" /> * NGC 3260<ref name="SmithCastelli2008" /> * NGC 3267<ref name="SmithCastelli2008" /> * NGC 3268<ref name="SmithCastelli2008" /> * NGC 3273<ref name="SmithCastelli2008" /> {{Div col end}} {{clear}} ==Centaurus Cluster== [[Image:Centaurus cluster.jpg|right|thumb|300px|X-ray image shows the inner 6.7 arcminutes of the core of the Centaurus Cluster, with the hot intracluster medium, at temperatures of a few tens of MK. Credit: [[c:user:Xioxox|Xioxox]].{{tlx|free media}}]] [[Image:NGC 4696 (captured by the Hubble Space Telescope).jpg|300px|left|thumb|NGC 4696 is a cosmic question mark. Credit: ESA/Hubble and NASA.{{tlx|free media}}]] The cluster consists of two different sub-groups of galaxies with different velocities.<ref name="Lucey">{{cite journal | bibcode = 1986MNRAS.221..453L | title=The Centaurus cluster of galaxies. II - The bimodal velocity structure | journal=Monthly Notices of the Royal Astronomical Society | volume=221 | pages=453–472 | year=1986 | author=Lucey J. R. | author2=Currie M. J. | author3=Dickens R. J. | doi=10.1093/mnras/221.2.453 }}</ref> Cen 30 is the main subgroup containing NGC 4696. Cen 45 which is centered on NGC 4709, is moving at 1500&nbsp;km/s relative to Cen 30,<ref name="Lucey" /> and is believed to be merging with the main cluster.<ref>{{Cite journal |last=Churazov |first=E. |last2=Gilfanov |first2=M. |last3=Forman |first3=W. |last4=Jones |first4=C. |date=1999 |title=Evidence for Merging in the Centaurus Cluster |url=http://stacks.iop.org/0004-637X/520/i=1/a=105 |journal=The Astrophysical Journal |language=en |volume=520 |issue=1 |pages=105 |doi=10.1086/307421 |issn=0004-637X |arxiv=astro-ph/9802166 |bibcode=1999ApJ...520..105C }}</ref> {{clear}} ==Hydra A galaxy cluster== {{main|Radiation astronomy/Radios|Radio astronomy}} [[Image:Composite radio + x-ray.jpg|thumb|right|250px|This image has the radio image of Greg Taylor, NRAO, overlain on the X-ray image from Chandra. The radio source Hydra A originates in a galaxy near the center of the cluster. Optical observations show a few hundred galaxies in the cluster. Credit: NASA/CXC/SAO; Radio: NRAO.{{tlx|free media}}]] [[Image:Hydra A gas cloud.jpg|thumb|250px|left|This Chandra X-ray image reveals a large cloud of hot gas that extends throughout the Hydra A galaxy cluster. Image is 2.7 arcmin across. RA 09^h 18^m 06^s Dec] −12° 05' 45" in Hydra. Observation date: 30 October 1999. Instrument: ACIS.{{tlx|free media}}]] A large cloud of hot gas extends throughout the Hydra A galaxy cluster. {{clear}} ==Hydra Cluster== [[Image:Hyamap.gif|right|thumb|300px|Map shows Hydra cluster. Credit: Richard Powell.{{tlx|free media}}]] The Hydra Cluster (or Abell 1060) is a galaxy cluster that contains 157 bright galaxies, appearing in the constellation Hydra.<ref>Wehner and Harris, p.1</ref> The cluster spans about ten million light years and has an unusually high proportion of dark matter.<ref>{{ cite web |author=Nemiroff, R. |author2=Bonnell, J. |url=https://apod.nasa.gov/AP010416.html |publisher=NASA |date=16 April 2001 |title=The Hydra Cluster of Galaxies }}</ref> The cluster is part of the Hydra-Centaurus Supercluster located 158 million light years from earth. The cluster's largest galaxies are elliptical galaxies NGC 3309 and NGC 3311 and the spiral galaxy NGC 3312 all having a diameter of about 150,000 light years.<ref>[http://www.atlasoftheuniverse.com/superc/hya.html ''The Hydra Supercluster''] An Atlas of the Universe.com</ref> In spite of a nearly circular appearance on the sky, there is evidence in the galaxy velocities for a clumpy, three-dimensional distribution.<ref>{{Cite journal | doi = 10.1086/166902 | last = Fitchett | first = Michael | last2 = Merritt | first2 = David | title = Dynamics of the Hydra I Galaxy Cluster | journal = The Astrophysical Journal |date=December 1988 | volume = 335 | pages = 18–34 | bibcode = 1988ApJ...335...18F}}</ref> {{clear}} ==Leo Cluster== The Leo Cluster (Abell 1367) is a galaxy cluster about 330 million light-years distant (z = 0.022<ref name="ned"/>) in the constellation Leo, with at least 70 major galaxies. NGC 3842 is the brightest member of this cluster.<ref name=":0" /> Along with the Coma Cluster, it is one of the two major clusters comprising the Coma Supercluster,<ref>{{Cite web |url=http://www.atlasoftheuniverse.com/superc/com.html |title=The Coma Supercluster |website=www.atlasoftheuniverse.com |access-date=2018-04-19 }}</ref> which in turn is part of the CfA2 Great Wall, hundreds of millions light years long and one of the largest known structures in the universe.<ref>{{Cite web |url=https://www.webbdeepsky.com/galaxies/object?object=NGC3842 |title=Webb Deep-Sky Society: Galaxy of the Month: NGC3842 |website=www.webbdeepsky.com |language=en |access-date=2018-04-19 }}</ref> The Leo cluster and its stars are probably younger than most comparable clusters in the universe and evolve at a different pace.<ref>{{Cite journal |last=Yagi |first=Masafumi |last2=Yoshida |first2=Michitoshi |last3=Gavazzi |first3=Giuseppe |last4=Komiyama |first4=Yutaka |last5=Kashikawa |first5=Nobunari |last6=Sadanori Okamura |date=2017 |title=Extended Ionized Gas Clouds in the Abell 1367 Cluster |url=http://stacks.iop.org/0004-637X/839/i=1/a=65 |journal=The Astrophysical Journal |language=en |volume=839 |issue=1 |pages=65 |doi=10.3847/1538-4357/aa68e3 |issn=0004-637X |arxiv=1703.10301 |bibcode=2017ApJ...839...65Y }}</ref> In the center of NGC 3842 the black hole is 9.7 billion times more massive than our sun.<ref name=":0">{{Cite news |url=http://www.skyandtelescope.com/observing/are-you-ready-willing-and-abell/ |title=Are You Ready, Willing, and Abell? - Sky & Telescope |date=2017-04-26 |work=Sky & Telescope |access-date=2018-04-18 |language=en-US }}</ref> A "hot zone" exists where stars are unable to maintain their gas long enough to properly form.<ref>{{Cite web |url=http://www.beskeen.com/gallery/galaxy/abell1367/abell1367.shtml |title=Abell 1367 - The Leo Galaxy Cluster |website=www.beskeen.com |language=en-gb |access-date=2018-04-18 }}</ref> Subpopulations within the Leo Cluster: # elliptical galaxies that seem to be roughly as old as the universe, # red-sequence lenticular (lens shaped) galaxies whose ages are directly tied to their mass, # galaxies where star formation is still taking place, and are morphologically distributed.<ref>{{Cite journal |last=Mouhcine |first=M. |last2=Kriwattanawong |first2=W. |last3=James |first3=P. A. |date=2011-04-01 |title=The galaxy population of Abell 1367: the stellar mass–metallicity relation |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=412 |issue=2 |pages=1295–1308 |doi=10.1111/j.1365-2966.2010.17993.x |issn=0035-8711 |arxiv=1101.2074 |bibcode=2011MNRAS.412.1295M }}</ref> ==Ursa Major Cluster== "The Ursa Major Cluster is the most poorly defined, with a velocity dispersion of only 148 km s⁻¹ and a virial radius of 880 kpc [...], and contains essentially only late-type galaxies distributed with no particular concentration toward any center."<ref name=Tully1996>{{ cite journal |author=R. Brent Tully |author2=Marc A.W. Verheijen |author3=Michael J. Pierce |author4=Jia-Sheng Huang |author5=Richard J. Wainscoat |title=The Ursa Major Cluster of Galaxies. I. Cluster Definition and Photometric Data |journal=Astronomical Journal |date=December 1996 |volume=112 |issue=12 |pages=2471 |url=https://arxiv.org/pdf/astro-ph/9608124 |arxiv=astro-ph/9608124 |bibcode=1996AJ....112.2471T |doi=10.1086/118196 |pmid= |accessdate=1 June 2019 }}</ref> "The Ursa Major Cloud contains the Ursa Major Cluster."<ref name=Tully1996/> "Optical images have been acquired in the B, R_C, I_C (C=Cousins) passbands for all 79 galaxies with a variety of CCD and telescope combinations."<ref name=Tully1996/> "The 79 galaxies that are accepted lie within 7.5° of α = 11h56.9m, δ = +49°22′ and have measured velocities, V_helio + 300sinℓcosb, between 700 and 1210 km s⁻¹."<ref name=Tully1996/> The cluster includes NGC 3726, NGC 3769, NGC 3782, NGC 3870, NGC 3877, NGC 3893, NGC 3896, NGC 3906, NGC 3917, NGC 3931, NGC 3928, NGC 3938, NGC 3949, NGC 3953, NGC 3985, NGC 3972, NGC 3982, NGC 3985, NGC 3990, NGC 3992, NGC 3998, NGC 4010, NGC 4013, NGC 4026, NGC 4051, NGC 4085, NGC 4088, NGC 4100, NGC 4102, NGC 4111, NGC 4117, NGC 4118, NGC 4138, NGC 4143, NGC 4157, NGC 4183, NGC 4217, NGC 4218, NGC 4220, NGC 4346, and NGC 4389.<ref name=Tully1996/> ==Virgo Cluster== [[Image:ESO-M87.jpg|right|thumb|300px|Image shows the Virgo Cluster diffuse light between member galaxies, where Messier 87 is the largest galaxy (lower left). Credit: Chris Mihos (Case Western Reserve University)/ESO.{{tlx|free media}}]] The Virgo Cluster is a galaxy cluster whose center is 53.8 ± 0.3 Mly (16.5 ± 0.1 Mpc)<ref name="Mei2007">{{cite journal | author = Mei, Simona | author2 = Blakeslee, John P. | author3 = Côté, Patrick | author4 = Tonry, John L. | author5 = West, Michael J. | author6 = Ferrarese, Laura | author7 = Jordán, Andrés | author8 = Peng, Eric W. | author9 = Anthony, André | author10 = Merritt, Davi | title = The ACS Virgo Cluster Survey. XIII. SBF Distance Catalog and the Three-dimensional Structure of the Virgo Cluster | journal = The Astrophysical Journal | date = 2007 | volume = 655 | issue = 1 | pages = 144–162 | bibcode = 2007ApJ...655..144M | doi = 10.1086/509598 |arxiv = astro-ph/0702510 }}</ref> away in the constellation Virgo. Comprising approximately 1300 (and possibly up to 2000) member galaxies,<ref>{{cite web |url=http://astronomy.swin.edu.au/cosmos/V/Virgo+Cluster |title=Virgo Cluster |website=Cosmos |publisher=Swinburne University of Technology }}</ref> the cluster forms the heart of the larger Virgo Supercluster, of which the Local Group (containing our Milky Way) is a member. The Local Group actually experiences the mass of the Virgo Supercluster as the Virgocentric flow, where the Virgo Cluster's mass is 1.2{{e|15}} solar masses out to 8 degrees of the cluster's center or a radius of about 2.2 Mpc.<ref name="Fouquéetal2001">{{cite journal | author = Fouqué, P. | author2 = Solanes, J. M. | author3 = Sanchis, T. | author4 = Balkowski, C. | title = Structure, mass and distance of the Virgo cluster from a Tolman-Bondi model | journal = Astronomy and Astrophysics | date = 2001 | volume = 375 | issue = 3 | pages = 770–780 | bibcode = 2001A&A...375..770F | doi = 10.1051/0004-6361:20010833 | arxiv = astro-ph/0106261 }}</ref> The elliptical galaxy Messier 87 is located in the center of the cluster.<ref>{{Cite web |url=http://www.messier-objects.com/virgo-cluster/ |title=Virgo Cluster {{!}} Messier Objects |website=www.messier-objects.com |language=en-US |access-date=2018-06-24 }}</ref> The cluster is a fairly heterogeneous mixture of spirals and ellipticals.<ref>{{Cite journal | doi = 10.1086/421490 | last1 = Côté | first1 = Patrick | last2 = Blakeslee |first2 = John P. | last3 = Ferrarese |first3 = Laura | last4 = Jordán | first4 = Andrés | last5 = Mei | first5 = Simona | last6 = Merritt | first6 = David | last7 = Milosavljević | first7 = Miloš | last8 = Peng | first8 = Eric W. | last9 = Tonry | first9 = John L. | title = The ACS Virgo Cluster Survey | journal = The Astrophysical Journal | volume = 153 | issue = 1 | pages = 223–242 | date=July 2004 | bibcode = 2004ApJS..153..223C | arxiv = astro-ph/0404138 | display-authors = 9 | last10 = West | first10 = Michael J. }}</ref> The spiral galaxies of the cluster appear to be distributed in an oblong prolate filament, approximately four times as long as it is wide, stretching along the line of sight from the Milky Way.<ref name="Fukugitaetal1993">{{cite journal | author = M. Fukugita | author2 = S. Okamura | author3 = N. Yasuda | title = Spatial distribution of spiral galaxies in the Virgo Cluster from the Tully-Fisher relation | journal = Astrophysical Journal | date = 1993 | volume = 412 | pages = L13–L16 | bibcode = 1993ApJ...412L..13F | doi = 10.1086/186928 }}</ref> The elliptical galaxies are more centrally concentrated than the spiral galaxies.<ref>{{Cite web |url=https://ned.ipac.caltech.edu/level5/ESSAYS/Binggeli/binggeli.html |title=Virgo Cluster |website=ned.ipac.caltech.edu |access-date=2018-06-24 }}</ref> The cluster is an aggregrate of at least three separate subclumps: ''Virgo A'', centered on M87, a second centered on the galaxy M86, and ''Virgo B'', centered on the elliptical galaxy M49, with a ''Virgo C'' subcluster, centered on the galaxy M60 as well as a ''LVC'' (Low Velocity Cloud) subclump, centered on the large spiral galaxy NGC 4216.<ref name=Boselli2014>{{cite journal |last=Boselli |first1=A. |last2=Voyer |first2=E. |last3=Boissier |first3= S. |last4=Cucciati |first4= O. |last5=Consolandi |first5=G. |last6=Cortese |first6=L. |last7=Fumagalli |first7=M. |last8=Gavazzi |first8=G. |last9=Heinis |first9=S. |last10=Roehlly |first10=Y. |last11=Toloba |first11=E. |date=2014 |title=The GALEX Ultraviolet Virgo Cluster Survey (GUViCS). IV. The role of the cluster environment on galaxy evolution |journal=Astronomy & Astrophysics |volume=570 |id=A69 |arxiv=1407.4986 |doi=10.1051/0004-6361/201424419 |bibcode=2014A&A...570A..69B |pages=A69 }}</ref> Of all of the subclumps, ''Virgo A'', formed by a mixture of elliptical, lenticular, and (usually) gas-poor spiral galaxies,<ref name=Chamaraux1980>{{cite journal |last1=Chamaraux |first1=P. |last2=Balkowski |first2=C. |last3=Gerard |first3=E. |date=1980 |title=The H I deficiency of the Virgo cluster spirals |journal=Astronomy & Astrophysics |volume=83 |issue=1–2 |pages=38–51 |bibcode=1980A&A....83...38C }}</ref> is the dominant one, with a mass of approximately 10¹⁴ solar masses, which is approximately an order of magnitude larger than the other two subclumps.<ref name=BinggeliNED>''[http://nedwww.ipac.caltech.edu/level5/Binggeli/frames.html The Virgo Super Cluster: home of M87]'' (with frames)</ref> [[Image:14-296-GalaxyClusters-PerseusVirgo-ChandraXRay-20141027.jpg|thumb|left|250px|Turbulence may prevent galaxy clusters from cooling (Chandra X-ray observatory). Credit: NASA/CXC/Stanford/I. Zhuravleva et al.{{tlx|free media}}]] The three subgroups are in the process of merging to form a larger single cluster<ref name=BinggeliNED/> and are surrounded by other smaller galaxy clouds, mostly composed of spiral galaxies, known as ''N Cloud'', ''S Cloud'', and ''Virgo E'' that are in the process of infalling to merge with them,<ref name="Gavazzietal1999">{{cite journal | author=Gavazzi, G. | author2=Boselli, A. | author3=Scodeggio, M. | author4=Pierini, D. | author5=Belsole, E. | title=The 3D structure of the Virgo cluster from H-band Fundamental Plane and Tully-Fisher distance determinations | journal=Monthly Notices of the Royal Astronomical Society | date=1999 | volume=304 | pages=595–610 |arxiv = astro-ph/9812275 |bibcode = 1999MNRAS.304..595G |doi = 10.1046/j.1365-8711.1999.02350.x | issue=3 }}</ref> plus other farther isolated galaxies and galaxy groups (like the galaxy cloud Coma I) that are also attracted by the gravity of Virgo to merge with it in the future.<ref name="Tully1984">{{cite journal | author=Tully, R. B. | author2=Shaya, E. J. | title=Infall of galaxies into the Virgo cluster and some cosmological constraints | journal=Astrophysical Journal | date=1984 | volume=281 | pages=31–55 |bibcode = 1984ApJ...281...31T |doi = 10.1086/162073 }}</ref> This strongly suggests the Virgo cluster is a dynamically young cluster that is still forming.<ref name=Gavazzietal1999/> Other two nearby aggregations known as ''M Cloud'', ''W Cloud'', and ''W' Cloud''<ref name=Boselli2014/> seem to be background systems independent of the main cluster.<ref name=Gavazzietal1999/> As with many other rich galaxy clusters, Virgo's intracluster medium is filled with a hot, rarefied plasma at temperatures of 30 million K that emits X-Rays.<ref name="Lea1982">{{cite journal | author=Lea, S. M. | author2=Mushotzky, R. | author3=Holt, S. S. | title=Einstein Observatory solid state spectrometer observations of M87 and the Virgo cluster | journal=Astrophysical Journal | date=1982 | issue=1 | volume=262 | pages=24–32 |bibcode = 1982ApJ...262...24L |doi = 10.1086/160392 }}</ref> Within the intracluster medium (ICM) are found a large number of intergalactic stars<ref name="HST1997">{{cite journal | author=Ferguson, H. | title=Intergalactic Stars in the Virgo Cluster | journal=HST Proposal | date=1997 | bibcode=1997hst..prop.7411F| pages=7411 }}</ref><ref>{{Cite journal |last=Ferguson |first=Henry C. |last2=Tanvir |first2=Nial R. |last3=von Hippel |first3=Ted |date=January 1998 |title=Detection of intergalactic red-giant-branch stars in the Virgo cluster |journal=Nature |language=En |volume=391 |issue=6666 |pages=461–463 |doi=10.1038/35087 |issn=0028-0836 |arxiv=astro-ph/9801228 |bibcode=1998Natur.391..461F }}</ref> (up to 10% of the stars in the cluster),<ref name=Fergusonetal1998/> including some planetary nebulae.<ref name="Feldmeieretal1998">{{cite journal | author=Feldmeier, J. | author2=Ciardullo, R. | author3=Jacoby, G. | title=Intracluster Planetary Nebulae in the Virgo Cluster. I. Initial Results | journal=Astrophysical Journal | date=1998 | volume=503 | issue=1 | pages=109–117 |arxiv = astro-ph/9803062 |bibcode = 1998ApJ...503..109F |doi = 10.1086/305981 }}</ref> It is theorized that these were expelled from their home galaxies by interactions with other galaxies.<ref name="Fergusonetal1998">{{cite journal | author=Ferguson, Henry C. | author2=Tanvir, Nial R. | author3=von Hippel, Ted | title=Detection of intergalactic red-giant-branch stars in the Virgo cluster | journal=Nature | date=1998 | volume=391 | pages=461–463 |arxiv = astro-ph/9801228 |bibcode = 1998Natur.391..461F |doi = 10.1038/35087 | issue=6666 }}</ref> The ICM also contains some globular clusters,<ref name="Takamiya2009">{{cite book | author=Takamiya, Marianne | author2=West, Michael | author3=Côté, Patrick | author4=Jordán, Andrés | author5=Peng, Eric | author6=Ferrarese, Laura | title=IGCs in the Virgo Cluster, In: ''Globular Clusters – Guides to Galaxies, Eso Astrophysics Symposia'' | date=2009 | pages=361–365 | bibcode=2009gcgg.book..361T| doi=10.1007/978-3-540-76961-3_83 | series=Eso Astrophysics Symposia | isbn=978-3-540-76960-6 }}</ref><ref name="Durrell2010">{{cite journal | author=Durrell, Patrick R. | author2=Accetta, K. | author3=Feldmeier, J. J. | author4=Mihos, J. C. | author5=Ciardullo, R. | author6=Peng, E. W. | author7=Members of the NGVS team | title=Searching for Intracluster Globular Clusters in the Virgo Cluster | date=2010 | journal=Bulletin of the American Astronomical Society | volume=42 |pages=567 | bibcode=2010AAS...21547814D }}</ref><ref name="Park2010">{{cite journal | author=Lee, Myung Gyoon | author2=Park, Hong Soo | author3=Hwang, Ho Seong | title=Detection of a Large-Scale Structure of Intracluster Globular Clusters in the Virgo Cluster | journal=Science | date=2010 | volume=328 | pages=334– |arxiv = 1003.2499 |bibcode = 2010Sci...328..334L |doi = 10.1126/science.1186496 | issue=5976 | pmid=20223950 }}</ref> possibly stripped off dwarf galaxies,<ref name=Park2010/> and even at least one star formation H II region.<ref name="Ortwin2002">{{cite journal | author=Gerhard, Ortwin | author2=Arnaboldi, Magda | author3=Freeman, Kenneth C. | author4=Okamura, Sadanori | title=Isolated Star Formation: A Compact H II Region in the Virgo Cluster | journal=The Astrophysical Journal | date=2002 | volume=580 | pages=L121–L124 |arxiv = astro-ph/0211341 |bibcode = 2002ApJ...580L.121G |doi = 10.1086/345657 | issue=2 }}</ref> {{clear}} ==Boötes Supercluster== [[Image:Bootes_supercluster.gif|right|thumb|300px|This is a map of the Bootes Supercluster. Credit: Atlas of the Universe.{{tlx|free media}}]] "There are a couple of [prominent] superclusters in Bootes over 800 million light years away but this region of the sky is more famous for the large Bootes Void that lies next to them."<ref name=Powell/> The Bootes Supercluster is a super cluster of galaxies located in the direction of the Bootes constellation bordering the Super Corona of the Northern Crown with which it is probably connected by a filament of galaxies, and with the Void of Bootes, an area of the universe with a minimum concentration of galaxies (less than one hundred have been identified) with a diameter of about 300 million light years. In Bootes there are two concentrations of galaxy clusters called SCL 349 and SCL 351, placed respectively at 830 million and 1 billion light years from Earth.<ref>{{ cite journal |author = M. Chow-Martínez |author2=H. Andernach |author3=C. A. Caretta |date = 12/21/2014 |title = Two new catalogues of superclusters of Abell/ACO galaxy clusters out to redshift 0.15 |journal = Monthly Notices of the Royal Astronomical Society |volume = 445 |number = 4 |pp = 4073-4085 |accessdate = 2015-07-06 |doi = 10.1093/mnras/stu1961 |url = http://mnras.oxfordjournals.org/content/445/4/4073 }}</ref><ref>{{Cite journal |title = |journal = Astronomy and Astrophysics Supplement Series |accessdate = 2015-07-06 |url = http://www.edpsciences.org/10.1051/aas:1997340 }}</ref> {| class="wikitable" style="text-align:center;border-collapse:collapse;" cellpadding="2" |+'''Some clusters of galaxies from Bootes Supercluster''' |- ! style="background:#efefef;" | Name cluster (Abell) ! style="background:#efefef;" | R.A. ! style="background:#efefef;" | Dec. ! style="background:#efefef;" | Redshift (z) ! style="background:#efefef;" | Distance (million light years) ! style="background:#efefef;" | Richness of the cluster |- | Abell 1781 | {{RA|13|4|5}} | {{DEC|+29|51|}} | 0,0606 | 820 | 0 |- | Abell 1795 | {{RA|13|49|0}} | {{DEC|+26|35|}} | 0,0619 | 840 | 2 |- | Abell 1825 | {{RA|13|58|0}} | {{DEC|+20|39|}} | 0,0583 | 790 | 0 |- | Abell 1827 | {{RA|13|58|2}} | {{DEC|+21|42|}} | 0,0642 | 870 | 1 |- | Abell 1828 | {{RA|13|58|4}} | {{DEC|+18|23|}} | 0,0611 | 840 | 1 |- | Abell 1831 | {{RA|13|59|2}} | {{DEC|+27|59|}} | 0,0603 | 815 | 1 |- | | |- | Abell 1775 | {{RA|13|41|9}} | {{DEC|+26|22|}} | 0,0705 | 950 | 2 |- | Abell 1800 | {{RA|13|49|7}} | {{DEC|+28|04|}} | 0,0743 | 1000 | 0 |- | Abell 1861 | {{RA|14|07|5}} | {{DEC|+27|49|}} | uncertain | uncertain | 1 |- | Abell 1873 | {{RA|14|11|7}} | {{DEC|+28|09|}} | 0,0764 | 1025 | 0 |- | Abell 1898 | {{RA|14|20|6}} | {{DEC|+25|09|}} | 0,0762 | 1025 | 1 |- |} {{clear}} ==BOSS Great Wall== [[Image:28261Lietzen.jpg|thumb|right|250px|This figure shows the superclusters of the BOSS Great Wall, on Cartesian coordinates. Credit: H. Lietzen, E. Tempel, L. J. Liivamägi, A. Montero-Dorta, M. Einasto, A. Streblyanska, C. Maraston, J. A. Rubiño-Martín, and E. Saar.{{tlx|fairuse}}]] The BOSS Great Wall, a supercluster complex identified using the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey (SDSS), was discovered in early 2016.<ref name="2016A&A...588L...4L2">{{cite journal |author1=Lietzen, H. |author2=Tempel, E. |author3=Liivamägi, L. J. |author4=Montero-Dorta, A. |author5=Einasto, M. |author6=Streblyanska, A. |author7=Maraston, C. |author8=Rubiño-Martín, J. A. |author9=Saar, E. |date=February 2016 |title=Discovery of a massive supercluster system at z∼0.48 |journal=Astronomy & Astrophysics |volume=588 |arxiv=1602.08498 |bibcode=2016A&A...588L...4L |doi=10.1051/0004-6361/201628261 |id=L4 |publicationdate=April 2016 }}</ref> The BOSS Great Wall is one of the largest superstructures in the observable universe.<ref name="jimmy2">{{cite journal |date=Mar 12, 2016 |title=Billion-light year galactic wall may be largest object in cosmos |url=https://www.newscientist.com/article/2080040 |journal=New Scientist }}</ref> The large complex has a mean redshift of z ~ 0.47 (z times Hubble length ≈ 6800 million light years).<ref name="2016A&A...588L...4L2" /> It consists of two elongated superclusters, two large superclusters, and several smaller superclusters as well.<ref name="2016A&A...588L...4L2" /> The elongated superclusters form galaxy walls, with the larger of the two having a diameter of 186/h Mpc (supercluster A in the figure); the second wall's being 173/h Mpc (supercluster B), where the other two main superclusters are moderately large, having diameters of 91/h Mps and 64/h Mpc (superclusters D and C, respectively).<ref name="2016A&A...588L...4L2" /> The superstructure is roughly 1 billion light years in diameter, and has a total mass approximately 10,000 times the Milky Way galaxy.<ref name="jimmy2" /> It contains at least 830 visible galaxies (represented in the figure within their respective superclusters), as well as many others that aren't visible (dark galaxies).<ref name="jimmy2" /> The researchers used Minkowski functionals to verify the structure's overall shape and size; the first three quantifying the thickness, width, and length followed by the fourth determining the structure's overall curvature, and compared the luminosities and stellar masses within the superstructure to known high stellar mass galaxies within the SDSS's 7th data release, DR7.<ref>{{Cite web |url=http://classic.sdss.org/dr7/ |title=SDSS Data Release 7 |website=classic.sdss.org |access-date=2017-11-26 }}</ref> This allowed the team to scale the data using known values, from local superclusters, to determine the overall morphology of the BOSS Great Wall.<ref name=":02017">{{Cite journal |last=Einasto |first=Maret |last2=Lietzen |first2=Heidi |last3=Gramann |first3=Mirt |last4=Saar |first4=Enn |last5=Tempel |first5=Elmo |last6=Liivamägi |first6=Lauri Juhan |last7=Montero-Dorta |first7=Antonio D. |last8=Streblyanska |first8=Alina |last9=Maraston |first9=Claudia |date=2017-07-01 |title=BOSS Great Wall: morphology, luminosity, and mass |url=https://doi.org/10.1051/0004-6361/201629105 |journal=Astronomy & Astrophysics |language=en |volume=603 |doi=10.1051/0004-6361/201629105 |issn=0004-6361 |arxiv=1703.08444 |bibcode=2017A&A...603A...5E }}</ref> The question is whether the supercluster complex is moving together or being slowly separated by the expanding universe.<ref name="jimmy2" /> When compared to several other chain structures, such as the Sloan Great Wall, the BOSS Great Wall's superclusters are far richer, containing more dense, high stellar mass galaxies.<ref name=":02017" /> {{clear}} ==Caelum Supercluster== The Caelum Supercluster, also known as SCl 59, may be a massive supercluster; spanning 910 million light-years, it is perhaps the largest galaxy supercluster in the universe, has a mass of 2×10¹⁷ solar masses, 1.7 times the mass of Laniakea Supercluster and of the Horologium Supercluster, centered on coordinates right ascension {{RA|04|43}} and declination {{DEC|&minus;33|30}}.<ref name="sim">{{cite web |title=Simbad search results for "Caelum Supercluster" |url=http://simbad.u-strasbg.fr/simbad/sim-id?Ident=NAME+CAELUM+SUPERCL |accessdate=July 18, 2017 }}</ref> ==Centaurus Supercluster== "The nearest large supercluster[, the] Centaurus supercluster is a long supercluster containing four rich galaxy clusters - A3526, A3565, A3574 and A3581 [and] hundreds of smaller groups of galaxies. A3526 is the dominant cluster among these and lies 140 million light years away. Seen from a large distance, the Virgo and Hydra superclusters might look like appendages to the Centaurus supercluster. The Centaurus supercluster lies near the ''Great Attractor'' - a large collection of matter affecting the motion of our galaxy and others. It is obscured by the plane of our own galaxy, but it is [probably] the large cluster A3627 [...]."<ref name=Powell/> ==Coma Supercluster== [[Image:Com01.png|right|thumb|300px|Map shows the Coma Supercluster. Credit: Richard Powell.{{tlx|free media}}]] "This is a small [...] supercluster about 300 million light years away. There are two very rich galaxy clusters here - A1367 and A1656, both containing thousands of galaxies. A1656 is [...] known as the Coma cluster, [...]. The Coma supercluster lies at the centre of The Great Wall, a vast filament of galaxies that stretches over hundreds of millions of light years, one end of which terminates on the Hercules supercluster."<ref name=Powell/> The Coma Supercluster (SCl 117), a nearby supercluster that comprises the Coma Cluster (Abell 1656) and the Leo Cluster (Abell 1367) is located 300 million light-years from Earth,<ref>{{cite web |title=Superclusters - A Review of the Universe |url=https://universe-review.ca/F03-supercluster.htm |accessdate=1 January 2016 }}</ref> it is in the center of the Great Wall and a part of Coma Filament.<ref>'Astronomy and Astrophysics' ({{ISSN|0004-6361}}), vol. 138, no. 1, Sept. 1984, pp. 85-92. Research supported by Cornell University "The Coma/A 1367 filament of galaxies" ''09/1984'' {{bibcode|1984A&A...138...85F}}</ref> The Coma Supercluster is the nearest massive cluster of galaxies to our own Virgo Supercluster.<ref>{{cite web |title=The Cosmic Distance Scale |url=http://imagine.gsfc.nasa.gov/features/cosmic/nearest_superclusters_info.html |accessdate=1 January 2016 }}</ref> {{clear}} ==Corona Borealis Supercluster== "The most distant of the famous superclusters. It has long been recognised that there are a large number of rich galaxy clusters in this small constellation. A2065 is probably the dominant cluster here, but there are another nine or ten large clusters here which are also rich. The supercluster is about 1 billion light years away."<ref name=Powell/> The Corona Borealis Supercluster is a supercluster located in the constellation Corona Borealis and the most prominent example of its kind in the Northern Celestial Hemisphere.<ref name="Marini">{{cite journal |author1=Marini, F. |author2=Bardelli, S. |author3=Zucca, E. |author4=De Grandi, S. |author5=Cappi, A. |author6=Ettori, S. |author7=Moscardini, L. |author8=Tormen, G. |author9=Diaferio, A. |date=2004 |title=BeppoSAX temperature maps of galaxy clusters in the Corona Borealis supercluster: A2061, A2067 and A2124 |journal=Monthly Notices of the Royal Astronomical Society |volume=353 |issue=4 |pages=1219–30 |doi=10.1111/j.1365-2966.2004.08148.x |arxiv = astro-ph/0406538 |bibcode = 2004MNRAS.353.1219M }}</ref> Dense and compact compared with other superclusters, its mass has been calculated to lie somewhere between 0.6 and 12 × 10¹⁶ solar masses (M_⊙), which contains the galaxy clusters Abell 2056, Abell 2061, Abell 2065 (the most massive galaxy cluster within the supercluster), Abell 2067, Abell 2079, Abell 2089, and Abell 2092, where Abell 2056, 2061, 2065, 2067 and A2089 are gravitationally bound and in the process of collapsing to form a massive cluster.<ref name=pearson2014/> This entity has an estimated mass of around 1 × 10¹⁶ M_⊙. If there is inter-cluster mass present, then Abell 2092 may also be involved.<ref name=pearson2014>{{cite journal | title=The Largest Gravitationally Bound Structures: The Corona Borealis Supercluster - Mass and Bound Extent |author1=Pearson, David W. |author2=Batiste, Merida |author3=Batuski, David J. | arxiv=1404.1308 | journal=Mon. Not. R. Astron. Soc. | volume= 441 |issue=2 | pages=1601–1614 |doi=10.1093/mnras/stu693 |bibcode = 2014MNRAS.441.1601P }}</ref> It has been estimated to be 100 megaparsecs (330 million light-years) wide and 40 megaparsecs (130 million light years) deep,<ref name="Marini"/> which has a redshift of 0.07,<ref name=postman88/> which is equivalent to a distance of around 265.5 megaparsecs (964 million light-years). ==Draco Supercluster== [[Image:2billion.gif|right|thumb|300px|Map shows the Universe observable within a radius of 2 billion light years, where the Draco supercluster is on the right of the supergalactic plane. Credit: Atlas of the Universe.{{tlx|free media}}]] '''Draco Supercluster''' ('''SCL 114''') is a galaxy supercluster in the constellation Draco.<ref>{{cite web |last1=Andernach |first1=H. |last2=Einasto |first2=J. |last3=Jaaniste |first3=J. |last4=Tago |first4=E. |last5=Einasto |first5=M. |title=The supercluster–void network - I. The supercluster catalogue and large-scale distribution |url=https://aas.aanda.org/articles/aas/ps/1997/07/ds1185.ps.gz |website=Astronomy and Astrophysics Supplement Series |accessdate=7 May 2019 |pages=119–133 |language=en |doi=10.1051/aas:1997340 |date=1 May 1997 }}</ref><ref>{{cite book |editor=MAZURE, A. |editor2=LE F+VRE, O. |editor3=LE BRUN, V. |title=Clustering at High Redshift: Proceedings of a Conference Held at Marseille, France, 29 June-2 July 1999 |date=2000 |publisher=Astronomical Society of the Pacific |isbn=9781583810279 |url=https://books.google.ru/books?id=OYzvAAAAMAAJ&hl=en&sa=X&ved=0ahUKEwiCnr6hsIniAhUn2aYKHWoICxsQ6AEINDAC |accessdate=7 May 2018 |language=en }}</ref><ref>{{cite book |last1=BASU |first1=BAIDYANATH |last2=CHATTOPADHYAY |first2=TANUKA |last3=BISWAS |first3=SUDHINDRA NATH |title=AN INTRODUCTION TO ASTROPHYSICS |date=2010 |publisher=PHI Learning Pvt. Ltd. |isbn=9788120340718 |page=500 |url=https://books.google.ru/books?id=WG-HkqCXhKgC&pg=PA500&lpg=PA500&dq=Draco+Supercluster&source=bl&ots=hMTL-Cg69l&sig=ACfU3U1XYVXxWciOVCtK1NQuRdzfGBbOSg&hl=en&sa=X&ved=2ahUKEwiavJ7VuYHiAhW-wcQBHdXdBUQQ6AEwE3oECAgQAQ#v=onepage&f=false |accessdate=4 May 2018 |language=en }}</ref> It is located at a distance of 300 Mpc ''h''^-1 on a side of a void of diameter of about 130 Mpc ''h''^-1. The near side of the void is bordered by the Ursa Major supercluster. The estimated size of the supercluster reaches 410 million light years and a mass of 10¹⁷ solar mass, making it one of the largest and most massive superclusters known in the observable universe.<ref>{{cite web |title=Notes on very rich superclusters |url=https://aas.aanda.org/articles/aas/full/1997/07/ds1185/node2.html |website=aas.aanda.org |accessdate=4 May 2018 }}</ref><ref>{{cite web |title=NAME DRACO SUPERCLUSTER |url=http://simbad.u-strasbg.fr/simbad/sim-id?Ident=NAME+DRACO+SUPERCLUSTER |website=sim-id |accessdate=4 May 2018 }}</ref> {{clear}} ==Giant Arc== [[Image:Giant Arc cropped.png|thumb|right|300px|The "Giant Arc,” violates the cosmological principle because of its outsized heterogeneity. Credit: Alexia Lopez.{{tlx|fairuse}}]] A ""giant arc" of galaxies stretching more than 3 billion light-years across."<ref name=Hart>{{ cite journal |author=Matthew Hart |title=A New Space Discovery May ‘Overturn Cosmology As We Know It’ |journal=Nerdist |date=11 June 2021 |volume= |issue= |pages= |url=https://www.yahoo.com/lifestyle/space-discovery-may-overturn-cosmology-202749490.html |arxiv= |bibcode= |doi= |pmid= |accessdate=11 June 2021 }}</ref> The guiding heuristic "expects homogeneity of matter on sections of [the] universe larger than 1.2 billion light-years across. But the Giant Arc is heterogenous on a scale ''three times that size''."<ref name=Hart/> "That means THREE of these arcs could fit between us and the edge of the observable universe-- 10 degrees on the sky, or 20 full moons!"<ref name=Hart/> The "Giant Arc’s “signature” on the electromagnetic spectrum is in magnesium atoms that have lost one electron; meaning the light we receive from the quasars behind the arc is absorbed and emitted by these magnesium atoms, and thusly has a particular wavelength when we receive it on Earth."<ref name=Hart/> {{clear}} ==Hercules–Corona Borealis Great Wall== Hercules–Corona Borealis Great Wall<ref name=HBHT2>{{cite journal |last1=Horváth |first1=István |last2=Bagoly |first2=Zsolt |last3=Hakkila |first3=Jon |last4=Tóth |first4=L. Viktor |title=New data support the existence of the Hercules-Corona Borealis Great Wall |journal=Astronomy & Astrophysics |volume = 584 |pages = A48 |arxiv=1510.01933 |year = 2015 |doi = 10.1051/0004-6361/201424829 |bibcode = 2015A&A...584A..48H }}</ref><ref name=HBHT>{{cite journal |last1=Horváth |first1=István |last2=Bagoly |first2=Zsolt |last3=Hakkila |first3=Jon |last4=Tóth |first4=L. Viktor |title=Anomalies in the GRB spatial distribution |journal=Proceedings of Science |arxiv=1507.05528 |bibcode = 2014styd.confE..78H }}</ref> or the Great GRB Wall<ref name=cookie>{{Cite journal |arxiv =1507.00675 |last1 = Balazs |first1 = L. G. |title = A giant ring-like structure at 0.78<z<0.86 displayed by GRBs |journal = Monthly Notices of the Royal Astronomical Society |volume = 452 |issue = 3 |pages = 2236 |last2 = Bagoly |first2 = Z. |last3 = Hakkila |first3 = J. E. |last4 = Horváth |first4 = I. |last5 = Kobori |first5 = J. |last6 = Racz |first6 = I. |last7 = Tóth |first7 = L. V. |year = 2015 |doi = 10.1093/mnras/stv1421 |bibcode = 2015MNRAS.452.2236B }}</ref> is a massive galactic superstructure in a region of the sky seen in the data set mapping of gamma-ray bursts (GRBs) that has been found to have an unusually higher concentration of similarly distanced GRBs than the expected average distribution.<ref name=2014paper/><ref name=original/> It was discovered in early November 2013 by a team of American and Hungarian astronomers led by István Horváth, Jon Hakkila and Zsolt Bagoly while analyzing data from the Swift Gamma-Ray Burst Mission, together with other data from ground-based telescopes.<ref name=2014paper>{{cite journal | arxiv=1401.0533 | bibcode=2014A&A...561L..12H | title=Possible structure in the GRB sky distribution at redshift two | accessdate= | last1=Horváth | first1=István | last2=Hakkila | first2=Jon | last3=Bagoly | first3=Zsolt | journal=Astronomy & Astrophysics | date=2014 | volume=561 | pages=id.L12 | doi=10.1051/0004-6361/201323020 }}</ref><ref name=original>{{cite journal |author = Horváth I. |author2 = Hakkila J. |author3 = Bagoly Z. |last-author-amp = yes |title = The largest structure of the Universe, defined by Gamma-Ray Bursts |journal =7th Huntsville Gamma-Ray Burst Symposium, GRB 2013: paper 33 in eConf Proceedings C1304143 |volume = 1311 |pages = 1104 |date = 2013 |arxiv=1311.1104 |bibcode = 2013arXiv1311.1104H }}</ref> It is the largest known formation in the universe, exceeding the size of the prior Huge-LQG by about two times.<ref>{{cite web |url= https://www.youtube.com/watch?v=36ngn5rS3Og |title= The Impossibly Huge Quasar Group |author= SciShow Space |date= 21 July 2016 }}</ref> ==Hercules Supercluster== [[Image:Nearsc.gif|right|thumb|300px|Hercules Superclusters are shown at the top right. Credit: Richard Powell.{{tlx|free media}}]] "Two famous and prominant superclusters lie here. The smaller and nearer one is probably the most famous being dominated by two rich clusters - A2197 and A2199 that lie very close to each other. This supercluster lies 400 million light years away. The second supercluster is only slightly further - 500 million light years, but it is a lot bigger and contains lots of rich galaxy clusters scattered around hundreds of smaller galaxy groups."<ref name=Powell/> The Hercules Superclusters (SCl 160) refers to a set of two nearby superclusters of galaxies.<ref>{{cite web |url=http://www.atlasoftheuniverse.com/superc/her.html |title=The Hercules Superclusters |publisher=Atlasoftheuniverse.com |date= |accessdate=2011-11-19 }}</ref> {{clear}} ==Horologium Supercluster== [[Image:Hor.gif|right|thumb|300px|Map shows the Horologium Supercluster. Credit: [[w:user:El C|El C]].{{tlx|free media}}]] "This is a huge supercluster 900 million light years away. It is not as dense as the Shapley supercluster but it contains a large number of rich galaxy clusters scattered across half a billion light years making it one of the largest known superclusters. This is another region of the sky in which Harlow Shapley noticed an excess of galaxies. [...] In astronomy journals the Horologium supercluster is sometimes called the ''Horologium-Reticulum'' supercluster."<ref name=Powell/> The Horologium Supercluster is a massive supercluster spanning around 550 million light-years,<ref>{{Cite web |url=http://www.atlasoftheuniverse.com/superc/hor.html |title=The Horologium Supercluster |website=www.atlasoftheuniverse.com |access-date=2018-11-04 }}</ref> centered on coordinates right ascension {{RA|03|19}} and declination {{DEC|&minus;50|02}}, spans an angular area of 12° × 12°,<ref name=apj130_3>{{cite journal |author1=Fleenor, Matthew C. |author2=Rose, James A. |author3=Christiansen, Wayne A. |author4=Hunstead, Richard W. |author5=Johnston-Hollitt, Melanie |author6=Drinkwater, Michael J. |author7=Saunders, William | title=Large-Scale Velocity Structures in the Horologium-Reticulum Supercluster | journal=The Astronomical Journal | volume=130 | issue=3 | pages=957&ndash;967 |date=September 2005 | doi=10.1086/431972 | bibcode=2005AJ....130..957F |arxiv = astro-ph/0505361 }}</ref> and has about 5,000 galaxy groups (30,000 giant galaxies and 300,000 dwarf galaxies),<ref>{{Cite web |url=http://www.atlasoftheuniverse.com/superc/hor.html |title=The Horologium Supercluster |website=www.atlasoftheuniverse.com |access-date=2018-11-04 }}</ref> and includes the galaxy cluster Abell 3266. {{clear}} ==Hydra-Centaurus Supercluster== [[Image:Hyamap.gif|right|thumb|250px|Three-dimensional map shows the Hydra Supercluster. Credit: Richard Powell.{{tlx|free media}}]] Within the proximity of this supercluster lies the Great Attractor, dominated by the Norma Cluster (Abell 3627), where this massive cluster of galaxies exerts a large gravitational force, causing all matter within 50 Mpc to experience a bulk flow of 600&nbsp;km/s toward the Norma Cluster<ref name="plionis91">{{cite journal |author1=Plionis, Manolis |author2=Valdarnini, Riccardo | title = Evidence for large-scale structure on scales about 300/h MPC | journal = Monthly Notices of the Royal Astronomical Society | date = March 1, 1991 | volume = 249 | issue = March 1, 1991 | pages = 46–61 | bibcode = 1991MNRAS.249...46P | doi = 10.1093/mnras/249.1.46 }}</ref> {{clear}} ==Hydra Supercluster== This nearby supercluster "is very similar in size and shape to the Virgo supercluster. The Hydra supercluster is also dominated by one rich cluster of galaxies - A1060, [...]."<ref name=Powell/> ==Hyperion proto-supercluster== [[Image:The Hyperion Proto-Supercluster.jpg|right|thumb|300px|Visualization projects the Hyperion proto-supercluster. Credit: ESO/L. Calçada & Olga Cucciati ''et al''.{{tlx|free media}}]] The Hyperion proto-supercluster is the largest and earliest known proto-supercluster, 5,000 times the mass of the Milky Way and seen at 20% of the current age of the universe, discovered in 2018 by analysing the redshifts of 10,000 objects observed with the Very Large Telescope in Chile.<ref>{{citation |work=Newsweek |via=MSN |title=Astronomers Find Largest Galaxy Proto-supercluster |author=Katherine Hignett |date=October 17, 2018 |url=https://www.msn.com/en-us/news/technology/astronomers-find-largest-galaxy-proto-supercluster/ar-BBOvra5 }}</ref><ref>{{citation |title=Largest Galaxy Proto-Supercluster Found - Astronomers using ESO's Very Large Telescope uncover a cosmic titan lurking in the early Universe |url=https://www.eso.org/public/news/eso1833/ |publisher=European Southern Observatory (ESO) |id=Science Release eso1833 |date=17 October 2018 |accessdate=18 October 2018 }}</ref><ref>{{citation |work=Newsweek |via=MSN |title=Astronomers Find Largest Galaxy Proto-supercluster |author=Katherine Hignett |date=October 17, 2018 |url=https://www.msn.com/en-us/news/technology/astronomers-find-largest-galaxy-proto-supercluster/ar-BBOvra5 }}</ref><ref>{{citation |title=Largest Galaxy Proto-Supercluster Found - Astronomers using ESO's Very Large Telescope uncover a cosmic titan lurking in the early Universe |url=https://www.eso.org/public/news/eso1833/ |publisher=European Southern Observatory (ESO) |id=Science Release eso1833 |date=17 October 2018 |accessdate=18 October 2018 }}</ref> {{clear}} ==Laniakea Supercluster== [[Image:07-Laniakea (LofE07240).png|right|thumb|300px|Map shows the Laniakea Supercluster and its component galaxy clusters. Credit: [[c:user:AZcolvin429|Andrew Z. Colvin]].{{tlx|free media}}]] [[Image:Laniakea.gif|left|thumb|250px|Map shows the superclusters within the nearby universe, with Laniakea in yellow. Credit: Richard Powell.{{tlx|free media}}]] The Laniakea Supercluster (Laniakea, Hawaiian for ''open skies'' or ''immense heaven''; also called the Local Supercluster or 'Local SCl or sometimes Lenakaeia)<ref>{{Cite book |title=Science Encyclopedia |last=Taylor |first=Charles |publisher=Kingfisher |year=2014 |isbn= |location= |pages= |quote= |via= }}</ref> is the galaxy supercluster that is home to the Milky Way and approximately 100,000 other nearby galaxies.<ref name="The road map to the Universe">{{cite news |title=The road map to the Universe |url=http://www.dailymail.co.uk/sciencetech/article-2995066/The-road-map-Universe-Pathways-Milky-Way-100-000-galaxies-charted-10-year-quest-scientists.html?ito=social-facebook |accessdate=14 March 2015 |work=DailyMail UK |date=14 March 2015 }}</ref>, defined in September 2014, when a group of astronomers including R. Brent Tully of the University of Hawaii at Manoa, Hélène Courtois of the University of Lyon, Yehuda Hoffman of the Hebrew University of Jerusalem, and Daniel Pomarède of CEA Université Paris-Saclay published a new way of defining superclusters according to the relative velocities of galaxies, where the new definition of the local supercluster subsumes the prior defined local supercluster, the Virgo Supercluster, as an appendage.<ref name=NRAO-2014-09-03>{{cite news |work= National Radio Astronomy Observatory |publisher= ScienceDaily |date= 3 September 2014 |url= https://www.sciencedaily.com/releases/2014/09/140903133319.htm |title= Newly identified galactic supercluster is home to the Milky Way }}</ref><ref name= Reuters-2014-09-03>{{cite web |work= Reuters |publisher= Reuters |date= 2014-09-03 |url= https://www.reuters.com/article/us-space-galaxies-idUSKBN0GY2C820140903 |author= Irene Klotz |title= New map shows Milky Way lives in Laniakea galaxy complex }}</ref><ref name=Nature-2014-09-03>{{cite news |publisher= Nature |url= http://www.nature.com/news/earth-s-new-address-solar-system-milky-way-laniakea-1.15819 |title= Earth's new address: 'Solar System, Milky Way, Laniakea' |author= Elizabeth Gibney |date= 3 September 2014 |doi= 10.1038/nature.2014.15819 }}</ref><ref name=S&T-2014-09-03>{{cite news |url= http://www.skyandtelescope.com/astronomy-news/laniakea-home-supercluster-09032014/ |title= Laniakea: Our Home Supercluster |author= Camille M. Carlisle |date= 3 September 2014 |publisher= Sky and Telescope }}</ref> <ref name="NYT-20140903">{{cite news |last=Quenqua |first=Douglas |title=Astronomers Give Name to Network of Galaxies |url=https://www.nytimes.com/2014/09/09/science/space/astronomers-give-name-to-network-of-galaxies.html |date=3 September 2014 |work=New York Times |accessdate=4 September 2014 }}</ref> Subsequent studies suggest that Laniakea is not gravitationally bound and will disperse rather than continue to maintain itself as an overdensity relative to surrounding areas.<ref name=chon>{{cite journal |bibcode=2015A&A...575L..14C |arxiv=1502.04584 |title=On the definition of superclusters |journal=Astronomy & Astrophysics |volume=575 |pages=L14 |author1=Chon |first1=Gayoung |last2=Böhringer |first2=Hans |last3=Zaroubi |first3=Saleem |year=2015 |doi=10.1051/0004-6361/201425591 }}</ref> {{clear}} ==Leo Supercluster== "Several large galaxy clusters on the border of Leo and Ursa Major at a distance of 450 million light years mark the presence of another large supercluster. The dominant clusters here are A1185 and A1228."<ref name=Powell/> The Leo Supercluster, in the Northern Celestial Hemisphere stretches across the constellations Ursa Major and Leo that covers an area approximately 130 megaparsecs long by 60 megaparsecs wide, as the redshifts of member galaxy cluster]s range from 0.032 to 0.043, with the brightest cluster in the system is Abell 1185.<ref name="Kopylova">{{cite journal |last=Kopylova |first=F. G. |author2=Kopylov, A. I. |date=2011 |title=Analysis of the Properties of Galaxy Clusters in the Leo Supercluster Region |journal=Astronomy Letters |volume=37 |issue=4 |pages=219–32 |issn=1562-6873 | doi=10.1134/S1063773711030029 |bibcode = 2011AstL...37..219K }}</ref> ==Local Sheet== The Local Sheet is a nearby extragalactic region of space where the Milky Way, the members of the Local Group and other galaxies share a similar peculiar velocity.<ref name="apj676_1_184">{{cite journal | last1=Tully | first=R. Brent | last2=Shaya | first2=Edward J. | last3=Karachentsev | first3=Igor D. | last4=Courtois | first4=Hélène M. | last5=Kocevski | first5=Dale D. | last6=Rizzi | first6=Luca | last7=Peel | first7=Alan | title=Our Peculiar Motion Away from the Local Void | journal=The Astrophysical Journal | volume=676 | issue=1 | pages=184–205 |date=March 2008 | doi=10.1086/527428 | arxiv=0705.4139 | bibcode=2008ApJ...676..184T }}</ref> This region lies within a radius of about 7 Mpc (23 Mly),<ref name="tully2008" /> {{convert|1.5|Mly|Mpc|abbr=on|order=flip}} thick,<ref name="ScienceDaily-2014-03-11" /> and galaxies beyond that distance show markedly different velocities.<ref name="tully2008">{{citation | last1=Tully | first1=R. Brent | contribution=The Local Void is Really Empty | title=Dark Galaxies and Lost Baryons, Proceedings of the International Astronomical Union, IAU Symposium | volume=244 | pages=146–151 |date=May 2008 | doi=10.1017/S1743921307013932 | bibcode=2008IAUS..244..146T | arxiv=0708.0864 }}</ref> The Local Group has only a relatively small peculiar velocity of {{Val|66|ul=km.s^-1}} with respect to the Local Sheet. Typical velocity dispersion of galaxies is only {{Val|40|u=km.s^-1}} in the radial direction.<ref name="apj676_1_184" /> Nearly all nearby bright galaxies belong to the Local Sheet.<ref name="ScienceDaily-2014-03-11">{{cite news |url=https://www.sciencedaily.com/releases/2014/03/140311100606.htm |title=Milky Way amidst a 'Council of Giants' |date=11 March 2014 |publisher=Science Daily }}</ref> The Local Sheet is part of the Local Volume and is in the Virgo Supercluster (Local Supercluster).<ref name="10.1093/mnras/stu199"/> The Local Sheet forms a wall of galaxies delineating one boundary of the Local Void.<ref name="2013MNRAS.436.2096S">{{cite journal |title= The Formation of the Local Group Planes of Galaxies |authors= Shaya, Ed J.; Tully, R. Brent; |journal= Monthly Notices of the Royal Astronomical Society |volume= 436 |issue= 3 |pages= 2096–2119 |date= December 2013 |publisher= Oxford University Press |agency= Royal Astronomical Society |arxiv= 1307.4297 |doi= 10.1093/mnras/stt1714 |bibcode= 2013MNRAS.436.2096S }}</ref> A significant component of the mean velocity of the galaxies in the Local Sheet appears as the result of the gravitational attraction of the Virgo Cluster of galaxies, resulting in a peculiar motion ~{{Val|185|u=km.s^-1}} toward the cluster.<ref name="apj676_1_184" /> A second component is directed away from the center of the Local Void; an expanding region of space spanning an estimated {{convert|45|Mpc|Mly|abbr=on}} that is only sparsely populated with galaxies.<ref name="tully2008" /> This component has a velocity of {{Val|259|u=km.s^-1}}.<ref name="apj676_1_184" /> The Local Sheet is inclined 8° from the Local Supercluster (Virgo Supercluster).<ref name="10.1093/mnras/stu199"> {{cite journal |title=A Council of Giants |first=Marshall L. |last=McCall |date=29 April 2013 |publication-date=10 March 2014 |doi=10.1093/mnras/stu199 |url=http://mnras.oxfordjournals.org/content/440/1/405 |journal=Monthly Notices of the Royal Astronomical Society |volume=440 |issue=1 |pages=405–426 |arxiv=1403.3667 |bibcode=2014MNRAS.440..405M }}</ref> The so-called '''Council of Giants''' is a ring of twelve large galaxies surrounding the Local Group in the Local Sheet, with a radius of {{convert|3.75|Mpc|Mly|abbr=on}}.<ref name="10.1093/mnras/stu199"/> Ten of these are spiral galaxies, while the remaining two are elliptical galaxies: ellipticals (Maffei 1 and Centaurus A) lie on opposite sides of the Local Group, and their formation may have prompted the development of the Local Group, where the Local Sheet's own development outlines a concentration of dark matter in a filament.<ref name="ScienceDaily-2014-03-11" /> {| class="wikitable" |+ Galaxies in the "Council of Giants"<ref name="10.1093/mnras/stu199"/> |- ! Catalog ID !! Name !! Constellation !! Distance (Mly) !! Mass * |- | NGC 253 || Sculptor Galaxy || Sculptor || 11 || 10.805 |- | PGC 9892 || Maffei 1 || Cassiopeia || 11 || 10.928 |- | PGC 10217 || Maffei 2 || Cassiopeia || 11 || 10.493 |- | IC 342 || &nbsp; || Camelopardalis || 11 || 10.302 |- | NGC 3031 || M 81 || Ursa Major || 12 || 10.905 |- | NGC 3034 || M 82 || Ursa Major || 11 || 10.573 |- | NGC 4736 || M 94 || Canes Venatici || 15 || 10.458 |- | NGC 4826 || M 64 || Coma Berenices || 16 || 10.496 |- | NGC 5236 || M 83 || Hydra || 16 || 10.642 |- | NGC 5128 || Centaurus A || Centaurus || 11 || 11.169 |- | NGC 4945 || &nbsp; || Centaurus || 12 || 10.528 |- | ESO 97-G13 || Circinus Galaxy || Circinus || 14 || 10.559 |} <nowiki>*</nowiki> The mass is given as the logarithm of the mass in solar masses. ==Lynx Supercluster== The Lynx Supercluster was discovered in 1999<ref>{{cite journal |author=Rosati, P. |display-authors=etal |date=1999 |title=An X-Ray-Selected Galaxy Cluster at z = 1.26 |journal=The Astronomical Journal |volume=118 |issue=1 |pages=76–85 |arxiv=astro-ph/9903381 |bibcode=1999AJ....118...76R |doi=10.1086/300934 }}</ref> as ClG J0848+4453, a name now used to describe the western cluster, with ClG J0849+4452 being the eastern one,<ref>{{cite web |title=Lynx Supercluster |url=http://simbad.u-strasbg.fr/simbad/sim-id?Ident=NAME%20LYNX%20SUPERCLUSTER |work=SIMBAD }}</ref> containing at least two clusters, designated RXJ 0848.9+4452 (at redshift z=1.26) and RXJ 0848.6+4453 (redshift z=1.27), the most distant known supercluster<ref>{{cite conference |author=Nakata, F. |display-authors=etal |date=2004 |title=Discovery of a large-scale clumpy structure of the Lynx supercluster at z∼1.27 |journal=Proceedings of the International Astronomical Union |volume=2004 |pages=29–33 |publisher=Cambridge University Press |bibcode=2004ogci.conf...29N |doi=10.1017/S1743921304000080 |isbn=0-521-84908-X }}</ref> with a comoving distance of 12.9 billion light years, with seven smaller groups of galaxies are associated with the supercluster.<ref>{{cite journal |author=Ohta, K. |display-authors=etal |date=2003 |title=Optical Identification of the ASCA Lynx Deep Survey: An Association of Quasi-Stellar Objects and a Supercluster at z = 1.3? |journal=The Astrophysical Journal |volume=598 |pages=210–215 |arxiv=astro-ph/0308066 |bibcode=2003ApJ...598..210O |doi=10.1086/378690 }}</ref> Through electromagnetic radiation and how it reacts with matter, we have been able to find three groupings of stars and two x-ray clusters within the Lynx.<ref>{{Cite journal |last=Kim |first=Jae-Woo |last2=Im |first2=Myungshin |last3=Lee |first3=Seong-Kook |last4=Edge |first4=Alastair C. |last5=Hyun |first5=Minhee |last6=Kim |first6=Dohyeong |last7=Choi |first7=Changsu |last8=Jueun Hong |last9=Jeon |first9=Yiseul |date=2016 |title=Discovery of a Supercluster at z 0.91 and Testing the ΛCDM Cosmological Model |url=http://stacks.iop.org/2041-8205/821/i=1/a=L10 |journal=The Astrophysical Journal Letters |language=en |volume=821 |issue=1 |pages=L10 |doi=10.3847/2041-8205/821/1/L10 |issn=2041-8205 |arxiv=1604.03254 |bibcode=2016ApJ...821L..10K }}</ref> ==Microscopium Supercluster== The Microscopium Supercluster is a supercluster located in the constellation Microscopium composed of Abell clusters 3695 and 3696 that likely are, while the relations of Abell clusters 3693 and 3705 in the same field are unclear.<ref name=pearson>{{cite journal |last=Pearson |first=David W. |author2=Batuski, David J. |date=2013 |title=Locating bound structure in an accelerating universe |journal=Monthly Notices of the Royal Astronomical Society |volume=000 |pages=1–12 |doi=10.1093/mnras/stt1614 |arxiv = 1308.5154 |bibcode = 2013MNRAS.436..796P }}</ref> ==MS 0302+17== MS 0302 + 17 is a galaxy supercluster located in the constellation Aries at a distance of 4.485 billion light years (lookback time), equivalent to a comoving distance of 5.338 billion light years, dimensions around 6 million parsecs.<ref name="A1">{{cite web |last1=Dantel-Fort |first1=M. |last2=Cuillandre |first2=J.-C. |last3=Fort |first3=B. |last4=Mellier |first4=Y. |last5=Gavazzi |first5=R. |title=Mass and Light in the Supercluster of galaxies : MS0302+17 |url=https://arxiv.org/abs/astro-ph/0401403 |accessdate=19 April 2019 |language=en |doi=10.1051/0004-6361:20047109 |date=20 January 2004 }}</ref><ref>{{cite book |last1=Schneider |first1=Peter |last2=Kochanek |first2=Christopher |last3=Wambsganss |first3=Joachim |title=Gravitational Lensing: Strong, Weak and Micro: Saas-Fee Advanced Course 33 |date=2006 |publisher=Springer Science & Business Media |isbn=9783540303107 |page=335 |url=https://books.google.ru/books?id=AF8-ErlCb94C&pg=PA335&hl=en&sa=X&ved=0ahUKEwj55K6b79vhAhVRzqYKHeshCOcQ6AEILDAB#v=onepage&f=false |accessdate=19 April 2019 |language=en }}</ref> The MS prefix derives from Medium Sensitivity because X-ray observations are part of the Einstein Medium Sensitivity Survey.<ref name="A2">{{cite web |last1=Fabricant |first1=Daniel G. |last2=Bautz |first2=Marshall W. |last3=McClintock |first3=Jeffrey E. |title=Galaxy evolution in distant, x-ray selected clusters of galaxies, 2: CL 0303+1658 and CL 0303+1717 |url=http://adsabs.harvard.edu/cgi-bin/bib_query?1994AJ....107....8F |website=The Astronomical Journal |accessdate=19 April 2019 |pages=8–23 |doi=10.1086/116831 |date=1 January 1994 }}</ref><ref name="A1"/> An interesting fact of the survey is a couple of giant arches located near the luminous central galaxies of MS0302 + 1659, images of remote galaxies enhanced by the gravitational lensing phenomenon created by the supercluster.<ref name="A2" /> ==Ophiuchus Supercluster== [[Image:Nearsc.gif|right|thumb|300px|The local Universe includes the Ophiuchus Supercluster. Credit: Ken-ichi Wakamatsu and Matthew Malkan.{{tlx|free media}}]] Ophiuchus Supercluster is a nearby galaxy supercluster in the constellation Ophiuchus.<ref name="RG">{{cite web |last1=Wakamatsu |first1=Ken-ichi |title=The Ophiuchus Supercluster Observed with FLAIR |url=https://www.researchgate.net/publication/234384028_The_Ophiuchus_Supercluster_Observed_with_FLAIR |publisher=ResearchGate |accessdate=18 April 2019 |date=January 2000 }}</ref><ref>{{cite web |last1=Okamura |first1=Sadanori |last2=Karoji |first2=Hiroshi |last3=Jugaku |first3=Jun |last4=Parker |first4=Quentin A. |last5=Menzies |first5=John W. |last6=Sekiguchi |first6=Kazuhiro |last7=Malkan |first7=Matthew |last8=Wakamatsu |first8=Ken-ichi |last9=Hasegawa |first9=Takashi |title=Large-scale structure of galaxies in the Ophiuchus region |url=https://academic.oup.com/mnras/article/316/2/326/1020202 |website=Monthly Notices of the Royal Astronomical Society |accessdate=18 April 2019 |pages=326–344 |language=en |doi=10.1046/j.1365-8711.2000.03531.x |date=1 August 2000 }}</ref> The supercluster forms the far wall of the Ophiuchus Void; it may also be connected in a filament, with the Pavo-Indus-Telescopium Supercluster and the Hercules Supercluster.<ref>{{cite book |title=Mysteries of the Milky Way |date=2008 |publisher=The Rosen Publishing Group |isbn=9781404214040 |page=129 |url=https://books.google.ru/books?id=x0iKqa3CdY0C&pg=PA129&hl=en&sa=X&ved=0ahUKEwi_iJ6M0NnhAhVR0aYKHbv9CvcQ6AEIKDAA#v=onepage&f=false |accessdate=18 April 2019 |language=en }}</ref> {{clear}} ==Pavo-Indus Supercluster== "This is a fairly weak supercluster that marks one end of a long wall of galaxies that encompasses the Centaurus supercluster and probably the Virgo supercluster [...]. The Pavo-Indus supercluster contains three rich galaxy clusters - A3656, A3698 and A3742."<ref name=Powell/> Other groups and clusters in the supercluster include the NGC 6769 Group and Abell S805 (IC 4765 Group, Pavo II, DRCG 1842-63).<ref>{{Cite journal |last=Winkler |first=H. |date=1983 |title=The Spatial Distribution of Galaxies in the Southern Sky |url=http://adsabs.harvard.edu/abs/1983MNSSA..42...74W |journal=Monthly Notes of the Astronomical Society of South Africa |volume=42 |pages=74 |issn=0024-8266 }}</ref><ref>{{Cite journal |last=Fairall |first=A. P. |date=1988-01-01 |title=A redshift map of the Triangulum Australe-Ara region - Further indication that Centaurus and Pavo are one and the same supercluster |url=http://adsabs.harvard.edu/abs/1988MNRAS.230...69F |journal=Monthly Notices of the Royal Astronomical Society |volume=230 |pages=69–77 |doi=10.1093/mnras/230.1.69 |issn=0035-8711 }}</ref> ==Perseus-Pisces Supercluster== [[Image:Supercúmulo Perseo Piscis.gif|right|thumb|300px|Map shows the Perseus-Pisces Supercluster. Credit: Richard Powell.{{tlx|free media}}]] "This supercluster is a large sheet of galaxy groups scattered around three rich clusters - A262, A347 and A426. A426 [contains] thousands of galaxies."<ref name=Powell/> The Perseus-Pisces Supercluster (SCl 40) borders a prominent void, the Taurus Void, and is part of the Perseus–Pegasus Filament which stretches for roughly a billion light years.<ref>{{cite web |title=Superclusters - Large Scale Structures |url=http://science.jrank.org/pages/6614/Superclusters-Large-scale-structures.html |publisher=science.jrank.org |accessdate=25 May 2017 }}</ref><ref>{{cite web |title=Astronomy & Cosmology - Large Scale Structure of the Universe |url=http://www.whillyard.com/science-pages/filaments-walls.html |publisher=whillyard.com |accessdate=25 May 2017 }}</ref><ref>'Astrophysical Journal', Part 1 ({{ISSN|0004-637X}}), vol. 299, Dec. 1, 1985, p. 5-14. "A possible 300 megaparsec filament of clusters of galaxies in Perseus-Pegasus" ''12/1985'' {{bibcode|1985ApJ...299....5B}}</ref> {{clear}} ==Pisces-Cetus Supercluster== "This is a region containing several major superclusters over 800 million light years [...]. There are several very large superclusters here forming long wall structures hundreds of millions of light years in length."<ref name=Powell/> The Pisces–Cetus Supercluster Complex is a galaxy filament that includes the Virgo Supercluster which in turn contains the Local Group, the galaxy cluster that includes the Milky Way.<ref name="tully86">{{Cite journal | doi = 10.1086/164049 | volume = 303 | pages = 25–38 | last = Tully | first = R. B. | title = Alignment of clusters and galaxies on scales up to 0.1 C | journal = The Astrophysical Journal | accessdate = 2011-05-03 | date = 1986-04-01 | bibcode = 1986ApJ...303...25T }}</ref> ==Saraswati Supercluster== The Saraswati Supercluster is a massive galaxy supercluster about 1.2 gigaparsecs (4,000 million light years) away within the Stripe 82 region of Sloan Digital Sky Survey (SDSS), in the direction of the constellation Pisces.<ref name=Bagchi2017>{{cite journal |url=http://iopscience.iop.org/article/10.3847/1538-4357/aa7949 |doi=10.3847/1538-4357/aa7949 |arxiv=1707.03082 |volume=844 |pages=25 |title=Saraswati: An Extremely Massive ~ 200 Megaparsec Scale Supercluster |year=2017 |first1=Joydeep |last1=Bagchi |first2=Shishir |last2=Sankhyayan |first3=Prakash |last3=Sarkar |first4=Somak |last4=Raychaudhury |first5=Joe |last5=Jacob |first6=Pratik |last6=Dabhade |accessdate = 2017-07-30 |journal=The Astrophysical Journal |bibcode = 2017ApJ...844...25B }}</ref><ref>{{cite web |url=https://elpais.com/elpais/2017/07/13/ciencia/1499967116_043113.html |title=Descubierta Sarasvati, una de las mayores estructuras del universo |language=es |date=14 July 2017 |accessdate=14 July 2017 |publisher=El País }}</ref> It is one of the largest structures found in the universe, with a major axis in diameter of about 200 Mpc (652 million light years), consisting of at least 43 galaxy clusters, and has the mass of 2 × 10¹⁶ Solar mass, forming a galaxy filament.<ref name=IUCAA>{{cite web | title = “Saraswati”- one of the most massive large-scale structures in the Universe discovered | url = http://www.iucaa.in/Saraswati-General.html | accessdate = 14 July 2017 | archiveurl = https://web.archive.org/web/20170729142754/http://www.iucaa.in/Saraswati-General.html | archivedate = 29 July 2017 | website = IUCAA }}</ref> ==Sculptor Supercluster== [[Image:Nearsc.gif|thumb|right|250px|The local universe includes the Sculptor Wall. Credit: Richard Powell.{{tlx|free media}}]] [[Image:2MASS LSS chart-NEW Nasa.jpg|thumb|left|250px|2MASS distance map of the local universe includes the primary Sculptor Supercluster. Credit: IPAC/Caltech, by Thomas Jarrett.{{tlx|free media}}]] "Two superclusters in the Sculptor and Phoenix regions of the sky mark the position of a very long wall of thousands of galaxy groups stretching over nearly a billion light years of space."<ref name=Powell/> The Sculptor Wall is a superstructure of galaxies ("wall of galaxies") relatively near to the Milky Way Galaxy (redshift of approximately z=0.03), also known as the Sculptor superclusters.<ref name=ApJ-2010-05>Taotao Fang, David A. Buote, Philip J. Humphrey, Claude R. Canizares, Luca Zappacosta, Roberto Maiolino, Gianpiero Tagliaferri and Fabio Gastaldello; ''CONFIRMATION OF X-RAY ABSORPTION BY WARM-HOT INTERGALACTIC MEDIUM IN THE SCULPTOR WALL''; 2010 ApJ 714 1715, {{doi|10.1088/0004-637X/714/2/1715}}, {{bibcode|2010ApJ...714.1715F}}, {{arxiv|1001.3692}}, [http://iopscience.iop.org/0004-637X/714/2/1715?fromSearchPage=true&v_showaffiliations=no]</ref><ref name=RAS-1990-11-15>Fairall, A. P., Palumbo, G. G. C., Vettolani, G., Kauffman, G., Jones, A., & Baiesi-Pillastrini, G., ''Largescale Structure in the Universe - Plots from the Updated Catalogue of Radial Velocities of Galaxies and the Southern Redshift Catalogue'' Journal: R.A.S. MONTHLY NOTICES V.247, NO.2/NOV15, P. 23P, 1990. Bibliographic Code: {{bibcode|1990MNRAS.247P..21F}} [http://adsabs.harvard.edu/full/1990MNRAS.247P..21F] (slices 8 and 10 under SGH)</ref> The superstructure is also called "Southern Great Wall", "Great Southern Wall", "Southern Wall", in reference to the Northern Great Wall, or just "Great Wall" &mdash; the CfA2 Great Wall, is 8000&nbsp;km/s long, 5000&nbsp;km/s wide, 1000&nbsp;km/s deep, in ''redshift space'' dimensions.<ref name=LzLSS>Unveiling large-scale structures behind the Milky Way. Astronomical Society of the Pacific Conference Series, Vol. 67; Proceedings of a workshop at the Observatoire de Paris-Meudon; 18–21 January 1994; San Francisco: Astronomical Society of the Pacific (ASP); c1994; edited by Chantal Balkowski and R. C. Kraan-Korteweg, p.21 ; [http://adsabs.harvard.edu/full/1994ASPC...67...21F Visualization of Nearby Large-Scale Structures] ; Fairall, A. P., Paverd, W. R., & Ashley, R. P. ; {{bibcode|1994ASPC...67...21F}}</ref><ref name=LSSg>'Astrophysics and Space Science', Volume 230, Issue 1-2, pp. 225-235 '''Large-Scale Structures in the Distribution of Galaxies''' ''08/1995'' {{bibcode|1995Ap&SS.230..225F}}</ref> {{clear}} ==Shapley Supercluster== [[Image:Shapley.gif|right|thumb|300px|Map shows the Shapley Supercluster. Credit: Richard Powell.{{tlx|free media}}]] "The Shapley supercluster is a massive supercluster [...], it is certainly one of the densest. There are two main concentrations - one at 500 million light years and a larger one at 650 million light years. There are at least twenty rich galaxy clusters among the thousands of galaxy groups in this supercluster, including three of the richest galaxy clusters known: A3558, A3559 and A3560."<ref name=Powell/> The nearest large underdense area has been labelled the dipole repeller.<ref name=Hoffman2017>{{cite journal |journal=Nature Astronomy |url=http://www.nature.com/articles/s41550-016-0036 |title=The dipole repeller |first1=Yehuda|last1=Hoffman |first2=Daniel|last2=Pomarède |first3=R. Brent|last3=Tully |first4=Hélène M.|last4=Courtois |date=30 January 2017 |volume=1 |issue=2 |doi=10.1038/s41550-016-0036 |arxiv = 1702.02483 |bibcode = 2017NatAs...1E..36H }}</ref> {{clear}} ==Vela Supercluster== The Vela Supercluster<ref name = badass>{{cite journal |title= Discovery of a supercluster in the ZOA in Vela |author= Renée C. Kraan-Korteweg |author2= Michelle E. Cluver |author3= Maciej Bilicki |author4= Thomas H. Jarrett |author5= Matthew Colless |author6= Hans Böhringer |author7= Gayoung Chon |publicationdate= November 2016 |doi= 10.1093/mnrasl/slw229 |bibcode= 2017MNRAS.466L..29K |arxiv= 1611.04615 |journal= Monthly Notices of the Royal Astronomical Society: Letters }}</ref> (Vela SCl, VSCL) is a massive galactic supercluster about 265.5 megaparsecs (870 million light-years)<ref name = badass /> away within the vicinity of the Zone of Avoidance, centered on the constellation Velal one of the largest structures found in the universe; covering about 25 × 20 degrees of the sky, consisting of two walls: a broad main wall and a secondary merging wall, where the combined dimensions of the walls are 115&nbsp;km/s Mpc on the major dimensions and 90&nbsp;km/s Mpc on the minor ones, which corresponds to about 385 million and 300 million light years, respectively, about "1 000 times the mass of the Milky Way galaxy", which corresponds to a mass of 1 × 10¹⁵ solar masses, about 20 initial galaxy clusters have been identified spectroscopically.<ref name = badass /> ==Virgo Supercluster== '''Def.''' a "supercluster that includes the Milky Way galaxy"<ref name=VirgoSuperclusterWikt>{{ cite web |author=[[wikt:User:DAVilla|DAVilla]] |title=Virgo Supercluster |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=1 January 2011 |url=https://en.wiktionary.org/wiki/Virgo_Supercluster |accessdate=31 May 2019 }}</ref> is called the '''Virgo Supercluster'''. ==Rings== Circular "patterns of galaxies [are] scattered across the sky".<ref name=Conover>{{ cite book |author=Emily Conover |title=Hidden ancient neutrinos may shape the patterns of galaxies |publisher=Science News |location= |date=March 4, 2019 |url=https://www.sciencenews.org/article/hidden-ancient-neutrinos-may-shape-patterns-galaxies |accessdate=7 March 2019 }}</ref> ==Local Superclusters== '''Def.''' a "supercluster which includes the Milky Way galaxy"<ref name=LocalSuperclusterWikt>{{ cite web |author=[[wikt:User:Mahagaja|Mahagaja]] |title=Local Supercluster |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=31 December 2010 |url=https://en.wiktionary.org/wiki/Local_Supercluster |accessdate=31 May 2019 }}</ref> is called a '''Local Supercluster'''. ==See also== {{div col|colwidth=20em}} * [[Radiation astronomy/Active galactic nuclei|Active galactic nuclei]] * [[Radiation astronomy/Clouds|Cloud astronomy]] * [[Stars/Galaxies|Galaxies]] * [[Stars/Galaxies/Laboratory|Galaxies laboratory]] * [[Stars/Galaxies/Quiz|Galaxies quiz]] * [[Radiation astronomy/Galaxies|Galaxy astronomy]] * [[Radiation astronomy/Galaxy clusters|Galaxy cluster astronomy]] * [[Radiation astronomy/High-velocity galaxies|High-velocity galaxy astronomy]] * [[Radiation astronomy/Nebulas|Nebula astronomy]] {{Div col end}} ==References== {{reflist|2}} ==External links== <!-- footer templates --> {{Radiation astronomy resources}}{{Sisterlinks|Galaxy clusters}} <!-- footer categories --> [[Category:Radiation astronomy/Lectures]] hbqg28jaxt8plolpdnwt4akggxvf0rq 0 242097 2412489 2403568 2022-08-07T06:29:47Z 154.160.1.240 How was the US so lucky to have gotten good old {{w|George Washington}} and not someone like {{w|Joseph Stalin|Joe Stalin}} (poisoned to death) or {{w|Pol Pot}} (poisoned himself to death)? wikitext text/x-wiki {{Research project}} :''This essay is on Wikiversity to encourage a wide discussion of the issues it raises moderated by the Wikimedia rules that invite contributors to [[w:Wikipedia:Be bold|“be bold but not reckless,”]] contributing revisions written from a [[Wikiversity:Disclosures|neutral point of view]], [[Wikiversity:Cite sources|citing credible sources]] -- and raising other questions and concerns on the associated [[Wikiversity:FAQ|''''“Discuss”'''' page]].'' [[File:Great American Paradox.webm|thumb|Video based on this article]] Many people believe that the [[w:United States|United States]] got freedom and democracy, liberty and justice for all from the violence of the {{w|American Revolution}}. There are several problems with this belief. Perhaps most important is that it suggests that the {{w|American Revolution}} is different from nearly all the other violent revolutions of human history, which rarely contributed to democracy.<ref>{{w|David Graeber}} documented how people with power have established the rules to exalt themselves and impoverish and enslave everyone else, at least during the most recent 5,000 years. This pattern has occasionally been interrupted by revolts by peasants and slaves, after which the cycle begins anew. The growth of democracy, free press, and nonviolence have introduced nonviolent means that peasants and slaves are starting to use to effectively limit the predations by the powerful. See Greaber's ''{{w|Debt:The first 5,000 years}}''.</ref> Why does the [[w:American Revolution|American Revolution]] seems so different from other violent revolutions like the [[w:French Revolution|French]], [[w:Latin American wars of independence|Latin American]], [[w:Russian Revolution|Russian]], [[w:Chinese Revolution|Chinese]], [[w:Cuban revolution|Cuban]], [[w:Algerian War|Algerian]], [[w:Vietnam War|Vietnamese]], [[w:Laotian Civil War|Laotian]], and [[w:Cambodian Civil War|Cambodian]] revolutions, each of which arguably replaced one brutal repressive system with another? How was the US so lucky to have gotten good old {{w|George Washington}} and not someone like {{w|Joseph Stalin|Joe Stalin}} (poisoned to death) or {{w|Pol Pot}} (poisoned himself to death)? [[File:Simón Bolívar, 1825.jpg|thumb|Simón Bolívar, 1825]] == Why did the US grow and prosper when other newly independent countries fractured, shrank, and stagnated economically? == The land claimed by the 13 British colonies in America that declared independence from Britain on July 4, 1776, was roughly a third of that of the contemporary Spanish colony of [[w:New Spain|New Spain]], most of which became Mexico in 1821. Since then, the US grew substantially, while Mexico shrank. Why? Simón Bolívar, the acknowledged “Liberator” of much of Latin America complained shortly before he died in 1830 that, :"America is ungovernable ... . He who serves a revolution plows in the sea. ... This country will fall unfailingly into the hands of ... tyrants".<ref>{{Citation | editor-last = Gutiérrez Escudero | editor-first = Antonio | date = 2005 | title = Simón Bolívar: aproximación al pensamiento del Libertador (approximations to the thoughts of the liberator) | chapter = 6. Carta al general Juan José Flores, jefe del estado de Ecuador (Barranquilla, 9 de noviembre de 1830) [Letter to General Juan José Flores, head of state of Ecuador, Barranquilla, November 9, 1830] | publisher = Escuela de Estudios Hispano-Americanos (CSIC), Sevilla | language = Spanish | page = 12 | url = http://digital.csic.es/bitstream/10261/28362/1/BolivarPen.pdf | accessdate = 2017-11-06}} In this quote, “This country” referred specifically to Columbia. However, his comment seems relevant to all of Latin America.</ref> How did the US avoid the level of internal conflict that contributed to the dismemberment and disturbingly slow economic growth that plagued Mexico and other countries after independence? [[File:Non-Native American Nations Control over N America 1784.png|thumb|Non-Native American Nations Control over N America 1784: The US had a third the area of New Spain, most of which became Mexico in 1821. New Spain at that time also included substantial territory outside North American including Central America north of Panama, Cuba, Hispañola, Puerto Rico, the Philippines, most of modern-day Venezuela, and other smaller territories.]] == Three contributors == By some accounts, these differences can be explained by three things:<ref>Some might also add the basic expansionist character of the new nation and its relatively welcoming attitude toward immigrants. However, that expansionist character could be a result of the three points mentioned here rather than a direct contributor itself to the growth of the US. The famous term [[w:Manifest destiny|"manifest destiny"]] became fashionable only after it had already been achieved. It seems to have been coined in 1845 but "did not reflect the national spirit. The thesis that it embodied nationalism, found in much historical writing, is backed by little real supporting evidence", according to {{Citation | last = Merk | first = Frederick | last2 = Merk | first2 = Lois Bannister | year = 1963 | title = Manifest Destiny and Mission in American History: A Reinterpretation | publisher = Harvard U. Pr. | page = 215 | isbn = 0674548051 | url = https://books.google.com/books?id=GhYJTaZiuxwC | accessdate = 2017-11-19}}, cited from the Wikipedia article on [[w:Manifest destiny|"manifest destiny"]]</ref> :1. '''Advanced democracy before the revolution''': The British colonies that rebelled in 1776 already had possibly the most advanced democratic culture on the planet at that time:<ref>Acemoglu and Robinson say that the English colonies in North America all initially failed until they switched from autocratic, extractive governance to a more democratic, inclusive political economy. Further South, the Spaniards encountered the Aztec and the Inca civilizations, which dominated neighboring tribes, demanding among other things human sacrifice to their gods. When a tiny number of Spanish arrived with guns and horses, it proved that the Aztec and Incas were not gods, and the neighboring tribes supported the Spanish, hoping for better life. That option was not available to the English colonies established further north. {{cite Q|Q7997840}}<!-- Why Nations Fail: The Origins of Power, Prosperity, and Poverty -->.</ref> Almost 60 percent of adult white males could vote in 1776, and the Revolution did not change that.<ref>{{Citation | last = Keyssar | first = Alexander | year = 2000 | title = The Right to Vote: The Contested History of Democracy in the United States | publisher = Basic Books | pages = 7, 24 | isbn = 0465005020 }}; see also {{cite Q|Q58635938}}. Claims that the rebellious colonists learned democratic governance from the [[w:Iroquois|Iroquois confederation]] are controversial, as noted in the Wikipedia article on the Iroquois.</ref> By comparison, the British Prime Minister in 1765 said that less than 5% of the population of Great Britain itself was directly represented in Parliament.<ref>Peter D. G. Thomas (2000) “The Grenville Program, 1763-1765, ch. 15 in Jack P. Greene and J. R. Pole, A Companion to the American Revolution (Malden, MA: Blackwell). See also Eric Foner (1998) The Story of American Freedom (NY: Norton, esp. pp. 5-7). Cited from {{cite Q|Q58635938}}.</ref> ::1.1. This democratic culture made it easier for the leaders in the early United States to settle their disagreements in ways that maintained their cohesion. ::1.2. Research by Chenoweth and Stephan identified 55 major successful violent revolutions in the twentieth century. These revolutions on average had no substantive impact on democracy. Similarly, the American Revolution had no impact on democracy.<ref>Even the [[w:United States Bill of Rights|US Bill of Rights]] was not uniquely American: The common citizens of the brand new United States of American ''demanded'' that they retain the rights they had had under legal documents like the [[w:Bill of Rights 1689|English Bill of Rights of 1689]], which itself updated and secured rights English citizens had officially had since the [[w:Magna Carta|Magna Carta of 1215]]. And the rights promised by the US Bill of Rights were too often only unenforceable words on paper until the [[w:American Civil Liberties Union|American Civil Liberties Union (ACLU)]] initiated a program of litigation, activism and education following its founding in 1920.</ref> In this regard, the American Revolution was ''not'' different from other violent revolutions.<ref>Chenoweth and Stephan (2011)</ref> :2. '''Citizen-directed subsidies for news''': Citizen-directed subsidies for newspapers provided by the [[w:Postal Service Act|US Postal Service Act of 1792]] helped limit political corruption and encourage literacy, both of which contributed to the cohesion and economic growth of the brand new United States of America. :3. '''Washington did not win the Revolution''': George Washington knew that he did not win the American Revolution.<ref>Washington insisted on civilian control of the military. He actively worked to suppress mutinies, noting that attempts to use military force to obtain needed money and supplies contradicted their reason for fighting. See, e.g., Glenn A. Phelps, “The Republican General”, ch. 7 in {{cite Q|Q59362787}}</ref> His role was keeping an army in the field, irritating the British enough to keep them doing stupid things. Washington was [[w:Landing at Kip's Bay|almost captured on Manhattan island]].<ref>{{cite Q|Q59297825}}, p. 170</ref> He was perpetually short of supplies. His own state of Virginia often could not send their allotment of troops, because they were needed for slave patrols.<ref>{{cite Q|Q59319726}}, pp. 344-345.</ref> Many in Washington's army often did not have shoes. This made it hard for them to move, especially in the winter, because the British could easily follow the blood in the snow.<ref>{{cite Q|Q102951790}}<!-- A People's History of the American Revolution -->, p. 89.</ref> It's difficult to know in war how much support each side has among the population. However, by 1778 the British had lost several battles in the north and decided they had more support in the south.<ref>"The Germain letters"; Clements Library, University of Michigan', cited in [[w:Southern theater of the American Revolutionary War#The Loyalist question]].</ref> In late 1778 they [[w:Capture of Savannah|captured Savannah, Georgia]].<ref>{{cite Q|Q59384214}}. Cited from [[w:Capture of Savannah]].</ref> And in 1780 they defeated continental armies at [[w:Siege of Charleston|Charlston]] and [[w:Battle of Camden|Camden, South Carolina]].<ref>{{cite Q|Q59394153}}, cited from [[w:Siege of Charleston]] and [[w:Battle of Camden]].</ref> Washington sent General {{w|Nathanial Greene}} into South Carolina to collect the remnants of the defeated continental army and organize the partisans. Greene adopted a guerrilla war strategy, nipping at the heels of the British army, then running away. This pulled the British beyond their lines of supply. To continue pursuing Greene, they took what they needed at gun point from the locals, manufacturing recruits for Greene and Washington in the process. After winning several battles in South Carolina, the British General Cornwallis decided he could no longer stay there and retreated to North Carolina, where the pattern was repeated. Cornwallis continued winning battles and manufacturing enemies faster than he could neutralize them. In 1781, he left North Carolina for Yorktown, Virginia.<ref>{{cite Q|Q59402701}} and other works cited in [[w:Southern theater of the American Revolutionary War]] and {{cite Q|Q58635938}}.</ref> The French Navy then bottled up the Chesapeake and prevented Cornwallis from being resupplied or evacuated while the French Army ''paid'' Washington's army to come with them to [[w:Siege of Yorktown|Yorktown]] and defeat the British.<ref>{{cite Q|Q23763149}}, cited from [[w:Siege of Yorktown]].</ref> But there were also ''nonviolent'' actions at that time<ref>Conser et al. (1986).</ref> that threatened the financial and social status of the colonial elites.<ref>{{cite Q|Q59418433}}<!-- Forced Founders -->.</ref> The destruction of property in the Boston Tea Party increased support for hard liners in London,<ref>On 2 Feb. 1774, Ben Franklin, then a lobbyist in London, wrote, “The violent destruction of the tea seems to have united all parties here against us.” Conser et al. (1986, p. 222). See also {{cite Q|Q106843214}}<!-- David L. Ammerman (2000) “The Tea Crisis and Its Consequences, through 1775”, ch. 24 in Greene and Pole, eds. (2000)-->.</ref> who then passed the so-called "Intolerable Acts". These included placing Massachusetts under martial law. Nonviolent protests all across Massachusetts closed the King's courts, which prevented creditors from confiscating property of debtors.<ref>{{cite Q|Q59420225}}<!-- Raphael, The First American Revolution -->.</ref> Demands for greater power sharing continued into the writing of state constitutions that followed the Declaration of Independence, at least in Pennsylvania and Massachusetts.<ref>{{cite Q|Q59319726}}</ref> Democracy threatened the aristocracy in both the brand new United States and in Britain. [[w:John Adams|John Adams]], a leader of the American Revolution and the second President of the US after Washington, wrote later, "What do we mean by the Revolution? The war? That was no part of the revolution; it was only an effect and consequence of it. The revolution was in the minds of the people, and this was effected from 1760–1775, in the course of fifteen years, before a drop of blood was shed at Lexington."<ref>This was in a letter to Thomas Jefferson (24 August 1815), The Works of John Adams; he later expressed similar sentiments in a letter to Hezekiah Niles (13 February 1818). Cited from [[Wikiquote:John Adams]].</ref> Beyond that, there were 26 British colonies in America at that time, and only half of them rebelled.<ref>{{cite Q|Q58635938}}</ref> If the Quakers and other pacifist groups in the colonies at that time had managed to limit the violence initiated by Washington and others, the British aristocracy might have had bigger problems in the colonies that did NOT rebel and among the more than 95 percent of the population of England that was not represented in Parliament. It is impossible to know what would have happened if the American Revolution had stayed nonviolent. * However, we know that in Chenoweth and Stephan's study of all the major violent and nonviolent governmental change efforts of the twentieth century, 53% of the nonviolent campaigns were successful, while less than half that, 25%, of the violent revolutions succeeded.<ref>Chenoweth and Stephan (2011)</ref> * ''More importantly, the nonviolent campaigns on average helped improve democracy, unlike the violent campaigns.'' == US vs. New Spain / Mexico == Let us now compare the US experience with [[w:New Spain|New Spain]] and its successors, primarily [[w:Mexico|Mexico]]. They had neither (1) a comparable tradition of local self governance nor (2) a comparably subsidized and diverse adversarial press, discussed further below, nor (3) a chief executive with the understanding that George Washington seemed to have had of the limits of his own abilities. These three points provide a plausible explanation for why the US grew by a factor of more than four while Mexico shrank, losing territory to the US in the north and to new countries between Guatemala and Venezuela to the south.<ref>In 1800 New Spain lost the Louisiana territory to France. A small portion of that is now part of Canada. In 1931 Mexico lost [[w:Clipperton Island|Clipperton Island]] to France.</ref> This is also consistent with the database of all the major violent and nonviolent governmental change efforts of the twentieth century created by Chenoweth and Stephan, previously mentioned.<ref>Chenoweth and Stephan (2011)</ref> :''In general, gratuitous violence -- collateral damage -- strengthens the will of the opposition to resist and drives people off the sidelines to support the aggrieved opposition.'' More recently, in the US war in Vietnam and now in the War on Terror, the US has arguably followed the British strategy for victory in the American Revolution. :''It is hard to win people's hearts and minds by killing them.'' This did not work for the British in the American Revolution nor for the Americans in Vietnam. And it has not so far worked in the War on Terror. We next look more closely at the [[w:Postal Service Act|US Postal Service Act of 1792]]. [[File:Evolution of the areas of the United States and Mexico.svg|thumb|Areas of the United States and Mexico 1783-2010.]] == US Postal Service Act of 1792 == [[File:Non-Native American Nations Control over N America 1999.png|thumb|Non-Native American Nations Control over N America 1999: The US now has 4.6 times the area of Mexico.]] The [[w:Postal Service Act|US Postal Service Act of 1792]] is not well known but may be the single greatest achievement of the men who organized and led the American Revolution: Under this act, newspapers were delivered up to 100 miles for a penny, when first class postage was between six and twenty-five cents depending on distance. * The revolutionaries who passed that act were upset that King George's postal service censored their mail. * ''They believed that this new experiment in republican government would likely NOT succeed without an informed electorate.''<ref>{{cite Q|Q59426473}}, cited from [[w:Postal Service Act]].</ref> These were citizen-directed subsidies for media. As such they make it difficult for government bureaucrats and others with power to censor the information available to the public. They amounted to roughly 0.2 percent of US Gross Domestic Product (GDP), according to media scholars McChesney and Nichols.<ref>McChesney and Nichols (2016, p. 167).</ref> With average annual income (GDP per capita) in 2017 of roughly $60,000, a subsidy of 0.2 percent would be $120 per year per person, which is roughly what McChesney and Nichols recommended. This subsidy for newspapers seems to have impacted the evolution of the US political economy during its first 70-100 years in two important ways: * It limited political corruption. * It encouraged literacy. Both of these factors tend to increase economic growth.<ref>The impact of both corruption and education are discussed in the Wikiversity article on [[Winning the War on Terror]], accessed 2018-12-04.</ref> Comparing the post-revolutionary experience of the US with that of the other violent and nonviolent governmental change efforts mentioned above suggests the following: * ''Democracy, liberty and justice for all would likely have advanced quicker if the American revolutionaries had limited themselves to nonviolent actions.''<ref>[[w:Ray Raphael|Ray Raphael]] claims that the "First American Revolution" occurred in Massachusetts in 1774, as local farmers demanded the reinstatement of the [[w:Massachusetts Charter|Massachusetts Charter of 1691]] with substantial success, after the British government had suspended it in response to the [[w:Boston Tea Party|Boston Tea Party]], December 16, 1773. This "First American Revolution" was essentially nonviolent, involving in some locations half of the adult male population. See the section on the [[w:Ray Raphael#American Revolution|American Revolution]] in the Wikipedia article on Ray Raphael as well as {{cite Q|Q59420225}}. This is consistent with the conclusions of Chenoweth and Stephan from their inventory of all the major violent and nonviolent governmental change efforts of the twentieth century. Only a quarter, 25 percent, of the violent revolutions they identified were successful vs. 53 precent of the nonviolent campaigns. More importantly, 5 and 10 years after the end of the conflict, the impact on democracy from violent revolutions were on average negligible. Meanwhile, nonviolent campaigns, win or lose, tended to improve the level of democratization. See the Wikiversity articles in [[Effective defense]] and [[Effective defense and ISIL]], and the literature cited therein.</ref> * The citizen-directed subsidies for journalism provided by the US Postal Service Act of 1792 and the relative democratic character of the new US likely made substantially greater contributions to extending democracy and justice for all than the violence of the American Revolution. == Human psychology and the power of media == Why have so many other revolutionaries been more likely to follow Washington than Gandhi? A partial answer to this question appears in research in recent decades into how people think and make decisions, led by {{w|Daniel Kahneman}}. Kahneman won the 2002 {{w|Nobel Memorial Prize in Economic Sciences}} for inventing many ways of documenting how people think. He's a psychologist, not an economist. He won the prize in economics for establishing that standard economics models of the “rational person” do not adequately describe how people actually think. In particular, people make most decisions based on what comes most readily to mind -- the “fast thinking” in Kahneman's (2011) ''Thinking, Fast and Slow.''<ref>{{cite Q|Q983718}}</ref> Humans are capable of conscious deliberation, searching for alternative evidence, etc. -- Kahneman's “slow thinking”. However, we rarely do enough of that when we should. This has profound implications for understanding virtually every aspect of human behavior. * For example, in violent conflict, {{w|collateral damage}} that “they” commit proves to us that “they” are subhuman or at best criminally misled and must be resisted by any means necessary. * Meanwhile, {{w|collateral damage}} that we commit is unfortunate but necessary -- from our perspective. But, of course, it proves to “them” that we are subhuman or at best criminally misled, and must by resisted by any means necessary.<ref>For an expanded discussion of the role of collateral damage in the evolution of conflict, see {{cite Q|Q58635572}}. For an expanded discussion of these principles in the context of the American Revolution, see {{cite Q|Q58635938}}.</ref> == Implications == The implications of this analysis of “The Great American Paradox” are substantial. Most obviously, it affects the inferences that potential revolutionaries everywhere might draw from US history. For example, how might the world be different today if more of the violent revolutionaries of the twentieth century tried to follow [[w:Mahatma Gandhi|Gandhi]] rather than Washington? This article also has more subtle implications for {{w|gun control}} and for [[Effective defense|foreign and defense policies]] of countries like the US. There are also implications for how [[Confirmation bias and conflict|media organizations should be funded and governed]]. Further discussions of these questions are beyond the scope of this article. == References == * {{cite Q|Q88725216}}<!-- Why Civil Resistance Works: The Strategic Logic of Nonviolent Conflict -->. For their data see, {{Citation | last = Chenoweth | first = Erica | title = NAVCO Data Project | publisher = Sié Chéou-Kang Center for International Security & Diplomacy, Josef Korbel School of International Studies, University of Denver | url = http://www.du.edu/korbel/sie/research/chenow_navco_data.html | accessdate = 2017-03-17}}. For further discussion of this work, see [[Winning the War on Terror]]. * {{cite Q|Q7315585}}<!-- Conser, McCarthy, Toscano, and Sharp, eds. (1986) Resistance, Politics, and the American Struggle for Independence, 1765-1775 -->. * {{Citation | last = McChesney | first = Robert W. | last2 = Nichols | first2 = John | author-link = w:Robert W. McChesney | author2-link = w:John Nichols (journalist) | year = 2016 | title = People get ready: The fight against a jobless economy and a citizenless democracy| publisher = Nation Books | isbn = 9781568585215}} == Notes == {{reflist}} [[Category:Original research]] [[Category:Research]] [[Category:Political science]] [[Category:Media]] [[Category:Freedom and abundance]] cmlcie5qlbwhk07d2hnrocfl461ufmv 0 249961 2412487 2408733 2022-08-07T05:03:12Z Marshallsumter 311529 wikitext text/x-wiki [[Image:Whirlpool M51-pr.jpg|thumb|right|200px|This is a composite image of the Whirlpool Galaxy (also known as M51). Credit: Joint Astronomy Centre, University of British Columbia and NASA/HST (STScI).{{tlx|fairuse}}]] '''[[Radiation_astronomy/Galaxy_clusters|Galaxy cluster astronomy]]''' is a lecture for the [[Portal:Radiation astronomy|radiation astronomy department]] course on the [[principles of radiation astronomy]]. You are free to take this quiz based on [[Radiation_astronomy/Galaxy_clusters|Galaxy cluster astronomy]] at any time. To improve your score, read and study the lecture, the links contained within, listed under [[Radiation_astronomy/Galaxy_clusters/Quiz#See also|'''See also''']], [[Radiation_astronomy/Galaxy_clusters/Quiz#External links|'''External links''']], and in the {{tlx|principles of radiation astronomy}} template. This should give you adequate background to get 100 %. As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score. '''Suggestion:''' Have the lecture available in a separate window. To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association. Enjoy learning by doing! {{clear}} ==Quiz== <quiz> {Yes or No, Particle radiation consists of a stream of charged or neutral particles, from the size of subatomic elementary particles upwards of rocky, liquid, plasma, and gaseous objects to even larger more loosely bound entities such as galaxies, galaxy clusters and strings with measurable motion. |type="()"} + Yes - No {Which of the following are associated with globular clusters as a standard candle? |type="[]"} - characteristic mottling + luminosity functions + turnover point - incipient resolution + dispersion of the distribution - easy to recognize + log-normal function {Yes or No, An intergalactic medium is a medium in between interplanetary and interstellar media. |type="()"} - Yes + No {Complete the text: |type="{}"} Match up the item letter with each of the possibilities below: Intracluster medium - A Mayall's object - B M82 PAHs - C Milky Way bubbles - D Local Hot Bubble - E Stephan's Quintet - F UGC 8335 - G Arp 272 - H [[Image:Hubble Interacting Galaxy UGC 8335 (2008-04-24).jpg|thumb|left|100px]] { G (i) } [[Image:Outflow from M82 galaxy.jpg|thumb|left|100px]] { C (i) }. [[Image:Stephan's Quintet with annotation.jpg|thumb|left|100px]] { F (i) }. [[Image:Local_bubble.jpg|thumb|left|100px]] { E (i) }. [[Image:800 nasa structure renderin2.jpg|thumb|left|100px]] { D (i) }. [[Image:A2199 Xray Optical2.jpg|thumb|left|100px]] { A (i) }. [[Image:Hubble Interacting Galaxy NGC 6050 (2008-04-24).jpg|thumb|left|100px]] { H (i) }. [[Image:Hubble Interacting Galaxy Arp 148 (2008-04-24).jpg|thumb|left|100px]] { B (i) }. {{clear}} {True or False, An intergalactic medium is a rarefied plasma rather than a gaseous medium. |type="()"} + TRUE - FALSE {Which of the following is not a characteristic of X-radiation in the IGM? |type="()"} - X-rays come from the IGM - an X-ray background + shock heating - secondary ionizations and excitations - far more likely to be absorbed by He I rather than H I {Do we know enough about the intergalactic medium to trust measurements of background sources seen through foreground |type="{}"} { structure (i) }? {Complete the text: |type="{}"} Whether the thermal IGM is { collisional (i) } or collisionless at scales smaller than the scale { Coulomb (i) } scale depends on the effect of reduced { mean free path (i) } that is mediated by the plasma { instabilities (i) }. {True or False, Star clusters have been discovered to occur outside a galaxy. |type="()"} + TRUE - FALSE {Which of the following are phenomena associated with strong forces in the IGM? |type="[]"} + stochastic acceleration + hottest clusters + scaling of the acceleration efficiency with IGM temperature - collisionless IGM - placid magnetic compressions + the smaller the mean free path - cold regions - least effective for inducing the instability {True or False, O VI is a lithium-like ion. |type="()"} + TRUE - FALSE {Which of the following are phenomena associated with electromagnetic cascades? |type="[]"} + spectral and timing properties of astronomical sources + very high-energy γ-rays + the way from the source to the Earth - soft X-rays - redshifts + ambient radiation fields inside the γ-ray source - source stability - protons {True or False, The hierarchical clustering model has the gravitational effects of dark matter drive the evolution of structure from the near-uniform recombination epoch until the present day. |type="()"} + TRUE - FALSE {Complete the text: |type="{}"} Match up the item letter with each of the cosmogonic possibilities below: interior models of the giant planets - A high interest for cosmogony, geophysics and nuclear physics - B hierarchical accumulation - C clouds and globular clusters - D cosmic helium abundance - E deuterium fusion - F a large deficiency of light elements - G after galactic sized systems had collapsed - H the motions of hydrogen { D (i) } formation of luminous quasars { H (i) }. stars with an initial mass less than the solar mass { G (i) }. rotating liquid drops { B|F (i) }. primordial is less than 26 per cent { E (i) }. a solar mixture of elements dominated by hydrogen and helium gas { A (i) }. around 13 Jupiter masses { F (i) }. smaller rocky objects { C (i) }. {True or False, As a galaxy is made up of millions or billions of stars, a solitary star does not exist in a galaxy. |type="()"} - TRUE + FALSE {Spiral galaxies have which of the following in common? |type="[]"} + spiral arms - a spheroidal shape - may appear lenticular - is irregular + arms of younger stars + may contain star clusters + dust lanes {Phenomena associated with the Milky Way are? |type="[]"} + spiral arms - a spheroidal shape + a standard to differentiate dwarf galaxies + often referred to as the Galaxy + arms of younger stars + contains star clusters + dust lanes + extended red emission (ERE) + a faint galaxy heavy with dark matter may orbit it - larger than the Andromeda galaxy {Complete the text: |type="{}"} Match up the standard candle with a representative image: Tully-Fisher relation - A surface brightness fluctuations - B absolute magnitude - C globular clusters - D active galactic nuclei - E Type Ia supernova - F classical Cepheid variable - G novae - H planetary nebula - I [[Image:65Cyb-LB3-apmag.jpg|thumb|left|100px]] { C (i) } [[Image:Maximum magnitude-rate of decline for novae.gif|thumb|left|100px]] { H (i) }. [[Image:B-, R-, I-, and H-band Tully-Fisher relations.gif|thumb|left|100px]] { A (i) }. [[Image:Blackbody spectral density.gif|thumb|left|100px]] { G (i) }. [[Image:SN2005ke labels.jpg|thumb|left|100px]] { F (i) }. [[Image:A further away schematic galaxy.gif|thumb|left|100px]] { B (i) }. [[Image:1-agnsasanewst.jpg|thumb|left|100px]] { E (i) }. [[Image:Planetary nebulae H-R.gif|thumb|left|100px]] { I (i) } [[Image:Luminosity function for globular clusters.gif|thumb|left|100px]] { D (i) }. {{clear}} {Complete the text: |type="{}"} Match up the item letter with each of the possibilities below: Einstein ring - A stellar nebula - B Andromeda galaxy - C Triplet galaxies interacting - D Hubble galaxies - E Dark matter halo simulation - F Fairall 9 (Seyfert galaxy in X-rays) - G Tycho Brahe observatory, remotely controlled telescope, captured galaxy - H [[Image:Andromeda's Colorful Rings.jpg|thumb|left|100px]] { C (i) }. [[Image:Galax.png|thumb|left|100px]] { H (i) }. [[Image:A Horseshoe Einstein Ring from Hubble.JPG|thumb|left|100px]] { A (i) }. [[Image:SWIFT J0123.9-5846 Hard X-ray.jpg|thumb|left|100px]] { G (i) }. [[Image:Dark matter halo.png|thumb|left|100px]] { F (i) }. [[Image:AmCyc Nebula - Stellar Nebula.jpg|thumb|left|100px]] { B (i) }. [[Image:Dorian Gray.jpg|thumb|left|100px]] { E (i) }. [[Image:Cosmic Interactions.jpg|thumb|left|100px]] { D (i) }. {{clear}} {Complete the text: |type="{}"} Match up the item letter with each of the possibilities below: Sa - A Sb - B Sc - C SBa - D SBb - E SBc - F Irr - G S0 - H [[Image:M101 hires STScI-PRC2006-10a.jpg|thumb|left|100px]] { C (i) }. [[Image:Ngc5866 hst big.png|thumb|left|100px]] { H (i) }. [[Image:M104 - Sombrero.jpg|thumb|left|100px]] { A (i) }. [[Image:Starburst in NGC 4449 (captured by the Hubble Space Telescope).jpg|thumb|left|100px]] { G (i) }. [[Image:Caldwell 44.jpg|thumb|left|100px]] { F (i) }. [[Image:NGC2841.jpg|thumb|left|100px]] { B (i) }. [[Image:The VLT goes lion hunting.jpg|thumb|left|100px]] { E (i) }. [[Image:NGC 2859.jpg|thumb|left|100px]] { D (i) }. {{clear}} {True or False, 3C 295 is a galaxy cluster filled with a vast cloud of 50 MK gas and plasma. |type="()"} + TRUE - FALSE {Complete the text: |type="{}"} Match up the item letter with each of the possibilities below: E0 - A E1 - B E2 - C E3 - D E4 - E E5 - F E6 - G E7 - H [[Image:Maf1atlas.jpg|thumb|left|100px]] { D (i) }. [[Image:M32 Lanoue.png|thumb|left|100px]] { C (i) }. [[Image:Messier 105 2MASS.jpg|thumb|left|100px]] { H (i) }. [[Image:Ngc185 rgb combined.jpg|thumb|left|100px]] { A (i) }. [[Image:2MASS NGC 4125 JHK.jpg|thumb|left|100px]] { G (i) }. [[Image:NGC 1427 Hubble WikiSky.jpg|thumb|left|100px]] { F (i) }. [[Image:M105 (37482401952).jpg|thumb|left|100px]] { B (i) }. [[Image:Coma Cluster of Galaxies (visible, wide field).jpg|thumb|left|100px]] { E (i) }. {{clear}} {Which of the following are associated with elliptical galaxies as a standard candle? |type="[]"} - observations made through a narrow band 5007 filter + luminous galaxies - star forming regions + the Faber-Jackson relation + relationship between luminosity and central velocity dispersion + quantitative techniques based on Fourier or cross correlation methods + strongly clustered - single dominant young stellar population {Which of the following are characteristics of cosmogonic X-rays? |type="[]"} - gravitationally unbound + an X-ray emitting gas that is roughly a homogeneous intercluster medium + ultra-hot hidden gas - gas can be hidden in intergalactic space + X-ray background - stellar coronal X-rays </quiz> ==Hypotheses== {{main|Hypotheses}} # Meteors range in size from galaxy clusters to dust grains and molecular clusters. ==See also== {{div col|colwidth=20em}} * [[Green astronomy/Quiz]] * [[Planetary science/Quiz]] * [[Radiation chemistry/Quiz|Radiation astrochemistry/Quiz]] * [[Radiation geography/Quiz|Radiation astrogeography/Quiz]] * [[Radiation history/Quiz|Radiation astrohistory/Quiz]] * [[Radiation astronomy/Quiz]] * [[Theoretical radiation astronomy/Quiz]] {{Div col end}} ==External links== * [http://www.iau.org/ International Astronomical Union] * [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED] * [http://nssdc.gsfc.nasa.gov/ NASA's National Space Science Data Center] * [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System] * [http://cas.sdss.org/astrodr6/en/tools/quicklook/quickobj.asp SDSS Quick Look tool: SkyServer] * [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database] * [http://simbad.harvard.edu/simbad/ SIMBAD Web interface, Harvard alternate] * [http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp Spacecraft Query at NASA] * [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl Universal coordinate converter] <!-- footer templates --> {{tlx|Radiation astronomy resources}}{{Principles of radiation astronomy}}{{Sisterlinks|Galaxy cluster astronomy}} <!-- categories --> [[Category:Astrophysics quizzes]] [[Category:Meteorology quizzes]] [[Category:Meteors quizzes]] [[Category:Radiation astronomy quizzes]] 9wjgy630ckuujncjo4zhwxve311xbdb 0 252446 2412421 2349025 2022-08-06T22:29:21Z Tamika Afeaki 2947781 title wikitext text/x-wiki {{title|Cultural influences on shame, guilt, and pride:<br>How does culture influence shame, guilt, and pride? - Tamika Afeaki}} {{MECR3|1=https://www.youtube.com/watch?v=atafN2vDwYE}} __TOC__ ==Overview== Shame, guilt and pride are complex, self-conscious emotions.{{gr}}They impact our sense of self, self-worth and self-esteem. In society;{{gr}} shame, quilt and pride are often viewed as negatively impactful, though,{{gr}} they can be useful emotions to encourage motivation, and social harmony. This chapter aims to understand the ''impacts that culture has on shame guilt and pride'', as well as provide definitions and examples of '''culture''' and '''emotion'''. There are many theories of emotion that not only apply to past knowledge, but impact our current understanding of what influences and promotes emotion. These include the two-factor theory of emotion, proposed by Schacter and Singer's{{gr}} (1962); the cognitive appraisal theory, founded by Lazarus (1982); and the Cannon-Bard theory of emotion (1927). Current literature lacks an explanation as to the direct relationship between culture and secondary emotions (shame, guilt, embarrassment and pride) so linkages will be made incorperating{{sp}} modern culture the emotions independently. Understanding the relationship between culture and emotion is important for maximising positive outcomes like motivation, self-esteem, {{missing}} belonging. {{RoundBoxTop|theme=5}} ;Focus questions * What are emotions? * How do you define shame, guilt and pride? * What are some theories of emotion? * What is culture? * How does culture influence shame, guilt and pride? {{RoundBoxBottom}} ==Emotion == {{expand}} === Emotion definition === [[File:Primary Emotions.jpg|thumb|280x280px|list of primary emotions ]] [[Emotion|Emotions]] are biologically-based psychological states that are caused by neurophysiological changes. They are associated with a variety of thoughts, feelings, behavioural responses, and a level of pleasure or displeasure. Emotions are often impacted my ones'{{gr}} circumstances, relationships, location and mood (Adolphs, 2010). [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0033-295X.99.3.550 Paul Ekman] (1992) studied emotions through facial expression, and theorised that we have “basic emotions”: '''happiness, anger, surprise, disgust, fear and sadness'''. All other variations of emotions under this theory link or are morphed from the 6 basic emotions. [https://www.tandfonline.com/doi/abs/10.1080/02699930244000246?casa_token=KpL3uXbNU0EAAAAA:WebRV-ataOEKqKdZtcXYbfm81rlK7h_VKXojOOIIyzCAZCyN4IvfhScyVF-_lZx-cJpPhyNLSMC4pEI Considine et al.] (2003) study expanded on Ekman’s original theory. The investigation sought 123 males and 213 females from 4 different continents to read text descriptions of “emotional” [[w:Behaviour|behaviour]]. Results found '''anger, happiness, fear and sadness''' to be more readily identified than more cognitively complex emotions such as '''guilt, shame and pride'''. This gives insights into motor{{huh}} features of emotion (behavioural responses to emotion) and outlines how complex emotions often go unidentified and are harder to act/reflect upon. === What is shame, guilt and pride? === [[File:Emotions according to the Atlas of Personality, Emotion and Behaviour.svg|thumb|Images of emotions: facial expression|283x283px]] {{expand}} ==== Shame ==== [[w:Shame|Shame]] Is a painful feeling of humiliation or distress caused by the consciousness of wrong or foolish behaviour (oxford languages, 2003). ''Shame is an emotion that often fuels people to make a change in their life, or hide their wrong doings''. Shame is often invisible in modern societies because of [[w:Taboo|taboo]]. While shame primarily remains hidden, it is often used across cultures and individuals on platforms such as social media to influence others. Strong feelings of shame stimulate the [[w:Sympathetic nervous system|sympathetic nervous system]] which leads to a '''fight/flight reaction''', and is associated with: [[w:Panic attacks|panic attacks]], [[w:Anxiety|anxiety]], [[w:Panic disorder|panic disorder]] and [[w:Major depressive disorder|major depressive disorder]]. Shame-based beliefs are a sign of '''toxic shame''' and can include thoughts such as: "I’m unattractive, especially to a romantic partner; I don’t matter, to others or myself; I’m a failure, I shouldn’t have been born" etc. ==== Guilt ==== [[w:Guilt|Guilt]] is defined as having committed a specified or implied offence or crime (Oxford Languages, 2004){{huh}}{{ic|Just because an offence is committed, doesn't mean people will feel guilty}}. Often people feel guilty when they believe their personal morals, or the morals of those around them have been violated by their words/actions. Guilty people generally feel significant responsibility for the actions and behaviour they display (however this is not always the case). People can feel guilty for their personal actions, or for those whom they are close to (e.g., you may feel guilty for your partners{{gr}} behaviour on a night out with family or friends). '''Guilt, like shame and pride is a self-conscience{{sp}} emotion'''. One of the best ways to cope with guilt is to apologise for, and correct, your actions (Bem, Strelan & Proeve, 2021). Some people experience excessive guilt, and while it does not always indicate a further reaching problem, it can be a symptom of [[w:Bipolar disorder|bipolar disorder]] and depression.     ==== Pride ==== {{RoundBoxTop|theme=13}}"In so far as a man amounts to anything, stands for anything, is truly an individual, he has an ego about him to which his passions cluster, and to aggrandize which must be a principle aim within him" - Cooley (1902, p. 216) {{RoundBoxBottom}} [[w:Pride|Pride]], in comparison to other emotions, has received very little research attention. {{gr}}it is generally viewed as a self-conscious, secondary emotion. Pride is defined as a deep pleasure or satisfaction derived from one's own achievements, the accomplishments of those with whom one is closely associated, or widely admired qualities or assets (Oxford Languages, 2000). Hart and Mastaba (2007) dictate pride to be an important psychological and adaptive emotion, due to its '''pleasurable''' and '''reinforcing''' attributes. Feelings of pride have also been found to contribute to the development of '''self-esteem''' and positive self-worth (Brown & Marshall, 2001). Pride, also, has been found to '''motivate perseverance''', as people wish to be proud of their actions, contributions, [[w:Economic status|economic status]], associates etc. (Williams & DeSento, 2008). Pride can be seen as positive (it increases self-esteem and motivation) or negative (it encourages egotistical views and people can become immodest). Pride is often villainised in ancient and modern society, for example through its incorporation in the [[w:7 deadly sins|7 deadly sins]]. This pessimistic taint has lead to it being a deprecated emotion. === '''Theories of emotion''' === {{expand}} ==== '''Schacter and Singer's''' two-factor theory of emotion ==== According to ''Schacter and Singer’s two-factor theory of emotion (1962)'', emotion has two key components (refer to Table 1): '''physical arousal''' (a physiological response) and a '''cognitive label''' (your mind identifying the response of your physical state). Schacter et al. (1962) expressed the importance of understanding one’s physiological response and why it is occurring; ''“we must identify the arousal in order to feel the emotion”''. Schacter and Singers{{gr}} experiment used a test sample of 184 male participants. The participants were injected with the hormone [[w:Epinephrine|epinephrine]] which produces arousal. Participants were split into two groups; those who had been told of the risks associated with the experiment, and those who had not. A confederate was assigned to each group and acted either happy or angry. Results showed that those whom were in the uninformed group labelled their emotions using their feelings in current time and overall displayed more intense emotions. The underlying theory and findings indicate that when the brain cannot decipher why it feels a particular emotion, it relies on '''external stimulations''' for cues on how to label the emotion. {| class="wikitable mw-collapsible" |+Table 1: ''Two-factor theory examples'' |Situations/ stimulus |physical arousal |cognitive label |- |A spider lands on you |increased heart rate |I am frightened |- |you see a strange person walking toward you |shakes/ trembling |I am nervous |- |you hear a loud noise from somewhere nearby |freeze/ increased heart rate |I am scared |} ==== '''Lazarus''' cognitive appraisal theory of emotion ==== [[File:Stress and cognitive appraisal.png|left|thumb|362x362px|Stress and cognitive appraisal: how the process works]] ''Cognitive appraisal'' is the assessment of an emotional situation, in which a person will '''evaluate''' how a particular event will affect them, '''interpret''' the event and actions that took place, and arrive at a '''response''' based on that interpretation (Lazarus, 1982). Furthermore, cognitive appraisal is subdivided into 3 categories: [[w:Primary appraisal|Primary appraisal]], referring to the initial evaluation of the situation, deeming a situation as positive, negative (stress) or neutral; [[w:Secondary appraisal|secondary appraisal]], the evaluation of one’s ability to cope with the situation; and [[w:Reappraisal|reappraisal]], recognising the pattern of your thoughts and altering them for the situation at hand, as well as re-evaluating the situation (Smith & Curby, 2001). Cognitive appraisal is generally used when there is little evidence or indication of how one should act in a particular situation, as it is on a basic level: perception of surroundings and situations. For example, you go to a new restaurant with your partner and find the restaurant to be cluttered and unorganised when you first arrive, you might view this situation as negative and feel you cannot eat there as it makes you uncomfortable, you may re-evaluate the situation and find that you can sit at one table away from the clutter comfortably. The emotion you feel under this theory, stems from your personal perception and evaluation of a situation.     ==== '''Cannon-Bard''' theory of emotion ==== [[File:Thalamus.gif|thumb|Thalamus location in the brain]] ''Cannon-Bard’s (1927) theory of emotion'' (also known as the thalamic theory of emotion) interprets how physiological functions produce and alter emotion. More specifically, the theory proposes the thalamus sends a message to the brain in response to a catalyst, which in turn results in the formation of an emotion. For example, you see a spider, you are frightened, your heart beat increases and you begin to shake. The emotion of the described experience is fear which can be identified through the physical symptoms you display. The reaction to the stimuli and the emotion occur in unison as the [[w:Thalamus|thalamus]] (responsible for receiving sensory information) transmits a signal to the [[w:Amygdala|amygdala]] when an event occurs. The amygdala is located in the limbic system, in the centre of the brain. The amygdala is the combining centre for emotion, emotional behaviour and motivation (Swanson & Petrovich, 1998). The thalamus may also send signals to the [[w:Cerebral cortex|Cerebral cortex]] (which stimulates and controls continuous thoughts). Simultaneously, the thalamus can send signals to the [[w:Automatic nervous system|automatic nervous system]] which initiates a physical reaction. While Cannon's theory provides some interesting insights, the soundness has been questioned in relation to the thalamus' contribution and the hypothalamus. == Culture == [[File:Coolamon with dot-painting.JPG|left|thumb|312x312px|Aboriginal dot painting: a part of aboriginal culture ]] {{expand}} === What is culture? === [[w:Culture|Culture]] is a notoriously difficult term to define, {{gr}} this is due to culture belonging to different [[w:Paradigms|paradigms]] in social sciences and evolution. The term ‘culture’ has been interpreted differently, and '''evolution''' has seen changes in theory and definition of the word and its meaning. Today, we primarily view culture as a group or society in which someone identifies and relates to (Schein, 1991). However, culture can also be attributed to wider reaching ideas such as “[[w:Pop culture|pop culture]]” which refers to popular behaviours and interests, which many view as positive and desirable. '''Culture is learned''', not inherited, {{gr}} it derives from one’s social environment, not one’s genes and is dissimilar to human nature and individuality (Spencer-Oatey & Franklin, 2012). Culture is learned through processes of socialisation and "norms" within the geographical location in which one finds themselves. All human societies have [[w:Cultural universals|cultural universals]]. These include forms of expression such as painting and sculpture, dance, music, cooking, ritual, and religion, and further technologies including tool usages, shelter and clothing. Please refer to the list below for some modern thoughts and understandings relating to culture.     {{RoundBoxTop|theme=8}}Definitions of culture{{fact}}: * The arts and other manifestations of human intellectual achievement regarded collectively. * The ideas, customs, and social behaviour of a particular people or society * A group that we identify with on an individual level * A sacred way of life from past to present * Attitudes, beliefs, behaviour, food, music, language, customs, rituals and religion {{RoundBoxBottom}} === '''How does culture effect us?''' === [[File:Jar with dragon design, Korea, Joseon dynasty, 1750-1850 AD, porcelain with underglaze cobalt - Asian Art Museum of San Francisco - DSC01433.JPG|left|thumb|250x250px|Asian art- dragon painted pot]] Culture effects{{sp}} individuals in a holistic way. As people often use culture to define part of who they are- it plays a huge role in self-perception, self-esteem and morals (Clarke, 2008). Culture, also, introduces negative effects on an individual’s life, it is not through belonging to a culture its self, but identification from out-group members who view your culture to be harmful or unlikeable. [[w:Racism|Racism]] and [[w:Stereotyping|stereotyping]] typify this negative effect. Some cultures (such as [[w:Aboriginal|aboriginal]] culture) have been ridiculed for their customs and traditions, and labelled ‘primitive’ the effect of such a label on aboriginal culture has seen suppression and lack of opportunity (Christie, 1998). Culture also effects ''behaviour'', ''social norms'' and ''morals'', differentiating one culture from the next. In Islamic culture, religion (worshiping Allah) and wearing hijabs is a social norm (although not all Muslims follow these practises). These customs are unalike any others in the world and are unique to Islam (Moaddel, 2002). Asian culture has customs of art, music and philosophy, the customs and practises are very different to those of Islam, for example. In simple terms, '''culture differentiates us from others in the world''', and yet gives us '''belonging''' to a group which we share ideals. A sense of belonging and uniqueness have a positive impact on our lives as it can eradicate loneliness and feelings of worthlessness (Tsai, Knutson & Fung, 2006).   == Influence of culture on emotion == {{expand}} === Culture and shame === Shame is not only respected in many non-western cultural contexts, but is also seen as an appropriate emotional response to failure. The positive value placed on shame in non-westernised cultural contexts is consistent with goals of ''self-effacement, conformity to norms, and self-improvement''. (Wong, Y & Tsai, 2007). Shame is often confused with guilt (see table 2) but has different effects and cultural processes associated with it. Kitayama et al. 1997 {{gr}} case study discovered two things about shame: first, that American situations are relatively conducive to self-enhancement, and, {{gr}} that Americans are relatively likely to engage in self-enhancement. Secondly, Japanese situations are amenable to self-criticism, and Japanese people are more likely to engage in self-criticism. Not only do dissimilar cultures view shame differently, but, {{gr}} the influence of shame between cultural groups is opposing. For example, America is known for having “shame culture”, in which deviating from norms is seen as unacceptable. In this sense, American culture has an influence on ''eschewing shame'', making the very essence and feeling of shame a negative thing. Due to this, American citizens may mask and supress{{sp}} their shame, which ultimately can lead to issues in mental health e.g., [[w:Depression|depression]].   Additionally, in many westernised cultures, shame is used as a tool to regulate ''social systems and hierarchies'' (Fessler, 2004). Use of shame in cultural groups can cause social rejection (when an individual is deliberately excluded from a social relationship) as it can be used to deliberately alter someone’s self-confidence, and, cause discern as a response to the ‘failure to meet cultural expectation’. Shame is not only used for ‘in-group culture’ but also used in relation to other cultures in which one is not a part of. This often occurs to stimulate hierarchies and alpha mentality on a national scale. Often cultures are shamed for traditions and customs which out-group members do not understand or prioritise as part of their morals. For example, the '''LBGT culture''' are shamed for their core belief “love is love” from those who do not belong within the culture themselves.      === Culture and guilt === [[File:Risk and protective factors of guilt.jpg|thumb|340x340px|Guilt: risk and protective factors]] Guilt is often labelled as being a culturally conditioned emotion and phenomenon{{fact}}. Feelings of guilt create intimidation and the need for punishment (Bierbrauer, 1992). Guilt in culture can lead to [[w:Authoritarian|authoritarian]] behaviours and manipulation, which one culture can project onto the next. '''Guilt culture''' behaviour is regulated via internal sanctions and is more prevalent in modern western cultures (Wallbott & Scherer, 1995). A lack of '''empathy''' among a culture/ cultures has also been associated with expansive feelings of guilt (Pedersen, Beven, Walker & Griffiths, 2004). Empathic emotions encourage and sense understanding for an individual's position, and the ability to 'put one's self in another shoes'. Typically, cultures that prioritise 'togetherness' and supportive behaviours practice and display empathy more than those that don't{{example}}. Thus, it can be said that cultures whom {{gr}} empathise more, inflict less guilt for wrong-doing and violation of cultural norms{{fact}}. Interestingly, ''connections between displaying empathy and being guilty have been made'', {{gr}} those who empathise understand what it feels like to be guilty because they too, in the past {{gr}} have been a victim of personal or cultural guilt (Basil, Ridgway & Basil, 2008). It is supposed, that some cultures experience feelings and emotions of guilt more than others- this has been studied through the '''transgressions''' used to measure guilt{{fact}}. {{RoundBoxTop|theme=9}}Case study: Biaggio (1969) investigated whether guilt feelings were more internalised in Americans than in Brazilians (using a sample of adolescents). The responses of the participants to several incomplete stories in which the main character committed a transgression were used to calculate their level of guilt internalisation in the investigation. To evaluate the responses, the author's proposed criterion for distinguishing between "internalised" and "externalised" guilt had been used: There was "internalised guilt" when the main character's reaction to a transgression occurred in the absence of any external threat; other indicators of internalised guilt included the presence of remorse or regret. When the main character's reaction appeared to be motivated by some external punishment, immanent{{sp}} punishment, or fear, there was "externalised guilt". Analyses revealed that American adolescents had more internalised guilt feelings than Brazilians, confirming the author's hypothesis (Etxebarría, 2004). {{RoundBoxBottom}} {| class="wikitable" |+Table 2: Shame vs guilt !Feelings of shame !Feelings of guilt |- |Focus on self |Focus on behaviour |- |Feeling worthless and powerless |Feeling regret and remorse |- |Desire to escape |Desire to confess |- |Feel bad about who you are |Feel bad about what you did |- |Blame others |Take personal responsibility |- |"I am bad" |"I did something bad" |} === Culture and pride === Pride often has positive connotations associated with it, and is seen as a '''desirable emotion''' for cultures to procure. Current publications and literature such as Eriksen & Heimestøl (2017) suggest how to better integrate pride in culture to facilitate confidence and trust. The frequency and intensity of pride has been found to differ between cultures, with lower feelings of pride in ''collectivistic'' cultures than in ''individualistic'' ones (Liu, Li, Chen, Wu, Yuan & Yu, 2021). This is, perhaps due to individualistic cultures focusing more on [[w:Intrinsic|intrinsic]] accomplishments rather than the accomplishments of a group. Group accomplishments are more difficult to observe, due to their expansive nature and necessity for communication. For example, you will not know your neighbour has accomplished their steps’{{gr}} goal for the day, unless they inform you of their accomplishment. Culture of men (''masculinity'') has also been strongly associated with pride{{fact}}. However, this association in many ways is negative, as the expectation in male culture is that one should demonstrate proud behaviours{{fact}}. This often discourages men from feeling oppositional emotions such as feeling ashamed{{fact}}. The effect of male culture on pride, in a way, sees that the actual emotion of feeling proud is often “faked” and is “owned by masculinity” (Boeuf, 2020). The effect this has on ''femininity'' (or the culture of women) is a lack in feeling pride, or discouragement to express pride in personal growth, such as: financial, physical and educational pride{{fact}}. ==Conclusion== Over a range of theories and studies discussed to locate the influence of '''culture''' on '''shame, guilt and pride''', it is clear that further study in the field needs to be conducted{{vague}}. Emotions and culture are wide ranging topics with many interesting concepts to discuss and discover, however the direct links between culture and the self-conscious emotions stated prior still remains unknown{{vague}}. Current connections have been made about shame and culture, in relation to deviating norms, and acceptance of shame emotions. Western culture has established shame as a negative emotion, and has incorporated “shame culture” to shun individuals who do not adhere to the social standards and morals associated with the culture. While Japanese culture welcomes feelings of shame and interprets the emotion as a sign of potential growth and a motivational influencer{{gr}}. Culture, also, {{gr}} influences emotions of guilt culture behaviour (primarily in westernised society). A lack of empathy, further, has been studied in relation to the placement of guilt between differing cultural groups{{vague}}. Finally, linkages between culture and pride have been made in relation to masculinity and individualistic culture. Male culture is often forced into the conformity and expression of pride so as to seem “manly”. The positive, {{gr}} is that the concept of cultures{{gr}} impact on behaviour is still relatively novel, and, {{gr}} the contributions to the topic will influence future psychological understanding of both culture and emotions: separately and in correlation{{vague}}. == See also == {{ic|Use bullet points. Use alphabetical order.}} * [[Motivation and emotion/Book/2022/Cultural influences on shame, guilt, and pride|Cultural influences on shame, guilt, and pride]] (Book chapter, 2022) [[w:Social emotions|Social emotions]] (Wikipedia) [[w:Modern culture|Modern culture]] (Wikipedia) [[w:Emotion classification|Emotion classification]] (Wikipedia) [[w:Body shaming|Body shaming]] (Wikipedia) [[w:Guilt trip|Guilt trip]] (Wikipedia) [[Motivation and emotion/Book/2017/Pride|Pride]] (Book chapter, 2017) ==References== {{Hanging indent|1= Bard, P. (1934). On emotional expression after decortication with some remarks on certain theoretical views: Part 1. Psychological Review, 41(4), 309-329. https://doi.org/10.1037/h0070765 Basil, D. Z., Ridgway, N. M., & Basil, M. D. (2008). Guilt and giving: A process model of empathy and efficacy. Psychology & Marketing, 25(1), 1-23. https://doi.org/10.1002/mar.20200 Bem, J. R., Strelan, P., & Proeve, M. (2021). Roads less travelled to self-forgiveness: Can psychological flexibility overcome chronic guilt/shame to achieve genuine self-forgiveness?. Journal of Contextual Behavioral Science, 21, 203-211. https://doi.org/10.1016/j.jcbs.2021.08.001 Bierbrauer, G. (1992). Reactions to violation of normative standards: A cross-cultural analysis of shame and guilt. International Journal of Psychology, 27(2), 181-193. https://doi.org/10.1080/00207599208246874 Boeuf, B. (2020). Boys do not cry: the negative effects of brand masculinity on brand emotions. Marketing Letters, 31(2), 247-264. https://doi.org/10.1007/s11002-020-09519-7 Brown, J. D., & Marshall, M. A. (2001). Self-esteem and emotion: Some thoughts about feelings. Personality and Social Psychology Bulletin, 27(5), 575-584. doi:10.1177/0146167201275006 Christie, G. (1998). Aboriginal rights, aboriginal culture, and protection. Osgoode Hall LJ, 36, 447. Clarke, S. (2008). Culture and identity. The Sage handbook of cultural analysis, 510-529. Consedine, N., Strongman, K., & Magai, C. (2003). Emotions and behaviour: Data from a cross‐cultural recognition study. Cognition and Emotion, 17(6), 881-902. https://doi.org/10.1080/02699930244000246 Cooley, C. H. (1902). Looking-glass self. The production of reality: Essays and readings on social interaction, 6, 126-128. Crystal, D. S., Parrott, W. G., Okazaki, Y., & Watanabe, H. (2001). Examining relations between shame and personality among university students in the United States and Japan: A developmental perspective. International Journal of Behavioral Development, 25(2), 113-123. https://doi.org/10.1080/01650250042000177 Dana, L. P. (1990). Saint Martin/Sint Maarten: a case study of the effects of culture on economic development. Journal of small business management, 28(4), 91. Dror, O. E. (2014). The Cannon–Bard thalamic theory of emotions: A brief genealogy and reappraisal. Emotion Review, 6(1), 13-20. https://doi.org/10.1177/1754073913494898 Ekman, P. E., & Davidson, R. J. (1994). The nature of emotion: Fundamental questions. Oxford University Press. https://psycnet.apa.org/record/1995-97541-000 Eriksen, K. Å., & Heimestøl, S. (2017). Developing a culture of pride, confidence and trust: enhanced collaboration in an interdicisplinary team. https://doi.org/10.19043/ipdj.7SP.004 Hart, D., & Matsuba, M. K. (2007). The development of pride and moral life. The self-conscious emotions: Theory and research, 114-133. Kitayama, S., Markus, H. R., Matsumoto, H., & Norasakkunkit, V. (1997). Individual and collective processes in the construction of the self: self-enhancement in the United States and self-criticism in Japan. Journal of personality and social psychology, 72(6), 1245. https://doi.org/10.1037/0022-3514.72.6.1245 Lashley, K. S. (1938). The thalamus and emotion. Psychological Review, 45(1), 42. https://doi.org/10.1037/h0054323 Lazarus, R. S. (1982). Thoughts on the relations between emotion and cognition. American psychologist, 37(9), 1019. https://doi.org/10.1037/0003-066X.37.9.1019 Li, J., Wang, L., & Fischer, K. (2004). The organisation of Chinese shame concepts?. Cognition and emotion, 18(6), 767-797. https://doi.org/10.1080/02699930341000202 Liu, C., Li, J., Chen, C., Wu, H., Yuan, L., & Yu, G. (2021). Individual Pride and Collective Pride: Differences Between Chinese and American Corpora. Frontiers in Psychology, 12. doi: 10.3389/fpsyg.2021.513779 Moaddel, M. (2002). The study of Islamic culture and politics: An overview and assessment. Annual Review of Sociology, 28(1), 359-386. https://www.annualreviews.org/doi/abs/10.1146/annurev.soc.28.110601.140928 Mosquera, P. M. R., Fischer, A. H., & Manstead, A. S. (2004). Inside the heart of emotion: On culture and relational concerns. The Social Life of Emotions. Cambridge: Cambridge UP, 187-202. Neumann, R., Steinhäuser, N., & Roeder, U. R. (2009). How self-construal shapes emotion: Cultural differences in the feeling of pride. Social Cognition, 27(2), 327-337. https://doi.org/10.1521/soco.2009.27.2.327 Oyserman, D., & Lee, S. W. (2008). Does culture influence what and how we think? Effects of priming individualism and collectivism. Psychological bulletin, 134(2), 311. https://doi.org/10.1037/0033-2909.134.2.311 Pedersen, A., Beven, J., Walker, I., & Griffiths, B. (2004). Attitudes toward indigenous Australians: The role of empathy and guilt. Journal of community & applied social psychology, 14(4), 233-249. https://doi.org/10.1002/casp.771 Pettigrove, G., & Parsons, N. (2012). Shame: A case study of collective emotion. Social theory and practice, 38(3), 504-530. https://www.jstor.org/stable/23562146 Reisenzein, R. (1983). The Schachter theory of emotion: Two decades later. Psychological bulletin, 94(2), 239. https://doi.org/10.1037/0033-2909.94.2.239 Schein, E. H. (1991). What is culture. Newbury Park, CA: Sage, 243-253. Smith, C. A., & Kirby, L. D. (2001). Affect and cognitive appraisal processes. https://psycnet.apa.org/record/2000-16445-004 Spencer-Oatey, H., & Franklin, P. (2012). What is culture. A compilation of quotations. GlobalPAD Core Concepts, 1-22. Sullivan, G. B. (2018). Collective emotions: A case study of South African pride, euphoria and unity in the context of the 2010 FIFA World Cup. Frontiers in psychology, 9, 1252. https://doi.org/10.3389/fpsyg.2018.01252 Swanson, L. W., & Petrovich, G. D. (1998). What is the amygdala?. Trends in neurosciences, 21(8), 323-331. https://doi.org/10.1016/S0166-2236(98)01265-X Tracy, J. L., & Robins, R. W. (2007). The nature of pride. The self-conscious emotions: Theory and research, 263-282. Tsai, J. L., Knutson, B., & Fung, H. H. (2006). Cultural variation in affect valuation. Journal of personality and social psychology, 90(2), 288. https://doi.org/10.1037/0022-3514.90.2.288 Wallbott, H. G., & Scherer, K. R. (1995). Cultural determinants in experiencing shame and guilt. Guilford Press. Williams, L. A., & DeSteno, D. (2008). Pride and perseverance: the motivational role of pride. Journal of personality and social psychology, 94(6), 1007. https://doi.org/10.1037/0022-3514.94.6.1007 Wong, Y., & Tsai, J. (2007). Cultural models of shame and guilt. The self-conscious emotions: Theory and research, 209, 223. }} == External links == {{ic|Use bullet points. Use alphabetical order.}} [https://www.tandfonline.com/doi/abs/10.1080/01488376.2018.1479676?journalCode=wssr20 The role of pride, shame, guilt and humiliation in social service organisations] (journal of social service research) [https://www.nytimes.com/2016/03/15/opinion/the-shame-culture.html The shame culture] (The New York Times) [https://www.psychologytoday.com/au/basics/guilt Guilt] (PsychologyToday) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Guilt]] [[Category:Motivation and emotion/Book/Pride]] [[Category:Motivation and emotion/Book/Shame]] skju6mdgp5wlx2qj41amyl4dplvhyn4 2412432 2412421 2022-08-06T23:07:24Z Dave Braunschweig 426084 Reverted edits by [[Special:Contributions/Tamika Afeaki|Tamika Afeaki]] ([[User_talk:Tamika Afeaki|talk]]) to last version by [[User:Jtneill|Jtneill]] using [[Wikiversity:Rollback|rollback]] wikitext text/x-wiki {{title|Cultural influences on shame, guilt, and pride:<br>How does culture influence shame, guilt, and pride?}} {{MECR3|1=https://www.youtube.com/watch?v=atafN2vDwYE}} __TOC__ ==Overview== Shame, guilt and pride are complex, self-conscious emotions.{{gr}}They impact our sense of self, self-worth and self-esteem. In society;{{gr}} shame, quilt and pride are often viewed as negatively impactful, though,{{gr}} they can be useful emotions to encourage motivation, and social harmony. This chapter aims to understand the ''impacts that culture has on shame guilt and pride'', as well as provide definitions and examples of '''culture''' and '''emotion'''. There are many theories of emotion that not only apply to past knowledge, but impact our current understanding of what influences and promotes emotion. These include the two-factor theory of emotion, proposed by Schacter and Singer's{{gr}} (1962); the cognitive appraisal theory, founded by Lazarus (1982); and the Cannon-Bard theory of emotion (1927). Current literature lacks an explanation as to the direct relationship between culture and secondary emotions (shame, guilt, embarrassment and pride) so linkages will be made incorperating{{sp}} modern culture the emotions independently. Understanding the relationship between culture and emotion is important for maximising positive outcomes like motivation, self-esteem, {{missing}} belonging. {{RoundBoxTop|theme=5}} ;Focus questions * What are emotions? * How do you define shame, guilt and pride? * What are some theories of emotion? * What is culture? * How does culture influence shame, guilt and pride? {{RoundBoxBottom}} ==Emotion == {{expand}} === Emotion definition === [[File:Primary Emotions.jpg|thumb|280x280px|list of primary emotions ]] [[Emotion|Emotions]] are biologically-based psychological states that are caused by neurophysiological changes. They are associated with a variety of thoughts, feelings, behavioural responses, and a level of pleasure or displeasure. Emotions are often impacted my ones'{{gr}} circumstances, relationships, location and mood (Adolphs, 2010). [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0033-295X.99.3.550 Paul Ekman] (1992) studied emotions through facial expression, and theorised that we have “basic emotions”: '''happiness, anger, surprise, disgust, fear and sadness'''. All other variations of emotions under this theory link or are morphed from the 6 basic emotions. [https://www.tandfonline.com/doi/abs/10.1080/02699930244000246?casa_token=KpL3uXbNU0EAAAAA:WebRV-ataOEKqKdZtcXYbfm81rlK7h_VKXojOOIIyzCAZCyN4IvfhScyVF-_lZx-cJpPhyNLSMC4pEI Considine et al.] (2003) study expanded on Ekman’s original theory. The investigation sought 123 males and 213 females from 4 different continents to read text descriptions of “emotional” [[w:Behaviour|behaviour]]. Results found '''anger, happiness, fear and sadness''' to be more readily identified than more cognitively complex emotions such as '''guilt, shame and pride'''. This gives insights into motor{{huh}} features of emotion (behavioural responses to emotion) and outlines how complex emotions often go unidentified and are harder to act/reflect upon. === What is shame, guilt and pride? === [[File:Emotions according to the Atlas of Personality, Emotion and Behaviour.svg|thumb|Images of emotions: facial expression|283x283px]] {{expand}} ==== Shame ==== [[w:Shame|Shame]] Is a painful feeling of humiliation or distress caused by the consciousness of wrong or foolish behaviour (oxford languages, 2003). ''Shame is an emotion that often fuels people to make a change in their life, or hide their wrong doings''. Shame is often invisible in modern societies because of [[w:Taboo|taboo]]. While shame primarily remains hidden, it is often used across cultures and individuals on platforms such as social media to influence others. Strong feelings of shame stimulate the [[w:Sympathetic nervous system|sympathetic nervous system]] which leads to a '''fight/flight reaction''', and is associated with: [[w:Panic attacks|panic attacks]], [[w:Anxiety|anxiety]], [[w:Panic disorder|panic disorder]] and [[w:Major depressive disorder|major depressive disorder]]. Shame-based beliefs are a sign of '''toxic shame''' and can include thoughts such as: "I’m unattractive, especially to a romantic partner; I don’t matter, to others or myself; I’m a failure, I shouldn’t have been born" etc. ==== Guilt ==== [[w:Guilt|Guilt]] is defined as having committed a specified or implied offence or crime (Oxford Languages, 2004){{huh}}{{ic|Just because an offence is committed, doesn't mean people will feel guilty}}. Often people feel guilty when they believe their personal morals, or the morals of those around them have been violated by their words/actions. Guilty people generally feel significant responsibility for the actions and behaviour they display (however this is not always the case). People can feel guilty for their personal actions, or for those whom they are close to (e.g., you may feel guilty for your partners{{gr}} behaviour on a night out with family or friends). '''Guilt, like shame and pride is a self-conscience{{sp}} emotion'''. One of the best ways to cope with guilt is to apologise for, and correct, your actions (Bem, Strelan & Proeve, 2021). Some people experience excessive guilt, and while it does not always indicate a further reaching problem, it can be a symptom of [[w:Bipolar disorder|bipolar disorder]] and depression.     ==== Pride ==== {{RoundBoxTop|theme=13}}"In so far as a man amounts to anything, stands for anything, is truly an individual, he has an ego about him to which his passions cluster, and to aggrandize which must be a principle aim within him" - Cooley (1902, p. 216) {{RoundBoxBottom}} [[w:Pride|Pride]], in comparison to other emotions, has received very little research attention. {{gr}}it is generally viewed as a self-conscious, secondary emotion. Pride is defined as a deep pleasure or satisfaction derived from one's own achievements, the accomplishments of those with whom one is closely associated, or widely admired qualities or assets (Oxford Languages, 2000). Hart and Mastaba (2007) dictate pride to be an important psychological and adaptive emotion, due to its '''pleasurable''' and '''reinforcing''' attributes. Feelings of pride have also been found to contribute to the development of '''self-esteem''' and positive self-worth (Brown & Marshall, 2001). Pride, also, has been found to '''motivate perseverance''', as people wish to be proud of their actions, contributions, [[w:Economic status|economic status]], associates etc. (Williams & DeSento, 2008). Pride can be seen as positive (it increases self-esteem and motivation) or negative (it encourages egotistical views and people can become immodest). Pride is often villainised in ancient and modern society, for example through its incorporation in the [[w:7 deadly sins|7 deadly sins]]. This pessimistic taint has lead to it being a deprecated emotion. === '''Theories of emotion''' === {{expand}} ==== '''Schacter and Singer's''' two-factor theory of emotion ==== According to ''Schacter and Singer’s two-factor theory of emotion (1962)'', emotion has two key components (refer to Table 1): '''physical arousal''' (a physiological response) and a '''cognitive label''' (your mind identifying the response of your physical state). Schacter et al. (1962) expressed the importance of understanding one’s physiological response and why it is occurring; ''“we must identify the arousal in order to feel the emotion”''. Schacter and Singers{{gr}} experiment used a test sample of 184 male participants. The participants were injected with the hormone [[w:Epinephrine|epinephrine]] which produces arousal. Participants were split into two groups; those who had been told of the risks associated with the experiment, and those who had not. A confederate was assigned to each group and acted either happy or angry. Results showed that those whom were in the uninformed group labelled their emotions using their feelings in current time and overall displayed more intense emotions. The underlying theory and findings indicate that when the brain cannot decipher why it feels a particular emotion, it relies on '''external stimulations''' for cues on how to label the emotion. {| class="wikitable mw-collapsible" |+Table 1: ''Two-factor theory examples'' |Situations/ stimulus |physical arousal |cognitive label |- |A spider lands on you |increased heart rate |I am frightened |- |you see a strange person walking toward you |shakes/ trembling |I am nervous |- |you hear a loud noise from somewhere nearby |freeze/ increased heart rate |I am scared |} ==== '''Lazarus''' cognitive appraisal theory of emotion ==== [[File:Stress and cognitive appraisal.png|left|thumb|362x362px|Stress and cognitive appraisal: how the process works]] ''Cognitive appraisal'' is the assessment of an emotional situation, in which a person will '''evaluate''' how a particular event will affect them, '''interpret''' the event and actions that took place, and arrive at a '''response''' based on that interpretation (Lazarus, 1982). Furthermore, cognitive appraisal is subdivided into 3 categories: [[w:Primary appraisal|Primary appraisal]], referring to the initial evaluation of the situation, deeming a situation as positive, negative (stress) or neutral; [[w:Secondary appraisal|secondary appraisal]], the evaluation of one’s ability to cope with the situation; and [[w:Reappraisal|reappraisal]], recognising the pattern of your thoughts and altering them for the situation at hand, as well as re-evaluating the situation (Smith & Curby, 2001). Cognitive appraisal is generally used when there is little evidence or indication of how one should act in a particular situation, as it is on a basic level: perception of surroundings and situations. For example, you go to a new restaurant with your partner and find the restaurant to be cluttered and unorganised when you first arrive, you might view this situation as negative and feel you cannot eat there as it makes you uncomfortable, you may re-evaluate the situation and find that you can sit at one table away from the clutter comfortably. The emotion you feel under this theory, stems from your personal perception and evaluation of a situation.     ==== '''Cannon-Bard''' theory of emotion ==== [[File:Thalamus.gif|thumb|Thalamus location in the brain]] ''Cannon-Bard’s (1927) theory of emotion'' (also known as the thalamic theory of emotion) interprets how physiological functions produce and alter emotion. More specifically, the theory proposes the thalamus sends a message to the brain in response to a catalyst, which in turn results in the formation of an emotion. For example, you see a spider, you are frightened, your heart beat increases and you begin to shake. The emotion of the described experience is fear which can be identified through the physical symptoms you display. The reaction to the stimuli and the emotion occur in unison as the [[w:Thalamus|thalamus]] (responsible for receiving sensory information) transmits a signal to the [[w:Amygdala|amygdala]] when an event occurs. The amygdala is located in the limbic system, in the centre of the brain. The amygdala is the combining centre for emotion, emotional behaviour and motivation (Swanson & Petrovich, 1998). The thalamus may also send signals to the [[w:Cerebral cortex|Cerebral cortex]] (which stimulates and controls continuous thoughts). Simultaneously, the thalamus can send signals to the [[w:Automatic nervous system|automatic nervous system]] which initiates a physical reaction. While Cannon's theory provides some interesting insights, the soundness has been questioned in relation to the thalamus' contribution and the hypothalamus. == Culture == [[File:Coolamon with dot-painting.JPG|left|thumb|312x312px|Aboriginal dot painting: a part of aboriginal culture ]] {{expand}} === What is culture? === [[w:Culture|Culture]] is a notoriously difficult term to define, {{gr}} this is due to culture belonging to different [[w:Paradigms|paradigms]] in social sciences and evolution. The term ‘culture’ has been interpreted differently, and '''evolution''' has seen changes in theory and definition of the word and its meaning. Today, we primarily view culture as a group or society in which someone identifies and relates to (Schein, 1991). However, culture can also be attributed to wider reaching ideas such as “[[w:Pop culture|pop culture]]” which refers to popular behaviours and interests, which many view as positive and desirable. '''Culture is learned''', not inherited, {{gr}} it derives from one’s social environment, not one’s genes and is dissimilar to human nature and individuality (Spencer-Oatey & Franklin, 2012). Culture is learned through processes of socialisation and "norms" within the geographical location in which one finds themselves. All human societies have [[w:Cultural universals|cultural universals]]. These include forms of expression such as painting and sculpture, dance, music, cooking, ritual, and religion, and further technologies including tool usages, shelter and clothing. Please refer to the list below for some modern thoughts and understandings relating to culture.     {{RoundBoxTop|theme=8}}Definitions of culture{{fact}}: * The arts and other manifestations of human intellectual achievement regarded collectively. * The ideas, customs, and social behaviour of a particular people or society * A group that we identify with on an individual level * A sacred way of life from past to present * Attitudes, beliefs, behaviour, food, music, language, customs, rituals and religion {{RoundBoxBottom}} === '''How does culture effect us?''' === [[File:Jar with dragon design, Korea, Joseon dynasty, 1750-1850 AD, porcelain with underglaze cobalt - Asian Art Museum of San Francisco - DSC01433.JPG|left|thumb|250x250px|Asian art- dragon painted pot]] Culture effects{{sp}} individuals in a holistic way. As people often use culture to define part of who they are- it plays a huge role in self-perception, self-esteem and morals (Clarke, 2008). Culture, also, introduces negative effects on an individual’s life, it is not through belonging to a culture its self, but identification from out-group members who view your culture to be harmful or unlikeable. [[w:Racism|Racism]] and [[w:Stereotyping|stereotyping]] typify this negative effect. Some cultures (such as [[w:Aboriginal|aboriginal]] culture) have been ridiculed for their customs and traditions, and labelled ‘primitive’ the effect of such a label on aboriginal culture has seen suppression and lack of opportunity (Christie, 1998). Culture also effects ''behaviour'', ''social norms'' and ''morals'', differentiating one culture from the next. In Islamic culture, religion (worshiping Allah) and wearing hijabs is a social norm (although not all Muslims follow these practises). These customs are unalike any others in the world and are unique to Islam (Moaddel, 2002). Asian culture has customs of art, music and philosophy, the customs and practises are very different to those of Islam, for example. In simple terms, '''culture differentiates us from others in the world''', and yet gives us '''belonging''' to a group which we share ideals. A sense of belonging and uniqueness have a positive impact on our lives as it can eradicate loneliness and feelings of worthlessness (Tsai, Knutson & Fung, 2006).   == Influence of culture on emotion == {{expand}} === Culture and shame === Shame is not only respected in many non-western cultural contexts, but is also seen as an appropriate emotional response to failure. The positive value placed on shame in non-westernised cultural contexts is consistent with goals of ''self-effacement, conformity to norms, and self-improvement''. (Wong, Y & Tsai, 2007). Shame is often confused with guilt (see table 2) but has different effects and cultural processes associated with it. Kitayama et al. 1997 {{gr}} case study discovered two things about shame: first, that American situations are relatively conducive to self-enhancement, and, {{gr}} that Americans are relatively likely to engage in self-enhancement. Secondly, Japanese situations are amenable to self-criticism, and Japanese people are more likely to engage in self-criticism. Not only do dissimilar cultures view shame differently, but, {{gr}} the influence of shame between cultural groups is opposing. For example, America is known for having “shame culture”, in which deviating from norms is seen as unacceptable. In this sense, American culture has an influence on ''eschewing shame'', making the very essence and feeling of shame a negative thing. Due to this, American citizens may mask and supress{{sp}} their shame, which ultimately can lead to issues in mental health e.g., [[w:Depression|depression]].   Additionally, in many westernised cultures, shame is used as a tool to regulate ''social systems and hierarchies'' (Fessler, 2004). Use of shame in cultural groups can cause social rejection (when an individual is deliberately excluded from a social relationship) as it can be used to deliberately alter someone’s self-confidence, and, cause discern as a response to the ‘failure to meet cultural expectation’. Shame is not only used for ‘in-group culture’ but also used in relation to other cultures in which one is not a part of. This often occurs to stimulate hierarchies and alpha mentality on a national scale. Often cultures are shamed for traditions and customs which out-group members do not understand or prioritise as part of their morals. For example, the '''LBGT culture''' are shamed for their core belief “love is love” from those who do not belong within the culture themselves.      === Culture and guilt === [[File:Risk and protective factors of guilt.jpg|thumb|340x340px|Guilt: risk and protective factors]] Guilt is often labelled as being a culturally conditioned emotion and phenomenon{{fact}}. Feelings of guilt create intimidation and the need for punishment (Bierbrauer, 1992). Guilt in culture can lead to [[w:Authoritarian|authoritarian]] behaviours and manipulation, which one culture can project onto the next. '''Guilt culture''' behaviour is regulated via internal sanctions and is more prevalent in modern western cultures (Wallbott & Scherer, 1995). A lack of '''empathy''' among a culture/ cultures has also been associated with expansive feelings of guilt (Pedersen, Beven, Walker & Griffiths, 2004). Empathic emotions encourage and sense understanding for an individual's position, and the ability to 'put one's self in another shoes'. Typically, cultures that prioritise 'togetherness' and supportive behaviours practice and display empathy more than those that don't{{example}}. Thus, it can be said that cultures whom {{gr}} empathise more, inflict less guilt for wrong-doing and violation of cultural norms{{fact}}. Interestingly, ''connections between displaying empathy and being guilty have been made'', {{gr}} those who empathise understand what it feels like to be guilty because they too, in the past {{gr}} have been a victim of personal or cultural guilt (Basil, Ridgway & Basil, 2008). It is supposed, that some cultures experience feelings and emotions of guilt more than others- this has been studied through the '''transgressions''' used to measure guilt{{fact}}. {{RoundBoxTop|theme=9}}Case study: Biaggio (1969) investigated whether guilt feelings were more internalised in Americans than in Brazilians (using a sample of adolescents). The responses of the participants to several incomplete stories in which the main character committed a transgression were used to calculate their level of guilt internalisation in the investigation. To evaluate the responses, the author's proposed criterion for distinguishing between "internalised" and "externalised" guilt had been used: There was "internalised guilt" when the main character's reaction to a transgression occurred in the absence of any external threat; other indicators of internalised guilt included the presence of remorse or regret. When the main character's reaction appeared to be motivated by some external punishment, immanent{{sp}} punishment, or fear, there was "externalised guilt". Analyses revealed that American adolescents had more internalised guilt feelings than Brazilians, confirming the author's hypothesis (Etxebarría, 2004). {{RoundBoxBottom}} {| class="wikitable" |+Table 2: Shame vs guilt !Feelings of shame !Feelings of guilt |- |Focus on self |Focus on behaviour |- |Feeling worthless and powerless |Feeling regret and remorse |- |Desire to escape |Desire to confess |- |Feel bad about who you are |Feel bad about what you did |- |Blame others |Take personal responsibility |- |"I am bad" |"I did something bad" |} === Culture and pride === Pride often has positive connotations associated with it, and is seen as a '''desirable emotion''' for cultures to procure. Current publications and literature such as Eriksen & Heimestøl (2017) suggest how to better integrate pride in culture to facilitate confidence and trust. The frequency and intensity of pride has been found to differ between cultures, with lower feelings of pride in ''collectivistic'' cultures than in ''individualistic'' ones (Liu, Li, Chen, Wu, Yuan & Yu, 2021). This is, perhaps due to individualistic cultures focusing more on [[w:Intrinsic|intrinsic]] accomplishments rather than the accomplishments of a group. Group accomplishments are more difficult to observe, due to their expansive nature and necessity for communication. For example, you will not know your neighbour has accomplished their steps’{{gr}} goal for the day, unless they inform you of their accomplishment. Culture of men (''masculinity'') has also been strongly associated with pride{{fact}}. However, this association in many ways is negative, as the expectation in male culture is that one should demonstrate proud behaviours{{fact}}. This often discourages men from feeling oppositional emotions such as feeling ashamed{{fact}}. The effect of male culture on pride, in a way, sees that the actual emotion of feeling proud is often “faked” and is “owned by masculinity” (Boeuf, 2020). The effect this has on ''femininity'' (or the culture of women) is a lack in feeling pride, or discouragement to express pride in personal growth, such as: financial, physical and educational pride{{fact}}. ==Conclusion== Over a range of theories and studies discussed to locate the influence of '''culture''' on '''shame, guilt and pride''', it is clear that further study in the field needs to be conducted{{vague}}. Emotions and culture are wide ranging topics with many interesting concepts to discuss and discover, however the direct links between culture and the self-conscious emotions stated prior still remains unknown{{vague}}. Current connections have been made about shame and culture, in relation to deviating norms, and acceptance of shame emotions. Western culture has established shame as a negative emotion, and has incorporated “shame culture” to shun individuals who do not adhere to the social standards and morals associated with the culture. While Japanese culture welcomes feelings of shame and interprets the emotion as a sign of potential growth and a motivational influencer{{gr}}. Culture, also, {{gr}} influences emotions of guilt culture behaviour (primarily in westernised society). A lack of empathy, further, has been studied in relation to the placement of guilt between differing cultural groups{{vague}}. Finally, linkages between culture and pride have been made in relation to masculinity and individualistic culture. Male culture is often forced into the conformity and expression of pride so as to seem “manly”. The positive, {{gr}} is that the concept of cultures{{gr}} impact on behaviour is still relatively novel, and, {{gr}} the contributions to the topic will influence future psychological understanding of both culture and emotions: separately and in correlation{{vague}}. == See also == {{ic|Use bullet points. Use alphabetical order.}} * [[Motivation and emotion/Book/2022/Cultural influences on shame, guilt, and pride|Cultural influences on shame, guilt, and pride]] (Book chapter, 2022) [[w:Social emotions|Social emotions]] (Wikipedia) [[w:Modern culture|Modern culture]] (Wikipedia) [[w:Emotion classification|Emotion classification]] (Wikipedia) [[w:Body shaming|Body shaming]] (Wikipedia) [[w:Guilt trip|Guilt trip]] (Wikipedia) [[Motivation and emotion/Book/2017/Pride|Pride]] (Book chapter, 2017) ==References== {{Hanging indent|1= Bard, P. (1934). On emotional expression after decortication with some remarks on certain theoretical views: Part 1. Psychological Review, 41(4), 309-329. https://doi.org/10.1037/h0070765 Basil, D. Z., Ridgway, N. M., & Basil, M. D. (2008). Guilt and giving: A process model of empathy and efficacy. Psychology & Marketing, 25(1), 1-23. https://doi.org/10.1002/mar.20200 Bem, J. R., Strelan, P., & Proeve, M. (2021). Roads less travelled to self-forgiveness: Can psychological flexibility overcome chronic guilt/shame to achieve genuine self-forgiveness?. Journal of Contextual Behavioral Science, 21, 203-211. https://doi.org/10.1016/j.jcbs.2021.08.001 Bierbrauer, G. (1992). Reactions to violation of normative standards: A cross-cultural analysis of shame and guilt. International Journal of Psychology, 27(2), 181-193. https://doi.org/10.1080/00207599208246874 Boeuf, B. (2020). Boys do not cry: the negative effects of brand masculinity on brand emotions. Marketing Letters, 31(2), 247-264. https://doi.org/10.1007/s11002-020-09519-7 Brown, J. D., & Marshall, M. A. (2001). Self-esteem and emotion: Some thoughts about feelings. Personality and Social Psychology Bulletin, 27(5), 575-584. doi:10.1177/0146167201275006 Christie, G. (1998). Aboriginal rights, aboriginal culture, and protection. Osgoode Hall LJ, 36, 447. Clarke, S. (2008). Culture and identity. The Sage handbook of cultural analysis, 510-529. Consedine, N., Strongman, K., & Magai, C. (2003). Emotions and behaviour: Data from a cross‐cultural recognition study. Cognition and Emotion, 17(6), 881-902. https://doi.org/10.1080/02699930244000246 Cooley, C. H. (1902). Looking-glass self. The production of reality: Essays and readings on social interaction, 6, 126-128. Crystal, D. S., Parrott, W. G., Okazaki, Y., & Watanabe, H. (2001). Examining relations between shame and personality among university students in the United States and Japan: A developmental perspective. International Journal of Behavioral Development, 25(2), 113-123. https://doi.org/10.1080/01650250042000177 Dana, L. P. (1990). Saint Martin/Sint Maarten: a case study of the effects of culture on economic development. Journal of small business management, 28(4), 91. Dror, O. E. (2014). The Cannon–Bard thalamic theory of emotions: A brief genealogy and reappraisal. Emotion Review, 6(1), 13-20. https://doi.org/10.1177/1754073913494898 Ekman, P. E., & Davidson, R. J. (1994). The nature of emotion: Fundamental questions. Oxford University Press. https://psycnet.apa.org/record/1995-97541-000 Eriksen, K. Å., & Heimestøl, S. (2017). Developing a culture of pride, confidence and trust: enhanced collaboration in an interdicisplinary team. https://doi.org/10.19043/ipdj.7SP.004 Hart, D., & Matsuba, M. K. (2007). The development of pride and moral life. The self-conscious emotions: Theory and research, 114-133. Kitayama, S., Markus, H. R., Matsumoto, H., & Norasakkunkit, V. (1997). Individual and collective processes in the construction of the self: self-enhancement in the United States and self-criticism in Japan. Journal of personality and social psychology, 72(6), 1245. https://doi.org/10.1037/0022-3514.72.6.1245 Lashley, K. S. (1938). The thalamus and emotion. Psychological Review, 45(1), 42. https://doi.org/10.1037/h0054323 Lazarus, R. S. (1982). Thoughts on the relations between emotion and cognition. American psychologist, 37(9), 1019. https://doi.org/10.1037/0003-066X.37.9.1019 Li, J., Wang, L., & Fischer, K. (2004). The organisation of Chinese shame concepts?. Cognition and emotion, 18(6), 767-797. https://doi.org/10.1080/02699930341000202 Liu, C., Li, J., Chen, C., Wu, H., Yuan, L., & Yu, G. (2021). Individual Pride and Collective Pride: Differences Between Chinese and American Corpora. Frontiers in Psychology, 12. doi: 10.3389/fpsyg.2021.513779 Moaddel, M. (2002). The study of Islamic culture and politics: An overview and assessment. Annual Review of Sociology, 28(1), 359-386. https://www.annualreviews.org/doi/abs/10.1146/annurev.soc.28.110601.140928 Mosquera, P. M. R., Fischer, A. H., & Manstead, A. S. (2004). Inside the heart of emotion: On culture and relational concerns. The Social Life of Emotions. Cambridge: Cambridge UP, 187-202. Neumann, R., Steinhäuser, N., & Roeder, U. R. (2009). How self-construal shapes emotion: Cultural differences in the feeling of pride. Social Cognition, 27(2), 327-337. https://doi.org/10.1521/soco.2009.27.2.327 Oyserman, D., & Lee, S. W. (2008). Does culture influence what and how we think? Effects of priming individualism and collectivism. Psychological bulletin, 134(2), 311. https://doi.org/10.1037/0033-2909.134.2.311 Pedersen, A., Beven, J., Walker, I., & Griffiths, B. (2004). Attitudes toward indigenous Australians: The role of empathy and guilt. Journal of community & applied social psychology, 14(4), 233-249. https://doi.org/10.1002/casp.771 Pettigrove, G., & Parsons, N. (2012). Shame: A case study of collective emotion. Social theory and practice, 38(3), 504-530. https://www.jstor.org/stable/23562146 Reisenzein, R. (1983). The Schachter theory of emotion: Two decades later. Psychological bulletin, 94(2), 239. https://doi.org/10.1037/0033-2909.94.2.239 Schein, E. H. (1991). What is culture. Newbury Park, CA: Sage, 243-253. Smith, C. A., & Kirby, L. D. (2001). Affect and cognitive appraisal processes. https://psycnet.apa.org/record/2000-16445-004 Spencer-Oatey, H., & Franklin, P. (2012). What is culture. A compilation of quotations. GlobalPAD Core Concepts, 1-22. Sullivan, G. B. (2018). Collective emotions: A case study of South African pride, euphoria and unity in the context of the 2010 FIFA World Cup. Frontiers in psychology, 9, 1252. https://doi.org/10.3389/fpsyg.2018.01252 Swanson, L. W., & Petrovich, G. D. (1998). What is the amygdala?. Trends in neurosciences, 21(8), 323-331. https://doi.org/10.1016/S0166-2236(98)01265-X Tracy, J. L., & Robins, R. W. (2007). The nature of pride. The self-conscious emotions: Theory and research, 263-282. Tsai, J. L., Knutson, B., & Fung, H. H. (2006). Cultural variation in affect valuation. Journal of personality and social psychology, 90(2), 288. https://doi.org/10.1037/0022-3514.90.2.288 Wallbott, H. G., & Scherer, K. R. (1995). Cultural determinants in experiencing shame and guilt. Guilford Press. Williams, L. A., & DeSteno, D. (2008). Pride and perseverance: the motivational role of pride. Journal of personality and social psychology, 94(6), 1007. https://doi.org/10.1037/0022-3514.94.6.1007 Wong, Y., & Tsai, J. (2007). Cultural models of shame and guilt. The self-conscious emotions: Theory and research, 209, 223. }} == External links == {{ic|Use bullet points. Use alphabetical order.}} [https://www.tandfonline.com/doi/abs/10.1080/01488376.2018.1479676?journalCode=wssr20 The role of pride, shame, guilt and humiliation in social service organisations] (journal of social service research) [https://www.nytimes.com/2016/03/15/opinion/the-shame-culture.html The shame culture] (The New York Times) [https://www.psychologytoday.com/au/basics/guilt Guilt] (PsychologyToday) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Guilt]] [[Category:Motivation and emotion/Book/Pride]] [[Category:Motivation and emotion/Book/Shame]] 7zso6u1jubl0dngm99ap4p3lu572lxr 0 257925 2412441 2388331 2022-08-07T01:56:13Z Marshallsumter 311529 /* Absorptions */ wikitext text/x-wiki [[Image:800crab.png|thumb|right|300px|This image is a composite of several types of radiation astronomy: radio, infrared, visual, ultraviolet, soft and hard X-ray. Credit: NASA.{{tlx|free media}}]] '''Radiation astronomy''' is astronomy applied to the various extraterrestrial sources of radiation, especially at night. It is also conducted above the Earth's atmosphere and at locations away from the Earth, by satellites and space probes, as a part of explorational (or exploratory) radiation astronomy. Seeing the [[Stars/Sun|Sun]] and feeling the warmth of its rays is probably a student's first encounter with an astronomical radiation source. This will happen from a very early age, but a first understanding of the concepts of radiation may occur at a secondary educational level. Radiation is all around us on top of the Earth's crust, regolith, and soil, where we live. The study of radiation, including radiation astronomy, usually intensifies at the university undergraduate level. {{clear}} ==Absorptions== {{main|Radiation astronomy/Absorptions|Absorption astronomy}} [[Image:Spectrum of blue sky.svg|thumb|right|A spectrum is taken of blue sky clearly showing solar [[w:Fraunhofer lines|Fraunhofer lines]] and atmospheric water absorption band. Credit: [[w:user:Remember the dot|Remember the dot]].{{tlx|free media}}]] "[P]referential absorption of sunlight by ozone over long horizon paths gives the zenith sky its blueness when the sun is near the horizon".<ref name=Bohren>{{ cite book |url=http://homepages.wmich.edu/%7Ekorista/atmospheric_optics.pdf |title=Atmospheric Optics |author=Craig F. Bohren }}</ref> "For quenched galaxies, the Hα absorption trough is deep and can be traced through the nucleus and along the major axis. It extends to a radius at or beyond 2 R_''d'' [where R_''d'' is the galaxy disk scale length] in all but three cases. This makes it possible to determine a velocity width from the optical spectrum as is done for emission line flux, with appropriate corrections between stellar and gas velocities (see discussion in Paper I, also Neistein, Maoz, Rix, & Tonry, 1999). In the few cases where a velocity width can also be measured from the H I data, it is found to be in good agreement with that taken from the Hα absorption line flux."<ref name="Vogt">{{cite journal |author=Nicole P. Vogt |author2=Martha P. Haynes |author3=Riccardo Giovanelli |author4=Terry Herter |title=M/L, Hα Rotation Curves, and HI Gas Measurements for 329 Nearby Cluster and Field Spirals. III. Evolution in Fundamental Galaxy Parameters |journal=The Astronomical Journal |month=June |year=2004 |volume=127 |issue=6 |pages=3325-37 |url=http://iopscience.iop.org/1538-3881/127/6/3325 |arxiv=astro-ph/0402651 |bibcode=2004AJ....127.3325V |doi=10.1086/420703 |pmid= |accessdate=2013-12-20 }}</ref> {{clear}} ==Acoustics== {{main|Radiation astronomy/Acoustics}} [[Image:Phase shift induced by free-streaming neutrinos.png|right|thumb|300px|Phase shift induced by free-streaming neutrinos and other light relics in the spectrum of baryon acoustic oscillations. Credit: Daniel Baumann, Florian Beutler, Raphael Flauger, Daniel Green, Anže Slosar, Mariana Vargas-Magaña, Benjamin Wallisch & Christophe Yèche.{{tlx|fairuse}}]] "A pattern caused by sound waves in the early universe — known as baryon acoustic oscillations — should be distorted by the [early] neutrinos. Those sound waves spread outward through the universe like circular ripples on a pond, compressing matter into denser pockets. Eventually, that process resulted in galaxies having a tendency to cluster in rings across the sky [...]."<ref name=Conover>{{ cite book |author=Emily Conover |title=Hidden ancient neutrinos may shape the patterns of galaxies |publisher=Science News |location= |date=March 4, 2019 |url=https://www.sciencenews.org/article/hidden-ancient-neutrinos-may-shape-patterns-galaxies |accessdate=7 March 2019 }}</ref> "Using data from the Baryon Oscillation Spectroscopic Survey, or BOSS, [to study] the circular patterns of galaxies [produced] evidence that the [early] neutrinos were, in fact, pulling matter around from the inner side of the ring band toward the outer side."<ref name=Conover/> "A complementary and more robust probe [of the cosmic neutrino background] is provided by a distinct shift in the temporal phase of sound waves in the primordial plasma that is produced by fluctuations in the neutrino density."<ref name=Baumann>{{ cite journal |author=Daniel Baumann |author2=Florian Beutler |author3=Raphael Flauger |author4=Daniel Green |author5=Anže Slosar |author6=Mariana Vargas-Magaña |author7=Benjamin Wallisch |author8=Christophe Yèche |title=First constraint on the neutrino-induced phase shift in the spectrum of baryon acoustic oscillations |journal=Nature Physics |date=25 February 2019 |volume= |issue= |pages= |url=https://www.nature.com/articles/s41567-019-0435-6 |arxiv= |bibcode= |doi=10.1038/s41567-019-0435-6 |pmid= |accessdate=7 March 2019 }}</ref> "The effect of neutrinos on perturbations in the primordial plasma has been shown to be a more robust probe of the CνB⁴. Neutrinos travel near the speed of light in the early Universe, significantly faster than sound waves in the hot plasma of photons and baryons, and can therefore propagate information ahead of the sound horizon of the plasma. The gravitational influence of this supersonic propagation induces a shift in the phase of the acoustic oscillations that cannot be mimicked by other properties of the plasma^4,5. This phase shift has recently been detected in the CMB^5,6, adding to the robustness of the cosmological evidence for the CνB."<ref name=Baumann/> "After recombination, photons decoupled from baryons and the sound waves lost their pressure support. The sudden halt to the propagation of these density waves leaves an overdensity of baryons at the scale of the acoustic horizon at recombination. Subsequent gravitational evolution transfers this overdensity to the matter distribution. The power spectrum of galaxies inherits this feature in the form of baryon acoustic oscillations (BAOs). It was recently pointed out that the BAO spectrum should not only exhibit the same phase shift from the supersonic propagation of neutrinos, but that this shift should also be robust to nonlinear gravitational evolution in the late Universe⁷."<ref name=Baumann/> "A key property of neutrinos is that they do not behave as a fluid, but as a collection of ultra-relativistic free-streaming particles. As a consequence, neutrinos travel at the speed of light c while the sound waves in a relativistic fluid, like the photon–baryon fluid, travel at c_s ≈ c/√3. The supersonic propagation speed of neutrino perturbations creates a characteristic phase shift [see image on the right (a)] in the sound waves of the primordial plasma. A useful way to understand the effect is to consider the evolution of a single initial overdensity^11,12. (For adiabatic fluctuations, the primordial density field is a superposition of such point-like overdensities.) The overdensities of photons, baryons and neutrinos will spread out as spherical shells, while the dark matter perturbation does not move much and will be left behind at the centre. Because the neutrinos travel faster than all other perturbations, they induce metric perturbations ahead of the sound horizon r_s of the acoustic waves of the photon–baryon fluid."<ref name=Baumann/> Image on the right part (a) shows the template "of the phase shift f(k) (blue) [...[, with the fitting function [...] shown as the red curve. The template was obtained numerically in ref.⁸ by sampling the phase shift in 100 different cosmologies with varying free-streaming radiation density. The blue bands indicate the 1σ and 2σ contours in these measurements."<ref name=Baumann/> In the image on the right part (b), "Linear BAO spectrum O(k) [is] a function of the amplitude of the phase shift β."<ref name=Baumann/> {{clear}} ==Active galactic nuclei== {{main|Radiation astronomy/Active galactic nuclei}} [[Image:3c111 lo.jpg|thumb|right|250px|The image contains a series of radio images at successive epochs using the VLBA of the jet in the broad-line radio galaxy 3C 111. Credit: M. Kadler, E. Ros, M. Perucho, Y. Y. Kovalev, D. C. Homan, I. Agudo, K. I. Kellermann, M. F. Aller, H. D. Aller, M. L. Lister, and J. A. Zensus.{{tlx|fairuse}}]] There is "a correlation between the arrival directions of cosmic rays with energy above 6 x 10¹⁹ electron volts and the positions of active galactic nuclei (AGN) lying within ~75 megaparsecs."<ref name="Abraham">{{cite journal |author=J Abraham |author2=P Abreu |author3=M Aglietta |author4=C Aguirre |author5=D Allard |author6=The Pierre Auger Collaboration |title=Correlation of the highest-energy cosmic rays with nearby extragalactic objects |journal=Science |month=November 9, |year=2007 |volume=318 |issue=5852 |pages=938-43 |url=http://www.sciencemag.org/content/318/5852/938.full |arxiv=0711.2256 |bibcode=2007Sci...318..938T |doi=10.1126/science.1151124 |pmid= |accessdate=2013-11-04 }}</ref> Some low energy cosmic rays originate or are associated with solar flares. Even these cosmic rays have too high an energy to originate from the solar photosphere. The [[coronal cloud]] in close proximity to the [[Stars/Sun|Sun]] may be a source or create them as it bombards the chromosphere from above. "In particular we recognize a first trace of Vela, brightest gamma and radio galactic source, and smeared sources along Galactic Plane and Center [as a source of ultra high energy cosmic rays (UHECR)]."<ref name="Fargion">{{cite journal |author=Daniele Fargion |title=UHECR besides ''Cen''_''A'': Hints of galactic sources |journal=Progress in Particle and Nuclear Physics |month=April |year=2010 |volume=64 |issue=2 |pages=363-5 |url=http://www.sciencedirect.com/science/article/pii/S0146641009001276 |arxiv=0911.4176 |bibcode=2010PrPNP..64..363F |doi=10.1016/j.ppnp.2009.12.049 |pmid= |accessdate=2014-01-09 }}</ref> "The main correlated map is the 408 MHz one. The first astronomical source that seem to correlate is the main multiplet along ''Cen''_''A''. This AGN source, the nearest extragalactic one, sits in the same direction of a far Centaurus Cluster (part of the Super-Galactic Plane). The blurring by random galactic magnetic field might spread the nearest AGN event along the same Super-Galactic Plane, explaining the AUGER group miss-understanding [3]."<ref name="Fargion"/> {{clear}} ==Aerometeors== {{main|Radiation astronomy/Aerometeors}} [[Image:April18 AR.gif|right|thumb|300px|An atmospheric river forms over Hawai'i then heads toward California 10-11 April 2017. Credit: UW-CIMSS.{{tlx|fairuse}}]] "Several times a year an atmospheric river [shown in the image on the right forming over Hawai'i]—a long, narrow conveyor belt of storms that stream in relentlessly from the Pacific Ocean—drops inches of rain or feet of snow on the U.S. west coast. Such a system triggered floods and mudslides in central and southern California this past weekend [2-3 February 2019]."<ref name=Fischetti>{{ cite book |author=Mark Fischetti |title=Warning Scale Unveiled for Dangerous Rivers in the Sky |publisher=Scientific American |location= |date=February 5, 2019 |url=https://www.scientificamerican.com/article/warning-scale-unveiled-for-dangerous-rivers-in-the-sky/ |accessdate=8 February 2019 }}</ref> "Atmospheric rivers flow through the sky about a mile above the ocean surface, and may extend across a thousand miles of ocean to the coast. Some bring routine rain but the more intense systems can carry as much water as 15 Mississippi Rivers. The series of storms striking land can arrive for days or, occasionally, weeks on end. They hit west-facing coastlines worldwide, although the U.S. experiences more than most other national coasts."<ref name=Fischetti/> The “atmospheric river scale” "ranks severity and impacts, from category 1 (weak) to category 5 (exceptional)."<ref name=Fischetti/> "Without a scale, we really had no way to objectively communicate what would be a strong storm or a weak one."<ref name=Ralph>{{ cite book |author=Martin Ralph |title=Warning Scale Unveiled for Dangerous Rivers in the Sky |publisher=Scientific American |location= |date=February 5, 2019 |url=https://www.scientificamerican.com/article/warning-scale-unveiled-for-dangerous-rivers-in-the-sky/ |accessdate=8 February 2019 }}</ref> "Scientists, the media and the public viewed atmospheric rivers as primarily a hazard, but the weaker ARs are quite beneficial. Water managers made it clear to us that a rating scale would be helpful."<ref name=Ralph/> "The scale, published Tuesday in the ''Bulletin of the American Meteorological Society'', ranks atmospheric rivers on five levels:"<ref name=Fischetti/> * Category 1: Weak—primarily beneficial * Category 2: Moderate—mostly beneficial, but also somewhat hazardous * Category 3: Strong—balance of beneficial and hazardous * Category 4: Extreme—mostly hazardous, but also beneficial (if persistent drought) * Category 5—Exceptional—primarily hazardous {{clear}} ==Alpha particles== {{main|Radiation astronomy/Alpha particles}} [[Image:Alpha particle and electrons from a thorium rod in a cloud chamber.jpg|thumb|right|250px|Alpha particle is detected in an isopropanol cloud chamber. Credit: [[c:user:Cloudylabs|Cloudylabs]].]] Regarding alpha particles, as with beta and gamma particles/rays, the name used for the particle carries some mild connotations about its production process and energy, but these are not rigorously applied.<ref>{{ Cite journal |last=Darling |first=David |date= |title=Alpha particle |url=http://www.daviddarling.info/encyclopedia/A/alphapart.html |journal=Encyclopedia of Science |accessdate=7 December 2010 |archiveurl=https://web.archive.org/web/20101214053417/http://daviddarling.info/encyclopedia/A/alphapart.html |archivedate=14 December 2010 }}</ref> {{clear}} ==Asteroids== {{main|Radiation astronomy/Asteroids}} [[Image:Asteroids by size and number.svg|center|thumb|500px|Asteroids in the solar system are categorized by size and number. Credit: Marco Colombo, DensityDesign Research Lab.{{tlx|free media}}]] The center image is a log-log plot of frequency vs. size for asteroids in the solar system. {{clear}} ==Atomics== {{main|Radiation astronomy/Atomics}} [[Image:Neutrons strip2.jpg|thumb|right|250px|The image shows the hydrogen concentrations on the Moon detected by the Lunar Prospector. Credit: NASA.]] Atomics are usually neutral atoms and molecules of a few atoms. At right is the result of an all Moon survey by the Lunar Prospector using an onboard neutron spectrometer (NS). Cosmic rays impacting the lunar surface generate neutrons which in turn loose much of their energy in collisions with hydrogen atoms trapped within the Moon's surface.<ref name=Williams/> Some of these thermal neutrons collide with the helium atoms within the NS to yield an energy signature which is detected and counted.<ref name=Williams/> The NS aboard the Lunar Prospector has a surface resolution of 150 km.<ref name=Williams>{{ cite book |author=David R. Williams |title=Lunar Prospector Neutron Spectrometer (NS) |publisher=National Aeronautics and Space Administration |location=Goddard Space Flight Laboratory |date=November 2011 |url=http://nssdc.gsfc.nasa.gov/nmc/experimentDisplay.do?id=1998-001A-02 |accessdate=2012-01-11 }}</ref> {{clear}} ==Backgrounds== {{main|Radiation astronomy/Backgrounds}} [[Image:Extragalactic-background-power-density.jpg|thumb|right|250px|This graph shows the power density spectrum of the extragalactic or cosmic gamma-ray background (CGB). Credit: pkisscs@konkoly.hu.{{tlx|free media}}]] In the figure at right, CUVOB stands for the cosmic ultraviolet and optical background. The diffuse '''extragalactic background light''' (EBL) is all the accumulated radiation in the Universe due to star formation processes, plus a contribution from [[w:active galactic nuclei|active galactic nuclei]] (AGNs). This [[Draft:Keynote lectures/Radiation|radiation]] covers the wavelength range between ~ 0.1-1000 microns (these are the [[Ultraviolet astronomy|ultraviolet]], [[Optical astronomy|optical]], and [[Infrared astronomy|infrared]] regions of the electromagnetic spectrum). The EBL is part of the diffuse extragalactic background radiation (DEBRA), which by definition covers the overall electromagnetic spectrum. After the cosmic microwave background, the EBL produces the second-most energetic diffuse background, thus being essential for understanding the full energy balance of the universe. {{clear}} ==Bands== {{main|Radiation astronomy/Bands}} [[Image:Saturn H2On.jpg|thumb|right|250px|This is Saturn imaged with the Stockholm Infrared Camera (SIRCA) in the H₂O band. Credit: M. Gålfalk, G. Olofsson and H.-G. Florén, Nordic Optical Telescope.{{tlx|fairuse}}]] At the right is Saturn imaged by the Stockholm Infrared Camera (SIRCA) in the H₂O infrared band to show the presence of water vapor. The image is cut off near the top due to the presence of Saturn's rings. The Sun's emission in the lowest UV bands, the UVA, UVB, and UVC bands, are of interest, as these are the UV bands commonly encountered from artificial sources on Earth. The shorter bands of UVC, as well as even more energetic radiation as produced by the Sun, generate the ozone in the ozone layer when single oxygen atoms produced by UV photolysis of dioxygen react with more dioxygen. The ozone layer is especially important in blocking UVB and part of UVC, since the shortest wavelengths of UVC (and those even shorter) are blocked by ordinary air. {{clear}} ==Baryons== {{main|Radiation astronomy/Baryons|Baryons}} [[Image:652977main gle-20120523-12.10.22PM.jpg|thumb|right|250px|"This graph shows the neutrons detected by a neutron detector at the University of Oulu in Finland from May 16 through May 18, 2012. The peak on May 17 represents an increase in the number of neutrons detected, a phenomenon dubbed a ground level enhancement or GLE. This was the first GLE since December of 2006. Credit: University of Oulu/NASA's Integrated Space Weather Analysis System"<ref name=Fox>{{ cite book |author=Karen C. Fox |title=Science Nugget: Catching Solar Particles Infiltrating Earth's Atmosphere |publisher=NASA Goddard Space Flight Center |location=Greenbelt, Maryland |date=May 31, 2012 |url=http://www.nasa.gov/mission_pages/sunearth/news/particles-gle.html |accessdate=2012-08-17 }}</ref>.{{tlx|free media}}]] A '''baryon''' is a composite subatomic particle bound together by the strong interaction, whereas leptons are not. The most familiar baryons are the protons and neutrons that make up most of the mass of the visible matter in the universe. Electrons (the other major component of the atom) are leptons. Each baryon has a corresponding antiparticle (antibaryon). Baryonic matter is matter composed mostly of baryons (by mass), which includes atoms of any sort (and thus includes nearly all matter that may be encountered or experienced in everyday life). {{clear}} ==Beta particles== {{main|Radiation astronomy/Beta particles}} [[Image:How thunderstorms launch particle beams into space 300dpi.jpg|thumb|right|300px|The simulation attempts to answer how thunderstorms launch particle beams into space. Credit: NASA/Goddard Space Flight Center.{{tlx|free media}}]] A number of subatomic reactions can be detected in astronomy that yield beta particles. The detection of beta particles or the reactions that include them in an astronomical situation is '''beta-particles astronomy'''. '''Beta particles''' are high-energy, high-speed electrons or positrons. Beta particles may be the key to fusion. "If the exterior of the capsule is maintained at a uniform temperature of about 19.5 K, the natural beta decay energy of the tritium will accomplish this through a process known as "beta layering." The very low energy beta particles from tritium decay deposit their energy very close to the location of the original tritium atoms."<ref name="Schultz">{{cite journal |author=K. R. Schultz |title=Cost Effective Steps to Fusion power: IFE target fabrication, injection and tracking |journal=Journal of Fusion Energy |month=September |year=1998 |volume=17 |issue=3 |pages=237-46 |url=http://www.springerlink.com/content/r7u527p786144l7k/ |arxiv= |bibcode= |doi=10.1023/A:1021814514091 |pmid= |accessdate=2012-06-08 }}</ref> "Beta-particles leaving the upper surface of the lunar sample could trigger the upper beta detector, while the lower beta-detector was triggered by beta particles from the lower surface of the sample."<ref name="Rancitelli">{{cite journal |author=L. A. Rancitelli |author2=R. W. Perkins |author3=W. D. Felix |author4=N. A. Wogman |title=Erosion and mixing of the lunar surface from cosmogenic and primordial radio-nuclide measurements in Apollo 12 lunar samples |journal=Proceedings of the Lunar Science Conference |month= |year=1971 |volume=2 |issue= |pages=1757-72 |url=http://adsabs.harvard.edu/full/1971LPSC....2.1757R |arxiv= |bibcode=1971LPSC....2.1757R |doi= |pmid= |accessdate=2012-06-08 }}</ref> '''Notation''': let the symbol β⁻ designate an unbound electron in motion. '''Notation''': let β⁺ designate an unbound positron in motion. '''Notation:''' let '''TGF''' stand for a '''Terrestrial Gamma-ray Flash'''. {{clear}} ==Blues== {{main|Radiation astronomy/Blues|Blue astronomy}} [[Image:Neptune.jpg|thumb|right|250px|This picture from the Voyager 2 sequence shows two of the four cloud features which have been tracked by the Voyager cameras during the past two months. Credit: NASA.{{tlx|free media}}]] '''Blue astronomy''' is focused on the wavelength range 450-475 nm. Stars are often referred to by their predominant color. For example, '''blue stragglers''' are found among the galactic halo globular clusters.<ref name="Preston">{{cite journal |author=Preston, G. W. |author2=Beers, T. C. |author3=Shectman, S. A. |title=The Space Density and Kinematics of Metal-Poor Blue Main Sequence Stars Near the Solar Circle |journal=Bulletin of the American Astronomical Society |month=December |year=1993 |volume=25 |issue=12 |pages=1415 |url= |arxiv= |bibcode=1993BAAS...25Q1415P |doi= |pmid= |accessdate=2011-11-24 }}</ref> Blue main sequence stars that are metal poor ([Fe/H] ≤ -1.0) are most likely very different in origin from blue stragglers.<ref name="Preston"/> "[G]round-based UV [and blue astronomy] is a powerful facility for [the] study of [the] chemical evolution of [the] early Galaxy."<ref name="Klochkova">{{cite book |author=Klochkova, Valentina |author2=Ermakov, Sergey |author3=Panchuk, Vladimir |author4=Zhao, Gang |title=High resolution spectroscopy of halo stars within the spectral region 3550-5000 °A°A, In: ''UV Astronomy: Stars from Birth to Death. Proceedings of the Joint Discussion n.4 during the IAU general Assembly of 2006'' |publisher=International Astronomical Union |location= |date=July 2007 |editor=Ana I. Gómez de Castro |editor2=Martin A. Barstow |pages=161 |url= |bibcode=2007uasb.conf..161K |doi= |pmid= |isbn=978-84-7491-852-6 }}</ref> UV and B astronomy use radiation over the wavelength range 355.0-500.0 nm.<ref name="Klochkova"/> “To date, all of the reported hypervelocity stars (HVSs), which are believed to be ejected from the Galactic center, are blue and therefore almost certainly young.”<ref name="Kollmeier">{{cite journal |author=Juna A. Kollmeier |author2=Andrew Gould |title=Where Are the Old-Population Hypervelocity Stars? |journal=The Astrophysical Journal |month=July 20, |year=2007 |volume=664 |issue=1 |pages=343-8 |url=http://iopscience.iop.org/0004-637X/664/1/343 |arxiv= |bibcode= |doi=10.1086/518405 |pmid= |accessdate=2012-03-05 }}</ref> A trace amount of methane is also present. Prominent absorption bands of methane occur at wavelengths above 600&nbsp;nm, in the red and infrared portion of the spectrum. As with Uranus, this absorption of red light by the atmospheric methane is part of what gives Neptune its blue hue,<ref name="Crisp">{{cite web |author=D. Crisp |author2=H. B. Hammel |date=June 14, 1995 |url =http://hubblesite.org/newscenter/archive/releases/1995/09/image/a/ |title =Hubble Space Telescope Observations of Neptune |publisher = Hubble News Center |accessdate = April 22, 2007 }}</ref> although Neptune's vivid azure differs from Uranus's milder cyan. Since Neptune's atmospheric methane content is similar to that of Uranus, some unknown atmospheric constituent is thought to contribute to Neptune's colour.<ref name="Munsell">{{cite book |author=Kirk Munsell |author2=Harman Smith |author3=Samantha Harvey |date=November 13, 2007 |url=http://solarsystem.nasa.gov/planets/profile.cfm?Object=Neptune&Display=OverviewLong |title=Neptune overview, In: ''Solar System Exploration'' |publisher=NASA |accessdate=February 20, 2008 }}</ref> {{clear}} ==Chemicals== {{main|Radiation astronomy/Chemistry|Radiation chemistry}} [[Image:Atmospheric Water Vapor Mean.2005.030.jpg|thumb|right|250px|This is a graph of the global mean atmospheric water vapor superimposed on an outline of the Earth. Credit: NASA.]] The study of the abundance and reactions of chemical elements and molecules in the universe, as can be assessed by their interaction with radiation is part of astronomical '''[[radiation chemistry]]''', or '''radiation [[Introduction to Astrochemistry|astrochemistry]]'''. {{clear}} ==Clouds== {{main|Radiation astronomy/Clouds}} [[Image:Img20050526 0007 at tannheim cumulus.jpg|thumb|right|250px|This image shows a cumulus cloud above Lechtaler Alps, Austria. Credit: [[c:User:Glg|Glg]].{{tlx|free media}}]] [[Image:Cumulus clouds in fair weather.jpeg|thumb|left|250px|Cumulus clouds in fair weather are white. Credit: [http://legacy.openphoto.net/image_view.html?image_id=17977 Michael Jastremski].{{tlx|free media}}]] '''Def.''' a "large white puffy cloud"<ref name=CumulusWikt>{{ cite web |title=cumulus |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=February 8, 2013 |url=http://en.wiktionary.org/wiki/cumulus |accessdate=2013-02-17 }}</ref> is called a '''cumulus''' cloud. Cumulus clouds look white because the water droplets reflect and scatter the sunlight without absorbing other colors. "On any given day, about half of Earth is covered by clouds, which reflect more sunlight than land and water. Clouds keep Earth cool by reflecting sunlight, but they can also serve as blankets to trap warmth."<ref name="livescience">{{ cite web |url=http://www.livescience.com/environment/060124_earth_albedo.html |title=Baffled Scientists Say Less Sunlight Reaching Earth |publisher=LiveScience |date=2006-01-24 |accessdate=2011-08-19 }}</ref> {{clear}} ==Colors== {{main|Radiation astronomy/Colors}} [[Image:Gammaspektrum Uranerz.jpg|thumb|right|250px|This gamma-ray spectrum contains the typical isotopes of the uranium-radium decay line. Credit: [[c:User:Wusel007|Wusel007]].{{tlx|free media}}]] The peak at 40 keV is not from the mineral. From the color of the rock shown the yellowish mineral is likely to be autunite. Autunite occurs as an oxidizing product of uranium minerals in granite pegmatites and hydrothermal deposits. {{clear}} ==Comets== {{main|Radiation astronomy/Comets}} [[Image:Rosetta OSIRIS NAC comet 67P 20140803 2 625.jpg|thumb|right|250px|This image shows Comet 67P/Churyumov-Gerasimenko. Credit: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/ UPM/DASP/IDA.]] [[Image:Rosetta OSIRIS NAC comet 67P 20140803 1 625.jpg|thumb|left|250px|This image shows Comet 67P/Churyumov-Gerasimenko rotated around a vertical axis from the right. Credit: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/ UPM/DASP/IDA.]] The image at the right is an optical astronomy image of the comet 67P/Churyumov-Gerasimenko. Rosetta's OSIRIS narrow-angle camera made the image on 3 August 2014 from a distance of 285 km. The image resolution is 5.3 metres/pixel. The left image is rotated 90° from the right. The location of the right image is the front view of the left side just out of view in the left image. The object rotates by the right hand rule from the left image to the right. Note that due to the evaporation of volatiles, the surface of the rocky object appears pitted or cratered. {{clear}} ==Continua== {{main|Radiation astronomy/Continua}} [[Image:Venus Transit Baader Herschel Wedge Continuum Filter 8421 - 5 June 2012.jpg|right|thumb|300px|The 15" refractor at Comanche Springs Astronomy Campus had its finder scope (a Stellarvue 80/9D achromat) equipped with a Baader Herschel Solar Wedge and a Solar Continuum Filter for today's transit of Venus. Credit: [https://www.flickr.com/people/79653922@N00 Jeff Barton from Richardson, TX, USA].{{tlx|free media}}]] Lyc photon or Ly continuum photon or Lyman continuum photon are a kind of photon emitted from stars. Hydrogen is ionized by absorption of Lyc photons. Lyc photons are in the ultraviolet portion of the electromagnetic spectrum of the hydrogen atom and immediately next to the limit of the Lyman series of the spectrum with wavelengths that are shorter than 91.1267 nanometres and with energy above 13.6 eV. {{clear}} ==Cosmic rays== {{main|Radiation/Cosmic rays}} [[Image:NeutronMonitor.GIF|right|thumb|400px|Cosmic Ray Intensity (blue) and Sunspot Number (green) is shown from 1951 to 2006 Credit: University of New Hampshire.{{tlx|fairuse}}]] The graph on the right shows an inverse correlation between sunspot numbers (solar activity) and neutron production from galactic cosmic rays. There is "a correlation between the arrival directions of cosmic rays with energy above 6 x 10¹⁹ electron volts and the positions of active galactic nuclei (AGN) lying within ~75 megaparsecs."<ref name="Abraham"/> The '''Oh-My-God particle''' was observed on the evening of 15 October 1991 over Dugway Proving Ground, Utah. Its observation was a shock to astrophysicists, who estimated its energy to be approximately {{val|3|e=20|u=eV}}<ref name="Baez">[http://www.desy.de/user/projects/Physics/General/open_questions.html Open Questions in Physics.] German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.</ref>(50&nbsp;joules)&mdash;in other words, a subatomic particle with kinetic energy equal to that of a baseball (142&nbsp;g or 5&nbsp;oz) traveling at 100&nbsp;km/h (60&nbsp;mph). It was most probably a proton with a speed very close to the [[w:speed of light|speed of light]], so close, in fact, [(1 − {{val|5|e=-24}}) &times; ''c''], that in a year-long race between light and the cosmic ray, the ray would fall behind only 46 nanometers ({{val|5|e=-24}} light-years), or 0.15 femtoseconds ({{val|1.5|e=-16|u=s}}).<ref name="Walker"> {{cite web | author=J. Walker | date=January 4, 1994 | title=The Oh-My-God Particle | url=http://www.fourmilab.ch/documents/OhMyGodParticle/ | publisher=Fourmilab }}</ref> {{clear}} ==Cryometeors== {{main|Radiation astronomy/Cryometeors}} [[Image:Malaspina Glacier in Southeastern Alaska.jpg|thumb|right|300px|Malaspina Glacier in southeastern Alaska is considered the classic example of a piedmont glacier. Credit: NASA.]] A cryometeor is a meteor of variable size that has been radiated and is still moving composed of ice, e.g. water or methane ice. A cryometeor that has stopped moving has become a cryometeorite. '''Def.''' a glacier that occurs on a gentle slope leading from the base of mountains to a region of flat land, any region of foothills of a mountain range, or formed or lying at the foot of a mountain range is called a '''piedmont glacier'''. {{clear}} ==Cyans== {{main|Radiation astronomy/Cyans|Cyan astronomy}} [[Image:C2007N3Lulin2panel brimacombe.jpg|thumb|right|250px|Recent changes in Comet Lulin's greenish coma and tails are shown in these two panels taken on January 31st (top) and February 4th (bottom) 2009. In both views the comet has an apparent antitail to the left of the coma of dust. Credit: Joseph Brimacombe, Cairns, Australia.{{tlx|free media}}]] Perhaps the most prominent cyan planetary source is Uranus, which has only been visited by the space probe Voyager 2. More recent images come from the Hubble Space Telescope in orbit around Earth. Methane possesses prominent absorption bands in the visible and near-infrared (IR) making Uranus [[w:aquamarine (color)|aquamarine]] or cyan in color.<ref name="Lunine">{{cite journal |title=The Atmospheres of Uranus and Neptune |author=Jonathan I. Lunine |journal = Annual Review of Astronomy and Astrophysics |volume=31 |pages=217–263 |year=1993 |doi=10.1146/annurev.aa.31.090193.001245 | bibcode=1993ARA&A..31..217L }}</ref> “During the Halley Monitoring Program at La Silla from Feb.17 to Apr.17,1986 ... In the light of the neutral CN-radical a continuous formation and expansion of [cyan] gas-shells could be observed.”<ref name="Schlosser">{{cite book |author=Wolfhard Schlosser |author2=Rita Schulz |author3=Paul Koczet |title=The cyan shells of Comet P/Halley, In: ''Proceedings of the 20th ESLAB Symposium on the Exploration of Halley's Comet'' |publisher=European Space Agency |location= |date=1986 |volume=3 |editor= |pages=495-8 |url= |arxiv= |bibcode=1986ESASP.250c.495S |doi= |pmid= |isbn= }}</ref> “The gas-expansion velocity decreases with increasing heliocentric distance from 1 km/s in early March to 0.8 km/s in April.”<ref name="Schlosser"/> Shown at right, "Lulin's green color comes from the gases that make up its Jupiter-sized atmosphere. Jets spewing from the comet's nucleus contain cyanogen (CN: a poisonous gas found in many comets) and diatomic carbon (C₂). Both substances glow green when illuminated by sunlight"<ref name="Phillips">{{cite book |author=James A. Phillips |title=Green Comet Approaches Earth |publisher=National Aeronautics and Space Administration Science News |location= |date=2009 |url=http://science.nasa.gov/science-news/science-at-nasa/2009/04feb_greencomet/ |accessdate=2012-05-05 }}</ref> The electric blue glow of electricity results from the spectral emission of the excited ionized atoms (or excited molecules) of air (mostly oxygen and nitrogen) falling back to unexcited states, which happens to produce an abundance of electric blue light. This is the reason electrical sparks in air, including lightning, appear electric blue. It is a coincidence that the color of Cherenkov radiation and light emitted by ionized air are a very similar blue despite their very different methods of production. {{clear}} ==Detectors== {{main|Radiation astronomy/Detectors}} [[Image:Detectors summary 3.png|thumb|right|250px|This tree diagram shows the relationship between types and classification of most common particle detectors. Credit: [[commons:User:Wdcf|Wdcf]].{{tlx|free media}}]] '''Radiation detectors''' provide a signal that is converted to an electric current. The device is designed so that the current provided is proportional to the characteristics of the incident radiation. There are detectors that provide a change in substance as the signal and these may be automated to provide an electric current or quantified proportional to the amount of new substance. {{clear}} ==Distributionals== {{main|Radiation astronomy/Distributionals}} [[Image:Electronic nuclear stopping Al in Al.png|thumb|right|250px|Diagram shows the electronic and nuclear stopping power for aluminum ions in aluminum. Credit: HPaul.]] [[Image:Ion slowing.png|thumb|right|250px|This is an illustration of the slowing down of a single ion in a solid material. Credit: Kai Nordlund.]] [[Image:Bragg Curve for Alphas in Air.png|thumb|right|250px|A Bragg curve of 5.49 MeV alpha particles in air is illustrated. Credit: Helmut Paul.]] '''Def.''' a "frequency of occurrence or extent of existence"<ref name=DistributionWikt>{{ cite web |author=[[wikt:User:JamesR1701E~enwiktionary|JamesR1701E~enwiktionary]] |title=distribution |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=4 August 2004 |url=https://en.wiktionary.org/wiki/distribution |accessdate=23 December 2019 }}</ref> or "the relative arrangements of the elements of a statistical population based on some criterion, as frequency, time, or location"<ref name=DistributionWikt/> is called a '''distribution'''. '''Def.''' "the fraction of photoelectric events which end up in the photopeak of the measured energy spectrum"<ref name="Krawczynski">{{cite book |author=Henric S. Krawczynski |author2=Ira Jung |author3=Jeremy S. Perkins |author4=Arnold Burger |author5=Michael Groza |title=Thick CZT Detectors for Space-Borne X-ray Astronomy, In: ''Hard X-Ray and Gamma-Ray Detector Physics VI, 1'' |publisher=The International Society for Optical Engineering |location=Denver, Colorado USA |date=October 21, 2004 |volume=5540 |issue= |pages=13 |url=http://arxiv.org/pdf/astro-ph/0410077 |arxiv=astro-ph/0410077 |bibcode= |doi=10.1117/12.558912 |pmid= |accessdate=2013-05-20 }}</ref> is called the '''photopeak efficiency''' (ε). Ending up in the photopeak means within ± 1 full-width at half maximum (FWHM) of the peak of the distribution.<ref name="Krawczynski"/> "The peak to valley ratio is commonly used as a token for ε."<ref name="Krawczynski"/> "Another common practice is to fit an exponential function to the “valley” and to extrapolate the fit to lower pulse heights to estimate the fraction of counts hidden in the Compton continuum."<ref name="Krawczynski"/> "We have used a calibrated Cs¹³⁷ source to determine the absolute photopeak efficiency at 662 keV. The source was placed at a sufficiently large distance from the detector so that the event rate was low and the dead time was less than 20%. Based on a log-histogram of the time intervals between events, the dead-time has been estimated to a fractional accuracy of better than 5%. We determine the photopeak efficiency by comparing the dead-time corrected event rate in the photopeak with the theoretical expectation assuming a perfect detector."<ref name="Krawczynski"/> '''Def.''' the average energy loss of the particle per unit path length is called the '''stopping power'''. '''Def.''' the slowing down of a projectile ion due to the inelastic collisions between bound electrons in the medium and the ion moving through it is called the '''electronic stopping power'''. '''Def.''' the elastic collisions between the projectile ion and atoms in the sample involving the interaction of the ion with the ''nuclei'' in the target is called the '''nuclear stopping power'''. The second figure on the right shows the electronic and nuclear stopping power of aluminum single crystal for aluminum ions. These stopping powers are versus particle energy per nucleon. The maximum of the nuclear stopping curve typically occurs at energies of the order of 1 keV per nucleon. The second figure at right illustrates the slowing down of a single ion in a solid material. In the beginning of the slowing-down process at high energies, the ion is slowed down mainly by electronic stopping, and it moves almost in a straight path. When the ion has slowed down sufficiently, the collisions with nuclei (the nuclear stopping) become more and more probable, finally dominating the slowing down. When atoms of the solid receive significant recoil energies when struck by the ion, they will be removed from their [[w:crystal structure|lattice]] positions, and produce a [[w:collision cascade|cascade of further collisions]] in the material. These [[w:collision cascade|collision cascade]]s are the main cause of damage production during ion implantation in metals and semiconductors. When the energies of all atoms in the system have fallen below the [[w:threshold displacement energy|threshold displacement energy]], the production of new damage ceases, and the concept of nuclear stopping is no longer meaningful. The total amount of energy deposited by the nuclear collisions to atoms in the materials is called the nuclear deposited energy. The inset in the figure shows a typical range distribution of ions deposited in the solid. The case shown here might for instance be the slowing down of a 1 MeV silicon ion in silicon. The mean range for a 1 MeV ion is typically in the micrometer range. Third right is an illustration of a ''Bragg'' curve. The '''stopping power''' and hence, the density of ionization, usually increases toward the end of range and reaches a maximum, the Bragg peak, shortly before the energy drops to zero. {{clear}} ==Electromagnetic forces== {{main|Charges/Interactions/Electromagnetics}} [[Image:PKS0521-36 2 cm.gif|thumb|right|250px|The electric vectors of PKS0521-36 show clear structure and alignment. Credit: Keel.{{tlx|fairuse}}]] "The emission of electromagnetic radiation from a superluminal (faster-than-light in vacuo) charged particle [is such] that no physical principle forbids emission by extended, massless superluminal sources. A polarization current density (d'''P'''/dt; see Maxwell's fourth equation) can provide such a source; the individual charged particles creating the polarization do not move faster than c, the speed of light, and yet it is relatively trivial to make the envelope of the polarization current density to do so."<ref name="Singleton">{{cite book |author=J. Singleton |author2=A. Ardavan |author3=H. Ardavan |author4=J. Fopma |author5=D. Halliday |title=Non-spherically-decaying radiation from an oscillating superluminal polarization current: possible low-power, deep-space communication applications in the MHz and THz bands, ''16th International Symposium on Space Terahertz Technology'' |volume= |publisher= |location= |date=2005 |editor= |pages=117 |url=http://www.nrao.edu/meetings/isstt/papers/2005/2005117000.pdf |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2014-03-18 }}</ref> The "emitted radiation has many unusual characteristics, including: (i) the intensity of some components decays as the inverse of the distance from the source, rather than as 1/(distance)2 (i.e. these components are non-spherically-decaying); (ii) the emission is tightly beamed, the exact direction of the beam depending on the source speed; and (iii) the emission contains very high frequencies not present in the synthesis of the source. Note that the non-spherically decaying components of the radiation do not violate energy conservation. They result from the reception, during a short time period, of radiation emitted over a considerably longer period of (retarded) source time; their strong electromagnetic fields are compensated by weak fields elsewhere [1]."<ref name="Singleton"/> The "emission occupies a very small polar angular width of order 0.8 degrees in the far field. Based on these findings, we suggest that a superluminal source could act as a highly directional transmitter of MHz or THz signals over very long distances."<ref name="Singleton"/> "The magnetic field is well-ordered in many jets, as shown by polarization measurements. Synchrotron radiation can be very highly polarized (50%) if the field is globally ordered, and some sources [approach] this level. The electric vectors show clear structure and alignment; an especially common pattern is for the field lines to be along the jet in the inner portions and transition to an azimuthal configuration farther out. This is seen in [PKS0521-36 at 2 cm]."<ref name="Keel">{{cite book |author=Bill Keel |title=Jets, Superluminal Motion, and Gamma-Ray Bursts |publisher=University of Arizona |location=Tucson, Arizona USA |date=October 2003 |url=http://www.astr.ua.edu/keel/galaxies/jets.html |accessdate=2014-03-19 }}</ref> {{clear}} ==Electromagnetics== {{main|Radiation astronomy/Electromagnetics|Electromagnetics}} [[Image:Glowing Stellar Nurseries.jpg|thumb|right|250px|This is a colour composite image of RCW120. Credit: ESO/APEX/DSS2/ SuperCosmos/ Deharveng(LAM)/ Zavagno(LAM).{{tlx|free media}}]] Radiation astronomy is often performed using electromagnetics. Electromagnetics are most familiar as light, or electromagnetic radiation. The image at right is a colour "composite image of RCW120. It reveals how an expanding bubble of ionised gas about ten light-years across is causing the surrounding material to collapse into dense clumps where new stars are then formed. The 870-micron submillimetre-wavelength data were taken with the LABOCA camera on the 12-m Atacama Pathfinder Experiment (APEX) telescope. Here, the submillimetre emission is shown as the blue clouds surrounding the reddish glow of the ionised gas (shown with data from the SuperCosmos H-alpha survey). The image also contains data from the Second Generation Digitized Sky Survey (I-band shown in blue, R-band shown in red)."<ref name="Deharveng">{{cite book |author= Deharveng |title=Glowing Stellar Nurseries |publisher=European Southern Observatory |location= |date=November 11, 2008 |url=http://www.eso.org/public/images/eso0840a/ |accessdate=2014-03-13 }}</ref> '''Electromagnetic radiation astronomy''' is a broader concept, physics subject heading used by the American Physical Society (APS).<ref name=APS>{{ cite book |author=APS |title=Physics Subject Headings |publisher=American Physical Society |location=College Park, MD |date= |editor= |pages= |url=https://physh.aps.org/concepts/893ecc24-c678-4687-bd3a-0b4a1bcb4cfc |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2018-01-08 }}</ref> {{clear}} ==Electrons== {{main|Radiation astronomy/Electrons|Electron astronomy}} [[Image:Aurore australe - Aurora australis.jpg|thumb|right|250px|Aurorae are mostly caused by energetic electrons precipitating into the atmosphere.<ref name="Wolpert">{{cite book | author = S. Wolpert | date = July 24, 2008 | title = Scientists solve 30-year-old aurora borealis mystery | url = http://www.universityofcalifornia.edu/news/article/18277 | publisher = University of California | accessdate = 2008-10-11 }}</ref> Credit: [[commons:User:Ehquionest|Samuel Blanc]][http://www.sblanc.com/].{{tlx|free media}}]] Although '''[[electron astronomy]]''' is usually not recognized as a formal branch of astronomy, the measurement of electron fluxes help to understand a variety of natural phenomena. Particles such as electrons are used as tracers of cosmic magnetic fields.<ref name="Hudson">{{cite book |author=H. S. Hudson |author2=A. B. Galvin |title=Correlated Studies at Activity Maximum: the Sun and the Solar Wind, In: ''Correlated Phenomena at the Sun, in the Heliosphere and in Geospace'' |publisher=European Space Agency |location=Noordwijk, The Netherlands |date=September 1997 |editor=A. Wilson |pages=275-82 |url= |bibcode=1997ESASP.415..275H |doi= |pmid= |isbn=92-9092-660-0 }}</ref> "From a plasma-physics point of view, the particles represent the correct way to identify magnetic field lines."<ref name="Hudson"/> "The suprathermal electrons in the solar wind and in solar particle events have excellent properties for this application: they move rapidly, they remain tightly bound to their field lines, and they may arrive "scatter-free" even at low energies, and from deep in the solar atmosphere (Lin 1985)."<ref name="Hudson"/> These electrons "provide remote-sensing observations of distant targets in the heliosphere - the Sun, the Moon, Jupiter, and various heliospheric structures."<ref name="Hudson"/> ""[E]lectron astronomy" has an interesting future".<ref name="Hudson"/> A '''delta ray''' is characterized by very fast electrons produced in quantity by alpha particles or other fast energetic charged particles knocking orbiting electrons out of atoms. Collectively, these electrons are defined as delta radiation when they have sufficient energy to ionize further atoms through subsequent interactions on their own. "The conventional procedure of delta-ray counting to measure charge (Powell, Fowler, and Perkins 1959), which was limited to resolution σ_z = 1-2 because of uncertainties of the criterion of delta-ray ranges, has been significantly improved by the application of delta-ray range distribution measurements for ¹⁶O and ³²S data of 200 GeV per nucleon (Takahashi 1988; Parnell ''et al.'' 1989)."<ref name="Burnett">{{cite journal |author=T. H. Burnett ''et al.'' |author2=The JACEE Collaboration |title=Energy spectra of cosmic rays above 1 TeV per nucleon |journal=The Astrophysical Journal |month=January |year=1990 |volume=349 |issue=1 |pages=L25-8 |url=http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990ApJ...349L..25B&link_type=GIF&db_key=AST |arxiv= |bibcode=1990ApJ...349L..25B |doi=10.1086/185642 |pmid= |pdf=http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990ApJ...349L..25B&link_type=ARTICLE&db_key=AST&high= |accessdate=2011-11-25 }}</ref> Here, the delta-ray tracks in emulsion chambers have been used for "[d]irect measurements of cosmic-ray nuclei above 1 TeV/nucleon ... in a series of balloon-borne experiments".<ref name="Burnett"/> {{clear}} ==Emissions== {{main|Radiation astronomy/Emissions}} [[Image:The Red Rectangle around the star HD 44179.jpg|thumb|right|250px|The Hubble Space Telescope [Advanced Camera for Surveys] ACS image has H-alpha emission of the Red Rectangle shown in blue. Credit: ESA/Hubble and NASA.{{tlx|free media}}]] "[T]he extended red emission (ERE) [is] observed in many dusty astronomical environments, in particular, the diffuse interstellar medium of the Galaxy. ... silicon nanoparticles provide the best match to the spectrum and the efficiency requirement of the ERE."<ref name="Witt">{{cite journal |author=Adolf N. Witt |author2=Karl D. Gordon |author3=Douglas G. Furton |title=Silicon Nanoparticles: Source of Extended Red Emission? |journal=The Astrophysical Journal Letters |month=July 1, |year=1998 |volume=501 |issue=1 |pages=L111-5 |url=http://iopscience.iop.org/1538-4357/501/1/L111 |arxiv=astro-ph/9805006 |bibcode= |doi=10.1086/311453 |pmid= |accessdate=2013-07-30 }}</ref> {{clear}} ==Empiricisms== {{main|Radiation astronomy/Empiricisms|Empirical radiation astronomy}} [[Image:Centre of the Milky Way.jpg|thumb|right|250px|The best empirical evidence that supermassive black holes do really exist is the orbits of these stars around the center of the [[Milky Way]]. Credit: Stefan Gillessen, Reinhard Genzel, Frank Eisenhauer, ESO.]] A list or catalog of the specific principles incorporated into the development of the various radiation astronomies may be helpful to students and researchers alike. These principles can be included in [[mathematical astronomy]], astrophysics, [[astrochemistry]], and theoretical radiation astronomy as summaries, or, a lecture on '''empirical radiation astronomy'''. {{clear}} ==Entities== {{main|Radiation astronomy/Entities}} [[Image:Johannes Vermeer - The Astronomer - 1668.jpg|thumb|right|250px|This is an image of Johannes Vermeer's ''The astronomer''. Credit: www.essentialvermeer.com : [http://www.essentialvermeer.com Home] : [http://www.essentialvermeer.com/catalogue/astronomer.html Info] : [http://www.essentialvermeer.com/catalogue_xxl/xxl_astronomer.jpg Pic].{{tlx|free media}}]] '''Radiation astronomy entities''', '''radiation entities''', are any astronomical persons or things that have separate and distinct existences in empirical, objective or conceptual reality. Some of them, like the astronomers of today, or at any time in the past, are relatively known. But there are many entities that are far less known or understood, such as the observers of ancient times who suggested that deities occupied the sky or the heavens. Likewise, these alleged deities may be entities, or perhaps something a whole lot less. Astronomical X-ray entities are often discriminated further into sources or objects when more information becomes available, including that from other radiation astronomies. A researcher who turns on an X-ray generator to study the X-ray emissions in a laboratory so as to understand an apparent astronomical X-ray source is an astronomical X-ray entity. So is one who writes an article about such efforts or a computer simulation to possibly represent such a source. "The X-ray luminosity of the [[dominant group]] [an entity] is an order of magnitude fainter than that of the X-ray jet."<ref name="Finoguenov">{{cite journal |author=A. Finoguenov |author2=M.G. Watson |author3=M. Tanaka |author4=C.Simpson |author5=M. Cirasuolo |author6=J.S. Dunlop |author7=J.A. Peacock |author8=D. Farrah |author9=M. Akiyama |author10=Y. Ueda |author11=V. Smolčič |author12=G. Stewart |author13=S. Rawlings |author14=C.vanBreukelen |author15=O. Almaini |author16=L.Clewley |author17=D.G. Bonfield |author18=M.J. Jarvis |author19=J.M. Barr |author20=S. Foucaud |author21=R.J. McLure |author22=K. Sekiguchi |author23=E. Egami |title=X-ray groups and clusters of galaxies in the Subaru-XMM Deep Field |journal=Monthly Notices of the Royal Astronomical Society |month=April |year=2010 |volume=403 |issue=4 |pages=2063-76 |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2010.16256.x/full |arxiv= |bibcode= |doi=10.1111/j.1365-2966.2010.16256.x |pmid= |pdf=http://arxiv.org/pdf/0912.0039 |accessdate=2011-12-09 }}</ref> {{clear}} ==Fieries== {{main|Radiation astronomy/Fieries}} [[Image:2013-02-15T101834Z 1461539070 GM1E92F1EHS01 RTRMADP 3 RUSSIA-METEORITE.JPG|thumb|right|350px|This is a fireball meteor trail with some burning still visible above the Urals city of Chelyabinsk, Russia, on February 15, 2013. Credit: Reuters/www.chelyabinsk.ru.]] On the right is a [[visual astronomy]] image of a fireball trail with some burning still visible from a meteor as it passed overhead in Chelyabinsk, Russia, on February 15, 2013. This image shows "[t]he trail of a falling object ... seen above the Urals city of Chelyabinsk [on] February 15, 2013".<ref name=Reuters>{{ cite book |author=Reuters |title=Meteorite hits central Russia, more than 500 people hurt |publisher=Yahoo! News |location=Chelyabinsk, Russia |date=February 15, 2013 |url=http://news.yahoo.com/photos/trail-falling-object-seen-above-urals-city-chelyabinsk-photo-101834569.html |accessdate=2013-02-15 }}</ref> {{clear}} ==Galaxies== {{main|Radiation astronomy/Galaxies}} [[Image:M81 wide Galex.jpg|thumb|right|250px|This Galaxy Evolution Explorer (GALEX) image of the spiral galaxy Messier 81 is in ultraviolet light. Credit: NASA/JPL-Caltech/J. Huchra (Harvard-Smithsonian CfA).{{tlx|free media}}]] The radiation astronomy of galaxies generally is about the galaxy as a radiated or radiation emitting astronomical object. The stellar aspects of individual galaxies are in [[Stars/Galaxies|galaxies of stars]]. A galaxy is often perceived as a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter.<ref name=Sparke>{{Cite book |last1=Sparke |first1=L. S. |last2=Gallagher |first2=J. S. III |date=2000 |title=Galaxies in the Universe: An Introduction |publisher=Cambridge University Press |isbn=978-0-521-59740-1 |accessdate=July 25, 2018 |archive-date=March 24, 2021 |url=https://web.archive.org/web/20210324072126/https://books.google.com/books?id=tzNF79roUfoC }}</ref><ref name=nasa060812>{{cite web |last1=Hupp |first1=E. |last2=Roy |first2=S. |last3=Watzke |first3=M. |date=August 12, 2006 |title=NASA Finds Direct Proof of Dark Matter |url=http://www.nasa.gov/home/hqnews/2006/aug/HQ_06297_CHANDRA_Dark_Matter.html |publisher=NASA |accessdate=April 17, 2007 }}</ref> Galaxies range in size from dwarfs with just a few hundred million ({{10^|8}}) stars to giants with one hundred trillion ({{10^|14}}) stars,<ref name=science250_4980_539>{{cite journal |last1=Uson |first1=J. M. |last2=Boughn |first2=S. P. |last3=Kuhn |first3=J. R. |date=1990 |title=The central galaxy in Abell 2029&nbsp;– An old supergiant |journal=Science |volume=250 |issue=4980 |pages=539–540 |bibcode=1990Sci...250..539U |doi=10.1126/science.250.4980.539 |pmid=17751483 }}</ref> each orbiting its galaxy's center of mass. Galaxies are categorized according to their visual morphology as elliptical,<ref name=uf030616>{{cite news |last1=Hoover |first1=A. |date=June 16, 2003 |title=UF Astronomers: Universe Slightly Simpler Than Expected |url=http://news.ufl.edu/2003/06/16/galaxies/ |publisher=Hubble News Desk |accessdate=March 4, 2011 |archiveurl=https://web.archive.org/web/20110720083835/http://news.ufl.edu/2003/06/16/galaxies/ |archivedate=July 20, 2011 |df=mdy-all }} Based upon: * {{Cite journal |last1=Graham |first1=A. W. |last2=Guzman |first2=R. |date=2003 |title=HST Photometry of Dwarf Elliptical Galaxies in Coma, and an Explanation for the Alleged Structural Dichotomy between Dwarf and Bright Elliptical Galaxies |journal=The Astronomical Journal |volume=125 |issue=6 |pages=2936–2950 |bibcode=2003AJ....125.2936G |doi=10.1086/374992 |arxiv = astro-ph/0303391 }}</ref> spiral, or irregular.<ref name="IRatlas">{{cite web |last1=Jarrett |first1=T. H. |title=Near-Infrared Galaxy Morphology Atlas |url=http://www.ipac.caltech.edu/2mass/gallery/galmorph/ |publisher=California Institute of Technology |accessdate=January 9, 2007 }}</ref> The number of galaxies in the observable universe has increased from a previous estimate of 200&nbsp;billion ({{val|2e11}})<ref name="apj624_2">{{cite journal |last1=Gott III |first1=J. R. |year=2005 |display-authors=etal |title=A Map of the Universe |journal=The Astrophysical Journal |volume=624 |issue=2 |pages=463–484 |bibcode=2005ApJ...624..463G |doi=10.1086/428890 |arxiv = astro-ph/0310571 }}</ref> to a suggested 2 trillion ({{val|2e12}}) or more,<ref name="Conselice">{{cite journal |title=The Evolution of Galaxy Number Density at z < 8 and its Implications |author=Christopher J. Conselice ''et al.'' |journal=The Astrophysical Journal |volume=830 |issue=2 |year=2016 |arxiv=1607.03909v2 |bibcode= 2016ApJ...830...83C |doi=10.3847/0004-637X/830/2/83 |page=83 }}</ref><ref name="NYT-20161017">{{cite news |last=Fountain |first=Henry |title=Two Trillion Galaxies, at the Very Least |url=https://www.nytimes.com/2016/10/18/science/two-trillion-galaxies-at-the-very-least.html |date=17 October 2016 |work=The New York Times |accessdate=17 October 2016 }}</ref> containing more [[stars]] than all the grains of sand on planet Earth.<ref name="SU-20020201">{{cite web |last=Mackie |first=Glen |title=To see the Universe in a Grain of Taranaki Sand |url=http://astronomy.swin.edu.au/~gmackie/billions.html |date=1 February 2002 |work=Centre for Astrophysics and Supercomputing |accessdate=28 January 2017 }}</ref> {{clear}} ==Galaxy clusters== {{main|Radiation astronomy/Galaxy clusters}} [[Image:Superclusters atlasoftheuniverse.gif|thumb|250px|right|The universe within 1 billion light-years (307 Mpc) of Earth is shown to contain the local superclusters, galaxy filaments and voids. Credit: Richard Powell.{{tlx|free media}}]] "Galaxies and clusters of galaxies are not uniformly distributed in the Universe, instead they collect into vast clusters and sheets and walls of galaxies interspersed with large voids in which very few galaxies seem to exist. The map above shows many of these superclusters including the Virgo supercluster - the minor supercluster of which our galaxy is just a minor member. The entire map is approximately 7 percent of the diameter of the entire visible Universe."<ref name=Powell>{{ cite book |author=Richard Powell |title=The Universe within 1 billion Light Years The Neighbouring Superclusters |publisher=Atlas of the Universe |location= |date=30 July 2006 |url=http://www.atlasoftheuniverse.com/superc.html |accessdate=2018-04-01 }}</ref> {{clear}} ==Gamma rays== {{main|Radiation astronomy/Gamma rays|Gamma-ray astronomy}} [[Image:Moon egret.jpg|thumb|right|250px|The Moon is seen by the [[w:Compton Gamma Ray Observatory|Compton Gamma Ray Observatory]], in gamma rays of greater than 20 MeV. Credit: D. J. Thompson, D. L. Bertsch (NASA/GSFC), D. J. Morris (UNH), R. Mukherjee (NASA/GSFC/USRA).{{tlx|free media}}]] Most astronomical gamma-rays are thought to be produced not from radioactive decay, however, but from the same type of accelerations of electrons, and electron-photon interactions, that produce X-rays in astronomy (but occurring at a higher energy in the production of gamma-rays). For [[gamma-ray astronomy]], the Vela satellites were the first devices ever to detect cosmic gamma ray bursts. '''Gamma-ray bursts''' ('''GRBs''') are flashes of gamma rays associated with extremely energetic explosions that have been observed in distant [[galaxies]]. They are the most luminous electromagnetic events known to occur in the [[universe]]. Bursts can last from ten milliseconds to several minutes, although a typical burst lasts 20–40 seconds. The initial burst is usually followed by a longer-lived "afterglow" emitted at longer wavelengths (X-ray, ultraviolet, optical, infrared, microwave and radio).<ref name="Vedrenne">{{cite book |author=Vedrenne G |author2=Atteia J.-L. |year=2009 |title=Gamma-Ray Bursts: The brightest explosions in the Universe |url=http://books.google.com/?id=jZHSdrvzz0gC&printsec=frontcover#v=onepage&q&f=false |publisher=Springer/Praxis Books |isbn=978-3-540-39085-5 }}</ref> {{clear}} ==Gaseous objects== {{main|Gases/Gaseous objects}} [[Image:Mars xray 420.jpg|thumb|right|250px|This Chandra X-ray Observatory image is the first look at X-rays from Mars. Credit: NASA/CXC/MPE/K.Dennerl et al.{{tlx|free media}}]] "In the sparse upper atmosphere of Mars, about 120 (75 miles) kilometers above its surface, the observed X-rays [shown in the image at right] are produced by fluorescent radiation from oxygen atoms."<ref name="Dennerl02">{{cite book |author=K. Dennerl |display-authors=etal |title=Mars: Mars Glows in X-rays |publisher=NASA, Harvard University |location=Boston, Massachusetts, USA |date=November 7, 2002 |url=http://chandra.harvard.edu/photo/2002/mars/ |accessdate=2012-11-26 }}</ref> "X-radiation from the Sun impacts oxygen atoms, knock electrons out of the inner parts of their electron clouds, and excite the atoms to a higher energy level in the process. The atoms almost immediately return to their lower energy state and may emit a fluorescent X-ray in this process with an energy characteristic of the atom involved - oxygen in this case. A similar process involving ultraviolet light produces the visible light from fluorescent lamps."<ref name="Dennerl02"/> "The X-ray power detected from the Martian atmosphere is very small, amounting to only 4 megawatts, comparable to the X-ray power of about ten thousand medical X-ray machines. Chandra was scheduled to observe Mars when it was only 70 million kilometers from Earth, and also near the point in its orbit when it is closest to the Sun."<ref name="Dennerl02"/> "At the time of the Chandra observation, a huge dust storm developed on Mars that covered about one hemisphere, later to cover the entire planet. This hemisphere rotated out of view over the course of the 9-hour observation but no change was observed in the X-ray intensity, implying that the dust storm did not affect the upper atmosphere."<ref name="Dennerl02"/> "The astronomers also found evidence for a faint halo of X-rays that extends out to 7,000 kilometers above the surface of Mars. Scientists believe the X-rays are produced by collisions of ions racing away from the Sun (the solar wind) with oxygen and hydrogen atoms in the tenuous exosphere of Mars."<ref name="Dennerl02"/> {{clear}} ==Geographies== {{main|Radiation astronomy/Geography}} [[Image:Caltech-Submillimeter-Observatory (straightened).jpg|thumb|right|250px|The Caltech Submillimeter Observatory at Mauna Kea Observatory has a 10.4 m (34 ft) dish. Credit: [http://www.flickr.com/people/62472689@N00 Samuel Bouchard] from Quebec City, Canada.]] Each individual or small group of astronomical knowledge recorders among the hominins after some effort has realized that they are on the surface of a planet, an approximately spheroidal object. Further, when any of them study the sky, they have realized they are only sensing a small portion relative to their location (such as in the enjoyment of [[Backyard Astronomy|backyard astronomy]]). To combine what they've learned, when they get together to discuss it or record it, they have to locate that knowledge where that knowledge occurred. This locating eventually included the radiation received to form the knowledge and science of '''astronomical radiation geography'''. '''Geographical radiation astronomy''' is the study of the effect of geography on radiation astronomy. Both astronomical radiation geography and geographical radiation astronomy are part of '''astrogeography''', or '''astrography'''. {{clear}} ==Gravitationals== {{main|Radiation astronomy/Gravitationals}} [[Image:LIGO measurement of gravitational waves.svg|right|thumb|300px|The images show LIGO and Livingston, Louisiana, measurement of gravitational waves. Credit: B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration).{{tlx|free media}}]] [[Image:Aerial View Of LIGO Livingston 599x400.jpg|left|thumb|300px|This photo shows the Livingston LIGO detector. Credit: Caltech/MIT/LIGO Laboratory.{{tlx|free media}}]] [[Image:The Gravitational wave spectrum Sources and Detectors.jpg|right|thumb|300px|This gravitational wave spectrum includes sources and detectors. Credit: NASA Goddard Space Flight Center.{{tlx|free media}}]] '''Gravitational radiation''' appears to be cylindrical waves of radiation produced by relativistic, undulatory gravitational fields in Euclidean space.<ref name=Einstein>{{ cite journal |author=A. Einstein |author2=N. Rosen |title=On gravitational waves |journal=Journal of the Franklin Institute |month=January |year=1937 |volume=223 |issue=1 |pages=43-54 |url=http://www.sciencedirect.com/science/article/pii/S0016003237905830?via%3Dihub |arxiv= |bibcode=1937FrInJ.223...43E |doi=10.1016/S0016-0032(37)90583-0 |pmid= |accessdate=2018-1-03 }}</ref> {| class="wikitable" |- ! Interaction !! Mediator !! Relative Magnitude !! Behavior !! Range |- | [[Strong interaction]] || gluon || 10³⁸ || 1 || 10⁻¹⁵ m |- | [[Electromagnetic interaction]] || photon || 10³⁶ || 1/''r''² || universal |- | [[Weak interaction]] || W and Z bosons || 10²⁵ || 1/''r''⁵ to 1/''r''⁷ || 10⁻¹⁶ m |- | [[Gravitational interaction]] || photon or graviton ? || 10 || 1/''r''² || universal |} As the gravitational interaction is 10^-36 that of the electromagnetic interaction to produce gravitational radiation requires a massive oscillator. At right are the results from the first gravitational radiation detection. The images show the radiation signals received by the Laser Interferometer Gravitational Observatory (LIGO) instruments at Hanford, Washington (left) and Livingston, Louisiana (right) and comparisons of these signals to the signals expected due to a black hole merger event. The wavelength of the gravitational waves is given by for example: 3 x 10⁸ m‧s^-1/400 Hz = 750,000 m, which is way longer than radio waves but expected for such a weak oscillator. 35 Hz corresponds to 8,600,000 m. LIGO operates two detectors located 3000 km (1800 miles) apart: One in eastern Washington near Hanford, and the other near Livingston, Louisiana. The photo on the left shows the Livingston detector. "According to general relativity, a pair of black holes orbiting around each other lose energy through the emission of gravitational waves, causing them to gradually approach each other over billions of years, and then much more quickly in the final minutes. During the final fraction of a second, the two black holes collide at nearly half the speed of light and form a single, more massive black hole, converting a portion of the combined black holes' mass to energy, according to Einstein's formula E=mc². This energy is emitted as a final strong burst of gravitational waves. These are the gravitational waves that LIGO observed."<ref name=Kupec>{{ cite book |author=Ivy F. Kupec |title=Gravitational waves detected 100 years after Einstein's prediction |publisher=National Science Foundation |location=Alexandria, Virginia, USA |date=11 February 2016 |editor= |pages=1 |url=https://www.nsf.gov/news/news_summ.jsp?cntn_id=137628 |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2018-01-03 }}</ref> "LIGO’s twin interferometers bounce laser beams between mirrors at the opposite ends of 4-kilometre-long vacuum pipes that are set perpendicularly to each other. A gravitational wave passing through will alter the length of one of the arms, causing the laser beams to shift slightly out of sync."<ref name=Castelvecchi>{{ cite journal |author=Davide Castelvecchi |author2=Alexandra Witze |title=Einstein's gravitational waves found at last LIGO 'hears' space-time ripples produced by black-hole collision |journal=Nature |month=11 February |year=2016 |volume= |issue= |pages= |url=http://www.nature.com/news/einstein-s-gravitational-waves-found-at-last-1.19361 |arxiv= |bibcode= |doi=10.1038/nature.2016.19361 |pmid= |accessdate=2018-1-03 }}</ref> Later detection confirmed the fusion of two massive stellar-sized objects, a binary neutron star merger.<ref name=Abbott>{{ cite journal |author=B. P. Abbott |author2=the LIGO Scientific Collaboration]] |author3=the Virgo Collaboration |title=GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral |journal=Physical Review Letters |month=16 October |year=2017 |volume=119 |issue=16 |doi=10.1103/PhysRevLett.119.161101 }}</ref> "According to Einstein's field equations, photon matter subject to quadruple oscillations is a source of gravitational waves."<ref name=Sandu>{{ cite book |author=Constantin Sandu |author2=Dan Brasoveanu |title=Sonic Electromagnetic Gravitational Spacecraft, Part - Principles, In: ''AIAA SPACE 2007 Conference & Exposition'' |volume=6203 |publisher=American Institute of Aeronautics and Astronautics |location= |date= |editor= |pages= |url=https://arc.aiaa.org/doi/abs/10.2514/6.2007-6203 |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2018-01-10 }}</ref> "In this work, we present a solution to the first stage of a new two-stage global treatment of the vacuum binary black hole problem [1, 2]. The approach, based upon characteristic evolution, has been carried out in the regime of Schwarzschild perturbations where advanced and retarded solutions of the linearized problem can be rigorously identified [3]. Computational experiments are necessary to study the applicability of the approach to the nonlinear regime. From a time-reversed viewpoint, this first stage is equivalent to the determination of the outgoing radiation emitted from the fission of a white hole in the absence of ingoing radiation. This provides the physically correct “retarded” waveform for a white hole fission, were such events to occur in the universe. Although there is no standard astrophysical mechanism for producing white holes from a nonsingular matter distribution, white holes of primordial or quantum gravitational origin cannot be ruled out."<ref name=Gomez>{{ cite journal |author=Roberto Gómez |author2=Sascha Husa |author3=Luis Lehner |author4=Jeffrey Winicour |title=Gravitational waves from a fissioning white hole |journal=Physical Review D |month=15 September |year=2002 |volume=66 |issue=6 |pages=1-9 |url=https://arxiv.org/pdf/gr-qc/0205038 |arxiv= |bibcode= |doi=10.1103/PhysRevD.66.064019 |pmid= |accessdate=2018-01-10 }}</ref> "This fission problem has a simpler formulation as a characteristic initial value problem than the black hole merger problem. The boundary of the (conformally compactified) exterior spacetime contains two null hypersurfaces where boundary conditions must be satisfied: past null infinity I−, where the incoming radiation must vanish, and the white hole event horizon H−, which must describe a white hole, which is initially in equilibrium with no ingoing radiation and then distorts and ultimately fissions into two white holes with the emission of outgoing gravitational waves."<ref name=Gomez/> An almost identical signal could originate from a comparable much more massive neutron star fission. "This is an exciting time to study gravitation, astrophysics and cosmology. Through challenging cosmic microwave background (CMB) and supernovae observations cosmology has been turned on its head. Gravitational radiation astronomy should be the next contributor to this revolution in astrophysics and cosmology."<ref name="Christensen">{{ cite journal |author=Nelson Christensen |author2=Renate Meyer |author3=Adam Libson |year=2003 |title=A Metropolis–Hastings routine for estimating parameters from compact binary inspiral events with laser interferometric gravitational radiation data |url=http://people.carleton.edu/~nchriste/CQG03.pdf |journal=Classical and Quantum Gravity |volume=21 |issue=1 |pages=317-330 |arxiv= |bibcode= |doi=10.1088/0264-9381/21/1/023 |pmid= |accessdate=2018-01-19 |month=1 December }}</ref> {{clear}} ==Greens== {{main|Radiation astronomy/Greens|Green astronomy}} [[Image:LASCO C1 coronagraph of solar corona.png|right|thumb|250px|A picture of the solar corona taken with the LASCO C1 coronagraph. The image is color coded for the doppler shift of the FeXIV 530.8 nm line. Credit: NASA and NRL.{{tlx|fairuse}}]] Green objects or emission lines in the green portion of the visible spectrum are the subject of [[green astronomy]]. In the image at right the iron (Fe XIV) green line is followed by doppler imaging to show associated relative coronal plasma velocity towards (-7 km/s side) and away from (+7 km/s side) the large angle spectrometric coronagraph LASCO satellite camera. "Carroll and McCormack (1972) in Dublin reported complex spectra in the blue and green wavelength regions of both FeH and FeD".<ref name="JGPhillips">{{cite journal |author=John G. Phillips |author2=Sumner P. Davis |author3=Bo Lindgren |author4=Walter J. Balfour |title=The near-infrared spectrum of the FeH molecule |journal=The Astrophysical Journal Supplement Series |month=December |year=1987 |volume=65 |issue=12 |pages=721-78 |url= |arxiv= |bibcode=1987ApJS...65..721P |doi=10.1086/191241 |pmid= |accessdate=2011-12-08 }}</ref> For elongated dust particles in cometary comas an investigation is performed at 535.0 nm (green) and 627.4 nm (red) peak transmission wavelengths of the Rosetta spacecraft's OSIRIS Wide Angle Camera broadband green and red filters, respectively.<ref name="Bertini">{{cite journal |author=I. Bertini |author2=N. Thomas |author3=C. Barbieri |title=Modeling of the light scattering properties of cometary dust using fractal aggregates |journal=Astronomy & Astrophysics |month=January |year=2007 |volume=461 |issue=1 |pages=351-64 |url=http://www.aanda.org/articles/aa/full/2007/01/aa5461-06/aa5461-06.html |arxiv= |bibcode=2007A&A...461..351B |doi=10.1051/0004-6361:20065461 |pmid= |pdf=http://www.aanda.org/articles/aa/pdf/2007/01/aa5461-06.pdf |accessdate=2011-12-08 }}</ref> "In the green, the polarization of the pure silicate composition qualitatively appears a better fit to the shape of the observed polarization curves".<ref name="Bertini"/> "[B]ut they are characterized by a high albedo."<ref name="Bertini"/> The silicates used to model the cometary coma dust are olivene (Mg-rich is green) and the pyroxene, enstatite.<ref name="Bertini"/> In December 2006, seven papers were published in the scientific journal, ''Science'', discussing initial details of the sample analysis. Among the findings are: a wide range of organic compounds, including two that contain biologically usable nitrogen; indigenous aliphatic hydrocarbons with longer chain lengths than those observed in the diffuse interstellar medium; abundant amorphous silicates in addition to crystalline silicates such as olivine and pyroxene, proving consistency with the mixing of solar system and interstellar matter, previously deduced spectroscopically from ground observations;<ref name="Nottingham">{{cite book |title=The building blocks of planets within the `terrestrial' region of protoplanetary disks |url=http://ukads.nottingham.ac.uk/cgi-bin/nph-bib_query?bibcode=2004Natur.432..479V&amp;db_key=AST |publisher=nottingham.ac.uk |accessdate=2008-03-04 }}</ref> hydrous silicates and carbonate minerals were found to be absent, suggesting a lack of aqueous processing of the cometary dust; limited pure carbon (CHON) was also found in the samples returned; methylamine and ethylamine was found in the aerogel but was not associated with specific particles. {{clear}} ==Hadrons== {{main|Radiation astronomy/Hadrons}} [[Image:Installing the ATLAS Calorimeter.jpg|right|thumb|300px|The eight toroid magnets can be seen surrounding the calorimeter that is later moved into the middle of the detector. Credit: Maximilien Brice.{{tlx|free media}}]] '''Hadrons''' are subatomic particles of a type including [[Radiation astronomy/Baryons|baryons]] and [[Radiation astronomy/Mesons|mesons]] that can take part in the [[strong interaction]] and may be useful in radiation astronomy. At right a person works lower center left in front of the huge ATLAS detector, one of six detectors attached to the Large Hadron Collider at CERN. {{clear}} ==High-velocity galaxies== {{main|Radiation astronomy/High-velocity galaxies}} [[Image:Irregular galaxy NGC 1427A (captured by the Hubble Space Telescope).jpg|thumb|right|200px|The irregular galaxy NGC 1427A is passing through the Fornax cluster at nearly 600 kilometers per second (400 miles per second). Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA).{{tlx|free media}}]] "The irregular galaxy NGC 1427A is a spectacular example of the resulting stellar rumble. Under the gravitational grasp of a large gang of galaxies, called the Fornax cluster, the small bluish galaxy is plunging headlong into the group at 600 kilometers per second or nearly 400 miles per second."<ref name=Gregg>{{ cite web |author=M. Gregg |title=The Impending Destruction of NGC 1427A |publisher=Hubblesite.org |location=Baltimore, Maryland USA |date=3 March 2005 |url=http://hubblesite.org/newscenter/archive/releases/2005/09/image/a/ |accessdate=2016-11-05 }}</ref> "Galaxy clusters, like the Fornax cluster, contain hundreds or even thousands of individual galaxies. Within the Fornax cluster, there is a considerable amount of gas lying between the galaxies. When the gas within NGC 1427A collides with the Fornax gas, it is compressed to the point that it starts to collapse under its own gravity. This leads to formation of the myriad of new stars seen across NGC 1427A, which give the galaxy an overall arrowhead shape that appears to point in the direction of the galaxy's high-velocity motion."<ref name=Gregg/> {{clear}} ==Histories== {{main|Radiation astronomy/History}} [[Image:Stonehenge.jpg|thumb|right|250px|Stonehenge is a Neolithic monument that may have functioned as a celestial observatory.<ref name=Hawkins>{{ cite book |author=GS Hawkins | date=1966 | title = Stonehenge Decoded | isbn= 978-0880291477 }}</ref> Credit: Wigulf.]] The ''Hominidae'', or hominins have apparently been on Earth for around seven to eight million years, at least somewhere in [[Africa]] and elsewhere. Fortunately and deliberately, many of these have worked out ways to record knowledge about the objects or entities in the sky observed by the radiation they produce. '''[[Special:Search |Original research/Radiation astronomy]]''' as an observational [[science]] has a long '''[[radiation history]]'''. {{clear}} ==Hydrometeors== {{main|Radiation astronomy/Hydrometeors}} [[Image:Regnbyge.jpg|thumb|right|400px|This image shows a late-summer rainstorm in the village Lunde, The north of Funen, Denmark. Credit: [[commons:User:Malene|Malene Thyssen]].]] The nearly black color of the cloud's base indicates the foreground cloud is probably cumulonimbus. {{clear}} ==Hypervelocity stars== {{main|Radiation astronomy/Hypervelocity stars}} [[Image:Hs-2009-03-a-web_print.jpg|thumb|right|250px|The Hubble Space Telescope image shows four high-velocity, runaway stars plowing through their local interstellar medium. Credit: NASA - Hubble's Advanced Camera for Surveys.{{tlx|free media}}]] '''Def.''' a star moving faster than 65 km/s to 100 km/s relative to the average motion of the stars in the Sun's neighbourhood is called a '''high-velocity star'''. '''Def.''' a high-velocity star moving through space with an abnormally high velocity relative to the surrounding interstellar medium is called a '''runaway star'''. '''Def.''' a star whose elliptical orbit takes it well outside the plane of [its galaxy] at steep angles is called a '''halo star'''. {{clear}} ==Infrareds== {{main|Radiation astronomy/Infrareds|Infrared astronomy}} [[Image:Far-Infrared Image of M51.jpg|right|thumb|300px|This is a three-color far-infrared image of M51, the Whirlpool Galaxy. Credit: ESA and the PACS Consortium.{{tlx|free media}}]] The wavelength of infrared light ranges from 0.75 to 300 micrometers. Infrared falls in between visible radiation, which ranges from 380 to 750 nanometers, and terahertz radiation submillimeter waves. Infrared and [[optical astronomy]] are often practiced using the same telescopes, as the same mirrors or lenses are usually effective over a wavelength range that includes both visible and infrared light. '''Far-infrared astronomy''' deals with objects visible in far-infrared radiation extending from 30 micron (µm) towards submillimeter wavelengths around 450 µm. Huge, cold clouds of gas and dust in [the Milky Way] our own galaxy, as well as in nearby [[galaxies]], glow in far-infrared light. This is due to thermal radiation of interstellar dust contained in molecular clouds. Visually dark infrared sources can be radiative cosmic dust, hydrogen gas such as an H II region (e.g. the Orion Nebula), an H I region of hydrogen, a molecular cloud, or a coronal cloud. There are about 1,892,100 infrared (IR) objects in the SIMBAD database. Some of these like IRAS 20542+3631 are only IR objects. 1RXS J205444.6+361116 is an IR and an X-ray object only. These objects are visibly dark infrared sources. As is 2MASS J21074764+3802561, which is an IR and UV object only. {{clear}} ==Intensities== {{main|Radiation astronomy/Intensities}} [[Image:Positrons from a terrestrial gamma ray flash detected by the Fermi gamma ray telescope.png|thumb|right|250px|Positrons from a terrestrial gamma ray flash are detected by the Fermi gamma ray telescope. Credit: NASA Goddard Space Flight Center.]] '''Intensity astronomy''' focuses on creating a sufficient intensity for a desired property or characteristic that a signal may be converted in a detector to an electric current. {{clear}} ==Kuiper belts== {{main|Radiation astronomy/Kuiper belts}} [[Image:Outersolarsystem objectpositions labels comp.png|thumb|350px|Known objects in the Kuiper belt, are derived from data from the [[w:Minor Planet Center|Minor Planet Center]]. Credit: [[w:User:WilyD|WilyD]]. Legend: {| style="width: 100%; margin-bottom: 8px;" |- | valign=top width=45% | {{legend2|red|border=1px solid black|Sun}}<br /> {{legend2|aquamarine|border=1px solid black|Giant Planet}}&nbsp;{{small|(6,178)}}<br /> {{legend2|#0BDA51|border=1px solid black|Kuiper belt object}}&nbsp;{{small|(&gt;300)}} {{legend2|Orange|border=1px solid black|Scattered disc object&nbsp;{{small|(9)}}}} | valign=top | {{legend2|Magenta|border=1px solid black|Trojan of Jupiter: J{{·}}S{{·}}U{{·}}N}}<br /> {{legend2|Yellow|border=1px solid black|Neptune trojan}}&nbsp;{{small|(44,000)}}<br /> |}]] The '''Kuiper belt''' is a region of the solar system extending from the orbit of Neptune (at 30 AU to approximately 60 AU from the Sun.<ref name=Stern>{{ cite journal | author=Alan Stern | title=Collisional Erosion in the Primordial Edgeworth-Kuiper Belt and the Generation of the 30–50 AU Kuiper Gap | journal=The Astrophysical Journal | volume=490 | issue=2 | pages=879–882 | year=1997 | doi=10.1086/304912 | last2=Colwell | first2=Joshua E. | bibcode=1997ApJ...490..879S }}</ref> It consists mainly of [[w:small Solar System body|small bodies]]. "[B]roadband optical photometry of Centaurs and Kuiper Belt objects from the Keck 10 m, the University of Hawaii 2.2 m, and the Cerro Tololo InterAmerican (CTIO) 1.5 m telescopes [shows] a wide dispersion in the optical colors of the objects, indicating nonuniform surface properties. The color dispersion [may] be understood in the context of the expected steady reddening due to bombardment by the ubiquitous flux of cosmic rays."<ref name="Luu">{{cite journal |author=Jane Luu |author2=David Jewitt |title=Color Diversity among the Centaurs and Kuiper Belt Objects |journal=The Astronomical Journal |month=November |year=1996 |volume=112 |issue=5 |pages=2310-8 |url=http://adsabs.harvard.edu/full/1996AJ....112.2310L |arxiv= |bibcode=1996AJ....112.2310L |doi= |pmid= |accessdate=2013-11-05 }}</ref> In the image at right, objects in the main part of the Kuiper belt are coloured green, while scattered objects are coloured orange. The four outer planets are blue. Neptune's few known [[w:Neptune trojan|trojans]] are yellow, while Jupiter's are pink. The scattered objects between Jupiter's orbit and the Kuiper belt are known as [[w:Centaur (minor planet)|centaurs]]. The scale is in [[w:astronomical unit|astronomical unit]]s. The pronounced gap at the bottom is due to difficulties in detection against the background of the plane of the [[w:Milky Way|Milky Way]]. Axes list distances in [[w:Astronomical unit|AU]], projected onto the [[w:ecliptic|ecliptic]], with [[w:ecliptic longitude|ecliptic longitude]] zero being to the right, along the "x" axis). Positions are accurate for January 1st, 2000 ([[w:eEpoch (astronomy)#J2000.0|J2000 epoch]]) with some caveats: For planets, positions should be exact. For minor bodies, positions are extrapolated from other epochs assuming purely [[w:eosculating orbit|Keplerian motion]]. As all data is from an epoch between 1993 and 2007, this should be a reasonable approximation. Data from the [[w:Minor Planet Center|Minor Planet Center]]<ref name=mpc>{{ cite book |url=http://www.cfa.harvard.edu/iau/MPCORB.html |title=The MPC Orbit (MPCORB) Database }}</ref> or Murray and Dermott<ref name=murraydermott>{{ cite book |author=Carl D. Murray |author2=Stanley F. Dermott |title=Solar System Dynamics |publisher=Cambridge University Press |year=1999 |isbn=0 521 57295 9 }}</ref> as needed. Radial "spokes" of higher density in this image, or gaps in particular directions are due to observational bias (i.e. where objects were searched for), rather than any real physical structure. The pronounced gap at the bottom is due to obscuration by the band of the Milky Way. {{clear}} ==Lensing== {{main|Radiation astronomy/Lensings}} [[Image:grav.lens1.arp.750pix.jpg|thumb|250px|This image shows a cluster of yellow galaxies near the middle of the photograph. Credit: STScl/NASA.]] The image at right shows several blue, loop-shaped objects that are multiple images of the same galaxy, duplicated by the [[w:gravitational lens|gravitational lens]] effect of the cluster of yellow galaxies near the middle of the photograph. The lens is produced by the cluster's gravitational field that bends light to magnify and distort the image of a more distant object. {{clear}} ==Lightnings== {{main|Radiation astronomy/Lightnings}} [[Image:Upperatmoslight1.jpg|300px|thumb|right|Representation of upper-atmospheric lightning and electrical-discharge phenomena are displayed. Credit: [[commons:User:Abestrobi|Abestrobi]].]] [[Image:Lightning sprites2.png|left|thumb|300px|An illustration of different kinds of transient luminous events (TLEs) is displayed. Credit: Carlos Miralles (AeroVironment) and Tom Nelson (FMA).{{tlx|fairuse}}]] Lightning is more than ground-to-cloud electron transfer. "Cloud flashes sometimes have visible channels that extend out into the air around the storm (cloud-to-air or CA), but do not strike the ground. The terms sheet lightning or intra-cloud lightning (IC) refers to lightning embedded within a cloud that lights up as a sheet of luminosity during the flash. A related term, heat lightning, is lightning or lightning-induced illumination that is too far away for thunder to be heard. Lightning can also travel from cloud-to-cloud (CC). Spider lightning refers to long, horizontally traveling flashes often seen on the underside of stratiform clouds."<ref name=Miralles>{{ cite web |author=Carlos Miralles (AeroVironment) |author2=Tom Nelson (FMA) |title=SEVERE WEATHER 101 Lightning Types |publisher=NSSL, NOAA |location= |date=25 June 2019 |url=https://www.nssl.noaa.gov/education/svrwx101/lightning/types/ |accessdate=25 June 2019 }}</ref> "Large thunderstorms are capable of producing other kinds of electrical phenomena called transient luminous events (TLEs) that occur high in the atmosphere. They are rarely observed visually and not well understood. The most common TLEs include red sprites, blue jets, and elves."<ref name=Miralles/> The illustration on the left labels Elves, Sprites, and tendrils, a stratiform region producing positive cloud-to-ground flashes with spider lightning on the right to conventional cloud-to-air discharge, upward superbolt, blue jets and negative cloud-to-ground flash near convective core. Approximate altitudes in the Earth's atmosphere and ionosphere are indicated. {{clear}} ==Liquid objects== {{main|Liquid objects}} [[Image:Earth Pacific jul 30 2010.jpg|thumb|right|250px|This is a detailed, photo-like view of Earth based largely on observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite. Credit: Robert Simmon and Marit Jentoft-Nilsen, NASA.{{tlx|free media}}]] '''Def.''' precipitation products of the [[wikt:condensation|condensation]] of atmospheric water vapour are called '''hydrometeors'''. "Condensation or sublimation of atmospheric water vapor produces a hydrometeor. It forms in the free atmosphere, or at the earth's surface, and includes frozen water lifted by the wind. Hydrometeors which can cause a surface visibility reduction, generally fall into one of the following two categories: # '''Precipitation'''. Precipitation includes all forms of water particles, both liquid and solid, which fall from the atmosphere and reach the ground; these include: liquid precipitation (drizzle and rain), freezing precipitation (freezing drizzle and freezing rain), and solid (frozen) precipitation (ice pellets, hail, snow, snow pellets, snow grains, and ice crystals). # '''Suspended (Liquid or Solid) Water Particles'''. Liquid or solid water particles that form and remain suspended in the air (damp haze, cloud, fog, ice fog, and mist), as well as liquid or solid water particles that are lifted by the wind from the earth’s surface (drifting snow, blowing snow, blowing spray) cause restrictions to visibility. One of the more unusual causes of reduced visibility due to suspended water/ice particles is whiteout, while the most common cause is fog."<ref name="Mireles">{{cite web |author=Mark R. Mireles |author2=Kirth L. Pederson |author3=Charles H. Elford |title=Meteorologial Techniques |publisher=Air Force Weather Agency/DNT |location=Offutt Air Force Base, Nebraska, USA |date=February 21, 2007 |editor= |pages= |url=http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA466107 |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2013-02-17 }}</ref> {{clear}} ==Lithometeors== {{main|Radiation astronomy/Lithometeors}} [[Image:Ssc2006-16a.jpg|thumb|right|250px|The image shows the Orion nebula surrounded by a ring of dust. Credit: NASA/JPL-Caltech/T. Megeath(University of Toledo).]] '''Def.''' a suspension of dry dust in an atmosphere is called a '''lithometeor'''. "A lithometeor consists of solid particles suspended in the air or lifted by the wind from the ground."<ref name=Ozer95>{{ cite journal |author=PJ Ozer |title=Lithometeors in relation with desertification in the Sahelian area of Niger, In: ''Desertification in a European context: physical and socio-economic aspects'' |publisher=Office for Official Publications of the European Community |location=Luxembourg |month= |year=1995 |editor=Fantechi, R. |editor2=Peter, D. |editor3=Balabanis, P. |editor4=Rubio, J. L. |pages=567-74 |url=http://www.cabdirect.org/abstracts/19971901329.html |arxiv= |bibcode= |doi= |pmid= |isbn=92-827-4163-X |accessdate=2013-02-17 }}</ref> "A lithometeor is the general term for particles suspended in a dry atmosphere; these include dry haze, smoke, dust, and sand."<ref name=Mireles/> "Dry haze is an accumulation of very fine dust or salt particles in the atmosphere; it does not block light, but instead causes light rays to scatter. Dry haze particles produce a bluish color when viewed against a dark background, but look yellowish when viewed against a lighter background. This light-scattering phenomenon (called ''Mie scattering'') also causes the visual ranges within a uniformly dense layer of haze to vary depending on whether the observer is looking into the sun or away from it."<ref name=Mireles/> Heavy metal pollution may occur in lithometeors.<ref name=Yu>{{ cite journal |author=Jian-qiao Yu |author2=Xia1 Wang |author3=Li Wen |author4=Jing-shun Wang |title=Studies on Correlation of Heavy Metal Pollution in Soil, Lithometeor| and Leaves Around both Sides of Highway |journal=Journal of Agricultural Science and Technology |month=April |year=2008 |volume= |issue=04 |pages= |url=http://en.cnki.com.cn/Article_en/CJFDTOTAL-NKDB200804025.htm |arxiv= |bibcode= |doi= |pmid= |accessdate=2013-02-17 }}</ref> "The rise of airborne dust is constantly augmenting from the desert (Bilma) to the southern Sahelian stations (Niamey) where it has increased by a factor five. ... the Sahelian zone with airborne dust during the 80s ... All stations have recorded a general increase of wind velocity. The increase of lithometeors frequency as well as the wind velocity during the drought period is not explained by the aridification."<ref name=Ozer>{{ cite book |author=P. Ozer |title=Lithometeors and wind velocity in relation with desertification during the dry season from 1951 to 1994 in Niger, In: ''International Conference on tropical climatology, meteorology and hydrology in memoriam Franz Bultot'' |publisher=Royal Meteorological Institute of Belgium; Royal Academy of Overseas Sciences |location=Bruxelles (Belgium) |date=1998 |editor=G. Demaree |editor2=J. Alexandre |editor3=M. de Dapper |pages=212-27 |url=http://agris.fao.org/agris-search/search/display.do?f=1999/BE/BE99007.xml;BE1999001164# |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2013-02-17 }}</ref> {{clear}} ==Mathematics== {{main|Radiation astronomy/Mathematics}} [[Image:Andromeda and Milky Way collision.ogv|thumb|right|250px|This animation depicts the collision between our Milky Way galaxy and the Andromeda galaxy. Credit: Visualization Credit: NASA; ESA; and F. Summers, STScI; Simulation Credit: NASA; ESA; G. Besla, Columbia University; and R. van der Marel, STScI.]] Most of the mathematics needed to understand the information acquired through astronomical radiation observation comes from physics. But, there are special needs for situations that intertwine mathematics with phenomena that may not yet have sufficient physics to explain the observations. Both uses constitute '''radiation mathematics''', or '''astronomical radiation mathematics''', or a portion of '''mathematical radiation astronomy'''. '''Astronomical radiation mathematics''' is the laboratory mathematics such as simulations that are generated to try to understand the observations of radiation astronomy. The mathematics needed to understand radiation astronomy starts with arithmetic and often needs various topics in calculus and differential equations to produce likely models. {{clear}} ==Mesons== {{main|Radiation astronomy/Mesons|Meson astronomy}} [[Image:LHCb data on B0 meson production.png|right|thumb|300px|Comparison of the LHCb data on B<sup>0</sup> meson production, both for central and for forward rapidities, with the theoretical predictions from POWHEG and aMC@NLO. Credit: Rhorry Gauld, Juan Rojo, Luca Rottoli and Jim Talbert.{{tlx|fairuse}}]] A '''meson''' is a composite subatomic particle "bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometre, which is about 2/3 the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Charged mesons decay (sometimes through intermediate particles) to form electrons and neutrinos. Uncharged mesons may decay to photons. Mesons are not produced by radioactive decay, but appear in nature only as short-lived products of very high-energy interactions in matter. In cosmic ray interactions, for example, such particles are ordinary protons and neutrons. Mesons are also frequently produced artificially in high-energy particle accelerators that collide protons, anti-protons, or other particles. In nature, the importance of lighter mesons is that they are the associated quantum-field particles that transmit the nuclear force, in the same way that photons are the particles that transmit the electromagnetic force. Each type of meson has a corresponding antiparticle (antimeson) in which quarks are replaced by their corresponding antiquarks and vice-versa. Mesons are subject to both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction. While no meson is stable, those of lower mass are nonetheless more stable than the most massive mesons, and are easier to observe and study in particle accelerators or in cosmic ray experiments. They are also typically less massive than baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher energy phenomena more readily than baryons composed of the same quarks would. {{clear}} ==Meteorites== {{main|Rocks/Meteorites}} [[Image:Widmanstatten patterns 2.jpg|thumb|right|250px|This image is a cross-section of the Laguna Manantiales meteorite showing Widmanstätten patterns. Credit: [[commons:User:Aramgutang|Aram Dulyan]].{{tlx|free media}}]] '''Def.''' a [[wikt:metallic|metallic]] or [[wikt:stony|stony]] object that is the remains of a [[wikt:meteor|meteor]] is called a '''meteorite'''. '''Widmanstätten patterns''', also called '''Thomson structures''', are unique figures of long nickel-iron crystals, found in the octahedrite iron meteorites and some pallasite]]s. They consist of a fine interleaving of kamacite and taenite bands or ribbons called ''lamellæ''. Commonly, in gaps between the lamellæ, a fine-grained mixture of kamacite and taenite called plessite can be found. {{clear}} ==Meteoroids== {{main|Radiation astronomy/Meteoroids}} [[Image:Earth-grazing meteoroid, 13 October 1990 (2) TFA.jpg|right|thumb|300px|This is a scanned photograph of the bolide EN131090, originally captured on a glass photographic plate. Credit: European Fireball Network.{{tlx|free media}}]] This is a scanned photograph on the right of the bolide EN131090, originally captured on a glass photographic plate. The Earth-grazing meteoroid flew above Czechoslovakia and Poland on 13 October 1990 and left to space again. It was taken by an all-sky camera equipped with a fish-eye objective Zeiss Distagon 3.5/30mm located at the hydrometeorological station at Červená hora, Czechoslovakia (now in the Czech Republic). The bolide travels from the south to the north and its track is interrupted by a shutter rotating 12.5 times per second, which allows determining its speed. "As of 2011 the International Astronomical Union officially defines a meteoroid as a solid object moving in interplanetary space, of a size considerably smaller than an asteroid and considerably larger than an atom".<ref name=Millman>{{ cite journal |author=Peter M. Millman |year=1961 |title=A report on meteor terminology |journal=JRASC |volume=55 |pages=265–267 |bibcode=1961JRASC..55..265M }}</ref><ref name=Glossary>{{ cite book |url=http://www.imo.net/glossary |title=Glossary International Meteor Organization |publisher=Imo.net |date=2008-11-18 |accessdate=2011-09-16}}</ref> {{clear}} ==Meteors== {{main|Radiation/Meteors}} [[Image:Paola-Castillo.jpg|thumb|right|250px|This meteor image of October 17, 2012, is prior to the meteorite fall on the same day. Credit: Paola-Castillo; and Petrus M. Jenniskens, SETI Institute/NASA ARC.{{tlx|free media}}]] A '''meteor''' is the visible path of a meteoroid that has entered the Earth's atmosphere. Although there are many definitions of a meteor ranging from any atmospheric phenomenon to a fast-moving streak of light in the night sky caused by the entry of extraterrestrial matter into the earth's atmosphere: A shooting star or falling star, for radiation astronomy, an alternative definition is used. Here's a [[Definitions/Theory#Theoretical definition|theoretical definition]] of a meteor from a radiation point of view: '''Def.''' any natural object radiating through a portion or all of the Earth's or another natural object's atmosphere is called a '''meteor'''. A hypervelocity star "snow-plowing" through the [[interstellar medium]] of a galaxy is a meteor and the subject of meteor astronomy. Meteor astronomy (radiated meteors) is radiation astronomy of large matter objects moving rapidly relative to apparently fixed objects. A meteor may be as small as an electron. Astronomical objects that are atoms, nuclei, or subatomic particles are part of cosmic-ray astronomy. {{clear}} ==Meteor showers== {{main|Radiation astronomy/Showers}} [[Image:Aurigids - Jeremie Vaubaillon.jpg|right|thumb|300px|The Aurigid meteor shower is observed by a group of astronomers on a NASA mission at 47,000 feet. Credit: Jeremie Vaubaillon, Caltech, NASA.{{tlx|free media}}]] Meteors may occur in showers, which arise when the Earth passes through a trail of debris left by a comet, or as "random" or "sporadic" meteors, not associated with a specific single cause. A number of specific meteors have been observed, largely by members of the public and largely by accident, but with enough detail that orbits of the meteoroids producing the meteors have been calculated. All of the orbits passed through the asteroid belt.<ref name=Uregina>{{ cite book |url=http://uregina.ca/~astro/mb_5.html |title=Diagram 2: the orbit of the Peekskill meteorite along with the orbits derived for several other meteorite falls |publisher=Uregina.ca |date= |accessdate=2011-09-16 }}</ref> "Named meteor showers recur at approximately the same dates each year. They appear to "radiate" from a certain point in the sky (the radiant) and vary in the speed, frequency and brightness of the meteors."<ref name=ListofMeteorShowers>{{ cite web |author=[[w:User:Noyster|Noyster]] |title=List of meteor showers |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=7 September 2017 |url=https://en.wikipedia.org/wiki/List_of_meteor_showers |accessdate=29 June 2019 }}</ref> As of November 2018, there are 112 established meteor showers.<ref>[https://www.ta3.sk/IAUC22DB/MDC2007/Roje/sortowanie_roje.php?corobic_roje=1 Meteor Data Centre, IAU] </ref> {{clear}} ==Microwaves== {{main|Radiation astronomy/Microwaves|Microwave astronomy}} [[Image:Milky-way-microwaves-planck.jpg|thumb|center|400px|A view of the Milky Way galaxy in microwaves is captured by the European Space Agency's Planck satellite. Credit: ESA/NASA/JPL-Caltech.{{tlx|fairuse}}]] Radiation astronomy specifically focused at the microwave portion of the electromagnetic spectrum is '''microwave astronomy'''. '''Microwaves''', a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300&nbsp;MHz (0.3&nbsp;GHz) and 300&nbsp;GHz.<ref name="Pozer">Pozar, David M. (1993). ''Microwave Engineering'' Addison-Wesley Publishing Company. {{ISBN|0-201-50418-9}}.</ref> This broad definition includes both UHF and Extremely high frequency (EHF) (millimeter waves), and various sources use different boundaries.<ref name="googlegloss">http://www.google.com/search?hl=en&defl=en&q=define:microwave&ei=e6CMSsWUI5OHmQee2si1DQ&sa=X&oi=glossary_definition&ct=title</ref> In all cases, microwave includes the entire super high frequency (SHF) band (3 to 30&nbsp;GHz, or 10 to 1&nbsp;cm) at minimum, with RF engineering often putting the lower boundary at 1&nbsp;GHz (30&nbsp;cm), and the upper around 100&nbsp;GHz (3 mm). {{clear}} ==Minerals== {{main|Radiation astronomy/Minerals}} [[Image:Pitchblende schlema-alberoda.JPG|thumb|right|250px|This is an image of the mineral pitchblende, or uraninite. Credit: [[commons:User:Geomartin|Geomartin]].{{tlx|free media}}]] [[Image:Uraninite-usa32abg.jpg|thumb|left|150px|These crystals are uraninite from Trebilcock Pit, Topsham, Maine. Credit: [[commons:User:Robert Lavinsky|Robert Lavinsky]].{{tlx|free media}}]] '''Uraninite''' is a radioactive, uranium-rich mineral and ore with a chemical composition that is largely [uranium dioxide] UO<sub>2</sub>, but also contains [uranium trioxide] UO<sub>3</sub> and oxides of lead, thorium, and rare earth elements. It is most commonly known as '''pitchblende''' (from ''pitch'', because of its black color. All uraninite minerals contain a small amount of radium as a radioactive decay product of uranium. Uraninite also always contains small amounts of the lead isotopes <sup>206</sup>Pb and <sup>207</sup>Pb, the end products of the decay series of the uranium isotopes <sup>238</sup>U and <sup>235</sup>U respectively. The extremely rare element technetium can be found in uraninite in very small quantities (about 0.2 ng/kg), produced by the spontaneous fission of uranium-238. The image at left shows well-formed crystals of uraninite. The image at right shows botryoidal uraninite. Because of the uranium decay products, both sources are gamma-ray emitters. {{clear}} ==Molecules== {{main|Radiation astronomy/Molecules}} [[Image:Nhsc2009-021a.jpg|thumb|right|250px|Shown here is a portion of the SPIRE spectrum of VY Canis Majoris (VY CMa). Credit: ESA/NASA/JPL-Caltech.]] "This is one of the early spectra obtained with the SPIRE fourier transform spectrometer on Herschel. Shown here is a portion of the SPIRE spectrum of VY Canis Majoris (VY CMa), a red supergiant star near the end of its life, which is ejecting huge quantities of gas and dust into interstellar space. The inset is a SPIRE camera map of VY CMa, in which it appears as a bright compact source near the edge of a large extended cloud."<ref name=Groenewegen>{{ cite book |author=M. Groenewegen |title=SPIRE spectrum of VY Canis Majoris |publisher=Caltech |location=Pasadena, California USA |date=November 27, 2009 |url=http://www.herschel.caltech.edu/image/nhsc2009-021a |accessdate=2014-03-12 }}</ref> "The VY CMa spectrum is amazingly rich, with prominent features from carbon monoxide (CO) and water (H<sub>2</sub>O). More than 200 other spectral features have been identified so far in the full spectrum, and several unidentified features are being investigated. Many of the features are due to water, showing that the star is surrounded by large quantities of hot steam. Observations like these will help to establish a detailed picture of the mass loss from stars and the complex chemistry occurring in their extended envelopes. As in all of the SPIRE spectra, the underlying emission increases towards shorter wavelengths, and is due to the emission from dust grains. The shape of the dust spectrum provides information on the properties of the dust."<ref name=Groenewegen/> "VY Canis Majoris (VY CMa) is a red supergiant star located about 4900 light years from Earth in the constellation Canis Major. It is the largest known star, with a size of 2600 solar radii, and also one of the most luminous, with a luminosity in excess of 100 000 times that of the Sun. The mass of VY CMa lies in the range 30-40 solar masses, and it has a mass-loss rate of 2 x 10<sup>-4</sup> solar masses per year."<ref name=Groenewegen/> "The shell of gas it has ejected displays a complex structure; the circumstellar envelope is among the most remarkable chemical laboratories known in the Universe, creating a rich set of organic and inorganic molecules and dust species. Through stellar winds, these inorganic and organic compounds are injected into the interstellar medium, from which new stars orbited by new planets may form. Most of the carbon supporting life on Earth was forged by this kind of evolved star. VY CMa truly is a spectacular object, it is close to the end of its life and could explode as a supernova at any time."<ref name=Groenewegen/> {{clear}} ==Muons== {{main|Radiation astronomy/Muons|Muon astronomy}} [[Image:Issue27muons1 l.jpg|thumb|right|250px|This is an image obtained from muon radiography of Japan's Asama volcano. Credit: H T M Tanaka.{{tlx|fairuse}}]] "TeV muons from γ ray primaries ... are rare because they are only produced by higher energy γ rays whose flux is suppressed by the decreasing flux at the source and by absorption on interstellar light."<ref name="Halzen">{{cite journal |author=Francis Halzen |author2=Todor Stanev |author3=Gaurang B. Yodh |title=γ ray astronomy with muons |journal=Physical Review D Particles, Fields, Gravitation, and Cosmology |month=April 1, |year=1997 |volume=55 |issue=7 |pages=4475-9 |url=http://prd.aps.org/abstract/PRD/v55/i7/p4475_1 |arxiv=astro-ph/9608201 |bibcode=1997PhRvD..55.4475H |doi=10.1103/PhysRevD.55.4475 |pmid= |accessdate=2013-01-18 }}</ref> Muon decay produces three particles, an [[electron]] plus two neutrinos of different types. {{clear}} ==Nebulas== {{main|Radiation astronomy/Nebulas}} [[Image:The Horsehead Nebula by NOAO 2.jpg|thumb|right|250px|This color picture was made by combining several exposures taken on the night of December 28th 1994 at the 0.9 m telescope of the Kitt Peak National Observatory. Credit: N.A.Sharp/NOAO/AURA/NSF.{{tlx|fairuse}}]] "The Horsehead Nebula, a part of the optical nebula IC434 and also known as Barnard 33, was first recorded in 1888 on a photographic plate taken at the Harvard College Observatory. Its coincidental appearance as the profile of a horse's head and neck has led to its becoming one of the most familiar astronomical objects. It is, in fact, an extremely dense cloud projecting in front of the ionized gas that provides the pink glow so nicely revealed in this picture. We know this not only because the underside of the 'neck' is especially dark, but because it actually casts a shadow on the field to its east (below the 'muzzle')."<ref name="Sharp">{{cite book |author=N. A. Sharp |title=The Horsehead Nebula |publisher=National Optical Astronomy Observatory (NOAO) |location=Kitt Peak, Arizona USA |date=28 December 1994 |url=https://www.noao.edu/image_gallery/html/im0057.html |accessdate=2015-09-25 }}</ref> {{clear}} ==Neutrals== {{main|Radiation astronomy/Neutrals|Neutrals astronomy}} [[Image:Article-2025275-0D6687D100000578-167 634x704.jpg|thumb|right|250px|The Necklace Nebula glows brightly in this Nasa Hubble Space Telescope image. Credit: NASA.{{tlx|fairuse}}]] "A giant cosmic necklace glows brightly in this Nasa Hubble Space Telescope image."<ref name="Reporter">{{cite book |author=DAILY MAIL REPORTER |title=Giant Necklace Nebula brightly glows with dense knots of blue, green and red gases |publisher=Daily Mail |location=United Kingdom |date=12 August 2011 |url=http://www.dailymail.co.uk/sciencetech/article-2025275/Necklace-Nebula-brightly-glows-dense-knots-blue-green-red-gases.html |accessdate=24 February 2014 }}</ref> "The object, aptly named the Necklace Nebula, is a recently discovered planetary nebula, the glowing remains of an ordinary, sun-like star."<ref name="Reporter"/> "The nebula consists of a bright ring, measuring 12trillion miles wide, dotted with dense, bright knots of gas that resemble diamonds in a necklace."<ref name="Reporter"/> "Newly discovered: The Necklace Nebula glows brightly in this composite image taken by the Hubble Space Telescope last month. The glow of hydrogen, oxygen, and nitrogen are shown by the colours blue, green and red respectively".<ref name="Reporter"/> "It is located 15,000 light-years away in the constellation Sagitta."<ref name="Reporter"/> "A pair of stars orbiting close together produced the nebula, also called PN G054.2-03.4."<ref name="Reporter"/> "About 10,000 years ago, one of the ageing stars ballooned to the point where it engulfed its companion star. The smaller star continued orbiting inside its larger companion, increasing the giant’s rotation rate. The bloated companion star spun so fast that a large part of its gaseous envelope expanded into space. Due to centrifugal force, most of the gas escaped along the star’s equator, producing a ring. The embedded bright knots are dense gas clumps in the ring. The pair is so close, only a few million miles apart, that they appear as one bright dot in the centre. The stars are furiously whirling around each other, completing an orbit in a little more than a day."<ref name="Reporter"/> {{clear}} ==Neutrinos== {{main|Radiation astronomy/Neutrinos|Neutrino astronomy}} [[Image:Neusun1 superk1.jpg|thumb|right|250px|This "neutrino image" of the Sun is by using the Super-Kamiokande to detect the neutrinos from nuclear fusion in the solar interior. Credit: R. Svoboda and K. Gordan (LSU).{{tlx|fairuse}}]] The field of '''neutrino astronomy''' is still very much in its infancy &ndash; the only confirmed extraterrestrial sources so far are the [[Sun (star)|Sun]] and supernova SN1987A. Neutrino astronomy observes astronomical objects with neutrino detectors in special observatories. Because neutrinos are only weakly interacting with other particles of matter, neutrino detectors must be very large in order to detect a significant number of neutrinos. Neutrino detectors are often built underground to isolate the detector from cosmic rays and other background radiation.<ref name="twsP16">{{cite book |author= KENNETH CHANG |title= Tiny, Plentiful and Really Hard to Catch, In: ''The New York Times'' |quote= In 1987, astronomers counted 19 neutrinos from an explosion of a star in the nearby Large Magellanic Cloud, 19 out of the billion trillion trillion trillion trillion neutrinos that flew from the supernova. |date= April 26, 2005 |url= http://www.nytimes.com/2005/04/26/science/26neut.html?pagewanted=print&position= |accessdate= 2011-06-16 }}</ref> The Super-Kamiokande, or "Super-K" is a large-scale experiment constructed in an unused mine in Japan to detect and study neutrinos. The image at right required 500 days worth of data to produce the "neutrino image" of the Sun. The image is centered on the Sun's position. This image covers a 90° x 90° octant of the sky (in right ascension and declination). The higher the brightness of the color, the larger is the neutrino flux. {{clear}} ==Neutrons== {{main|Radiation/Neutrons}} [[Image:Neutrons strip2.jpg|thumb|right|250px|The image shows the hydrogen concentrations on the Moon detected by the Lunar Prospector. Credit: NASA.{{tlx|free media}}]] Around EeV (10<sup>18</sup> eV) energies, there may be associated ultra high energy neutrons "observed in anisotropic clustering ... because of the relativistic neutrons boosted lifetime."<ref name="Fargion2003">{{cite journal |author=Fargion D |author2=Khlopov M |author3=Konoplich R |author4=De Sanctis Lucentini PG |author5=De Santis M |author6=Mele B |title=Ultra High Energy Particle Astronomy, Neutrino Masses and Tau Airshowers |journal=Recent Research and Development in Astrophysics |month=March |year=2003 |volume=1 |issue=3 |pages=395-454 |url=http://arxiv.org/pdf/astro-ph/0303233 |doi= |bibcode=2003astro.ph..3233F |arxiv=astro-ph/0303233 |pdf=http://arxiv.org/pdf/astro-ph/0303233v2 |access=2011-11-25 }}</ref> “[A]t ''E''<sub>n</sub> = 10<sup>20</sup> eV, [these neutrons] are flying a Mpc, with their directional arrival (or late decayed proton arrival) ... more on-line toward the source.”<ref name="Fargion2003"/> From “neutron (and anti-neutron) life-lengths (while being marginal or meaningless at tens of Mpcs)", the growth of their half-lives with energy may naturally explain an associated, showering neutrino halo.<ref name="Fargion2003"/> Fairly large fluxes of neutrons have been observed during [[w:solar flare|solar flare]]s such as that of November 12, 1960, with a flux of 30-70 neutrons per cm<sup>-2</sup> s<sup>-1</sup>.<ref name="Lingenfelter">{{cite journal |author=Lingenfelter RE |author2=Flamm EJ |author3=Canfield EH |author4=Kellman S |title=High-Energy Solar Neutrons 2. Flux at the Earth |journal=Journal of Geophysical Research |month=September |year=1965 |volume=70 |issue=17 |pages=4087–95 |bibcode=1965JGR....70.4087L |doi=10.1029/JZ070i017p04087 |accessdate=2011-11-25 }}</ref> At right is the result of an all Moon survey by the Lunar Prospector using an onboard neutron spectrometer (NS). Cosmic rays impacting the lunar surface generate neutrons which in turn lose much of their energy in collisions with hydrogen atoms trapped within the Moon's surface.<ref name="Williams"/> Some of these thermal neutrons collide with the helium atoms within the NS to yield an energy signature which is detected and counted.<ref name="Williams"/> The NS aboard the Lunar Prospector has a surface resolution of 150 km.<ref name="Williams"/> {{clear}} ==Objects== {{main|Radiation astronomy/Objects|Object astronomy}} [[Image:Chain of impact craters on Ganymede.jpg|thumb|right|250px|The image shows a chain of craters on Ganymede. Credit: Galileo Project, Brown University, JPL, NASA.{{tlx|free media}}]] '''Def.''' a hemispherical pit a basinlike opening or mouth about which a cone is often built up any large roughly circular depression or hole is called a '''crater'''. The image at right shows a chain of 13 craters (Enki Catena) on Ganymede measuring 161.3 km in length. "The Enki craters formed across the sharp boundary between areas of bright terrain and dark terrain, delimited by a thin trough running diagonally across the center of this image. The ejecta deposit surrounding the craters appears very bright on the bright terrain. Even though all the craters formed nearly simultaneously, it is difficult to discern any ejecta deposit on the dark terrain. {{clear}} ==Oort clouds== {{main|Radiation astronomy/Oort clouds}} {{multiple image |direction = vertical |align = right |width = 285 |image1=PIA17046 - Voyager 1 Goes Interstellar.jpg |image2=Kuiper oort-en.svg |caption1=This graphic shows the distance from the Oort cloud to the rest of the Solar System and two of the nearest stars measured in astronomical units (AU). The scale is logarithmic, with each specified distance ten times further out than the previous one. |caption2=An artist's rendering is of the Oort cloud and the Kuiper belt (inset). Sizes of individual objects have been exaggerated for visibility. }} The '''Oort cloud''' or the '''Öpik–Oort cloud'''<ref name = "Whipple">{{ cite journal | author = Fred Lawrence Whipple |author2=G. Turner |author3=J. A. M. McDonnell |author4=M. K. Wallis | title = A Review of Cometary Sciences | url = http://rsta.royalsocietypublishing.org/content/323/1572/339.short | journal = Philosophical Transactions of the Royal Society A | volume = 323 | issue = 1572 | pages = 339–347 [341] | publisher = Royal Society Publishing | date = 1987-09-30 | bibcode = 1987RSPTA.323..339W | doi = 10.1098/rsta.1987.0090 }}</ref> is a hypothesized spherical cloud of comets which may lie roughly 50,000 [[w:astronomical unit|AU]], or nearly a [[w:light-year|light-year]], from the [[Stars/Sun|Sun]].<ref name="Morbidelli2006">{{ cite book |author=Alessandro Morbidelli |year=2006 |title=Origin and dynamical evolution of comets and their reservoirs of water ammonia and methane. |url=https://arxiv.org/abs/astro-ph/0512256 |arxiv=astro-ph/0512256 }}</ref> This places the cloud at nearly a quarter of the distance to [[w:Proxima Centauri|Proxima Centauri]], the nearest [[w:star|star]] to the Sun. The outer limit of the Oort cloud defines the [[w:Cosmography|cosmographical]] boundary of the [[Solar System]] and the region of the Sun's gravitational dominance.<ref name="NASA_SSE_oort">{{ cite book |title=Kuiper Belt & Oort Cloud |url=http://solarsystem.nasa.gov/planets/profile.cfm?Object=KBOs&Display=OverviewLong |publisher=NASA |accessdate=2011-08-08 }}</ref> The Oort cloud is divided into two regions: a circumstellar disc-shaped inner Oort cloud (or Hills cloud) and a circumstellar envelope, spherical outer Oort cloud. Both regions lie beyond the heliosphere and in interstellar space.<ref name="Morbidelli2006a">{{cite arXiv |author=Alessandro Morbidelli |date=2006 |title=Origin and dynamical evolution of comets and their reservoirs of water ammonia and methane |eprint=astro-ph/0512256 }}</ref><ref name="jpl.PIA17046">{{cite web |url=http://photojournal.jpl.nasa.gov/catalog/PIA17046 |title=Catalog Page for PIA17046 |work=Photo Journal |publisher=NASA |date= |accessdate=April 27, 2014 }}</ref> ''Voyager 1'', the fastest<ref name="New_Horizons2006">{{cite web |url=http://pluto.jhuapl.edu/news_center/news/081706.php |title=New Horizons Salutes Voyager |date=August 17, 2006 |publisher=New Horizons |accessdate=November 3, 2009 |archiveurl=https://www.webcitation.org/5x3s4O3KH?url=http://pluto.jhuapl.edu/news_center/news/081706.php |archivedate=March 9, 2011 |df= }}</ref> and farthest<ref name="g.2013sep13">{{cite news |last=Clark |first=Stuart |title=Voyager 1 leaving solar system matches feats of great human explorers |url=https://www.theguardian.com/science/across-the-universe/2013/sep/13/voyager-1-solar-system-great-explorers |newspaper=The Guardian |date=September 13, 2013 }}</ref><ref>{{cite news |url=http://www.spacetoday.org/SolSys/Voyagers20years.html |title=Voyagers are leaving the Solar System |work=Space Today |date=2011 |accessdate=May 29, 2014 }}</ref> of the interplanetary space probes currently leaving the Solar System, will reach the Oort cloud in about 300 years<ref name="jpl.PIA17046"/><ref name="ut.104717">{{cite web |url=http://www.universetoday.com/104717/its-official-voyager-1-is-now-in-interstellar-space/ |title=It's Official: Voyager 1 Is Now In Interstellar Space |work=UniverseToday |date= 2013-09-12 |accessdate=April 27, 2014 }}</ref> and would take about 30,000 years to pass through it.<ref name="Ghose2013">{{cite web |last=Ghose |first=Tia |title=Voyager 1 Really Is In Interstellar Space: How NASA Knows |work=Space.com |publisher=TechMedia Network |date=September 13, 2013 |url=http://www.space.com/22797-voyager-1-interstellar-space-nasa-proof.html |accessdate=September 14, 2013 }}</ref><ref name="How_We_Know">{{cite web |last=Cook |first=J.-R |title=How Do We Know When Voyager Reaches Interstellar Space? |publisher=NASA / Jet Propulsion Lab | date=September 12, 2013 |url=http://www.jpl.nasa.gov/news/news.php?release=2013-278 |accessdate=September 15, 2013 }}</ref> However, around 2025, the radioisotope thermoelectric generators on ''Voyager 1'' will no longer supply enough power to operate any of its scientific instruments, preventing any further exploration by ''Voyager 1.'' {{clear}} ==Opticals== {{main|Radiation astronomy/Opticals|Optical astronomy}} [[Image:GTC Active Optics Acutators.jpg|thumb|right|250px|Actuators are part of the active optics of the {{lang|es|Gran Telescopio Canarias}}. Credit: [[commons:User:Vesta|Vesta]].{{tlx|free media}}]] [[Optical astronomy]] includes those portions of [[Ultraviolet astronomy|ultraviolet]], [[Visual astronomy|visual]], and [[infrared astronomy]] that benefit from the use of quartz crystal or silica glass telescope components. Observations at these wavelengths generally use ''optical components'' (mirrors, lenses and solid state digital detectors). In popular culture '''optical astronomy''' encompasses a wide variety of observations via telescopes that are sensitive in the range of visible light. Scientists would call this visible-light astronomy. It includes ''imaging'', where a picture of some sort is made of the object; ''photometry'', where the amount of light coming from an object is measured, ''spectroscopy'', where the distribution of that light with respect to its wavelength is measured, and ''polarimetry'' where the polarisation state of that light is measured. '''Def.''' astronomy using infrared, visible and/or ultraviolet wavelengths is called '''optical astronomy'''. '''Def.''' an optical system in telescopes that reduces atmospheric distortion by dynamically measuring and correcting wavefront aberrations in real time, often by using a deformable mirror is called '''adaptive optics'''. "Already it has allowed ground-based telescopes to produce images with sharpness rivalling those from the Hubble Space Telescope. The technique is expected to revolutionize the future of ground-based optical astronomy."<ref name="Roddier">{{cite book |author= |title=Adaptive Optics in Astronomy |publisher=Cambridge University Press |location=Cambridge, United Kingdom |date=1999 |editor=François Roddier |pages=411 |url=http://catdir.loc.gov/catdir/samples/cam031/00500597.pdf |arxiv= |bibcode= |doi= |pmid= |isbn=0 521 55375 X |accessdate=2012-02-15 }}</ref> The '''color index''' is a simple numerical expression that determines the color of an object, which in the case of a star gives its temperature. To measure the index, one observes the magnitude of an object successively through two different filters, such as U and B, or B and V, where U is sensitive to ultraviolet rays, B is sensitive to blue light, and V is sensitive to visible (green-yellow) light (see also: UBV system). The set of passbands or filters is called a photometric system. The difference in magnitudes found with these filters is called the U-B or B–V color index, respectively. The smaller the color index, the more blue (or hotter) the object is. Conversely, the larger the color index, the more red (or cooler) the object is. This is a consequence of the logarithmic magnitude scale, in which brighter objects have smaller (more negative) magnitudes than dimmer ones. For comparison, the yellowish [[Stars/Sun|Sun]] has a B–V index of {{nowrap|0.656 ± 0.005}},<ref name="Gray">David F. Gray (1992), ''[http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1992PASP..104.1035G&amp;db_key=AST&amp;data_type=HTML&amp;format=&amp;high=44b52c369023103 The Inferred Color Index of the Sun]'', Publications of the Astronomical Society of the Pacific, vol. 104, no. 681, pp. 1035-1038 (November 1992)</ref> while the bluish [[w:Rigel|Rigel]] has B–V –0.03 (its B magnitude is 0.09 and its V magnitude is 0.12, B–V = –0.03).<ref name="rigel">The [http://simbad.u-strasbg.fr Simbad Astronomical Database]' [http://simbad.u-strasbg.fr/sim-id.pl?protocol=html&Ident=Rigel&NbIdent=1&Radius=10&Radius.unit=arcmin&CooFrame=FK5&CooEpoch=2000&CooEqui=2000&output.max=all&o.catall=on&output.mesdisp=N&Bibyear1=1983&Bibyear2=2006&Frame1=FK5&Frame2=FK4&Frame3=G&Equi1=2000.0&Equi2=1950.0&Equi3=2000.0&Epoch1=2000.0&Epoch2=1950.0&Epoch3=2000.0 Rigel page]</ref> The passbands most optical astronomers use are the UBVRI filters, where the U, B, and V filters are as mentioned above, the R filter passes red light, and the I filter passes infrared light. These filters were specified as particular combinations of glass filters and photomultiplier tubes. An optical telescope gathers and focuses light mainly from the visible part of the electromagnetic spectrum (although some work in the infrared and ultraviolet).<ref name="Jones">{{cite book |url=http://books.google.com/books?id=5wX9aHqfBS0C&pg=PA111&lr=&cd=55#v=onepage&f=false |author=Barrie William Jones |title=The search for life continued: planets around other stars |page=111 }}</ref> {{clear}} ==Oranges== {{main|Radiation astronomy/Oranges|Orange astronomy}} [[Image:Jupiter.jpg|left|thumb|250px|Cloud bands are clearly visible on [[Jupiter]]. Credit: NASA/JPL/USGS.{{tlx|free media}}]] "[O]range [is] the color of Jupiter"<ref name="Birren">{{cite journal |author= Faber Birren |title=Color and human response |journal=Color Research and Application |month=Summer |year=1983 |volume=8 |issue=2 |pages=75-81 |url=http://onlinelibrary.wiley.com/doi/10.1002/col.5080080204/abstract |arxiv= |bibcode= |doi=10.1002/col.5080080204 |pmid= |accessdate=2012-04-23 }}</ref>. The orange and brown coloration in the clouds of Jupiter are caused by upwelling compounds that change color when they are exposed to ultraviolet light from the Sun. The exact makeup remains uncertain, but the substances are believed to be phosphorus, sulfur or possibly hydrocarbons.<ref name="elkins-tanton">{{cite book |first=Linda T.|last=Elkins-Tanton|year=2006 |title=Jupiter and Saturn|publisher=Chelsea House |location=New York|isbn=0-8160-5196-8}}</ref><ref>{{cite book |author=Strycker, P. D. |author2=Chanover, N. |author3=Sussman, M. |author4=Simon-Miller, A. |title = A Spectroscopic Search for Jupiter's Chromophores, In: ''DPS meeting #38, #11.15'' |publisher = American Astronomical Society|year = 2006 |bibcode = 2006DPS....38.1115S }}</ref> These colorful compounds, known as chromophores, mix with the warmer, lower deck of clouds. The zones are formed when rising convection cells form crystallizing ammonia that masks out these lower clouds from view.<ref name="worldbook">{{cite book |author=Gierasch, Peter J. |author2=Nicholson, Philip D. |year = 2004 |url = http://www.nasa.gov/worldbook/jupiter_worldbook.html |title = Jupiter |publisher = World Book @ NASA |accessdate = 2006-08-10 }}</ref> The '''orange system''' [in [[orange astronomy]]] is a number of emission lines very close together forming a band in the orange portion of the visible spectrum. These lines are usually associated with particular molecular species, including ScO, YO, and TiO.<ref name="Herbig">{{cite journal |author=G. H. Herbig |title=VY Canis Majoris. IV. The emission bands of ScO |journal=The Astrophysical Journal |month=March |year=1974 |volume=188 |issue=3 |pages=533-8 |url= |arxiv= |bibcode=1974ApJ...188..533H |doi=10.1086/152744 |pmid= |accessdate=2012-02-01 }}</ref> The orange band from molecular CaCl is "observed in the spectra of many carbon stars."<ref name="Littleton">{{cite journal |author=J. E. Littleton |author2=Sumner P. Davis |title=Transition strength data for the orange and red bands of CaCl |journal=The Astrophysical Journal |month=October |year=1988 |volume=333 |issue=10 |pages=1026-34 |url= |arxiv= |bibcode=1988ApJ...333.1026L |doi=10.1086/166809 |pmid= |accessdate=2012-02-01 }}</ref> The Fe VII emission line at 608.7 nm, "frequently observed in the spectra of astrophysical plasmas", has been detected in planetary nebulae, Seyfert galaxies, and quasars.<ref name="Keenan">{{cite journal |author=F. P. Keenan |author2=P. H. Norrington |title=Relative emission line strengths for Fe VII in astrophysical plasmas |journal=Astronomy and Astrophysics |month=July |year=1987 |volume=181 |issue=2 |pages=370-2 |url= |arxiv= |bibcode=1987A&A...181..370K |doi= |pmid= |accessdate=2012-01-17 }}</ref> {{clear}} ==Particles== {{main|Radiation astronomy/Particles}} [[Image:Dark Flight Incoming.jpg|thumb|right|250px|The image shows the first film ever of a meteor plunging down at terminal velocity. Credit: Anders Helstrup / Dark Flight, montage, Hans Erik Foss Amundsen.]] "A skydiver may have captured the first film ever of a meteorite plunging down at terminal velocity, also known as its “dark flight” stage."<ref name=Fang>{{ cite book |author=Janet Fang |title=Skydiver Almost Hit by Meteorite |publisher=IFLScience |location= |date=April 4, 2014 |url=http://www.iflscience.com/space/skydiver-almost-hit-meteorite |accessdate=2014-08-31 }}</ref> "The footage was captured in 2012 by a helmet cam worn by Anders Helstrup as he and other members of the Oslo Parachute Club jumped from a small plane that took off from an airport in Hedmark, Norway."<ref name=Fang/> “It can’t be anything else. The shape is typical of meteorites -- a fresh fracture surface on one side, while the other side is rounded.”<ref name=Amundsen>{{ cite book |author=Hans Erik Foss Amundsen |title=Skydiver Almost Hit by Meteorite |publisher=IFLScience |location= |date=April 4, 2014 |url=http://www.iflscience.com/space/skydiver-almost-hit-meteorite |accessdate=2014-08-31 }}</ref> “It has never happened before that a meteorite has been filmed during dark flight; this is the first time in world history.”<ref name=Amundsen/> "Having the rock in hand would certainly help. But despite triangulations and analyses, Helstrup and his recruits still haven’t found it."<ref name=Fang/> {{clear}} ==Planets== {{main|Radiation astronomy/Planets|Planetary astronomy}} [[Image:Ganymede g1 true-edit1.jpg|thumb|right|250px|A true color image of Ganymede is acquired by the Galileo spacecraft on June 26, 1996. Credit: [[commons:User:PlanetUser|PlanetUser]], NASA, JPL.{{tlx|free media}}]] '''Planetary science''' is the scientific study of planets (including [[Rocks/Rocky objects/Earth|Earth]]), natural satellite, moons, and planetary systems, in particular those of the [[Solar System|solar system]] and the processes that form them using the radiation they emit, reflect, fluoresce, or absorb. It studies objects ranging in size from micrometeoroids to gas giants, aiming to determine their composition, dynamics, formation, interrelations and history. It is a strongly interdisciplinary field, originally growing from astronomy and earth science,<ref name="Taylor"/> but which now incorporates many disciplines, including planetary astronomy, planetary geology (together with geochemistry and geophysics), atmospheric science, oceanography, [[hydrology]], theoretical planetary science, glaciology, and the study of extrasolar planets.<ref name="Taylor">{{cite journal |author=Stuart Ross Taylor |date=29 July 2004 |title=Why can't planets be like stars? |journal=Nature |pmid=15282586 |volume=430 |issue=6999 |pages=509 |doi=10.1038/430509a |url=http://www.nature.com/nature/journal/v430/n6999/full/430509a.html |bibcode = 2004Natur.430..509T }}</ref> {{clear}} ==Plasmas== {{main|Radiation astronomy/Plasmas}} [[Image:Media 1.ogv|thumb|right|250px|On July 19, 2012, an eruption occurred on the sun that produced a moderately powerful solar flare and a dazzling magnetic display known as coronal rain. Credit: NASA Goddard Space Flight Center, Music: 'Thunderbolt' by Lars Leonhard, courtesy of artist.]] "[A] medium-strength flare erupted from the sun on July 19, 2012. The blast also generated the enormous, shimmering plasma loops, which are an example of a phenomenon known as "coronal rain," agency officials said."<ref name="Wall">{{cite book |author=Mike Wall |title=Super-Hot Plasma 'Rain' Falls on Sun in Amazing Video |publisher=Yahoo! News |location= |date=February 21, 2013 |url=http://news.yahoo.com/super-hot-plasma-rain-falls-sun-amazing-video-190147271.html |accessdate=2013-02-23 }}</ref> "Hot plasma in the corona cooled and condensed along strong magnetic fields in the region" slowly falling back to the solar surface as plasma "rain".<ref name="Wall"/> A [[coronal cloud]] is a cloud, or cloud-like, natural astronomical entity, composed of plasma and usually associated with a star or other astronomical object where the temperature is such that X-rays are emitted. While small coronal clouds are above the photosphere of many different visual spectral type stars, others occupy parts of the [[interstellar medium]] (ISM), extending sometimes millions of kilometers into space, or thousands of light-years, depending on the size of the associated object such as a galaxy. {{clear}} ==Positrons== {{main|Radiation astronomy/Positrons|Positron astronomy}} [[Image:509305main GBM positron event 300dpi.jpg|thumb|right|250px|Observation of positrons from a terrestrial gamma ray flash is performed by the Fermi gamma ray telescope. Credit: NASA Goddard Space Flight Center.{{tlx|free media}}]] "[[Positron astronomy]] is 30 years old but remains in its infancy."<ref name="Milne">{{cite book |author=P.A.Milne |author2=J.D.Kurfess |author3=R.L.Kinzer |author4=M.D.Leising |author5=D.D.Dixon |title=Investigations of positron annihilation radiation, In: ''Proceedings of the 5th COMPTON Symposium'' |publisher=American Institute of Physics |location=Washington, DC |date=April 2000 |volume=510 |issue=4 |pages=21-30 |url=http://arxiv.org/pdf/astro-ph/9911184 |arxiv=astro-ph/9911184v1 |bibcode=2000AIPC..510...21M |doi=10.1063/1.1303167 |pmid= |accessdate=2011-11-25 }}</ref> "[P]ositron astronomy results ... have been obtained using the INTEGRAL spectrometer SPI".<ref name=" Weidenspointner ">{{cite journal |author=G. Weidenspointner |author2=G.K. Skinner |author3=P. Jean |author4=J. Knödlseder |author5=P. von Ballmoos |author6=R. Diehl |author7=A. Strong |author8=B. Cordier |author9=S. Schanne |author10=C. Winkler |title=Positron astronomy with SPI/INTEGRAL |journal=New Astronomy Reviews |month=October |year=2008 |volume=52 |issue=7-10 |pages=454-6 |url=http://www.sciencedirect.com/science/article/pii/S1387647308001164 |arxiv= |bibcode= |doi=10.1016/j.newar.2008.06.019 |pmid= |accessdate=2011-11-25 }}</ref> The positrons are not directly observed by the INTEGRAL space telescope, but "the 511 keV positron annihilation emission is".<ref name="Weidenspointner"/> During solar flares “[s]everal radioactive nuclei that emit positrons are also produced; [which] slow down and annihilate in flight with the emission of two 511 keV photons or form positronium with the emission of either a three gamma continuum (each photon < 511 keV) or two 511 keV photons."<ref name="Share">{{cite book |author=Gerald H. Share |author2=Ronald J. Murphy |title=Solar Gamma-Ray Line Spectroscopy – Physics of a Flaring Star, In: ''Stars as Suns: Activity, Evolution and Planets'' |publisher=Astronomical Society of the Pacific |location=San Francisco, CA |date=January 2004 |editor=Andrea K. Dupree |editor2=A. O. Benz |pages=133-44 |url=http://heseweb.nrl.navy.mil/gamma/solar/papers/share_iau_04.pdf |arxiv= |bibcode=2004IAUS..219..133S |doi= |pmid= |isbn=158381163X |accessdate=2012-03-15 }}</ref> {{clear}} ==Protons== {{main|Radiation astronomy/Protons|Proton astronomy}} [[Image:GOES protons.jpg|thumb|right|250px|This graph displays the flux of high energy protons measured by GOES 11 over four days from November 2, 2003, to November 5, 2003. Credit: NOAA.{{tlx|free media}}]] "[[Proton astronomy]] should be possible; it may also provide indirect information on inter-galactic magnetic fields."<ref name="Halzen2002">{{cite journal |author=Francis Halzen |author2=Dan Hooper |title=High-energy neutrino astronomy: the cosmic ray connection |journal=Reports on Progress in Physics |month=July |year=2002 |volume=65 |issue=7 |pages=1025-78 |url=http://arxiv.org/pdf/astro-ph/0204527 |arxiv= |bibcode=2002RPPh...65.1025H |doi=10.1088/0034-4885/65/7/201 |pmid= |accessdate=2011-11-24 }}</ref> Proton astronomy ''per se'' often consists of directly or indirectly detecting the protons and deconvoluting a spatial, temporal, and spectral distribution. “[A]t the high end of the proton energy spectrum (above ≈ 10<sup>18</sup> eV) [the Larmor radius] deflection becomes small enough that proton astronomy becomes possible.”<ref name="Hoffman">{{cite journal |author=K. D. Hoffman |title=High energy neutrino telescopes |journal=New Journal of Physics |month=May 12, |year=2009 |volume=11 |issue=5 |pages=055006 |url=http://arxiv.org/pdf/astro-ph/0204527 |arxiv= |bibcode= |doi=10.1088/1367-2630/11/5/055006 |pmid= |accessdate=2012-03-28 }}</ref> "The third largest solar proton event in the past thirty years took place during July 14-16, 2000, and had a significant impact on the earth's atmosphere."<ref name="Jackman">{{cite journal |author=Charles H. Jackman |author2=Richard D. McPeters |author3=Gordon J. Labow |author4=Eric L.Fleming |author5=Cid J. Praderas |author6=James M. Russell |title=Northern Hemisphere atmospheric effects due to the July 2000 solar proton event |journal=Geophysical Research Letters |month=August |year=2001 |volume=28 |issue=15 |pages=2883-6 |url=http://cdaw.gsfc.nasa.gov/meetings/2009_gle/data/Jackman/Jackman_2001.pdf |arxiv= |bibcode= |doi= |pmid= |accessdate=2011-11-24 }}</ref> {{clear}} ==Radars== {{main|Radiation astronomy/Radars|Radar astronomy}} [[Image:2012 LZ1.jpg|thumb|right|250px|This image is of asteroid 2012 LZ1 by the Arecibo Observatory in Puerto Rico using the Arecibo Planetary Radar. Credit: Arecibo Observatory.{{tlx|fairuse}}]] '''Radar astronomy''' is used to detect and study astronomical objects that reflect radio rays. "The advantages of radar in planetary astronomy result from (1) the observer's control of all the attributes of the coherent signal used to illuminate the target, especially the wave form's time/frequency modulation and polarization; (2) the ability of radar to resolve objects spatially via measurements of the distribution of echo power in time delay and Doppler frequency; (3) the pronounced degree to which delay-Doppler measurements constrain orbits and spin vectors; and (4) centimeter-to-meter wavelengths, which easily penetrate optically opaque planetary clouds and cometary comae, permit investigation of near-surface macrostructure and bulk density, and are sensitive to high concentrations of metal or, in certain situations, ice."<ref name="Ostro">{{cite journal |author=Steven J. Ostro |title=Planetary radar astronomy |journal=Reviews of Modern Physics |month=October-December |year=1993 |volume=65 |issue=4 |pages=1235-79 |url=http://rmp.aps.org/abstract/RMP/v65/i4/p1235_1 |arxiv= |bibcode= |doi=10.1103/RevModPhys.65.1235 |pmid= |accessdate=2012-02-09 }}</ref> {{clear}} ==Radiation== {{main|Radiation}} [[Image:Lead shielding.jpg|thumb|right|250px|A lead castle is built to shield a radioactive sample. Credit: [[commons:User:Changlc|Changlc]].{{tlx|free media}}]] In physics, '''radiation''' is a process in which energetic particles or energetic waves travel through a medium or space. '''Def.''' an action or process of throwing or sending out a traveling ray of energy in a line, beam, or stream of small cross section is called '''radiation'''. '''Def.''' the shooting forth of anything from a point or surface, like the diverging rays of light is called '''radiation'''. The term '''radiation''' is often used to refer to the ray itself. Different types of ionizing radiation behave in different ways, so different shielding techniques are used. {{clear}} ==Radios== {{main|Radiation astronomy/Radios|Radio astronomy}} [[Image:Composite radio + x-ray.jpg|thumb|right|250px|This image has the radio image of Greg Taylor, NRAO, overlain on the X-ray image from Chandra. The radio source Hydra A originates in a galaxy near the center of the cluster. Optical observations show a few hundred galaxies in the cluster. Credit: NASA/CXC/SAO; Radio: NRAO.{{tlx|free media}}]] '''Radio waves''' are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies from 300 [Gigahertz] GHz to as low as 3 [kilohertz] kHz, and corresponding wavelengths from 1 millimeter to 100 kilometers. Several satellites have served as observatories for radio waves and specifically for microwaves. The Radio Astronomy Explorer (RAE) 1 is launched into orbit on July 4, 1968, around Earth, while the [Explorer 49] RAE 2 is launched on June 10, 1973, around the Moon. The COBE is launched into Earth orbit on November 18, 1989. The WMAP is launched on June 30, 2001, into orbit at the [Lissajous orbit] Lagrange 2 location. Both satellites have aboard detectors designed to perform '''microwave astronomy''', as these are limited to only the microwave band. {{clear}} ==Reds== {{main|Radiation astronomy/Reds|Red astronomy}} [[Image:AZCancriCloseup.jpg|thumb|right|150px|AZ Cancri. Credit: SDSS Data Release 6.{{tlx|free media}}]] With respect to the color 'red', there are studies of the redness of objects such as the red dwarf AZ Cancri shown in the visual image at right. Cool stars of spectral class M appear red; they are (depending on their size) referred to as "red giants" or "red dwarfs". "Ideally all intrinsic colours should be found from unreddened stars. This is possible for dwarf and giant stars later than about A0 (Johnson, 1964) ... However, it cannot be used for stars of other spectral classes since they are all relatively infrequent in space, and generally reddened."<ref name="FitzGerald">{{cite journal |author=M. Pim FitzGerald |title=The Intrinsic Colours of Stars and Two-Colour Reddening Lines |journal=Astronomy and Astrophysics |month=February |year=1970 |volume=4 |issue=2 |pages=234-43 |url= |arxiv= |bibcode=1970A&A.....4..234F |doi= |pmid= |accessdate=2011-11-24 }}</ref> A very important wavelength in this region is the Balmer alpha line, 656.28 nm. It is emitted or absorbed by hydrogen atoms when electrons move between the second and third electron shells. Other Balmer lines, known as beta, gamma and delta, have wavelengths of 486.13, 434.05 and 410.17 nm respectively;[http://www.phys.utk.edu/labs/modphys/BalmerSeries.pdf] these are also in the visual range but are less important than the alpha line. {{clear}} ==Reflections== {{main|Radiation astronomy/Reflections}} [[Image:Ash and Steam Plume, Soufriere Hills Volcano, Montserrat.jpg|thumb|right|250px|This oblique astronaut photograph from the International Space Station (ISS) captures a white-to-grey ash and steam plume extending westwards from the Soufriere Hills volcano. Credit: NASA Expedition 21 crew.]] Oblique images such as the one at right are taken by astronauts looking out from the International Space Station (ISS) at an angle, rather than looking straight downward toward the Earth (a perspective called a nadir view), as is common with most remotely sensed data from satellites. An oblique view gives the scene a more three-dimension quality, and provides a look at the vertical structure of the volcanic plume. While much of the island is covered in green vegetation, grey deposits that include pyroclastic flows and volcanic mud-flows (lahars) are visible extending from the volcano toward the coastline. When compared to its extent in earlier views, the volcanic debris has filled in more of the eastern coastline. Urban areas are visible in the northern and western portions of the island; they are recognizable by linear street patterns and the presence of bright building rooftops. The silver-grey appearance of the Caribbean Sea surface is due to sun-glint, which is the mirror-like '''reflection''' of sunlight off the water surface back towards the hand-held camera on-board the ISS. The sun-glint highlights surface wave patterns around the island. {{clear}} ==Refractions== {{main|Radiation astronomy/Refractions}} [[Image:Calcite ShortwaveUV HAGAM.jpg|thumb|left|250px|Calcite fluoresces blue under short wave ultraviolet light. Credit: Herbert Art Gallery and Museum, Coventry.]] [[File:Calcite - Blue (2933075912).jpg|thumb|right|250px|Natural radiation interacts with sheared calcite to produce blue colors. Credit: Stephanie Clifford]] Between 190 and 1700&nbsp;nm, the ordinary refractive index varies roughly between 1.9 and 1.5, while the extraordinary refractive index varies between 1.6 and 1.4.<ref name=Thompson>{{ cite journal |author = D.W. Thompson |year=1998 |title=Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry |journal= Thin Solid Films |volume=313–4 |issue= 1-2 |pages=341–6 |doi=10.1016/S0040-6090(97)00843-2 |bibcode=1998TSF...313..341T }}</ref> On the right is blue calcite produced by natural irradiation. {{clear}} ==Rocks== {{main|Radiation astronomy/Rocks}} [[Image:BlueRock.jpg|thumb|right|250px|This Sin-Kamen (''Blue Rock'') near Lake Pleshcheyevo used to be a Meryan shrine Credit: Viktorianec.]] [[Image:Blue rock from Berkeley hills.jpg|thumb|left|250px|This is a blue rock, probably various copper minerals, from the Berkeley hills near San Francisco, California. Credit: [[w:User:Looie496|Looie496]].]] [[Image:243 ida crop.jpg|thumb|right|250px|This is an approximately natural color picture of the asteroid 243 Ida on August 28, 1993. Credit: NASA/JPL.]] '''Sin-Kamen''' ({{lang|ru|Синь-Камень}}, in Russian literally – '''Blue Stone''', or '''Blue Rock''') is a type of pagan sacred stones, widespread in Russia, in areas historically inhabited by both Eastern Slavic (Russian), and Uralic tribes (Merya, Muroma<ref>[http://www.bogorodsk-noginsk.ru/atlas/sinie_kamni.html И.Д. Маланин. Материалы разведки Синих камней Подмосковья в 2003 году // Краеведение и регионоведение. Межвузовский сборник научных трудов. ч.1. Владимир, 2004.] (Russian)</ref>). While in the majority of cases, the stones belonging to the ''Blue Stones'' type, have a black, or dark gray color, this particular stone [in the image] does indeed look dark blue, when wet.<ref name="berdnikov">[http://pki.botik.ru/dl.php?b=articles&a=n-sinii1985berd.pdf Бердников,&nbsp;В. Синий камень Плещеева озера] // Наука и жизнь. – 1985. – № 1. – С.&nbsp;134–139. (Russian)</ref> "Several types of rock surface materials can be recognized at the two sites [Viking Lander 1 and Viking Lander 2]; dark, relatively 'blue' rock surfaces are probably minimally weathered igneous rock, whereas bright rock surfaces, with a green/(blue + red) ratio higher than that of any other surface material, are interpreted as a weathering product formed in situ on the rock."<ref name="Strickland">{{cite book |author=Edwin L. Strickland III |title=Martian soil stratigraphy and rock coatings observed in color-enhanced Viking Lander images, In: ''Lunar and Planetary Science Conference Proceedings'' |publisher=Pergamon Press, Inc. |location=New York |date=March 19, 1979 |volume=3 |issue= |pages=3055-77 |url=http://adsabs.harvard.edu/abs/1979LPSC...10.3055S |arxiv= |bibcode=1979LPSC...10.3055S |doi= |pmid= |accessdate=2013-05-31 }}</ref> At second right is an approximately natural color image of the asteroid 243 Ida. "There are brighter areas, appearing bluish in the picture, around craters on the upper left end of Ida, around the small bright crater near the center of the asteroid, and near the upper right-hand edge (the limb). This is a combination of more reflected blue light and greater absorption of near infrared light, suggesting a difference in the abundance or composition of iron-bearing minerals in these areas."<ref name="Lavoie96">{{cite book |author=Sue Lavoie |title=PIA00069: Ida and Dactyl in Enhanced Color |publisher=NASA/JPL |location=Pasadena, California USA |date=January 29, 1996 |url=http://photojournal.jpl.nasa.gov/catalog/?IDNumber=PIA00069 |accessdate=2013-06-01 }}</ref> "The [Sloan Digital Sky Survey] SDSS “blue” asteroids are related to the C-type (carbonaceous) asteroids, but not all of them are C-type. They are a mixture of C-, E-, M-, and P-types."<ref name="Yoshida">{{cite journal |author=F Yoshida, T Nakamura |title=Subaru main belt asteroid survey (SMBAS)—size and color distributions of small main-belt asteroids |journal=Planetary and Space Science |month=June |year=2007 |volume=55 |issue=9 |pages=1113-25 |url=http://www.sciencedirect.com/science/article/pii/S0032063306003357 |arxiv= |bibcode= |doi=10.1016/j.pss.2006.11.016 |pmid= |accessdate=2013-06-01 }}</ref> {{clear}} ==Satellites== {{main|Radiation astronomy/Satellites}} [[Image:IBEX spacecraft.jpg|thumb|right|250px|This is an artist's rendering of the Interstellar Boundary Explorer (IBEX) satellite. Credit: NASA/Goddard Space Flight Center Conceptual Image Lab.{{tlx|free media}}]] '''Radiation satellites''' may be designed and built for detection in one particular radiation astronomy or for many. Some have been built for more than one purpose or for a different purpose entirely. To place sensors (or detectors) above the [[w:Earth’s atmosphere|Earth’s atmosphere]] is often a necessity for radiation astronomy. “The sensors at once lose the basic advantage of both radio and optical telescopes, a rigid, well-surveyed foundation upon a well-behaved earth.”<ref name=Ouellette>{{ cite journal |author=Gerald A. Ouellette |title=Development of a Catalogue of Galactic X-Ray Sources |journal=The Astronomical Journal |month=June |year=1967 |volume=72 |issue=5 |pages=597-600 |url= |arxiv= |bibcode=1967AJ.....72..597O |doi=10.1086/110278 |pmid= |accessdate=2012-03-17 }}</ref> “The source locations, therefore, reflect uncertainties in both the sensor data and in vehicle aspect.”<ref name=Ouellette/> {{clear}} ==Scattered disks== {{main|Radiation astronomy/Scattered disks}} [[Image:TheKuiperBelt 100AU SDO.svg|thumb|center|400px|The diagram shows scattered disc objects out to 100 AU. Credit: [[commons:User:Eurocommuter|Eurocommuter]].]] Scattered Disk Objects (up to 100 AU): Kuiper Belt objects are shown in grey, resonant objects within the Scattered Disk are shown in green. The position of an object represents * its orbit’s semi-major axis '''a''' in AU and the orbital period in years (horizontal axis) * its orbit’s inclination '''i''' in degrees (vertical axis). The size of the circle illustrates the object’s size relative to others. For a few large objects, the diameter drawn represents the best current estimates. For all others, the circles represent the absolute magnitude of the object. The eccentricity of the orbit is shown indirectly by a segment extending from the left (perihelion) to the aphelion to the right. In other words, the segment illustrates the variations of the object's distance from the Sun. Objects with nearly circular orbits will show short segments while highly elliptical orbits will be represented by long segments. Main resonances with Neptune are marked with vertical bars; 1:1 marks the position of Neptune’s orbit (and its Trojan asteroids), 2:3 marks the orbit of Pluto (and plutinos) etc. The scattered disc (or scattered disk) is a distant region of the [[Solar System]] that is sparsely populated by icy minor planets, a subset of the broader family of trans-Neptunian objects. The scattered-disc objects (SDOs) have orbital eccentricities ranging as high as 0.8, inclinations as high as 40°, and perihelia greater than 30 astronomical units (4.5 x 10<sup>9</sup> km; 2.8 x 10<sup>9</sup> mi.). While the nearest distance to the Sun approached by scattered objects is about 30–35&nbsp;AU, their orbits can extend well beyond 100&nbsp;AU. This makes scattered objects "among the most distant and cold objects in the Solar System".<ref name=Masetti>Maggie Masetti. (2007). ''[http://heasarc.gsfc.nasa.gov/docs/cosmic/solar_system_info.html Cosmic Distance Scales&nbsp;– The Solar System]''. Website of NASA's High Energy Astrophysics Science Archive Research Center. Retrieved 2008 07-12.</ref> The innermost portion of the scattered disc overlaps with a torus-shaped region of orbiting objects traditionally called the Kuiper belt,<ref name=Morbidelli2008>{{cite arXiv |title=Origin and dynamical evolution of comets and their reservoirs |first=Alessandro |last= Morbidelli |eprint=astro-ph/0512256 |date=2005 }}</ref> but its outer limits reach much farther away from the Sun and farther above and below the ecliptic than the Kuiper belt proper. The literature is inconsistent in the use of the phrases "scattered disc" and "Kuiper belt"; for some, they are distinct populations; for others, the scattered disc is part of the Kuiper belt and authors may even switch between these two uses in a single publication.<ref>McFadden, Weissman, & Johnson (2007). ''Encyclopedia of the Solar System'', footnote p. 584</ref> {{clear}} ==Scatterings== {{main|Radiation astronomy/Scatterings}} Neutrons react with a number of materials through elastic scattering producing a recoiling nucleus, [[w:Inelastic scattering|inelastic scattering]] producing an excited nucleus, or absorption with transmutation of the resulting nucleus. Most detection approaches rely on detecting the various reaction products. {{clear}} ==Skys== [[Image:Hajiali.jpg|thumb|left|250px|An orange sunset in the Mahim Bay is shown around the Haji Ali Dargah in India. Credit: [http://www.flickr.com/people/82341349@N00 Humayunn Peerzaada].]] [[Image:Clouds over the Atlantic Ocean.jpg|thumb|right|250px|Although the image contains a layer of cumulus clouds, at the horizon, the Atlantic Ocean meets the edge of the sky. Location: Salvador, Bahia, Brazil, July 4, 2008. Credit: [[commons:User:Tfioreze|Tiago Fioreze]].]] [[Image:MarsPanoramaa.jpg|thumb|left|280px|This is a 360° view of the surrounding terrain, horizon and Martian sky, taken on November 23-28, 2005, by the Exploration Rover 'Spirit'. Credit: NASA.]] [[Image:ALSEP AS16-113-18369.jpg|thumb|right|150px|A view of the horizon on the Moon's solid surface shows a black sky without stars because of sunlight coming from the left. Credit: NASA.]] Seeing an orange [[Sun (star)|Sun]] due to atmospheric effects and feeling the warmth of its rays is probably a student's first encounter with an apparent astronomical orange radiation source. '''Def.''' "the expanse of space that seems to be over the earth like a dome"<ref name=Gove>{{ cite book |author= |title=Webster's Seventh New Collegiate Dictionary |publisher=G. & C. Merriam Company |location=Springfield, Massachusetts |year=1963 |editor=Philip B. Gove |pages=1221 |bibcode= |doi= |pmid= |isbn= }}</ref> is called the '''sky''', or sometimes the '''heavens'''. This definition applies especially well to an individual on top of the Earth's solid crust looking around at what lies above and off to the horizon in all directions. Similarly, it applies to an individual's visual view while floating on a large body of water, where off on the horizon is still water. The image at upper right shows the horizon marking the lower edge of the sky and the upper edge of the Atlantic Ocean, with a layer of cumulus clouds just above. A more general definition of 'sky' allows for skies as seen on other worlds. At left is a 360° panarama of the horizon on Mars as perceived in the visual true-color range of the NASA Mars Exploration Rover 'Spirit' on November 23-8, 2005. '''Def.''' an "expanse of space that seems to be [overhead] like a dome"<ref name=Gove/> is called a '''sky'''. Even in day light, the sky may seem absent of objects if a nearby source tends to overwhelm other luminous objects. At lower right is a view of the horizon on the Moon's solid surface taken by an Apollo 16 astronaut. The image shows a black sky without stars because the sunlight coming from the left is overwhelming. {{clear}} ==Sources== {{main|Radiation astronomy/Sources}} [[Image:Crmo volcanic bomb 20070516123632.jpg|thumb|right|250px|Volcanic bombs are thrown into the sky and travel some distance before returning to the ground. This bomb is in the Craters of the Moon National Monument and Preserve, Idaho, USA. Credit: National Park Service.{{tlx|free media}}]] In [[source astronomy]], the question is "Where did it come from?" '''Source astronomy''' has its origins in the actions of intelligent life on Earth when they noticed things or entities falling from above and became aware of the '''sky'''. Sometimes what they noticed is an acorn or walnut being dropped on them or thrown at them by a squirrel in a tree. Other events coupled with keen intellect allowed these life forms to deduce that some entities falling from the sky are coming down from locations higher than the tops of local trees. '''Def.''' a source or apparent source detected or “[[wikt:created|created]] at or near the [[wikt:time|time]] of the [ [[wikt:event|event]] or] events” is called a '''primary source'''. Direct observation and tracking of the origination and trajectories of falling entities such as volcanic bombs presented early intelligent life with vital albeit sometimes dangerous opportunities to compose the science that led to [[source astronomy]]. {{clear}} ==Spallations== {{main|Radiation astronomy/Spallations}} '''Def.''' a [[wikt:nuclear reaction|nuclear reaction]] in which a [[wikt:nucleus|nucleus]] [[wikt:fragment|fragment]]s into many [[wikt:nucleon|nucleon]]s is called '''spallation'''. "THE first suggestion that appreciable {{chem|14|C}} might be produced ''in situ'' in polar ice was made by Fireman and Norris<sup>1</sup>, who studied {{chem|14|C}} in CO<sub>2</sub> extracted from both accumulation and ablation samples. In some ablation samples they observed {{chem|14|C}} activities between four and six times higher than those expected due to trapped atmospheric CO<sub>2</sub>."<ref name=Lal>{{ cite journal |author=D Lal |author2=AJT Jull |author3=DJ Donahue |author4=D Burtner |author5=K Nishiizumi |title=Polar ice ablation rates measured using ''in situ'' cosmogenic {{chem|14|C}} |journal=Nature |year=1990 |volume=346 |issue= |pages=350-352 |url=https://www.nature.com/articles/346350a0 |arxiv= |bibcode=1990Natur.346..350L |doi=10.1038/346350a0 |pmid= |accessdate=2017-12-05 }}</ref> "The <sup>14</sup>C is produced mainly by nuclear spallations of oxygen in ice. The observed concentration of <sup>14</sup>C in ablation ice samples is 1–3 x 10<sup>3</sup> atom per g ice, three orders of magnitude higher than expected from the amount of trapped atmospheric CO<sub>2</sub> in this ice."<ref name=Lal/> "Spallation of atmospheric oxygen nuclei might contribute up to 20% to production of {{chem|14|C}} produced in the atmosphere (Lal and Peters 1967)."<ref name=Lal2001>{{ cite journal |author=D Lal |author2=A J T Jull |title=In-situ cosmogenic {{chem|14|C}}: Production and examples of its unique applications in studies of terrestrial and extraterrestrial processes |journal=Radiocarbon |year=2001 |volume=43 |issue=28 |pages=731-742 |url=https://journals.uair.arizona.edu/index.php/radiocarbon/article/download/3905/3330 |arxiv= |bibcode= |doi= |pmid= |accessdate=2017-12-06 }}</ref> {{clear}} ==Spatials== {{main|Radiation astronomy/Spatials}} [[Image:Rosat 0.25kev all-sky survey.gif|thumb|250px|right|This [[w:ROSAT|ROSAT]] image is an Aitoff-Hammer equal-area map in galactic coordinates with the Galactic center in the middle of the 0.25 keV diffuse X-ray background. Credit: NASA.]] A '''spatial distribution''' is a spatial [[w:frequency|frequency]] of [[w:occurrence|occurrence]] or [[w:extent|extent]] of astronomical entities, sources, or objects. A space is a volume large enough to accommodate an astronomical thing. There is an “extensive 1/4 keV emission in the Galactic halo”, an “observed 1/4 keV [X-ray emission originating] in a Local Hot Bubble (LHB) that surrounds the Sun. ... and an isotropic extragalactic component.”<ref name=Snowden>{{ cite journal |author=S. L. Snowden |author2=R. Egger |author3=D. P. Finkbiner |author4=M. J. Freyberg |author5=P. P. Plucinsky |title=Progress on Establishing the Spatial Distribution of Material Responsible for the 1/4 keV Soft X-Ray Diffuse Background Local and Halo Components |journal=The Astrophysical Journal |month=February 1, |year=1998 |volume=493 |issue=1 |pages=715-29 |url=http://iopscience.iop.org/0004-637X/493/2/715/fulltext/ |arxiv= |bibcode=1998ApJ...493..715S |doi=10.1086/305135 |pmid= |accessdate=2012-06-14 }}</ref> In addition to this “distribution of emission responsible for the soft X-ray diffuse background (SXRB) ... there are the distinct enhancements of supernova remnants, superbubbles, and clusters of galaxies.”<ref name=Snowden/> The ROSAT soft X-ray diffuse background (SXRB) image shows the general increase in intensity from the Galactic plane to the poles. At the lowest energies, 0.1 - 0.3 keV, nearly all of the observed soft X-ray background (SXRB) is thermal emission from ~10<sup>6</sup> K plasma. {{clear}} ==Spectrals== {{main|Radiation astronomy/Spectrals}} [[Image:TheElectromagneticSpectrum.jpg|thumb|450px|right|The electromagnetic spectrum. The red line indicates the room temperature thermal energy. Credit: [[b:nanotechnology|Opensource Handbook of Nanoscience and Nanotechnology]]. {{tlx|free media}}]] A '''spectral distribution''' is often a plot or intensity, brightness, flux density, or other characteristic of a spectrum versus the spectral property such as wavelength, frequency, energy, particle speed, refractive or reflective index, for example. The first three dozen or so astronomical X-ray objects detected other than the [[Sun (star)|Sun]] "represent a brightness range of about a thousandfold from the most intense source, Sco XR-1, ''ca.'' 5 x 10<sup>-10</sup> J m<sup>-2</sup> s<sup>-1</sup>, to the weakest sources at a few times 10<sup>-13</sup> J m<sup>-2</sup> s<sup>-1</sup>."<ref name=Friedman69>{{ cite journal |author=Friedman H |title=Cosmic X-ray observations |journal=Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences |month=November |year=1969 |volume=313 |issue=1514 |pages=301-15 |url=http://www.jstor.org/pss/2416439 |bibcode=1969RSPSA.313..301F |arxiv= |accessdate=2011-11-25 }}</ref> {{clear}} ==Spectrometers== {{main|Radiation astronomy/Spectrometers}} [[Image:Spectrometer schematic.svg|thumb|right|250px|This is schematic of a spectrometer. Credit: [[commons:User:Markboots|Markboots]].{{tlx|free media}}]] '''Def.''' a visual representation of the spectrum of a celestial body's radiation is called a '''spectrogram'''. '''Def.''' a machine for recording spectra, producing spectrograms is called a '''spectrograph'''. '''Def.''' an optical instrument for measuring the absorption of light by chemical substances; typically it will plot a graph of absorption versus wavelength or frequency, and the patterns produced are used to identify the substances present, and their internal structure is called a '''spectrometer'''. '''Def.''' the measurement of the wavelength of electromagnetic radiation, especially any of several techniques used to analyze the structure of molecules; the measurement of spectra of things other than radiation, such as the masses of molecules and their breakdown products is called '''spectrometry'''. '''Def.''' the scientific study of spectra often using spectrometers is called '''spectroscopy'''. {{clear}} ==Spectroscopy== {{main|Radiation astronomy/Spectroscopy|Spectroscopy}} [[Image:Ssc2003-06h.jpg|right|thumb|300px|NASA's Spitzer Space Telescope has observed the presence of water and organic molecules in the galaxy IRAS F00183-7111. Credit: NASA/JPL-Caltech/L. Armus (SSC/Caltech), H. Kline (JPL), Digital Sky Survey {{tlx|free media}}.]] '''Astronomical spectroscopy''' is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects. Spectroscopy can be used to derive many properties of distant stars and galaxies, such as their chemical composition, but also their motion by Doppler shift measurements. Temporal, spatial, and spectral distributions of radiation are the focus of the science of spectroscopy as applied to astronomy. "NASA's Spitzer Space Telescope has detected the building blocks of life in the distant universe, albeit in a violent milieu. Training its powerful infrared eye on a faint object located at a distance of 3.2 billion light-years (inset [in the image on the right]), Spitzer has observed the presence of water and organic molecules in the galaxy IRAS F00183-7111. With an active galactic nucleus, this is one of the most luminous galaxies in the universe, rivaling the energy output of a quasar. Because it is heavily obscured by dust, most of its luminosity is radiated at infrared wavelengths."<ref name=Armus>{{ cite book |author=Lee Armus |author2=James Houck |author3=Vassilis Charmandaris |author4=Henrik Spoon |author5=Harry Teplitz |author6=Daniel Devost |author7=Patrick Morris |author8=Phil Appleton |author9=Carl Grillmair |title=Galaxy IRAS F00183-7111 |publisher=Caltech |location=Pasadena, California USA |date=18 December 2003 |url=http://www.spitzer.caltech.edu/images/1098-ssc2003-06h-Galaxy-IRAS-F00183-7111 |accessdate=2017-05-25 }}</ref> "The infrared spectrograph instrument onboard Spitzer breaks light into its constituent colors, much as a prism does for visible light. The image shows a low-resolution spectrum of the galaxy obtained by the spectrograph at wavelengths between 4 and 20 microns. Spectra are graphical representations of a celestial object's unique blend of light. Characteristic patterns, or fingerprints, within the spectra allow astronomers to identify the object's chemical composition and to determine such physical properties as temperature and density."<ref name=Armus/> "The broad depression in the center of the spectrum denotes the presence of silicates (chemically similar to beach sand) in the galaxy. An emission peak (red) within the bottom of the trough is the chemical signature for molecular hydrogen. The hydrocarbons (orange) are organic molecules comprised of carbon and hydrogen, two of the most common elements on Earth. Since it has taken more than three billion years for the light from the galaxy to reach Earth, it is intriguing to note the presence of organics in a distant galaxy at a time when life is thought to have started forming on our home planet."<ref name=Armus/> "Additional features in the spectrum reveal the presence of water ice (blue), carbon dioxide ice (green) and carbon monoxide (purple) in both gas and solid forms. The magenta peak corresponds to singly ionized neon gas, a spectral line often used by astronomers as a diagnostic of star formation rates in distant galaxies."<ref name=Armus/> {{clear}} ==Standard candles== {{main|Radiation astronomy/Standard candles}} [[Image:Galactic.jpg|thumb|right|250px|This is a Hubble Space Telescope Image of NGC 4414. Credit: Hubble Heritage Team (AURA/STScI/NASA).]] [[Image:Pic iroberts1.jpg|thumb|right|250px|This is an image of Messier 31, the Andromeda galaxy from 1899. Credit: Isaac Roberts.]] "In 1995, the majestic spiral galaxy NGC 4414 was imaged by the Hubble Space Telescope as part of the HST Key Project on the Extragalactic Distance Scale. [The galaxy was] observed ... on 13 different occasions over the course of two months."<ref name=Freedman>{{ cite book |author=Wendy Freedman |title=MAGNIFICENT DETAILS IN A DUSTY SPIRAL GALAXY |publisher=NASA Goddard Space Flight Center |location=Greenbelt, Maryland USA |date=1999 |url=http://nssdc.gsfc.nasa.gov/photo_gallery/caption/hst_ngc4414_9925.txt |accessdate=2014-10-28 }}</ref> "Images were obtained with Hubble's Wide Field Planetary Camera 2 (WFPC2) through three different color filters."<ref name=Freedman/> "Based on [...] careful brightness measurements of variable stars in NGC 4414, [...] an accurate determination of the distance to the galaxy [was made]."<ref name=Freedman/> "The resulting distance to NGC 4414, 19.1 megaparsecs or about 60 million light-years, along with similarly determined distances to other nearby galaxies, contributes to astronomers' overall knowledge of the rate of expansion of the universe. The Hubble constant (H0) is the ratio of how fast galaxies are moving away from us to their distance from us. This astronomical value is used to determine distances, sizes, and the intrinsic luminosities for many objects in our universe, and the age of the universe itself."<ref name=Freedman/> "Due to the large size of the galaxy compared to the WFPC2 detectors, only half of the galaxy observed was visible in the datasets collected by the Key Project astronomers in 1995. In 1999, the Hubble Heritage Team revisited NGC 4414 and completed its portrait by observing the other half with the same filters as were used in 1995. The end result is a stunning full-color look at the entire dusty spiral galaxy. The new Hubble picture shows that the central regions of this galaxy, as is typical of most spirals, contain primarily older, yellow and red stars. The outer spiral arms are considerably bluer due to ongoing formation of young, blue stars, the brightest of which can be seen individually at the high resolution provided by the Hubble camera. The arms are also very rich in clouds of interstellar dust, seen as dark patches and streaks silhouetted against the starlight."<ref name=Freedman/> '''Standard-candles astronomy''' is the astronomical effort to find, study and develop standard-candle candidates for use as standard candles. '''Standard candles''' are stars in [[Radiation astronomy/Visuals|visual astronomy]] that may be used to calculate distances because their characteristics are, or appear to be, distance independent. {{clear}} ==Stars== {{main|Radiation astronomy/Stars|Stellar astronomy}} [[Image:Mira 1997.jpg|thumb|right|250px|This is a real visual image of the red giant [[w:Mira|Mira]] by the Hubble Space Telescope. Credit: Margarita Karovska (Harvard-Smithsonian Center for Astrophysics) and NASA.]] “A '''red giant''' is a luminous [[w:giant star|giant star]] The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower. The appearance of the red giant is from yellow orange to red, including the [[w:stellar classification|spectral types]] K and M, but also class S stars and most [[w:carbon star|carbon star]]s. The most common red giants are the so-called red giant branch stars (RGB stars). Another case of red giants are the [[w:asymptotic giant branch|asymptotic giant branch]] stars (AGB). To the AGB stars belong the carbon stars of type C-N and late C-R. The stellar limb of a red giant is not sharply-defined, as depicted in many illustrations. Instead, due to the very low mass density of the envelope, such stars lack a well-defined [[w:photosphere|photosphere]]. The body of the star gradually transitions into a '[[w:corona|corona]]' with increasing radii.<ref name=Orange>[http://solarscience.msfc.nasa.gov/feature1.shtml orange sphere of the sun]</ref> {{clear}} ==Strong forces== {{main|Charges/Interactions/Strong}} [[Image:Helium atom QM.svg|thumb|right|250px|The nucleus of a helium atom, where two [[proton]]s have the same charge, but still stay together due to the strong nuclear force. Credit: [[c:user:Yzmo|Yzmo]].{{tlx|free media}}]] "In field theory it is known that coupling constants “run”. This means that the values of the coupling constants that one measures depend on the energy at which the measurement is performed. [...] the three different coupling constants [one each for the strong force, electromagnetic force, and the weak force] of the standard model seem to converge to the same value at an energy scale of about 10<sup>16</sup> GeV [...] This suggests that there is only one coupling constant at high energies and most likely only one symmetry group. [...] The current belief [is] that the electromagnetic, weak and strong forces [are] unified at about 10<sup>16</sup> GeV [as such] one has to rely on [the] particle physics interactions which can lead to electromagnetic radiation and cosmic rays".<ref name="Vachaspati">{{cite journal |author=Tanmay Vachaspati |title=Topological defects in the cosmos and lab |journal=Contemporary Physics |month= |year=1998 |volume=39 |issue=4 |pages=225-37 |url=http://www.tandfonline.com/doi/abs/10.1080/001075198181928 |arxiv= |bibcode= |doi=10.1080/001075198181928 |pmid= |accessdate=2013-11-05 }}</ref> {{clear}} ==Subatomics== {{main|Radiation astronomy/Subatomics|Subatomic astronomy}} [[Image:Helios 2 acr.gif|right|thumb|250px|A mechanism is suggested for anomalous cosmic rays (ACRs) of the acceleration of pick-up ions at the solar wind termination shock. Credit: Eric R. Christian.{{tlx|fairuse}}]] An "analysis of the energy-loss distributions in the GRS HEM during the impulsive phase of this event indicates that γ-rays from the decay of π<sup>0</sup> mesons were detected [...] The production of pions, which is accompanied (on average) by neutrons, has an energy threshold of ~290 MeV for ''p''-''p'' and ~180 MeV for ''p''-α interactions, giving, therefore, a lower limit to the maximum energy of the particles accelerated at the Sun."<ref name="Chupp">{{cite journal |author=E. L. Chupp |author2=H. Debrunner |author3=E. Flueckiger |author4=D. J. Forrest |author5=F. Golliez |author6=G. Kanbach |author7=W. T. Vestrand |author8=J. Cooper |author9=G. Share |title=Solar neutron emissivity during the large flare on 1982 June 3 |journal=The Astrophysical Journal |month=July 15, |year=1987 |volume=318 |issue=7 |pages=913-25 |url=http://adsabs.harvard.edu/abs/1987ApJ...318..913C |arxiv= |bibcode=1987ApJ...318..913C |doi=10.1086/165423 |pmid= |accessdate=2014-04-08 }}</ref> {{clear}} ==Submillimeters== {{main|Radiation astronomy/Submillimeters|Submillimeter astronomy}} [[Image:Antennae Galaxies composite of ALMA and Hubble observations.jpg|thumb|right|250px|The ALMA observations — shown here in red, pink and yellow — were tuned to detect carbon monoxide molecules. Credit: ALMA (ESO/NAOJ/NRAO). Visible light image: the NASA/ESA Hubble Space Telescope.{{tlx|free media}}]] '''Submillimetre astronomy''' or '''submillimeter astronomy''' is the branch of [[observational astronomy]] that is conducted at submillimetre wavelengths of the electromagnetic spectrum. Astronomers place the submillimetre waveband between the far-infrared and microwave wavebands, typically taken to be between a few hundred micrometres and a millimetre." and "Using submillimetre observations, astronomers examine molecular clouds and dark cloud cores with a goal of clarifying the process of star formation from earliest collapse to stellar birth. These wavelengths are sometimes called '''Terahertz radiation''', since they have frequencies of the order of 1 THz. "The Antennae Galaxies (also known as NGC 4038 and 4039) are a pair of distorted colliding spiral galaxies about 70 million light-years away, in the constellation of Corvus (The Crow). This view combines ALMA observations, made in two different wavelength ranges during the observatory’s early testing phase, with visible-light observations from the NASA/ESA Hubble Space Telescope."<ref name=eso1137a>{{ cite book |author= eso1137a |title=Antennae Galaxies composite of ALMA and Hubble observations |publisher=European Southern Observatory |location=Parana, Chile |date=October 3, 2011 |url=http://www.eso.org/public/images/eso1137a/ |accessdate=2014-03-13 }}</ref> "The Hubble image is the sharpest view of this object ever taken and serves as the ultimate benchmark in terms of resolution. ALMA observes at much longer wavelengths which makes it much harder to obtain comparably sharp images. However, when the full ALMA array is completed its vision will be up to ten times sharper than Hubble."<ref name=eso1137a/> {{clear}} ==Superluminals== {{main|Radiation astronomy/Superluminals|Superluminal astronomy}} [[Image:M87 jet Hubble.gif|thumb|right|250px|The two images are a top panel of Hubble Space Telescope image showing the M87 jet streaming out from the galaxy's nucleus (bright round region at far left) and a bottom panel which contains a sequence of Hubble images showing motion of something at six times the speed of light. Credit: John Biretta/NASA/ESA/Space Telecsope Science Institute.{{tlx|fairuse}}]] '''Superluminal''' refers to the propagation of information or matter faster than the speed of light. Under the special theory of relativity, a particle (that has [mass in special relativity] rest mass) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times (tachyons). On the other hand, what some physicists refer to as "apparent" or "effective" FTL<ref name="Gonzalez">{{cite journal | last = Gonzalez-Diaz | first = P. F. | year = 2000 | title = Warp drive space-time | url = http://omnis.if.ufrj.br/~mbr/warp/etc/PRD62_44005.pdf | journal = Physical Review D | volume = 62 | issue = 4 | page = 044005 | arxiv=gr-qc/9907026 | doi = 10.1103/PhysRevD.62.044005 | bibcode = 2000PhRvD..62d4005G }}</ref><ref name="Loup">{{cite journal |author=F. Loup |author2=David Waite |author3=E. Halerewicz Jr. |year=2001 |title=Reduced Total Energy Requirements for a Modified Alcubierre Warp Drive Spacetime |url=ttp://arxiv.org/abs/gr-qc/0107097 |bibcode=2001gr.qc.....7097L |arxiv=gr-qc/0107097 }}</ref><ref name="Visser">{{cite journal |last1=Visser |first=M. |last2=Bassett |first2=B. |last3=Liberati |first3=S. |year=2000 |title=Superluminal censorship |journal=Nuclear Physics B: Proceedings Supplement |volume=88 |pages=267–270 |arxiv=gr-qc/9810026 |bibcode = 2000NuPhS..88..267V |doi=10.1016/S0920-5632(00)00782-9 }}</ref><ref name="Visser99">{{cite journal |last1=Visser |first=M. |last2=Bassett |first2=B. |last3=Liberati |first3=S. |year=1999 |title=Perturbative superluminal censorship and the null energy condition |journal=AIP Conference Proceedings |volume=493 |pages=301–305 |arxiv=gr-qc/9908023 |doi=10.1063/1.1301601 |isbn=1-56396-905-X }}</ref> depends on the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations in less time than light could in normal or undistorted spacetime. Although according to current theories matter is still required to travel subluminally with respect to the locally distorted spacetime region, ''apparent'' FTL is not excluded by general relativity. Tachyonic γ rays have not been observed directly as of 2007.<ref name="Tomaschitz">{{cite journal |author=Roman Tomaschitz |title=Superluminal cascade spectra of TeV [gamma]-ray sources |journal=Annals of Physics |month=March |year=2007 |volume=322 |issue=3 |pages=677-700 |url=http://wallpaintings.at/geminga/superluminal_cascade_spectra_TeV_gamma-ray_sources.pdf |arxiv= |bibcode= |doi=10.1016/j.aop.2006.11.005 |pmid= |accessdate=2011-11-24 }}</ref> "The tachyonic spectral densities generated by ultra-relativistic electrons in uniform motion are fitted to the high-energy spectra of Galactic supernova remnants, such as RX J0852.0−4622 and the pulsar wind nebulae in G0.9+0.1 and MSH 15-52. ... Tachyonic cascade spectra are quite capable of generating the spectral curvature seen ... Estimates on the electron/proton populations generating the tachyon flux are obtained from the spectral fits"<ref name="Tomaschitz"/> "Tachyonic radiation implies superluminal signal transfer [1-7], the energy quanta propagating faster than light in vacuum, in contrast to rotating superluminal light sources emitting vacuum Cherenkov radiation [8, 9]."<ref name="Tomaschitz10">{{cite journal |author=R Tomaschitz |title=Superluminal spectral densities of ultra-relativistic electrons in intense electromagnetic wave fields |journal=Applied Physics B Lasers and Optics |month=October |year=2010 |volume=101 |issue=1-2 |pages=143-64 |url=http://wallpaintings.at/geminga/superluminal_spectral_densities_ultra-relativistic_electrons_electromagnetic_wave_fields.pdf |arxiv= |bibcode= |doi=10.1007/s00340-010-4182-8 |pmid= |accessdate=2012-03-21 }}</ref> "The existence of superluminal energy transfer has not been established so far, and one may ask why. There is the possibility that superluminal quanta just do not exist, the vacuum speed of light being the definitive upper bound. There is another explanation, the interaction of superluminal radiation with matter is very small, the quotient of tachyonic and electric fine-structure constants being ''q''<sup>2</sup>/''e''<sup>2</sup> ≈ 1.4 x 10<sup>-11</sup> [5], and therefore superluminal quanta are hard to detect."<ref name="Tomaschitz10"/> “Observed variations concerning the brightness distributions in four extragalactic radio sources were so rapid that the apparent transverse velocity of expansion is greater than the velocity of light.”<ref name="Cohen">{{cite journal |author=M. H. Cohen |author2=K. I. Kellermann |author3=D. B. Shaffer |author4=R. P. Linfield |author5=A. T. Moffet |author6=J. D. Romney |author7=G. A. Seielstad |author8=I. I. K. Pauliny-Toth |author9=E. Preuss |author10=A. Witzel |author11=R. T. Schilizzi |author12=B. J. Geldzahler |title=Radio sources with superluminal velocities |journal=Nature |month=August |year=1977 |volume=268 |issue= |pages=405-9 |url= |arxiv= |bibcode=1977Natur.268..405C |doi=10.1038/268405a0 |pmid= |accessdate=2012-02-19 }}</ref> {{clear}} ==Synchrotrons== {{main|Radiation astronomy/Synchrotrons}} [[Image:PKS0521-36 2 cm.gif|thumb|right|250px|The electric vectors of PKS0521-36 show clear structure and alignment. Credit: Keel.]] '''Synchrotron radiation''' is radiation produced from particles traveling along curved paths near the speed of light. {{clear}} ==Tauons== {{main|Radiation astronomy/Tauons}} [[Image:EGB With Models v2.pdf|right|thumb|400px|Compilation is shown of the measurements of the total extragalactic gamma-ray intensity between 1 keV and 820 GeV, with different components from current models. Credit: The e-ASTROGAM Collaboration.{{tlx|free media}}]] "Previously, it was suggested that the [dark matter] DM consists of [weakly interacting massive particles] WIMPs that naturally emerge from the super-symmetric extension of the Standard model. Such a WIMP particle was predicted to have a mass of the order of 100 GeV. However, no such particle has been experimentally found and the search for DM candidates is now being broadened into other directions. Recently, the idea of involving a complete hidden sector of new particles was revitalized."<ref name=Kirilova>{{ cite journal |author=G. Vankova-Kirilova |author2=V. Bozhilov |author3=V. Kozhuharov |author4=S. Lalkovski |title=All-sky mapping in the 100 MeV region in search for point-like dark matter sources |journal=arxiv |month= |year=2017 |volume= |issue= |pages=112 |url=https://arxiv.org/pdf/1711.01265#page=106 |arxiv=1711.01265 |bibcode= |doi= |pmid= |accessdate=2018-4-04 }}</ref> {{clear}} ==Telescopes== {{main|Radiation astronomy/Telescopes}} [[Image:Brorfelde Schmidt Telescope.jpg|thumb|right|250px|The Schmidt Telescope at the former Brorfelde Observatory is now used by amateur astronomers. Credit: [[commons:User:Moeng|Mogens Engelund]].{{tlx|free media}}]] A '''radiation telescope''' is an instrument designed to collect and focus radiation so as to make distant sources appear nearer. {{clear}} ==Temporals== {{main|Radiation astronomy/Temporals}} [[Image:Gursky GX 263 +3 Vela X?.png|thumb|right|300px|These two spectra show the proportional counting rates during the roll maneuver for GX 263 +3. Credit: H. Gursky, E. M. Kellogg, and P. Gorenstein. {{tlx|fairuse}}]] A '''temporal distribution''' is a distribution over time. Also known as a time distribution. A temporal distribution usually has the independent variable 'Time' on the [[w:Abscissa|abscissa]] and other variables viewed approximately orthogonal to it. The time distribution can move forward in time, for example, from the present into the future, or backward in time, from the present into the past. Usually, the abscissa is plotted forward in time with the earlier time at the intersection with the [[w:Ordinate|ordinate]] variable at left. Geologic time is often plotted on the abscissa versus phenomena on the ordinate or as a twenty-four hour clock analogy. "An X-ray source was observed in the constellation Vela from an attitude-controlled Aerobee 150 rocket launched from the White Sands Missile Range on February 2, 1968. The object, which may be the previously reported Vel XR-1 (Chodil ''et al.'' 1967), lies close to the galactic plane; we designate it as GX263+3."<ref name=Gursky>{{ cite journal |author=H. Gursky |author2=E. M. Kellogg |author3=P. Gorenstein |title=The Location of the X-ray Source in Vela |journal=The Astrophysical Journal |month=November |year=1968 |volume=154 |issue=11 |pages=71-4 |url=http://adsabs.harvard.edu//abs/1968ApJ...154L..71G |arxiv= |bibcode=1968ApJ...154L..71G |doi= |pmid= |accessdate=2015-12-15 }}</ref> The image on the upper right "shows the counting rates plotted against time during the maneuver in which the new source was observed. The peaks labeled 1, 2, 3, anf 4 all refer to this source. Peaks 1 and 2 determine a location that is the same within experimental error as the location determined by peaks 3 and 4. The reduction in background level from 130 to 150 sec after launch occurs when a large portion of the field of view falls below the horizon."<ref name=Gursky/> The second image down on the right shows the most "probable celestial locations defined by the peaks in [the upper image on the right] and counting-rate ratios are shown as line segments. Separations between intersections are consistent with a single X-ray source and statistical errors in determination of times of peak counting rates. Shaded area around intersections, and enlargement, show the region of uncertainty of the source. Lines labeled ''1st pass'' and ''2d pass'' refer to the center of the field of view during scan. Area inclosed by dashed lines is the region of uncertainty [well within Vela and the Chodil polygon] of Vel XR-1 as reported by Chodil ''et al.'' (1967)."<ref name=Gursky/> {{clear}} ==Theoretical radiation astronomy== {{main|Radiation astronomy/Theory}} [[Image:Eclipsing binary star animation 2.gif|thumb|right|250px|At the bottom of this visible emission model is a visual intensity curve. Credit: [[commons:User:Stanlekub|Stanlekub]].{{tlx|free media}}]] At its simplest '''theoretical radiation astronomy''' is the definition of terms to be applied to astronomical radiation phenomena. '''Def.''' a theory of the science of the biological, chemical, physical, and logical laws (or principles) with respect to any natural radiation source in the sky especially at night is called '''theoretical radiation astronomy'''. Exploratory theory is the playtime activity that leads to discoveries which better our world. In the radiation physics laboratories here on Earth, the emission, reflection, transmission, absorption, and fluorescence of radiation is studied and laws relative to sources are proven. A '''principle''' is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting system's designed purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored.<ref name="Guido">{{cite journal |author=Guido Alpa |title=General Principles of Law |journal=Annual Survey of International & Comparative Law |month= |year=1994 |volume=1 |issue= |pages=1 |url=http://heinonlinebackup.com/hol-cgi-bin/get_pdf.cgi?handle=hein.journals/ansurintcl1&section=4 |arxiv= |bibcode= |doi= |pmid= |accessdate=2012-04-29 }}</ref> Radiation astronomy consists of three fundamental parts: # derivation of logical laws with respect to incoming radiation, # natural radiation sources outside the Earth, and # the sky and associated realms with respect to radiation. '''Def.''' a spontaneous emission of an α ray, β ray, or γ ray by the disintegration of an atomic nucleus is called '''radioactivity'''.<ref name="Gove"/> {{clear}} ==Transductions== {{main|Radiation astronomy/Transductions}} '''Def.''' the process to [[wikt:convert|convert]] [[wikt:energy|energy]] from one [[wikt:form|form]] to another is called '''transduction'''. {{clear}} ==Transmutations== {{main|Radiation astronomy/Transmutations}} [[Image:Fission_(PSF).png‎|center|thumb|This is a fission reaction. Credit: .]] Polonium-214 has a half life of 163 microseconds (a microsecond is one-millionth of a second).<ref>http://www.ieer.org/fctsheet/uranium.html</ref> When this process is started artificially, it is called transmutation.<ref>http://faculty.ncc.edu/LinkClick.aspx?fileticket=Fkhb0%2FAcPfE%3D&tabid=1920</ref> Center is an example of an artificial transmutation, this one being called a fission reaction. {{clear}} ==Ultraviolets== {{main|Radiation astronomy/Ultraviolets|Ultraviolet astronomy}} [[Image:STEREO B EUVI 171.jpg|thumb|right|250px|This is a [[w:False-color|false-color]] image of the Sun's [[w:corona|corona]] as seen in extreme ultraviolet (at 17.1 nm) by the Extreme ultraviolet Imaging Telescope aboard Stereo B. Credit: NASA.{{tlx|fairuse}}]] '''[[Ultraviolet astronomy]]''' is generally used to refer to observations of [[w:electromagnetic radiation|electromagnetic radiation]] at ultraviolet wavelengths between approximately 10 and 320 nanometres. There are many important spectral lines in these wavelengths. Among the most important are the Lyman lines, which are emitted or absorbed when an electron jumps to or from the innermost electron shell in a hydrogen atom. The first three (known as alpha, beta and gamma) have wavelengths of 121.52, 102.53 and 97.22 nm respectively.<ref name="Chieh">{{cite book |author=Chung Chieh |title=Hydrogen Spectra |publisher=University of Waterloo |location=Waterloo, Ontario, Canada |date=December 1997 |url=http://www.science.uwaterloo.ca/~cchieh/cact/c120/hspectra.html |accessdate=2012-06-06 }}</ref> Since the Earth's atmosphere strongly absorbs ultraviolet light, especially the shorter wavelengths, ultraviolet astronomy is mostly conducted by satellites. Longer wavelengths can be detected from baloons launched into the stratosphere. Like the English astronomer William Fox, "In the summer of 1980, reflecting his age, Walter Scott Houston finally underwent surgery to remove a cataract from his right eye. Now to just about anyone else, a cataract would spell the end of a sky gazing career. But not Houston. With his lens removed and a plastic UV-transparent replacement implanted, Scotty reported that a whole new world of star gazing was opened up. The flood of ultraviolet light onto his retina allowed him to see faint blue stars previously invisible by at least one magnitude above the visual limit (to normally sighted observers)."<ref name="Hilbert">{{cite book |author=Eric Hilbert |title=Deep-Sky Wonders |publisher=Starlight Astronomy Club |location=State College, Pennsylvania |date=May 28, 2012 |url=http://ehilbert.wso.net/Starlight/deep_sky_wonders.htm |accessdate=2012-06-06 }}</ref> {{clear}} ==Violets== {{main|Radiation astronomy/Violets|Violet astronomy}} [[Image:PIA00072 Venus Cloud Patterns - colorized and filtered.jpg|thumb|right|250px|This image of Venus is taken through a violet filter by the Galileo spacecraft on February 14, 1990. Credit: NASA/JPL-Caltech.{{tlx|free media}}]] "The aluminium abundance was derived from the resonance line at 394.4nm, and Al is underabundant by ∼ −0.7 dex with respect to iron."<ref name="Sivarani">{{cite journal |author=T. Sivarani |author2=P. Bonifacio |author3=P. Molaro |author4=R. Cayrel |author5=M. Spite |author6=F. Spite |author7=B. Plez |author8=J. Andersen |author9=B. Barbuy |author10=T. C. Beers |author11=E. Depagne |author12=V. Hill |author13=P. François |author14=B. Nordström |author15=F. Primas |title=First stars IV. CS 29497-030: Evidence for operation of the ''s''-process at very low metallicity |journal=Astronomy and Astrophysics |month=January |year=2004 |volume=413 |issue=1 |pages=1073-85 |url=http://arxiv.org/pdf/astro-ph/0310291.pdf |arxiv=astro-ph/0310291 |bibcode=2004A&A...413.1073S |doi=10.1051/0004-6361:20031590 |pmid= |accessdate=2012-06-02 }}</ref> "These abundances are the LTE values; no NLTE corrections, as prescribed by Baum ̈uller and Gehren (1997) and Baumüller et al. (1998), have been applied. The prescribed NLTE corrections for T<sub>eff</sub> = 6500K, log g = 4.0, [Fe/H] = –3.0 are –0.11 ... for ... Al .... If we assume these values to apply for our lower-gravity star [CS 29497-030], then Al follows iron"<ref name="Sivarani"/>. The elemental abundance ratios for CS 29497-030 of aluminum are [Al/H] = -3.37, [Al/Fe] = -0.67.<ref name="Sivarani"/> A discovery in [[violet astronomy]] is that "carbon stars are enormously fainter in the violet region than expected from appropriate blackbody spectra."<ref name="Bregman">{{cite journal |author=Jesse D. Bregman |author2=Joel N. Bregman |title=The violet opacity of carbon stars |journal=The Astrophysical Journal |month=May 15, |year=1978 |volume=222 |issue=5 |pages=L41-3 |url= |arxiv= |bibcode=1978ApJ...222L..41B |doi=10.1086/182688 |pmid= |accessdate=2012-02-27 }}</ref> Violet photographs of the planet Venus taken in 1927 “recorded two nebulous bright streaks, or bands, running ... approximately at right angles to the terminator” that may be from the upper atmosphere.<ref name="Wright">{{cite journal |author=W. H. Wright |title=Photographs of Venus made by Infra-red and by Violet Light |journal=Publications of the Astronomical Society of the Pacific |month=August |year=1927 |volume=39 |issue=230 |pages=220-1 |url= |arxiv= |bibcode=1927PASP...39..220W |doi=10.1086/123718 |pmid= |accessdate=2011-11-24 }}</ref> "The “Purple Haze” is a diffuse blueish/purple glow within a few arcseconds of the central star in HST images of the Homunculus (Morse et al. 1998; Smith et al. 2000, 2004). This emission is seen in excess of violet starlight scattered by dust, and the strength of the excess increases into the far UV (Smith et al. 2004; hereafter Paper I)."<ref name="NSmith">{{cite journal |author=Nathan Smith |author2=Jon A. Morse |author3=Nicholas R. Collins |author4=Theodore R. Gull |title=The Purple Haze of η Carinae: Binary-induced Variability? |journal=The Astrophysical Journal |month=August |year=2004 |volume=610 |issue=2 |pages=L105-8 |url= |arxiv=astro-ph/0406408v1 |bibcode=2004ApJ...610L.105S |doi=10.1086/423341 |pmid= |accessdate=2012-01-08 }}</ref> {{clear}} ==Visuals== {{main|Radiation astronomy/Visuals|Visual astronomy}} [[Image:USNO Refractor 1904.jpg|thumb|right|250px|This image shows the 26-inch Warner & Swasey refracting telescope at the United States Naval Observatory. Credit: Waldon Fawcett.{{tlx|free media}}]] What is “the “old-fashioned” spirit of real-time visual astronomy”?<ref name=Cooke>{{ cite book |author=Antony Cooke |title=Visual Astronomy Under Dark Skies: A New Approach to Observing Deep Space |publisher=Springer-Verlag |location=London |date=2005 |editor= |pages=180 |url=http://books.google.com/books?id=SXmrBfl4H3sC&lr=&source=gbs_navlinks_s |bibcode= |doi= |pmid= |isbn=1852339012 |accessdate=2011-11-06 }}</ref> “I think everyone can conjure up a mental image of astronomers at every level and place in history, gazing through the eyepieces of their telescopes at sights far away - true visual astronomy.”<ref name=Cooke/> {{clear}} ==Wavelength shifts== [[Image:Doppler shift caused by exoplanet.jpeg|thumb|350px|Illustrating the red and blue shift for the observer from an exoplanet.]] Doppler Shift is the basis for a Spectroscopic Binary system. It is found by either two separate shifts in spectra or a single shift generated by an unseen companion on the primary star. It is important because the shifts can be used to find the radial velocity of both stars or the visible one if only one spectrum is observed. The equation to determine radial velocity is: <math>{\frac{\Delta \lambda}{\lambda_0}} = {\frac{v_r}{c}}</math> c is the speed of light in a vacuum (3x10<sup>8</sup> m/s) λ<sub>0</sub> is the rest wavelength of the spectra Δλ is the change from the rest wavelength to the measured wavelength v<sub>r</sub> is the radial velocity in m/s If the period is known this can be paired with it to determine the semi-major axis. {{clear}} ==Weak forces== {{main|Charges/Interactions/Weak}} [[Image:Beta-minus Decay.svg|thumb|right|250px|The diagram shows beta-minus decay from a nucleus. Credit: [[commons:User:Inductiveload|Inductiveload]].{{tlx|free media}}]] The '''weak interaction''' is expressed with respect to nuclear electrons and the continuous ''β''-ray emission spectrum of ''β'' decay.<ref name=Wilson>{{ cite journal |author=Fred L. Wilson |title=Fermi's Theory of Beta Decay |journal=American Journal of Physics |month=December |year=1968 |volume=36 |issue=12 |pages=1150-60 |url=http://microboone-docdb.fnal.gov/cgi-bin/RetrieveFile?docid=953;filename=FermiBetaDecay1934.pdf;version=1 |arxiv= |bibcode= |doi= |pmid= |accessdate=2012-06-24 }}</ref> "The observation of a neutrino burst within 3 h of the associated optical burst from supernova 1987A in the Large Magellanic Cloud provides a new test of the weak equivalence principle, by demonstrating that neutrinos and photons follow the same trajectories in the gravitational field of the galaxy."<ref name="Krauss">{{cite journal |author=Lawrence M. Krauss, Scott Tremaine |title=Test of the Weak Equivalence Principle for Neutrinos and Photons |journal=Physical Review Letters |month=January |year=1988 |volume=60 |issue=3 |pages=176–7 |url=http://link.aps.org/doi/10.1103/PhysRevLett.60.176 |doi=10.1103/PhysRevLett.60.176 |bibcode=1988PhRvL..60..176K }}</ref> {{clear}} ==X-rays== {{main|Radiation astronomy/X-rays|X-ray astronomy}} [[Image:M31 Core in X-rays.jpg|thumb|right|250px|This image captures the core of Messier 31 (M31) in X-rays using the Chandra X-ray Observatory. Credit: S. Murray, M. Garcia, et al., Authors & editors: Robert Nemiroff (MTU) & Jerry Bonnell (USRA) NASA.{{tlx|free media}}]] X-rays are electromagnetic radiation from a portion of the wavelength spectrum of about 5 to 8 nanometers (nm)s down to approximately 5 to 8 picometers (pm)s (ranging over three orders of magnitude). An astronomical X-ray source may have one or more positional locations, plus associated error circles or boxes, from which incoming X-radiation (X-rays) has been detected. Generally, a [[coronal cloud]], a cloud composed of plasma, is usually associated with a star or other celestial or astronomical body, extending sometimes millions of kilometers into space, or thousands of light-years, depending on the associated body. The high temperature of the coronal cloud gives it unusual spectral features. These features have been traced to highly ionized atoms of elements such as iron which indicate a plasma's temperature in excess of 10<sup>6</sup> K (MK) and associated emission of X-rays. The importance of [[X-ray astronomy]] is exemplified in the use of an X-ray imager such as the one on GOES 14 for the early detection of solar flares, coronal mass ejections (CME)s and other X-ray generating phenomena that impact the Earth. {{clear}} ==Yellows== {{main|Radiation astronomy/Yellows|Yellow astronomy}} [[Image:Io highest resolution true color.jpg|thumb|right|250px|This is a true-color image of Io taken by the ''Galileo'' probe. Credit: NASA.{{tlx|free media}}]] '''Yellow astronomy''' is astronomy applied to the various extraterrestrial yellow sources of radiation, especially at night. It is also conducted above the Earth's atmosphere and at locations away from the Earth as a part of explorational (or exploratory) yellow astronomy. There are yellow objects and emission lines in the yellow portion of the visible spectrum from 570 to 590 nm in wavelength. '''Io''' is the innermost of the four Galilean moons of the planet [[Jupiter]] and, with a diameter of 3,642 kilometres (2,263 mi), the fourth-largest moon in the [[Solar System]]. With over 400 active volcanoes, Io is the most geologically active object in the Solar System.<ref name="book">{{cite book |title=Encyclopedia of the Solar System |chapter=Io: The Volcanic Moon |author=Rosaly MC Lopes |publisher=Academic Press |year=2006 |editor=Lucy-Ann McFadden |editor2=Paul R. Weissman |editor3=Torrence V. Johnson |pages=419–431 |isbn=978-0-12-088589-3 }}</ref><ref name="Lopes2004">{{cite journal |title=Lava lakes on Io: Observations of Io’s volcanic activity from Galileo NIMS during the 2001 fly-bys |journal=Icarus |last=Lopes |first=R. M. C. |coauthors=''et al.'' |pages=140–174 |volume=169 |issue= 1 |year=2004 |doi=10.1016/j.icarus.2003.11.013 |bibcode=2004Icar..169..140L }}</ref> Most of Io's surface is characterized by extensive plains coated with sulfur and sulfur dioxide frost. Io's volcanism is responsible for many of the satellite's unique features. Its volcanic plumes and lava flows produce large surface changes and paint the surface in various shades of yellow, red, white, black, and green, largely due to allotropes and compounds of sulfur. {{clear}} ==See also== {{div col|colwidth=20em}} * [[Radiation astronomy/Aircraft|Aircraft]] * [[Observatories/Astronomy|Astronomical observatories]] * [[Radiation astronomy/Astrophysics|Astrophysics]] * [[Radiation astronomy/Atmospheres|Atmospheres]] * [[Radiation astronomy/Balloons|Balloons]] * [[Theory/Cosmogony|Cosmogony]] * [[Radiation astronomy/Distillations|Distillations]] * [[Radiation astronomy/Fluorescences|Fluorescences]] * [[Radiation astronomy/Intensities|Intensities]] * [[Radiation astronomy/Luminescences|Luminescences]] * [[Radiation astronomy/Materials|Materials]] * [[Radiation astronomy/Polarizations|Polarizations]] * [[Radiation astronomy/Courses|Radiation astronomy courses]] * [[Radiation astronomy/Rocketry|Rocketry]] * [[Theoretical astronomy]] * [[X-ray trigonometric parallax|X-ray trigonometric parallax]] {{Div col end}} ==References== {{reflist|2}} ==External links== <!-- footer templates --> {{Radiation astronomy resources}}{{Sisterlinks|Radiation astronomy}} <!-- footer categories --> [[Category:Radiation resources]] swsnomi5joae64li25r98slnj84moku 2412463 2412441 2022-08-07T02:45:15Z Marshallsumter 311529 wikitext text/x-wiki [[Image:800crab.png|thumb|right|300px|This image is a composite of several types of radiation astronomy: radio, infrared, visual, ultraviolet, soft and hard X-ray. Credit: NASA.{{tlx|free media}}]] '''Radiation astronomy''' is astronomy applied to the various extraterrestrial sources of radiation, especially at night. It is also conducted above the Earth's atmosphere and at locations away from the Earth, by satellites and space probes, as a part of explorational (or exploratory) radiation astronomy. Seeing the [[Stars/Sun|Sun]] and feeling the warmth of its rays is probably a student's first encounter with an astronomical radiation source. This will happen from a very early age, but a first understanding of the concepts of radiation may occur at a secondary educational level. Radiation is all around us on top of the Earth's crust, regolith, and soil, where we live. The study of radiation, including radiation astronomy, usually intensifies at the university undergraduate level. {{clear}} ==Absorptions== {{main|Radiation astronomy/Absorptions|Absorption astronomy}} [[Image:Spectrum of blue sky.svg|thumb|right|A spectrum is taken of blue sky clearly showing solar [[w:Fraunhofer lines|Fraunhofer lines]] and atmospheric water absorption band. Credit: [[w:user:Remember the dot|Remember the dot]].{{tlx|free media}}]] "[P]referential absorption of sunlight by ozone over long horizon paths gives the zenith sky its blueness when the sun is near the horizon".<ref name=Bohren>{{ cite book |url=http://homepages.wmich.edu/%7Ekorista/atmospheric_optics.pdf |title=Atmospheric Optics |author=Craig F. Bohren }}</ref> "For quenched galaxies, the Hα absorption trough is deep and can be traced through the nucleus and along the major axis. It extends to a radius at or beyond 2 R<sub>''d''</sub> [where R<sub>''d''</sub> is the galaxy disk scale length] in all but three cases. This makes it possible to determine a velocity width from the optical spectrum as is done for emission line flux, with appropriate corrections between stellar and gas velocities (see discussion in Paper I, also Neistein, Maoz, Rix, & Tonry, 1999). In the few cases where a velocity width can also be measured from the H I data, it is found to be in good agreement with that taken from the Hα absorption line flux."<ref name="Vogt">{{cite journal |author=Nicole P. Vogt |author2=Martha P. Haynes |author3=Riccardo Giovanelli |author4=Terry Herter |title=M/L, Hα Rotation Curves, and HI Gas Measurements for 329 Nearby Cluster and Field Spirals. III. Evolution in Fundamental Galaxy Parameters |journal=The Astronomical Journal |month=June |year=2004 |volume=127 |issue=6 |pages=3325-37 |url=http://iopscience.iop.org/1538-3881/127/6/3325 |arxiv=astro-ph/0402651 |bibcode=2004AJ....127.3325V |doi=10.1086/420703 |pmid= |accessdate=2013-12-20 }}</ref> {{clear}} ==Acoustics== {{main|Radiation astronomy/Acoustics}} [[Image:Phase shift induced by free-streaming neutrinos.png|right|thumb|300px|Phase shift induced by free-streaming neutrinos and other light relics in the spectrum of baryon acoustic oscillations. Credit: Daniel Baumann, Florian Beutler, Raphael Flauger, Daniel Green, Anže Slosar, Mariana Vargas-Magaña, Benjamin Wallisch & Christophe Yèche.{{tlx|fairuse}}]] "A pattern caused by sound waves in the early universe — known as baryon acoustic oscillations — should be distorted by the [early] neutrinos. Those sound waves spread outward through the universe like circular ripples on a pond, compressing matter into denser pockets. Eventually, that process resulted in galaxies having a tendency to cluster in rings across the sky [...]."<ref name=Conover>{{ cite book |author=Emily Conover |title=Hidden ancient neutrinos may shape the patterns of galaxies |publisher=Science News |location= |date=March 4, 2019 |url=https://www.sciencenews.org/article/hidden-ancient-neutrinos-may-shape-patterns-galaxies |accessdate=7 March 2019 }}</ref> "Using data from the Baryon Oscillation Spectroscopic Survey, or BOSS, [to study] the circular patterns of galaxies [produced] evidence that the [early] neutrinos were, in fact, pulling matter around from the inner side of the ring band toward the outer side."<ref name=Conover/> "A complementary and more robust probe [of the cosmic neutrino background] is provided by a distinct shift in the temporal phase of sound waves in the primordial plasma that is produced by fluctuations in the neutrino density."<ref name=Baumann>{{ cite journal |author=Daniel Baumann |author2=Florian Beutler |author3=Raphael Flauger |author4=Daniel Green |author5=Anže Slosar |author6=Mariana Vargas-Magaña |author7=Benjamin Wallisch |author8=Christophe Yèche |title=First constraint on the neutrino-induced phase shift in the spectrum of baryon acoustic oscillations |journal=Nature Physics |date=25 February 2019 |volume= |issue= |pages= |url=https://www.nature.com/articles/s41567-019-0435-6 |arxiv= |bibcode= |doi=10.1038/s41567-019-0435-6 |pmid= |accessdate=7 March 2019 }}</ref> "The effect of neutrinos on perturbations in the primordial plasma has been shown to be a more robust probe of the CνB<sup>4</sup>. Neutrinos travel near the speed of light in the early Universe, significantly faster than sound waves in the hot plasma of photons and baryons, and can therefore propagate information ahead of the sound horizon of the plasma. The gravitational influence of this supersonic propagation induces a shift in the phase of the acoustic oscillations that cannot be mimicked by other properties of the plasma<sup>4,5</sup>. This phase shift has recently been detected in the CMB<sup>5,6</sup>, adding to the robustness of the cosmological evidence for the CνB."<ref name=Baumann/> "After recombination, photons decoupled from baryons and the sound waves lost their pressure support. The sudden halt to the propagation of these density waves leaves an overdensity of baryons at the scale of the acoustic horizon at recombination. Subsequent gravitational evolution transfers this overdensity to the matter distribution. The power spectrum of galaxies inherits this feature in the form of baryon acoustic oscillations (BAOs). It was recently pointed out that the BAO spectrum should not only exhibit the same phase shift from the supersonic propagation of neutrinos, but that this shift should also be robust to nonlinear gravitational evolution in the late Universe<sup>7</sup>."<ref name=Baumann/> "A key property of neutrinos is that they do not behave as a fluid, but as a collection of ultra-relativistic free-streaming particles. As a consequence, neutrinos travel at the speed of light c while the sound waves in a relativistic fluid, like the photon–baryon fluid, travel at c<sub>s</sub> ≈ c/√3. The supersonic propagation speed of neutrino perturbations creates a characteristic phase shift [see image on the right (a)] in the sound waves of the primordial plasma. A useful way to understand the effect is to consider the evolution of a single initial overdensity<sup>11,12</sup>. (For adiabatic fluctuations, the primordial density field is a superposition of such point-like overdensities.) The overdensities of photons, baryons and neutrinos will spread out as spherical shells, while the dark matter perturbation does not move much and will be left behind at the centre. Because the neutrinos travel faster than all other perturbations, they induce metric perturbations ahead of the sound horizon r<sub>s</sub> of the acoustic waves of the photon–baryon fluid."<ref name=Baumann/> Image on the right part (a) shows the template "of the phase shift f(k) (blue) [...[, with the fitting function [...] shown as the red curve. The template was obtained numerically in ref.<sup>8</sup> by sampling the phase shift in 100 different cosmologies with varying free-streaming radiation density. The blue bands indicate the 1σ and 2σ contours in these measurements."<ref name=Baumann/> In the image on the right part (b), "Linear BAO spectrum O(k) [is] a function of the amplitude of the phase shift β."<ref name=Baumann/> {{clear}} ==Active galactic nuclei== {{main|Radiation astronomy/Active galactic nuclei}} [[Image:3c111 lo.jpg|thumb|right|250px|The image contains a series of radio images at successive epochs using the VLBA of the jet in the broad-line radio galaxy 3C 111. Credit: M. Kadler, E. Ros, M. Perucho, Y. Y. Kovalev, D. C. Homan, I. Agudo, K. I. Kellermann, M. F. Aller, H. D. Aller, M. L. Lister, and J. A. Zensus.{{tlx|fairuse}}]] There is "a correlation between the arrival directions of cosmic rays with energy above 6 x 10<sup>19</sup> electron volts and the positions of active galactic nuclei (AGN) lying within ~75 megaparsecs."<ref name="Abraham">{{cite journal |author=J Abraham |author2=P Abreu |author3=M Aglietta |author4=C Aguirre |author5=D Allard |author6=The Pierre Auger Collaboration |title=Correlation of the highest-energy cosmic rays with nearby extragalactic objects |journal=Science |month=November 9, |year=2007 |volume=318 |issue=5852 |pages=938-43 |url=http://www.sciencemag.org/content/318/5852/938.full |arxiv=0711.2256 |bibcode=2007Sci...318..938T |doi=10.1126/science.1151124 |pmid= |accessdate=2013-11-04 }}</ref> Some low energy cosmic rays originate or are associated with solar flares. Even these cosmic rays have too high an energy to originate from the solar photosphere. The [[coronal cloud]] in close proximity to the [[Stars/Sun|Sun]] may be a source or create them as it bombards the chromosphere from above. "In particular we recognize a first trace of Vela, brightest gamma and radio galactic source, and smeared sources along Galactic Plane and Center [as a source of ultra high energy cosmic rays (UHECR)]."<ref name="Fargion">{{cite journal |author=Daniele Fargion |title=UHECR besides ''Cen''<sub>''A''</sub>: Hints of galactic sources |journal=Progress in Particle and Nuclear Physics |month=April |year=2010 |volume=64 |issue=2 |pages=363-5 |url=http://www.sciencedirect.com/science/article/pii/S0146641009001276 |arxiv=0911.4176 |bibcode=2010PrPNP..64..363F |doi=10.1016/j.ppnp.2009.12.049 |pmid= |accessdate=2014-01-09 }}</ref> "The main correlated map is the 408 MHz one. The first astronomical source that seem to correlate is the main multiplet along ''Cen''<sub>''A''</sub>. This AGN source, the nearest extragalactic one, sits in the same direction of a far Centaurus Cluster (part of the Super-Galactic Plane). The blurring by random galactic magnetic field might spread the nearest AGN event along the same Super-Galactic Plane, explaining the AUGER group miss-understanding [3]."<ref name="Fargion"/> {{clear}} ==Aerometeors== {{main|Radiation astronomy/Aerometeors}} [[Image:April18 AR.gif|right|thumb|300px|An atmospheric river forms over Hawai'i then heads toward California 10-11 April 2017. Credit: UW-CIMSS.{{tlx|fairuse}}]] "Several times a year an atmospheric river [shown in the image on the right forming over Hawai'i]—a long, narrow conveyor belt of storms that stream in relentlessly from the Pacific Ocean—drops inches of rain or feet of snow on the U.S. west coast. Such a system triggered floods and mudslides in central and southern California this past weekend [2-3 February 2019]."<ref name=Fischetti>{{ cite book |author=Mark Fischetti |title=Warning Scale Unveiled for Dangerous Rivers in the Sky |publisher=Scientific American |location= |date=February 5, 2019 |url=https://www.scientificamerican.com/article/warning-scale-unveiled-for-dangerous-rivers-in-the-sky/ |accessdate=8 February 2019 }}</ref> "Atmospheric rivers flow through the sky about a mile above the ocean surface, and may extend across a thousand miles of ocean to the coast. Some bring routine rain but the more intense systems can carry as much water as 15 Mississippi Rivers. The series of storms striking land can arrive for days or, occasionally, weeks on end. They hit west-facing coastlines worldwide, although the U.S. experiences more than most other national coasts."<ref name=Fischetti/> The “atmospheric river scale” "ranks severity and impacts, from category 1 (weak) to category 5 (exceptional)."<ref name=Fischetti/> "Without a scale, we really had no way to objectively communicate what would be a strong storm or a weak one."<ref name=Ralph>{{ cite book |author=Martin Ralph |title=Warning Scale Unveiled for Dangerous Rivers in the Sky |publisher=Scientific American |location= |date=February 5, 2019 |url=https://www.scientificamerican.com/article/warning-scale-unveiled-for-dangerous-rivers-in-the-sky/ |accessdate=8 February 2019 }}</ref> "Scientists, the media and the public viewed atmospheric rivers as primarily a hazard, but the weaker ARs are quite beneficial. Water managers made it clear to us that a rating scale would be helpful."<ref name=Ralph/> "The scale, published Tuesday in the ''Bulletin of the American Meteorological Society'', ranks atmospheric rivers on five levels:"<ref name=Fischetti/> * Category 1: Weak—primarily beneficial * Category 2: Moderate—mostly beneficial, but also somewhat hazardous * Category 3: Strong—balance of beneficial and hazardous * Category 4: Extreme—mostly hazardous, but also beneficial (if persistent drought) * Category 5—Exceptional—primarily hazardous {{clear}} ==Alpha particles== {{main|Radiation astronomy/Alpha particles}} [[Image:Alpha particle and electrons from a thorium rod in a cloud chamber.jpg|thumb|right|250px|Alpha particle is detected in an isopropanol cloud chamber. Credit: [[c:user:Cloudylabs|Cloudylabs]].{{tlx|free media}}]] Regarding alpha particles, as with beta and gamma particles/rays, the name used for the particle carries some mild connotations about its production process and energy, but these are not rigorously applied.<ref>{{ Cite journal |last=Darling |first=David |date= |title=Alpha particle |url=http://www.daviddarling.info/encyclopedia/A/alphapart.html |journal=Encyclopedia of Science |accessdate=7 December 2010 |archiveurl=https://web.archive.org/web/20101214053417/http://daviddarling.info/encyclopedia/A/alphapart.html |archivedate=14 December 2010 }}</ref> {{clear}} ==Asteroids== {{main|Radiation astronomy/Asteroids}} [[Image:Asteroids by size and number.svg|center|thumb|500px|Asteroids in the solar system are categorized by size and number. Credit: Marco Colombo, DensityDesign Research Lab.{{tlx|free media}}]] The center image is a log-log plot of frequency vs. size for asteroids in the solar system. {{clear}} ==Atomics== {{main|Radiation astronomy/Atomics}} [[Image:Neutrons strip2.jpg|thumb|right|250px|The image shows the hydrogen concentrations on the Moon detected by the Lunar Prospector. Credit: NASA.{{tlx|free media}}]] Atomics are usually neutral atoms and molecules of a few atoms. At right is the result of an all Moon survey by the Lunar Prospector using an onboard neutron spectrometer (NS). Cosmic rays impacting the lunar surface generate neutrons which in turn loose much of their energy in collisions with hydrogen atoms trapped within the Moon's surface.<ref name=Williams/> Some of these thermal neutrons collide with the helium atoms within the NS to yield an energy signature which is detected and counted.<ref name=Williams/> The NS aboard the Lunar Prospector has a surface resolution of 150 km.<ref name=Williams>{{ cite book |author=David R. Williams |title=Lunar Prospector Neutron Spectrometer (NS) |publisher=National Aeronautics and Space Administration |location=Goddard Space Flight Laboratory |date=November 2011 |url=http://nssdc.gsfc.nasa.gov/nmc/experimentDisplay.do?id=1998-001A-02 |accessdate=2012-01-11 }}</ref> {{clear}} ==Backgrounds== {{main|Radiation astronomy/Backgrounds}} [[Image:Extragalactic-background-power-density.jpg|thumb|right|250px|This graph shows the power density spectrum of the extragalactic or cosmic gamma-ray background (CGB). Credit: pkisscs@konkoly.hu.{{tlx|free media}}]] In the figure at right, CUVOB stands for the cosmic ultraviolet and optical background. The diffuse '''extragalactic background light''' (EBL) is all the accumulated radiation in the Universe due to star formation processes, plus a contribution from [[w:active galactic nuclei|active galactic nuclei]] (AGNs). This [[Draft:Keynote lectures/Radiation|radiation]] covers the wavelength range between ~ 0.1-1000 microns (these are the [[Ultraviolet astronomy|ultraviolet]], [[Optical astronomy|optical]], and [[Infrared astronomy|infrared]] regions of the electromagnetic spectrum). The EBL is part of the diffuse extragalactic background radiation (DEBRA), which by definition covers the overall electromagnetic spectrum. After the cosmic microwave background, the EBL produces the second-most energetic diffuse background, thus being essential for understanding the full energy balance of the universe. {{clear}} ==Bands== {{main|Radiation astronomy/Bands}} [[Image:Saturn H2On.jpg|thumb|right|250px|This is Saturn imaged with the Stockholm Infrared Camera (SIRCA) in the H<sub>2</sub>O band. Credit: M. Gålfalk, G. Olofsson and H.-G. Florén, Nordic Optical Telescope.{{tlx|fairuse}}]] At the right is Saturn imaged by the Stockholm Infrared Camera (SIRCA) in the H<sub>2</sub>O infrared band to show the presence of water vapor. The image is cut off near the top due to the presence of Saturn's rings. The Sun's emission in the lowest UV bands, the UVA, UVB, and UVC bands, are of interest, as these are the UV bands commonly encountered from artificial sources on Earth. The shorter bands of UVC, as well as even more energetic radiation as produced by the Sun, generate the ozone in the ozone layer when single oxygen atoms produced by UV photolysis of dioxygen react with more dioxygen. The ozone layer is especially important in blocking UVB and part of UVC, since the shortest wavelengths of UVC (and those even shorter) are blocked by ordinary air. {{clear}} ==Baryons== {{main|Radiation astronomy/Baryons|Baryons}} [[Image:652977main gle-20120523-12.10.22PM.jpg|thumb|right|250px|"This graph shows the neutrons detected by a neutron detector at the University of Oulu in Finland from May 16 through May 18, 2012. The peak on May 17 represents an increase in the number of neutrons detected, a phenomenon dubbed a ground level enhancement or GLE. This was the first GLE since December of 2006. Credit: University of Oulu/NASA's Integrated Space Weather Analysis System"<ref name=Fox>{{ cite book |author=Karen C. Fox |title=Science Nugget: Catching Solar Particles Infiltrating Earth's Atmosphere |publisher=NASA Goddard Space Flight Center |location=Greenbelt, Maryland |date=May 31, 2012 |url=http://www.nasa.gov/mission_pages/sunearth/news/particles-gle.html |accessdate=2012-08-17 }}</ref>.{{tlx|free media}}]] A '''baryon''' is a composite subatomic particle bound together by the strong interaction, whereas leptons are not. The most familiar baryons are the protons and neutrons that make up most of the mass of the visible matter in the universe. Electrons (the other major component of the atom) are leptons. Each baryon has a corresponding antiparticle (antibaryon). Baryonic matter is matter composed mostly of baryons (by mass), which includes atoms of any sort (and thus includes nearly all matter that may be encountered or experienced in everyday life). {{clear}} ==Beta particles== {{main|Radiation astronomy/Beta particles}} [[Image:How thunderstorms launch particle beams into space 300dpi.jpg|thumb|right|300px|The simulation attempts to answer how thunderstorms launch particle beams into space. Credit: NASA/Goddard Space Flight Center.{{tlx|free media}}]] A number of subatomic reactions can be detected in astronomy that yield beta particles. The detection of beta particles or the reactions that include them in an astronomical situation is '''beta-particles astronomy'''. '''Beta particles''' are high-energy, high-speed electrons or positrons. Beta particles may be the key to fusion. "If the exterior of the capsule is maintained at a uniform temperature of about 19.5 K, the natural beta decay energy of the tritium will accomplish this through a process known as "beta layering." The very low energy beta particles from tritium decay deposit their energy very close to the location of the original tritium atoms."<ref name="Schultz">{{cite journal |author=K. R. Schultz |title=Cost Effective Steps to Fusion power: IFE target fabrication, injection and tracking |journal=Journal of Fusion Energy |month=September |year=1998 |volume=17 |issue=3 |pages=237-46 |url=http://www.springerlink.com/content/r7u527p786144l7k/ |arxiv= |bibcode= |doi=10.1023/A:1021814514091 |pmid= |accessdate=2012-06-08 }}</ref> "Beta-particles leaving the upper surface of the lunar sample could trigger the upper beta detector, while the lower beta-detector was triggered by beta particles from the lower surface of the sample."<ref name="Rancitelli">{{cite journal |author=L. A. Rancitelli |author2=R. W. Perkins |author3=W. D. Felix |author4=N. A. Wogman |title=Erosion and mixing of the lunar surface from cosmogenic and primordial radio-nuclide measurements in Apollo 12 lunar samples |journal=Proceedings of the Lunar Science Conference |month= |year=1971 |volume=2 |issue= |pages=1757-72 |url=http://adsabs.harvard.edu/full/1971LPSC....2.1757R |arxiv= |bibcode=1971LPSC....2.1757R |doi= |pmid= |accessdate=2012-06-08 }}</ref> '''Notation''': let the symbol β<sup>−</sup> designate an unbound electron in motion. '''Notation''': let β<sup>+</sup> designate an unbound positron in motion. '''Notation:''' let '''TGF''' stand for a '''Terrestrial Gamma-ray Flash'''. {{clear}} ==Blues== {{main|Radiation astronomy/Blues|Blue astronomy}} [[Image:Neptune.jpg|thumb|right|250px|This picture from the Voyager 2 sequence shows two of the four cloud features which have been tracked by the Voyager cameras during the past two months. Credit: NASA.{{tlx|free media}}]] '''Blue astronomy''' is focused on the wavelength range 450-475 nm. Stars are often referred to by their predominant color. For example, '''blue stragglers''' are found among the galactic halo globular clusters.<ref name="Preston">{{cite journal |author=Preston, G. W. |author2=Beers, T. C. |author3=Shectman, S. A. |title=The Space Density and Kinematics of Metal-Poor Blue Main Sequence Stars Near the Solar Circle |journal=Bulletin of the American Astronomical Society |month=December |year=1993 |volume=25 |issue=12 |pages=1415 |url= |arxiv= |bibcode=1993BAAS...25Q1415P |doi= |pmid= |accessdate=2011-11-24 }}</ref> Blue main sequence stars that are metal poor ([Fe/H] ≤ -1.0) are most likely very different in origin from blue stragglers.<ref name="Preston"/> "[G]round-based UV [and blue astronomy] is a powerful facility for [the] study of [the] chemical evolution of [the] early Galaxy."<ref name="Klochkova">{{cite book |author=Klochkova, Valentina |author2=Ermakov, Sergey |author3=Panchuk, Vladimir |author4=Zhao, Gang |title=High resolution spectroscopy of halo stars within the spectral region 3550-5000 °A°A, In: ''UV Astronomy: Stars from Birth to Death. Proceedings of the Joint Discussion n.4 during the IAU general Assembly of 2006'' |publisher=International Astronomical Union |location= |date=July 2007 |editor=Ana I. Gómez de Castro |editor2=Martin A. Barstow |pages=161 |url= |bibcode=2007uasb.conf..161K |doi= |pmid= |isbn=978-84-7491-852-6 }}</ref> UV and B astronomy use radiation over the wavelength range 355.0-500.0 nm.<ref name="Klochkova"/> “To date, all of the reported hypervelocity stars (HVSs), which are believed to be ejected from the Galactic center, are blue and therefore almost certainly young.”<ref name="Kollmeier">{{cite journal |author=Juna A. Kollmeier |author2=Andrew Gould |title=Where Are the Old-Population Hypervelocity Stars? |journal=The Astrophysical Journal |month=July 20, |year=2007 |volume=664 |issue=1 |pages=343-8 |url=http://iopscience.iop.org/0004-637X/664/1/343 |arxiv= |bibcode= |doi=10.1086/518405 |pmid= |accessdate=2012-03-05 }}</ref> A trace amount of methane is also present. Prominent absorption bands of methane occur at wavelengths above 600&nbsp;nm, in the red and infrared portion of the spectrum. As with Uranus, this absorption of red light by the atmospheric methane is part of what gives Neptune its blue hue,<ref name="Crisp">{{cite web |author=D. Crisp |author2=H. B. Hammel |date=June 14, 1995 |url =http://hubblesite.org/newscenter/archive/releases/1995/09/image/a/ |title =Hubble Space Telescope Observations of Neptune |publisher = Hubble News Center |accessdate = April 22, 2007 }}</ref> although Neptune's vivid azure differs from Uranus's milder cyan. Since Neptune's atmospheric methane content is similar to that of Uranus, some unknown atmospheric constituent is thought to contribute to Neptune's colour.<ref name="Munsell">{{cite book |author=Kirk Munsell |author2=Harman Smith |author3=Samantha Harvey |date=November 13, 2007 |url=http://solarsystem.nasa.gov/planets/profile.cfm?Object=Neptune&Display=OverviewLong |title=Neptune overview, In: ''Solar System Exploration'' |publisher=NASA |accessdate=February 20, 2008 }}</ref> {{clear}} ==Chemicals== {{main|Radiation astronomy/Chemistry|Radiation chemistry}} [[Image:Atmospheric Water Vapor Mean.2005.030.jpg|thumb|right|250px|This is a graph of the global mean atmospheric water vapor superimposed on an outline of the Earth. Credit: NASA.{{tlx|free media}}]] The study of the abundance and reactions of chemical elements and molecules in the universe, as can be assessed by their interaction with radiation is part of astronomical '''[[radiation chemistry]]''', or '''radiation [[Introduction to Astrochemistry|astrochemistry]]'''. {{clear}} ==Clouds== {{main|Radiation astronomy/Clouds}} [[Image:Img20050526 0007 at tannheim cumulus.jpg|thumb|right|250px|This image shows a cumulus cloud above Lechtaler Alps, Austria. Credit: [[c:User:Glg|Glg]].{{tlx|free media}}]] [[Image:Cumulus clouds in fair weather.jpeg|thumb|left|250px|Cumulus clouds in fair weather are white. Credit: [http://legacy.openphoto.net/image_view.html?image_id=17977 Michael Jastremski].{{tlx|free media}}]] '''Def.''' a "large white puffy cloud"<ref name=CumulusWikt>{{ cite web |title=cumulus |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=February 8, 2013 |url=http://en.wiktionary.org/wiki/cumulus |accessdate=2013-02-17 }}</ref> is called a '''cumulus''' cloud. Cumulus clouds look white because the water droplets reflect and scatter the sunlight without absorbing other colors. "On any given day, about half of Earth is covered by clouds, which reflect more sunlight than land and water. Clouds keep Earth cool by reflecting sunlight, but they can also serve as blankets to trap warmth."<ref name="livescience">{{ cite web |url=http://www.livescience.com/environment/060124_earth_albedo.html |title=Baffled Scientists Say Less Sunlight Reaching Earth |publisher=LiveScience |date=2006-01-24 |accessdate=2011-08-19 }}</ref> {{clear}} ==Colors== {{main|Radiation astronomy/Colors}} [[Image:Gammaspektrum Uranerz.jpg|thumb|right|250px|This gamma-ray spectrum contains the typical isotopes of the uranium-radium decay line. Credit: [[c:User:Wusel007|Wusel007]].{{tlx|free media}}]] The peak at 40 keV is not from the mineral. From the color of the rock shown the yellowish mineral is likely to be autunite. Autunite occurs as an oxidizing product of uranium minerals in granite pegmatites and hydrothermal deposits. {{clear}} ==Comets== {{main|Radiation astronomy/Comets}} [[Image:Rosetta OSIRIS NAC comet 67P 20140803 2 625.jpg|thumb|right|250px|This image shows Comet 67P/Churyumov-Gerasimenko. Credit: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/ UPM/DASP/IDA.{{tlx|fairuse}}]] [[Image:Rosetta OSIRIS NAC comet 67P 20140803 1 625.jpg|thumb|left|250px|This image shows Comet 67P/Churyumov-Gerasimenko rotated around a vertical axis from the right. Credit: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/ UPM/DASP/IDA.{{tlx|fairuse}}]] The image at the right is an optical astronomy image of the comet 67P/Churyumov-Gerasimenko. Rosetta's OSIRIS narrow-angle camera made the image on 3 August 2014 from a distance of 285 km. The image resolution is 5.3 metres/pixel. The left image is rotated 90° from the right. The location of the right image is the front view of the left side just out of view in the left image. The object rotates by the right hand rule from the left image to the right. Note that due to the evaporation of volatiles, the surface of the rocky object appears pitted or cratered. {{clear}} ==Continua== {{main|Radiation astronomy/Continua}} [[Image:Venus Transit Baader Herschel Wedge Continuum Filter 8421 - 5 June 2012.jpg|right|thumb|300px|The 15" refractor at Comanche Springs Astronomy Campus had its finder scope (a Stellarvue 80/9D achromat) equipped with a Baader Herschel Solar Wedge and a Solar Continuum Filter for today's transit of Venus. Credit: [https://www.flickr.com/people/79653922@N00 Jeff Barton from Richardson, TX, USA].{{tlx|free media}}]] Lyc photon or Ly continuum photon or Lyman continuum photon are a kind of photon emitted from stars. Hydrogen is ionized by absorption of Lyc photons. Lyc photons are in the ultraviolet portion of the electromagnetic spectrum of the hydrogen atom and immediately next to the limit of the Lyman series of the spectrum with wavelengths that are shorter than 91.1267 nanometres and with energy above 13.6 eV. {{clear}} ==Cosmic rays== {{main|Radiation/Cosmic rays}} [[Image:NeutronMonitor.GIF|right|thumb|400px|Cosmic Ray Intensity (blue) and Sunspot Number (green) is shown from 1951 to 2006 Credit: University of New Hampshire.{{tlx|fairuse}}]] The graph on the right shows an inverse correlation between sunspot numbers (solar activity) and neutron production from galactic cosmic rays. There is "a correlation between the arrival directions of cosmic rays with energy above 6 x 10<sup>19</sup> electron volts and the positions of active galactic nuclei (AGN) lying within ~75 megaparsecs."<ref name="Abraham"/> The '''Oh-My-God particle''' was observed on the evening of 15 October 1991 over Dugway Proving Ground, Utah. Its observation was a shock to astrophysicists, who estimated its energy to be approximately {{val|3|e=20|u=eV}}<ref name="Baez">[http://www.desy.de/user/projects/Physics/General/open_questions.html Open Questions in Physics.] German Electron-Synchrotron. A Research Centre of the Helmholtz Association. Updated March 2006 by JCB. Original by John Baez.</ref>(50&nbsp;joules)&mdash;in other words, a subatomic particle with kinetic energy equal to that of a baseball (142&nbsp;g or 5&nbsp;oz) traveling at 100&nbsp;km/h (60&nbsp;mph). It was most probably a proton with a speed very close to the [[w:speed of light|speed of light]], so close, in fact, [(1 − {{val|5|e=-24}}) &times; ''c''], that in a year-long race between light and the cosmic ray, the ray would fall behind only 46 nanometers ({{val|5|e=-24}} light-years), or 0.15 femtoseconds ({{val|1.5|e=-16|u=s}}).<ref name="Walker"> {{cite web | author=J. Walker | date=January 4, 1994 | title=The Oh-My-God Particle | url=http://www.fourmilab.ch/documents/OhMyGodParticle/ | publisher=Fourmilab }}</ref> {{clear}} ==Cryometeors== {{main|Radiation astronomy/Cryometeors}} [[Image:Malaspina Glacier in Southeastern Alaska.jpg|thumb|right|300px|Malaspina Glacier in southeastern Alaska is considered the classic example of a piedmont glacier. Credit: NASA.{{tlx|free media}}]] A cryometeor is a meteor of variable size that has been radiated and is still moving composed of ice, e.g. water or methane ice. A cryometeor that has stopped moving has become a cryometeorite. '''Def.''' a glacier that occurs on a gentle slope leading from the base of mountains to a region of flat land, any region of foothills of a mountain range, or formed or lying at the foot of a mountain range is called a '''piedmont glacier'''. {{clear}} ==Cyans== {{main|Radiation astronomy/Cyans|Cyan astronomy}} [[Image:C2007N3Lulin2panel brimacombe.jpg|thumb|right|250px|Recent changes in Comet Lulin's greenish coma and tails are shown in these two panels taken on January 31st (top) and February 4th (bottom) 2009. In both views the comet has an apparent antitail to the left of the coma of dust. Credit: Joseph Brimacombe, Cairns, Australia.{{tlx|free media}}]] Perhaps the most prominent cyan planetary source is Uranus, which has only been visited by the space probe Voyager 2. More recent images come from the Hubble Space Telescope in orbit around Earth. Methane possesses prominent absorption bands in the visible and near-infrared (IR) making Uranus [[w:aquamarine (color)|aquamarine]] or cyan in color.<ref name="Lunine">{{cite journal |title=The Atmospheres of Uranus and Neptune |author=Jonathan I. Lunine |journal = Annual Review of Astronomy and Astrophysics |volume=31 |pages=217–263 |year=1993 |doi=10.1146/annurev.aa.31.090193.001245 | bibcode=1993ARA&A..31..217L }}</ref> “During the Halley Monitoring Program at La Silla from Feb.17 to Apr.17,1986 ... In the light of the neutral CN-radical a continuous formation and expansion of [cyan] gas-shells could be observed.”<ref name="Schlosser">{{cite book |author=Wolfhard Schlosser |author2=Rita Schulz |author3=Paul Koczet |title=The cyan shells of Comet P/Halley, In: ''Proceedings of the 20th ESLAB Symposium on the Exploration of Halley's Comet'' |publisher=European Space Agency |location= |date=1986 |volume=3 |editor= |pages=495-8 |url= |arxiv= |bibcode=1986ESASP.250c.495S |doi= |pmid= |isbn= }}</ref> “The gas-expansion velocity decreases with increasing heliocentric distance from 1 km/s in early March to 0.8 km/s in April.”<ref name="Schlosser"/> Shown at right, "Lulin's green color comes from the gases that make up its Jupiter-sized atmosphere. Jets spewing from the comet's nucleus contain cyanogen (CN: a poisonous gas found in many comets) and diatomic carbon (C<sub>2</sub>). Both substances glow green when illuminated by sunlight"<ref name="Phillips">{{cite book |author=James A. Phillips |title=Green Comet Approaches Earth |publisher=National Aeronautics and Space Administration Science News |location= |date=2009 |url=http://science.nasa.gov/science-news/science-at-nasa/2009/04feb_greencomet/ |accessdate=2012-05-05 }}</ref> The electric blue glow of electricity results from the spectral emission of the excited ionized atoms (or excited molecules) of air (mostly oxygen and nitrogen) falling back to unexcited states, which happens to produce an abundance of electric blue light. This is the reason electrical sparks in air, including lightning, appear electric blue. It is a coincidence that the color of Cherenkov radiation and light emitted by ionized air are a very similar blue despite their very different methods of production. {{clear}} ==Detectors== {{main|Radiation astronomy/Detectors}} [[Image:Detectors summary 3.png|thumb|right|250px|This tree diagram shows the relationship between types and classification of most common particle detectors. Credit: [[commons:User:Wdcf|Wdcf]].{{tlx|free media}}]] '''Radiation detectors''' provide a signal that is converted to an electric current. The device is designed so that the current provided is proportional to the characteristics of the incident radiation. There are detectors that provide a change in substance as the signal and these may be automated to provide an electric current or quantified proportional to the amount of new substance. {{clear}} ==Distributionals== {{main|Radiation astronomy/Distributionals}} [[Image:Electronic nuclear stopping Al in Al.png|thumb|right|250px|Diagram shows the electronic and nuclear stopping power for aluminum ions in aluminum. Credit: Helmut Paul.{{tlx|free media}}]] [[Image:Ion slowing.png|thumb|right|250px|This is an illustration of the slowing down of a single ion in a solid material. Credit: Kai Nordlund.{{tlx|free media}}]] [[Image:Bragg Curve for Alphas in Air.png|thumb|right|250px|A Bragg curve of 5.49 MeV alpha particles in air is illustrated. Credit: Helmut Paul.{{tlx|free media}}]] '''Def.''' a "frequency of occurrence or extent of existence"<ref name=DistributionWikt>{{ cite web |author=[[wikt:User:JamesR1701E~enwiktionary|JamesR1701E~enwiktionary]] |title=distribution |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=4 August 2004 |url=https://en.wiktionary.org/wiki/distribution |accessdate=23 December 2019 }}</ref> or "the relative arrangements of the elements of a statistical population based on some criterion, as frequency, time, or location"<ref name=DistributionWikt/> is called a '''distribution'''. '''Def.''' "the fraction of photoelectric events which end up in the photopeak of the measured energy spectrum"<ref name="Krawczynski">{{cite book |author=Henric S. Krawczynski |author2=Ira Jung |author3=Jeremy S. Perkins |author4=Arnold Burger |author5=Michael Groza |title=Thick CZT Detectors for Space-Borne X-ray Astronomy, In: ''Hard X-Ray and Gamma-Ray Detector Physics VI, 1'' |publisher=The International Society for Optical Engineering |location=Denver, Colorado USA |date=October 21, 2004 |volume=5540 |issue= |pages=13 |url=http://arxiv.org/pdf/astro-ph/0410077 |arxiv=astro-ph/0410077 |bibcode= |doi=10.1117/12.558912 |pmid= |accessdate=2013-05-20 }}</ref> is called the '''photopeak efficiency''' (ε). Ending up in the photopeak means within ± 1 full-width at half maximum (FWHM) of the peak of the distribution.<ref name="Krawczynski"/> "The peak to valley ratio is commonly used as a token for ε."<ref name="Krawczynski"/> "Another common practice is to fit an exponential function to the “valley” and to extrapolate the fit to lower pulse heights to estimate the fraction of counts hidden in the Compton continuum."<ref name="Krawczynski"/> "We have used a calibrated Cs<sup>137</sup> source to determine the absolute photopeak efficiency at 662 keV. The source was placed at a sufficiently large distance from the detector so that the event rate was low and the dead time was less than 20%. Based on a log-histogram of the time intervals between events, the dead-time has been estimated to a fractional accuracy of better than 5%. We determine the photopeak efficiency by comparing the dead-time corrected event rate in the photopeak with the theoretical expectation assuming a perfect detector."<ref name="Krawczynski"/> '''Def.''' the average energy loss of the particle per unit path length is called the '''stopping power'''. '''Def.''' the slowing down of a projectile ion due to the inelastic collisions between bound electrons in the medium and the ion moving through it is called the '''electronic stopping power'''. '''Def.''' the elastic collisions between the projectile ion and atoms in the sample involving the interaction of the ion with the ''nuclei'' in the target is called the '''nuclear stopping power'''. The second figure on the right shows the electronic and nuclear stopping power of aluminum single crystal for aluminum ions. These stopping powers are versus particle energy per nucleon. The maximum of the nuclear stopping curve typically occurs at energies of the order of 1 keV per nucleon. The second figure at right illustrates the slowing down of a single ion in a solid material. In the beginning of the slowing-down process at high energies, the ion is slowed down mainly by electronic stopping, and it moves almost in a straight path. When the ion has slowed down sufficiently, the collisions with nuclei (the nuclear stopping) become more and more probable, finally dominating the slowing down. When atoms of the solid receive significant recoil energies when struck by the ion, they will be removed from their [[w:crystal structure|lattice]] positions, and produce a [[w:collision cascade|cascade of further collisions]] in the material. These [[w:collision cascade|collision cascade]]s are the main cause of damage production during ion implantation in metals and semiconductors. When the energies of all atoms in the system have fallen below the [[w:threshold displacement energy|threshold displacement energy]], the production of new damage ceases, and the concept of nuclear stopping is no longer meaningful. The total amount of energy deposited by the nuclear collisions to atoms in the materials is called the nuclear deposited energy. The inset in the figure shows a typical range distribution of ions deposited in the solid. The case shown here might for instance be the slowing down of a 1 MeV silicon ion in silicon. The mean range for a 1 MeV ion is typically in the micrometer range. Third right is an illustration of a ''Bragg'' curve. The '''stopping power''' and hence, the density of ionization, usually increases toward the end of range and reaches a maximum, the Bragg peak, shortly before the energy drops to zero. {{clear}} ==Electromagnetic forces== {{main|Charges/Interactions/Electromagnetics}} [[Image:PKS0521-36 2 cm.gif|thumb|right|250px|The electric vectors of PKS0521-36 show clear structure and alignment. Credit: Keel.{{tlx|fairuse}}]] "The emission of electromagnetic radiation from a superluminal (faster-than-light in vacuo) charged particle [is such] that no physical principle forbids emission by extended, massless superluminal sources. A polarization current density (d'''P'''/dt; see Maxwell's fourth equation) can provide such a source; the individual charged particles creating the polarization do not move faster than c, the speed of light, and yet it is relatively trivial to make the envelope of the polarization current density to do so."<ref name="Singleton">{{cite book |author=J. Singleton |author2=A. Ardavan |author3=H. Ardavan |author4=J. Fopma |author5=D. Halliday |title=Non-spherically-decaying radiation from an oscillating superluminal polarization current: possible low-power, deep-space communication applications in the MHz and THz bands, ''16th International Symposium on Space Terahertz Technology'' |volume= |publisher= |location= |date=2005 |editor= |pages=117 |url=http://www.nrao.edu/meetings/isstt/papers/2005/2005117000.pdf |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2014-03-18 }}</ref> The "emitted radiation has many unusual characteristics, including: (i) the intensity of some components decays as the inverse of the distance from the source, rather than as 1/(distance)2 (i.e. these components are non-spherically-decaying); (ii) the emission is tightly beamed, the exact direction of the beam depending on the source speed; and (iii) the emission contains very high frequencies not present in the synthesis of the source. Note that the non-spherically decaying components of the radiation do not violate energy conservation. They result from the reception, during a short time period, of radiation emitted over a considerably longer period of (retarded) source time; their strong electromagnetic fields are compensated by weak fields elsewhere [1]."<ref name="Singleton"/> The "emission occupies a very small polar angular width of order 0.8 degrees in the far field. Based on these findings, we suggest that a superluminal source could act as a highly directional transmitter of MHz or THz signals over very long distances."<ref name="Singleton"/> "The magnetic field is well-ordered in many jets, as shown by polarization measurements. Synchrotron radiation can be very highly polarized (50%) if the field is globally ordered, and some sources [approach] this level. The electric vectors show clear structure and alignment; an especially common pattern is for the field lines to be along the jet in the inner portions and transition to an azimuthal configuration farther out. This is seen in [PKS0521-36 at 2 cm]."<ref name="Keel">{{cite book |author=Bill Keel |title=Jets, Superluminal Motion, and Gamma-Ray Bursts |publisher=University of Arizona |location=Tucson, Arizona USA |date=October 2003 |url=http://www.astr.ua.edu/keel/galaxies/jets.html |accessdate=2014-03-19 }}</ref> {{clear}} ==Electromagnetics== {{main|Radiation astronomy/Electromagnetics}} [[Image:Glowing Stellar Nurseries.jpg|thumb|right|250px|This is a colour composite image of RCW120. Credit: ESO/APEX/DSS2/ SuperCosmos/ Deharveng(LAM)/ Zavagno(LAM).{{tlx|free media}}]] Radiation astronomy is often performed using electromagnetics. Electromagnetics are most familiar as light, or electromagnetic radiation. The image at right is a colour "composite image of RCW120. It reveals how an expanding bubble of ionised gas about ten light-years across is causing the surrounding material to collapse into dense clumps where new stars are then formed. The 870-micron submillimetre-wavelength data were taken with the LABOCA camera on the 12-m Atacama Pathfinder Experiment (APEX) telescope. Here, the submillimetre emission is shown as the blue clouds surrounding the reddish glow of the ionised gas (shown with data from the SuperCosmos H-alpha survey). The image also contains data from the Second Generation Digitized Sky Survey (I-band shown in blue, R-band shown in red)."<ref name="Deharveng">{{cite book |author= Deharveng |title=Glowing Stellar Nurseries |publisher=European Southern Observatory |location= |date=November 11, 2008 |url=http://www.eso.org/public/images/eso0840a/ |accessdate=2014-03-13 }}</ref> '''Electromagnetic radiation astronomy''' is a broader concept, physics subject heading used by the American Physical Society (APS).<ref name=APS>{{ cite book |author=APS |title=Physics Subject Headings |publisher=American Physical Society |location=College Park, MD |date= |editor= |pages= |url=https://physh.aps.org/concepts/893ecc24-c678-4687-bd3a-0b4a1bcb4cfc |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2018-01-08 }}</ref> {{clear}} ==Electrons== {{main|Radiation astronomy/Electrons|Electron astronomy}} [[Image:Aurore australe - Aurora australis.jpg|thumb|right|250px|Aurorae are mostly caused by energetic electrons precipitating into the atmosphere.<ref name="Wolpert">{{cite book | author = S. Wolpert | date = July 24, 2008 | title = Scientists solve 30-year-old aurora borealis mystery | url = http://www.universityofcalifornia.edu/news/article/18277 | publisher = University of California | accessdate = 2008-10-11 }}</ref> Credit: [[commons:User:Ehquionest|Samuel Blanc]][http://www.sblanc.com/].{{tlx|free media}}]] Although '''[[electron astronomy]]''' is usually not recognized as a formal branch of astronomy, the measurement of electron fluxes help to understand a variety of natural phenomena. Particles such as electrons are used as tracers of cosmic magnetic fields.<ref name="Hudson">{{cite book |author=H. S. Hudson |author2=A. B. Galvin |title=Correlated Studies at Activity Maximum: the Sun and the Solar Wind, In: ''Correlated Phenomena at the Sun, in the Heliosphere and in Geospace'' |publisher=European Space Agency |location=Noordwijk, The Netherlands |date=September 1997 |editor=A. Wilson |pages=275-82 |url= |bibcode=1997ESASP.415..275H |doi= |pmid= |isbn=92-9092-660-0 }}</ref> "From a plasma-physics point of view, the particles represent the correct way to identify magnetic field lines."<ref name="Hudson"/> "The suprathermal electrons in the solar wind and in solar particle events have excellent properties for this application: they move rapidly, they remain tightly bound to their field lines, and they may arrive "scatter-free" even at low energies, and from deep in the solar atmosphere (Lin 1985)."<ref name="Hudson"/> These electrons "provide remote-sensing observations of distant targets in the heliosphere - the Sun, the Moon, Jupiter, and various heliospheric structures."<ref name="Hudson"/> ""[E]lectron astronomy" has an interesting future".<ref name="Hudson"/> A '''delta ray''' is characterized by very fast electrons produced in quantity by alpha particles or other fast energetic charged particles knocking orbiting electrons out of atoms. Collectively, these electrons are defined as delta radiation when they have sufficient energy to ionize further atoms through subsequent interactions on their own. "The conventional procedure of delta-ray counting to measure charge (Powell, Fowler, and Perkins 1959), which was limited to resolution σ<sub>z</sub> = 1-2 because of uncertainties of the criterion of delta-ray ranges, has been significantly improved by the application of delta-ray range distribution measurements for <sup>16</sup>O and <sup>32</sup>S data of 200 GeV per nucleon (Takahashi 1988; Parnell ''et al.'' 1989)."<ref name="Burnett">{{cite journal |author=T. H. Burnett ''et al.'' |author2=The JACEE Collaboration |title=Energy spectra of cosmic rays above 1 TeV per nucleon |journal=The Astrophysical Journal |month=January |year=1990 |volume=349 |issue=1 |pages=L25-8 |url=http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990ApJ...349L..25B&link_type=GIF&db_key=AST |arxiv= |bibcode=1990ApJ...349L..25B |doi=10.1086/185642 |pmid= |pdf=http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990ApJ...349L..25B&link_type=ARTICLE&db_key=AST&high= |accessdate=2011-11-25 }}</ref> Here, the delta-ray tracks in emulsion chambers have been used for "[d]irect measurements of cosmic-ray nuclei above 1 TeV/nucleon ... in a series of balloon-borne experiments".<ref name="Burnett"/> {{clear}} ==Emissions== {{main|Radiation astronomy/Emissions}} [[Image:The Red Rectangle around the star HD 44179.jpg|thumb|right|250px|The Hubble Space Telescope [Advanced Camera for Surveys] ACS image has H-alpha emission of the Red Rectangle shown in blue. Credit: ESA/Hubble and NASA.{{tlx|free media}}]] "[T]he extended red emission (ERE) [is] observed in many dusty astronomical environments, in particular, the diffuse interstellar medium of the Galaxy. ... silicon nanoparticles provide the best match to the spectrum and the efficiency requirement of the ERE."<ref name="Witt">{{cite journal |author=Adolf N. Witt |author2=Karl D. Gordon |author3=Douglas G. Furton |title=Silicon Nanoparticles: Source of Extended Red Emission? |journal=The Astrophysical Journal Letters |month=July 1, |year=1998 |volume=501 |issue=1 |pages=L111-5 |url=http://iopscience.iop.org/1538-4357/501/1/L111 |arxiv=astro-ph/9805006 |bibcode= |doi=10.1086/311453 |pmid= |accessdate=2013-07-30 }}</ref> {{clear}} ==Empiricisms== {{main|Radiation astronomy/Empiricisms|Empirical radiation astronomy}} [[Image:Centre of the Milky Way.jpg|thumb|right|250px|The best empirical evidence that supermassive black holes do really exist is the orbits of these stars around the center of the [[Milky Way]]. Credit: Stefan Gillessen, Reinhard Genzel, Frank Eisenhauer, ESO.{{tlx|free media}}]] A list or catalog of the specific principles incorporated into the development of the various radiation astronomies may be helpful to students and researchers alike. These principles can be included in [[mathematical astronomy]], astrophysics, [[astrochemistry]], and theoretical radiation astronomy as summaries, or, a lecture on '''empirical radiation astronomy'''. {{clear}} ==Entities== {{main|Radiation astronomy/Entities}} [[Image:Johannes Vermeer - The Astronomer - 1668.jpg|thumb|right|250px|This is an image of Johannes Vermeer's ''The astronomer''. Credit: www.essentialvermeer.com : [http://www.essentialvermeer.com Home] : [http://www.essentialvermeer.com/catalogue/astronomer.html Info] : [http://www.essentialvermeer.com/catalogue_xxl/xxl_astronomer.jpg Pic].{{tlx|free media}}]] '''Radiation astronomy entities''', '''radiation entities''', are any astronomical persons or things that have separate and distinct existences in empirical, objective or conceptual reality. Some of them, like the astronomers of today, or at any time in the past, are relatively known. But there are many entities that are far less known or understood, such as the observers of ancient times who suggested that deities occupied the sky or the heavens. Likewise, these alleged deities may be entities, or perhaps something a whole lot less. Astronomical X-ray entities are often discriminated further into sources or objects when more information becomes available, including that from other radiation astronomies. A researcher who turns on an X-ray generator to study the X-ray emissions in a laboratory so as to understand an apparent astronomical X-ray source is an astronomical X-ray entity. So is one who writes an article about such efforts or a computer simulation to possibly represent such a source. "The X-ray luminosity of the [[dominant group]] [an entity] is an order of magnitude fainter than that of the X-ray jet."<ref name="Finoguenov">{{cite journal |author=A. Finoguenov |author2=M.G. Watson |author3=M. Tanaka |author4=C.Simpson |author5=M. Cirasuolo |author6=J.S. Dunlop |author7=J.A. Peacock |author8=D. Farrah |author9=M. Akiyama |author10=Y. Ueda |author11=V. Smolčič |author12=G. Stewart |author13=S. Rawlings |author14=C.vanBreukelen |author15=O. Almaini |author16=L.Clewley |author17=D.G. Bonfield |author18=M.J. Jarvis |author19=J.M. Barr |author20=S. Foucaud |author21=R.J. McLure |author22=K. Sekiguchi |author23=E. Egami |title=X-ray groups and clusters of galaxies in the Subaru-XMM Deep Field |journal=Monthly Notices of the Royal Astronomical Society |month=April |year=2010 |volume=403 |issue=4 |pages=2063-76 |url=http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2010.16256.x/full |arxiv= |bibcode= |doi=10.1111/j.1365-2966.2010.16256.x |pmid= |pdf=http://arxiv.org/pdf/0912.0039 |accessdate=2011-12-09 }}</ref> {{clear}} ==Fieries== {{main|Radiation astronomy/Fieries}} [[Image:2013-02-15T101834Z 1461539070 GM1E92F1EHS01 RTRMADP 3 RUSSIA-METEORITE.JPG|thumb|right|350px|This is a fireball meteor trail with some burning still visible above the Urals city of Chelyabinsk, Russia, on February 15, 2013. Credit: Reuters/www.chelyabinsk.ru.{{tlx|fairuse}}]] On the right is a [[visual astronomy]] image of a fireball trail with some burning still visible from a meteor as it passed overhead in Chelyabinsk, Russia, on February 15, 2013. This image shows "[t]he trail of a falling object ... seen above the Urals city of Chelyabinsk [on] February 15, 2013".<ref name=Reuters>{{ cite book |author=Reuters |title=Meteorite hits central Russia, more than 500 people hurt |publisher=Yahoo! News |location=Chelyabinsk, Russia |date=February 15, 2013 |url=http://news.yahoo.com/photos/trail-falling-object-seen-above-urals-city-chelyabinsk-photo-101834569.html |accessdate=2013-02-15 }}</ref> {{clear}} ==Galaxies== {{main|Radiation astronomy/Galaxies}} [[Image:M81 wide Galex.jpg|thumb|right|250px|This Galaxy Evolution Explorer (GALEX) image of the spiral galaxy Messier 81 is in ultraviolet light. Credit: NASA/JPL-Caltech/J. Huchra (Harvard-Smithsonian CfA).{{tlx|free media}}]] The radiation astronomy of galaxies generally is about the galaxy as a radiated or radiation emitting astronomical object. The stellar aspects of individual galaxies are in [[Stars/Galaxies|galaxies of stars]]. A galaxy is often perceived as a gravitationally bound system of stars, stellar remnants, interstellar gas, dust, and dark matter.<ref name=Sparke>{{Cite book |last1=Sparke |first1=L. S. |last2=Gallagher |first2=J. S. III |date=2000 |title=Galaxies in the Universe: An Introduction |publisher=Cambridge University Press |isbn=978-0-521-59740-1 |accessdate=July 25, 2018 |archive-date=March 24, 2021 |url=https://web.archive.org/web/20210324072126/https://books.google.com/books?id=tzNF79roUfoC }}</ref><ref name=nasa060812>{{cite web |last1=Hupp |first1=E. |last2=Roy |first2=S. |last3=Watzke |first3=M. |date=August 12, 2006 |title=NASA Finds Direct Proof of Dark Matter |url=http://www.nasa.gov/home/hqnews/2006/aug/HQ_06297_CHANDRA_Dark_Matter.html |publisher=NASA |accessdate=April 17, 2007 }}</ref> Galaxies range in size from dwarfs with just a few hundred million ({{10^|8}}) stars to giants with one hundred trillion ({{10^|14}}) stars,<ref name=science250_4980_539>{{cite journal |last1=Uson |first1=J. M. |last2=Boughn |first2=S. P. |last3=Kuhn |first3=J. R. |date=1990 |title=The central galaxy in Abell 2029&nbsp;– An old supergiant |journal=Science |volume=250 |issue=4980 |pages=539–540 |bibcode=1990Sci...250..539U |doi=10.1126/science.250.4980.539 |pmid=17751483 }}</ref> each orbiting its galaxy's center of mass. Galaxies are categorized according to their visual morphology as elliptical,<ref name=uf030616>{{cite news |last1=Hoover |first1=A. |date=June 16, 2003 |title=UF Astronomers: Universe Slightly Simpler Than Expected |url=http://news.ufl.edu/2003/06/16/galaxies/ |publisher=Hubble News Desk |accessdate=March 4, 2011 |archiveurl=https://web.archive.org/web/20110720083835/http://news.ufl.edu/2003/06/16/galaxies/ |archivedate=July 20, 2011 |df=mdy-all }} Based upon: * {{Cite journal |last1=Graham |first1=A. W. |last2=Guzman |first2=R. |date=2003 |title=HST Photometry of Dwarf Elliptical Galaxies in Coma, and an Explanation for the Alleged Structural Dichotomy between Dwarf and Bright Elliptical Galaxies |journal=The Astronomical Journal |volume=125 |issue=6 |pages=2936–2950 |bibcode=2003AJ....125.2936G |doi=10.1086/374992 |arxiv = astro-ph/0303391 }}</ref> spiral, or irregular.<ref name="IRatlas">{{cite web |last1=Jarrett |first1=T. H. |title=Near-Infrared Galaxy Morphology Atlas |url=http://www.ipac.caltech.edu/2mass/gallery/galmorph/ |publisher=California Institute of Technology |accessdate=January 9, 2007 }}</ref> The number of galaxies in the observable universe has increased from a previous estimate of 200&nbsp;billion ({{val|2e11}})<ref name="apj624_2">{{cite journal |last1=Gott III |first1=J. R. |year=2005 |display-authors=etal |title=A Map of the Universe |journal=The Astrophysical Journal |volume=624 |issue=2 |pages=463–484 |bibcode=2005ApJ...624..463G |doi=10.1086/428890 |arxiv = astro-ph/0310571 }}</ref> to a suggested 2 trillion ({{val|2e12}}) or more,<ref name="Conselice">{{cite journal |title=The Evolution of Galaxy Number Density at z < 8 and its Implications |author=Christopher J. Conselice ''et al.'' |journal=The Astrophysical Journal |volume=830 |issue=2 |year=2016 |arxiv=1607.03909v2 |bibcode= 2016ApJ...830...83C |doi=10.3847/0004-637X/830/2/83 |page=83 }}</ref><ref name="NYT-20161017">{{cite news |last=Fountain |first=Henry |title=Two Trillion Galaxies, at the Very Least |url=https://www.nytimes.com/2016/10/18/science/two-trillion-galaxies-at-the-very-least.html |date=17 October 2016 |work=The New York Times |accessdate=17 October 2016 }}</ref> containing more [[stars]] than all the grains of sand on planet Earth.<ref name="SU-20020201">{{cite web |last=Mackie |first=Glen |title=To see the Universe in a Grain of Taranaki Sand |url=http://astronomy.swin.edu.au/~gmackie/billions.html |date=1 February 2002 |work=Centre for Astrophysics and Supercomputing |accessdate=28 January 2017 }}</ref> {{clear}} ==Galaxy clusters== {{main|Radiation astronomy/Galaxy clusters}} [[Image:Superclusters atlasoftheuniverse.gif|thumb|250px|right|The universe within 1 billion light-years (307 Mpc) of Earth is shown to contain the local superclusters, galaxy filaments and voids. Credit: Richard Powell.{{tlx|free media}}]] "Galaxies and clusters of galaxies are not uniformly distributed in the Universe, instead they collect into vast clusters and sheets and walls of galaxies interspersed with large voids in which very few galaxies seem to exist. The map above shows many of these superclusters including the Virgo supercluster - the minor supercluster of which our galaxy is just a minor member. The entire map is approximately 7 percent of the diameter of the entire visible Universe."<ref name=Powell>{{ cite book |author=Richard Powell |title=The Universe within 1 billion Light Years The Neighbouring Superclusters |publisher=Atlas of the Universe |location= |date=30 July 2006 |url=http://www.atlasoftheuniverse.com/superc.html |accessdate=2018-04-01 }}</ref> {{clear}} ==Gamma rays== {{main|Radiation astronomy/Gamma rays|Gamma-ray astronomy}} [[Image:Moon egret.jpg|thumb|right|250px|The Moon is seen by the [[w:Compton Gamma Ray Observatory|Compton Gamma Ray Observatory]], in gamma rays of greater than 20 MeV. Credit: D. J. Thompson, D. L. Bertsch (NASA/GSFC), D. J. Morris (UNH), R. Mukherjee (NASA/GSFC/USRA).{{tlx|free media}}]] Most astronomical gamma-rays are thought to be produced not from radioactive decay, however, but from the same type of accelerations of electrons, and electron-photon interactions, that produce X-rays in astronomy (but occurring at a higher energy in the production of gamma-rays). For [[gamma-ray astronomy]], the Vela satellites were the first devices ever to detect cosmic gamma ray bursts. '''Gamma-ray bursts''' ('''GRBs''') are flashes of gamma rays associated with extremely energetic explosions that have been observed in distant [[galaxies]]. They are the most luminous electromagnetic events known to occur in the [[universe]]. Bursts can last from ten milliseconds to several minutes, although a typical burst lasts 20–40 seconds. The initial burst is usually followed by a longer-lived "afterglow" emitted at longer wavelengths (X-ray, ultraviolet, optical, infrared, microwave and radio).<ref name="Vedrenne">{{cite book |author=Vedrenne G |author2=Atteia J.-L. |year=2009 |title=Gamma-Ray Bursts: The brightest explosions in the Universe |url=http://books.google.com/?id=jZHSdrvzz0gC&printsec=frontcover#v=onepage&q&f=false |publisher=Springer/Praxis Books |isbn=978-3-540-39085-5 }}</ref> {{clear}} ==Gaseous objects== {{main|Gases/Gaseous objects}} [[Image:Mars xray 420.jpg|thumb|right|250px|This Chandra X-ray Observatory image is the first look at X-rays from Mars. Credit: NASA/CXC/MPE/K.Dennerl et al.{{tlx|free media}}]] "In the sparse upper atmosphere of Mars, about 120 (75 miles) kilometers above its surface, the observed X-rays [shown in the image at right] are produced by fluorescent radiation from oxygen atoms."<ref name="Dennerl02">{{cite book |author=K. Dennerl |display-authors=etal |title=Mars: Mars Glows in X-rays |publisher=NASA, Harvard University |location=Boston, Massachusetts, USA |date=November 7, 2002 |url=http://chandra.harvard.edu/photo/2002/mars/ |accessdate=2012-11-26 }}</ref> "X-radiation from the Sun impacts oxygen atoms, knock electrons out of the inner parts of their electron clouds, and excite the atoms to a higher energy level in the process. The atoms almost immediately return to their lower energy state and may emit a fluorescent X-ray in this process with an energy characteristic of the atom involved - oxygen in this case. A similar process involving ultraviolet light produces the visible light from fluorescent lamps."<ref name="Dennerl02"/> "The X-ray power detected from the Martian atmosphere is very small, amounting to only 4 megawatts, comparable to the X-ray power of about ten thousand medical X-ray machines. Chandra was scheduled to observe Mars when it was only 70 million kilometers from Earth, and also near the point in its orbit when it is closest to the Sun."<ref name="Dennerl02"/> "At the time of the Chandra observation, a huge dust storm developed on Mars that covered about one hemisphere, later to cover the entire planet. This hemisphere rotated out of view over the course of the 9-hour observation but no change was observed in the X-ray intensity, implying that the dust storm did not affect the upper atmosphere."<ref name="Dennerl02"/> "The astronomers also found evidence for a faint halo of X-rays that extends out to 7,000 kilometers above the surface of Mars. Scientists believe the X-rays are produced by collisions of ions racing away from the Sun (the solar wind) with oxygen and hydrogen atoms in the tenuous exosphere of Mars."<ref name="Dennerl02"/> {{clear}} ==Geographies== {{main|Radiation astronomy/Geography}} [[Image:Caltech-Submillimeter-Observatory (straightened).jpg|thumb|right|250px|The Caltech Submillimeter Observatory at Mauna Kea Observatory has a 10.4 m (34 ft) dish. Credit: [http://www.flickr.com/people/62472689@N00 Samuel Bouchard] from Quebec City, Canada.{{tlx|free media}}]] Each individual or small group of astronomical knowledge recorders among the hominins after some effort has realized that they are on the surface of a planet, an approximately spheroidal object. Further, when any of them study the sky, they have realized they are only sensing a small portion relative to their location (such as in the enjoyment of [[Backyard Astronomy|backyard astronomy]]). To combine what they've learned, when they get together to discuss it or record it, they have to locate that knowledge where that knowledge occurred. This locating eventually included the radiation received to form the knowledge and science of '''astronomical radiation geography'''. '''Geographical radiation astronomy''' is the study of the effect of geography on radiation astronomy. Both astronomical radiation geography and geographical radiation astronomy are part of '''astrogeography''', or '''astrography'''. {{clear}} ==Gravitationals== {{main|Radiation astronomy/Gravitationals}} [[Image:LIGO measurement of gravitational waves.svg|right|thumb|300px|The images show LIGO and Livingston, Louisiana, measurement of gravitational waves. Credit: B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration).{{tlx|free media}}]] [[Image:Aerial View Of LIGO Livingston 599x400.jpg|left|thumb|300px|This photo shows the Livingston LIGO detector. Credit: Caltech/MIT/LIGO Laboratory.{{tlx|free media}}]] [[Image:The Gravitational wave spectrum Sources and Detectors.jpg|right|thumb|300px|This gravitational wave spectrum includes sources and detectors. Credit: NASA Goddard Space Flight Center.{{tlx|free media}}]] '''Gravitational radiation''' appears to be cylindrical waves of radiation produced by relativistic, undulatory gravitational fields in Euclidean space.<ref name=Einstein>{{ cite journal |author=A. Einstein |author2=N. Rosen |title=On gravitational waves |journal=Journal of the Franklin Institute |month=January |year=1937 |volume=223 |issue=1 |pages=43-54 |url=http://www.sciencedirect.com/science/article/pii/S0016003237905830?via%3Dihub |arxiv= |bibcode=1937FrInJ.223...43E |doi=10.1016/S0016-0032(37)90583-0 |pmid= |accessdate=2018-1-03 }}</ref> {| class="wikitable" |- ! Interaction !! Mediator !! Relative Magnitude !! Behavior !! Range |- | [[Strong interaction]] || gluon || 10<sup>38</sup> || 1 || 10<sup>−15</sup> m |- | [[Electromagnetic interaction]] || photon || 10<sup>36</sup> || 1/''r''<sup>2</sup> || universal |- | [[Weak interaction]] || W and Z bosons || 10<sup>25</sup> || 1/''r''<sup>5</sup> to 1/''r''<sup>7</sup> || 10<sup>−16</sup> m |- | Gravitational interaction || photon or graviton ? || 10 || 1/''r''<sup>2</sup> || universal |} As the gravitational interaction is 10<sup>-36</sup> that of the electromagnetic interaction to produce gravitational radiation requires a massive oscillator. At right are the results from the first gravitational radiation detection. The images show the radiation signals received by the Laser Interferometer Gravitational Observatory (LIGO) instruments at Hanford, Washington (left) and Livingston, Louisiana (right) and comparisons of these signals to the signals expected due to a black hole merger event. The wavelength of the gravitational waves is given by for example: 3 x 10<sup>8</sup> m‧s<sup>-1</sup>/400 Hz = 750,000 m, which is way longer than radio waves but expected for such a weak oscillator. 35 Hz corresponds to 8,600,000 m. LIGO operates two detectors located 3000 km (1800 miles) apart: One in eastern Washington near Hanford, and the other near Livingston, Louisiana. The photo on the left shows the Livingston detector. "According to general relativity, a pair of black holes orbiting around each other lose energy through the emission of gravitational waves, causing them to gradually approach each other over billions of years, and then much more quickly in the final minutes. During the final fraction of a second, the two black holes collide at nearly half the speed of light and form a single, more massive black hole, converting a portion of the combined black holes' mass to energy, according to Einstein's formula E=mc<sup>2</sup>. This energy is emitted as a final strong burst of gravitational waves. These are the gravitational waves that LIGO observed."<ref name=Kupec>{{ cite book |author=Ivy F. Kupec |title=Gravitational waves detected 100 years after Einstein's prediction |publisher=National Science Foundation |location=Alexandria, Virginia, USA |date=11 February 2016 |editor= |pages=1 |url=https://www.nsf.gov/news/news_summ.jsp?cntn_id=137628 |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2018-01-03 }}</ref> "LIGO’s twin interferometers bounce laser beams between mirrors at the opposite ends of 4-kilometre-long vacuum pipes that are set perpendicularly to each other. A gravitational wave passing through will alter the length of one of the arms, causing the laser beams to shift slightly out of sync."<ref name=Castelvecchi>{{ cite journal |author=Davide Castelvecchi |author2=Alexandra Witze |title=Einstein's gravitational waves found at last LIGO 'hears' space-time ripples produced by black-hole collision |journal=Nature |month=11 February |year=2016 |volume= |issue= |pages= |url=http://www.nature.com/news/einstein-s-gravitational-waves-found-at-last-1.19361 |arxiv= |bibcode= |doi=10.1038/nature.2016.19361 |pmid= |accessdate=2018-1-03 }}</ref> Later detection confirmed the fusion of two massive stellar-sized objects, a binary neutron star merger.<ref name=Abbott>{{ cite journal |author=B. P. Abbott |author2=the LIGO Scientific Collaboration]] |author3=the Virgo Collaboration |title=GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral |journal=Physical Review Letters |month=16 October |year=2017 |volume=119 |issue=16 |doi=10.1103/PhysRevLett.119.161101 }}</ref> "According to Einstein's field equations, photon matter subject to quadruple oscillations is a source of gravitational waves."<ref name=Sandu>{{ cite book |author=Constantin Sandu |author2=Dan Brasoveanu |title=Sonic Electromagnetic Gravitational Spacecraft, Part - Principles, In: ''AIAA SPACE 2007 Conference & Exposition'' |volume=6203 |publisher=American Institute of Aeronautics and Astronautics |location= |date= |editor= |pages= |url=https://arc.aiaa.org/doi/abs/10.2514/6.2007-6203 |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2018-01-10 }}</ref> "In this work, we present a solution to the first stage of a new two-stage global treatment of the vacuum binary black hole problem [1, 2]. The approach, based upon characteristic evolution, has been carried out in the regime of Schwarzschild perturbations where advanced and retarded solutions of the linearized problem can be rigorously identified [3]. Computational experiments are necessary to study the applicability of the approach to the nonlinear regime. From a time-reversed viewpoint, this first stage is equivalent to the determination of the outgoing radiation emitted from the fission of a white hole in the absence of ingoing radiation. This provides the physically correct “retarded” waveform for a white hole fission, were such events to occur in the universe. Although there is no standard astrophysical mechanism for producing white holes from a nonsingular matter distribution, white holes of primordial or quantum gravitational origin cannot be ruled out."<ref name=Gomez>{{ cite journal |author=Roberto Gómez |author2=Sascha Husa |author3=Luis Lehner |author4=Jeffrey Winicour |title=Gravitational waves from a fissioning white hole |journal=Physical Review D |month=15 September |year=2002 |volume=66 |issue=6 |pages=1-9 |url=https://arxiv.org/pdf/gr-qc/0205038 |arxiv= |bibcode= |doi=10.1103/PhysRevD.66.064019 |pmid= |accessdate=2018-01-10 }}</ref> "This fission problem has a simpler formulation as a characteristic initial value problem than the black hole merger problem. The boundary of the (conformally compactified) exterior spacetime contains two null hypersurfaces where boundary conditions must be satisfied: past null infinity I−, where the incoming radiation must vanish, and the white hole event horizon H−, which must describe a white hole, which is initially in equilibrium with no ingoing radiation and then distorts and ultimately fissions into two white holes with the emission of outgoing gravitational waves."<ref name=Gomez/> An almost identical signal could originate from a comparable much more massive neutron star fission. "This is an exciting time to study gravitation, astrophysics and cosmology. Through challenging cosmic microwave background (CMB) and supernovae observations cosmology has been turned on its head. Gravitational radiation astronomy should be the next contributor to this revolution in astrophysics and cosmology."<ref name="Christensen">{{ cite journal |author=Nelson Christensen |author2=Renate Meyer |author3=Adam Libson |year=2003 |title=A Metropolis–Hastings routine for estimating parameters from compact binary inspiral events with laser interferometric gravitational radiation data |url=http://people.carleton.edu/~nchriste/CQG03.pdf |journal=Classical and Quantum Gravity |volume=21 |issue=1 |pages=317-330 |arxiv= |bibcode= |doi=10.1088/0264-9381/21/1/023 |pmid= |accessdate=2018-01-19 |month=1 December }}</ref> {{clear}} ==Greens== {{main|Radiation astronomy/Greens|Green astronomy}} [[Image:LASCO C1 coronagraph of solar corona.png|right|thumb|250px|A picture of the solar corona taken with the LASCO C1 coronagraph. The image is color coded for the doppler shift of the FeXIV 530.8 nm line. Credit: NASA and NRL.{{tlx|fairuse}}]] Green objects or emission lines in the green portion of the visible spectrum are the subject of [[green astronomy]]. In the image at right the iron (Fe XIV) green line is followed by doppler imaging to show associated relative coronal plasma velocity towards (-7 km/s side) and away from (+7 km/s side) the large angle spectrometric coronagraph LASCO satellite camera. "Carroll and McCormack (1972) in Dublin reported complex spectra in the blue and green wavelength regions of both FeH and FeD".<ref name="JGPhillips">{{cite journal |author=John G. Phillips |author2=Sumner P. Davis |author3=Bo Lindgren |author4=Walter J. Balfour |title=The near-infrared spectrum of the FeH molecule |journal=The Astrophysical Journal Supplement Series |month=December |year=1987 |volume=65 |issue=12 |pages=721-78 |url= |arxiv= |bibcode=1987ApJS...65..721P |doi=10.1086/191241 |pmid= |accessdate=2011-12-08 }}</ref> For elongated dust particles in cometary comas an investigation is performed at 535.0 nm (green) and 627.4 nm (red) peak transmission wavelengths of the Rosetta spacecraft's OSIRIS Wide Angle Camera broadband green and red filters, respectively.<ref name="Bertini">{{cite journal |author=I. Bertini |author2=N. Thomas |author3=C. Barbieri |title=Modeling of the light scattering properties of cometary dust using fractal aggregates |journal=Astronomy & Astrophysics |month=January |year=2007 |volume=461 |issue=1 |pages=351-64 |url=http://www.aanda.org/articles/aa/full/2007/01/aa5461-06/aa5461-06.html |arxiv= |bibcode=2007A&A...461..351B |doi=10.1051/0004-6361:20065461 |pmid= |pdf=http://www.aanda.org/articles/aa/pdf/2007/01/aa5461-06.pdf |accessdate=2011-12-08 }}</ref> "In the green, the polarization of the pure silicate composition qualitatively appears a better fit to the shape of the observed polarization curves".<ref name="Bertini"/> "[B]ut they are characterized by a high albedo."<ref name="Bertini"/> The silicates used to model the cometary coma dust are olivene (Mg-rich is green) and the pyroxene, enstatite.<ref name="Bertini"/> In December 2006, seven papers were published in the scientific journal, ''Science'', discussing initial details of the sample analysis. Among the findings are: a wide range of organic compounds, including two that contain biologically usable nitrogen; indigenous aliphatic hydrocarbons with longer chain lengths than those observed in the diffuse interstellar medium; abundant amorphous silicates in addition to crystalline silicates such as olivine and pyroxene, proving consistency with the mixing of solar system and interstellar matter, previously deduced spectroscopically from ground observations;<ref name="Nottingham">{{cite book |title=The building blocks of planets within the `terrestrial' region of protoplanetary disks |url=http://ukads.nottingham.ac.uk/cgi-bin/nph-bib_query?bibcode=2004Natur.432..479V&amp;db_key=AST |publisher=nottingham.ac.uk |accessdate=2008-03-04 }}</ref> hydrous silicates and carbonate minerals were found to be absent, suggesting a lack of aqueous processing of the cometary dust; limited pure carbon (CHON) was also found in the samples returned; methylamine and ethylamine was found in the aerogel but was not associated with specific particles. {{clear}} ==Hadrons== {{main|Radiation astronomy/Hadrons}} [[Image:Installing the ATLAS Calorimeter.jpg|right|thumb|300px|The eight toroid magnets can be seen surrounding the calorimeter that is later moved into the middle of the detector. Credit: Maximilien Brice.{{tlx|free media}}]] '''Hadrons''' are subatomic particles of a type including [[Radiation astronomy/Baryons|baryons]] and [[Radiation astronomy/Mesons|mesons]] that can take part in the [[strong interaction]] and may be useful in radiation astronomy. At right a person works lower center left in front of the huge ATLAS detector, one of six detectors attached to the Large Hadron Collider at CERN. {{clear}} ==High-velocity galaxies== {{main|Radiation astronomy/High-velocity galaxies}} [[Image:Irregular galaxy NGC 1427A (captured by the Hubble Space Telescope).jpg|thumb|right|200px|The irregular galaxy NGC 1427A is passing through the Fornax cluster at nearly 600 kilometers per second (400 miles per second). Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA).{{tlx|free media}}]] "The irregular galaxy NGC 1427A is a spectacular example of the resulting stellar rumble. Under the gravitational grasp of a large gang of galaxies, called the Fornax cluster, the small bluish galaxy is plunging headlong into the group at 600 kilometers per second or nearly 400 miles per second."<ref name=Gregg>{{ cite web |author=M. Gregg |title=The Impending Destruction of NGC 1427A |publisher=Hubblesite.org |location=Baltimore, Maryland USA |date=3 March 2005 |url=http://hubblesite.org/newscenter/archive/releases/2005/09/image/a/ |accessdate=2016-11-05 }}</ref> "Galaxy clusters, like the Fornax cluster, contain hundreds or even thousands of individual galaxies. Within the Fornax cluster, there is a considerable amount of gas lying between the galaxies. When the gas within NGC 1427A collides with the Fornax gas, it is compressed to the point that it starts to collapse under its own gravity. This leads to formation of the myriad of new stars seen across NGC 1427A, which give the galaxy an overall arrowhead shape that appears to point in the direction of the galaxy's high-velocity motion."<ref name=Gregg/> {{clear}} ==Histories== {{main|Radiation astronomy/History}} [[Image:Stonehenge.jpg|thumb|right|250px|Stonehenge is a Neolithic monument that may have functioned as a celestial observatory.<ref name=Hawkins>{{ cite book |author=GS Hawkins | date=1966 | title = Stonehenge Decoded | isbn= 978-0880291477 }}</ref> Credit: Wigulf.{{tlx|free media}}]] The ''Hominidae'', or hominins have apparently been on Earth for around seven to eight million years, at least somewhere in [[Africa]] and elsewhere. Fortunately and deliberately, many of these have worked out ways to record knowledge about the objects or entities in the sky observed by the radiation they produce. '''Radiation astronomy''' as an observational [[science]] has a long '''[[radiation history]]'''. {{clear}} ==Hydrometeors== {{main|Radiation astronomy/Hydrometeors}} [[Image:Regnbyge.jpg|thumb|right|400px|This image shows a late-summer rainstorm in the village Lunde, The north of Funen, Denmark. Credit: [[c:User:Malene|Malene Thyssen]].{{tlx|free media}}]] The nearly black color of the cloud's base indicates the foreground cloud is probably cumulonimbus. {{clear}} ==Hypervelocity stars== {{main|Radiation astronomy/Hypervelocity stars}} [[Image:Hs-2009-03-a-web_print.jpg|thumb|right|250px|The Hubble Space Telescope image shows four high-velocity, runaway stars plowing through their local interstellar medium. Credit: NASA - Hubble's Advanced Camera for Surveys.{{tlx|free media}}]] '''Def.''' a star moving faster than 65 km/s to 100 km/s relative to the average motion of the stars in the Sun's neighbourhood is called a '''high-velocity star'''. '''Def.''' a high-velocity star moving through space with an abnormally high velocity relative to the surrounding interstellar medium is called a '''runaway star'''. '''Def.''' a star whose elliptical orbit takes it well outside the plane of [its galaxy] at steep angles is called a '''halo star'''. {{clear}} ==Infrareds== {{main|Radiation astronomy/Infrareds|Infrared astronomy}} [[Image:Far-Infrared Image of M51.jpg|right|thumb|300px|This is a three-color far-infrared image of M51, the Whirlpool Galaxy. Credit: ESA and the PACS Consortium.{{tlx|free media}}]] The wavelength of infrared light ranges from 0.75 to 300 micrometers. Infrared falls in between visible radiation, which ranges from 380 to 750 nanometers, and terahertz radiation submillimeter waves. Infrared and [[optical astronomy]] are often practiced using the same telescopes, as the same mirrors or lenses are usually effective over a wavelength range that includes both visible and infrared light. '''Far-infrared astronomy''' deals with objects visible in far-infrared radiation extending from 30 micron (µm) towards submillimeter wavelengths around 450 µm. Huge, cold clouds of gas and dust in [the Milky Way] our own galaxy, as well as in nearby [[galaxies]], glow in far-infrared light. This is due to thermal radiation of interstellar dust contained in molecular clouds. Visually dark infrared sources can be radiative cosmic dust, hydrogen gas such as an H II region (e.g. the Orion Nebula), an H I region of hydrogen, a molecular cloud, or a coronal cloud. There are about 1,892,100 infrared (IR) objects in the SIMBAD database. Some of these like IRAS 20542+3631 are only IR objects. 1RXS J205444.6+361116 is an IR and an X-ray object only. These objects are visibly dark infrared sources. As is 2MASS J21074764+3802561, which is an IR and UV object only. {{clear}} ==Intensities== {{main|Radiation astronomy/Intensities}} [[Image:Positrons from a terrestrial gamma ray flash detected by the Fermi gamma ray telescope.png|thumb|right|250px|Positrons from a terrestrial gamma ray flash are detected by the Fermi gamma ray telescope. Credit: NASA Goddard Space Flight Center.{{tlx|fairuse}}]] '''Intensity astronomy''' focuses on creating a sufficient intensity for a desired property or characteristic that a signal may be converted in a detector to an electric current. {{clear}} ==Kuiper belts== {{main|Radiation astronomy/Kuiper belts}} [[Image:Outersolarsystem objectpositions labels comp.png|thumb|350px|Known objects in the Kuiper belt, are derived from data from the [[w:Minor Planet Center|Minor Planet Center]]. Credit: [[w:User:WilyD|WilyD]].{{tlx|free media}} Legend: {| style="width: 100%; margin-bottom: 8px;" |- | valign=top width=45% | {{legend2|red|border=1px solid black|Sun}}<br /> {{legend2|aquamarine|border=1px solid black|Giant Planet}}&nbsp;{{small|(6,178)}}<br /> {{legend2|#0BDA51|border=1px solid black|Kuiper belt object}}&nbsp;{{small|(&gt;300)}} {{legend2|Orange|border=1px solid black|Scattered disc object&nbsp;{{small|(9)}}}} | valign=top | {{legend2|Magenta|border=1px solid black|Trojan of Jupiter: J{{·}}S{{·}}U{{·}}N}}<br /> {{legend2|Yellow|border=1px solid black|Neptune trojan}}&nbsp;{{small|(44,000)}}<br /> |}]] The '''Kuiper belt''' is a region of the solar system extending from the orbit of Neptune (at 30 AU to approximately 60 AU from the Sun.<ref name=Stern>{{ cite journal | author=Alan Stern | title=Collisional Erosion in the Primordial Edgeworth-Kuiper Belt and the Generation of the 30–50 AU Kuiper Gap | journal=The Astrophysical Journal | volume=490 | issue=2 | pages=879–882 | year=1997 | doi=10.1086/304912 | last2=Colwell | first2=Joshua E. | bibcode=1997ApJ...490..879S }}</ref> It consists mainly of [[w:small Solar System body|small bodies]]. "[B]roadband optical photometry of Centaurs and Kuiper Belt objects from the Keck 10 m, the University of Hawaii 2.2 m, and the Cerro Tololo InterAmerican (CTIO) 1.5 m telescopes [shows] a wide dispersion in the optical colors of the objects, indicating nonuniform surface properties. The color dispersion [may] be understood in the context of the expected steady reddening due to bombardment by the ubiquitous flux of cosmic rays."<ref name="Luu">{{cite journal |author=Jane Luu |author2=David Jewitt |title=Color Diversity among the Centaurs and Kuiper Belt Objects |journal=The Astronomical Journal |month=November |year=1996 |volume=112 |issue=5 |pages=2310-8 |url=http://adsabs.harvard.edu/full/1996AJ....112.2310L |arxiv= |bibcode=1996AJ....112.2310L |doi= |pmid= |accessdate=2013-11-05 }}</ref> In the image at right, objects in the main part of the Kuiper belt are coloured green, while scattered objects are coloured orange. The four outer planets are blue. Neptune's few known [[w:Neptune trojan|trojans]] are yellow, while Jupiter's are pink. The scattered objects between Jupiter's orbit and the Kuiper belt are known as [[w:Centaur (minor planet)|centaurs]]. The scale is in [[w:astronomical unit|astronomical unit]]s. The pronounced gap at the bottom is due to difficulties in detection against the background of the plane of the [[w:Milky Way|Milky Way]]. Axes list distances in [[w:Astronomical unit|AU]], projected onto the [[w:ecliptic|ecliptic]], with [[w:ecliptic longitude|ecliptic longitude]] zero being to the right, along the "x" axis). Positions are accurate for January 1st, 2000 ([[w:eEpoch (astronomy)#J2000.0|J2000 epoch]]) with some caveats: For planets, positions should be exact. For minor bodies, positions are extrapolated from other epochs assuming purely [[w:eosculating orbit|Keplerian motion]]. As all data is from an epoch between 1993 and 2007, this should be a reasonable approximation. Data from the [[w:Minor Planet Center|Minor Planet Center]]<ref name=mpc>{{ cite book |url=http://www.cfa.harvard.edu/iau/MPCORB.html |title=The MPC Orbit (MPCORB) Database }}</ref> or Murray and Dermott<ref name=murraydermott>{{ cite book |author=Carl D. Murray |author2=Stanley F. Dermott |title=Solar System Dynamics |publisher=Cambridge University Press |year=1999 |isbn=0 521 57295 9 }}</ref> as needed. Radial "spokes" of higher density in this image, or gaps in particular directions are due to observational bias (i.e. where objects were searched for), rather than any real physical structure. The pronounced gap at the bottom is due to obscuration by the band of the Milky Way. {{clear}} ==Lensing== {{main|Radiation astronomy/Lensings}} [[Image:grav.lens1.arp.750pix.jpg|thumb|250px|This image shows a cluster of yellow galaxies near the middle of the photograph. Credit: STScl/NASA.{{tlx|free media}}]] The image at right shows several blue, loop-shaped objects that are multiple images of the same galaxy, duplicated by the [[w:gravitational lens|gravitational lens]] effect of the cluster of yellow galaxies near the middle of the photograph. The lens is produced by the cluster's gravitational field that bends light to magnify and distort the image of a more distant object. {{clear}} ==Lightnings== {{main|Radiation astronomy/Lightnings}} [[Image:Upperatmoslight1.jpg|300px|thumb|right|Representation of upper-atmospheric lightning and electrical-discharge phenomena are displayed. Credit: [[c:User:Abestrobi|Abestrobi]].{{tlx|free media}}]] [[Image:Lightning sprites2.png|left|thumb|300px|An illustration of different kinds of transient luminous events (TLEs) is displayed. Credit: Carlos Miralles (AeroVironment) and Tom Nelson (FMA).{{tlx|fairuse}}]] Lightning is more than ground-to-cloud electron transfer. "Cloud flashes sometimes have visible channels that extend out into the air around the storm (cloud-to-air or CA), but do not strike the ground. The terms sheet lightning or intra-cloud lightning (IC) refers to lightning embedded within a cloud that lights up as a sheet of luminosity during the flash. A related term, heat lightning, is lightning or lightning-induced illumination that is too far away for thunder to be heard. Lightning can also travel from cloud-to-cloud (CC). Spider lightning refers to long, horizontally traveling flashes often seen on the underside of stratiform clouds."<ref name=Miralles>{{ cite web |author=Carlos Miralles (AeroVironment) |author2=Tom Nelson (FMA) |title=SEVERE WEATHER 101 Lightning Types |publisher=NSSL, NOAA |location= |date=25 June 2019 |url=https://www.nssl.noaa.gov/education/svrwx101/lightning/types/ |accessdate=25 June 2019 }}</ref> "Large thunderstorms are capable of producing other kinds of electrical phenomena called transient luminous events (TLEs) that occur high in the atmosphere. They are rarely observed visually and not well understood. The most common TLEs include red sprites, blue jets, and elves."<ref name=Miralles/> The illustration on the left labels Elves, Sprites, and tendrils, a stratiform region producing positive cloud-to-ground flashes with spider lightning on the right to conventional cloud-to-air discharge, upward superbolt, blue jets and negative cloud-to-ground flash near convective core. Approximate altitudes in the Earth's atmosphere and ionosphere are indicated. {{clear}} ==Liquid objects== {{main|Liquid objects}} [[Image:Earth Pacific jul 30 2010.jpg|thumb|right|250px|This is a detailed, photo-like view of Earth based largely on observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite. Credit: Robert Simmon and Marit Jentoft-Nilsen, NASA.{{tlx|free media}}]] '''Def.''' precipitation products of the [[wikt:condensation|condensation]] of atmospheric water vapour are called '''hydrometeors'''. "Condensation or sublimation of atmospheric water vapor produces a hydrometeor. It forms in the free atmosphere, or at the earth's surface, and includes frozen water lifted by the wind. Hydrometeors which can cause a surface visibility reduction, generally fall into one of the following two categories: # '''Precipitation'''. Precipitation includes all forms of water particles, both liquid and solid, which fall from the atmosphere and reach the ground; these include: liquid precipitation (drizzle and rain), freezing precipitation (freezing drizzle and freezing rain), and solid (frozen) precipitation (ice pellets, hail, snow, snow pellets, snow grains, and ice crystals). # '''Suspended (Liquid or Solid) Water Particles'''. Liquid or solid water particles that form and remain suspended in the air (damp haze, cloud, fog, ice fog, and mist), as well as liquid or solid water particles that are lifted by the wind from the earth’s surface (drifting snow, blowing snow, blowing spray) cause restrictions to visibility. One of the more unusual causes of reduced visibility due to suspended water/ice particles is whiteout, while the most common cause is fog."<ref name="Mireles">{{cite web |author=Mark R. Mireles |author2=Kirth L. Pederson |author3=Charles H. Elford |title=Meteorologial Techniques |publisher=Air Force Weather Agency/DNT |location=Offutt Air Force Base, Nebraska, USA |date=February 21, 2007 |editor= |pages= |url=http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA466107 |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2013-02-17 }}</ref> {{clear}} ==Lithometeors== {{main|Radiation astronomy/Lithometeors}} [[Image:Ssc2006-16a.jpg|thumb|right|250px|The image shows the Orion nebula surrounded by a ring of dust. Credit: NASA/JPL-Caltech/T. Megeath(University of Toledo).{{tlx|free media}}]] '''Def.''' a suspension of dry dust in an atmosphere is called a '''lithometeor'''. "A lithometeor consists of solid particles suspended in the air or lifted by the wind from the ground."<ref name=Ozer95>{{ cite journal |author=PJ Ozer |title=Lithometeors in relation with desertification in the Sahelian area of Niger, In: ''Desertification in a European context: physical and socio-economic aspects'' |publisher=Office for Official Publications of the European Community |location=Luxembourg |month= |year=1995 |editor=Fantechi, R. |editor2=Peter, D. |editor3=Balabanis, P. |editor4=Rubio, J. L. |pages=567-74 |url=http://www.cabdirect.org/abstracts/19971901329.html |arxiv= |bibcode= |doi= |pmid= |isbn=92-827-4163-X |accessdate=2013-02-17 }}</ref> "A lithometeor is the general term for particles suspended in a dry atmosphere; these include dry haze, smoke, dust, and sand."<ref name=Mireles/> "Dry haze is an accumulation of very fine dust or salt particles in the atmosphere; it does not block light, but instead causes light rays to scatter. Dry haze particles produce a bluish color when viewed against a dark background, but look yellowish when viewed against a lighter background. This light-scattering phenomenon (called ''Mie scattering'') also causes the visual ranges within a uniformly dense layer of haze to vary depending on whether the observer is looking into the sun or away from it."<ref name=Mireles/> Heavy metal pollution may occur in lithometeors.<ref name=Yu>{{ cite journal |author=Jian-qiao Yu |author2=Xia1 Wang |author3=Li Wen |author4=Jing-shun Wang |title=Studies on Correlation of Heavy Metal Pollution in Soil, Lithometeor| and Leaves Around both Sides of Highway |journal=Journal of Agricultural Science and Technology |month=April |year=2008 |volume= |issue=04 |pages= |url=http://en.cnki.com.cn/Article_en/CJFDTOTAL-NKDB200804025.htm |arxiv= |bibcode= |doi= |pmid= |accessdate=2013-02-17 }}</ref> "The rise of airborne dust is constantly augmenting from the desert (Bilma) to the southern Sahelian stations (Niamey) where it has increased by a factor five. ... the Sahelian zone with airborne dust during the 80s ... All stations have recorded a general increase of wind velocity. The increase of lithometeors frequency as well as the wind velocity during the drought period is not explained by the aridification."<ref name=Ozer>{{ cite book |author=P. Ozer |title=Lithometeors and wind velocity in relation with desertification during the dry season from 1951 to 1994 in Niger, In: ''International Conference on tropical climatology, meteorology and hydrology in memoriam Franz Bultot'' |publisher=Royal Meteorological Institute of Belgium; Royal Academy of Overseas Sciences |location=Bruxelles (Belgium) |date=1998 |editor=G. Demaree |editor2=J. Alexandre |editor3=M. de Dapper |pages=212-27 |url=http://agris.fao.org/agris-search/search/display.do?f=1999/BE/BE99007.xml;BE1999001164# |arxiv= |bibcode= |doi= |pmid= |isbn= |accessdate=2013-02-17 }}</ref> {{clear}} ==Mathematics== {{main|Radiation astronomy/Mathematics}} [[Image:Andromeda and Milky Way collision.ogv|thumb|right|250px|This animation depicts the collision between our Milky Way galaxy and the Andromeda galaxy. Credit: Visualization Credit: NASA; ESA; and F. Summers, STScI; Simulation Credit: NASA; ESA; G. Besla, Columbia University; and R. van der Marel, STScI.{{tlx|free media}}]] Most of the mathematics needed to understand the information acquired through astronomical radiation observation comes from physics. But, there are special needs for situations that intertwine mathematics with phenomena that may not yet have sufficient physics to explain the observations. Both uses constitute '''radiation mathematics''', or '''astronomical radiation mathematics''', or a portion of '''mathematical radiation astronomy'''. '''Astronomical radiation mathematics''' is the laboratory mathematics such as simulations that are generated to try to understand the observations of radiation astronomy. The mathematics needed to understand radiation astronomy starts with arithmetic and often needs various topics in calculus and differential equations to produce likely models. {{clear}} ==Mesons== {{main|Radiation astronomy/Mesons|Meson astronomy}} [[Image:LHCb data on B0 meson production.png|right|thumb|300px|Comparison of the LHCb data on B⁰ meson production, both for central and for forward rapidities, with the theoretical predictions from POWHEG and aMC@NLO. Credit: Rhorry Gauld, Juan Rojo, Luca Rottoli and Jim Talbert.{{tlx|fairuse}}]] A '''meson''' is a composite subatomic particle "bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometre, which is about 2/3 the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Charged mesons decay (sometimes through intermediate particles) to form electrons and neutrinos. Uncharged mesons may decay to photons. Mesons are not produced by radioactive decay, but appear in nature only as short-lived products of very high-energy interactions in matter. In cosmic ray interactions, for example, such particles are ordinary protons and neutrons. Mesons are also frequently produced artificially in high-energy particle accelerators that collide protons, anti-protons, or other particles. In nature, the importance of lighter mesons is that they are the associated quantum-field particles that transmit the nuclear force, in the same way that photons are the particles that transmit the electromagnetic force. Each type of meson has a corresponding antiparticle (antimeson) in which quarks are replaced by their corresponding antiquarks and vice-versa. Mesons are subject to both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction. While no meson is stable, those of lower mass are nonetheless more stable than the most massive mesons, and are easier to observe and study in particle accelerators or in cosmic ray experiments. They are also typically less massive than baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher energy phenomena more readily than baryons composed of the same quarks would. {{clear}} ==Meteorites== {{main|Rocks/Meteorites}} [[Image:Widmanstatten patterns 2.jpg|thumb|right|250px|This image is a cross-section of the Laguna Manantiales meteorite showing Widmanstätten patterns. Credit: [[commons:User:Aramgutang|Aram Dulyan]].{{tlx|free media}}]] '''Def.''' a [[wikt:metallic|metallic]] or [[wikt:stony|stony]] object that is the remains of a [[wikt:meteor|meteor]] is called a '''meteorite'''. '''Widmanstätten patterns''', also called '''Thomson structures''', are unique figures of long nickel-iron crystals, found in the octahedrite iron meteorites and some pallasite]]s. They consist of a fine interleaving of kamacite and taenite bands or ribbons called ''lamellæ''. Commonly, in gaps between the lamellæ, a fine-grained mixture of kamacite and taenite called plessite can be found. {{clear}} ==Meteoroids== {{main|Radiation astronomy/Meteoroids}} [[Image:Earth-grazing meteoroid, 13 October 1990 (2) TFA.jpg|right|thumb|300px|This is a scanned photograph of the bolide EN131090, originally captured on a glass photographic plate. Credit: European Fireball Network.{{tlx|free media}}]] This is a scanned photograph on the right of the bolide EN131090, originally captured on a glass photographic plate. The Earth-grazing meteoroid flew above Czechoslovakia and Poland on 13 October 1990 and left to space again. It was taken by an all-sky camera equipped with a fish-eye objective Zeiss Distagon 3.5/30mm located at the hydrometeorological station at Červená hora, Czechoslovakia (now in the Czech Republic). The bolide travels from the south to the north and its track is interrupted by a shutter rotating 12.5 times per second, which allows determining its speed. "As of 2011 the International Astronomical Union officially defines a meteoroid as a solid object moving in interplanetary space, of a size considerably smaller than an asteroid and considerably larger than an atom".<ref name=Millman>{{ cite journal |author=Peter M. Millman |year=1961 |title=A report on meteor terminology |journal=JRASC |volume=55 |pages=265–267 |bibcode=1961JRASC..55..265M }}</ref><ref name=Glossary>{{ cite book |url=http://www.imo.net/glossary |title=Glossary International Meteor Organization |publisher=Imo.net |date=2008-11-18 |accessdate=2011-09-16}}</ref> {{clear}} ==Meteors== {{main|Radiation/Meteors}} [[Image:Paola-Castillo.jpg|thumb|right|250px|This meteor image of October 17, 2012, is prior to the meteorite fall on the same day. Credit: Paola-Castillo; and Petrus M. Jenniskens, SETI Institute/NASA ARC.{{tlx|free media}}]] A '''meteor''' is the visible path of a meteoroid that has entered the Earth's atmosphere. Although there are many definitions of a meteor ranging from any atmospheric phenomenon to a fast-moving streak of light in the night sky caused by the entry of extraterrestrial matter into the earth's atmosphere: A shooting star or falling star, for radiation astronomy, an alternative definition is used. Here's a [[Definitions/Theory#Theoretical definition|theoretical definition]] of a meteor from a radiation point of view: '''Def.''' any natural object radiating through a portion or all of the Earth's or another natural object's atmosphere is called a '''meteor'''. A hypervelocity star "snow-plowing" through the [[interstellar medium]] of a galaxy is a meteor and the subject of meteor astronomy. Meteor astronomy (radiated meteors) is radiation astronomy of large matter objects moving rapidly relative to apparently fixed objects. A meteor may be as small as an electron. Astronomical objects that are atoms, nuclei, or subatomic particles are part of cosmic-ray astronomy. {{clear}} ==Meteor showers== {{main|Radiation astronomy/Showers}} [[Image:Aurigids - Jeremie Vaubaillon.jpg|right|thumb|300px|The Aurigid meteor shower is observed by a group of astronomers on a NASA mission at 47,000 feet. Credit: Jeremie Vaubaillon, Caltech, NASA.{{tlx|free media}}]] Meteors may occur in showers, which arise when the Earth passes through a trail of debris left by a comet, or as "random" or "sporadic" meteors, not associated with a specific single cause. A number of specific meteors have been observed, largely by members of the public and largely by accident, but with enough detail that orbits of the meteoroids producing the meteors have been calculated. All of the orbits passed through the asteroid belt.<ref name=Uregina>{{ cite book |url=http://uregina.ca/~astro/mb_5.html |title=Diagram 2: the orbit of the Peekskill meteorite along with the orbits derived for several other meteorite falls |publisher=Uregina.ca |date= |accessdate=2011-09-16 }}</ref> "Named meteor showers recur at approximately the same dates each year. They appear to "radiate" from a certain point in the sky (the radiant) and vary in the speed, frequency and brightness of the meteors."<ref name=ListofMeteorShowers>{{ cite web |author=[[w:User:Noyster|Noyster]] |title=List of meteor showers |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=7 September 2017 |url=https://en.wikipedia.org/wiki/List_of_meteor_showers |accessdate=29 June 2019 }}</ref> As of November 2018, there are 112 established meteor showers.<ref>[https://www.ta3.sk/IAUC22DB/MDC2007/Roje/sortowanie_roje.php?corobic_roje=1 Meteor Data Centre, IAU] </ref> {{clear}} ==Microwaves== {{main|Radiation astronomy/Microwaves|Microwave astronomy}} [[Image:Milky-way-microwaves-planck.jpg|thumb|center|400px|A view of the Milky Way galaxy in microwaves is captured by the European Space Agency's Planck satellite. Credit: ESA/NASA/JPL-Caltech.{{tlx|fairuse}}]] Radiation astronomy specifically focused at the microwave portion of the electromagnetic spectrum is '''microwave astronomy'''. '''Microwaves''', a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300&nbsp;MHz (0.3&nbsp;GHz) and 300&nbsp;GHz.<ref name="Pozer">Pozar, David M. (1993). ''Microwave Engineering'' Addison-Wesley Publishing Company. {{ISBN|0-201-50418-9}}.</ref> This broad definition includes both UHF and Extremely high frequency (EHF) (millimeter waves), and various sources use different boundaries.<ref name="googlegloss">http://www.google.com/search?hl=en&defl=en&q=define:microwave&ei=e6CMSsWUI5OHmQee2si1DQ&sa=X&oi=glossary_definition&ct=title</ref> In all cases, microwave includes the entire super high frequency (SHF) band (3 to 30&nbsp;GHz, or 10 to 1&nbsp;cm) at minimum, with RF engineering often putting the lower boundary at 1&nbsp;GHz (30&nbsp;cm), and the upper around 100&nbsp;GHz (3 mm). {{clear}} ==Minerals== {{main|Radiation astronomy/Minerals}} [[Image:Pitchblende schlema-alberoda.JPG|thumb|right|250px|This is an image of the mineral pitchblende, or uraninite. Credit: [[commons:User:Geomartin|Geomartin]].{{tlx|free media}}]] [[Image:Uraninite-usa32abg.jpg|thumb|left|150px|These crystals are uraninite from Trebilcock Pit, Topsham, Maine. Credit: [[commons:User:Robert Lavinsky|Robert Lavinsky]].{{tlx|free media}}]] '''Uraninite''' is a radioactive, uranium-rich mineral and ore with a chemical composition that is largely [uranium dioxide] UO₂, but also contains [uranium trioxide] UO₃ and oxides of lead, thorium, and rare earth elements. It is most commonly known as '''pitchblende''' (from ''pitch'', because of its black color. All uraninite minerals contain a small amount of radium as a radioactive decay product of uranium. Uraninite also always contains small amounts of the lead isotopes ²⁰⁶Pb and ²⁰⁷Pb, the end products of the decay series of the uranium isotopes ²³⁸U and ²³⁵U respectively. The extremely rare element technetium can be found in uraninite in very small quantities (about 0.2 ng/kg), produced by the spontaneous fission of uranium-238. The image at left shows well-formed crystals of uraninite. The image at right shows botryoidal uraninite. Because of the uranium decay products, both sources are gamma-ray emitters. {{clear}} ==Molecules== {{main|Radiation astronomy/Molecules}} [[Image:Nhsc2009-021a.jpg|thumb|right|250px|Shown here is a portion of the SPIRE spectrum of VY Canis Majoris (VY CMa). Credit: ESA/NASA/JPL-Caltech.{{tlx|fairuse}}]] "This is one of the early spectra obtained with the SPIRE fourier transform spectrometer on Herschel. Shown here is a portion of the SPIRE spectrum of VY Canis Majoris (VY CMa), a red supergiant star near the end of its life, which is ejecting huge quantities of gas and dust into interstellar space. The inset is a SPIRE camera map of VY CMa, in which it appears as a bright compact source near the edge of a large extended cloud."<ref name=Groenewegen>{{ cite book |author=M. Groenewegen |title=SPIRE spectrum of VY Canis Majoris |publisher=Caltech |location=Pasadena, California USA |date=November 27, 2009 |url=http://www.herschel.caltech.edu/image/nhsc2009-021a |accessdate=2014-03-12 }}</ref> "The VY CMa spectrum is amazingly rich, with prominent features from carbon monoxide (CO) and water (H₂O). More than 200 other spectral features have been identified so far in the full spectrum, and several unidentified features are being investigated. Many of the features are due to water, showing that the star is surrounded by large quantities of hot steam. Observations like these will help to establish a detailed picture of the mass loss from stars and the complex chemistry occurring in their extended envelopes. As in all of the SPIRE spectra, the underlying emission increases towards shorter wavelengths, and is due to the emission from dust grains. The shape of the dust spectrum provides information on the properties of the dust."<ref name=Groenewegen/> "VY Canis Majoris (VY CMa) is a red supergiant star located about 4900 light years from Earth in the constellation Canis Major. It is the largest known star, with a size of 2600 solar radii, and also one of the most luminous, with a luminosity in excess of 100 000 times that of the Sun. The mass of VY CMa lies in the range 30-40 solar masses, and it has a mass-loss rate of 2 x 10^-4 solar masses per year."<ref name=Groenewegen/> "The shell of gas it has ejected displays a complex structure; the circumstellar envelope is among the most remarkable chemical laboratories known in the Universe, creating a rich set of organic and inorganic molecules and dust species. Through stellar winds, these inorganic and organic compounds are injected into the interstellar medium, from which new stars orbited by new planets may form. Most of the carbon supporting life on Earth was forged by this kind of evolved star. VY CMa truly is a spectacular object, it is close to the end of its life and could explode as a supernova at any time."<ref name=Groenewegen/> {{clear}} ==Muons== {{main|Radiation astronomy/Muons|Muon astronomy}} [[Image:Issue27muons1 l.jpg|thumb|right|250px|This is an image obtained from muon radiography of Japan's Asama volcano. Credit: H T M Tanaka.{{tlx|fairuse}}]] "TeV muons from γ ray primaries ... are rare because they are only produced by higher energy γ rays whose flux is suppressed by the decreasing flux at the source and by absorption on interstellar light."<ref name="Halzen">{{cite journal |author=Francis Halzen |author2=Todor Stanev |author3=Gaurang B. Yodh |title=γ ray astronomy with muons |journal=Physical Review D Particles, Fields, Gravitation, and Cosmology |month=April 1, |year=1997 |volume=55 |issue=7 |pages=4475-9 |url=http://prd.aps.org/abstract/PRD/v55/i7/p4475_1 |arxiv=astro-ph/9608201 |bibcode=1997PhRvD..55.4475H |doi=10.1103/PhysRevD.55.4475 |pmid= |accessdate=2013-01-18 }}</ref> Muon decay produces three particles, an [[electron]] plus two neutrinos of different types. {{clear}} ==Nebulas== {{main|Radiation astronomy/Nebulas}} [[Image:The Horsehead Nebula by NOAO 2.jpg|thumb|right|250px|This color picture was made by combining several exposures taken on the night of December 28th 1994 at the 0.9 m telescope of the Kitt Peak National Observatory. Credit: N.A.Sharp/NOAO/AURA/NSF.{{tlx|fairuse}}]] "The Horsehead Nebula, a part of the optical nebula IC434 and also known as Barnard 33, was first recorded in 1888 on a photographic plate taken at the Harvard College Observatory. Its coincidental appearance as the profile of a horse's head and neck has led to its becoming one of the most familiar astronomical objects. It is, in fact, an extremely dense cloud projecting in front of the ionized gas that provides the pink glow so nicely revealed in this picture. We know this not only because the underside of the 'neck' is especially dark, but because it actually casts a shadow on the field to its east (below the 'muzzle')."<ref name="Sharp">{{cite book |author=N. A. Sharp |title=The Horsehead Nebula |publisher=National Optical Astronomy Observatory (NOAO) |location=Kitt Peak, Arizona USA |date=28 December 1994 |url=https://www.noao.edu/image_gallery/html/im0057.html |accessdate=2015-09-25 }}</ref> {{clear}} ==Neutrals== {{main|Radiation astronomy/Neutrals|Neutrals astronomy}} [[Image:Article-2025275-0D6687D100000578-167 634x704.jpg|thumb|right|250px|The Necklace Nebula glows brightly in this Nasa Hubble Space Telescope image. Credit: NASA.{{tlx|fairuse}}]] "A giant cosmic necklace glows brightly in this Nasa Hubble Space Telescope image."<ref name="Reporter">{{cite book |author=DAILY MAIL REPORTER |title=Giant Necklace Nebula brightly glows with dense knots of blue, green and red gases |publisher=Daily Mail |location=United Kingdom |date=12 August 2011 |url=http://www.dailymail.co.uk/sciencetech/article-2025275/Necklace-Nebula-brightly-glows-dense-knots-blue-green-red-gases.html |accessdate=24 February 2014 }}</ref> "The object, aptly named the Necklace Nebula, is a recently discovered planetary nebula, the glowing remains of an ordinary, sun-like star."<ref name="Reporter"/> "The nebula consists of a bright ring, measuring 12trillion miles wide, dotted with dense, bright knots of gas that resemble diamonds in a necklace."<ref name="Reporter"/> "Newly discovered: The Necklace Nebula glows brightly in this composite image taken by the Hubble Space Telescope last month. The glow of hydrogen, oxygen, and nitrogen are shown by the colours blue, green and red respectively".<ref name="Reporter"/> "It is located 15,000 light-years away in the constellation Sagitta."<ref name="Reporter"/> "A pair of stars orbiting close together produced the nebula, also called PN G054.2-03.4."<ref name="Reporter"/> "About 10,000 years ago, one of the ageing stars ballooned to the point where it engulfed its companion star. The smaller star continued orbiting inside its larger companion, increasing the giant’s rotation rate. The bloated companion star spun so fast that a large part of its gaseous envelope expanded into space. Due to centrifugal force, most of the gas escaped along the star’s equator, producing a ring. The embedded bright knots are dense gas clumps in the ring. The pair is so close, only a few million miles apart, that they appear as one bright dot in the centre. The stars are furiously whirling around each other, completing an orbit in a little more than a day."<ref name="Reporter"/> {{clear}} ==Neutrinos== {{main|Radiation astronomy/Neutrinos|Neutrino astronomy}} [[Image:Neusun1 superk1.jpg|thumb|right|250px|This "neutrino image" of the Sun is by using the Super-Kamiokande to detect the neutrinos from nuclear fusion in the solar interior. Credit: R. Svoboda and K. Gordan (LSU).{{tlx|fairuse}}]] The field of '''neutrino astronomy''' is still very much in its infancy &ndash; the only confirmed extraterrestrial sources so far are the [[Sun (star)|Sun]] and supernova SN1987A. Neutrino astronomy observes astronomical objects with neutrino detectors in special observatories. Because neutrinos are only weakly interacting with other particles of matter, neutrino detectors must be very large in order to detect a significant number of neutrinos. Neutrino detectors are often built underground to isolate the detector from cosmic rays and other background radiation.<ref name="twsP16">{{cite book |author= KENNETH CHANG |title= Tiny, Plentiful and Really Hard to Catch, In: ''The New York Times'' |quote= In 1987, astronomers counted 19 neutrinos from an explosion of a star in the nearby Large Magellanic Cloud, 19 out of the billion trillion trillion trillion trillion neutrinos that flew from the supernova. |date= April 26, 2005 |url= http://www.nytimes.com/2005/04/26/science/26neut.html?pagewanted=print&position= |accessdate= 2011-06-16 }}</ref> The Super-Kamiokande, or "Super-K" is a large-scale experiment constructed in an unused mine in Japan to detect and study neutrinos. The image at right required 500 days worth of data to produce the "neutrino image" of the Sun. The image is centered on the Sun's position. This image covers a 90° x 90° octant of the sky (in right ascension and declination). The higher the brightness of the color, the larger is the neutrino flux. {{clear}} ==Neutrons== {{main|Radiation/Neutrons}} [[Image:Neutrons strip2.jpg|thumb|right|250px|The image shows the hydrogen concentrations on the Moon detected by the Lunar Prospector. Credit: NASA.{{tlx|free media}}]] Around EeV (10¹⁸ eV) energies, there may be associated ultra high energy neutrons "observed in anisotropic clustering ... because of the relativistic neutrons boosted lifetime."<ref name="Fargion2003">{{cite journal |author=Fargion D |author2=Khlopov M |author3=Konoplich R |author4=De Sanctis Lucentini PG |author5=De Santis M |author6=Mele B |title=Ultra High Energy Particle Astronomy, Neutrino Masses and Tau Airshowers |journal=Recent Research and Development in Astrophysics |month=March |year=2003 |volume=1 |issue=3 |pages=395-454 |url=http://arxiv.org/pdf/astro-ph/0303233 |doi= |bibcode=2003astro.ph..3233F |arxiv=astro-ph/0303233 |pdf=http://arxiv.org/pdf/astro-ph/0303233v2 |access=2011-11-25 }}</ref> “[A]t ''E''_n = 10²⁰ eV, [these neutrons] are flying a Mpc, with their directional arrival (or late decayed proton arrival) ... more on-line toward the source.”<ref name="Fargion2003"/> From “neutron (and anti-neutron) life-lengths (while being marginal or meaningless at tens of Mpcs)", the growth of their half-lives with energy may naturally explain an associated, showering neutrino halo.<ref name="Fargion2003"/> Fairly large fluxes of neutrons have been observed during [[w:solar flare|solar flare]]s such as that of November 12, 1960, with a flux of 30-70 neutrons per cm^-2 s^-1.<ref name="Lingenfelter">{{cite journal |author=Lingenfelter RE |author2=Flamm EJ |author3=Canfield EH |author4=Kellman S |title=High-Energy Solar Neutrons 2. Flux at the Earth |journal=Journal of Geophysical Research |month=September |year=1965 |volume=70 |issue=17 |pages=4087–95 |bibcode=1965JGR....70.4087L |doi=10.1029/JZ070i017p04087 |accessdate=2011-11-25 }}</ref> At right is the result of an all Moon survey by the Lunar Prospector using an onboard neutron spectrometer (NS). Cosmic rays impacting the lunar surface generate neutrons which in turn lose much of their energy in collisions with hydrogen atoms trapped within the Moon's surface.<ref name="Williams"/> Some of these thermal neutrons collide with the helium atoms within the NS to yield an energy signature which is detected and counted.<ref name="Williams"/> The NS aboard the Lunar Prospector has a surface resolution of 150 km.<ref name="Williams"/> {{clear}} ==Objects== {{main|Radiation astronomy/Objects|Object astronomy}} [[Image:Chain of impact craters on Ganymede.jpg|thumb|right|250px|The image shows a chain of craters on Ganymede. Credit: Galileo Project, Brown University, JPL, NASA.{{tlx|free media}}]] '''Def.''' a hemispherical pit a basinlike opening or mouth about which a cone is often built up any large roughly circular depression or hole is called a '''crater'''. The image at right shows a chain of 13 craters (Enki Catena) on Ganymede measuring 161.3 km in length. "The Enki craters formed across the sharp boundary between areas of bright terrain and dark terrain, delimited by a thin trough running diagonally across the center of this image. The ejecta deposit surrounding the craters appears very bright on the bright terrain. Even though all the craters formed nearly simultaneously, it is difficult to discern any ejecta deposit on the dark terrain. {{clear}} ==Oort clouds== {{main|Radiation astronomy/Oort clouds}} {{multiple image |direction = vertical |align = right |width = 285 |image1=PIA17046 - Voyager 1 Goes Interstellar.jpg |image2=Kuiper oort-en.svg |caption1=This graphic shows the distance from the Oort cloud to the rest of the Solar System and two of the nearest stars measured in astronomical units (AU). The scale is logarithmic, with each specified distance ten times further out than the previous one. Credit: NASA/JPL-Caltech.{{tlx|free media}} |caption2=An artist's rendering is of the Oort cloud and the Kuiper belt (inset). Sizes of individual objects have been exaggerated for visibility. Credit: NASA.{{tlx|free media}} }} The '''Oort cloud''' or the '''Öpik–Oort cloud'''<ref name = "Whipple">{{ cite journal | author = Fred Lawrence Whipple |author2=G. Turner |author3=J. A. M. McDonnell |author4=M. K. Wallis | title = A Review of Cometary Sciences | url = http://rsta.royalsocietypublishing.org/content/323/1572/339.short | journal = Philosophical Transactions of the Royal Society A | volume = 323 | issue = 1572 | pages = 339–347 [341] | publisher = Royal Society Publishing | date = 1987-09-30 | bibcode = 1987RSPTA.323..339W | doi = 10.1098/rsta.1987.0090 }}</ref> is a hypothesized spherical cloud of comets which may lie roughly 50,000 [[w:astronomical unit|AU]], or nearly a [[w:light-year|light-year]], from the [[Stars/Sun|Sun]].<ref name="Morbidelli2006">{{ cite book |author=Alessandro Morbidelli |year=2006 |title=Origin and dynamical evolution of comets and their reservoirs of water ammonia and methane. |url=https://arxiv.org/abs/astro-ph/0512256 |arxiv=astro-ph/0512256 }}</ref> This places the cloud at nearly a quarter of the distance to [[w:Proxima Centauri|Proxima Centauri]], the nearest [[w:star|star]] to the Sun. The outer limit of the Oort cloud defines the [[w:Cosmography|cosmographical]] boundary of the [[Solar System]] and the region of the Sun's gravitational dominance.<ref name="NASA_SSE_oort">{{ cite book |title=Kuiper Belt & Oort Cloud |url=http://solarsystem.nasa.gov/planets/profile.cfm?Object=KBOs&Display=OverviewLong |publisher=NASA |accessdate=2011-08-08 }}</ref> The Oort cloud is divided into two regions: a circumstellar disc-shaped inner Oort cloud (or Hills cloud) and a circumstellar envelope, spherical outer Oort cloud. Both regions lie beyond the heliosphere and in interstellar space.<ref name="Morbidelli2006a">{{cite arXiv |author=Alessandro Morbidelli |date=2006 |title=Origin and dynamical evolution of comets and their reservoirs of water ammonia and methane |eprint=astro-ph/0512256 }}</ref><ref name="jpl.PIA17046">{{cite web |url=http://photojournal.jpl.nasa.gov/catalog/PIA17046 |title=Catalog Page for PIA17046 |work=Photo Journal |publisher=NASA |date= |accessdate=April 27, 2014 }}</ref> ''Voyager 1'', the fastest<ref name="New_Horizons2006">{{cite web |url=http://pluto.jhuapl.edu/news_center/news/081706.php |title=New Horizons Salutes Voyager |date=August 17, 2006 |publisher=New Horizons |accessdate=November 3, 2009 |archiveurl=https://www.webcitation.org/5x3s4O3KH?url=http://pluto.jhuapl.edu/news_center/news/081706.php |archivedate=March 9, 2011 |df= }}</ref> and farthest<ref name="g.2013sep13">{{cite news |last=Clark |first=Stuart |title=Voyager 1 leaving solar system matches feats of great human explorers |url=https://www.theguardian.com/science/across-the-universe/2013/sep/13/voyager-1-solar-system-great-explorers |newspaper=The Guardian |date=September 13, 2013 }}</ref><ref>{{cite news |url=http://www.spacetoday.org/SolSys/Voyagers20years.html |title=Voyagers are leaving the Solar System |work=Space Today |date=2011 |accessdate=May 29, 2014 }}</ref> of the interplanetary space probes currently leaving the Solar System, will reach the Oort cloud in about 300 years<ref name="jpl.PIA17046"/><ref name="ut.104717">{{cite web |url=http://www.universetoday.com/104717/its-official-voyager-1-is-now-in-interstellar-space/ |title=It's Official: Voyager 1 Is Now In Interstellar Space |work=UniverseToday |date= 2013-09-12 |accessdate=April 27, 2014 }}</ref> and would take about 30,000 years to pass through it.<ref name="Ghose2013">{{cite web |last=Ghose |first=Tia |title=Voyager 1 Really Is In Interstellar Space: How NASA Knows |work=Space.com |publisher=TechMedia Network |date=September 13, 2013 |url=http://www.space.com/22797-voyager-1-interstellar-space-nasa-proof.html |accessdate=September 14, 2013 }}</ref><ref name="How_We_Know">{{cite web |last=Cook |first=J.-R |title=How Do We Know When Voyager Reaches Interstellar Space? |publisher=NASA / Jet Propulsion Lab | date=September 12, 2013 |url=http://www.jpl.nasa.gov/news/news.php?release=2013-278 |accessdate=September 15, 2013 }}</ref> However, around 2025, the radioisotope thermoelectric generators on ''Voyager 1'' will no longer supply enough power to operate any of its scientific instruments, preventing any further exploration by ''Voyager 1.'' {{clear}} ==Opticals== {{main|Radiation astronomy/Opticals|Optical astronomy}} [[Image:GTC Active Optics Acutators.jpg|thumb|right|250px|Actuators are part of the active optics of the {{lang|es|Gran Telescopio Canarias}}. Credit: [[commons:User:Vesta|Vesta]].{{tlx|free media}}]] [[Optical astronomy]] includes those portions of [[Ultraviolet astronomy|ultraviolet]], [[Visual astronomy|visual]], and [[infrared astronomy]] that benefit from the use of quartz crystal or silica glass telescope components. Observations at these wavelengths generally use ''optical components'' (mirrors, lenses and solid state digital detectors). In popular culture '''optical astronomy''' encompasses a wide variety of observations via telescopes that are sensitive in the range of visible light. Scientists would call this visible-light astronomy. It includes ''imaging'', where a picture of some sort is made of the object; ''photometry'', where the amount of light coming from an object is measured, ''spectroscopy'', where the distribution of that light with respect to its wavelength is measured, and ''polarimetry'' where the polarisation state of that light is measured. '''Def.''' astronomy using infrared, visible and/or ultraviolet wavelengths is called '''optical astronomy'''. '''Def.''' an optical system in telescopes that reduces atmospheric distortion by dynamically measuring and correcting wavefront aberrations in real time, often by using a deformable mirror is called '''adaptive optics'''. "Already it has allowed ground-based telescopes to produce images with sharpness rivalling those from the Hubble Space Telescope. The technique is expected to revolutionize the future of ground-based optical astronomy."<ref name="Roddier">{{cite book |author= |title=Adaptive Optics in Astronomy |publisher=Cambridge University Press |location=Cambridge, United Kingdom |date=1999 |editor=François Roddier |pages=411 |url=http://catdir.loc.gov/catdir/samples/cam031/00500597.pdf |arxiv= |bibcode= |doi= |pmid= |isbn=0 521 55375 X |accessdate=2012-02-15 }}</ref> The '''color index''' is a simple numerical expression that determines the color of an object, which in the case of a star gives its temperature. To measure the index, one observes the magnitude of an object successively through two different filters, such as U and B, or B and V, where U is sensitive to ultraviolet rays, B is sensitive to blue light, and V is sensitive to visible (green-yellow) light (see also: UBV system). The set of passbands or filters is called a photometric system. The difference in magnitudes found with these filters is called the U-B or B–V color index, respectively. The smaller the color index, the more blue (or hotter) the object is. Conversely, the larger the color index, the more red (or cooler) the object is. This is a consequence of the logarithmic magnitude scale, in which brighter objects have smaller (more negative) magnitudes than dimmer ones. For comparison, the yellowish [[Stars/Sun|Sun]] has a B–V index of {{nowrap|0.656 ± 0.005}},<ref name="Gray">David F. Gray (1992), ''[http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1992PASP..104.1035G&amp;db_key=AST&amp;data_type=HTML&amp;format=&amp;high=44b52c369023103 The Inferred Color Index of the Sun]'', Publications of the Astronomical Society of the Pacific, vol. 104, no. 681, pp. 1035-1038 (November 1992)</ref> while the bluish [[w:Rigel|Rigel]] has B–V –0.03 (its B magnitude is 0.09 and its V magnitude is 0.12, B–V = –0.03).<ref name="rigel">The [http://simbad.u-strasbg.fr Simbad Astronomical Database]' [http://simbad.u-strasbg.fr/sim-id.pl?protocol=html&Ident=Rigel&NbIdent=1&Radius=10&Radius.unit=arcmin&CooFrame=FK5&CooEpoch=2000&CooEqui=2000&output.max=all&o.catall=on&output.mesdisp=N&Bibyear1=1983&Bibyear2=2006&Frame1=FK5&Frame2=FK4&Frame3=G&Equi1=2000.0&Equi2=1950.0&Equi3=2000.0&Epoch1=2000.0&Epoch2=1950.0&Epoch3=2000.0 Rigel page]</ref> The passbands most optical astronomers use are the UBVRI filters, where the U, B, and V filters are as mentioned above, the R filter passes red light, and the I filter passes infrared light. These filters were specified as particular combinations of glass filters and photomultiplier tubes. An optical telescope gathers and focuses light mainly from the visible part of the electromagnetic spectrum (although some work in the infrared and ultraviolet).<ref name="Jones">{{cite book |url=http://books.google.com/books?id=5wX9aHqfBS0C&pg=PA111&lr=&cd=55#v=onepage&f=false |author=Barrie William Jones |title=The search for life continued: planets around other stars |page=111 }}</ref> {{clear}} ==Oranges== {{main|Radiation astronomy/Oranges|Orange astronomy}} [[Image:Jupiter.jpg|left|thumb|250px|Cloud bands are clearly visible on [[Jupiter]]. Credit: NASA/JPL/USGS.{{tlx|free media}}]] "[O]range [is] the color of Jupiter"<ref name="Birren">{{cite journal |author= Faber Birren |title=Color and human response |journal=Color Research and Application |month=Summer |year=1983 |volume=8 |issue=2 |pages=75-81 |url=http://onlinelibrary.wiley.com/doi/10.1002/col.5080080204/abstract |arxiv= |bibcode= |doi=10.1002/col.5080080204 |pmid= |accessdate=2012-04-23 }}</ref>. The orange and brown coloration in the clouds of Jupiter are caused by upwelling compounds that change color when they are exposed to ultraviolet light from the Sun. The exact makeup remains uncertain, but the substances are believed to be phosphorus, sulfur or possibly hydrocarbons.<ref name="elkins-tanton">{{cite book |first=Linda T.|last=Elkins-Tanton|year=2006 |title=Jupiter and Saturn|publisher=Chelsea House |location=New York|isbn=0-8160-5196-8}}</ref><ref>{{cite book |author=Strycker, P. D. |author2=Chanover, N. |author3=Sussman, M. |author4=Simon-Miller, A. |title = A Spectroscopic Search for Jupiter's Chromophores, In: ''DPS meeting #38, #11.15'' |publisher = American Astronomical Society|year = 2006 |bibcode = 2006DPS....38.1115S }}</ref> These colorful compounds, known as chromophores, mix with the warmer, lower deck of clouds. The zones are formed when rising convection cells form crystallizing ammonia that masks out these lower clouds from view.<ref name="worldbook">{{cite book |author=Gierasch, Peter J. |author2=Nicholson, Philip D. |year = 2004 |url = http://www.nasa.gov/worldbook/jupiter_worldbook.html |title = Jupiter |publisher = World Book @ NASA |accessdate = 2006-08-10 }}</ref> The '''orange system''' [in [[orange astronomy]]] is a number of emission lines very close together forming a band in the orange portion of the visible spectrum. These lines are usually associated with particular molecular species, including ScO, YO, and TiO.<ref name="Herbig">{{cite journal |author=G. H. Herbig |title=VY Canis Majoris. IV. The emission bands of ScO |journal=The Astrophysical Journal |month=March |year=1974 |volume=188 |issue=3 |pages=533-8 |url= |arxiv= |bibcode=1974ApJ...188..533H |doi=10.1086/152744 |pmid= |accessdate=2012-02-01 }}</ref> The orange band from molecular CaCl is "observed in the spectra of many carbon stars."<ref name="Littleton">{{cite journal |author=J. E. Littleton |author2=Sumner P. Davis |title=Transition strength data for the orange and red bands of CaCl |journal=The Astrophysical Journal |month=October |year=1988 |volume=333 |issue=10 |pages=1026-34 |url= |arxiv= |bibcode=1988ApJ...333.1026L |doi=10.1086/166809 |pmid= |accessdate=2012-02-01 }}</ref> The Fe VII emission line at 608.7 nm, "frequently observed in the spectra of astrophysical plasmas", has been detected in planetary nebulae, Seyfert galaxies, and quasars.<ref name="Keenan">{{cite journal |author=F. P. Keenan |author2=P. H. Norrington |title=Relative emission line strengths for Fe VII in astrophysical plasmas |journal=Astronomy and Astrophysics |month=July |year=1987 |volume=181 |issue=2 |pages=370-2 |url= |arxiv= |bibcode=1987A&A...181..370K |doi= |pmid= |accessdate=2012-01-17 }}</ref> {{clear}} ==Particles== {{main|Radiation astronomy/Particles}} [[Image:Dark Flight Incoming.jpg|thumb|right|250px|The image shows the first film ever of a meteor plunging down at terminal velocity. Credit: Anders Helstrup / Dark Flight, montage, Hans Erik Foss Amundsen.{{tlx|fairuse}}]] "A skydiver may have captured the first film ever of a meteorite plunging down at terminal velocity, also known as its “dark flight” stage."<ref name=Fang>{{ cite book |author=Janet Fang |title=Skydiver Almost Hit by Meteorite |publisher=IFLScience |location= |date=April 4, 2014 |url=http://www.iflscience.com/space/skydiver-almost-hit-meteorite |accessdate=2014-08-31 }}</ref> "The footage was captured in 2012 by a helmet cam worn by Anders Helstrup as he and other members of the Oslo Parachute Club jumped from a small plane that took off from an airport in Hedmark, Norway."<ref name=Fang/> “It can’t be anything else. The shape is typical of meteorites -- a fresh fracture surface on one side, while the other side is rounded.”<ref name=Amundsen>{{ cite book |author=Hans Erik Foss Amundsen |title=Skydiver Almost Hit by Meteorite |publisher=IFLScience |location= |date=April 4, 2014 |url=http://www.iflscience.com/space/skydiver-almost-hit-meteorite |accessdate=2014-08-31 }}</ref> “It has never happened before that a meteorite has been filmed during dark flight; this is the first time in world history.”<ref name=Amundsen/> "Having the rock in hand would certainly help. But despite triangulations and analyses, Helstrup and his recruits still haven’t found it."<ref name=Fang/> {{clear}} ==Planets== {{main|Radiation astronomy/Planets|Planetary astronomy}} [[Image:Ganymede g1 true-edit1.jpg|thumb|right|250px|A true color image of Ganymede is acquired by the Galileo spacecraft on June 26, 1996. Credit: [[c:User:PlanetUser|PlanetUser]], NASA, JPL.{{tlx|free media}}]] '''Planetary science''' is the scientific study of planets (including [[Rocks/Rocky objects/Earth|Earth]]), natural satellite, moons, and planetary systems, in particular those of the [[Solar System|solar system]] and the processes that form them using the radiation they emit, reflect, fluoresce, or absorb. It studies objects ranging in size from micrometeoroids to gas giants, aiming to determine their composition, dynamics, formation, interrelations and history. It is a strongly interdisciplinary field, originally growing from astronomy and earth science,<ref name="Taylor"/> but which now incorporates many disciplines, including planetary astronomy, planetary geology (together with geochemistry and geophysics), atmospheric science, oceanography, [[hydrology]], theoretical planetary science, glaciology, and the study of extrasolar planets.<ref name="Taylor">{{cite journal |author=Stuart Ross Taylor |date=29 July 2004 |title=Why can't planets be like stars? |journal=Nature |pmid=15282586 |volume=430 |issue=6999 |pages=509 |doi=10.1038/430509a |url=http://www.nature.com/nature/journal/v430/n6999/full/430509a.html |bibcode = 2004Natur.430..509T }}</ref> {{clear}} ==Plasmas== {{main|Radiation astronomy/Plasmas}} [[Image:Media 1.ogv|thumb|right|250px|On July 19, 2012, an eruption occurred on the sun that produced a moderately powerful solar flare and a dazzling magnetic display known as coronal rain. Credit: NASA Goddard Space Flight Center, Music: 'Thunderbolt' by Lars Leonhard, courtesy of artist.{{tlx|free media}}]] "[A] medium-strength flare erupted from the sun on July 19, 2012. The blast also generated the enormous, shimmering plasma loops, which are an example of a phenomenon known as "coronal rain," agency officials said."<ref name="Wall">{{cite book |author=Mike Wall |title=Super-Hot Plasma 'Rain' Falls on Sun in Amazing Video |publisher=Yahoo! News |location= |date=February 21, 2013 |url=http://news.yahoo.com/super-hot-plasma-rain-falls-sun-amazing-video-190147271.html |accessdate=2013-02-23 }}</ref> "Hot plasma in the corona cooled and condensed along strong magnetic fields in the region" slowly falling back to the solar surface as plasma "rain".<ref name="Wall"/> A [[coronal cloud]] is a cloud, or cloud-like, natural astronomical entity, composed of plasma and usually associated with a star or other astronomical object where the temperature is such that X-rays are emitted. While small coronal clouds are above the photosphere of many different visual spectral type stars, others occupy parts of the [[interstellar medium]] (ISM), extending sometimes millions of kilometers into space, or thousands of light-years, depending on the size of the associated object such as a galaxy. {{clear}} ==Positrons== {{main|Radiation astronomy/Positrons|Positron astronomy}} [[Image:509305main GBM positron event 300dpi.jpg|thumb|right|250px|Observation of positrons from a terrestrial gamma ray flash is performed by the Fermi gamma ray telescope. Credit: NASA Goddard Space Flight Center.{{tlx|free media}}]] "[[Positron astronomy]] is 30 years old but remains in its infancy."<ref name="Milne">{{cite book |author=P.A.Milne |author2=J.D.Kurfess |author3=R.L.Kinzer |author4=M.D.Leising |author5=D.D.Dixon |title=Investigations of positron annihilation radiation, In: ''Proceedings of the 5th COMPTON Symposium'' |publisher=American Institute of Physics |location=Washington, DC |date=April 2000 |volume=510 |issue=4 |pages=21-30 |url=http://arxiv.org/pdf/astro-ph/9911184 |arxiv=astro-ph/9911184v1 |bibcode=2000AIPC..510...21M |doi=10.1063/1.1303167 |pmid= |accessdate=2011-11-25 }}</ref> "[P]ositron astronomy results ... have been obtained using the INTEGRAL spectrometer SPI".<ref name=" Weidenspointner ">{{cite journal |author=G. Weidenspointner |author2=G.K. Skinner |author3=P. Jean |author4=J. Knödlseder |author5=P. von Ballmoos |author6=R. Diehl |author7=A. Strong |author8=B. Cordier |author9=S. Schanne |author10=C. Winkler |title=Positron astronomy with SPI/INTEGRAL |journal=New Astronomy Reviews |month=October |year=2008 |volume=52 |issue=7-10 |pages=454-6 |url=http://www.sciencedirect.com/science/article/pii/S1387647308001164 |arxiv= |bibcode= |doi=10.1016/j.newar.2008.06.019 |pmid= |accessdate=2011-11-25 }}</ref> The positrons are not directly observed by the INTEGRAL space telescope, but "the 511 keV positron annihilation emission is".<ref name="Weidenspointner"/> During solar flares “[s]everal radioactive nuclei that emit positrons are also produced; [which] slow down and annihilate in flight with the emission of two 511 keV photons or form positronium with the emission of either a three gamma continuum (each photon < 511 keV) or two 511 keV photons."<ref name="Share">{{cite book |author=Gerald H. Share |author2=Ronald J. Murphy |title=Solar Gamma-Ray Line Spectroscopy – Physics of a Flaring Star, In: ''Stars as Suns: Activity, Evolution and Planets'' |publisher=Astronomical Society of the Pacific |location=San Francisco, CA |date=January 2004 |editor=Andrea K. Dupree |editor2=A. O. Benz |pages=133-44 |url=http://heseweb.nrl.navy.mil/gamma/solar/papers/share_iau_04.pdf |arxiv= |bibcode=2004IAUS..219..133S |doi= |pmid= |isbn=158381163X |accessdate=2012-03-15 }}</ref> {{clear}} ==Protons== {{main|Radiation astronomy/Protons|Proton astronomy}} [[Image:GOES protons.jpg|thumb|right|250px|This graph displays the flux of high energy protons measured by GOES 11 over four days from November 2, 2003, to November 5, 2003. Credit: NOAA.{{tlx|free media}}]] "[[Proton astronomy]] should be possible; it may also provide indirect information on inter-galactic magnetic fields."<ref name="Halzen2002">{{cite journal |author=Francis Halzen |author2=Dan Hooper |title=High-energy neutrino astronomy: the cosmic ray connection |journal=Reports on Progress in Physics |month=July |year=2002 |volume=65 |issue=7 |pages=1025-78 |url=http://arxiv.org/pdf/astro-ph/0204527 |arxiv= |bibcode=2002RPPh...65.1025H |doi=10.1088/0034-4885/65/7/201 |pmid= |accessdate=2011-11-24 }}</ref> Proton astronomy ''per se'' often consists of directly or indirectly detecting the protons and deconvoluting a spatial, temporal, and spectral distribution. “[A]t the high end of the proton energy spectrum (above ≈ 10¹⁸ eV) [the Larmor radius] deflection becomes small enough that proton astronomy becomes possible.”<ref name="Hoffman">{{cite journal |author=K. D. Hoffman |title=High energy neutrino telescopes |journal=New Journal of Physics |month=May 12, |year=2009 |volume=11 |issue=5 |pages=055006 |url=http://arxiv.org/pdf/astro-ph/0204527 |arxiv= |bibcode= |doi=10.1088/1367-2630/11/5/055006 |pmid= |accessdate=2012-03-28 }}</ref> "The third largest solar proton event in the past thirty years took place during July 14-16, 2000, and had a significant impact on the earth's atmosphere."<ref name="Jackman">{{cite journal |author=Charles H. Jackman |author2=Richard D. McPeters |author3=Gordon J. Labow |author4=Eric L.Fleming |author5=Cid J. Praderas |author6=James M. Russell |title=Northern Hemisphere atmospheric effects due to the July 2000 solar proton event |journal=Geophysical Research Letters |month=August |year=2001 |volume=28 |issue=15 |pages=2883-6 |url=http://cdaw.gsfc.nasa.gov/meetings/2009_gle/data/Jackman/Jackman_2001.pdf |arxiv= |bibcode= |doi= |pmid= |accessdate=2011-11-24 }}</ref> {{clear}} ==Radars== {{main|Radiation astronomy/Radars|Radar astronomy}} [[Image:2012 LZ1.jpg|thumb|right|250px|This image is of asteroid 2012 LZ1 by the Arecibo Observatory in Puerto Rico using the Arecibo Planetary Radar. Credit: Arecibo Observatory.{{tlx|fairuse}}]] '''Radar astronomy''' is used to detect and study astronomical objects that reflect radio rays. "The advantages of radar in planetary astronomy result from (1) the observer's control of all the attributes of the coherent signal used to illuminate the target, especially the wave form's time/frequency modulation and polarization; (2) the ability of radar to resolve objects spatially via measurements of the distribution of echo power in time delay and Doppler frequency; (3) the pronounced degree to which delay-Doppler measurements constrain orbits and spin vectors; and (4) centimeter-to-meter wavelengths, which easily penetrate optically opaque planetary clouds and cometary comae, permit investigation of near-surface macrostructure and bulk density, and are sensitive to high concentrations of metal or, in certain situations, ice."<ref name="Ostro">{{cite journal |author=Steven J. Ostro |title=Planetary radar astronomy |journal=Reviews of Modern Physics |month=October-December |year=1993 |volume=65 |issue=4 |pages=1235-79 |url=http://rmp.aps.org/abstract/RMP/v65/i4/p1235_1 |arxiv= |bibcode= |doi=10.1103/RevModPhys.65.1235 |pmid= |accessdate=2012-02-09 }}</ref> {{clear}} ==Radiation== {{main|Radiation}} [[Image:Lead shielding.jpg|thumb|right|250px|A lead castle is built to shield a radioactive sample. Credit: [[commons:User:Changlc|Changlc]].{{tlx|free media}}]] In physics, '''radiation''' is a process in which energetic particles or energetic waves travel through a medium or space. '''Def.''' an action or process of throwing or sending out a traveling ray of energy in a line, beam, or stream of small cross section is called '''radiation'''. '''Def.''' the shooting forth of anything from a point or surface, like the diverging rays of light is called '''radiation'''. The term '''radiation''' is often used to refer to the ray itself. Different types of ionizing radiation behave in different ways, so different shielding techniques are used. {{clear}} ==Radios== {{main|Radiation astronomy/Radios|Radio astronomy}} [[Image:Composite radio + x-ray.jpg|thumb|right|250px|This image has the radio image of Greg Taylor, NRAO, overlain on the X-ray image from Chandra. The radio source Hydra A originates in a galaxy near the center of the cluster. Optical observations show a few hundred galaxies in the cluster. Credit: NASA/CXC/SAO; Radio: NRAO.{{tlx|free media}}]] '''Radio waves''' are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies from 300 [Gigahertz] GHz to as low as 3 [kilohertz] kHz, and corresponding wavelengths from 1 millimeter to 100 kilometers. Several satellites have served as observatories for radio waves and specifically for microwaves. The Radio Astronomy Explorer (RAE) 1 is launched into orbit on July 4, 1968, around Earth, while the [Explorer 49] RAE 2 is launched on June 10, 1973, around the Moon. The COBE is launched into Earth orbit on November 18, 1989. The WMAP is launched on June 30, 2001, into orbit at the [Lissajous orbit] Lagrange 2 location. Both satellites have aboard detectors designed to perform '''microwave astronomy''', as these are limited to only the microwave band. {{clear}} ==Reds== {{main|Radiation astronomy/Reds|Red astronomy}} [[Image:AZCancriCloseup.jpg|thumb|right|150px|AZ Cancri. Credit: SDSS Data Release 6.{{tlx|free media}}]] With respect to the color 'red', there are studies of the redness of objects such as the red dwarf AZ Cancri shown in the visual image at right. Cool stars of spectral class M appear red; they are (depending on their size) referred to as "red giants" or "red dwarfs". "Ideally all intrinsic colours should be found from unreddened stars. This is possible for dwarf and giant stars later than about A0 (Johnson, 1964) ... However, it cannot be used for stars of other spectral classes since they are all relatively infrequent in space, and generally reddened."<ref name="FitzGerald">{{cite journal |author=M. Pim FitzGerald |title=The Intrinsic Colours of Stars and Two-Colour Reddening Lines |journal=Astronomy and Astrophysics |month=February |year=1970 |volume=4 |issue=2 |pages=234-43 |url= |arxiv= |bibcode=1970A&A.....4..234F |doi= |pmid= |accessdate=2011-11-24 }}</ref> A very important wavelength in this region is the Balmer alpha line, 656.28 nm. It is emitted or absorbed by hydrogen atoms when electrons move between the second and third electron shells. Other Balmer lines, known as beta, gamma and delta, have wavelengths of 486.13, 434.05 and 410.17 nm respectively;[http://www.phys.utk.edu/labs/modphys/BalmerSeries.pdf] these are also in the visual range but are less important than the alpha line. {{clear}} ==Reflections== {{main|Radiation astronomy/Reflections}} [[Image:Ash and Steam Plume, Soufriere Hills Volcano, Montserrat.jpg|thumb|right|250px|This oblique astronaut photograph from the International Space Station (ISS) captures a white-to-grey ash and steam plume extending westwards from the Soufriere Hills volcano. Credit: NASA Expedition 21 crew.{{tlx|free media}}]] Oblique images such as the one at right are taken by astronauts looking out from the International Space Station (ISS) at an angle, rather than looking straight downward toward the Earth (a perspective called a nadir view), as is common with most remotely sensed data from satellites. An oblique view gives the scene a more three-dimension quality, and provides a look at the vertical structure of the volcanic plume. While much of the island is covered in green vegetation, grey deposits that include pyroclastic flows and volcanic mud-flows (lahars) are visible extending from the volcano toward the coastline. When compared to its extent in earlier views, the volcanic debris has filled in more of the eastern coastline. Urban areas are visible in the northern and western portions of the island; they are recognizable by linear street patterns and the presence of bright building rooftops. The silver-grey appearance of the Caribbean Sea surface is due to sun-glint, which is the mirror-like '''reflection''' of sunlight off the water surface back towards the hand-held camera on-board the ISS. The sun-glint highlights surface wave patterns around the island. {{clear}} ==Refractions== {{main|Radiation astronomy/Refractions}} [[Image:Calcite ShortwaveUV HAGAM.jpg|thumb|left|250px|Calcite fluoresces blue under short wave ultraviolet light. Credit: Herbert Art Gallery and Museum, Coventry.{{tlx|free media}}]] [[File:Calcite - Blue (2933075912).jpg|thumb|right|250px|Natural radiation interacts with sheared calcite to produce blue colors. Credit: Stephanie Clifford.{{tlx|free media}}]] Between 190 and 1700&nbsp;nm, the ordinary refractive index varies roughly between 1.9 and 1.5, while the extraordinary refractive index varies between 1.6 and 1.4.<ref name=Thompson>{{ cite journal |author = D.W. Thompson |year=1998 |title=Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry |journal= Thin Solid Films |volume=313–4 |issue= 1-2 |pages=341–6 |doi=10.1016/S0040-6090(97)00843-2 |bibcode=1998TSF...313..341T }}</ref> On the right is blue calcite produced by natural irradiation. {{clear}} ==Rocks== {{main|Radiation astronomy/Rocks}} [[Image:BlueRock.jpg|thumb|right|250px|This Sin-Kamen (''Blue Rock'') near Lake Pleshcheyevo used to be a Meryan shrine Credit: Viktorianec.{{tlx|free media}}]] [[Image:Blue rock from Berkeley hills.jpg|thumb|left|250px|This is a blue rock, probably various copper minerals, from the Berkeley hills near San Francisco, California. Credit: [[w:User:Looie496|Looie496]].{{tlx|free media}}]] [[Image:243 ida crop.jpg|thumb|right|250px|This is an approximately natural color picture of the asteroid 243 Ida on August 28, 1993. Credit: NASA/JPL.{{tlx|free media}}]] '''Sin-Kamen''' ({{lang|ru|Синь-Камень}}, in Russian literally – '''Blue Stone''', or '''Blue Rock''') is a type of pagan sacred stones, widespread in Russia, in areas historically inhabited by both Eastern Slavic (Russian), and Uralic tribes (Merya, Muroma<ref>[http://www.bogorodsk-noginsk.ru/atlas/sinie_kamni.html И.Д. Маланин. Материалы разведки Синих камней Подмосковья в 2003 году // Краеведение и регионоведение. Межвузовский сборник научных трудов. ч.1. Владимир, 2004.] (Russian)</ref>). While in the majority of cases, the stones belonging to the ''Blue Stones'' type, have a black, or dark gray color, this particular stone [in the image] does indeed look dark blue, when wet.<ref name="berdnikov">[http://pki.botik.ru/dl.php?b=articles&a=n-sinii1985berd.pdf Бердников,&nbsp;В. Синий камень Плещеева озера] // Наука и жизнь. – 1985. – № 1. – С.&nbsp;134–139. (Russian)</ref> "Several types of rock surface materials can be recognized at the two sites [Viking Lander 1 and Viking Lander 2]; dark, relatively 'blue' rock surfaces are probably minimally weathered igneous rock, whereas bright rock surfaces, with a green/(blue + red) ratio higher than that of any other surface material, are interpreted as a weathering product formed in situ on the rock."<ref name="Strickland">{{cite book |author=Edwin L. Strickland III |title=Martian soil stratigraphy and rock coatings observed in color-enhanced Viking Lander images, In: ''Lunar and Planetary Science Conference Proceedings'' |publisher=Pergamon Press, Inc. |location=New York |date=March 19, 1979 |volume=3 |issue= |pages=3055-77 |url=http://adsabs.harvard.edu/abs/1979LPSC...10.3055S |arxiv= |bibcode=1979LPSC...10.3055S |doi= |pmid= |accessdate=2013-05-31 }}</ref> At second right is an approximately natural color image of the asteroid 243 Ida. "There are brighter areas, appearing bluish in the picture, around craters on the upper left end of Ida, around the small bright crater near the center of the asteroid, and near the upper right-hand edge (the limb). This is a combination of more reflected blue light and greater absorption of near infrared light, suggesting a difference in the abundance or composition of iron-bearing minerals in these areas."<ref name="Lavoie96">{{cite book |author=Sue Lavoie |title=PIA00069: Ida and Dactyl in Enhanced Color |publisher=NASA/JPL |location=Pasadena, California USA |date=January 29, 1996 |url=http://photojournal.jpl.nasa.gov/catalog/?IDNumber=PIA00069 |accessdate=2013-06-01 }}</ref> "The [Sloan Digital Sky Survey] SDSS “blue” asteroids are related to the C-type (carbonaceous) asteroids, but not all of them are C-type. They are a mixture of C-, E-, M-, and P-types."<ref name="Yoshida">{{cite journal |author=F Yoshida, T Nakamura |title=Subaru main belt asteroid survey (SMBAS)—size and color distributions of small main-belt asteroids |journal=Planetary and Space Science |month=June |year=2007 |volume=55 |issue=9 |pages=1113-25 |url=http://www.sciencedirect.com/science/article/pii/S0032063306003357 |arxiv= |bibcode= |doi=10.1016/j.pss.2006.11.016 |pmid= |accessdate=2013-06-01 }}</ref> {{clear}} ==Satellites== {{main|Radiation astronomy/Satellites}} [[Image:IBEX spacecraft.jpg|thumb|right|250px|This is an artist's rendering of the Interstellar Boundary Explorer (IBEX) satellite. Credit: NASA/Goddard Space Flight Center Conceptual Image Lab.{{tlx|free media}}]] '''Radiation satellites''' may be designed and built for detection in one particular radiation astronomy or for many. Some have been built for more than one purpose or for a different purpose entirely. To place sensors (or detectors) above the [[w:Earth’s atmosphere|Earth’s atmosphere]] is often a necessity for radiation astronomy. “The sensors at once lose the basic advantage of both radio and optical telescopes, a rigid, well-surveyed foundation upon a well-behaved earth.”<ref name=Ouellette>{{ cite journal |author=Gerald A. Ouellette |title=Development of a Catalogue of Galactic X-Ray Sources |journal=The Astronomical Journal |month=June |year=1967 |volume=72 |issue=5 |pages=597-600 |url= |arxiv= |bibcode=1967AJ.....72..597O |doi=10.1086/110278 |pmid= |accessdate=2012-03-17 }}</ref> “The source locations, therefore, reflect uncertainties in both the sensor data and in vehicle aspect.”<ref name=Ouellette/> {{clear}} ==Scattered disks== {{main|Radiation astronomy/Scattered disks}} [[Image:TheKuiperBelt 100AU SDO.svg|thumb|center|400px|The diagram shows scattered disc objects out to 100 AU. Credit: [[c:User:Eurocommuter|Eurocommuter]].{{tlx|free media}}]] Scattered Disk Objects (up to 100 AU): Kuiper Belt objects are shown in grey, resonant objects within the Scattered Disk are shown in green. The position of an object represents * its orbit’s semi-major axis '''a''' in AU and the orbital period in years (horizontal axis) * its orbit’s inclination '''i''' in degrees (vertical axis). The size of the circle illustrates the object’s size relative to others. For a few large objects, the diameter drawn represents the best current estimates. For all others, the circles represent the absolute magnitude of the object. The eccentricity of the orbit is shown indirectly by a segment extending from the left (perihelion) to the aphelion to the right. In other words, the segment illustrates the variations of the object's distance from the Sun. Objects with nearly circular orbits will show short segments while highly elliptical orbits will be represented by long segments. Main resonances with Neptune are marked with vertical bars; 1:1 marks the position of Neptune’s orbit (and its Trojan asteroids), 2:3 marks the orbit of Pluto (and plutinos) etc. The scattered disc (or scattered disk) is a distant region of the [[Solar System]] that is sparsely populated by icy minor planets, a subset of the broader family of trans-Neptunian objects. The scattered-disc objects (SDOs) have orbital eccentricities ranging as high as 0.8, inclinations as high as 40°, and perihelia greater than 30 astronomical units (4.5 x 10⁹ km; 2.8 x 10⁹ mi.). While the nearest distance to the Sun approached by scattered objects is about 30–35&nbsp;AU, their orbits can extend well beyond 100&nbsp;AU. This makes scattered objects "among the most distant and cold objects in the Solar System".<ref name=Masetti>Maggie Masetti. (2007). ''[http://heasarc.gsfc.nasa.gov/docs/cosmic/solar_system_info.html Cosmic Distance Scales&nbsp;– The Solar System]''. Website of NASA's High Energy Astrophysics Science Archive Research Center. Retrieved 2008 07-12.</ref> The innermost portion of the scattered disc overlaps with a torus-shaped region of orbiting objects traditionally called the Kuiper belt,<ref name=Morbidelli2008>{{cite arXiv |title=Origin and dynamical evolution of comets and their reservoirs |first=Alessandro |last= Morbidelli |eprint=astro-ph/0512256 |date=2005 }}</ref> but its outer limits reach much farther away from the Sun and farther above and below the ecliptic than the Kuiper belt proper. The literature is inconsistent in the use of the phrases "scattered disc" and "Kuiper belt"; for some, they are distinct populations; for others, the scattered disc is part of the Kuiper belt and authors may even switch between these two uses in a single publication.<ref>McFadden, Weissman, & Johnson (2007). ''Encyclopedia of the Solar System'', footnote p. 584</ref> {{clear}} ==Scatterings== {{main|Radiation astronomy/Scatterings}} [[Image:Empire State Building Night.jpg|thumb|right|250px|This time [[w:exposure (photography)|exposure]] photo of [[w:New York City|New York City]] at night shows [[w:skyglow|skyglow]], one form of light pollution. Credit: Charliebrown7034.{{tlx|free media}}]] Neutrons react with a number of materials through elastic scattering producing a recoiling nucleus, [[w:Inelastic scattering|inelastic scattering]] producing an excited nucleus, or absorption with transmutation of the resulting nucleus. Most detection approaches rely on detecting the various reaction products. {{clear}} ==Skys== [[Image:Hajiali.jpg|thumb|left|250px|An orange sunset in the Mahim Bay is shown around the Haji Ali Dargah in India. Credit: [http://www.flickr.com/people/82341349@N00 Humayunn Peerzaada].{{tlx|free media}}]] [[Image:Clouds over the Atlantic Ocean.jpg|thumb|right|250px|Although the image contains a layer of cumulus clouds, at the horizon, the Atlantic Ocean meets the edge of the sky. Location: Salvador, Bahia, Brazil, July 4, 2008. Credit: [[c:User:Tfioreze|Tiago Fioreze]].{{tlx|free media}}]] [[Image:MarsPanoramaa.jpg|thumb|left|280px|This is a 360° view of the surrounding terrain, horizon and Martian sky, taken on November 23-28, 2005, by the Exploration Rover 'Spirit'. Credit: NASA.{{tlx|free media}}]] [[Image:ALSEP AS16-113-18369.jpg|thumb|right|150px|A view of the horizon on the Moon's solid surface shows a black sky without stars because of sunlight coming from the left. Credit: NASA.{{tlx|free media}}]] Seeing an orange [[Sun (star)|Sun]] due to atmospheric effects and feeling the warmth of its rays is probably a student's first encounter with an apparent astronomical orange radiation source. '''Def.''' "the expanse of space that seems to be over the earth like a dome"<ref name=Gove>{{ cite book |author= |title=Webster's Seventh New Collegiate Dictionary |publisher=G. & C. Merriam Company |location=Springfield, Massachusetts |year=1963 |editor=Philip B. Gove |pages=1221 |bibcode= |doi= |pmid= |isbn= }}</ref> is called the '''sky''', or sometimes the '''heavens'''. This definition applies especially well to an individual on top of the Earth's solid crust looking around at what lies above and off to the horizon in all directions. Similarly, it applies to an individual's visual view while floating on a large body of water, where off on the horizon is still water. The image at upper right shows the horizon marking the lower edge of the sky and the upper edge of the Atlantic Ocean, with a layer of cumulus clouds just above. A more general definition of 'sky' allows for skies as seen on other worlds. At left is a 360° panarama of the horizon on Mars as perceived in the visual true-color range of the NASA Mars Exploration Rover 'Spirit' on November 23-8, 2005. '''Def.''' an "expanse of space that seems to be [overhead] like a dome"<ref name=Gove/> is called a '''sky'''. Even in day light, the sky may seem absent of objects if a nearby source tends to overwhelm other luminous objects. At lower right is a view of the horizon on the Moon's solid surface taken by an Apollo 16 astronaut. The image shows a black sky without stars because the sunlight coming from the left is overwhelming. {{clear}} ==Sources== {{main|Radiation astronomy/Sources}} [[Image:Crmo volcanic bomb 20070516123632.jpg|thumb|right|250px|Volcanic bombs are thrown into the sky and travel some distance before returning to the ground. This bomb is in the Craters of the Moon National Monument and Preserve, Idaho, USA. Credit: National Park Service.{{tlx|free media}}]] In [[source astronomy]], the question is "Where did it come from?" '''Source astronomy''' has its origins in the actions of intelligent life on Earth when they noticed things or entities falling from above and became aware of the '''sky'''. Sometimes what they noticed is an acorn or walnut being dropped on them or thrown at them by a squirrel in a tree. Other events coupled with keen intellect allowed these life forms to deduce that some entities falling from the sky are coming down from locations higher than the tops of local trees. '''Def.''' a source or apparent source detected or “[[wikt:created|created]] at or near the [[wikt:time|time]] of the [ [[wikt:event|event]] or] events” is called a '''primary source'''. Direct observation and tracking of the origination and trajectories of falling entities such as volcanic bombs presented early intelligent life with vital albeit sometimes dangerous opportunities to compose the science that led to [[source astronomy]]. {{clear}} ==Spallations== {{main|Radiation astronomy/Spallations}} [[Image:Absolute flux of cosmic–ray elements at 1 TeV-nucleus versus nuclear charge.png|right|thumb|300px|Absolute flux Φ⁰_Z of cosmic–ray elements at ''E''₀ = 1 TeV/nucleus is plotted versus nuclear charge. Credit: Jörg R. Hörandel.{{tlx|fairuse}}]] '''Def.''' a [[wikt:nuclear reaction|nuclear reaction]] in which a [[wikt:nucleus|nucleus]] [[wikt:fragment|fragment]]s into many [[wikt:nucleon|nucleon]]s is called '''spallation'''. "THE first suggestion that appreciable {{chem|14|C}} might be produced ''in situ'' in polar ice was made by Fireman and Norris¹, who studied {{chem|14|C}} in CO₂ extracted from both accumulation and ablation samples. In some ablation samples they observed {{chem|14|C}} activities between four and six times higher than those expected due to trapped atmospheric CO₂."<ref name=Lal>{{ cite journal |author=D Lal |author2=AJT Jull |author3=DJ Donahue |author4=D Burtner |author5=K Nishiizumi |title=Polar ice ablation rates measured using ''in situ'' cosmogenic {{chem|14|C}} |journal=Nature |year=1990 |volume=346 |issue= |pages=350-352 |url=https://www.nature.com/articles/346350a0 |arxiv= |bibcode=1990Natur.346..350L |doi=10.1038/346350a0 |pmid= |accessdate=2017-12-05 }}</ref> "The ¹⁴C is produced mainly by nuclear spallations of oxygen in ice. The observed concentration of ¹⁴C in ablation ice samples is 1–3 x 10³ atom per g ice, three orders of magnitude higher than expected from the amount of trapped atmospheric CO₂ in this ice."<ref name=Lal/> "Spallation of atmospheric oxygen nuclei might contribute up to 20% to production of {{chem|14|C}} produced in the atmosphere (Lal and Peters 1967)."<ref name=Lal2001>{{ cite journal |author=D Lal |author2=A J T Jull |title=In-situ cosmogenic {{chem|14|C}}: Production and examples of its unique applications in studies of terrestrial and extraterrestrial processes |journal=Radiocarbon |year=2001 |volume=43 |issue=28 |pages=731-742 |url=https://journals.uair.arizona.edu/index.php/radiocarbon/article/download/3905/3330 |arxiv= |bibcode= |doi= |pmid= |accessdate=2017-12-06 }}</ref> {{clear}} ==Spatials== {{main|Radiation astronomy/Spatials}} [[Image:Rosat 0.25kev all-sky survey.gif|thumb|250px|right|This [[w:ROSAT|ROSAT]] image is an Aitoff-Hammer equal-area map in galactic coordinates with the Galactic center in the middle of the 0.25 keV diffuse X-ray background. Credit: NASA.{{tlx|free media}}]] A '''spatial distribution''' is a spatial [[w:frequency|frequency]] of [[w:occurrence|occurrence]] or [[w:extent|extent]] of astronomical entities, sources, or objects. A space is a volume large enough to accommodate an astronomical thing. There is an “extensive 1/4 keV emission in the Galactic halo”, an “observed 1/4 keV [X-ray emission originating] in a Local Hot Bubble (LHB) that surrounds the Sun. ... and an isotropic extragalactic component.”<ref name=Snowden>{{ cite journal |author=S. L. Snowden |author2=R. Egger |author3=D. P. Finkbiner |author4=M. J. Freyberg |author5=P. P. Plucinsky |title=Progress on Establishing the Spatial Distribution of Material Responsible for the 1/4 keV Soft X-Ray Diffuse Background Local and Halo Components |journal=The Astrophysical Journal |month=February 1, |year=1998 |volume=493 |issue=1 |pages=715-29 |url=http://iopscience.iop.org/0004-637X/493/2/715/fulltext/ |arxiv= |bibcode=1998ApJ...493..715S |doi=10.1086/305135 |pmid= |accessdate=2012-06-14 }}</ref> In addition to this “distribution of emission responsible for the soft X-ray diffuse background (SXRB) ... there are the distinct enhancements of supernova remnants, superbubbles, and clusters of galaxies.”<ref name=Snowden/> The ROSAT soft X-ray diffuse background (SXRB) image shows the general increase in intensity from the Galactic plane to the poles. At the lowest energies, 0.1 - 0.3 keV, nearly all of the observed soft X-ray background (SXRB) is thermal emission from ~10⁶ K plasma. {{clear}} ==Spectrals== {{main|Radiation astronomy/Spectrals}} [[Image:TheElectromagneticSpectrum.jpg|thumb|450px|right|The electromagnetic spectrum. The red line indicates the room temperature thermal energy. Credit: [[b:nanotechnology|Opensource Handbook of Nanoscience and Nanotechnology]]. {{tlx|free media}}]] A '''spectral distribution''' is often a plot or intensity, brightness, flux density, or other characteristic of a spectrum versus the spectral property such as wavelength, frequency, energy, particle speed, refractive or reflective index, for example. The first three dozen or so astronomical X-ray objects detected other than the [[Sun (star)|Sun]] "represent a brightness range of about a thousandfold from the most intense source, Sco XR-1, ''ca.'' 5 x 10^-10 J m^-2 s^-1, to the weakest sources at a few times 10^-13 J m^-2 s^-1."<ref name=Friedman69>{{ cite journal |author=Friedman H |title=Cosmic X-ray observations |journal=Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences |month=November |year=1969 |volume=313 |issue=1514 |pages=301-15 |url=http://www.jstor.org/pss/2416439 |bibcode=1969RSPSA.313..301F |arxiv= |accessdate=2011-11-25 }}</ref> {{clear}} ==Spectrometers== {{main|Radiation astronomy/Spectrometers}} [[Image:Spectrometer schematic.svg|thumb|right|250px|This is schematic of a spectrometer. Credit: [[commons:User:Markboots|Markboots]].{{tlx|free media}}]] '''Def.''' a visual representation of the spectrum of a celestial body's radiation is called a '''spectrogram'''. '''Def.''' a machine for recording spectra, producing spectrograms is called a '''spectrograph'''. '''Def.''' an optical instrument for measuring the absorption of light by chemical substances; typically it will plot a graph of absorption versus wavelength or frequency, and the patterns produced are used to identify the substances present, and their internal structure is called a '''spectrometer'''. '''Def.''' the measurement of the wavelength of electromagnetic radiation, especially any of several techniques used to analyze the structure of molecules; the measurement of spectra of things other than radiation, such as the masses of molecules and their breakdown products is called '''spectrometry'''. '''Def.''' the scientific study of spectra often using spectrometers is called '''spectroscopy'''. {{clear}} ==Spectroscopy== {{main|Radiation astronomy/Spectroscopy|Spectroscopy}} [[Image:Ssc2003-06h.jpg|right|thumb|300px|NASA's Spitzer Space Telescope has observed the presence of water and organic molecules in the galaxy IRAS F00183-7111. Credit: NASA/JPL-Caltech/L. Armus (SSC/Caltech), H. Kline (JPL), Digital Sky Survey.{{tlx|free media}}]] '''Astronomical spectroscopy''' is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects. Spectroscopy can be used to derive many properties of distant stars and galaxies, such as their chemical composition, but also their motion by Doppler shift measurements. Temporal, spatial, and spectral distributions of radiation are the focus of the science of spectroscopy as applied to astronomy. "NASA's Spitzer Space Telescope has detected the building blocks of life in the distant universe, albeit in a violent milieu. Training its powerful infrared eye on a faint object located at a distance of 3.2 billion light-years (inset [in the image on the right]), Spitzer has observed the presence of water and organic molecules in the galaxy IRAS F00183-7111. With an active galactic nucleus, this is one of the most luminous galaxies in the universe, rivaling the energy output of a quasar. Because it is heavily obscured by dust, most of its luminosity is radiated at infrared wavelengths."<ref name=Armus>{{ cite book |author=Lee Armus |author2=James Houck |author3=Vassilis Charmandaris |author4=Henrik Spoon |author5=Harry Teplitz |author6=Daniel Devost |author7=Patrick Morris |author8=Phil Appleton |author9=Carl Grillmair |title=Galaxy IRAS F00183-7111 |publisher=Caltech |location=Pasadena, California USA |date=18 December 2003 |url=http://www.spitzer.caltech.edu/images/1098-ssc2003-06h-Galaxy-IRAS-F00183-7111 |accessdate=2017-05-25 }}</ref> "The infrared spectrograph instrument onboard Spitzer breaks light into its constituent colors, much as a prism does for visible light. The image shows a low-resolution spectrum of the galaxy obtained by the spectrograph at wavelengths between 4 and 20 microns. Spectra are graphical representations of a celestial object's unique blend of light. Characteristic patterns, or fingerprints, within the spectra allow astronomers to identify the object's chemical composition and to determine such physical properties as temperature and density."<ref name=Armus/> "The broad depression in the center of the spectrum denotes the presence of silicates (chemically similar to beach sand) in the galaxy. An emission peak (red) within the bottom of the trough is the chemical signature for molecular hydrogen. The hydrocarbons (orange) are organic molecules comprised of carbon and hydrogen, two of the most common elements on Earth. Since it has taken more than three billion years for the light from the galaxy to reach Earth, it is intriguing to note the presence of organics in a distant galaxy at a time when life is thought to have started forming on our home planet."<ref name=Armus/> "Additional features in the spectrum reveal the presence of water ice (blue), carbon dioxide ice (green) and carbon monoxide (purple) in both gas and solid forms. The magenta peak corresponds to singly ionized neon gas, a spectral line often used by astronomers as a diagnostic of star formation rates in distant galaxies."<ref name=Armus/> {{clear}} ==Standard candles== {{main|Radiation astronomy/Standard candles}} [[Image:Galactic.jpg|thumb|right|250px|This is a Hubble Space Telescope Image of NGC 4414. Credit: Hubble Heritage Team (AURA/STScI/NASA).{{tlx|free media}}]] [[Image:Pic iroberts1.jpg|thumb|right|250px|This is an image of Messier 31, the Andromeda galaxy from 1899. Credit: Isaac Roberts.{{tlx|free media}}]] "In 1995, the majestic spiral galaxy NGC 4414 was imaged by the Hubble Space Telescope as part of the HST Key Project on the Extragalactic Distance Scale. [The galaxy was] observed ... on 13 different occasions over the course of two months."<ref name=Freedman>{{ cite book |author=Wendy Freedman |title=MAGNIFICENT DETAILS IN A DUSTY SPIRAL GALAXY |publisher=NASA Goddard Space Flight Center |location=Greenbelt, Maryland USA |date=1999 |url=http://nssdc.gsfc.nasa.gov/photo_gallery/caption/hst_ngc4414_9925.txt |accessdate=2014-10-28 }}</ref> "Images were obtained with Hubble's Wide Field Planetary Camera 2 (WFPC2) through three different color filters."<ref name=Freedman/> "Based on [...] careful brightness measurements of variable stars in NGC 4414, [...] an accurate determination of the distance to the galaxy [was made]."<ref name=Freedman/> "The resulting distance to NGC 4414, 19.1 megaparsecs or about 60 million light-years, along with similarly determined distances to other nearby galaxies, contributes to astronomers' overall knowledge of the rate of expansion of the universe. The Hubble constant (H0) is the ratio of how fast galaxies are moving away from us to their distance from us. This astronomical value is used to determine distances, sizes, and the intrinsic luminosities for many objects in our universe, and the age of the universe itself."<ref name=Freedman/> "Due to the large size of the galaxy compared to the WFPC2 detectors, only half of the galaxy observed was visible in the datasets collected by the Key Project astronomers in 1995. In 1999, the Hubble Heritage Team revisited NGC 4414 and completed its portrait by observing the other half with the same filters as were used in 1995. The end result is a stunning full-color look at the entire dusty spiral galaxy. The new Hubble picture shows that the central regions of this galaxy, as is typical of most spirals, contain primarily older, yellow and red stars. The outer spiral arms are considerably bluer due to ongoing formation of young, blue stars, the brightest of which can be seen individually at the high resolution provided by the Hubble camera. The arms are also very rich in clouds of interstellar dust, seen as dark patches and streaks silhouetted against the starlight."<ref name=Freedman/> '''Standard-candles astronomy''' is the astronomical effort to find, study and develop standard-candle candidates for use as standard candles. '''Standard candles''' are stars in [[Radiation astronomy/Visuals|visual astronomy]] that may be used to calculate distances because their characteristics are, or appear to be, distance independent. {{clear}} ==Stars== {{main|Radiation astronomy/Stars|Stellar astronomy}} [[Image:Mira 1997.jpg|thumb|right|250px|This is a real visual image of the red giant [[w:Mira|Mira]] by the Hubble Space Telescope. Credit: Margarita Karovska (Harvard-Smithsonian Center for Astrophysics) and NASA.{{tlx|free media}}]] “A '''red giant''' is a luminous [[w:giant star|giant star]] The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower. The appearance of the red giant is from yellow orange to red, including the [[w:stellar classification|spectral types]] K and M, but also class S stars and most [[w:carbon star|carbon star]]s. The most common red giants are the so-called red giant branch stars (RGB stars). Another case of red giants are the [[w:asymptotic giant branch|asymptotic giant branch]] stars (AGB). To the AGB stars belong the carbon stars of type C-N and late C-R. The stellar limb of a red giant is not sharply-defined, as depicted in many illustrations. Instead, due to the very low mass density of the envelope, such stars lack a well-defined [[w:photosphere|photosphere]]. The body of the star gradually transitions into a '[[w:corona|corona]]' with increasing radii.<ref name=Orange>[http://solarscience.msfc.nasa.gov/feature1.shtml orange sphere of the sun]</ref> {{clear}} ==Strong forces== {{main|Charges/Interactions/Strong}} [[Image:Helium atom QM.svg|thumb|right|250px|The nucleus of a helium atom, where two [[proton]]s have the same charge, but still stay together due to the strong nuclear force. Credit: [[c:user:Yzmo|Yzmo]].{{tlx|free media}}]] "In field theory it is known that coupling constants “run”. This means that the values of the coupling constants that one measures depend on the energy at which the measurement is performed. [...] the three different coupling constants [one each for the strong force, electromagnetic force, and the weak force] of the standard model seem to converge to the same value at an energy scale of about 10¹⁶ GeV [...] This suggests that there is only one coupling constant at high energies and most likely only one symmetry group. [...] The current belief [is] that the electromagnetic, weak and strong forces [are] unified at about 10¹⁶ GeV [as such] one has to rely on [the] particle physics interactions which can lead to electromagnetic radiation and cosmic rays".<ref name="Vachaspati">{{cite journal |author=Tanmay Vachaspati |title=Topological defects in the cosmos and lab |journal=Contemporary Physics |month= |year=1998 |volume=39 |issue=4 |pages=225-37 |url=http://www.tandfonline.com/doi/abs/10.1080/001075198181928 |arxiv= |bibcode= |doi=10.1080/001075198181928 |pmid= |accessdate=2013-11-05 }}</ref> {{clear}} ==Subatomics== {{main|Radiation astronomy/Subatomics|Subatomic astronomy}} [[Image:Helios 2 acr.gif|right|thumb|250px|A mechanism is suggested for anomalous cosmic rays (ACRs) of the acceleration of pick-up ions at the solar wind termination shock. Credit: Eric R. Christian.{{tlx|fairuse}}]] An "analysis of the energy-loss distributions in the GRS HEM during the impulsive phase of this event indicates that γ-rays from the decay of π⁰ mesons were detected [...] The production of pions, which is accompanied (on average) by neutrons, has an energy threshold of ~290 MeV for ''p''-''p'' and ~180 MeV for ''p''-α interactions, giving, therefore, a lower limit to the maximum energy of the particles accelerated at the Sun."<ref name="Chupp">{{cite journal |author=E. L. Chupp |author2=H. Debrunner |author3=E. Flueckiger |author4=D. J. Forrest |author5=F. Golliez |author6=G. Kanbach |author7=W. T. Vestrand |author8=J. Cooper |author9=G. Share |title=Solar neutron emissivity during the large flare on 1982 June 3 |journal=The Astrophysical Journal |month=July 15, |year=1987 |volume=318 |issue=7 |pages=913-25 |url=http://adsabs.harvard.edu/abs/1987ApJ...318..913C |arxiv= |bibcode=1987ApJ...318..913C |doi=10.1086/165423 |pmid= |accessdate=2014-04-08 }}</ref> {{clear}} ==Submillimeters== {{main|Radiation astronomy/Submillimeters|Submillimeter astronomy}} [[Image:Antennae Galaxies composite of ALMA and Hubble observations.jpg|thumb|right|250px|The ALMA observations — shown here in red, pink and yellow — were tuned to detect carbon monoxide molecules. Credit: ALMA (ESO/NAOJ/NRAO). Visible light image: the NASA/ESA Hubble Space Telescope.{{tlx|free media}}]] '''Submillimetre astronomy''' or '''submillimeter astronomy''' is the branch of [[observational astronomy]] that is conducted at submillimetre wavelengths of the electromagnetic spectrum. Astronomers place the submillimetre waveband between the far-infrared and microwave wavebands, typically taken to be between a few hundred micrometres and a millimetre." and "Using submillimetre observations, astronomers examine molecular clouds and dark cloud cores with a goal of clarifying the process of star formation from earliest collapse to stellar birth. These wavelengths are sometimes called '''Terahertz radiation''', since they have frequencies of the order of 1 THz. "The Antennae Galaxies (also known as NGC 4038 and 4039) are a pair of distorted colliding spiral galaxies about 70 million light-years away, in the constellation of Corvus (The Crow). This view combines ALMA observations, made in two different wavelength ranges during the observatory’s early testing phase, with visible-light observations from the NASA/ESA Hubble Space Telescope."<ref name=eso1137a>{{ cite book |author= eso1137a |title=Antennae Galaxies composite of ALMA and Hubble observations |publisher=European Southern Observatory |location=Parana, Chile |date=October 3, 2011 |url=http://www.eso.org/public/images/eso1137a/ |accessdate=2014-03-13 }}</ref> "The Hubble image is the sharpest view of this object ever taken and serves as the ultimate benchmark in terms of resolution. ALMA observes at much longer wavelengths which makes it much harder to obtain comparably sharp images. However, when the full ALMA array is completed its vision will be up to ten times sharper than Hubble."<ref name=eso1137a/> {{clear}} ==Superluminals== {{main|Radiation astronomy/Superluminals|Superluminal astronomy}} [[Image:M87 jet Hubble.gif|thumb|right|250px|The two images are a top panel of Hubble Space Telescope image showing the M87 jet streaming out from the galaxy's nucleus (bright round region at far left) and a bottom panel which contains a sequence of Hubble images showing motion of something at six times the speed of light. Credit: John Biretta/NASA/ESA/Space Telecsope Science Institute.{{tlx|fairuse}}]] '''Superluminal''' refers to the propagation of information or matter faster than the speed of light. Under the special theory of relativity, a particle (that has [mass in special relativity] rest mass) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times (tachyons). On the other hand, what some physicists refer to as "apparent" or "effective" FTL<ref name="Gonzalez">{{cite journal | last = Gonzalez-Diaz | first = P. F. | year = 2000 | title = Warp drive space-time | url = http://omnis.if.ufrj.br/~mbr/warp/etc/PRD62_44005.pdf | journal = Physical Review D | volume = 62 | issue = 4 | page = 044005 | arxiv=gr-qc/9907026 | doi = 10.1103/PhysRevD.62.044005 | bibcode = 2000PhRvD..62d4005G }}</ref><ref name="Loup">{{cite journal |author=F. Loup |author2=David Waite |author3=E. Halerewicz Jr. |year=2001 |title=Reduced Total Energy Requirements for a Modified Alcubierre Warp Drive Spacetime |url=ttp://arxiv.org/abs/gr-qc/0107097 |bibcode=2001gr.qc.....7097L |arxiv=gr-qc/0107097 }}</ref><ref name="Visser">{{cite journal |last1=Visser |first=M. |last2=Bassett |first2=B. |last3=Liberati |first3=S. |year=2000 |title=Superluminal censorship |journal=Nuclear Physics B: Proceedings Supplement |volume=88 |pages=267–270 |arxiv=gr-qc/9810026 |bibcode = 2000NuPhS..88..267V |doi=10.1016/S0920-5632(00)00782-9 }}</ref><ref name="Visser99">{{cite journal |last1=Visser |first=M. |last2=Bassett |first2=B. |last3=Liberati |first3=S. |year=1999 |title=Perturbative superluminal censorship and the null energy condition |journal=AIP Conference Proceedings |volume=493 |pages=301–305 |arxiv=gr-qc/9908023 |doi=10.1063/1.1301601 |isbn=1-56396-905-X }}</ref> depends on the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations in less time than light could in normal or undistorted spacetime. Although according to current theories matter is still required to travel subluminally with respect to the locally distorted spacetime region, ''apparent'' FTL is not excluded by general relativity. Tachyonic γ rays have not been observed directly as of 2007.<ref name="Tomaschitz">{{cite journal |author=Roman Tomaschitz |title=Superluminal cascade spectra of TeV [gamma]-ray sources |journal=Annals of Physics |month=March |year=2007 |volume=322 |issue=3 |pages=677-700 |url=http://wallpaintings.at/geminga/superluminal_cascade_spectra_TeV_gamma-ray_sources.pdf |arxiv= |bibcode= |doi=10.1016/j.aop.2006.11.005 |pmid= |accessdate=2011-11-24 }}</ref> "The tachyonic spectral densities generated by ultra-relativistic electrons in uniform motion are fitted to the high-energy spectra of Galactic supernova remnants, such as RX J0852.0−4622 and the pulsar wind nebulae in G0.9+0.1 and MSH 15-52. ... Tachyonic cascade spectra are quite capable of generating the spectral curvature seen ... Estimates on the electron/proton populations generating the tachyon flux are obtained from the spectral fits"<ref name="Tomaschitz"/> "Tachyonic radiation implies superluminal signal transfer [1-7], the energy quanta propagating faster than light in vacuum, in contrast to rotating superluminal light sources emitting vacuum Cherenkov radiation [8, 9]."<ref name="Tomaschitz10">{{cite journal |author=R Tomaschitz |title=Superluminal spectral densities of ultra-relativistic electrons in intense electromagnetic wave fields |journal=Applied Physics B Lasers and Optics |month=October |year=2010 |volume=101 |issue=1-2 |pages=143-64 |url=http://wallpaintings.at/geminga/superluminal_spectral_densities_ultra-relativistic_electrons_electromagnetic_wave_fields.pdf |arxiv= |bibcode= |doi=10.1007/s00340-010-4182-8 |pmid= |accessdate=2012-03-21 }}</ref> "The existence of superluminal energy transfer has not been established so far, and one may ask why. There is the possibility that superluminal quanta just do not exist, the vacuum speed of light being the definitive upper bound. There is another explanation, the interaction of superluminal radiation with matter is very small, the quotient of tachyonic and electric fine-structure constants being ''q''²/''e''² ≈ 1.4 x 10^-11 [5], and therefore superluminal quanta are hard to detect."<ref name="Tomaschitz10"/> “Observed variations concerning the brightness distributions in four extragalactic radio sources were so rapid that the apparent transverse velocity of expansion is greater than the velocity of light.”<ref name="Cohen">{{cite journal |author=M. H. Cohen |author2=K. I. Kellermann |author3=D. B. Shaffer |author4=R. P. Linfield |author5=A. T. Moffet |author6=J. D. Romney |author7=G. A. Seielstad |author8=I. I. K. Pauliny-Toth |author9=E. Preuss |author10=A. Witzel |author11=R. T. Schilizzi |author12=B. J. Geldzahler |title=Radio sources with superluminal velocities |journal=Nature |month=August |year=1977 |volume=268 |issue= |pages=405-9 |url= |arxiv= |bibcode=1977Natur.268..405C |doi=10.1038/268405a0 |pmid= |accessdate=2012-02-19 }}</ref> {{clear}} ==Synchrotrons== {{main|Radiation astronomy/Synchrotrons}} [[Image:PKS0521-36 2 cm.gif|thumb|right|250px|The electric vectors of PKS0521-36 show clear structure and alignment. Credit: Keel.{{tlx|fairuse}}]] '''Synchrotron radiation''' is radiation produced from particles traveling along curved paths near the speed of light. {{clear}} ==Tauons== {{main|Radiation astronomy/Tauons}} [[Image:EGB With Models v2.pdf|right|thumb|400px|Compilation is shown of the measurements of the total extragalactic gamma-ray intensity between 1 keV and 820 GeV, with different components from current models. Credit: The e-ASTROGAM Collaboration.{{tlx|free media}}]] "Previously, it was suggested that the [dark matter] DM consists of [weakly interacting massive particles] WIMPs that naturally emerge from the super-symmetric extension of the Standard model. Such a WIMP particle was predicted to have a mass of the order of 100 GeV. However, no such particle has been experimentally found and the search for DM candidates is now being broadened into other directions. Recently, the idea of involving a complete hidden sector of new particles was revitalized."<ref name=Kirilova>{{ cite journal |author=G. Vankova-Kirilova |author2=V. Bozhilov |author3=V. Kozhuharov |author4=S. Lalkovski |title=All-sky mapping in the 100 MeV region in search for point-like dark matter sources |journal=arxiv |month= |year=2017 |volume= |issue= |pages=112 |url=https://arxiv.org/pdf/1711.01265#page=106 |arxiv=1711.01265 |bibcode= |doi= |pmid= |accessdate=2018-4-04 }}</ref> {{clear}} ==Telescopes== {{main|Radiation astronomy/Telescopes}} [[Image:Brorfelde Schmidt Telescope.jpg|thumb|right|250px|The Schmidt Telescope at the former Brorfelde Observatory is now used by amateur astronomers. Credit: [[commons:User:Moeng|Mogens Engelund]].{{tlx|free media}}]] A '''radiation telescope''' is an instrument designed to collect and focus radiation so as to make distant sources appear nearer. {{clear}} ==Temporals== {{main|Radiation astronomy/Temporals}} [[Image:Gursky GX 263 +3 Vela X?.png|thumb|right|300px|These two spectra show the proportional counting rates during the roll maneuver for GX 263 +3. Credit: H. Gursky, E. M. Kellogg, and P. Gorenstein. {{tlx|fairuse}}]] A '''temporal distribution''' is a distribution over time. Also known as a time distribution. A temporal distribution usually has the independent variable 'Time' on the [[w:Abscissa|abscissa]] and other variables viewed approximately orthogonal to it. The time distribution can move forward in time, for example, from the present into the future, or backward in time, from the present into the past. Usually, the abscissa is plotted forward in time with the earlier time at the intersection with the [[w:Ordinate|ordinate]] variable at left. Geologic time is often plotted on the abscissa versus phenomena on the ordinate or as a twenty-four hour clock analogy. "An X-ray source was observed in the constellation Vela from an attitude-controlled Aerobee 150 rocket launched from the White Sands Missile Range on February 2, 1968. The object, which may be the previously reported Vel XR-1 (Chodil ''et al.'' 1967), lies close to the galactic plane; we designate it as GX263+3."<ref name=Gursky>{{ cite journal |author=H. Gursky |author2=E. M. Kellogg |author3=P. Gorenstein |title=The Location of the X-ray Source in Vela |journal=The Astrophysical Journal |month=November |year=1968 |volume=154 |issue=11 |pages=71-4 |url=http://adsabs.harvard.edu//abs/1968ApJ...154L..71G |arxiv= |bibcode=1968ApJ...154L..71G |doi= |pmid= |accessdate=2015-12-15 }}</ref> The image on the upper right "shows the counting rates plotted against time during the maneuver in which the new source was observed. The peaks labeled 1, 2, 3, anf 4 all refer to this source. Peaks 1 and 2 determine a location that is the same within experimental error as the location determined by peaks 3 and 4. The reduction in background level from 130 to 150 sec after launch occurs when a large portion of the field of view falls below the horizon."<ref name=Gursky/> The second image down on the right shows the most "probable celestial locations defined by the peaks in [the upper image on the right] and counting-rate ratios are shown as line segments. Separations between intersections are consistent with a single X-ray source and statistical errors in determination of times of peak counting rates. Shaded area around intersections, and enlargement, show the region of uncertainty of the source. Lines labeled ''1st pass'' and ''2d pass'' refer to the center of the field of view during scan. Area inclosed by dashed lines is the region of uncertainty [well within Vela and the Chodil polygon] of Vel XR-1 as reported by Chodil ''et al.'' (1967)."<ref name=Gursky/> {{clear}} ==Theoretical radiation astronomy== {{main|Radiation astronomy/Theory}} [[Image:Eclipsing binary star animation 2.gif|thumb|right|250px|At the bottom of this visible emission model is a visual intensity curve. Credit: [[commons:User:Stanlekub|Stanlekub]].{{tlx|free media}}]] At its simplest '''theoretical radiation astronomy''' is the definition of terms to be applied to astronomical radiation phenomena. '''Def.''' a theory of the science of the biological, chemical, physical, and logical laws (or principles) with respect to any natural radiation source in the sky especially at night is called '''theoretical radiation astronomy'''. Exploratory theory is the playtime activity that leads to discoveries which better our world. In the radiation physics laboratories here on Earth, the emission, reflection, transmission, absorption, and fluorescence of radiation is studied and laws relative to sources are proven. A '''principle''' is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting system's designed purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored.<ref name="Guido">{{cite journal |author=Guido Alpa |title=General Principles of Law |journal=Annual Survey of International & Comparative Law |month= |year=1994 |volume=1 |issue= |pages=1 |url=http://heinonlinebackup.com/hol-cgi-bin/get_pdf.cgi?handle=hein.journals/ansurintcl1&section=4 |arxiv= |bibcode= |doi= |pmid= |accessdate=2012-04-29 }}</ref> Radiation astronomy consists of three fundamental parts: # derivation of logical laws with respect to incoming radiation, # natural radiation sources outside the Earth, and # the sky and associated realms with respect to radiation. '''Def.''' a spontaneous emission of an α ray, β ray, or γ ray by the disintegration of an atomic nucleus is called '''radioactivity'''.<ref name="Gove"/> {{clear}} ==Transductions== {{main|Radiation astronomy/Transductions}} '''Def.''' the process to [[wikt:convert|convert]] [[wikt:energy|energy]] from one [[wikt:form|form]] to another is called '''transduction'''. {{clear}} ==Transmutations== {{main|Radiation astronomy/Transmutations}} [[Image:Fission_(PSF).png‎|center|thumb|This is a fission reaction. Credit: [[w:user:Pearson Scott Foresman|Pearson Scott Foresman]].{{tlx|free media}}]] Polonium-214 has a half life of 163 microseconds (a microsecond is one-millionth of a second).<ref>http://www.ieer.org/fctsheet/uranium.html</ref> When this process is started artificially, it is called transmutation.<ref>http://faculty.ncc.edu/LinkClick.aspx?fileticket=Fkhb0%2FAcPfE%3D&tabid=1920</ref> Center is an example of an artificial transmutation, this one being called a fission reaction. {{clear}} ==Ultraviolets== {{main|Radiation astronomy/Ultraviolets|Ultraviolet astronomy}} [[Image:STEREO B EUVI 171.jpg|thumb|right|250px|This is a [[w:False-color|false-color]] image of the Sun's [[w:corona|corona]] as seen in extreme ultraviolet (at 17.1 nm) by the Extreme ultraviolet Imaging Telescope aboard Stereo B. Credit: NASA.{{tlx|fairuse}}]] '''[[Ultraviolet astronomy]]''' is generally used to refer to observations of [[w:electromagnetic radiation|electromagnetic radiation]] at ultraviolet wavelengths between approximately 10 and 320 nanometres. There are many important spectral lines in these wavelengths. Among the most important are the Lyman lines, which are emitted or absorbed when an electron jumps to or from the innermost electron shell in a hydrogen atom. The first three (known as alpha, beta and gamma) have wavelengths of 121.52, 102.53 and 97.22 nm respectively.<ref name="Chieh">{{cite book |author=Chung Chieh |title=Hydrogen Spectra |publisher=University of Waterloo |location=Waterloo, Ontario, Canada |date=December 1997 |url=http://www.science.uwaterloo.ca/~cchieh/cact/c120/hspectra.html |accessdate=2012-06-06 }}</ref> Since the Earth's atmosphere strongly absorbs ultraviolet light, especially the shorter wavelengths, ultraviolet astronomy is mostly conducted by satellites. Longer wavelengths can be detected from baloons launched into the stratosphere. Like the English astronomer William Fox, "In the summer of 1980, reflecting his age, Walter Scott Houston finally underwent surgery to remove a cataract from his right eye. Now to just about anyone else, a cataract would spell the end of a sky gazing career. But not Houston. With his lens removed and a plastic UV-transparent replacement implanted, Scotty reported that a whole new world of star gazing was opened up. The flood of ultraviolet light onto his retina allowed him to see faint blue stars previously invisible by at least one magnitude above the visual limit (to normally sighted observers)."<ref name="Hilbert">{{cite book |author=Eric Hilbert |title=Deep-Sky Wonders |publisher=Starlight Astronomy Club |location=State College, Pennsylvania |date=May 28, 2012 |url=http://ehilbert.wso.net/Starlight/deep_sky_wonders.htm |accessdate=2012-06-06 }}</ref> {{clear}} ==Violets== {{main|Radiation astronomy/Violets|Violet astronomy}} [[Image:PIA00072 Venus Cloud Patterns - colorized and filtered.jpg|thumb|right|250px|This image of Venus is taken through a violet filter by the Galileo spacecraft on February 14, 1990. Credit: NASA/JPL-Caltech.{{tlx|free media}}]] "The aluminium abundance was derived from the resonance line at 394.4nm, and Al is underabundant by ∼ −0.7 dex with respect to iron."<ref name="Sivarani">{{cite journal |author=T. Sivarani |author2=P. Bonifacio |author3=P. Molaro |author4=R. Cayrel |author5=M. Spite |author6=F. Spite |author7=B. Plez |author8=J. Andersen |author9=B. Barbuy |author10=T. C. Beers |author11=E. Depagne |author12=V. Hill |author13=P. François |author14=B. Nordström |author15=F. Primas |title=First stars IV. CS 29497-030: Evidence for operation of the ''s''-process at very low metallicity |journal=Astronomy and Astrophysics |month=January |year=2004 |volume=413 |issue=1 |pages=1073-85 |url=http://arxiv.org/pdf/astro-ph/0310291.pdf |arxiv=astro-ph/0310291 |bibcode=2004A&A...413.1073S |doi=10.1051/0004-6361:20031590 |pmid= |accessdate=2012-06-02 }}</ref> "These abundances are the LTE values; no NLTE corrections, as prescribed by Baum ̈uller and Gehren (1997) and Baumüller et al. (1998), have been applied. The prescribed NLTE corrections for T_eff = 6500K, log g = 4.0, [Fe/H] = –3.0 are –0.11 ... for ... Al .... If we assume these values to apply for our lower-gravity star [CS 29497-030], then Al follows iron"<ref name="Sivarani"/>. The elemental abundance ratios for CS 29497-030 of aluminum are [Al/H] = -3.37, [Al/Fe] = -0.67.<ref name="Sivarani"/> A discovery in [[violet astronomy]] is that "carbon stars are enormously fainter in the violet region than expected from appropriate blackbody spectra."<ref name="Bregman">{{cite journal |author=Jesse D. Bregman |author2=Joel N. Bregman |title=The violet opacity of carbon stars |journal=The Astrophysical Journal |month=May 15, |year=1978 |volume=222 |issue=5 |pages=L41-3 |url= |arxiv= |bibcode=1978ApJ...222L..41B |doi=10.1086/182688 |pmid= |accessdate=2012-02-27 }}</ref> Violet photographs of the planet Venus taken in 1927 “recorded two nebulous bright streaks, or bands, running ... approximately at right angles to the terminator” that may be from the upper atmosphere.<ref name="Wright">{{cite journal |author=W. H. Wright |title=Photographs of Venus made by Infra-red and by Violet Light |journal=Publications of the Astronomical Society of the Pacific |month=August |year=1927 |volume=39 |issue=230 |pages=220-1 |url= |arxiv= |bibcode=1927PASP...39..220W |doi=10.1086/123718 |pmid= |accessdate=2011-11-24 }}</ref> "The “Purple Haze” is a diffuse blueish/purple glow within a few arcseconds of the central star in HST images of the Homunculus (Morse et al. 1998; Smith et al. 2000, 2004). This emission is seen in excess of violet starlight scattered by dust, and the strength of the excess increases into the far UV (Smith et al. 2004; hereafter Paper I)."<ref name="NSmith">{{cite journal |author=Nathan Smith |author2=Jon A. Morse |author3=Nicholas R. Collins |author4=Theodore R. Gull |title=The Purple Haze of η Carinae: Binary-induced Variability? |journal=The Astrophysical Journal |month=August |year=2004 |volume=610 |issue=2 |pages=L105-8 |url= |arxiv=astro-ph/0406408v1 |bibcode=2004ApJ...610L.105S |doi=10.1086/423341 |pmid= |accessdate=2012-01-08 }}</ref> {{clear}} ==Visuals== {{main|Radiation astronomy/Visuals|Visual astronomy}} [[Image:USNO Refractor 1904.jpg|thumb|right|250px|This image shows the 26-inch Warner & Swasey refracting telescope at the United States Naval Observatory. Credit: Waldon Fawcett.{{tlx|free media}}]] What is “the “old-fashioned” spirit of real-time visual astronomy”?<ref name=Cooke>{{ cite book |author=Antony Cooke |title=Visual Astronomy Under Dark Skies: A New Approach to Observing Deep Space |publisher=Springer-Verlag |location=London |date=2005 |editor= |pages=180 |url=http://books.google.com/books?id=SXmrBfl4H3sC&lr=&source=gbs_navlinks_s |bibcode= |doi= |pmid= |isbn=1852339012 |accessdate=2011-11-06 }}</ref> “I think everyone can conjure up a mental image of astronomers at every level and place in history, gazing through the eyepieces of their telescopes at sights far away - true visual astronomy.”<ref name=Cooke/> {{clear}} ==Wavelength shifts== [[Image:Doppler shift caused by exoplanet.jpeg|thumb|350px|Illustrating the red and blue shift for the observer from an exoplanet. Credit: NASA/JPL-Caltech.{{tlx|free media}}]] Doppler Shift is the basis for a Spectroscopic Binary system. It is found by either two separate shifts in spectra or a single shift generated by an unseen companion on the primary star. It is important because the shifts can be used to find the radial velocity of both stars or the visible one if only one spectrum is observed. The equation to determine radial velocity is: <math>{\frac{\Delta \lambda}{\lambda_0}} = {\frac{v_r}{c}}</math> c is the speed of light in a vacuum (3x10⁸ m/s) λ₀ is the rest wavelength of the spectra Δλ is the change from the rest wavelength to the measured wavelength v_r is the radial velocity in m/s If the period is known this can be paired with it to determine the semi-major axis. {{clear}} ==Weak forces== {{main|Charges/Interactions/Weak}} [[Image:Beta-minus Decay.svg|thumb|right|250px|The diagram shows beta-minus decay from a nucleus. Credit: [[c:User:Inductiveload|Inductiveload]].{{tlx|free media}}]] The '''weak interaction''' is expressed with respect to nuclear electrons and the continuous ''β''-ray emission spectrum of ''β'' decay.<ref name=Wilson>{{ cite journal |author=Fred L. Wilson |title=Fermi's Theory of Beta Decay |journal=American Journal of Physics |month=December |year=1968 |volume=36 |issue=12 |pages=1150-60 |url=http://microboone-docdb.fnal.gov/cgi-bin/RetrieveFile?docid=953;filename=FermiBetaDecay1934.pdf;version=1 |arxiv= |bibcode= |doi= |pmid= |accessdate=2012-06-24 }}</ref> "The observation of a neutrino burst within 3 h of the associated optical burst from supernova 1987A in the Large Magellanic Cloud provides a new test of the weak equivalence principle, by demonstrating that neutrinos and photons follow the same trajectories in the gravitational field of the galaxy."<ref name="Krauss">{{cite journal |author=Lawrence M. Krauss, Scott Tremaine |title=Test of the Weak Equivalence Principle for Neutrinos and Photons |journal=Physical Review Letters |month=January |year=1988 |volume=60 |issue=3 |pages=176–7 |url=http://link.aps.org/doi/10.1103/PhysRevLett.60.176 |doi=10.1103/PhysRevLett.60.176 |bibcode=1988PhRvL..60..176K }}</ref> {{clear}} ==X-rays== {{main|Radiation astronomy/X-rays|X-ray astronomy}} [[Image:M31 Core in X-rays.jpg|thumb|right|250px|This image captures the core of Messier 31 (M31) in X-rays using the Chandra X-ray Observatory. Credit: S. Murray, M. Garcia, et al., Authors & editors: Robert Nemiroff (MTU) & Jerry Bonnell (USRA) NASA.{{tlx|free media}}]] X-rays are electromagnetic radiation from a portion of the wavelength spectrum of about 5 to 8 nanometers (nm)s down to approximately 5 to 8 picometers (pm)s (ranging over three orders of magnitude). An astronomical X-ray source may have one or more positional locations, plus associated error circles or boxes, from which incoming X-radiation (X-rays) has been detected. Generally, a [[coronal cloud]], a cloud composed of plasma, is usually associated with a star or other celestial or astronomical body, extending sometimes millions of kilometers into space, or thousands of light-years, depending on the associated body. The high temperature of the coronal cloud gives it unusual spectral features. These features have been traced to highly ionized atoms of elements such as iron which indicate a plasma's temperature in excess of 10⁶ K (MK) and associated emission of X-rays. The importance of [[X-ray astronomy]] is exemplified in the use of an X-ray imager such as the one on GOES 14 for the early detection of solar flares, coronal mass ejections (CME)s and other X-ray generating phenomena that impact the Earth. {{clear}} ==Yellows== {{main|Radiation astronomy/Yellows|Yellow astronomy}} [[Image:Io highest resolution true color.jpg|thumb|right|250px|This is a true-color image of Io taken by the ''Galileo'' probe. Credit: NASA.{{tlx|free media}}]] '''Yellow astronomy''' is astronomy applied to the various extraterrestrial yellow sources of radiation, especially at night. It is also conducted above the Earth's atmosphere and at locations away from the Earth as a part of explorational (or exploratory) yellow astronomy. There are yellow objects and emission lines in the yellow portion of the visible spectrum from 570 to 590 nm in wavelength. '''Io''' is the innermost of the four Galilean moons of the planet [[Jupiter]] and, with a diameter of 3,642 kilometres (2,263 mi), the fourth-largest moon in the [[Solar System]]. With over 400 active volcanoes, Io is the most geologically active object in the Solar System.<ref name="book">{{cite book |title=Encyclopedia of the Solar System |chapter=Io: The Volcanic Moon |author=Rosaly MC Lopes |publisher=Academic Press |year=2006 |editor=Lucy-Ann McFadden |editor2=Paul R. Weissman |editor3=Torrence V. Johnson |pages=419–431 |isbn=978-0-12-088589-3 }}</ref><ref name="Lopes2004">{{cite journal |title=Lava lakes on Io: Observations of Io’s volcanic activity from Galileo NIMS during the 2001 fly-bys |journal=Icarus |last=Lopes |first=R. M. C. |coauthors=''et al.'' |pages=140–174 |volume=169 |issue= 1 |year=2004 |doi=10.1016/j.icarus.2003.11.013 |bibcode=2004Icar..169..140L }}</ref> Most of Io's surface is characterized by extensive plains coated with sulfur and sulfur dioxide frost. Io's volcanism is responsible for many of the satellite's unique features. Its volcanic plumes and lava flows produce large surface changes and paint the surface in various shades of yellow, red, white, black, and green, largely due to allotropes and compounds of sulfur. {{clear}} ==See also== {{div col|colwidth=20em}} * [[Radiation astronomy/Aircraft|Aircraft]] * [[Observatories/Astronomy|Astronomical observatories]] * [[Radiation astronomy/Astrophysics|Astrophysics]] * [[Radiation astronomy/Atmospheres|Atmospheres]] * [[Radiation astronomy/Balloons|Balloons]] * [[Theory/Cosmogony|Cosmogony]] * [[Radiation astronomy/Distillations|Distillations]] * [[Radiation astronomy/Fluorescences|Fluorescences]] * [[Radiation astronomy/Intensities|Intensities]] * [[Radiation astronomy/Luminescences|Luminescences]] * [[Radiation astronomy/Materials|Materials]] * [[Radiation astronomy/Polarizations|Polarizations]] * [[Radiation astronomy/Courses|Radiation astronomy courses]] * [[Radiation astronomy/Rocketry|Rocketry]] * [[Theoretical astronomy]] * [[X-ray trigonometric parallax|X-ray trigonometric parallax]] {{Div col end}} ==References== {{reflist|2}} ==External links== <!-- footer templates --> {{Radiation astronomy resources}}{{Sisterlinks|Radiation astronomy}} <!-- footer categories --> [[Category:Radiation resources]] hg9dk66102quekvvh0wrgueyfgwt91j 0 260886 2412411 2392031 2022-08-06T20:55:18Z Scogdill 1331941 wikitext text/x-wiki =Devonshire House Fancy Dress Ball, 2 July 1897= ==Logistics== 1897 July 2, Friday, one of the major social events of the "season" of Queen Victoria's Diamond Jubilee The invitations were for 10:30 p.m., but people began to arrive about 10:00, and the Duke of Devonshire came down to greet the Prince and Princess of Wales at 11:00 p.m. The invitations asked people to dress as monarchs and their courts from the past or as goddesses or figures from antiquity. Weather: According to the ''Times'', it was 63 degrees at midnight in London, just as the ball was getting underway, with a dew point of 58, which means that it would not have been as oppressive in all those leather, velvet and satin costumes as well as metal armor as it could have been.<ref>"Weather, The." The London ''Times'' Saturday 3 July 1897: 10 [of 20], Col. 1A. The ''Times Digital Archive''. Web. 22 Mar. 2016.</ref> Location: The party was at Devonshire House, in Picadilly, hosted by [[Social Victorians/People/Louisa Montagu Cavendish | Louisa Cavendish]], the Duchess, and [[Social Victorians/People/Spencer Compton Cavendish | Spencer Compton Cavendish]], the 8th Duke of [[Social Victorians/People/Devonshire |Devonshire]]. ==Who Was There We Might Recognize Now== The people who attended this party belonged to the most elite circles of society and were in the social networks of Albert Edward, Prince of Wales and Louise Cavendish, Duchess of Devonshire. The people in these networks were not the same as the people in, for example, Queen Victoria's networks. The social network of the Prince of Wales did not exclude people who were divorced, involved in extra-marital relationships, or associated with scandal or gossip. It also included Jews, Americans, businessmen and the ''nouveau riche'', and actors and actresses, even if they were not particularly wealthy, so long as they were beautiful, witty and able to keep the prince amused. In their day, they were celebrities, the subjects of newspaper reports and were considered stylish, "fast," and social leaders. Many of these people would not be familiar now to many of us. The ones that we might find familiar include the following: * [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] later King Edward VII, and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]], later Queen Alexandra. * [[Social Victorians/People/George and Mary|George of Wales]], Duke of York and Duchess of York, Princess (Victoria Mary) May or [[Social Victorians/People/George and Mary|Mary of Teck]], later King George V and Queen Mary, Queen Elizabeth II's grandparents. (For fans of the tv series ''[[wikipedia:The_Crown_(TV_series)|The Crown]]'', the role of Queen Mary was played by [[wikipedia:Eileen_Atkins|Eileen Atkins]].) * Frederick Arthur Stanley, 16th Earl of[[Social Victorians/People/Derby | Derby]], who commissioned the first Stanley Cup and presented it to Canda.<ref>{{Cite journal|date=2020-08-12|title=Stanley Cup|url=https://en.wikipedia.org/w/index.php?title=Stanley_Cup&oldid=972518864|journal=Wikipedia|language=en}}</ref> The entire Stanley family were engaged with hockey when Frederick Arthur Stanley was Governor General of Canada (1888 to 1893).<ref>{{Cite journal|date=2020-08-27|title=Frederick Stanley, 16th Earl of Derby|url=https://en.wikipedia.org/w/index.php?title=Frederick_Stanley,_16th_Earl_of_Derby&oldid=975203053|journal=Wikipedia|language=en}}</ref> * Lady Frances, [[Social Victorians/People/Warwick|Countess of Warwick]], called Daisy, the person for whom the song "Bicycle Built for Two" was written. *Oscar Wilde dedicated ''A Woman of No Importance'' to Gwladys Robinson, [[Social Victorians/People/Ripon|Lady de Grey]]. * [[Social Victorians/People/Churchill|Winston Churchill]], who was at the ball by virtue of his mother's popularity in these social networks; he was 24 in 1897 and so little known that only the ''Gentlewoman'' reported his attendance. * A number of [[Social Victorians/People/Rothschild Family|Rothschilds]] were present: Lady (Emma Louise von Rothschild) and Lord Rothschild (Nathan Mayer de Rothschild), Baron F. de Rothschild, Mr. and Mrs. L. Rothschild (possibly Leopold and Marie Perugia Rothschild), Baron Ferdinand de Rothschild, Alfred Rothschild (?), Cyril Flower, Lord Battersea, and Constance de Rothschild Flower, Lady Battersea. Louisa, Lady de Rothschild also attended. *Prince Charles (or Carl) of Denmark was married to Princess Maud of Norway, the daughter of the Albert Edward, Prince and Wales and Alexandra, Princess of Wales. He became King Haakon VII of Norway, and Princess Maud of Wales Queen of Norway. The role of the old King Haakon VII in the tv series ''[[wikipedia:Atlantic_Crossing_(TV_series)|Atlantic Crossing]]'' was played by [[wikipedia:Søren_Pilmark|Søren Pilmark]]. *Some people will recognize the name Joe Cresswell, known for being the commanding officer for a destroyer that captured an intact Enigma machine; his father, [[Social Victorians/People/Cresswell|Addison Baker-Cresswell]], was at the ball. * [[Social Victorians/People/Midleton|William St. John Freemantle Brodrick, later Viscount Midleton]], related by marriage to Agatha Whitehead von Trapp,<ref>{{Cite journal|date=2020-08-18|title=Robert Whitehead|url=https://en.wikipedia.org/w/index.php?title=Robert_Whitehead&oldid=973672889|journal=Wikipedia|language=en}}</ref> first wife of Georg von Trapp and thus the mother of the 7 children in the von Trapp singers. (Agatha Whitehead von Trapp died of scarlet fever in 1922, and Georg von Trapp remarried in 1927 Maria August Kutschera, former novice of Nonnberg Abbey.<ref>{{Cite journal|date=2020-09-05|title=Georg von Trapp|url=https://en.wikipedia.org/w/index.php?title=Georg_von_Trapp&oldid=976801201|journal=Wikipedia|language=en}}</ref>) Some controversy exists about the accuracy of this genealogy. * While few of us would recognize the name [[Social Victorians/People/Bischoffsheim|Henri Louis Bischoffsheim]], we might recognize the bank he founded: Deutsche Bank. * [[Social Victorians/People/Beit|Alfred Beit]] was a Life Governor of De Beers and friend of Cecil Rhodes. *[[Social Victorians/People/Burton|Michael Arthur Bass]], 1st Baron Burton of Burton-on-Trent and of Rangemore and Chairman of Bass Brewery, which was founded in 1777 by Michael Arthur Bass's ancestor William Bass. According to the ''Wikipedia'' article on the Bass Brewery, by 1887 Bass was the largest brewery in the world.<ref>{{Cite journal|date=2021-03-19|title=Bass Brewery|url=https://en.wikipedia.org/w/index.php?title=Bass_Brewery&oldid=1012919731|journal=Wikipedia|language=en}}</ref> *[[Social Victorians/People/Iveagh|Edward Cecil Guinness]], 1st Earl of Iveagh and Chairman of Guiness Brewery, which was founded in 1759 by Edward Guiness's ancestor Arthur Guiness. ==Descriptions and Contextualizing Information== The attendees were presented to the royals in [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts |Quadrilles and the Courts]] of Female Monarchs, goddesses, and so on. ===Staff at the Ball=== A number of people were present not as people invited to the ball but as staff. Not all the Royals at the ball are described in the newspapers as having been accompanied by attendants — the courtiers who usually attended them — but it seems likely that they all would have been. Some of these attendants are described in the newspapers, perhaps those who were invited in their own right. Some, like [[Social Victorians/People/Lauder|the photographer Lafayette]] and the people who worked at that firm or the musicians, for example, served as staff of the party itself. Some were staff and servants working in Devonshire House or for the Duke and Duchess of Devonshire at one of his other properties. These people would have helped prepare for the ball, would have served dinner and cleaned up after people, or would have been responsible for the flowers and decorations, like the gardening staff at the Duke of [[Social Victorians/People/Devonshire |Devonshire]]'s manorial estate, Chatsworth House, who brought flowers from there for decorations at the ball. ==== Gardeners ==== According to the ''Belfast News-letter'', <blockquote>The elaborate floral decorations were all carried out under the direction of Mr. Chester, the head gardener of Chatsworth, and the whole of the lovely flowers and palms were sent up from the conservatories and gardens on the estate.<ref name=":10">"The Duchess of Devonshire's Fancy Dress Ball. Special Telegram." ''Belfast News-Letter'' Saturday 03 July 1897: 5 [of 8], Col. 9c [of 9]–6, Col. 1a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000038/18970703/015/0005.</ref>{{rp|p. 5, Col. 9a}}</blockquote> Describing a later social event in which the Duke and Duchess of Devonshire, as Mayor and Mayoress, decorated Devonshire House again, the ''Sussex Agricultural Express'' refers to some of the men who worked for the Duke and Duchess in January 1898, about half a year later: "Mr. J. P. Cockerell, the Duke of Devonshire's indefatigable agent called to his aid a willing and competent staff from Compton Place [in Eastbourne], including Mr. W. S. Lawrence, the house steward, and Mr. May, the gardener."<ref>"Sunday School Festival: Speech by the Duke." ''Sussex Agricultural Express'' 29 January 1898, Saturday: 7 [of 12], Col. 5b–6a. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000654/18980129/182/0007.</ref> Staff who were named as '''present at the 1897 ball''' included * Mr. J. P. Cockerell, agent for the Duke and Duchess of Devonshire * Mr. W. S. Lawrence, house steward for the Duke and Duchess of Devonshire * Mr. May, gardener for the Duke and Duchess of Devonshire ==== Serving Staff ==== It seems that the staff of Devonshire House was in costume. For example, after people were welcomed by the Duke and Duchess of Devonshire, "Masters of the Ceremonies in '''Louise Seize''' military uniforms passed the guests through into inner rooms."<ref name=":7">“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|p. 5, Col. 2c}} The article in the ''Gentlewoman'' says something very similar, although not identical: the Duchess of Devonshire's "Masters of the Ceremonies were in Louis Seize military uniforms, and they ushered the guests through into the inner rooms, with the exception of the Oriental queens, who, with their suites, assembled in the white and gold saloon, which was brilliantly lit by hundreds of wax '''Candles''', as were, indeed, all the rooms."<ref name=":42" />{{rp|p. 32, Col. 2a}} The people serving dinner were in costume, as the ''Westminster Gazette'' reported in its article on the ball: "The waiters moving about among the supper-folk were dressed as our great-grandfathers in the time of Pitt were dressed — the hair bunched in a black bag, black courtiers' coats, knee-breeches, stockings, and buckle shoes."<ref name=":7" />{{rp|p. 5, Col. 2a}} According to ''House Style: Five Centuries of Fashion at Chatsworth'', some of the staff who worked the ball were hired from the "outside," and some were already staff at Devonshire House.<blockquote>Then there was the mammoth task of organising costumes for the staff, as the Duchess had decided that they should all be in fancy dress. Those hired from outside were to wear Elizabethan and Egyptian costumes from a theatrical outfitter and, for the Devonshire House staff, the men were to be dressed in the blue and buff Devonshire livery of the eighteenth century and the maids in Elizabethan sprigged frocks.<ref name=":18">Burlington, Julia, and Hamish Bowles. ''House Style: Five Centuries of Fashion at Chatsworth''. Skira Rizzoli, 2017. Based on an exhibition 25 March to 22 October 2017.</ref>(137)</blockquote>Lady Violet Greville, who wrote the article on the ball in the ''Graphic'', says, "even the servants, in their own quaint and barbaric Eastern dress, carried out the illusion of antiquity to their knee breeches and white wigs."<ref>Greville, Violet, Lady. "Devonshire House Ball." ''The Graphic'' Saturday 10 July 1897: 15 [of 24]: Col. 1a–16, Col. 1c [of 3]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000057/18970710/019/0015.</ref>{{rp|p. 15, Col. 1b}} No evidence exists that Lady Greville was present at the ball, although her son and daughter in law were there. ====Artists Associated with this Event==== '''''Photographers''''' [[Social Victorians/People/Lauder|James Stack Lauder]], known as Lafayette because that was the name of his firm, was invited by the Duke of [[Social Victorians/People/Devonshire |Devonshire]] to set up a temporary studio in the garden and take portrait photographs of the guests in their costumes at the ball. While Lafayette is in many ways the most important photographer documenting the costumes for this event because he was present at the ball, with the imprimatur of the Duke of Devonshire, other photographers also took part in documenting this event. We see their work in the [[Social Victorians/1897 Fancy Dress Ball/Photographs|''Diamond Jubilee Fancy Dress Ball'' album of 286 photogravure portraits]] made of ones taken a week later by Lafayette as well as ones made by other photographers were collected as a hostess gift for the Duchess and given to her in 1899. A copy of this album is in the National Portrait Gallery and has been digitized.<ref>"Devonshire House Fancy Dress Ball (1897): photogravures by Walker & Boutall after various photographers." 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515</ref> '''''Painters''''' The "fashionable miniaturist" Amelie Küssner painted the Prince of Wales in his costume.<ref>"Notes — Mainly Personal." ''Dundee Evening Telegraph'' Monday 27 December 1897: 3 [of 6], Col. 2A. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000453/18971227/006/0003.</ref> According to the ''Western Daily Press'', H. A. Stock, a "much-admired" west-of-England painter, "represented one or two of the personages taking part in the Devonshire House fancy dress ball."<ref>"The Royal Institute of Painters in Water-Colours. West of England Artists." ''Western Daily Press'' Monday 20 March 1899: 3 [of 8], Col. 8B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000264/18990320/012/0003.</ref> At the 32nd Exhibition of the Royal Institute of Painters in Water-Colours that opened 12 March 1898, Mr. Stocks exhibited a "portrait of a well-known society lady in the costume she wore at the Devonshire House fancy dress ball."<ref>"From Our London Correspondent. By Special Wire." ''Dundee Advertiser'' 11 March 1898, Friday: 5 [of 10], Col. 7a. ''British Newspaper Archive''.</ref> At least one of the portraits in the ''Diamond Jubilee Fancy Dress Ball'' album is a painting rather than a photograph. '''''Sculptors''''' The Marchioness of Granby, who at this time was [[Social Victorians/People/Marion Margaret Violet Lindsay Manners|Violet Manners]], commissioned a bust by George Frampton.<ref>''Sevenoaks Chronicle and Kentish Advertiser'' 31 May 1901, Friday: 7 [of 8], Col. 7a. ''British Newspaper Archive''.</ref> ====Musicians==== At least two ensembles were present and providing music, Lacon and Ollier's Blue Hungarian Band and, early the next morning, the White Hungarian Band. One was called an orchestra and the other a band: according to the ''Guernsey Star'', "The orchestra was placed in close proximity to the ballroom, and another band played a programme in the garden."<ref>"Duchess of Devonshire's Fancy-Dress Ball. Brilliant Spectacle." ''The Star'' 6 July 1897, Tuesday: 1 [of 4], Col. 1–2. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000184/18970706/003/0001.</ref>{{rp|p. 1, Col. 2c}} The ''Gentlewoman'' says that the Blue Hungarian Band was near the saloon where the guests at the ball presented themselves to the Royals: <blockquote> About half-past eleven the Blue Hungarian Band, which was stationed in a small ante-room, announced the Prince of Wales' arrival with the stirring strains of "God Save the Queen," and His Royal Highness led the Princess up the centre of the saloon, which was lined by ladies dressed as Oriental queens and their suites.<ref name=":42" />{{rp|p. 32, Col. 2a}} </blockquote> The Blue Hungarian Band advertised in the ''Morning Post'': <blockquote> Lacon and Ollier's Blue Hungarian Band. Cymbalos, Berkes Geza and Miska. has arrived in town for the Season. — Engagements for balls, receptions, &c., to be made to 163A, New Bond-street, W. This band was specially engaged for the Duchess of Devonshire's ball on Friday last.<ref>[Advertisement]. ''Morning Post'' Wednesday 7 July 1897: 6 [of 12], Col. 3c. ''British Newspaper Archive'' <nowiki>http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970707/002/0006</nowiki>.</ref> </blockquote> According to a letter to the editor of the ''Pall Mall Gazette'' by "One Who Was There," the White Hungarian Band was present at the very end.<ref>One Who Was There. "Devonshire House: A Retrospect." Letters to the Editor. ''Pall Mall Gazette'' Tuesday 6 July 1897: 3 [of 12], Col. 2c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18970706/009/0003.</ref> Describing something that seems to be quite different, the ''Westminster Gazette'' says, "A mandoline band under the sycamore trees killed time."<ref>“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|p. 5, Col. 2a}} ==== Costumiers, Perruquiers, and Jewelers ==== Not present at the ball but certainly very involved in it were the people who made the clothing, hats, wigs, jewelry, and so forth. Besides people who made the costumes (costumiers, dressmakers, and modistes) and wigs (perruquiers), embroiderers, jewelers and shoemakers are occasionally mentioned although almost never named in the newspaper accounts. General, contextualizing descriptions of the costumes can be found in the [[Social Victorians/1897 Fancy Dress Ball/anthology#General Discussions of the Costumes|Anthology]]. '''''Costumiers for Theatres and Operas''''' * M. Comelli, designer and costumier at Covent Garden, designed the costumes that were constructed by Mr. Alias of Soho Square.<ref name=":42" />{{rp|p. 42, Col. 3b}} * Mr. Karl, artist, designed the costumes made by Messrs. L. and H. Nathan of Coventry-street<ref name=":42" />{{rp|p. 42, Col. 3b}} <ref name=":8" />{{rp|p. 3, Col. 5b}} * Messrs. John Simmons and Sons, Coventry House, Haymarket<ref name=":42" />{{rp|p. 42, Col. 3b}} * Simmons, 7 and 8, King Street, Covent Garden<ref name=":42" />{{rp|p. 42, Col. 3b}} * Mme. Auguste, of Wellington-street<ref name=":42" />{{rp|p. 42, Col. 3b}} * Harrison's, Ltd., 31, Bow-street<ref name=":42" />{{rp|p. 42, Col. 3b}} * Mr. W. Clarkson, 44, Wellington Street (costumes and wigs)<ref name=":42" />{{rp|p. 42, Col. 3b}} * Mme. or Miss Mary E. Fisher, 26, Bedford-street, Covent-garden<ref name=":9">{{Cite book|url=https://books.google.co.in/books?id=cVQZAAAAYAAJ&pg=RA3-PR2&dq=Mr.+May,+Garrick-street,+Covent-garden&hl=en&newbks=1&newbks_redir=0&sa=X&redir_esc=y|title=The Play-pictorial|date=1908|publisher=Greening & Company, Limited|language=en}} P. ADVT ii. ''Google Books'' https://books.google.com/books?id=cVQZAAAAYAAJ.</ref> <ref name=":42" />{{rp|p. 42, Col. 3b}} * Mr. May, Garrick-street, 9 & 11 Garrick Street, Covent-garden<ref name=":9" /> * "and many others"<ref name=":42" />{{rp|p. 42, Col. 3b}} '''''Fashion Houses and Modistes''''' Among those who helped construct the costumes and wigs include the following: * Mme Durrant made the dress for [[Social Victorians/People/Londonderry#Theresa, Marchioness of Londonderry|Theresa, Marchioness of Londonderry]], who was dressed as Empress Marie-Thérèse.<ref>"Lines for the Ladies." ''Daily Gazette for Middlesbrough'' Thursday 16 June 1898: 4 [of 4], Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000159/18980616/060/0004.</ref> The dress and fabrics for the Marchioness of Londonderry as well as her quadrille, were made in Britain or Ireland.<ref name=":02">"This Morning’s News." London ''Daily News'' 6 July 1897, Tuesday: 7 [of 12], Col. 3b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970706/038/0007.</ref> * The French "tailoring workshop"<ref>{{Cite web|url=https://fashion.mam-e.it/morin-blossier/|title=Morin-Blossier -|date=2016-02-05|language=it-IT|access-date=2022-04-07}}</ref> of Morin-Blossier made the dress worn by [[Social Victorians/People/Prince Charles of Denmark|Princess Maud of Wales]] (Princess Charles of Denmark).<ref name=":43">Harris, Russell. "Prince and Princess Carl of Denmark, later King Haakon VII (1872-1957) and Queen Maud of Norway (1869-1938), and Princess Victoria of Wales (1868-1935), as a 16th century Danish courtier, and Ladies-in-Waiting at to Marguerite de Valois." "List of Sitters." ''In Calm Prose''. 2011 http://www.rvondeh.dircon.co.uk/incalmprose/denmark.html.</ref> * The House of Worth * Doucet * Madame Frederic, of Lower Grosvenor Place * M. or Mrs. Mason, of New Burlington Street<ref name=":42" />{{rp|p. 42, Col. 3b}} * '''Mr. Caryl Craven<ref name=":42" />{{rp|p. 42, Col. 3b}}''' * M. Machinka, Conduit-street<ref name=":42" />{{rp|p. 42, Col. 3b}} * Paquin, of Dover-street<ref name=":42" />{{rp|p. 42, Col. 3b}} * Jays, Ltd., Regent-street<ref name=":42" />{{rp|p. 42, Col. 3b}} The ''Gentlewoman'' covered this topic explicitly: <blockquote> Very great credit is due to the taste and artistic powers of the designers of these dresses, and particular mention must be made of M. Comelli, of Covent Garden Theatre, whose facile pen designed most of the superb toilettes so ably carried out by Messrs. Alias, of Soho-square. Other theatrical costumiers who brought all their special talents to bear on the historical and fancy costumes required for this function were Messrs. Nathan (artist, Mr. Karl), of Coventry-street; Messrs. John Simmons & Sons, Haymarket; Mme. Auguste, of Wellington-street; Harrison's, Ltd., 31, Bow-street; Simmons, 7 and 8, King-street; Mr. Clarkson, 44, Wellington-street; Mme. Fisher, 26, Bedford-street; and many others. A great number of well-known modistes in London were also called upon to supply dresses. Amongst these we chronicle M. Mason, New Burlington-street; M. Machinka, Conduit-street; Paquin, of Dover-street; Jays, Ltd., Regent-street; Messrs. Durrant, 116, Bond-street (who made Lady Londonderry's magnificent gown), and numerous others.<ref name=":42" />{{rp|p. 42, Col. 3b}} </blockquote> The London ''Evening Standard'' cites the sources of its information about the costumes: <blockquote> We are indebted for some of the particulars of the dresses to Mr. Charles Alias, Soho-square; Messrs. L. and H. Nathan, Coventry-street, Haymarket; Messrs. John Simmons and Son, Coventry House, Haymarket; Mr. May, Garrick-street, Covent-garden; Miss Mary E. Fisher, 26 Bedford-street, Covent-garden; and the ''Lady'' newspaper.<ref name=":8">“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.</ref>{{rp|p. 3, Col. 5b}}</blockquote> The ''Morning Post'' also addressed the costumiers. It named Mr. Alias in association with the royals, as well as mentioning several other costumiers by name: <blockquote> The costumes worn by the Prince of Wales, the Duke of York, and the Duchess of Connaught, as well as many others were supplied by Mr. Alias, of Soho-square. Those worn by the Grand Duke Michael of Russia, the Duke of Manchester, Princess Victor of Hohenlohe, and others were made by Mr. W. Clarkson, of Wellington-street, who also supplied the wigs and headdresses for the Royal Family. Messrs. Simmons and Sons, of the Haymarket, made a large number of costumes, including those of the Duke of Somerset, the Marquis of Winchester, Earls Beauchamp, Carrington, Ellesmere, and Essex. Nathan, of Coventry-street, and Simmons, of King-street, Covent-garden; Madame Frederic, of Lower Grosvenor-place, and Mrs. Mason, of New Burlington-street, also made some of the principal costumes.<ref name=":0">"Fancy Dress Ball at Devonshire House." ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4A–8 Col. 2B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.</ref>{{rp|p. 8, Col. 2a}} </blockquote> On 3 July 1897, the day after the ball, the ''Belfast News-letter'' says, <blockquote>For weeks past all the leading London dressmakers and costumiers had been hard at work executing the orders for this great ball. At Alias Nathan's, Clarkson's, Auguste's, and Simmons' all hands set to with a will, and it is gratifying to know that the dresses entrusted to them more than held their own with those sent over from Paris.<ref name=":10" />{{rp|p. 5, Col. 9a}}</blockquote> According to the ''Derbyshire Times and Chesterfield Herald'', citing the ''Daily Mail'', <blockquote> Lady de Grey is going as Zenobia, and is getting her dress from Doucet, I hear, while Worth also is making a great many costumes; but the greatest number are being made in England. The Duchess of Portland, the Duchess of Hamilton, Lady Mar and Kellie, and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] are all going to the costumier in Soho-square, and Alias has also been summoned to Marlborough House for a consultation. Mr. Caryl Craven, who is so clever in such matters, is helping the Duchess of Leeds with her dress; in fact, everyone seems pressed into the service, and the result will be one of the most brilliant sights that ever was seen.<ref>“Derbyshire Sayings and Doings.” ''Derbyshire Times and Chesterfield Herald'' 12 June 1897, Saturday: 5 [of 8], Col. 2A. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000228/18970612/018/0005.</ref> </blockquote> Which costumier was this? "A well-known West End dressmaker booked for the Duchess of Devonshire's fancy dress ball orders representing £27000."<ref>"London Letter." ''Western Daily Press'' 15 July 1897, Thursday: 8 [of 8], Col. 7c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000264/18970715/146/0008.</ref> '''''Perruquiers''''' Mr. W. Clarkson "supplied the wigs and headdresses for the Royal Family."<ref name=":0" />{{rp|p. 8, Col. 2a}} <blockquote> At the Duchess of Devonshire's ball, on the 2d inst., the Prince of Wales looked as if he had stepped out of a masterpiece by one of the old painters. His wig, which completed a correct make-up as Knight of Malta, was specially made and fitted by that favoured "Royal Perruquier" Mr Willie Clarkson, who also had the honour of making and fitting the wigs worn by Prince Charles of Denmark, the Duke of York, and the Duke and Duchess of Connaught, and of dressing the hair of the Duchess of York and the Princess Victoria of Schleswig-Holstein. Mr Clarkson also supplied a number of the costumes, including those worn by the Grand Duke Michael of Russia, Princess Louise, and the Duke of Manchester. It would not be safe to say how many crowned heads have literally "passed through the hands" of Mr Clarkson. The art of the perruquier is a very difficult one, requiring historical knowledge, patient research, and great taste. It is most essential to the success of any theatrical performance or of an historical ball.<ref>“Foreign Plays and Players.” ''The Era'' 10 July 1897, Saturday: 15 [of 28], Col. 3c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000053/18970710/032/0015.</ref> </blockquote> Clarkson also provided costumes and wigs for the [[Social Victorians/Royals Amateur Theatricals|amateur theatricals]] that the royals took part in to entertain themselves. '''''Jewelers''''' After naming costumiers, the ''Gentlewoman'' specifically mentions the Parisian Company for its jewelry and Mr. Norman of Bond Street for the shoes he made: <blockquote> Among other firms [than the costumiers] who lent their aid to make the great ball a huge success was the Parisian Company, whose sparkling gems and jewels, and whose ropes of pearls and precious stones, enhanced the charms of many a fair dame in her dainty old-world costume, and the firm of Mr. Norman, 69, New Bond-street, who designed and made the shoes for the Princess of Wales, the Duchess of Buccleuch, &c., &c.<ref name=":42" />{{rp|p. 42, Col. 3c}} </blockquote> According to the ''Westminster Gazette'', "One very great lady indeed had been lent, by a jeweller, diamonds worth about £13,000."<ref name=":4">“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|p. 5, Col. 2c}} === Journalists and Newspaper Men Present === Several men who owned newspapers were present at the ball, but it seems very unlikely that they were invited because of their associations with journalism unless they were already part of the social network that the list of people who attended the ball can be seen to represent. Also, of course, given the class of people invited to the ball, they were not reporters but proprietors and editors. Still, their newspapers played a very important role in the reportage on the event, which makes them worth identifying separately: * [[Social Victorians/People/Borthwick|Algernon Borthwick, Lord Glenesk]], proprietor of the ''Morning Post'', and son and editor Oliver Borthwick * [[Social Victorians/People/Oppenheim|Henry Oppenheim]], one of three proprietors of the ''Daily News'' in July 1897; Oppenheim was apparently the only one of the three present at the ball. * [[Social Victorians/People/Grimthorpe|William Gervase Beckett]], proprietor and editor in chief of the ''Saturday Review'' While Borthwick and Oppenheim represented newspapers that gave a great deal of attention to the ball, their presence at the ball does not suggest their newspapers necessarily took it more seriously. The newspapers that had the biggest articles about the ball the day after are the following. The main article about the ball * on 10 July 1897 in the ''Gentlewoman'' is 8,489 words. * on 3 July 1897 in the London ''Morning Post'' is 7,719 words. * on 3 July 1897 in the London ''Evening Standard'' is 7,048 words. * on 3 July 1897 in the London ''Times'' is 5,675 words. * on 3 July 1897 in the London ''Daily News'' is 3,676 words. * on 3 July 1897 in the ''Westminster Gazette'' is 2,959 words. The articles in the ''Gentlewoman'' and the ''Graphic'' (this last one written by Lady Violet Greville), both 10 July 1897, had a very large number of illustrations, which made them longer than the number of words itself would suggest. ===[[Social Victorians/1897 Fancy Dress Ball/anthology |Anthology of Reports]]=== A collection of excerpts of descriptions from the newspaper and magazine reports, called here an [[Social Victorians/1897 Fancy Dress Ball/anthology |anthology]], gives a sense of what people read about the event. Reporting on this event began months before it, as soon I think as rumors that it would take place began to circulate, and continued for many months after; it occasionally shows up in a newspaper report years later. ==People Present== Most social events of this size that included the Prince and Princess of Wales, especially those hosted by them, were reported in the newspapers with a list of people invited, generally in order by rank. Royals, including royals from countries outside the U.K., were listed first, often as special guests. The ranks of the aristocracy followed, with dukes together, marquises, earls, and so on. Sometimes the toponyms were in alphabetical order; occasionally they were just grouped; I never saw a list that followed the orders of precedence beyond the general groupings by title. If members of a family were present and had a title, they were in the lists by their title with their family members listed with them. No newspaper printed a complete list of those invited to this ball, probably because the Duchess of Devonshire did not release such a list to the newspapers. This list, then, is the result of trawling through every contemporary account of the ball. It is possible, perhaps, to confirm the presence of some people, because, for example, they appear in the Album of portraits given as a thank-you gift to the Duchess in 1899. The fact that more than one newspaper mentions someone's presence may mean not confirmation but the fact that one or both of these newspaper were reprinting articles originally published somewhere else. The random quality to the list below, then, arises from the newspapers themselves. Further, the location of the names on the list depends on which newspaper article I was working from at the time. I began with the London ''Morning News'' because of its audience and reputation for gossip and social news for the aristocracy and oligarchy. Almost all other lists of attendees are made up only of what was published in the ''Times'', which is a good list but not the best (because of its repetitions) and nowhere near complete. Husbands and wives are often not listed together in the newspaper reports on the ball, and sometimes, as with the ''Times'', the same people are listed in several places with different titles and honorifics. Also influential in developing the list of attendees and identifying some who were mentioned in newspapers but without enough identifying information was the Album, which included the photographs of some of the attendees in their costumes, a copy of which is in the National Portrait Gallery, London, and another in the British Library. A list of people whom it would seem likely would have been at the ball but are not mentioned in the press are below, in the section [[1897 Fancy Dress Ball#People_Absent|People Absent]]. ===Missing from the List: Indian Dignitaries=== Missing from this list are the dignitaries from India, who were said to have been present. According to the ''Dundee Evening Telegraph'' dated 2 July 1897, the day of the party, "The Duchess [of Devonshire] has secured the attendance of many of the Indian Rajahs, who have merely to present themselves in the gorgeous dresses with which they have decorated London drawing-rooms during the past fortnight. ... — London Correspondent."<ref>“The Devonshire Ball.” ''Dundee Evening Telegraph'' 2 July 1897, Friday: 3 [of 6]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000453/18970702/017/0003.</ref> In a letter to the Editor of the ''Pall Mall Gazette'' on 6 July 1897, "One Who Was There" is lamenting about how, now that the ball was over, people would not see the beautiful costumes again. Unlike most of the people who attended, however, "The Indian princes were happy in their lot — no hired possessions theirs, but treasure trove, and they could play at dressing up whenever they pleased."<ref>One Who Was There. "Devonshire House: A Retrospect." Letters to the Editor. ''Pall Mall Gazette'' Tuesday 6 July 1897: 3 [of 12], Col. 2C. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18970706/009/0003.</ref> Describing wearing Indian late-19th-century native dress as "play[ing] at dressing up" reveals perhaps that part of the attraction of inviting these people, who were likely in London for Queen Victoria's Diamond Jubilee celebrations, were their colorful and exotic clothing. We know that "the Maharajah of Kapurthala" was present (at 195 in the list below) and at Table 10 in the first supper seating. No other newspapers stories talked about the presence of many Indian Rajahs, but perhaps the reporters didn't see them arrive or depart and didn't know who they were. These dignitaries are likely to have been in London to celebrate Queen Victoria's Diamond Jubilee; perhaps their names can be guessed from those named at other events from about this time. [[Social Victorians/People/Duleep Singh|Duleep Singh]] (at 605) was not a dignitary from India: he was living in London at this time. On [[Social Victorians/Timeline/1897#6 July 1897, Tuesday|6 July 1897, Tuesday]], just 4 days after the fancy-dress ball, the Duke and Duchess of Devonshire hosted a garden party that was attended by a number of people from South Asia, who were named in the ''Morning Post'' article about the garden party. Although Duleep Singh himself is not mentioned, his English wife, Princess Sophia Duleep Singh, Countess of Selkirk, was present and mentioned just after this:<blockquote>The company arrived in quick succession from four till nearly seven o'clock by the two side entrances to the grounds, as well as the principal entrance in Piccadilly, and the presence of our Indian and Colonial visitors in their picturesque and varied uniforms testified to the far-reaching popularity of the Duke of Devonshire and the hostess. The Maharajah of Kapurthala, the Thakur Sahib of Gondal and the Maharanee, the Maharajah Sir Pertab Singh, Thakur Hari Singh, Kumar Dhopal Singh, Rajah Khetri Singh, Rajah Agit Singh, Raj Kuman Umaid of Shapura, Bijey Singh, Sir Jamsetjee Jejeebhoy and Miss and the Messrs. Jejeebhoy, and the Maha Mudalayar of Kandy, besides the officers of the Imperial Service Troops and the Officers of the Native Cavalry Corps were present. Among those who attended were: Dona Solomon Dias Bandaranaike and Miss Amy Dias Bandaranaike, Senathi Rajah, Deir Senathi Rajah ....<ref>"Devonshire House." ''Morning Post'' 07 July 1897 Wednesday: 7 [of 12], Col. 6a–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970707/069/0007.</ref></blockquote>That is, assuming that those who were in London on 6 July 1897 were also likely in London on 2 July, these visitors from South Asia might have attended the fancy-dress ball as well: * The Maharajah of Kapurthala * The Thakur Sahib of Gondal and the Maharanee * The Maharajah Sir Pertab Singh * Thakur Hari Singh * Kumar Dhopal Singh * Rajah Khetri Singh * Rajah Agit Singh * Raj Kuman Umaid of Shapura * Bijey Singh * Sir Jamsetjee Jejeebhoy and Miss and the Messrs. Jejeebhoy * The Maha Mudalayar of Kandy * Dona Solomon Dias Bandaranaike and Miss Amy Dias Bandaranaike * Senathi Rajah * Deir Senathi Rajah The list of attendees to this garden party follows the pattern of the typical list for this kind of event that included royals, visiting dignitaries and officials, and aristocracy from other nations. That is, people are listed more or less in rank order and grouped by family, as if the newspaper had received a copy of the invitation list itself. The list of people who attended the fancy-dress ball is not ordered in these ways, as if the newspapers were not given the invitation list. This difference might explain why the ''Morning Post'' knew the names of these dignitaries from South Asia on 7 July but did not on 3 July. === Possible Errors === *Mr. and Mrs. Bourke, but Hon. Mr. and Hon. Mrs. A. Bourke are at 325 and 236, respectively. *Mr. S. Cavendish (at 656) may be an error; he may be [[Social Victorians/People/Cavendish|Mr. R. Cavendish]], who is already in the list (at 107) *The National Portrait Gallery letterpress on her portrait says that Lady Helen Stewart is Lady Mary Stewart, Helen Mary Theresa [[Social Victorians/People/Londonderry | Vane-Tempest-Stewart]] (at 43, right after her mother in this list). Helen Stewart-Murray, daughter of the [[Social Victorians/People/Atholl|Duke of Atholl]] (at 657) was probably a misidentification. *Lord [[Social Victorians/People/Hamilton Temple Blackwood|J. Blackwood]] (at 718) and Lady [[Social Victorians/People/Hamilton Temple Blackwood|J. Blackwood]] (at 719) are difficult to identify given the honorifics. Possibly the J. is a typo for T. in the ''Times'' report? *The [[Social Victorians/People/Villiers|Ladies Villiers]] were in a quadrille with the [[Social Victorians/People/Roxburghe|Ladies Ker]]: The [[Social Victorians/People/Roxburghe|Ladies Ker]] are at 23, two women. If each woman had one sash, then there were 2 ladies Villiers and 2 ladies Ker. Lady Edith Villiers (at 282) was definitely in the Cosway quadrille; Lady M. Villiers (at 433) is probably Lady Margaret Villiers, so that might be both the Ladies Villiers. (Mr. E. Villiers is at 326.) * The ''Times'' article<ref name=":2" /> lists both Mrs. George Curzon and then later Mr. and Mrs. Curzon; was George there? or was this another couple? Several people are treated this way, mentioned earlier in the ''Times'' article and then apparently showing up later, with fewer honorifics, especially if they are Hon.'s. Also, there may be duplicates because of variant spellings of the names. ===List of People Who Attended=== # [[Social Victorians/People/Albert Edward, Prince of Wales |Albert Edward, Prince of Wales]] #[[Social Victorians/People/Alexandra, Princess of Wales | Alexandra, Princess of Wales]], train borne by ##[[Social Victorians/People/Knollys#Hon. Louvima Knollys|Hon. Louvima Knollys]] # The [[Social Victorians/People/George and Mary|Prince George of Wales, Duke of York]], at this point heir to the throne. He and the Duchess of York were attended by ## Lady[[Social Victorians/People/Beauchamp | Mary Lygon]] (at 547) ## Sir Charles[[Social Victorians/People/Cust | Cust]] (at 152) # [[Social Victorians/People/George and Mary|Mary, Duchess of York]], who was Mary of Teck, in attendance on Alexandra. She and George, Duke of York were attended by ## Lady[[Social Victorians/People/Beauchamp | Mary Lygon]] (at 547) ## Sir Charles[[Social Victorians/People/Cust | Cust]] (at 152) # [[Social Victorians/People/Alfred of Edinburgh|Alfred Hereditary Prince of Saxe-Coburg and Gotha]] (son of "Affie," [[Social Victorians/People/Alfred of Edinburgh|Alfred, Duke of Edinburgh]]) # Prince[[Social Victorians/People/Christian of Schleswig-Holstein | Christian of Schleswig-Holstein]] # Helena Augusta Victoria, Princess[[Social Victorians/People/Christian of Schleswig-Holstein | Christian of Schleswig-Holstein]] # The[[Social Victorians/People/Grand Duke Michael of Russia | Grand Duke Michael of Russia]] # Princess Louise, Duchess of[[Social Victorians/People/Connaught | Connaught and Strathearn]] (Princess Louise Margaret Alexandra Victoria Agnes of Prussia) (Prince Arthur, Duke of Connaught is at 369) # Princess[[Social Victorians/People/Victoria of Schleswig-Holstein | Victoria of Schleswig-Holstein]] (her parents, Prince and Princess Christian of Schleswig-Holstein are at 6 and 7) # [[Social Victorians/People/Francis Duke of Teck | Francis, Duke of Teck]] #[[Social Victorians/People/Francis Duke of Teck|Princess Mary Adelaide, Duchess of Teck]] #[[Social Victorians/People/Francis Duke of Teck|Prince Alexander of Teck]] #[[Social Victorians/People/Francis Duke of Teck|Prince Francis of Teck]] # The [[Social Victorians/People/Fife |Duke of Fife]] (the Duchess of Fife is at 177) # Princess (Laura Williamina Seymour) Victor of [[Social Victorians/People/Gleichen#Laura Williamina Seymour of Hohenlohe-Langenburg|Hohenlohe Langenburg]] #[[Social Victorians/People/Gleichen |Countess Helena Gleichen]] #[[Social Victorians/People/Louisa Montagu Cavendish | Luise Cavendish]], the Duchess of Devonshire #[[Social Victorians/People/Spencer Compton Cavendish | Spencer Cavendish]], Duke of Devonshire # [[Social Victorians/People/Buccleuch |Duke of Buccleuch]], ([[Social Victorians/People/Buccleuch|the Duchess of Bucchleuch]] is at 24) #[[Social Victorians/People/William Angus Drogo Montagu | William Angus Drogo Montagu]], 9th Duke of [[Social Victorians/People/Manchester | Manchester]] (Consuelo, Duchess of Manchester is at 175) # The [[Social Victorians/People/Roxburghe |Duchess of Roxburghe]] (the Duke of Roxburghe, her son, is at 48) #[[Social Victorians/People/Roxburghe |Lady Margaret Innes-Ker]] (the Duchess of Roxburghe is at 21) #[[Social Victorians/People/Buccleuch|Louisa Jane Montagu Douglas Scott, Duchess of Buccleuch]] (the Duke of Buccleuch is at 20) # Lady [[Social Victorians/People/Katharine Mary Montagu Douglas Scott | Katharine Scott]] # Lady[[Social Victorians/People/Constance Anne Montagu Douglas Scott | Constance Scott]] # Algernon St. Maur, [[Social Victorians/People/Somerset |Duke of Somerset]] (Susan St. Maur, Duchess of Somerset at 209) # William Cavendish-Bentinck, 6th [[Social Victorians/People/Portland |Duke of Portland]] (Duchess of Portland at 29; Mildred Grenfell at 30) # Winifred Anna Dallas-Yorke Cavendish-Bentinck, the [[Social Victorians/People/Portland |Duchess of Portland]] (the Duke of Portland at 27) #[[Social Victorians/People/Mildred Grenfell | Mildred Grenfell]] # Rachel, [[Social Victorians/People/Dudley |Countess of Dudley]] (William, Earl of Dudley is at 63; the Hon. Gerald Ward is at 271) # The [[Social Victorians/People/Alva |Duke of Alva]]— probably Carlos María Fitz-James Stuart y Palafox, [[Social Victorians/People/Alva|16th Duke of Alba]] (possibly his son, Lord Alva, is at 405) # Millicent Fanny St. Clair-Erskine Leveson-Gower, [[Social Victorians/People/Sutherland |Duchess of Sutherland]] (the Duke of Sutherland is at 623) # Katherine Cavendish Grosvenor, the [[Social Victorians/People/Westminster |Duchess of Westminster]] (the Duke is at 173) # Katherine Frances Lambton Osborne, the [[Social Victorians/People/Leeds |Duchess of Leeds]] (the duke is at 455) # Constance Villiers Stanley, [[Social Victorians/People/Derby |Countess of Derby]] (Frederick, Earl of Derby is at 210) #[[Social Victorians/People/Forbes |Lady Angela St. Clair-Erskine Forbes]] (Mr. James Stewart Forbes is at 273) #[[Social Victorians/People/Cornwallis-West |Daisy (Mary Theresa) Cornwallis-West]], Princess Henry of [[Social Victorians/People/Pless | Pless]] (Prince Henry of Pless is at 40) # The [[Social Victorians/People/Keppel |Hon. George Keppel]] (Alice Keppel is at 231) #[[Social Victorians/People/Pless |Prince Henry of Pless]] ("Daisy" Mary Theresa [[Social Victorians/People/Cornwallis-West | Cornwallis-West]], Princess Henry of Pless, is at 38) # Evelyn, [[Social Victorians/People/Alington |Lady Alington]] (Humphrey Sturt is at 120) # Theresa Chetwynd-Talbot Vane-Tempest-Stewart, [[Social Victorians/People/Londonderry |Marchioness of Londonderry]] (the Marquess of Londonderry is at 511) # Lady Mary Stewart, Helen Mary Theresa [[Social Victorians/People/Londonderry | Vane-Tempest-Stewart]] # Lady Beatrix [[Social Victorians/People/Lansdowne | Petty-FitzMaurice]], daughter of the [[Social Victorians/People/Lansdowne |Marquess and Marchioness of Lansdowne]], in attendance on the Marchioness of Londonderry (at 42) #[[Social Victorians/People/Ormonde |Lady Beatrice Butler]] (Elizabeth Grosvenor Butler, the [[Social Victorians/People/Ormonde |Marchioness of Ormonde]], is at 372; Constance Butler is at 373) #[[Social Victorians/People/Abercorn |Lady Alexandra Hamilton]] (daughter of James Hamilton, 2nd [[Social Victorians/People/Abercorn |Duke of Abercorn]]) #[[Social Victorians/People/Stirling |Miss Stirling]] (possibly Evelyn Mary Caroline Lilah Stirling) # The [[Social Victorians/People/Zetland |Marchioness of Zetland]] (The Marquis of Zetland is at 59; son, Earl of Ronaldshay, is at 529) # The [[Social Victorians/People/Roxburghe |Duke of Roxburghe]] (The Duchess of Roxburghe, his mother, is at 22) # The [[Social Victorians/People/Winchester |Marquis of Winchester]] # Maud Hamilton Petty-FitzMaurice, [[Social Victorians/People/Lansdowne |Marchioness of Lansdowne]] (Beatrix Petty-FitzMaurice is at 43) # Henry Petty-FitzMaurice, [[Social Victorians/People/Lansdowne |Marquis of Lansdowne]] # Daisy, [[Social Victorians/People/Warwick |Countess of Warwick]] (the Earl of Warwick is at 525) # Marcia Anderson-Pelham, [[Social Victorians/People/Yarborough |Countess of Yarborough]] (the Earl is at 61) # Beatrix Jane Craven,[[Social Victorians/People/Cadogan | Countess Cadogan]] (Earl Cadogan is at 176) #[[Social Victorians/People/Lurgan |Lady Emily Lurgan]] (Lord Lurgan is at 165) #[[Social Victorians/People/Cadogan |Lady Sophie Scott]] (Sir Samuel Scott, Bart., is at 99) # The [[Social Victorians/People/Mar and Kellie | Earl of Mar and Kellie]] (the Countess of Mar and Kellie is at 160) # The [[Social Victorians/People/Zetland |Marquis of Zetland]] (The Marchioness of Zetland is at 48; son, Earl of Ronaldshay, is at 529) # William Lygon, 7th [[Social Victorians/People/Beauchamp |Earl Beauchamp]] (Lady Mary Lygon, his sister, is at 547) # Charles Anderson-Pelham, 4th [[Social Victorians/People/Yarborough |Earl of Yarborough]] (The Countess of Yarborough is at 54) # Henry Lascelles, 5th [[Social Victorians/People/Harewood |Earl Harewood]] (Lady Harewood is at 524) # William Humble Ward, 2nd [[Social Victorians/People/Dudley |Earl of Dudley]] (Rachel, Countess of Dudley is at 31; the Hon. Gerald Ward is at 271) # George Capell, 7th [[Social Victorians/People/Essex |Earl Essex]] (the Adele Grant Cappell, Countess of Essex is at 194) # Edward [[Social Victorians/People/Villiers | Villiers]], 5th [[Social Victorians/People/Villiers |Earl Clarendon]] #[[Social Victorians/People/Deym |Count Franz Deym]] (Countess Deym is at 67) #[[Social Victorians/People/Deym |Countess Isabel Deym]] (Count Deym is at 66) # Francis Egerton, 3rd [[Social Victorians/People/Ellesmere |Earl of Ellesmere]] (his daughter Lady Mabel Egerton is at 544) # Lord Carington: Charles Robert Wynn-Carington, [[Social Victorians/People/Carrington |Earl Carrington]] # William Waldegrave Palmer, 2nd [[Social Victorians/People/Selborne |Earl of Selborne]] (Beatrix Palmer, Lady Selborne is at 557) # Edward Montagu, 8th [[Social Victorians/People/Sandwich |Earl of Sandwich]] # Henry William Edmund Petty-FitzMaurice,[[Social Victorians/People/Kerry | Earl Kerry]] # Charles Stewart Henry Vane-Tempest-Stewart,[[Social Victorians/People/Londonderry | Viscount Castlereagh]] # Arthur Wellesley Peel, [[Social Victorians/People/Peel Family |1st Viscount Peel]] # Grace, [[Social Victorians/People/Londesborough |Viscountess Raincliffe]] (Lady Mildred [[Social Victorians/People/Londesborough | Denison]] is at 283) # William, [[Social Victorians/People/Londesborough |Viscount Raincliffe]] # Oliver Russell, [[Social Victorians/People/Ampthill |Lord Ampthill]] (Margaret Russell, Lady Ampthill is at 419; Emily, Lady Ampthill is at 420; Miss Constance [[Social Victorians/People/Ampthill | Russell]] is at 418) # Giles Fox-Strangways,[[Social Victorians/People/Ilchester | Lord Stavordale]] (Muriel Fox-Strangways is at 403) # Frederick Glyn, [[Social Victorians/People/Wolverton |Lord Wolverton]] (Edith, Lady Wolverton is at 130) #[[Social Victorians/People/Rodney |Lord Rodney]] (Lady Rodney is at 472) # Hon. [[Social Victorians/People/Grosvenor |R. Grosvenor]]: possibly [[Social Victorians/People/Grosvenor#Hon. R. Grosvenor|Hon. Robert Victor Grosvenor, 3rd Baron Ebury]] # Seymour Henry Bathurst,[[Social Victorians/People/Bathurst | 7th Earl Bathurst]] # Hon. Grosvenor [[Social Victorians/People/Hood | Hood]] #[[Social Victorians/People/Abercorn|Lord Frederick Hamilton]] (Lady Alexandra Hamilton is at 46; Lord Ronald Hamilton is at 105) # Fanny Marjoribanks, [[Social Victorians/People/Tweedmouth |Lady Tweedmouth]] (Edward Marjoribanks, Baron Tweedmouth is at 109; son Dudley Marjoribanks is at 319; his cousin, [[Social Victorians/People/Roxburghe|Duke of Roxburghe]] is at 49) # Arthur Balfour, [[Social Victorians/People/Balfour |the Right Hon. A. J. Balfour]] (Miss Balfour is at 486) # Algernon [[Social Victorians/People/Borthwick | Borthwick, Baron Glenesk]] (Lady Glenesk is at 88; Oliver Borthwick is at 89; Seymour Bathurst, [[Social Victorians/People/Bathurst |7th Earl Bathurst]], is at 82) # Alice [[Social Victorians/People/Borthwick | Borthwick]], Lady Glenesk (Baron Glenesk is at 87; Oliver Borthwick is at 89; Seymour Bathurst, [[Social Victorians/People/Bathurst |7th Earl Bathurst]], is at 82) # Hon. Oliver [[Social Victorians/People/Borthwick | Borthwick]] (Baron Glenesk is at 87; Lady Glenesk is at 88; Seymour Bathurst, [[Social Victorians/People/Bathurst |7th Earl Bathurst]], is at 82) # Minnie (Mary)[[Social Victorians/People/Paget Family | Paget]], Mrs. Arthur Paget (Arthur Paget is at 91) # Colonel Arthur [[Social Victorians/People/Paget Family | Paget]] (Minnie Paget is at 90) # Mrs. [[Social Victorians/People/Fanny Ronalds | Fanny Ronalds]] # The [[Social Victorians/People/Chamberlain |Right Hon. Joseph Chamberlain]] (Mrs. Mary Chamberlain is at 491; Miss Chamberlain is at 492) #[[Social Victorians/People/Harcourt |Lady Elizabeth Harcourt]] (Sir William Harcourt is at 128; Lewis Harcourt is at 664) # Mr. F. B. [[Social Victorians/People/Mildmay |(Francis Bingham) Mildmay]] #[[Social Victorians/People/Sarah Spencer-Churchill Wilson |Captain Gordon Wilson]] (Lady Sarah Wilson is at 392) # Sir John[[Social Victorians/People/Lister-Kaye | Lister Kaye, Bart.]] (Lady Maria Lister Kaye is at 499) #[[Social Victorians/People/Chaine |Colonel William Chaine]] (Maria Chaine is at 490) # Sir Samuel [[Social Victorians/People/Cadogan | Scott]], Bart. (Lady Sophie Scott, his wife, is at 57) # Mr. Gerald [[Social Victorians/People/Loder | Loder]], M.P. # Charles Chetwynd-Talbot, Earl of [[Social Victorians/People/Shrewsbury | Shrewsbury]] #[[Social Victorians/People/Salisbury |Lady Edward Cecil]] (Lord E. Cecil is at 411; Lord R. Cecil is at 126; Lady R. Cecil is at 450; Gwendolen Cecil is at 404) # [[Social Victorians/People/Cresswell |Addison Francis Baker-Cresswell]] (Mr. A. F. B. Cresswell) # Mr. Schomberg M'Donnell: [[Social Victorians/People/Antrim |Schomberg McDonnell]] # [[Social Victorians/People/Abercorn |Mr. Ronald Hamilton]] (possibly Ronald James Hamilton, nephew of the 1st Duke of Abercorn) (Lady Alexandra Hamilton is at 45; Lord Frederick Hamilton is at 83) # [[Social Victorians/People/Jarvis |Weston (Mr. A. W.) Jarvis]] # Mr. R. (possibly [[Social Victorians/People/Cavendish |Lord Richard) Cavendish]] (the Hon. Victor Cavendish is at 121; Lady E. Cavendish is at 164; Lady Edward Cavendish is at 393; Lady Moyra Cavendish is at 366) # [[Social Victorians/People/Gourko|Mr. Nicolas Gourko]] # Edward Marjoribanks, Baron [[Social Victorians/People/Tweedmouth | Tweedmouth]], as the Earl of Leicester (Fanny Marjoribanks, Lady Tweedmouth is at 85; son Dudley Marjoribanks is at 319; his cousin, Duke of Roxburghe is at 49) # Cyril Flower, [[Social Victorians/People/Rothschild Family#Cyril Flower, Lord Battersea and Constance de Rothschild Flower, Lady Battersea|Lord Battersea]] (Constance de Rothschild Flower, Lady Battersea, is at 328) # Sir [[Social Victorians/People/Hartopp |Charles Hartopp]] (Millicent, Lady Hartopp is at 488) # Emma Louise von Rothschild, [[Social Victorians/People/Rothschild Family#Emma, Lady Rothschild and Nathan Mayer, Lord Rothschild|Lady Rothschild]] (Nathan Mayer de Rothschild, Lord Rothschild is at 216) # Mr. [[Social Victorians/People/Portland | Cavendish-Bentinck]] (Mrs. Cavendish Bentinck is 263) # Sir [[Social Victorians/People/Donald Mackenzie Wallace | Donald Mackenzie Wallace]] # Mr. Montague [[Social Victorians/People/Guest | Guest]] (Ivor Bertie Guest, at 295; Frederick Guest, at 345) # Sir Henry [[Social Victorians/People/Meysey-Thompson|Meysey-Thompson]] (Lady Meysey Thompson is at 391) # Walter Hume [[Social Victorians/People/Long | Long]], the Right Hon. W. H. Long, M.P. (Lady Doreen Long is at 484) # Mr. [[Social Victorians/People/Arthur Stanley Wilson | Arthur Wilson]] # Lady [[Social Victorians/People/Lathom |Edith Wilbraham]] (Edward Bootle-Wilbraham, Earl Lathom, is at 125; Alice Bootle-Wilbraham, Countess Lathom, is at 213) # The [[Social Victorians/People/Alington|Hon. Humphrey Sturt, M.P.]] (Lady Alington is at 41) # The [[Social Victorians/People/Cavendish |Hon. Victor Cavendish]] (Lady E. Cavendish is at 164; Mr. R Cavendish is at 107; Lady Edward Cavendish is at 393; Lady Moyra Cavendish is at 366) # Lord [[Social Victorians/People/Henry James | James of Hereford]] (his niece, Miss James, is at 396) # [[Social Victorians/People/Talbot |Lord Edmund Talbot]] # Mr. C. Wyndham, M.P.: Colonel Sir Charles [[Social Victorians/People/Wyndham | Wyndham Murray]] # Edward Bootle-Wilbraham, the [[Social Victorians/People/Lathom |Earl of Lathom]] (The Countess of Lathom is at 213; Lady Edith Wilbraham is at 119) # [[Social Victorians/People/Salisbury |Lord Robert Cecil]] (Lady Edward Cecil is at 102; Lord E. Cecil is at 411; Lady Robert Cecil [Eleanor Lambton Gascoyne-Cecil] is at 450; Gwendolen Cecil is at 404). # Sir [[Social Victorians/People/Charles Hall | Charles Hall]], Q.C, M.P. # Sir [[Social Victorians/People/Harcourt |William Harcourt]] (Lady Elizabeth Harcourt is at 94; Lewis Harcourt is at 669) # Herbert Gardner, [[Social Victorians/People/Burghclere |Lord Burghclere]], as a Puritan (Lady Burghclere is at 437) # Edith Glyn, Lady [[Social Victorians/People/Wolverton | Wolverton]] (Lord Wolverton is at 79) # [[Social Victorians/People/Princess Louise | Princess Louise]] Marchioness of Lorne (the Marquis of Lorne is at 620; Elspeth Campbell is at 621) # [[Social Victorians/People/Churchill |Lady Randolph Churchill]] (her son Winston Churchill, is at 179; Jack Churchill is at 223) # Alphonse [[Social Victorians/People/de Courcel |Chodron de Courcel]] (Madame de Courcel is at 182; Mademoiselle Henriette de Courcel is at 371; Mademoiselle de Courcel is at 498) # Ernest Louis, the [[Social Victorians/People/Princess Alice | Grand Duke of Hesse]] (Princess Victoria, the Grand Duchess of Hesse, is at 138). # M. [[Social Victorians/People/de Soveral | de Soveral]] # Gwladys Robinson, [[Social Victorians/People/Ripon |Countess de Grey]] (Frederick Oliver Robinson, Earl de Grey is at 656) ## Ethiopian or Nubian attendant # [[Social Victorians/People/Georges de Staal | Georges de Staal]] # [[Social Victorians/People/Princess Alice | Princess Victoria]], the Grand Duchess of Hesse (the Grand Duke of Hesse is at 134). # Archibald Primrose, 5th [[Social Victorians/People/Rosebery |Earl of Rosebery]] # Louisa Acheson, [[Social Victorians/People/Gosford |Lady Gosford]] (the Earl of Gosford is at 143) # John Lambton, 3rd [[Social Victorians/People/Durham |Earl of Durham]] # Sunny (Charles Richard John) Spencer-Churchill, the [[Social Victorians/People/Marlborough |Duke of Marlborough]] (Consuelo, Duchess of Marlborough is at 174) # Archibald Acheson, 4th [[Social Victorians/People/Gosford |Earl of Gosford]] (Lady Gosford is at 140) # [[Social Victorians/People/Prince Charles of Denmark | Prince Charles of Denmark]] (Princess Charles of Denmark is at 159). The Prince and Princess Charles of Denmark were attended by ## Cecilia, [[Social Victorians/People/Suffield|Lady Suffield]] (at 536) ## [[Social Victorians/People/Knollys|Miss Charlotte Knollys]] (at 651) ## Major-General [[Social Victorians/People/Ellis|Arthur Ellis]] (at 654) # John Spencer, [[Social Victorians/People/Spencer |Earl Spencer]] (Charlotte, Countess Spencer is at 192) # Beatrix Herbert, the [[Social Victorians/People/Pembroke |Countess of Pembroke]] (the Earl of Pembroke is at 181; Lady Beatrix Herbert is at 648) # Hardinge Stanley Giffard, [[Social Victorians/People/Halsbury |Lord Halsbury]] (Lady Halsbury is at 515) # Ana, Countess de [[Social Victorians/People/Casa de Valencia | Casa Valencia]] (the Count is at 183) # [[Social Victorians/People/Francis Duke of Teck|Prince Adolphus of Teck]] # Kathleen Pelham-Clinton, the [[Social Victorians/People/Newcastle |Duchess of Newcastle]] (the Duke of Newcastle is at 564) # Mrs. White: [[Social Victorians/People/Henry White |Daisy (Margaret Stuyvesant Rutherford) White]] (Henry White is at 310) # [[Social Victorians/People/Cust |Sir Charles Cust]] , who accompanied the Duke and Duchess of York with Lady Mary Lygon # William Court [[Social Victorians/People/Gully Selby | Gully Selby]] (Mrs. Gully is at 441; Miss Gully at 442) # [[Social Victorians/People/John Milton Hay |Clara Stone Hay]] (John Milton Hay is at 187; Miss Helen Hay at 508) # Alice Anne Graham-Montgomery Temple-Nugent-Brydges-Chandos-Grenville Edgerton, [[Social Victorians/People/Buckingham and Chandos |Duchess of Buckingham]] (Lord Wilbraham Egerton of Tatton is at 591; Lady Gore-Langton is at 592) # [[Social Victorians/People/Gordon-Lennox |Princess Edward of Saxe-Weimar]] # Lady [[Social Victorians/People/Stanley |Alice Maude Olivia Montagu Stanley]] (her husband Lord Edward George Villiers Stanley is at 188) # Edwyn Scudamore-Stanhope, the [[Social Victorians/People/Chesterfield |Earl of Chesterfield]] # Princess [[Social Victorians/People/Prince Charles of Denmark | Charles of Denmark]] (Princess Maud of Wales) (Prince Charles of Denmark is at 144). The Prince and Princess Charles of Denmark were attended by ## Cecilia, [[Social Victorians/People/Suffield|Lady Suffield]] (at 536) ## [[Social Victorians/People/Knollys|Miss Charlotte Knollys]] (at 651) ## Major-General [[Social Victorians/People/Ellis|Arthur Ellis]] (at 654) # Lady Violet (Susan Violet) Erskine, [[Social Victorians/People/Mar and Kellie |Countess of Mar and Kellie]] (the Earl of Mar and Kellie is at 58) # Lord Charles Montagu, [[Social Victorians/People/Manchester | Charles William Augustus Montagu]] # Mildred Cadogan, [[Social Victorians/People/Cadogan |Viscountess Chelsea]] # Henry Arthur Cadogan, [[Social Victorians/People/Cadogan |Viscount Chelsea]] # Lady E., probably [[Social Victorians/People/Cavendish |Lady Evelyn, Cavendish]] (the Hon. Victor Cavendish is at 121; Mr. R. Cavendish is at 107; Lady Edward Cavendish is at 393; Lady Moyra Cavendish is at 366) # Lord William [[Social Victorians/People/Lurgan |Lurgan]] (Lady Lurgan is at 56) # Mary Louise Douglas-Hamilton, [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton |Duchess of Hamilton]] # Lord Kenyon, Baron [[Social Victorians/People/Lloyd Kenyon | Lloyd Tyrell-Kenyon]]. # Georgiana Elizabeth Spencer-Churchill Curzon, [[Social Victorians/People/Howe|Viscountess Curzon]] (Viscount Curzon is at 197) # Robert Crewe-Milnes, [[Social Victorians/People/Crewe-Milnes |Earl of Crewe]] # The [[Social Victorians/People/Montrose |Duke of Montrose]] (the Duchess of Montrose is at 186) # Viscount Garnet [[Social Victorians/People/Wolseley | Wolseley]] (Lady Wolseley is at 541; Miss Wolseley is at 542) # Lord Falmouth: Evelyn Edward Thomas Boscawen, [[Social Victorians/People/Falmouth |7th Viscount Falmouth]] (Lady Falmouth is at 471) # Hugh Grosvenor, [[Social Victorians/People/Westminster |Duke of Westminster]] (the Duchess of Westminster is at 34) #[[Social Victorians/People/Consuelo Vanderbilt Spencer-Churchill |Consuelo Vanderbilt Spencer-Churchill]], Duchess of [[Social Victorians/People/Marlborough | Marlborough]] (The Duke of Marlborough is at 142) # Consuelo, [[Social Victorians/People/Manchester|Duchess of Manchester]] (William, Duke of Manchester is at 21) # Earl [[Social Victorians/People/Cadogan | Cadogan]] (Countess Cadogan is at 55) # Princess Royal, Louise, [[Social Victorians/People/Fife |Duchess of Fife]] (the Duke of Fife is at 15) # M. de [[Social Victorians/People/Souza Correa | Souza Correa]] (João Arthur Souza Corrêa) #Winston [[Social Victorians/People/Churchill|Churchill]] (his mother, [[Social Victorians/People/Churchill|Lady Randolph Churchill]], is at 132; his brother, Jack Churchill, is at 223) # Albert, [[Social Victorians/People/Mensdorff |Count Mensdorff]] # Sidney Herbert, [[Social Victorians/People/Pembroke |14th Earl of Pembroke]] (the Countess of Pembroke is at 145; Lady Beatrix Herbert is at 648) # Madame [[Social Victorians/People/de Courcel | de Courcel]] (Alphonse Chodron de Courcel is at 133; Mademoiselle Henriette de Courcel is at 371; Mademoiselle de Courcel is at 498) # Count [[Social Victorians/People/Casa de Valencia | Casa de Valencia]] (the Countess is at 148) # Countess Torby: Sophia Nicholaievna, [[Social Victorians/People/Grand Duke Michael of Russia |Countess Torbi or Torby]] # Lord Ribblesdale: Thomas Lister, [[Social Victorians/People/Ribblesdale|4th Baron Ribblesdale]] (Lady Ribblesdale is at 206) # The [[Social Victorians/People/Montrose |Duchess of Montrose]] (the Duke of Montrose is at 170) # [[Social Victorians/People/John Milton Hay |John Milton Hay]] (Clara Stone Hay is at 154; Helen Hay at 508) # Lord Edward George Villiers [[Social Victorians/People/Stanley | Stanley]] (Lady A. Stanley [Lady Alice Maude Olivia Montagu Stanley] is at 157) # Lord Montagu: William Lowry-Corry, [[Social Victorians/People/Rowton |1st Baron Rowton]] #Lady H. Lennox: Lady [[Social Victorians/People/Richmond and Gordon|Amelia Gordon-Lennox]] # Countess Clary: Thérèse, [[Social Victorians/People/Clary Aldringen |Countess Clary-Aldringen]] (Count Siegfried Clary is at 205; [[Social Victorians/People/Kinsky|Count Charles Kinsky]] is at 575; [[Social Victorians/People/Kinsky|Countess Josephine Kinsky]] is at 394) # Charlotte, [[Social Victorians/People/Spencer |Countess Spencer]] (John, Earl Spencer is at 145) # Lily, [[Social Victorians/People/Marlborough|Duchess of Marlborough]] (William Beresford is at 581) # Adele Grant Cappell, [[Social Victorians/People/Essex |Countess Essex]] (George Capell, Earl of Essex is at 64) # The [[Social Victorians/People/Kapurthala|Maharajah of Kapurthala]] #Cicely Gascoyne-Cecil, [[Social Victorians/People/Salisbury|Viscountess Cranborne]] (Lord Cranborne is at 610) #Richard George Penn, [[Social Victorians/People/Curzon |Viscount Curzon]] (Georgiana, Viscountess Curzon is at 168; Countess Howe is at 489) #Georgina, [[Social Victorians/People/Dudley |Lady Dudley]] (Rachel, Countess of Dudley is at 31; William, Earl of Dudley is at 63; the Hon. Gerald Ward is at 271) #Windham, [[Social Victorians/People/Dunraven|Earl of Dunraven]] (Florence, [[Social Victorians/People/Dunraven|Countess of Dunraven]] is at 606) #[[Social Victorians/People/Grenfell |Ettie (Mrs. W. H.) Grenfell]] (Mr. W. H. Grenfell is at 222; Miss Mildred Grenfell is at 30) #Hugo Charteris, [[Social Victorians/People/Charteris|Lord Elcho]] (Mary Charteris, Lady Elcho is at 224) #Louise ([[Social Victorians/People/Arthur Sassoon |Mrs. Arthur) Sassoon]] (Mr. Arthur Sassoon is at 552), with nephews as attendants: ##Evelyn [[Social Victorians/People/Rothschild Family|de Rothschild]] (at 668 ##Anthony [[Social Victorians/People/Rothschild Family|de Rothschild]] (at 669) # Henry, [[Social Victorians/People/Suffolk|Earl of Suffolk]] (Lady Suffolk is at 538) # Lady Hastings: [[Social Victorians/People/Hastings |Elizabeth Evelyn Harbord Astley]] (Lord Hastings is at 425) # Count Clary, [[Social Victorians/People/Clary Aldringen |Siegfried Graf von Clary und Aldringen]] (Countess Thérèse Clary is at 191; [[Social Victorians/People/Kinsky|Count Charles Kinsky]] is at 575; [[Social Victorians/People/Kinsky|Countess Josephine Kinsky]] is at 394) # Lady Ribblesdale: [[Social Victorians/People/Ribblesdale|Charlotte, Baroness Ribblesdale]] (Lord Ribblesdale is at 185) # [[Social Victorians/People/Kilmorey |Nellie, Countess of Kilmorey]] # Lowry Egerton Cole, [[Social Victorians/People/Cole|4th Earl of Enniskillen]] (Charlotte, Countess of Enniskillen is at 597; Lady Florence Cole is at 239) # Susan St. Maur, [[Social Victorians/People/Somerset |Duchess of Somerset]] (Algernon St. Maur, Duke of Somerset is at 27) # Frederick Arthur Stanley, [[Social Victorians/People/Derby |16th Earl of Derby]] (Constance, Countess of Derby is at 36) # Grace, [[Social Victorians/People/Lowther |Countess of Lonsdale]] (Hugh Cecil Lowther, Earl of Lonsdale is at 225) # Mr. Goschen: [[Social Victorians/People/Goschen|George Joachim Goschen]] (Mrs. Lucy Goschen is at 423; Miss Goschen is at 424) # Lady Alice Villiers Bootle-Wilbraham, the [[Social Victorians/People/Lathom |Countess of Lathom]] (Edward Bootle-Wilbraham, Earl Lathom is at 125; Lady Edith Wilbraham is at 119) # The [[Social Victorians/People/Ribblesdale|Hon. Reginald Lister]] # Lady [[Social Victorians/People/Feversham | Helen Venetia Duncombe Vincent]] (Sir Edgar Vincent is at 226) # Nathan Mayer de Rothschild, [[Social Victorians/People/Rothschild Family#Emma, Lady Rothschild and Nathan Mayer, Lord Rothschild|Lord Rothschild]], as a Swiss Burgher (Emma Louise von Rothschild, Lady Rothschild is at 112) # [[Social Victorians/People/Asquith |Margot Asquith]] (Herbert Henry Asquith is at 381) # Colonel [[Social Victorians/People/Oliphant|Laurence Oliphant]] # Sybil Fane, [[Social Victorians/People/Westmorland |Countess of Westmorland]] (Anthony Mildmay Fane, Earl of Westmorland is at 257) # Lady Cynthia [[Social Victorians/People/Feversham|Graham of Netherby]] (Sir Richard Graham is at 464) # [[Social Victorians/People/Wyndham |Mr. George Wyndham]] #Mr. [[Social Victorians/People/Grenfell |William Henry Grenfell]] (Ethel Grenfell is at 200; Miss Mildred Grenfell is at 30) # [[Social Victorians/People/Churchill|Jack Churchill]] (his mother, Lady Randolph Churchill, is at 132; his brother, Winston Churchill, is at 179) #Mary Charteris, [[Social Victorians/People/Charteris|Lady Elcho]] (Hugo Charteris, Lord Elcho is at 201) # Hugh Cecil Lowther, [[Social Victorians/People/Lowther |5th Earl of Lonsdale]] (Grace, Countess of Lonsdale is at 211) # Sir [[Social Victorians/People/Feversham |Edgar Vincent]] (Lady Helen Vincent is at 215) #Miss West: Shelagh [[Social Victorians/People/Cornwallis-West |(Constance Edwina) Cornwallis-West]] # [[Social Victorians/People/Goelet |Mary Goelet]], Miss Ogden Göelet (Mr. Ogden Göelet is at 502; Mrs. May Göelet is at 503) #Lady [[Social Victorians/People/Westminster|C. Grosvenor]] (family of the [[Social Victorians/People/Westminster#Lady C. Grosvenor|Duke of Westminster]]) #Miss [[Social Victorians/People/Oppenheim|Rosalinda Oppenheim]] (Henry Oppenheim is at 397; Mrs. Isabel Oppenheim is at 408) #[[Social Victorians/People/Keppel |Alice Keppel]] (George Keppel is at 39). # [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]] #[[Social Victorians/People/Portman|Arthur B. Portman]] # Mr. [[Social Victorians/People/Halifax|Gordon Wood]] #The Hon. [[Social Victorians/People/Bourke |Algernon Bourke]] (Guendoline Bourke is at 236) #Hon. Mrs. [[Social Victorians/People/Bourke |A. (Guendoline) Bourke]] (Algernon Bourke is at 235) #[[Social Victorians/People/Paget Family|Gerald Paget Paget]]: likely Gerald Cecil Stewart Paget (Mrs. Arthur Paget is at 90; Arthur Paget is at 91) #Lady [[Social Victorians/People/de Trafford |Violet de Trafford]] # [[Social Victorians/People/Cole |Lady Florence Cole]] (Lowry, Earl of Inneskillen is at 208; Charlotte, Countess Inneskillen is at 597) #Hon. Mrs. [[Social Victorians/People/Peel Family |Julia Peel Maguire]] (Mr. Rochfort Maguire is at 241) #Mr. [[Social Victorians/People/Peel Family |Rochfort Maguire]] #Miss [[Social Victorians/People/Muriel Wilson | Muriel Wilson]] #[[Social Victorians/People/Fraser |Helena Violet Alice Fraser]] ("Miss Keith Fraser") (Captain Keith Fraser is at 244) #Captain Fraser: [[Social Victorians/People/Fraser |Keith Alexander Fraser]] (Helena Violet Alice Fraser is at 243) #[[Social Victorians/People/Hope-Vere |Marie Hope-Vere]] #Alexandra Harriet Paget, [[Social Victorians/People/Colebrooke | Lady Colebrooke]] # <!-- Unidentified still -->Mrs. Leo was in the Duchess procession. #<!-- [Unidentified still] -->[[Social Victorians/People/Stanley#E. Stanley|E. Stanley]] #Right Hon. [[Social Victorians/People/Stanley |George Frederick Stanley]] #Lady [[Social Victorians/People/Derby#Hon. J. Stanley|J. Stanley]] #Hon. F. C. Stanley: [[Social Victorians/People/Stanley |Ferdinand Charles Stanley]] #[[Social Victorians/People/Brassey|L. Brassey]] # Mr. [[Social Victorians/People/Brassey|Harold Brassey]] #Lady A. Acheson: Lady [[Social Victorians/People/Gosford |Alexandra Louise Elizabeth Acheson]] #Lord Acheson: Lord [[Social Victorians/People/Gosford |Archibald Charles Montagu Brabazon Acheson]] #Lady [[Social Victorians/People/Gerard |Mary Milner Gerard]] #Anthony Mildmay Julian Fane, [[Social Victorians/People/Westmorland |13th Earl of Westmorland]] (Sybil Fane, Countess of Westmorland is at 219) #Mrs. [[Social Victorians/People/Talbot |Talbot]] # Miss [[Social Victorians/People/Brienen|de Brienen]] (Baron Brienen is at 465; Baroness Brienen is at 466) # Mrs. [[Social Victorians/People/Leslie |Leonie Leslie]] (Col. John Leslie is at 261) # Colonel [[Social Victorians/People/Leslie |John Leslie]] (Leonie Leslie is at 260) # Lord [[Social Victorians/People/Cavendish Bentinck|Henry Cavendish Bentinck]] (Lady Olivia Cavendish Bentinck is at 263; Lady Ottoline Cavendish-Bentinck is at 543) # Lady [[Social Victorians/People/Cavendish Bentinck|Olivia Cavendish Bentinck]] (Lord Henry Cavendish Bentinck is at 262; Lady Ottoline Cavendish-Bentinck (is at 543) # Mrs. [[Social Victorians/People/Portland | Cavendish Bentinck]] (Mr. Cavendish Bentinck is at 112) # [[Social Victorians/People/Heeren|Count Heeren]] # <!-- Unidentified still. -->Mrs. [[Social Victorians/People/Barclay|H. T. Barclay]] # <!-- Unidentified still. -->Mr. [[Social Victorians/People/Barclay|H. T. Barclay]] # Mr. A. M. Biddulph, possibly [[Social Victorians/People/Myddleton-Biddulph |Algernon Myddleton Biddulph]] # Lord [[Social Victorians/People/Romilly|Romilly]], probably John Gaspard le Marchant Romilly, [[Social Victorians/People/Romilly|3rd Baron Romilly]] # <!-- Unidentified still. -->Captain [[Social Victorians/People/Cook|E. B. Cook]] # The [[Social Victorians/People/Dudley|Hon. Gerald Ward]] (the Countess of Dudley is at 31; William, Earl of Dudley is at 63; Georgina Lady Dudley is at 198) # The Hon. [[Social Victorians/People/Campbell |Cecil Campbell]] # Mr. [[Social Victorians/People/Forbes |James Stewart Forbes]] (Lady Angela Forbes is at 37) # Mr. [[Social Victorians/People/Arthur Stanley Wilson#Charles Henry Wellesley Wilson|C. H. Wellesley Wilson]] # Lord [[Social Victorians/People/Buchan |Shipley Cardross]] (Lady Rosalie Cardross is at 276; the Hon. Muriel Erskine is at 278) # Lady [[Social Victorians/People/Buchan |Rosalie Cardross]] (Lord Shipley Cardross is at 276; the Hon. Muriel Erskine is at 278) # Mr. [[Social Victorians/People/Stourton |Herbert Marmaduke Joseph Stourton]] # The Hon. [[Social Victorians/People/Buchan |Muriel Erskine]] (Lord Shipley Cardross is at 275; Lady Rosalie Cardross is at 276) # Mr. Elliot: the Right Hon. [[Social Victorians/People/Minto|Sir Henry Elliot]] (Lady Minto is at 544) # M. [[Social Victorians/People/Boulatzell | Boulatzell]] # Lady [[Social Victorians/People/Spicer |Margaret Spicer]] (Captain John Spicer is at 410) # Lady [[Social Victorians/People/Villiers |Edith Villiers]] (Lady May Julia Child-Villiers is at 372; Earl Clarendon is at 65; Lord Hyde is at 294) # Lady [[Social Victorians/People/Londesborough |Mildred Denison]] (Grace, Viscountess Raincliffe is at 75; William, Viscount Raincliffe is at 76) # Lady [[Social Victorians/People/Saint Oswald|St. Oswald]] (Lord St. Oswald is at 641) # Miss [[Social Victorians/People/Forbes |Blanche Forbes]] (Mr. James Stewart Forbes is at 273; Lady Angela Forbes is at 37) # Mr. [[Social Victorians/People/Schreiber|Schreiber, Charles Shuldham Schreiber]] # Mrs. [[Social Victorians/People/Higgins|Higgins]] # Mr. [[Social Victorians/People/Higgins|Higgins]] # Mrs. [[Social Victorians/People/Von Andre |Mary Von André]] (Herr Adolf Von André is at 386) # [[Social Victorians/People/Walter Murray Guthrie | Walter Murray Guthrie]] (Olive Guthrie is at 291) # Mrs. [[Social Victorians/People/Walter Murray Guthrie |Olive Guthrie]] (Walter Murray Guthrie is at 290) # [[Social Victorians/People/Montagu|Lady Alice Eleanor Louise Montagu]] (escorted by Lord Stavordale, at 78) # [[Social Victorians/People/Arthur Stanley Wilson|Miss Enid Wilson]] # [[Social Victorians/People/Villiers |George Herbert Hyde Villiers]], Lord Hyde (Earl Clarendon is at 65; Lady Edith Villiers is at 282) # Hon. [[Social Victorians/People/Guest |Ivor Guest]] (Montague Guest, at 115; Frederick Guest, at 345) # The Hon. [[Social Victorians/People/Fortescue |Seymour Fortescue]] # The [[Social Victorians/People/Warwick|Hon. Sidney Greville]] # The Hon. [[Social Victorians/People/Greville |Margaret (Mrs. Ronald) Greville]] (where was Ronald Greville?) # <!-- Still unidentified. -->The [[Social Victorians/People/Warwick|Hon. Mrs. Greville]] (probably not 298?) # [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Mr. Clarence Wilson]] # The Hon. Mrs. George Curzon: [[Social Victorians/People/Curzon |the Hon. Mary Curzon]] (The Hon. George Curzon is at 495) # The [[Social Victorians/People/Peel Family|Hon. George Peel]] (Arthur Wellesley Peel, [[Social Victorians/People/Peel Family|1st Viscount Peel]] is at 74) #The Hon. [[Social Victorians/People/Charteris |Evan Charteris]] # Lady [[Social Victorians/People/Westminster#Lady Lettice Grosvenor|Lettice Grosvenor]] (family of the [[Social Victorians/People/Westminster|Duke of Westminster]]) # Lord [[Social Victorians/People/Thynne|Alexander Thynne]] # Possibly [[Social Victorians/People/Lurgan|Hon. Francis Cecil Brownlow]], the Hon. Cecil Brownlow # [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Mr. Herbert Wilson]] # Mrs. [[Social Victorians/People/Leigh |Marion Leigh]] (Captain Gerard Leigh is at 570; Lady Rose Leigh is at 337; John Blundell Leigh is at 602) # Mrs. [[Social Victorians/People/Drummond |Katherine Mary Drummond]] # Mr. [[Social Victorians/People/Henry White | Henry White]] (Mrs. Daisy White is at 151) # <!-- Unidentified still -->Mr. Norton (MornPost Fancy 1897-07-03) or Mr. Morton (Times 1897-07-03) was dressed as Guyman di Silva in the 17th-century procession. # Mr. [[Social Victorians/People/Beraud|Jean Béraud]] # Mr. [[Social Victorians/People/Grimthorpe |Ernest William Beckett]] (Mr. Gervase Beckett is at 483; Mabel Beckett is at 359; Mr. Rupert Beckett is at 481; Muriel Beckett is at 482) # Mr. H. [[Social Victorians/People/Warrender | Warrender]]: probably Hugh Valdave Warrender (Captain Warrender, probably George John Scott Warrender, is at 519) # Sir [[Social Victorians/People/Jeune |Francis Jeune]] attended with (Lady Susan Jeune is at 550; Miss Madeline Stanley is at 551) # Violet [[Social Victorians/People/Powis|Countess of Powis]] # George [[Social Victorians/People/Powis|Earl of Powis]] # Mrs. [[Social Victorians/People/Cavendish Bentinck |Arthur (Mary Venetia) James]] (Mr. Arthur James is at 480) # Hon. [[Social Victorians/People/Tweedmouth |D. Marjoribanks]] (Fanny Lady Tweedmouth is at 85; Baron Tweedmouth is at 109; Henry Duke of Roxburghe is at 49; two "brother officers" are at 637 and 638) # Mr. [[Social Victorians/People/Ephrussi|Ephrussi]] # [[Social Victorians/People/Mann Thomson|Captain Mann Thomson]] # [[Social Victorians/People/Rose|Mr. Rose]] # [[Social Victorians/People/Edmonstone|Sir A. Edmonstone]] # [[Social Victorians/People/Edmonstone|Lady Edmonstone]] # Mr. [[Social Victorians/People/Holden |Henry Holden]] # Mr. [[Social Victorians/People/Villiers#Mr. E. Villiers|E. Villiers]] # Arthur, [[Social Victorians/People/Arran|Earl of Arran]] # Constance de Rothschild Flower, [[Social Victorians/People/Rothschild Family#Cyril Flower, Lord Battersea and Constance de Rothschild Flower, Lady Battersea|Lady Battersea]] (Cyril Flower, Lord Battersea is at 110) # Rosamond Fellowes, [[Social Victorians/People/de Ramsey |Lady de Ramsey]] # Baron [[Social Victorians/People/Rothschild Family#Baron Ferdinand de Rothschild|Ferdinand de Rothschild]] # Mr. [[Social Victorians/People/Webb|Godfrey Webb]] # The [[Social Victorians/People/Lyttelton |Hon. S. (George William Spencer) Lyttelton]] # Lady [[Social Victorians/People/Gordon-Lennox |Blanche Gordon-Lennox]] (Lord Algernon Gordon Lennox is at 623) # [[Social Victorians/People/Burton|Lady Harriet Burton]] # [[Social Victorians/People/Burton|Lord Michael Burton]] # Florence Canning, [[Social Victorians/People/Garvagh |Lady Garvagh]] # Lady [[Social Victorians/People/Leigh |Rose Leigh]] (John Blundell Leigh is at 602; Mrs. Marion Leigh is at 308; Captain Gerard Leigh is at 570) # Mrs. [[Social Victorians/People/Farquharson |Zoë Farquharson]] (Alexander Farquharson is at 458) # Miss [[Social Victorians/People/Naylor|Naylor]] # The Hon. Mrs. [[Social Victorians/People/Sackville West|Sackville West]] # Lord Camden: John Pratt, [[Social Victorians/People/Camden|4th Marquess Camden]] # Lord Annaly: Luke White, [[Social Victorians/People/Annaly|Baron Annaly]] # John George Stewart-Murray, [[Social Victorians/People/Atholl |Marquess of Tullibardine]] # Lord George [[Social Victorians/People/Atholl | Stewart-Murray]] # Hon. [[Social Victorians/People/Guest |Frederick Edward Guest]] # Captain [[Social Victorians/People/Durham|the Hon. W. Lambton]] # [[Social Victorians/People/Elliot|Captain Gilbert Elliot]] # Mr. [[Social Victorians/People/Warwick |Frank Dugdale]] (Lady Eva Dugdale is at 409) #Mr. [[Social Victorians/People/Arthur Stanley Wilson|Clive Wilson]] # Mr. [[Social Victorians/People/Lowe|W. M. Lowe]] # Mr. [[Social Victorians/People/Morley |Arnold Morley]] # Mr. [[Social Victorians/People/Gathorne-Hardy |Francis Gathorne-Hardy]] # Charles William Reginald Duncombe, [[Social Victorians/People/Helmsley |Viscount Helmsley]] # Muriel Duncombe Owen, [[Social Victorians/People/Helmsley |Viscountess Helmsley]] # Evelyn McGarel-Hogg, [[Social Victorians/People/Magheramorne|Lady Magheramorne]] #Lady [[Social Victorians/People/Beaumont|Aline Beaumont]] (Mr. Wentworth Beaumont is at 468) # [[Social Victorians/People/Hamilton Temple Blackwood|Earl of Ava]]: Archibald Hamilton-Temple-Blackwood # <!-- [Still unidentified?] -->Mr. [[Social Victorians/People/Ancaster|C. Willoughby]] # Mrs. G. Beckett: Mrs. [[Social Victorians/People/Grimthorpe |Mabel Beckett]] (Mr. Gervase Beckett is at 483) # Miss [[Social Victorians/People/Yznaga |Emilia Yznaga]] # [[Social Victorians/People/Hadik |Count Hadik]] # Lady [[Social Victorians/People/Midleton |Hilda Brodrick]] ([[Social Victorians/People/Midleton |St. John Brodrick]] is at 368) # Mr. [[Social Victorians/People/Arthur Stanley Wilson |Jack Graham Menzies]] # [[Social Victorians/People/William James |Evelyn Elizabeth Forbes James]] # Lady [[Social Victorians/People/Lansdowne#Edmond and Lady Caroline Fitzmaurice|C. (Caroline) FitzMaurice]] (Lord Edmond Fitzmaurice is at 626) # Lady [[Social Victorians/People/Cavendish |Moyra Cavendish]] (Mr. R. Cavendish: Richard Frederick Cavendish is at 107) # James Somerville, 2nd Baron [[Social Victorians/People/Athlumney | Athlumney]] # Mr. Brodrick: [[Social Victorians/People/Midleton |St. John Brodrick]] (Lady H. Brodrick is at 362) # [[Social Victorians/People/Connaught | Prince Arthur, Duke of Connaught]] (Princess Louise, Duchess of Connaught is at 9) # [[Social Victorians/People/Princess Victoria of Wales|Princess Victoria of Wales]] # Mademoiselle [[Social Victorians/People/de Courcel |Henriette de Courcel]] (Alphonse de Courcel is at 133; Marie-Elisabeth de Courcel is at 182; Mademoiselle de Courcel is at 498) # Lady [[Social Victorians/People/Jersey|May Julia Child-Villiers]] # Elizabeth Grosvenor Butler, the [[Social Victorians/People/Ormonde |Marchioness of Ormonde]] (Beatrice Butler is at 45; Constance Butler is at 374) # Constance [[Social Victorians/People/Ormonde | Butler]] (Beatrice Butler is at 45; the [[Social Victorians/People/Ormonde |Marchioness of Ormonde]] is at 373) # Mabel, Lady [[Social Victorians/People/Ashburton | Ashburton]] (Francis, Baron Ashburton is at 376) # Francis, Baron [[Social Victorians/People/Ashburton | Ashburton]] (Mabel, Lady Ashburton is at 375) # Lady Archibald [[Social Victorians/People/Argyll | Campbell]] # Mrs. Susannah Wilson [[Social Victorians/People/Arthur Stanley Wilson | Graham Menzies]] (Jack Graham Menzies is at 363) # Mr. Henry [[Social Victorians/People/Henry Chaplin | Chaplin]] (Hon. Edith Helen Chaplin is at 407; Eric Chaplin is at 616) # Sir [[Social Victorians/People/Farquhar |Horace Farquhar]], Bart. (Lady Emilie Farquhar is at 639) # The Right Hon. H. H. (Herbert Henry) [[Social Victorians/People/Asquith | Asquith]] (Margot Asquith is at 217) # Edward Cecil Guiness, [[Social Victorians/People/Iveagh |Lord Iveagh]] (Adelaide Guiness, Lady Iveagh is at 440) # Lady [[Social Victorians/People/Roxburghe#Lady Margaret Innes-Ker and Lady Victoria Innes-Kerr|Victoria Innes-Ker]] (the Duchess of Roxburghe is at 21) # Mr. [[Social Victorians/People/Beit |Alfred Beit]] # Captain [[Social Victorians/People/Holford|George Holford]] # Herr [[Social Victorians/People/Von Andre |Adolf Von André]] (Mrs. Mary Von André is at 289) # Pierre Louis Leopold d'Hautpoul, [[Social Victorians/People/Stonor |Marquis d'Hautpoul]] # Julia Caroline Stonor d'Hautpoul, the [[Social Victorians/People/Stonor |Marquise d'Hautpoul]] # Hon. [[Social Victorians/People/Stonor |Harry Julian Stonor]] # <!-- Unidentified still -->Mrs. [[Social Victorians/People/Adair|Adair]] # Lady [[Social Victorians/People/Meysey-Thompson |Ethel Meysey Thompson]] (Sir Henry Meysey-Thompson is at 116) # Lady [[Social Victorians/People/Sarah Spencer-Churchill Wilson | Sarah Wilson]] (Captain Gordon Wilson is at 96) # Lady [[Social Victorians/People/Cavendish |Edward Cavendish]] # Countess [[Social Victorians/People/Kinsky |Josephine Kinsky]] ([[Social Victorians/People/Clary Aldringen|Countess Thérèse Clary]] is at 191; [[Social Victorians/People/Clary Aldringen|Count Siegfried Clary]] is at 205; Count Charles Kinsky is at 575) # Mary ([[Social Victorians/People/Arthur Stanley Wilson |Mrs. Arthur) Wilson]] # Miss [[Social Victorians/People/Henry James | James]] (Lord James of Hereford is at 122) # [[Social Victorians/People/Oppenheim|Henry Maurice William Oppenheim]] (Mrs. Oppenheim is at 408; Miss Rosalina Oppenheim is at 230) # The Hon. [[Social Victorians/People/Suffield|Bridget Harbord]] (Lord Suffield is at 535; Lady Suffield is at 536) # Candida Hay, [[Social Victorians/People/Tweeddale |Marchioness of Tweeddale]] (the Marquis of Tweeddale is at 400), accompanied by two sons dressed as pages: ## Lord William George Montagu Hay ## Lord Arthur Vincent Hay # William Montagu Hay, the [[Social Victorians/People/Tweeddale |Marquis of Tweeddale]] (The Marchioness of Tweeddale is at 399) # Lady [[Social Victorians/People/Ancaster#Lady Evelyn Ewart|Evelyn Ewart]] (Sir Henry Ewart is at 430) # Lady Hilda FitzRoy, [[Social Victorians/People/Southampton |Baroness Southampton]] (Baron Southampton is at 569) # Lady Muriel [[Social Victorians/People/Ilchester | Fox Strangways]] (Giles Fox-Strangways, Lord Stavordale is at 78) # Lady [[Social Victorians/People/Salisbury |Gwendolen Cecil]] # Lord Alva: [[Social Victorians/People/Alva|Jacobo Fitz-James Stuart y Falcó]] (Carlos Duke Alba is at 32) # [[Social Victorians/People/Somerset|Miss Seymour]] # Miss Chaplin, probably Hon. Edith Helen [[Social Victorians/People/Henry Chaplin | Chaplin]] (Henry Chaplin is at 379; Eric Chaplin is at 616) #Mrs. Openheim: Mrs. [[Social Victorians/People/Oppenheim|Isabella Oppenheim]] (Mr. Henry Oppenheim is at 397; Miss Rosalina Oppenheim is at 230) # Lady [[Social Victorians/People/Warwick |Eva Dugdale]] (Mr. Frank Dugdale is at 348) # Captain [[Social Victorians/People/Spicer |John Spicer]] (Lady Margaret Spicer is at 281) # Lord [[Social Victorians/People/Salisbury |Edward Cecil]] (Edward Herbert [[Social Victorians/People/Salisbury | Gascoyne-Cecil]]) (Lady Edward Cecil is at 102; Lord R. Cecil is at 126). #Mr. C. Wilson: [[Social Victorians/People/Arthur Stanley Wilson|Charles Henry Wilson]] #Mrs. C. Wilson: [[Social Victorians/People/Arthur Stanley Wilson|Florence Wilson]] # Sir [[Social Victorians/People/Henry Irving | Henry Irving]] # Colonel [[Social Victorians/People/Swaine |Charles Edward Swaine]] # Lord Rosslyn: James, 5th [[Social Victorians/People/Forbes|Earl of Rosslyn]] # Lady Rosslyn: Violet, [[Social Victorians/People/Forbes|Countess of Rosslyn]] # Miss Constance [[Social Victorians/People/Ampthill | Russell]] (Lord Ampthill is at 77; Margaret Russell, Lady Ampthill is at 419; Emily, Lady Ampthill is at 420) # Margaret Russell, [[Social Victorians/People/Ampthill |Lady Ampthill]] (Lord Ampthill is at 77) # Emily, [[Social Victorians/People/Ampthill |Lady Ampthill]] (Lord Ampthill is at 77) # Mr. [[Social Victorians/People/Anstruther|Anstruther]] # Mrs. [[Social Victorians/People/Anstruther|Anstruther]] # [[Social Victorians/People/Goschen|Mrs. Goschen]]: Lucy Goschen (G. J. Goschen is at 212\) # [[Social Victorians/People/Goschen|Miss Goschen]] (G. J. Goschen is at 212) # Lord [[Social Victorians/People/Hastings | Hastings]]: George Manners Astley, 20th Baron Hastings (Lady Hastings is at 204) # Florence Chetwynd, [[Social Victorians/People/Florence Rawdon-Hastings Chetwynd |Marchioness of Hastings]] # [[Social Victorians/People/Florence Rawdon-Hastings Chetwynd|Miss Chetwynd]] # Mr. [[Social Victorians/People/Bischoffsheim |Henri Louis Bischoffsheim]] # Mrs. [[Social Victorians/People/Bischoffsheim |Clarissa Bischoffsheim]] # Sir [[Social Victorians/People/Ancaster |Henry Ewart]] (Lady Evelyn Ewart is at at 401) # Lord Jersey: Victor Child-Villiers, 7th [[Social Victorians/People/Jersey | Earl of Jersey]] # Lady Jersey: Margaret Child-Villiers, [[Social Victorians/People/Jersey | Countess of Jersey]] # Lady [[Social Victorians/People/Jersey |Margaret Villiers]] # Lord [[Social Victorians/People/Northampton |Alwyne Frederick Compton]] # Lady [[Social Victorians/People/Northampton |Mary Compton]] # Sir [[Social Victorians/People/Frere|Bartle Frere]] # Winifred Gardner, Lady [[Social Victorians/People/Burghclere | Burghclere]] (Lord Burghclere is at at 129) # Mr. [[Social Victorians/People/Burton|Hamar Bass]] (Lady Harriet Burton is at 334; Lord Michael Burton is at 335; Nellie Baillie is at 667) # [[Social Victorians/People/Burton|Mrs. Louisa Hamar Bass]] (Lady Harriet Burton is at 334; Lord Michael Burton is at 335; Nellie Baillie is at 667) # Adelaide Guiness, [[Social Victorians/People/Iveagh |Lady Iveagh]] (Edward Cecil Guiness, Lord Iveagh is at 382) # Elizabeth [[Social Victorians/People/Gully Selby |Selby Gully]] (William Court Gully is at 153) # Elizabeth Kate Shelley [[Social Victorians/People/Gully Selby | Gully]] (William Court Gully is at 153) # Lord Feversham: William Ernest Duncombe, 1st [[Social Victorians/People/Feversham | Earl of Feversham]] # Lady Feversham: Mabel Duncombe, [[Social Victorians/People/Feversham | Countess Feversham]] # Mr. [[Social Victorians/People/Tedeschi|Tadeschi]] # James McGarel-Hogg, [[Social Victorians/People/Magheramorne|Lord Magheramorne]] (Lady Magheramorne is at 355) # Lord Granby: [[Social Victorians/People/Marion Margaret Violet Lindsay Manners |Henry John Brinsley Manners]] # Lady Granby: [[Social Victorians/People/Marion Margaret Violet Lindsay Manners |Violet Manners]] # Sir Allen [[Social Victorians/People/Young|Young]] # Lady [[Social Victorians/People/Salisbury |R. Cecil]]: Eleanor Lambton [[Social Victorians/People/Salisbury |Gascoyne-Cecil]] (Lord Robert Cecil is at 126) #General Reginald Talbot: General Reginald [[Social Victorians/People/Shrewsbury|Chetwynd-Talbot]] (Mrs. Talbot, Margaret Jane Stuart-Wortley Chetwynd-Talbot is at 485) # Mr. [[Social Victorians/People/Neumann |Ludwig Neumann]] # [[Social Victorians/People/Duncombe|Lady Alicia Duncombe]] # [[Social Victorians/People/Duncombe |Mr. Alfred Duncombe]] (Lady Florence Duncombe is at 456) # George Godolphin Osborne, 10th [[Social Victorians/People/Leeds | Duke of Leeds]] (the duchess is at 35) # [[Social Victorians/People/Duncombe |Lady Florence Duncombe]] (Alfred Duncombe is at 454) # Mrs. [[Social Victorians/People/Williams|Owen Williams]]: Mrs. Nina Williams # Mr. Alexander [[Social Victorians/People/Farquharson | Farquharson]] (Zoë Farquharson is at 338) # Lord Dalkeith: John Charles Montagu Douglas Scott, [[Social Victorians/People/Dalkeith | Earl of Dalkeith]] # Lady Dalkeith: Margaret Montagu-Douglas-Scott, [[Social Victorians/People/Dalkeith | Countess of Dalkeith]] # The [[Social Victorians/People/Euston|Earl of Euston]]: Henry James FitzRoy # Mr. [[Social Victorians/People/Cassel |Ernest Joseph Cassel]] # Lady Cromer: [[Social Victorians/People/Maurice Baring#Edith, Countess Cromer|Edith, Countess of Cromer]] # Sir R. Graham: [[Social Victorians/People/Feversham#Lady Cynthia Graham and Sir Richard Graham|Sir Richard Graham]] (Lady Cynthia Graham is at 220) # [[Social Victorians/People/Brienen|Baron Brienen]] (Miss Brienen is at 259) # [[Social Victorians/People/Brienen|Baroness Brienen]] (Miss Brienen is at 259) #[[Social Victorians/People/Arran|Lady Esther Gore Smith]] # Mr. Beaumont: [[Social Victorians/People/Beaumont|Wentworth Canning Blackett Beaumont]] (Lady Aline Beaumont is at 356) # <!-- Identification uncertain. -->Lady M. Greville: possibly [[Social Victorians/People/Buckingham and Chandos#Mr. and Lady M. Grenville|Lady Mary Grenville]] # <!-- Identification uncertain. -->Mr. Greville: possibly Mr. [[Social Victorians/People/Buckingham and Chandos#Mr. and Lady M. Grenville|Luis Grenville]] # Lady Falmouth: Kathleen Douglas-Pennant Boscawen, [[Social Victorians/People/Falmouth | Viscountess Falmouth]] (Viscount Falmouth is at 172) # Lady Rodney: [[Social Victorians/People/Rodney |Corisande Rodney]] (Lord Rodney is at 80) # Lord W. Stanley: Lord [[Social Victorians/People/Stanley#Lord William Stanley and Lady Alexandra Stanley|Frederick William Stanley]] # <!-- [Unidentified still] -->Lady [[Social Victorians/People/Stanley#Lady W. Stanley|W. Stanley]] # Mr. C. Sykes: Mr. [[Social Victorians/People/Sykes|Christopher Sykes]] # Sir [[Social Victorians/People/Hicks-Beach|M. Hicks-Beach]] # Lady [[Social Victorians/People/Hicks-Beach|Lucy Hicks-Beach]] # Lord Leconfield: Henry Wyndham, [[Social Victorians/People/Wyndham|2nd Baron Leconfield]] # Lady Leconfield: Lady Constance Wyndham, [[Social Victorians/People/Wyndham#Lord and Lady Leconfield|Lady Leconfield]] # Mr. [[Social Victorians/People/Cavendish Bentinck |Arthur James]] (Mrs. [Mary Venetia] Arthur James is at 318) # Mr. R. Beckett: Mr. [[Social Victorians/People/Grimthorpe |Rupert Beckett]] # Muriel Beckett: Mrs. [[Social Victorians/People/Grimthorpe |R. Beckett]] # Mr. [[Social Victorians/People/Grimthorpe |Gervase Beckett]] (Mabel [Mrs. G.] Beckett is at 359) # Lady [[Social Victorians/People/Long |Doreen Long]] (Walter Hume Long is at 117) #Mrs. Talbot: [[Social Victorians/People/Shrewsbury |Margaret Jane Stuart-Wortley Chetwynd-Talbot]] (General Reginald Talbot is at 451) # Miss [[Social Victorians/People/Balfour | Balfour]] (Arthur Balfour is at 86) # <!-- Unidentified still -->Mr. Lu Rack [named in the ''Times'', spelling confirmed] # Millicent, [[Social Victorians/People/Hartopp |Lady Hartopp]] (Sir Charles Hartopp is at 111) # Lady Howe: Isabella,[[Social Victorians/People/Howe | Countess Howe]]) (Viscount Curzon is at 197) # [[Social Victorians/People/Chaine |Maria Chaine]] (William Chaine is at 97) # Mrs. Mary [[Social Victorians/People/Chamberlain | Chamberlain]] (Joseph Chamberlain is at 93; Miss Chamberlain is at 492) # Miss Beatrice (?) [[Social Victorians/People/Chamberlain | Chamberlain]] (Joseph Chamberlain is at 93) # Mr. R. Spencer ([[Social Victorians/People/Spencer|Charles Robert Spencer]]) # Mrs. R. Spencer ([[Social Victorians/People/Spencer|Margaret Baring Spencer]]) # Mr. [[Social Victorians/People/Curzon |George Curzon]] (The Hon. Mrs. George Curzon is at 301) # Lord [[Social Victorians/People/Herschell |Farrer Herschell]] # Lady [[Social Victorians/People/Herschell |Agnes Herschell]] # Mademoiselle [[Social Victorians/People/de Courcel | de Courcel]] (Alphonse de Courcel is at 133; Marie-Elisabeth de Courcel is at 182; Mademoiselle Henriette de Courcel is at 371) # Lady [[Social Victorians/People/Lister-Kaye |Natica (Maria) Lister Kaye]] (Sir John Lister Kaye is at 97) # Lord Milton: Viscount [[Social Victorians/People/Fitzwilliam |Billy Wentworth-Fitzwilliam]] # Lady Milton: [[Social Victorians/People/Fitzwilliam |Maud Wentworth-Fitzwilliam]] # Mr. [[Social Victorians/People/Goelet |Ogden Göelet]] (Mary Goelet, Miss Ogden Göelet is at 228) # Mrs. [[Social Victorians/People/Goelet |May Göelet]] (Mary Goelet, Miss Ogden Göelet is at 228) # Mr. [[Social Victorians/People/Cork and Orrery|W. Boyle]] # Mrs. Hartman: possibly Mrs. [[Social Victorians/People/Hartmann|Eliza Hartmann]] #Mr. [[Social Victorians/People/Rothschild Family#Mr. Lewis Flower|Lewis Flower]] #Major Drummond: [[Social Victorians/People/Drummond|Laurence Drummond]] # Miss Hay: [[Social Victorians/People/John Milton Hay |Helen Hay]] (Clara Stone Hay is at 154; John Milton Hay is at 187) # Hon. Mr. [[Social Victorians/People/Grosvenor#Hon. Catherine and Mr. Algernon Grosvenor|Algernon Grosvenor]] (family of the [[Social Victorians/People/Grosvenor|Baron of Ebury]]) # Mrs. [[Social Victorians/People/Grosvenor#Hon. Catherine and Mr. Algernon Grosvenor|Algernon (Catherine) Grosvenor]] (family of the [[Social Victorians/People/Grosvenor|Baron of Ebury]]) # The Marquis of Londonderry: Charles Vane-Tempest-Stewart, the [[Social Victorians/People/Londonderry | Marquis of Londonderry]] (the Marchioness of Londonderry is at 42) # Henry Strutt, [[Social Victorians/People/Belper | Baron Belper]] # Margaret, [[Social Victorians/People/Belper | Lady Belper]] # [[Social Victorians/People/Belper |Hon. Miss Strutt]], probably Norah Strutt (Margaret, Lady Belper is at 560) # Wilhelmina Giffard, Lady [[Social Victorians/People/Halsbury | Halsbury]] (Lord Halsbury is at 147) # The [[Social Victorians/People/Leicester|Countess of Leicester]]: Georgina Cavendish Coke # Lord Carnarvon: George Herbert, [[Social Victorians/People/Carnarvon|5th Earl of Carnarvon]] # Lady Carnarvon: Almina, [[Social Victorians/People/Carnarvon|Countess Carnarvon]] # Captain Warrender: [[Social Victorians/People/Warrender |George John Scott Warrender]] (Lady Maud Warrender is at 520) # Lady [[Social Victorians/People/Warrender |Maud Warrender]] (Captain George Warrender is at 519) # Major [[Social Victorians/People/Dawson |Vesey Dawson]] # Mr. [[Social Victorians/People/Walsh|Arthur Walsh]] # Lady [[Social Victorians/People/Walsh|Clementine Walsh]] # Lady Harewood: Florence Lascelles, [[Social Victorians/People/Harewood |Lady Harewood]] (the Earl of Harewood is at 62) # Francis, [[Social Victorians/People/Warwick | Earl of Warwick]] (Daisy, Countess of Warwick is at 53) # Lord [[Social Victorians/People/Buccleuch#Lord George Scott|George Scott]] # Mr. [[Social Victorians/People/Rothschild Family#Leopold de Rothschild and Marie Perugia Rothschild|Leopold Rothschild]] (Marie Perugia [Mrs. Leopold] Rothschild is at 528) # Mrs. L. ([[Social Victorians/People/Rothschild Family#Leopold de Rothschild and Marie Perugia Rothschild|Marie Perugia) Rothschild]] (sons Evelyn Achille de Rothschild, at 669, and Anthony Gustav de Rothschild, at 670) # Lawrence John Lumley Dundas, [[Social Victorians/People/Zetland | Earl of Ronaldshay]] #Mr. Brassey, [[Social Victorians/People/Brassey|Henry Leonard Campbell Brassey]] # [[Social Victorians/People/Brassey|Lady Violet Brassey]] # Mr. [[Social Victorians/People/Duberly|Grey Duberly]] # (Mr. R.) [[Social Victorians/People/Reuben David Sassoon | Reuben David Sassoon]] # [[Social Victorians/People/Reuben David Sassoon |Miss Sassoon]] # Charles, [[Social Victorians/People/Suffield|Lord Suffield]] # Cecilia, [[Social Victorians/People/Suffield|Lady Suffield]] # [[Social Victorians/People/Peel Family |Miss Peel]] (Arthur Wellesley Peel, 1st Viscount Peel is at 74; other family members are on the same page) # Lady Suffolk: Mary, [[Social Victorians/People/Suffolk|Countess of Suffolk]] (Henry, Earl of Suffolk is at 203) # The [[Social Victorians/People/Phipps|Hon. Harriet Phipps]] # The [[Social Victorians/People/Scarbrough|Earl of Scarbrough]] # Lady [[Social Victorians/People/Wolseley |Louisa Wolseley]] (Viscount Garnet Wolseley is at 171; Miss Frances Wolseley is at 542) # Miss Wolseley: [[Social Victorians/People/Wolseley |Frances Wolseley]] (Viscount Wolseley is at 171; Lady Louisa Wolseley is at 541) # Lady Ottoline [[Social Victorians/People/Cavendish Bentinck|Cavendish-Bentinck]] (Lord Henry Cavendish Bentinck is at 262; Lady Olivia Cavendish Bentinck is at 263) # Lady Minto: Mary Caroline Grey Elliot-Murray-Kynynmound, [[Social Victorians/People/Minto | Countess Minto]] # [[Social Victorians/People/Crawford and Balcarres|Lord Balcarres]]: David Alexander Edward Lindsay, Lord Balcarres # Sir [[Social Victorians/People/Poynter|Edward Poynter]] # Lady [[Social Victorians/People/Beauchamp |Mary Lygon]] (with Charles Cust, at 152, attended the Duke and Duchess of York) # Mr. B. Bathurst: Mr. [[Social Victorians/People/Bathurst#Mr. B. Bathurst|Benjamin Bathurst]] # Mr. [[Social Victorians/People/Portal |William Portal]] # Mrs. [[Social Victorians/People/Portal |Florence Portal]] # Lady Susan Mary Elizabeth ([[Social Victorians/People/Stanley | Stanley]]) [[Social Victorians/People/Jeune | Jeune]] (Sir Francis Jeune is at 315) # Miss Stanley: [[Social Victorians/People/Stanley#Madeline Stanley|Madeline Cecilia Carlyle Stanley]] (accompanying Sir Francis Jeune, at 314, and Lady Jeune, at 550) # Mr. [[Social Victorians/People/Arthur Sassoon | Arthur Sassoon]] (Louise [Mrs. Arthur] Sassoon is at 201) # Lady [[Social Victorians/People/Ellesmere |Mabel Egerton]] (with her father, the Earl of Ellesmere, at 68) # [[Social Victorians/People/Dyke|Sir W. Hart Dyke]] # [[Social Victorians/People/Dyke|Lady Emily Hart Dyke]] # Beatrix Palmer, [[Social Victorians/People/Selborne |Lady Selborne]] (the Earl of Selborne is at 70) #Prince [[Social Victorians/People/Duleep Singh |Victor Duleep Singh]] #Blanche, [[Social Victorians/People/Coventry | Countess of Coventry]] #Lady [[Social Victorians/People/Coventry |Anne Coventry]] #Lady [[Social Victorians/People/Coventry |Dorothy Coventry]] # Mr. [[Social Victorians/People/Hughes-Onslow|Somerset Hughes-Onslow]] # [[Social Victorians/People/Arthur|Sir George Arthur]] # Henry Pelham-Clinton,[[Social Victorians/People/Newcastle | Duke of Newcastle]] (the Duchess is at 150) # The [[Social Victorians/People/Dupplin#Hon. and Mrs. Claude Hay|Hon. Claude Hay]] # <!-- Unidentified still -->Mrs. Hay, attending with the [[Social Victorians/People/Dupplin#Hon. and Mrs. Claude Hay|Hon. Claude Hay]] #Monsieur [[Social Victorians/People/Baudon de Mony |Xavier Baudon de Mony]] #Madame [[Social Victorians/People/Baudon de Mony |de Courcel Baudon de Mony]] # Charles FitzRoy, [[Social Victorians/People/Southampton | Baron Southampton]] (Hilda FitzRoy, Lady Southampton is at 402) # Captain Gerard [[Social Victorians/People/Leigh | Leigh]] (Mrs. Marion Leigh is at 308) # Lady [[Social Victorians/People/Marlborough |Lilian Maud Spencer-Churchill]] # Lady [[Social Victorians/People/Marlborough |Norah Beatrice Henriette Spencer-Churchill]] # François, [[Social Victorians/People/De Jancourt|Marquis de Jancourt]] # Victoria Lina, [[Social Victorians/People/De Jancourt|Marchioness de Jancourt]] # [[Social Victorians/People/Kinsky | Count Charles Kinsky]] ([[Social Victorians/People/Clary Aldringen|Count Siegfried Clary]] is at 205; [[Social Victorians/People/Clary Aldringen|Countess Thérèse Clary]] is at 191; [[Social Victorians/People/Kinsky|Countess Josephine Kinsky]] is at 394) # Captain [[Social Victorians/People/Camden#Captain and Mrs. Philip Green|Philip Green]] # Mrs. [[Social Victorians/People/Camden#Captain and Mrs. Philip Green|Philip (Mabel) Green]] # [[Social Victorians/People/Montagliari|Marquis Paulac Montagliari]] # Mr. [[Social Victorians/People/Lyttelton |Alfred Lyttelton]] # Mrs. [[Social Victorians/People/Lyttelton |Edith Sophy Balfour Lyttelton]] # Lord William [[Social Victorians/People/Marlborough|Beresford]] (Lily, [[Social Victorians/People/Marlborough|Duchess of Marlborough]] is at 193) # Lord [[Social Victorians/People/Hamilton Temple Blackwood|Basil Blackwood]] # Mr. [[Social Victorians/People/Walker |Hall Walker]] # Mrs. [[Social Victorians/People/Walker |Sophie Walker]] # Lord Bingham: [[Social Victorians/People/Lucan |George Charles Bingham]] # Lady Bingham: [[Social Victorians/People/Lucan |Violet Bingham]] # [[Social Victorians/People/Farquhar#Mr. and Mrs. Almeric FitzRoy|Mr. Almeric FitzRoy]] # [[Social Victorians/People/Farquhar#Mr. and Mrs. Almeric FitzRoy|Mrs. Almeric (Katherine) FitzRoy]] #Colonel [[Social Victorians/People/Shrewsbury |Talbot]] (many Talbots attended; these are Chetwynd-Talbots) #Mrs. [[Social Victorians/People/Shrewsbury | Talbot]] (attending with Colonel Talbot) # Lord [[Social Victorians/People/Wilbraham Egerton of Tatton | Wilbraham Egerton of Tatton]] (Anne, Duchess of Buckingham is at 155) # Lady Gore-Langton: Lady Caroline Jemima Elizabeth [[Social Victorians/People/Buckingham and Chandos | Gore-Langton]] # Sir [[Social Victorians/People/Blois |Ralph Blois]] # [[Social Victorians/People/Mills|Lord Hillingdon]]: Charles Henry Mills, 1st Baron Hillingdon of Hillingdon # [[Social Victorians/People/Mills|Lady Hillingdon]]: Lady Louisa Isabella Lascelles Mills, Baroness Hillingdon # Miss Mills: the [[Social Victorians/People/Mills|Hon. Violet Mills]] # Charlotte, [[Social Victorians/People/Cole|Countess of Enniskillen]] (Lowry, Earl of Enniskillen is at 208; Lady Florence Cole is at 239) # Sir M. FitzGerald: Sir [[Social Victorians/People/Fitzgerald |Maurice FitzGerald]] # Lady FitzGerald: [[Social Victorians/People/Fitzgerald |Amelia Lady, FitzGerald]] # Mr. [[Social Victorians/People/Watson|Meyer Watson]] (identification highly uncertain) # The [[Social Victorians/People/Marlborough|Marchioness of Blandford]]: Albertha Spencer-Churchill # John Blundell [[Social Victorians/People/Leigh | Leigh]] (Lady Rose Leigh is at 337; Mrs. Marion Leigh is at 308; Captain Gerard Leigh is at 570) # Hon. Mr. Reginald Baliol [[Social Victorians/People/Brett | Brett]] # Hon. Mrs. Eleanor [[Social Victorians/People/Brett | Brett]] # Mr. [[Social Victorians/People/Rothschild Family |Alfred Rothschild]] #Florence, [[Social Victorians/People/Dunraven|Countess of Dunraven]] (Windham, [[Social Victorians/People/Dunraven|Earl of Dunraven]] is at 198) # Algernon Keith-Falconer, 9th [[Social Victorians/People/Kintore | Earl of Kintore]] (Sydney, Countess Kintore is at 607; Lady Hilda Madeleine Keith-Falconer is at 677) # Sydney, [[Social Victorians/People/Kintore | Countess Kintore]] # [[Social Victorians/People/Salmon|Mr. Arthur Salmon]] # [[Social Victorians/People/Salisbury|Lord Cranborne]]: James Edward Hubert Gascoyne-Cecil, [[Social Victorians/People/Salisbury|Viscount Cranborne]] (Lady Cranborne is at 196) # <!-- Identification uncertain. -->[[Social Victorians/People/Marlborough#Lord Churchill|Lord Churchill]] # Mr. H. Milner: [[Social Victorians/People/Milner|Harry (Marcus Henry) Milner]] # Mr. [[Social Victorians/People/Strong|Arthur Strong]] # [[Social Victorians/People/Peel Family|Captain R. Peel]] # [[Social Victorians/People/Tilney|Mr. Tilney]] # Mr. Eric [[Social Victorians/People/Henry Chaplin | Chaplin]] (Henry Chaplin is at 379; Hon. Edith Helen Chaplin is at 407) #Captain G. Milner: Captain [[Social Victorians/People/Milner|George Francis Milner]] # Lord [[Social Victorians/People/Westminster#Lord Gerald Grosvenor|Gerald Grosvenor]] (family of the [[Social Victorians/People/Westminster|Duke of Westminster]]) # Lord [[Social Victorians/People/Westminster#Lord Arthur Grosvenor|Arthur Grosvenor]] (family of the [[Social Victorians/People/Westminster|Duke of Westminster]]) # [[Social Victorians/People/Bagot|Lord William Bagot]] # John Campbell, [[Social Victorians/People/Princess Louise | Marquis of Lorne]], as a Tudor (Princess Louise, Marchioness of Lorne, is at 130) # Miss [[Social Victorians/People/Argyll |Elspeth Campbell]] # Lord Algernon [[Social Victorians/People/Gordon-Lennox | Gordon Lennox]] (Lady Blanche Gordon Lennox is at 333) # The [[Social Victorians/People/Sutherland | Duke of Sutherland]] (the Duchess of Sutherland is at 32) # [[Social Victorians/People/Burghclere#Mr. and Mrs. Alan Gardner|Colonel Alan Gardner]] # [[Social Victorians/People/Burghclere#Mr. and Mrs. Alan Gardner|Mrs. Alan Gardner]]: Mrs. Nora Gardner # [[Social Victorians/People/Lansdowne#Edmond and Lady Caroline Fitzmaurice|Edmond FitzMaurice]] (Lady C. FitzMaurice is at 364) # <!-- Still unidentified. -->The [[Social Victorians/People/Durham|Hon. Cecil Lambton]] # Lady Clementine [[Social Victorians/People/Tweeddale | Hay]] (William Hay, Marquis of Tweeddale is at 399; Candida Hay, Marchioness of Tweeddale is at 398) # Miss Tufnell: Gian, [[Social Victorians/People/Mount Stephen|Lady Mount Stephen]] #Mademoiselle [[Social Victorians/People/de Alcalo Galiano | de Alcalo Galiano]] # Mademoiselle [[Social Victorians/People/de Alcalo Galiano |Consuelo de Alcalo Galiano]] # Jesusa Murrieta del Campo Mello y Urritio (née Bellido), [[Social Victorians/People/Santurce | Marquisa de Santurce]] # Mr. F. Murrieta: possibly Don José Murrieta del Campo Mello y Urritio, [[Social Victorians/People/Santurce|Marques de Santurce]] # The Hon. Mrs. Reginald Fitzwilliam: Edith Isabella Georgina [[Social Victorians/People/Fitzwilliam | Wentworth Fitzwilliam]] #The Hon. Reginald Fitzwilliam: Hon. Reginald [[Social Victorians/People/Fitzwilliam | Wentworth Fitzwilliam]] # Lady Florence [[Social Victorians/People/Hamilton Temple Blackwood | Hamilton-Temple-Blackwood]] # Lord Terence [[Social Victorians/People/Hamilton Temple Blackwood | Hamilton-Temple-Blackwood]] # Lady [[Social Victorians/People/Farquhar |Emilie Farquhar]] (Sir Horace Farquhar, Bart., is at 380) # Geraldine ([[Social Victorians/People/Magniac |Sybil Aimée Geraldine) Magniac]] # Lord [[Social Victorians/People/Saint Oswald | St. Oswald]] (Lady St. Oswald is at 284) # The Hon. [[Social Victorians/People/Saint Oswald |Maud Julia Winn]] (with Lord and Lady St. Oswald, her mother, at 284) # Alice Emily White Coke, [[Social Victorians/People/Leicester | Viscountess Coke]] # Lady [[Social Victorians/People/Leicester|Mabel Coke]] # Lady [[Social Victorians/People/Stanley |Isobel Constance Mary Stanley]] # Lord Crichton: Henry William Crichton, [[Social Victorians/People/Crichton|Viscount Crichton]] # <!-- Unidentified still. -->Mr. [[Social Victorians/People/Crichton|Herbert Creighton]] # Lady [[Social Victorians/People/Pembroke |Beatrix Herbert]] (Beatrix Countess Pembroke is at 146; Sidney Herbert, Earl Pembroke is at 181) # Lt.-Col. John Dunville [[Social Victorians/People/Dunville | Dunville]] # Mrs. Violet [[Social Victorians/People/Dunville | Dunville]] # [[Social Victorians/People/Knollys#Miss Knollys|Miss Charlotte Knollys]] (attending Prince and Princess Charles of Denmark, at 159 and 144) # Mrs. Claud Cole-Hamilton: Lucy [[Social Victorians/People/Cole-Hamilton |Charlewood Cole-Hamilton]] # Claud George [[Social Victorians/People/Cole-Hamilton | Cole-Hamilton]] #General Ellis: Gen. Sir [[Social Victorians/People/Ellis#Major-General Ellis|Arthur Edward Augustus Ellis]], in attendance on Prince Charles of Denmark (at 143) # Miss [[Social Victorians/People/Ellis#Miss Alexandra Ellis|Alexandra Ellis]] # Frederick Oliver Robinson, [[Social Victorians/People/Ripon#Frederick Oliver Robinson, Earl de Grey|Earl de Grey]] (Gwladys Robinson, Countess de Grey is at 136) # James Albert Edward Hamilton, [[Social Victorians/People/Abercorn|Marquis of Hamilton]] # Mr. [[Social Victorians/People/Shaftesbury|W. W. Ashley]] #Lady [[Social Victorians/People/Durham|Anne Lambton]] #Captain [[Social Victorians/People/Durham|Hedworth Lambton]] # Lady [[Social Victorians/People/Dunraven |Aileen May Wyndham-Quin]] # Colonel [[Social Victorians/People/Burton|James Evan Bruce Baillie of Dochfour]] # [[Social Victorians/People/Burton|Nellie Bass Baillie]], Hon. Mrs. Baillie (Lady Harriet Burton is at 334) # Miss [[Social Victorians/People/Burton#Jane Thornewill|Jane Thornewill]] (or Miss Jane Thornville) # [[Social Victorians/People/Harcourt |Lewis Harcourt]] (Lady Elizabeth Harcourt is at 94; Sir William Harcourt is at 128) # [[Social Victorians/People/Portland#George Cavendish-Bentinck|George (William George) Cavendish-Bentinck]] # Mrs. Sneyd: [[Social Victorians/People/Sneyd|Mary Evelyn Ellis Sneyd]] # [[Social Victorians/People/Cadogan|Hon. Mrs. Cadogan]] #[[Social Victorians/People/Rothschild Family#Evelyn and Anthony de Rothschild|Evelyn Achille de Rothschild]] (Marie de Rothschild, his mother, at 527) # [[Social Victorians/People/Rothschild Family#Evelyn and Anthony de Rothschild|Anthony Gustav de Rothschild]] (Marie de Rothschild, his mother, at 527) # Mr. [[Social Victorians/People/Wombwell |Stephen Frederick Wombwell]] # The Hon. Mrs. Gwendoline [[Social Victorians/People/Lowther | Lowther]] # Col. [[Social Victorians/People/Dawson |Douglas Dawson]] # Louisa Montefiore, [[Social Victorians/People/Rothschild Family#Louisa, Lady de Rothschild|Lady de Rothschild]] # Hon. [[Social Victorians/People/Maurice Baring|John Baring]] # Hon. [[Social Victorians/People/Antrim |Alexander McDonnell]] # Lady [[Social Victorians/People/Kintore |Hilda Madeleine Keith-Falconer]] (Algernon Keith-Falconer, 9th Earl of Kintore is at 607) # [[Social Victorians/People/Maurice Baring|Hon. Maurice Baring]] # Hon. [[Social Victorians/People/Peel Family|W. G. Peel]] # Rose Towneley-Bertie, [[Social Victorians/People/Norreys | Lady Norreys]] # Major John Seymour [[Social Victorians/People/Peel Family | Wynne-Finch]] # Marie (Agnes Blanche Marie) [[Social Victorians/People/Dupplin | Hay-Drummond]] # Sir [[Social Victorians/People/Hamilton |Edward Walter Hamilton]] # Daisy (Marguerite Hyde) [[Social Victorians/People/Suffolk |Leiter]] # [[Social Victorians/People/Lukach |Joseph Harry Lukach]] # [[Social Victorians/People/William James | William Dodge James]] (Evelyn Forbes James is at 364) # Mrs. [[Social Victorians/People/Murray|Graham Murray]] # <!-- 688 Still unidentified. -->Mrs. Habington (mentioned as part of Queen Elizabeth's court by the ''Gentlewoman''.<ref name=":42" />{{rp|32, Col. 3c}} There is no doubt about the spelling in the ''Gentlewoman'' article.) # <!-- Unidentified still. -->Mr. [[Social Victorians/People/Longhurst|P. A. Longhurst]] #<!-- Unidentified still. -->Mr. [[Social Victorians/People/Foley|Foley]] #Carlo Ermes Visconti, [[Social Victorians/People/San Vito|Marquis of San Vito]] #[[Social Victorians/People/Malcolm|Mr. Ian Malcolm]], M.P. #Mr. E. [[Social Victorians/People/Crawley|Crawley]] #Mr. W. R. Chaine: Mr. [[Social Victorians/People/Chaine#Mr. W. R. Chaine|William Robert Chaine]] #The Hon. [[Social Victorians/People/Campbell|K. Campbell]] #The Hon. [[Social Victorians/People/Mar and Kellie|William Erskine]] #<!-- Highly uncertain ID -->Mr. [[Social Victorians/People/Carter|J. Carter]] #<!-- Still unidentified. -->Lord [[Social Victorians/People/Hamilton Temple Blackwood|J. Blackwood]] #<!-- Still unidentified. -->Lady [[Social Victorians/People/Hamilton Temple Blackwood|J. Blackwood]] #<!-- Still unidentified. -->[[Social Victorians/People/Cavendish |Mr. S. Cavendish]], possibly Mr. R. Cavendish (at 107) #<!-- 719 -->A "brother officer" of the [[Social Victorians/People/Roxburghe|Duke of Roxburghe]] in the Royal Horse Guards (see Fanny Marjoribanks, Lady Tweedmouth, at 85; the Duke of Roxburghe is at 49). #<!-- 720 -->A second "brother officer" of the [[Social Victorians/People/Roxburghe|Duke of Roxburghe]] in the Royal Horse Guards (see Fanny Marjoribanks, Lady Tweedmouth, at 85; the Duke of Roxburghe is at 49). #<!-- unidentified still? -->Mr. Bourke (the Hon. A. Bourke is at 235) #<!-- Unidentified still? -->Mrs. Bourke (the Hon. Mrs. A. Bourke is at 236) ===Attendants of the People Who Were Present=== A number of people present at the ball were not invited in their own right and were there as attendants. Listed in the descriptions of the people at the ball and their costumes are some people who were clearly there as attendants: # "Black attendants" followed the Court in the Empress Catherine II of Russia procession, preceding the Italian procession.<ref name=":0" /><ref name=":2">"Ball at Devonshire House." The ''Times'' Saturday 3 July 1897: 12, Cols. 1A–4C ''The Times Digital Archive''. Web. 28 Nov. 2015.</ref> # There were unnamed Imperial Trumpeters in the Court in the Empress Catherine II of Russia procession. They had to really be able to play the trumpet so perhaps were hired musicians? # Heralds led the Queen Elizabeth Procession, but they are not named, so they were probably not invited guests but servants or attendants of some kind? # According to the Leamington ''Spa Courier'', the Countess of Warwick's "four pages shared in the compliments."<ref>“Town Talk and Street Echoes.” ''Leamington Spa Courier'' 10 July 1897, Saturday: 5 [of 8], Col. 4B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000319/18970710/015/0005.</ref> According to the Guernsey ''Star'', Lady Warwick "was accompanied by four boys dressed in white satin, with three-cornered hats to match."<ref name=":1">"Duchess of Devonshire's Fancy-Dress Ball. Brilliant Spectacle." The [Guernsey] ''Star'' 6 July 1897, Tuesday: 1 [of 4], Col. 1–2. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000184/18970706/003/0001.</ref> # The Marchioness of Tweeddale also had two pages: "The Marchioness of Tweeddale was Joséphine, wife of Napoleon, in white satin, wrought with gold and a deep rose-coloured train, trimmed with ermine, and borne by two pages in mauve velvet, embroidered with gold."<ref name=":1" /> # Princess Henry of Pless had black and white pages: "As the Queen of Sheba, Princess Henry of Pless was attended by five black pages and five white, in gorgeous dresses, who carried her train."<ref name=":1" /> In the large list of people who were present for the ball, above, attendants are listed with the people for whom they worked; typically royals had attendants with them. ====Attendants of Color==== Clearly, some of these attendants were black people (especially at 1 and 6). The vocabulary the newspapers used ranged from "Black" to "Negro" to the actual n-word (for American Minnie Paget?). The Aberdeen ''Journal'' of 4 August 1897 ran a story, "Black Boys for London Ladies," that refers to the black attendants at the Duchess of Devonshire's ball: :Titian’s pictures (says London correspondent) have made us familiar with black boys forming part of the train of certain great ladies. The Prince of Wales brought a Nubian boy home, and for a time he was in the Marlborough House and Sandringham households. The Duchess of Marlborough is very often accompanied by a black boy in Oriental scarlet and gold, who seems '''but live''' to obey her grace’s behests; for his dark, piercing eyes follow her every movement, giving him a weird look, which is increased by the curious incision in his cheeks. At the Devonshire House fancy ball the glory of the great Oriental procession was much increased by the Nubian boys, who carried palm-leaves over some of the queenly heads.<ref>"Black Boys for London Ladies." ''Aberdeen Journal'' Wednesday 4 August 1897: 6 [of 8], Col. 5C. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000032/18970804/130/0006.</ref> We need to know more about these children. ==People Absent== The ''London Daily News'' and the ''Times'' reported as attending Lady Hindlip, who was not able to attend, according to the ''Morning Post'', suggesting that they may have gotten a list of people attending from something other than onsite reportage, perhaps from someone describing the costumes that had been made. Of the people who were not present but seem missing because their immediate family, for example, was present, some are women, the wives of the people named. So perhaps they did not court newspaper attention? Of the men who might have been there, logically, perhaps they did not dress in costume and thus did not receive mention? (We know some men attended the ball and were not in fancy dress.) # Samuel Allsopp, [[Social Victorians/People/Hindlip|Lord Hindlip]] and Georgina Allsopp, [[Social Victorians/People/Hindlip|Lady Hindlip]] were not present because Lord Hindlip was ill and died less than two weeks later. # Colonel Brabazon "unavoidably prevented" from attending.<ref>"The Queen's Sympathy." ''Morning Post'' Monday 05 July 1897: 7 [of 12], Col. 5B. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970705/070/0007.</ref> # Mrs. Hwfa Williams was reported in the Morning Post not to have attended because she was in mourning.<ref>“Arrangements for This Day.” ''Morning Post'' 2 July 1897, Friday: 5 [of 10], Col. 7B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970702/038/0005.</ref> Owen's and Hwfa Williams' sister Edith Peers-Williams had died. Although General or Mr. Owen Williams is not listed as having attended, his wife Mrs. Nina Williams (at 457) was said to have been present, but really it seems most likely that none of them attended. # Fanny Ronalds was there, but Arthur Sullivan's name is not listed; was he there but not in an interesting costume? Or not present? # Lady [[Social Victorians/People/de Trafford|Violet de Trafford]] was there (at 238, above), but her husband? or son?, Sir Humphrey Francis de Trafford, 3rd Baronet, is not listed. # Mrs. Henry White isn't listed as present, but Mr. Henry White is at 310, and Margaret "Daisy" Stuyvesant Rutherford White is now at 151. I believe she was present because both Whites were photographed in costume and that photograph is in the album at the NPG. # Even though Henry Maurice William Oppenheim and his daughter, Rosalinda Oppenheim were present, Mrs. Isabel Georgina Oppenheim (who does not appear to have been Rosalinda's mother) is not listed anywhere as being present. # Jesusa Murrieta del Campo Mello y Urritio (née Bellido), [[Social Victorians/People/Santurce|Marquisa de Santurce]] attended the Duchess of Devonshire's fancy-dress ball at Devonshire House. Mr. [[Social Victorians/People/Santurce|F. Murrieta]] (at 708) was present according to ''The Gentlewoman'', but who was he? Her husband, José Murrieta y del Campo Downey, 1st Marques de Santurce, is not listed as having been present although he was still alive. Possibly the F. is a mistake on the part of The Gentlewoman, and it was Don José who was there? # Baron [[Social Victorians/People/Gerard|William Cansfield Gerard]], Lady [[Social Victorians/People/Gerard|Mary Gerard]]'s husband: she was present (at 256) and represented in the album, but he's not mentioned. Was he there? # The Hon. Mrs. [[Social Victorians/People/Lowther|Gwendoline Lowther]] (at 672), was present, but her husband, whose brother was Hugh Cecil Lowther, 5th Earl of Lonsdale and who would be later in his own right, was not? # Rosamond Fellowes, [[Social Victorians/People/de Ramsey|Lady de Ramsey]] (at 329) was present, but William Fellowes, Baron de Ramsey was not? # Florence Canning, [[Social Victorians/People/Garvagh|Lady Garvagh]] (at 336) attended the ball. Where was Charles Canning, Lord Garvagh? Did he just not get mentioned? # Nellie, Countess of Kilmorey (at 207) attended the ball, but Francis Needham, Earl of Kilmorey did not? # Prince Leopold's wife, Helena, Duchess of Albany wasn't there? # Princess Beatrice didn't go? # [[Social Victorians/People/Bathurst|Lilias Bathurst]] is not listed has having attended the Duchess of Devonshire's ball, although her husband [[Social Victorians/People/Bathurst|Henry Bathurst, 7th Earl of Bathurst]], her parents [[Social Victorians/People/Borthwick|Algernon Borthwick, Lord Glenesk]] and [[Social Victorians/People/Borthwick|Alice, Lady Glenesk]] and her brother [[Social Victorians/People/Borthwick|Oliver Borthwick]] were there. A child was not born to her in 1897 as far as I can tell, although we may not be able to know about a miscarriage. Perhaps she was present and not reported on. # Mrs. [[Social Victorians/People/Loder|Louise Loder]] is not listed among the attendees at the ball; was she there and just not reported on? No child was born that year, but she was bearing children during this time. Gerald Loder is at 100. #Was [[Social Victorians/People/Talbot|Lady Mary Bertie Talbot]] at the ball? She is not mentioned. She isn't likely to be Mrs. Talbot because her father was an Earl? She would have been Lady Talbot? #Was [[Social Victorians/People/Hope-Vere|James Charles Hope-Vere]] present at the ball and just not mentioned? Marie Hope-Vere was not mentioned in the press, so without the Album of portraits of people in their costumes in the National Portrait Gallery, we might not know about her. #Did [[Social Victorians/People/Colebrooke|Ned (Edward Arthur) Colebrooke]] attend the ball? Alexandra Paget Colebrooke (at 246) did. #Was [[Social Victorians/People/Heeren|Countess Arthur de Heeren]] at the ball and not reported on? #Mrs. Margaret Greville (298) was there; was Ronald Greville but not mentioned in reports? #The wife of [[Social Victorians/People/Ephrussi|M. Ephrussi]], whichever one attended, is not mentioned as having been present; perhaps she was there but not recognized or described? #"The little daughter of Sir Francis and Lady Knollys"<ref name=":42">“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.</ref>{{rp|32, Col. 2a}} attended, as did her aunt, Hon. Charlotte Knollys, but were her parents not there? Francis Knollys was the Prince of Wales's private secretary at this point, as well as holding a number of other courtier positions in the Household at the same time. #Carlo Ermes Visconti, [[Social Victorians/People/San Vito|Marquis of San Vito]] (at 691) was present; was his wife? #If the Lord Churchill (at 610) is [[Social Victorians/People/Marlborough#Lord Churchill|Lord Edward Spencer-Churchill]], did his wife Lady Augusta Spencer-Churchill also attend? #Neither the [[Social Victorians/People/Leicester|Earl of Leicester]] nor [[Social Victorians/People/Leicester|Viscount Coke]] are listed as having attended the ball, but did they? #[[Social Victorians/People/Sneyd|Mary Evelyn Ellis Sneyd]] was present at the ball; where was Ralph de Tunstall Sneyd? #[[Social Victorians/People/Murray|Mary Graham Murray]] was present at the ball: where was Andrew Graham Murray? #Mr. [[Social Victorians/People/Strong|Arthur Strong]] was at the ball; was Eugénie Sellers, whom he married less than 6 months later? #Miss [[Social Victorians/People/Naylor|Mary Naylor]]'s sister, Mettie Lady Rossmore, is not listed as having attended the ball; where was she? #Was Juliette Gordon Low, wife of Mr. [[Social Victorians/People/Lowe|W. M. Low]], present and just not mentioned? #Was Maria del Rosario Falcó y Osorio, wife of [[Social Victorians/People/Alva|Carlos Duke of Alba]], present but not mentioned? #[[Social Victorians/People/Maurice Baring#Edith, Countess Cromer|Edith, Countess of Cromer]] (at 462) attended, but Evelyn, Earl of Cromer is not listed. He seems likely to have attended if she did? #Isabella, [[Social Victorians/People/Howe|Countess Howe]] (at 489) was present, but Richard, Earl Howe is not mentioned in any reports. Was he there? #Charles, [[Social Victorians/People/Carrington|Earl Carington]] was present, but his wife Cecilia, Countess Carington is not mentioned in any reports. Was she there? #If [[Social Victorians/People/Wyndham#Mr. George Wyndham|Mr. George Wyndham]] (at 221) is the Right Hon. George Wyndham, who married Sibell Mary [[Social Victorians/People/Scarbrough|Lumley]] Grosvenor, then was she at the ball? Her nephew Alfred Lumley, [[Social Victorians/People/Scarbrough|10th Earl Scarbrough]] attended. #Sir [[Social Victorians/People/Poynter|Edward Poynter]] (at 546) was at the ball, so where was Agnes Poynter? She attended other social events at this level with him. #Rose Towneley-Bertie, [[Social Victorians/People/Norreys|Lady Norreys]] was present at the ball, but Montagu Towneley-Bertie, [[Social Victorians/People/Norreys|Lord Norreys]] was not? #If [[Social Victorians/People/Reuben David Sassoon#Reuben David Sassoon|Reuben David Sassoon]] was at the ball, was his wife, Kate (Catherine Ezekiel) Sassoon? #Gilbert, [[Social Victorians/People/Minto#Mary, Countess of Minto|Earl of Minto]] was still alive; was he at the ball? #Anne Antrobus Elliot, wife of [[Social Victorians/People/Minto#The Right Hon. Henry George Elliot|Henry George Elliot]] (at 279), was still alive at this time; did she attend the ball? #George, [[Social Victorians/People/Coventry|Earl of Coventry]] was still alive at this point, and his wife and two daughters attended the ball. Where was he? #Sir [[Social Victorians/People/Fortescue|Seymour Fortescue]]'s wife Emily Ormsby-Gore Fortescue is not mentioned. Was she at the ball? #Was Lady [[Social Victorians/People/Kintore|Ethel Sydney Keith-Falconer]] at the ball? Her parents and younger sister were, assuming the Album's information is correct. #Neither [[Social Victorians/People/Norreys|Rose, Lady Norreys]] (at 680) nor Montagu, Lord Norreys was mentioned in any press reports, but her portrait was in the commemorative album of portraits. Was he present and just not mentioned? == Notes and Questions == # According to the ''Western Gazette'', three men dressed as Lorenzaccio, whom Sarah Bernhardt was performing at the Adelphi, appeared at the ball.<ref name=":5">"The Duchess of Devonshire's Great Ball. Remarkable Social Function. Crowds of Mimic Kings & Queens. Panorama of Historical Costume. An Array of Priceless Jewels." ''Western Gazette'' 9 July 1897: 2 [of 8], Col. 7A–C. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000407/18970709/009/0002.</ref>{{rp|p. 2, Col. 7C}} # Possibly another group of young women similarly dressed occurs here: "three young girls were noticeable as Reynolds's "Three Ladies Waldegrave"<ref>"The Duchess of Devonshire’s Historic Ball. Some of the Fancy Costumes." ''Leister Chronicle'' 10 July 1897: 11 [of 12], Col. 4a–b. ''British Newspaper Archive''.</ref>{{rp|11, 4a}} The 1780–81 Joshua Reynolds' ''The Ladies Walgrave'' shows 3 young women, probably in "Oriental cream satin," but no "coloured silk sashes" are apparent: https://en.wikipedia.org/wiki/The_Ladies_Waldegrave#/media/File:Sir_Joshua_Reynolds_-_The_Ladies_Waldegrave_-_Google_Art_Project.jpg. Cosway is not Reynolds, so unless one of the reports made a mistake, so these are not [[Social Victorians/People/Villiers|Villiers daughters]] or the [[Social Victorians/People/Roxburghe|Innes-Ker daughters]]. #Who was "Madame Rose" in the 25 June 1897 ''Northampton Mercury'' story<ref name=":6">"For Wives and Daughters." ''Northampton Mercury'' Friday 25 June 1897: 8 [of 10], Col. 3b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000317/18970625/078/0008.</ref> on the ball? A [[Social Victorians/People/Rose|Mr. Rose]] was present at the ball as one of the yeomen in the Queen Elizabeth procession, but she was a businesswoman and he must have been an oligarch or patrician. Madame Rose wrote a fashion column called "For Wives and Daughters" that was published in regional newspapers like the ''Sussex Express, Surrey Standard, Weald of Kent Mail, Hands and County Advertiser''; ''Northampton Mercury''; the ''Burnley Gazette''; and so on, as well as the story on the ball in the 25 June 1897 ''Northampton Mercury''.<ref name=":6" /> (1893–1897). In 1905, the column is called "Home and Fashion. A Letter for Mothers and Daughters," in similar papers as well as the ''Tottenham and Edmonton Herald''.<ref>"Home and Fashion. A Letter for Mothers and Daughters." Tottenham and Edmonton Weekly ''Herald'' 07 June 1905 Wednesday: 4 [of 4], Col. 6–7b–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001716/19050607/031/0004.</ref> A Madame Rose also advertised in the newspapers. For example, "Madame Rose, Court Dressmaker & Ladies' Taylor. Personally Superintends all orders and guarantees perfection in fit and elegance. Speciality in Evening Gowns. Mme. Rose, 30, Shaftesbury Avenue, Piccadilly, one door from Trocadore Restaurant, and 56, two doors from Wardocr-street [sic?]. Tel. 7341 Gerrard."<ref>"Madame Rose." ''The Referee'' 23 October 1904 Sunday: 10 [of 12], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002310/19041023/094/0010.</ref> #The report from the ''Western Gazette'' says some women were dressed as abbesses<ref name=":5" />; who were they? #The ''Westminster Gazette'' says that "There were two or three Napoleons."<ref name=":4" />{{rp|Col. 1}} #Several women came dressed as Princess Lamballe, one of Napoleon's sisters: [[Social Victorians/People/Gordon-Lennox|Lady Blanche (Algernon) Gordon-Lennox]] (at 333); [[Social Victorians/People/Ampthill|Emily, Lady Ampthill]] (at 420); [[Social Victorians/People/Deym|Countess Isabel Deym]] (at 67); [[Social Victorians/People/John Milton Hay|Clara Hay]] (at 153). #The Yeomen in the Queen Elizabeth procession are mostly not notable at this point in their lives though they were present at this event: Henry John Innes-Ker, 8th [[Social Victorians/People/Roxburghe|Duke of Roxburghe]], [[Social Victorians/People/Tweedmouth|Hon. D. (Dudley) Marjoribanks]], [[Social Victorians/People/Mann Thomson|Captain Mann Thomson]], Mr. Rose. According to the ''Gentlewoman'' Mr. E. Villiers, Mr. Harold Brassey were heralds.<ref name=":42" />{{rp|32, Col. 3c}} #The "eight officers of the Imperial Guard attending Catherine of Russia" were the following: "[[Social Victorians/People/Londesborough|Lord Raincliffe]], [[Social Victorians/People/Romilly|Lord Romilly]], Mr. [[Social Victorians/People/Barclay|H. T. Barclay]], Mr. [[Social Victorians/People/Forbes|J. Forbes]], Mr. [[Social Victorians/People/Arthur Stanley Wilson#Charles Henry Wellesley Wilson|C. H. Wellesley Wilson]], Captain [[Social Victorians/People/Cook|E. B. Cook]], the Hon. [[Social Victorians/People/Dudley#Hon. Gerald Ernest Francis Ward|Gerald Ward]], the Hon. [[Social Victorians/People/Campbell|Cecil Campbell]]."<ref name=":42" />{{rp|36, Col. 3b}} #According to the ''Morning Post'' and the ''Gentlewoman'', the Knights of the Round Table were George, [[Social Victorians/People/Rodney|Baron Rodney]]; [[Social Victorians/People/Grosvenor#Hon. R. Grosvenor|Hon. R. Grosvenor]]; Seymour Henry Bathurst, [[Social Victorians/People/Bathurst|7th Earl Bathurst]]; and Hon. Grosvenor [[Social Victorians/People/Hood|Hood]].<ref name=":0" />{{rp|8, Col. 1b}} <ref name=":42" />{{rp|40, Col. 1c}} According to the ''Daily News,'' the Knights of the Table Round were "[[Social Victorians/People/Ashburton|Lord Ashburton]], [[Social Victorians/People/Rodney|Lord Rodney]], [[Social Victorians/People/Bathurst|Lord Bathurst]], [[Social Victorians/People/Ampthill|Lord Ampthill]], and [[Social Victorians/People/Beauchamp|Lord Beauchamp]]."<ref name=":3">"Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses." ''London Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6A–6, Col. 1B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and http://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.</ref>{{rp|5, Col. 7a}} George, Baron Rodney was 40 years old at the time of the ball; [[Social Victorians/People/Grosvenor#Hon. R. Grosvenor|Hon. Robert Victor Grosvenor, 3rd Baron Ebury]] was 29; Seymour Henry Bathurst, [[Social Victorians/People/Bathurst|7th Earl Bathurst]] was nearly 33; Hon. Grosvenor [[Social Victorians/People/Hood|Hood]] was 29;  [[Social Victorians/People/Ashburton|Lord Francis Ashburton]] was nearly 31; [[Social Victorians/People/Ampthill|Lord Ampthill]] was 28; [[Social Victorians/People/Beauchamp|Lord Beauchamp]] was 25. ==References== {{reflist}} * [[Category:Lists]] 04v2x1mmeuzhv0hn9kjc0hlwk6d7354 2412412 2412411 2022-08-06T20:56:09Z Scogdill 1331941 /* Serving Staff */ wikitext text/x-wiki =Devonshire House Fancy Dress Ball, 2 July 1897= ==Logistics== 1897 July 2, Friday, one of the major social events of the "season" of Queen Victoria's Diamond Jubilee The invitations were for 10:30 p.m., but people began to arrive about 10:00, and the Duke of Devonshire came down to greet the Prince and Princess of Wales at 11:00 p.m. The invitations asked people to dress as monarchs and their courts from the past or as goddesses or figures from antiquity. Weather: According to the ''Times'', it was 63 degrees at midnight in London, just as the ball was getting underway, with a dew point of 58, which means that it would not have been as oppressive in all those leather, velvet and satin costumes as well as metal armor as it could have been.<ref>"Weather, The." The London ''Times'' Saturday 3 July 1897: 10 [of 20], Col. 1A. The ''Times Digital Archive''. Web. 22 Mar. 2016.</ref> Location: The party was at Devonshire House, in Picadilly, hosted by [[Social Victorians/People/Louisa Montagu Cavendish | Louisa Cavendish]], the Duchess, and [[Social Victorians/People/Spencer Compton Cavendish | Spencer Compton Cavendish]], the 8th Duke of [[Social Victorians/People/Devonshire |Devonshire]]. ==Who Was There We Might Recognize Now== The people who attended this party belonged to the most elite circles of society and were in the social networks of Albert Edward, Prince of Wales and Louise Cavendish, Duchess of Devonshire. The people in these networks were not the same as the people in, for example, Queen Victoria's networks. The social network of the Prince of Wales did not exclude people who were divorced, involved in extra-marital relationships, or associated with scandal or gossip. It also included Jews, Americans, businessmen and the ''nouveau riche'', and actors and actresses, even if they were not particularly wealthy, so long as they were beautiful, witty and able to keep the prince amused. In their day, they were celebrities, the subjects of newspaper reports and were considered stylish, "fast," and social leaders. Many of these people would not be familiar now to many of us. The ones that we might find familiar include the following: * [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] later King Edward VII, and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]], later Queen Alexandra. * [[Social Victorians/People/George and Mary|George of Wales]], Duke of York and Duchess of York, Princess (Victoria Mary) May or [[Social Victorians/People/George and Mary|Mary of Teck]], later King George V and Queen Mary, Queen Elizabeth II's grandparents. (For fans of the tv series ''[[wikipedia:The_Crown_(TV_series)|The Crown]]'', the role of Queen Mary was played by [[wikipedia:Eileen_Atkins|Eileen Atkins]].) * Frederick Arthur Stanley, 16th Earl of[[Social Victorians/People/Derby | Derby]], who commissioned the first Stanley Cup and presented it to Canda.<ref>{{Cite journal|date=2020-08-12|title=Stanley Cup|url=https://en.wikipedia.org/w/index.php?title=Stanley_Cup&oldid=972518864|journal=Wikipedia|language=en}}</ref> The entire Stanley family were engaged with hockey when Frederick Arthur Stanley was Governor General of Canada (1888 to 1893).<ref>{{Cite journal|date=2020-08-27|title=Frederick Stanley, 16th Earl of Derby|url=https://en.wikipedia.org/w/index.php?title=Frederick_Stanley,_16th_Earl_of_Derby&oldid=975203053|journal=Wikipedia|language=en}}</ref> * Lady Frances, [[Social Victorians/People/Warwick|Countess of Warwick]], called Daisy, the person for whom the song "Bicycle Built for Two" was written. *Oscar Wilde dedicated ''A Woman of No Importance'' to Gwladys Robinson, [[Social Victorians/People/Ripon|Lady de Grey]]. * [[Social Victorians/People/Churchill|Winston Churchill]], who was at the ball by virtue of his mother's popularity in these social networks; he was 24 in 1897 and so little known that only the ''Gentlewoman'' reported his attendance. * A number of [[Social Victorians/People/Rothschild Family|Rothschilds]] were present: Lady (Emma Louise von Rothschild) and Lord Rothschild (Nathan Mayer de Rothschild), Baron F. de Rothschild, Mr. and Mrs. L. Rothschild (possibly Leopold and Marie Perugia Rothschild), Baron Ferdinand de Rothschild, Alfred Rothschild (?), Cyril Flower, Lord Battersea, and Constance de Rothschild Flower, Lady Battersea. Louisa, Lady de Rothschild also attended. *Prince Charles (or Carl) of Denmark was married to Princess Maud of Norway, the daughter of the Albert Edward, Prince and Wales and Alexandra, Princess of Wales. He became King Haakon VII of Norway, and Princess Maud of Wales Queen of Norway. The role of the old King Haakon VII in the tv series ''[[wikipedia:Atlantic_Crossing_(TV_series)|Atlantic Crossing]]'' was played by [[wikipedia:Søren_Pilmark|Søren Pilmark]]. *Some people will recognize the name Joe Cresswell, known for being the commanding officer for a destroyer that captured an intact Enigma machine; his father, [[Social Victorians/People/Cresswell|Addison Baker-Cresswell]], was at the ball. * [[Social Victorians/People/Midleton|William St. John Freemantle Brodrick, later Viscount Midleton]], related by marriage to Agatha Whitehead von Trapp,<ref>{{Cite journal|date=2020-08-18|title=Robert Whitehead|url=https://en.wikipedia.org/w/index.php?title=Robert_Whitehead&oldid=973672889|journal=Wikipedia|language=en}}</ref> first wife of Georg von Trapp and thus the mother of the 7 children in the von Trapp singers. (Agatha Whitehead von Trapp died of scarlet fever in 1922, and Georg von Trapp remarried in 1927 Maria August Kutschera, former novice of Nonnberg Abbey.<ref>{{Cite journal|date=2020-09-05|title=Georg von Trapp|url=https://en.wikipedia.org/w/index.php?title=Georg_von_Trapp&oldid=976801201|journal=Wikipedia|language=en}}</ref>) Some controversy exists about the accuracy of this genealogy. * While few of us would recognize the name [[Social Victorians/People/Bischoffsheim|Henri Louis Bischoffsheim]], we might recognize the bank he founded: Deutsche Bank. * [[Social Victorians/People/Beit|Alfred Beit]] was a Life Governor of De Beers and friend of Cecil Rhodes. *[[Social Victorians/People/Burton|Michael Arthur Bass]], 1st Baron Burton of Burton-on-Trent and of Rangemore and Chairman of Bass Brewery, which was founded in 1777 by Michael Arthur Bass's ancestor William Bass. According to the ''Wikipedia'' article on the Bass Brewery, by 1887 Bass was the largest brewery in the world.<ref>{{Cite journal|date=2021-03-19|title=Bass Brewery|url=https://en.wikipedia.org/w/index.php?title=Bass_Brewery&oldid=1012919731|journal=Wikipedia|language=en}}</ref> *[[Social Victorians/People/Iveagh|Edward Cecil Guinness]], 1st Earl of Iveagh and Chairman of Guiness Brewery, which was founded in 1759 by Edward Guiness's ancestor Arthur Guiness. ==Descriptions and Contextualizing Information== The attendees were presented to the royals in [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts |Quadrilles and the Courts]] of Female Monarchs, goddesses, and so on. ===Staff at the Ball=== A number of people were present not as people invited to the ball but as staff. Not all the Royals at the ball are described in the newspapers as having been accompanied by attendants — the courtiers who usually attended them — but it seems likely that they all would have been. Some of these attendants are described in the newspapers, perhaps those who were invited in their own right. Some, like [[Social Victorians/People/Lauder|the photographer Lafayette]] and the people who worked at that firm or the musicians, for example, served as staff of the party itself. Some were staff and servants working in Devonshire House or for the Duke and Duchess of Devonshire at one of his other properties. These people would have helped prepare for the ball, would have served dinner and cleaned up after people, or would have been responsible for the flowers and decorations, like the gardening staff at the Duke of [[Social Victorians/People/Devonshire |Devonshire]]'s manorial estate, Chatsworth House, who brought flowers from there for decorations at the ball. ==== Gardeners ==== According to the ''Belfast News-letter'', <blockquote>The elaborate floral decorations were all carried out under the direction of Mr. Chester, the head gardener of Chatsworth, and the whole of the lovely flowers and palms were sent up from the conservatories and gardens on the estate.<ref name=":10">"The Duchess of Devonshire's Fancy Dress Ball. Special Telegram." ''Belfast News-Letter'' Saturday 03 July 1897: 5 [of 8], Col. 9c [of 9]–6, Col. 1a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000038/18970703/015/0005.</ref>{{rp|p. 5, Col. 9a}}</blockquote> Describing a later social event in which the Duke and Duchess of Devonshire, as Mayor and Mayoress, decorated Devonshire House again, the ''Sussex Agricultural Express'' refers to some of the men who worked for the Duke and Duchess in January 1898, about half a year later: "Mr. J. P. Cockerell, the Duke of Devonshire's indefatigable agent called to his aid a willing and competent staff from Compton Place [in Eastbourne], including Mr. W. S. Lawrence, the house steward, and Mr. May, the gardener."<ref>"Sunday School Festival: Speech by the Duke." ''Sussex Agricultural Express'' 29 January 1898, Saturday: 7 [of 12], Col. 5b–6a. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000654/18980129/182/0007.</ref> Staff who were named as '''present at the 1897 ball''' included * Mr. J. P. Cockerell, agent for the Duke and Duchess of Devonshire * Mr. W. S. Lawrence, house steward for the Duke and Duchess of Devonshire * Mr. May, gardener for the Duke and Duchess of Devonshire ==== Serving Staff ==== It seems that the staff of Devonshire House was in costume. For example, after people were welcomed by the Duke and Duchess of Devonshire, "Masters of the Ceremonies in '''Louise Seize''' military uniforms passed the guests through into inner rooms."<ref name=":7">“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|p. 5, Col. 2c}} The article in the ''Gentlewoman'' says something very similar, although not identical: the Duchess of Devonshire's "Masters of the Ceremonies were in Louis Seize military uniforms, and they ushered the guests through into the inner rooms, with the exception of the Oriental queens, who, with their suites, assembled in the white and gold saloon, which was brilliantly lit by hundreds of wax '''Candles''', as were, indeed, all the rooms."<ref name=":42" />{{rp|p. 32, Col. 2a}} The people serving dinner were in costume, as the ''Westminster Gazette'' reported in its article on the ball: "The waiters moving about among the supper-folk were dressed as our great-grandfathers in the time of Pitt were dressed — the hair bunched in a black bag, black courtiers' coats, knee-breeches, stockings, and buckle shoes."<ref name=":7" />{{rp|p. 5, Col. 2a}} According to ''House Style: Five Centuries of Fashion at Chatsworth'', some of the staff who worked the ball were hired from the "outside," and some were already staff at Devonshire House.<blockquote>Then there was the mammoth task of organising costumes for the staff, as the Duchess had decided that they should all be in fancy dress. Those hired from outside were to wear Elizabethan and Egyptian costumes from a theatrical outfitter and, for the Devonshire House staff, the men were to be dressed in the blue and buff Devonshire livery of the eighteenth century and the maids in Elizabethan sprigged frocks.<ref name=":18">Burlington, Julia, and Hamish Bowles. ''House Style: Five Centuries of Fashion at Chatsworth''. Skira Rizzoli, 2017. Based on an exhibition 25 March to 22 October 2017.</ref>{{rp|137}}</blockquote>Lady Violet Greville, who wrote the article on the ball in the ''Graphic'', says, "even the servants, in their own quaint and barbaric Eastern dress, carried out the illusion of antiquity to their knee breeches and white wigs."<ref>Greville, Violet, Lady. "Devonshire House Ball." ''The Graphic'' Saturday 10 July 1897: 15 [of 24]: Col. 1a–16, Col. 1c [of 3]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000057/18970710/019/0015.</ref>{{rp|p. 15, Col. 1b}} No evidence exists that Lady Greville was present at the ball, although her son and daughter in law were there. ====Artists Associated with this Event==== '''''Photographers''''' [[Social Victorians/People/Lauder|James Stack Lauder]], known as Lafayette because that was the name of his firm, was invited by the Duke of [[Social Victorians/People/Devonshire |Devonshire]] to set up a temporary studio in the garden and take portrait photographs of the guests in their costumes at the ball. While Lafayette is in many ways the most important photographer documenting the costumes for this event because he was present at the ball, with the imprimatur of the Duke of Devonshire, other photographers also took part in documenting this event. We see their work in the [[Social Victorians/1897 Fancy Dress Ball/Photographs|''Diamond Jubilee Fancy Dress Ball'' album of 286 photogravure portraits]] made of ones taken a week later by Lafayette as well as ones made by other photographers were collected as a hostess gift for the Duchess and given to her in 1899. A copy of this album is in the National Portrait Gallery and has been digitized.<ref>"Devonshire House Fancy Dress Ball (1897): photogravures by Walker & Boutall after various photographers." 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515</ref> '''''Painters''''' The "fashionable miniaturist" Amelie Küssner painted the Prince of Wales in his costume.<ref>"Notes — Mainly Personal." ''Dundee Evening Telegraph'' Monday 27 December 1897: 3 [of 6], Col. 2A. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000453/18971227/006/0003.</ref> According to the ''Western Daily Press'', H. A. Stock, a "much-admired" west-of-England painter, "represented one or two of the personages taking part in the Devonshire House fancy dress ball."<ref>"The Royal Institute of Painters in Water-Colours. West of England Artists." ''Western Daily Press'' Monday 20 March 1899: 3 [of 8], Col. 8B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000264/18990320/012/0003.</ref> At the 32nd Exhibition of the Royal Institute of Painters in Water-Colours that opened 12 March 1898, Mr. Stocks exhibited a "portrait of a well-known society lady in the costume she wore at the Devonshire House fancy dress ball."<ref>"From Our London Correspondent. By Special Wire." ''Dundee Advertiser'' 11 March 1898, Friday: 5 [of 10], Col. 7a. ''British Newspaper Archive''.</ref> At least one of the portraits in the ''Diamond Jubilee Fancy Dress Ball'' album is a painting rather than a photograph. '''''Sculptors''''' The Marchioness of Granby, who at this time was [[Social Victorians/People/Marion Margaret Violet Lindsay Manners|Violet Manners]], commissioned a bust by George Frampton.<ref>''Sevenoaks Chronicle and Kentish Advertiser'' 31 May 1901, Friday: 7 [of 8], Col. 7a. ''British Newspaper Archive''.</ref> ====Musicians==== At least two ensembles were present and providing music, Lacon and Ollier's Blue Hungarian Band and, early the next morning, the White Hungarian Band. One was called an orchestra and the other a band: according to the ''Guernsey Star'', "The orchestra was placed in close proximity to the ballroom, and another band played a programme in the garden."<ref>"Duchess of Devonshire's Fancy-Dress Ball. Brilliant Spectacle." ''The Star'' 6 July 1897, Tuesday: 1 [of 4], Col. 1–2. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000184/18970706/003/0001.</ref>{{rp|p. 1, Col. 2c}} The ''Gentlewoman'' says that the Blue Hungarian Band was near the saloon where the guests at the ball presented themselves to the Royals: <blockquote> About half-past eleven the Blue Hungarian Band, which was stationed in a small ante-room, announced the Prince of Wales' arrival with the stirring strains of "God Save the Queen," and His Royal Highness led the Princess up the centre of the saloon, which was lined by ladies dressed as Oriental queens and their suites.<ref name=":42" />{{rp|p. 32, Col. 2a}} </blockquote> The Blue Hungarian Band advertised in the ''Morning Post'': <blockquote> Lacon and Ollier's Blue Hungarian Band. Cymbalos, Berkes Geza and Miska. has arrived in town for the Season. — Engagements for balls, receptions, &c., to be made to 163A, New Bond-street, W. This band was specially engaged for the Duchess of Devonshire's ball on Friday last.<ref>[Advertisement]. ''Morning Post'' Wednesday 7 July 1897: 6 [of 12], Col. 3c. ''British Newspaper Archive'' <nowiki>http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970707/002/0006</nowiki>.</ref> </blockquote> According to a letter to the editor of the ''Pall Mall Gazette'' by "One Who Was There," the White Hungarian Band was present at the very end.<ref>One Who Was There. "Devonshire House: A Retrospect." Letters to the Editor. ''Pall Mall Gazette'' Tuesday 6 July 1897: 3 [of 12], Col. 2c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18970706/009/0003.</ref> Describing something that seems to be quite different, the ''Westminster Gazette'' says, "A mandoline band under the sycamore trees killed time."<ref>“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|p. 5, Col. 2a}} ==== Costumiers, Perruquiers, and Jewelers ==== Not present at the ball but certainly very involved in it were the people who made the clothing, hats, wigs, jewelry, and so forth. Besides people who made the costumes (costumiers, dressmakers, and modistes) and wigs (perruquiers), embroiderers, jewelers and shoemakers are occasionally mentioned although almost never named in the newspaper accounts. General, contextualizing descriptions of the costumes can be found in the [[Social Victorians/1897 Fancy Dress Ball/anthology#General Discussions of the Costumes|Anthology]]. '''''Costumiers for Theatres and Operas''''' * M. Comelli, designer and costumier at Covent Garden, designed the costumes that were constructed by Mr. Alias of Soho Square.<ref name=":42" />{{rp|p. 42, Col. 3b}} * Mr. Karl, artist, designed the costumes made by Messrs. L. and H. Nathan of Coventry-street<ref name=":42" />{{rp|p. 42, Col. 3b}} <ref name=":8" />{{rp|p. 3, Col. 5b}} * Messrs. John Simmons and Sons, Coventry House, Haymarket<ref name=":42" />{{rp|p. 42, Col. 3b}} * Simmons, 7 and 8, King Street, Covent Garden<ref name=":42" />{{rp|p. 42, Col. 3b}} * Mme. Auguste, of Wellington-street<ref name=":42" />{{rp|p. 42, Col. 3b}} * Harrison's, Ltd., 31, Bow-street<ref name=":42" />{{rp|p. 42, Col. 3b}} * Mr. W. Clarkson, 44, Wellington Street (costumes and wigs)<ref name=":42" />{{rp|p. 42, Col. 3b}} * Mme. or Miss Mary E. Fisher, 26, Bedford-street, Covent-garden<ref name=":9">{{Cite book|url=https://books.google.co.in/books?id=cVQZAAAAYAAJ&pg=RA3-PR2&dq=Mr.+May,+Garrick-street,+Covent-garden&hl=en&newbks=1&newbks_redir=0&sa=X&redir_esc=y|title=The Play-pictorial|date=1908|publisher=Greening & Company, Limited|language=en}} P. ADVT ii. ''Google Books'' https://books.google.com/books?id=cVQZAAAAYAAJ.</ref> <ref name=":42" />{{rp|p. 42, Col. 3b}} * Mr. May, Garrick-street, 9 & 11 Garrick Street, Covent-garden<ref name=":9" /> * "and many others"<ref name=":42" />{{rp|p. 42, Col. 3b}} '''''Fashion Houses and Modistes''''' Among those who helped construct the costumes and wigs include the following: * Mme Durrant made the dress for [[Social Victorians/People/Londonderry#Theresa, Marchioness of Londonderry|Theresa, Marchioness of Londonderry]], who was dressed as Empress Marie-Thérèse.<ref>"Lines for the Ladies." ''Daily Gazette for Middlesbrough'' Thursday 16 June 1898: 4 [of 4], Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000159/18980616/060/0004.</ref> The dress and fabrics for the Marchioness of Londonderry as well as her quadrille, were made in Britain or Ireland.<ref name=":02">"This Morning’s News." London ''Daily News'' 6 July 1897, Tuesday: 7 [of 12], Col. 3b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970706/038/0007.</ref> * The French "tailoring workshop"<ref>{{Cite web|url=https://fashion.mam-e.it/morin-blossier/|title=Morin-Blossier -|date=2016-02-05|language=it-IT|access-date=2022-04-07}}</ref> of Morin-Blossier made the dress worn by [[Social Victorians/People/Prince Charles of Denmark|Princess Maud of Wales]] (Princess Charles of Denmark).<ref name=":43">Harris, Russell. "Prince and Princess Carl of Denmark, later King Haakon VII (1872-1957) and Queen Maud of Norway (1869-1938), and Princess Victoria of Wales (1868-1935), as a 16th century Danish courtier, and Ladies-in-Waiting at to Marguerite de Valois." "List of Sitters." ''In Calm Prose''. 2011 http://www.rvondeh.dircon.co.uk/incalmprose/denmark.html.</ref> * The House of Worth * Doucet * Madame Frederic, of Lower Grosvenor Place * M. or Mrs. Mason, of New Burlington Street<ref name=":42" />{{rp|p. 42, Col. 3b}} * '''Mr. Caryl Craven<ref name=":42" />{{rp|p. 42, Col. 3b}}''' * M. Machinka, Conduit-street<ref name=":42" />{{rp|p. 42, Col. 3b}} * Paquin, of Dover-street<ref name=":42" />{{rp|p. 42, Col. 3b}} * Jays, Ltd., Regent-street<ref name=":42" />{{rp|p. 42, Col. 3b}} The ''Gentlewoman'' covered this topic explicitly: <blockquote> Very great credit is due to the taste and artistic powers of the designers of these dresses, and particular mention must be made of M. Comelli, of Covent Garden Theatre, whose facile pen designed most of the superb toilettes so ably carried out by Messrs. Alias, of Soho-square. Other theatrical costumiers who brought all their special talents to bear on the historical and fancy costumes required for this function were Messrs. Nathan (artist, Mr. Karl), of Coventry-street; Messrs. John Simmons & Sons, Haymarket; Mme. Auguste, of Wellington-street; Harrison's, Ltd., 31, Bow-street; Simmons, 7 and 8, King-street; Mr. Clarkson, 44, Wellington-street; Mme. Fisher, 26, Bedford-street; and many others. A great number of well-known modistes in London were also called upon to supply dresses. Amongst these we chronicle M. Mason, New Burlington-street; M. Machinka, Conduit-street; Paquin, of Dover-street; Jays, Ltd., Regent-street; Messrs. Durrant, 116, Bond-street (who made Lady Londonderry's magnificent gown), and numerous others.<ref name=":42" />{{rp|p. 42, Col. 3b}} </blockquote> The London ''Evening Standard'' cites the sources of its information about the costumes: <blockquote> We are indebted for some of the particulars of the dresses to Mr. Charles Alias, Soho-square; Messrs. L. and H. Nathan, Coventry-street, Haymarket; Messrs. John Simmons and Son, Coventry House, Haymarket; Mr. May, Garrick-street, Covent-garden; Miss Mary E. Fisher, 26 Bedford-street, Covent-garden; and the ''Lady'' newspaper.<ref name=":8">“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.</ref>{{rp|p. 3, Col. 5b}}</blockquote> The ''Morning Post'' also addressed the costumiers. It named Mr. Alias in association with the royals, as well as mentioning several other costumiers by name: <blockquote> The costumes worn by the Prince of Wales, the Duke of York, and the Duchess of Connaught, as well as many others were supplied by Mr. Alias, of Soho-square. Those worn by the Grand Duke Michael of Russia, the Duke of Manchester, Princess Victor of Hohenlohe, and others were made by Mr. W. Clarkson, of Wellington-street, who also supplied the wigs and headdresses for the Royal Family. Messrs. Simmons and Sons, of the Haymarket, made a large number of costumes, including those of the Duke of Somerset, the Marquis of Winchester, Earls Beauchamp, Carrington, Ellesmere, and Essex. Nathan, of Coventry-street, and Simmons, of King-street, Covent-garden; Madame Frederic, of Lower Grosvenor-place, and Mrs. Mason, of New Burlington-street, also made some of the principal costumes.<ref name=":0">"Fancy Dress Ball at Devonshire House." ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4A–8 Col. 2B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.</ref>{{rp|p. 8, Col. 2a}} </blockquote> On 3 July 1897, the day after the ball, the ''Belfast News-letter'' says, <blockquote>For weeks past all the leading London dressmakers and costumiers had been hard at work executing the orders for this great ball. At Alias Nathan's, Clarkson's, Auguste's, and Simmons' all hands set to with a will, and it is gratifying to know that the dresses entrusted to them more than held their own with those sent over from Paris.<ref name=":10" />{{rp|p. 5, Col. 9a}}</blockquote> According to the ''Derbyshire Times and Chesterfield Herald'', citing the ''Daily Mail'', <blockquote> Lady de Grey is going as Zenobia, and is getting her dress from Doucet, I hear, while Worth also is making a great many costumes; but the greatest number are being made in England. The Duchess of Portland, the Duchess of Hamilton, Lady Mar and Kellie, and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] are all going to the costumier in Soho-square, and Alias has also been summoned to Marlborough House for a consultation. Mr. Caryl Craven, who is so clever in such matters, is helping the Duchess of Leeds with her dress; in fact, everyone seems pressed into the service, and the result will be one of the most brilliant sights that ever was seen.<ref>“Derbyshire Sayings and Doings.” ''Derbyshire Times and Chesterfield Herald'' 12 June 1897, Saturday: 5 [of 8], Col. 2A. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000228/18970612/018/0005.</ref> </blockquote> Which costumier was this? "A well-known West End dressmaker booked for the Duchess of Devonshire's fancy dress ball orders representing £27000."<ref>"London Letter." ''Western Daily Press'' 15 July 1897, Thursday: 8 [of 8], Col. 7c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000264/18970715/146/0008.</ref> '''''Perruquiers''''' Mr. W. Clarkson "supplied the wigs and headdresses for the Royal Family."<ref name=":0" />{{rp|p. 8, Col. 2a}} <blockquote> At the Duchess of Devonshire's ball, on the 2d inst., the Prince of Wales looked as if he had stepped out of a masterpiece by one of the old painters. His wig, which completed a correct make-up as Knight of Malta, was specially made and fitted by that favoured "Royal Perruquier" Mr Willie Clarkson, who also had the honour of making and fitting the wigs worn by Prince Charles of Denmark, the Duke of York, and the Duke and Duchess of Connaught, and of dressing the hair of the Duchess of York and the Princess Victoria of Schleswig-Holstein. Mr Clarkson also supplied a number of the costumes, including those worn by the Grand Duke Michael of Russia, Princess Louise, and the Duke of Manchester. It would not be safe to say how many crowned heads have literally "passed through the hands" of Mr Clarkson. The art of the perruquier is a very difficult one, requiring historical knowledge, patient research, and great taste. It is most essential to the success of any theatrical performance or of an historical ball.<ref>“Foreign Plays and Players.” ''The Era'' 10 July 1897, Saturday: 15 [of 28], Col. 3c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000053/18970710/032/0015.</ref> </blockquote> Clarkson also provided costumes and wigs for the [[Social Victorians/Royals Amateur Theatricals|amateur theatricals]] that the royals took part in to entertain themselves. '''''Jewelers''''' After naming costumiers, the ''Gentlewoman'' specifically mentions the Parisian Company for its jewelry and Mr. Norman of Bond Street for the shoes he made: <blockquote> Among other firms [than the costumiers] who lent their aid to make the great ball a huge success was the Parisian Company, whose sparkling gems and jewels, and whose ropes of pearls and precious stones, enhanced the charms of many a fair dame in her dainty old-world costume, and the firm of Mr. Norman, 69, New Bond-street, who designed and made the shoes for the Princess of Wales, the Duchess of Buccleuch, &c., &c.<ref name=":42" />{{rp|p. 42, Col. 3c}} </blockquote> According to the ''Westminster Gazette'', "One very great lady indeed had been lent, by a jeweller, diamonds worth about £13,000."<ref name=":4">“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|p. 5, Col. 2c}} === Journalists and Newspaper Men Present === Several men who owned newspapers were present at the ball, but it seems very unlikely that they were invited because of their associations with journalism unless they were already part of the social network that the list of people who attended the ball can be seen to represent. Also, of course, given the class of people invited to the ball, they were not reporters but proprietors and editors. Still, their newspapers played a very important role in the reportage on the event, which makes them worth identifying separately: * [[Social Victorians/People/Borthwick|Algernon Borthwick, Lord Glenesk]], proprietor of the ''Morning Post'', and son and editor Oliver Borthwick * [[Social Victorians/People/Oppenheim|Henry Oppenheim]], one of three proprietors of the ''Daily News'' in July 1897; Oppenheim was apparently the only one of the three present at the ball. * [[Social Victorians/People/Grimthorpe|William Gervase Beckett]], proprietor and editor in chief of the ''Saturday Review'' While Borthwick and Oppenheim represented newspapers that gave a great deal of attention to the ball, their presence at the ball does not suggest their newspapers necessarily took it more seriously. The newspapers that had the biggest articles about the ball the day after are the following. The main article about the ball * on 10 July 1897 in the ''Gentlewoman'' is 8,489 words. * on 3 July 1897 in the London ''Morning Post'' is 7,719 words. * on 3 July 1897 in the London ''Evening Standard'' is 7,048 words. * on 3 July 1897 in the London ''Times'' is 5,675 words. * on 3 July 1897 in the London ''Daily News'' is 3,676 words. * on 3 July 1897 in the ''Westminster Gazette'' is 2,959 words. The articles in the ''Gentlewoman'' and the ''Graphic'' (this last one written by Lady Violet Greville), both 10 July 1897, had a very large number of illustrations, which made them longer than the number of words itself would suggest. ===[[Social Victorians/1897 Fancy Dress Ball/anthology |Anthology of Reports]]=== A collection of excerpts of descriptions from the newspaper and magazine reports, called here an [[Social Victorians/1897 Fancy Dress Ball/anthology |anthology]], gives a sense of what people read about the event. Reporting on this event began months before it, as soon I think as rumors that it would take place began to circulate, and continued for many months after; it occasionally shows up in a newspaper report years later. ==People Present== Most social events of this size that included the Prince and Princess of Wales, especially those hosted by them, were reported in the newspapers with a list of people invited, generally in order by rank. Royals, including royals from countries outside the U.K., were listed first, often as special guests. The ranks of the aristocracy followed, with dukes together, marquises, earls, and so on. Sometimes the toponyms were in alphabetical order; occasionally they were just grouped; I never saw a list that followed the orders of precedence beyond the general groupings by title. If members of a family were present and had a title, they were in the lists by their title with their family members listed with them. No newspaper printed a complete list of those invited to this ball, probably because the Duchess of Devonshire did not release such a list to the newspapers. This list, then, is the result of trawling through every contemporary account of the ball. It is possible, perhaps, to confirm the presence of some people, because, for example, they appear in the Album of portraits given as a thank-you gift to the Duchess in 1899. The fact that more than one newspaper mentions someone's presence may mean not confirmation but the fact that one or both of these newspaper were reprinting articles originally published somewhere else. The random quality to the list below, then, arises from the newspapers themselves. Further, the location of the names on the list depends on which newspaper article I was working from at the time. I began with the London ''Morning News'' because of its audience and reputation for gossip and social news for the aristocracy and oligarchy. Almost all other lists of attendees are made up only of what was published in the ''Times'', which is a good list but not the best (because of its repetitions) and nowhere near complete. Husbands and wives are often not listed together in the newspaper reports on the ball, and sometimes, as with the ''Times'', the same people are listed in several places with different titles and honorifics. Also influential in developing the list of attendees and identifying some who were mentioned in newspapers but without enough identifying information was the Album, which included the photographs of some of the attendees in their costumes, a copy of which is in the National Portrait Gallery, London, and another in the British Library. A list of people whom it would seem likely would have been at the ball but are not mentioned in the press are below, in the section [[1897 Fancy Dress Ball#People_Absent|People Absent]]. ===Missing from the List: Indian Dignitaries=== Missing from this list are the dignitaries from India, who were said to have been present. According to the ''Dundee Evening Telegraph'' dated 2 July 1897, the day of the party, "The Duchess [of Devonshire] has secured the attendance of many of the Indian Rajahs, who have merely to present themselves in the gorgeous dresses with which they have decorated London drawing-rooms during the past fortnight. ... — London Correspondent."<ref>“The Devonshire Ball.” ''Dundee Evening Telegraph'' 2 July 1897, Friday: 3 [of 6]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000453/18970702/017/0003.</ref> In a letter to the Editor of the ''Pall Mall Gazette'' on 6 July 1897, "One Who Was There" is lamenting about how, now that the ball was over, people would not see the beautiful costumes again. Unlike most of the people who attended, however, "The Indian princes were happy in their lot — no hired possessions theirs, but treasure trove, and they could play at dressing up whenever they pleased."<ref>One Who Was There. "Devonshire House: A Retrospect." Letters to the Editor. ''Pall Mall Gazette'' Tuesday 6 July 1897: 3 [of 12], Col. 2C. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18970706/009/0003.</ref> Describing wearing Indian late-19th-century native dress as "play[ing] at dressing up" reveals perhaps that part of the attraction of inviting these people, who were likely in London for Queen Victoria's Diamond Jubilee celebrations, were their colorful and exotic clothing. We know that "the Maharajah of Kapurthala" was present (at 195 in the list below) and at Table 10 in the first supper seating. No other newspapers stories talked about the presence of many Indian Rajahs, but perhaps the reporters didn't see them arrive or depart and didn't know who they were. These dignitaries are likely to have been in London to celebrate Queen Victoria's Diamond Jubilee; perhaps their names can be guessed from those named at other events from about this time. [[Social Victorians/People/Duleep Singh|Duleep Singh]] (at 605) was not a dignitary from India: he was living in London at this time. On [[Social Victorians/Timeline/1897#6 July 1897, Tuesday|6 July 1897, Tuesday]], just 4 days after the fancy-dress ball, the Duke and Duchess of Devonshire hosted a garden party that was attended by a number of people from South Asia, who were named in the ''Morning Post'' article about the garden party. Although Duleep Singh himself is not mentioned, his English wife, Princess Sophia Duleep Singh, Countess of Selkirk, was present and mentioned just after this:<blockquote>The company arrived in quick succession from four till nearly seven o'clock by the two side entrances to the grounds, as well as the principal entrance in Piccadilly, and the presence of our Indian and Colonial visitors in their picturesque and varied uniforms testified to the far-reaching popularity of the Duke of Devonshire and the hostess. The Maharajah of Kapurthala, the Thakur Sahib of Gondal and the Maharanee, the Maharajah Sir Pertab Singh, Thakur Hari Singh, Kumar Dhopal Singh, Rajah Khetri Singh, Rajah Agit Singh, Raj Kuman Umaid of Shapura, Bijey Singh, Sir Jamsetjee Jejeebhoy and Miss and the Messrs. Jejeebhoy, and the Maha Mudalayar of Kandy, besides the officers of the Imperial Service Troops and the Officers of the Native Cavalry Corps were present. Among those who attended were: Dona Solomon Dias Bandaranaike and Miss Amy Dias Bandaranaike, Senathi Rajah, Deir Senathi Rajah ....<ref>"Devonshire House." ''Morning Post'' 07 July 1897 Wednesday: 7 [of 12], Col. 6a–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970707/069/0007.</ref></blockquote>That is, assuming that those who were in London on 6 July 1897 were also likely in London on 2 July, these visitors from South Asia might have attended the fancy-dress ball as well: * The Maharajah of Kapurthala * The Thakur Sahib of Gondal and the Maharanee * The Maharajah Sir Pertab Singh * Thakur Hari Singh * Kumar Dhopal Singh * Rajah Khetri Singh * Rajah Agit Singh * Raj Kuman Umaid of Shapura * Bijey Singh * Sir Jamsetjee Jejeebhoy and Miss and the Messrs. Jejeebhoy * The Maha Mudalayar of Kandy * Dona Solomon Dias Bandaranaike and Miss Amy Dias Bandaranaike * Senathi Rajah * Deir Senathi Rajah The list of attendees to this garden party follows the pattern of the typical list for this kind of event that included royals, visiting dignitaries and officials, and aristocracy from other nations. That is, people are listed more or less in rank order and grouped by family, as if the newspaper had received a copy of the invitation list itself. The list of people who attended the fancy-dress ball is not ordered in these ways, as if the newspapers were not given the invitation list. This difference might explain why the ''Morning Post'' knew the names of these dignitaries from South Asia on 7 July but did not on 3 July. === Possible Errors === *Mr. and Mrs. Bourke, but Hon. Mr. and Hon. Mrs. A. Bourke are at 325 and 236, respectively. *Mr. S. Cavendish (at 656) may be an error; he may be [[Social Victorians/People/Cavendish|Mr. R. Cavendish]], who is already in the list (at 107) *The National Portrait Gallery letterpress on her portrait says that Lady Helen Stewart is Lady Mary Stewart, Helen Mary Theresa [[Social Victorians/People/Londonderry | Vane-Tempest-Stewart]] (at 43, right after her mother in this list). Helen Stewart-Murray, daughter of the [[Social Victorians/People/Atholl|Duke of Atholl]] (at 657) was probably a misidentification. *Lord [[Social Victorians/People/Hamilton Temple Blackwood|J. Blackwood]] (at 718) and Lady [[Social Victorians/People/Hamilton Temple Blackwood|J. Blackwood]] (at 719) are difficult to identify given the honorifics. Possibly the J. is a typo for T. in the ''Times'' report? *The [[Social Victorians/People/Villiers|Ladies Villiers]] were in a quadrille with the [[Social Victorians/People/Roxburghe|Ladies Ker]]: The [[Social Victorians/People/Roxburghe|Ladies Ker]] are at 23, two women. If each woman had one sash, then there were 2 ladies Villiers and 2 ladies Ker. Lady Edith Villiers (at 282) was definitely in the Cosway quadrille; Lady M. Villiers (at 433) is probably Lady Margaret Villiers, so that might be both the Ladies Villiers. (Mr. E. Villiers is at 326.) * The ''Times'' article<ref name=":2" /> lists both Mrs. George Curzon and then later Mr. and Mrs. Curzon; was George there? or was this another couple? Several people are treated this way, mentioned earlier in the ''Times'' article and then apparently showing up later, with fewer honorifics, especially if they are Hon.'s. Also, there may be duplicates because of variant spellings of the names. ===List of People Who Attended=== # [[Social Victorians/People/Albert Edward, Prince of Wales |Albert Edward, Prince of Wales]] #[[Social Victorians/People/Alexandra, Princess of Wales | Alexandra, Princess of Wales]], train borne by ##[[Social Victorians/People/Knollys#Hon. Louvima Knollys|Hon. Louvima Knollys]] # The [[Social Victorians/People/George and Mary|Prince George of Wales, Duke of York]], at this point heir to the throne. He and the Duchess of York were attended by ## Lady[[Social Victorians/People/Beauchamp | Mary Lygon]] (at 547) ## Sir Charles[[Social Victorians/People/Cust | Cust]] (at 152) # [[Social Victorians/People/George and Mary|Mary, Duchess of York]], who was Mary of Teck, in attendance on Alexandra. She and George, Duke of York were attended by ## Lady[[Social Victorians/People/Beauchamp | Mary Lygon]] (at 547) ## Sir Charles[[Social Victorians/People/Cust | Cust]] (at 152) # [[Social Victorians/People/Alfred of Edinburgh|Alfred Hereditary Prince of Saxe-Coburg and Gotha]] (son of "Affie," [[Social Victorians/People/Alfred of Edinburgh|Alfred, Duke of Edinburgh]]) # Prince[[Social Victorians/People/Christian of Schleswig-Holstein | Christian of Schleswig-Holstein]] # Helena Augusta Victoria, Princess[[Social Victorians/People/Christian of Schleswig-Holstein | Christian of Schleswig-Holstein]] # The[[Social Victorians/People/Grand Duke Michael of Russia | Grand Duke Michael of Russia]] # Princess Louise, Duchess of[[Social Victorians/People/Connaught | Connaught and Strathearn]] (Princess Louise Margaret Alexandra Victoria Agnes of Prussia) (Prince Arthur, Duke of Connaught is at 369) # Princess[[Social Victorians/People/Victoria of Schleswig-Holstein | Victoria of Schleswig-Holstein]] (her parents, Prince and Princess Christian of Schleswig-Holstein are at 6 and 7) # [[Social Victorians/People/Francis Duke of Teck | Francis, Duke of Teck]] #[[Social Victorians/People/Francis Duke of Teck|Princess Mary Adelaide, Duchess of Teck]] #[[Social Victorians/People/Francis Duke of Teck|Prince Alexander of Teck]] #[[Social Victorians/People/Francis Duke of Teck|Prince Francis of Teck]] # The [[Social Victorians/People/Fife |Duke of Fife]] (the Duchess of Fife is at 177) # Princess (Laura Williamina Seymour) Victor of [[Social Victorians/People/Gleichen#Laura Williamina Seymour of Hohenlohe-Langenburg|Hohenlohe Langenburg]] #[[Social Victorians/People/Gleichen |Countess Helena Gleichen]] #[[Social Victorians/People/Louisa Montagu Cavendish | Luise Cavendish]], the Duchess of Devonshire #[[Social Victorians/People/Spencer Compton Cavendish | Spencer Cavendish]], Duke of Devonshire # [[Social Victorians/People/Buccleuch |Duke of Buccleuch]], ([[Social Victorians/People/Buccleuch|the Duchess of Bucchleuch]] is at 24) #[[Social Victorians/People/William Angus Drogo Montagu | William Angus Drogo Montagu]], 9th Duke of [[Social Victorians/People/Manchester | Manchester]] (Consuelo, Duchess of Manchester is at 175) # The [[Social Victorians/People/Roxburghe |Duchess of Roxburghe]] (the Duke of Roxburghe, her son, is at 48) #[[Social Victorians/People/Roxburghe |Lady Margaret Innes-Ker]] (the Duchess of Roxburghe is at 21) #[[Social Victorians/People/Buccleuch|Louisa Jane Montagu Douglas Scott, Duchess of Buccleuch]] (the Duke of Buccleuch is at 20) # Lady [[Social Victorians/People/Katharine Mary Montagu Douglas Scott | Katharine Scott]] # Lady[[Social Victorians/People/Constance Anne Montagu Douglas Scott | Constance Scott]] # Algernon St. Maur, [[Social Victorians/People/Somerset |Duke of Somerset]] (Susan St. Maur, Duchess of Somerset at 209) # William Cavendish-Bentinck, 6th [[Social Victorians/People/Portland |Duke of Portland]] (Duchess of Portland at 29; Mildred Grenfell at 30) # Winifred Anna Dallas-Yorke Cavendish-Bentinck, the [[Social Victorians/People/Portland |Duchess of Portland]] (the Duke of Portland at 27) #[[Social Victorians/People/Mildred Grenfell | Mildred Grenfell]] # Rachel, [[Social Victorians/People/Dudley |Countess of Dudley]] (William, Earl of Dudley is at 63; the Hon. Gerald Ward is at 271) # The [[Social Victorians/People/Alva |Duke of Alva]]— probably Carlos María Fitz-James Stuart y Palafox, [[Social Victorians/People/Alva|16th Duke of Alba]] (possibly his son, Lord Alva, is at 405) # Millicent Fanny St. Clair-Erskine Leveson-Gower, [[Social Victorians/People/Sutherland |Duchess of Sutherland]] (the Duke of Sutherland is at 623) # Katherine Cavendish Grosvenor, the [[Social Victorians/People/Westminster |Duchess of Westminster]] (the Duke is at 173) # Katherine Frances Lambton Osborne, the [[Social Victorians/People/Leeds |Duchess of Leeds]] (the duke is at 455) # Constance Villiers Stanley, [[Social Victorians/People/Derby |Countess of Derby]] (Frederick, Earl of Derby is at 210) #[[Social Victorians/People/Forbes |Lady Angela St. Clair-Erskine Forbes]] (Mr. James Stewart Forbes is at 273) #[[Social Victorians/People/Cornwallis-West |Daisy (Mary Theresa) Cornwallis-West]], Princess Henry of [[Social Victorians/People/Pless | Pless]] (Prince Henry of Pless is at 40) # The [[Social Victorians/People/Keppel |Hon. George Keppel]] (Alice Keppel is at 231) #[[Social Victorians/People/Pless |Prince Henry of Pless]] ("Daisy" Mary Theresa [[Social Victorians/People/Cornwallis-West | Cornwallis-West]], Princess Henry of Pless, is at 38) # Evelyn, [[Social Victorians/People/Alington |Lady Alington]] (Humphrey Sturt is at 120) # Theresa Chetwynd-Talbot Vane-Tempest-Stewart, [[Social Victorians/People/Londonderry |Marchioness of Londonderry]] (the Marquess of Londonderry is at 511) # Lady Mary Stewart, Helen Mary Theresa [[Social Victorians/People/Londonderry | Vane-Tempest-Stewart]] # Lady Beatrix [[Social Victorians/People/Lansdowne | Petty-FitzMaurice]], daughter of the [[Social Victorians/People/Lansdowne |Marquess and Marchioness of Lansdowne]], in attendance on the Marchioness of Londonderry (at 42) #[[Social Victorians/People/Ormonde |Lady Beatrice Butler]] (Elizabeth Grosvenor Butler, the [[Social Victorians/People/Ormonde |Marchioness of Ormonde]], is at 372; Constance Butler is at 373) #[[Social Victorians/People/Abercorn |Lady Alexandra Hamilton]] (daughter of James Hamilton, 2nd [[Social Victorians/People/Abercorn |Duke of Abercorn]]) #[[Social Victorians/People/Stirling |Miss Stirling]] (possibly Evelyn Mary Caroline Lilah Stirling) # The [[Social Victorians/People/Zetland |Marchioness of Zetland]] (The Marquis of Zetland is at 59; son, Earl of Ronaldshay, is at 529) # The [[Social Victorians/People/Roxburghe |Duke of Roxburghe]] (The Duchess of Roxburghe, his mother, is at 22) # The [[Social Victorians/People/Winchester |Marquis of Winchester]] # Maud Hamilton Petty-FitzMaurice, [[Social Victorians/People/Lansdowne |Marchioness of Lansdowne]] (Beatrix Petty-FitzMaurice is at 43) # Henry Petty-FitzMaurice, [[Social Victorians/People/Lansdowne |Marquis of Lansdowne]] # Daisy, [[Social Victorians/People/Warwick |Countess of Warwick]] (the Earl of Warwick is at 525) # Marcia Anderson-Pelham, [[Social Victorians/People/Yarborough |Countess of Yarborough]] (the Earl is at 61) # Beatrix Jane Craven,[[Social Victorians/People/Cadogan | Countess Cadogan]] (Earl Cadogan is at 176) #[[Social Victorians/People/Lurgan |Lady Emily Lurgan]] (Lord Lurgan is at 165) #[[Social Victorians/People/Cadogan |Lady Sophie Scott]] (Sir Samuel Scott, Bart., is at 99) # The [[Social Victorians/People/Mar and Kellie | Earl of Mar and Kellie]] (the Countess of Mar and Kellie is at 160) # The [[Social Victorians/People/Zetland |Marquis of Zetland]] (The Marchioness of Zetland is at 48; son, Earl of Ronaldshay, is at 529) # William Lygon, 7th [[Social Victorians/People/Beauchamp |Earl Beauchamp]] (Lady Mary Lygon, his sister, is at 547) # Charles Anderson-Pelham, 4th [[Social Victorians/People/Yarborough |Earl of Yarborough]] (The Countess of Yarborough is at 54) # Henry Lascelles, 5th [[Social Victorians/People/Harewood |Earl Harewood]] (Lady Harewood is at 524) # William Humble Ward, 2nd [[Social Victorians/People/Dudley |Earl of Dudley]] (Rachel, Countess of Dudley is at 31; the Hon. Gerald Ward is at 271) # George Capell, 7th [[Social Victorians/People/Essex |Earl Essex]] (the Adele Grant Cappell, Countess of Essex is at 194) # Edward [[Social Victorians/People/Villiers | Villiers]], 5th [[Social Victorians/People/Villiers |Earl Clarendon]] #[[Social Victorians/People/Deym |Count Franz Deym]] (Countess Deym is at 67) #[[Social Victorians/People/Deym |Countess Isabel Deym]] (Count Deym is at 66) # Francis Egerton, 3rd [[Social Victorians/People/Ellesmere |Earl of Ellesmere]] (his daughter Lady Mabel Egerton is at 544) # Lord Carington: Charles Robert Wynn-Carington, [[Social Victorians/People/Carrington |Earl Carrington]] # William Waldegrave Palmer, 2nd [[Social Victorians/People/Selborne |Earl of Selborne]] (Beatrix Palmer, Lady Selborne is at 557) # Edward Montagu, 8th [[Social Victorians/People/Sandwich |Earl of Sandwich]] # Henry William Edmund Petty-FitzMaurice,[[Social Victorians/People/Kerry | Earl Kerry]] # Charles Stewart Henry Vane-Tempest-Stewart,[[Social Victorians/People/Londonderry | Viscount Castlereagh]] # Arthur Wellesley Peel, [[Social Victorians/People/Peel Family |1st Viscount Peel]] # Grace, [[Social Victorians/People/Londesborough |Viscountess Raincliffe]] (Lady Mildred [[Social Victorians/People/Londesborough | Denison]] is at 283) # William, [[Social Victorians/People/Londesborough |Viscount Raincliffe]] # Oliver Russell, [[Social Victorians/People/Ampthill |Lord Ampthill]] (Margaret Russell, Lady Ampthill is at 419; Emily, Lady Ampthill is at 420; Miss Constance [[Social Victorians/People/Ampthill | Russell]] is at 418) # Giles Fox-Strangways,[[Social Victorians/People/Ilchester | Lord Stavordale]] (Muriel Fox-Strangways is at 403) # Frederick Glyn, [[Social Victorians/People/Wolverton |Lord Wolverton]] (Edith, Lady Wolverton is at 130) #[[Social Victorians/People/Rodney |Lord Rodney]] (Lady Rodney is at 472) # Hon. [[Social Victorians/People/Grosvenor |R. Grosvenor]]: possibly [[Social Victorians/People/Grosvenor#Hon. R. Grosvenor|Hon. Robert Victor Grosvenor, 3rd Baron Ebury]] # Seymour Henry Bathurst,[[Social Victorians/People/Bathurst | 7th Earl Bathurst]] # Hon. Grosvenor [[Social Victorians/People/Hood | Hood]] #[[Social Victorians/People/Abercorn|Lord Frederick Hamilton]] (Lady Alexandra Hamilton is at 46; Lord Ronald Hamilton is at 105) # Fanny Marjoribanks, [[Social Victorians/People/Tweedmouth |Lady Tweedmouth]] (Edward Marjoribanks, Baron Tweedmouth is at 109; son Dudley Marjoribanks is at 319; his cousin, [[Social Victorians/People/Roxburghe|Duke of Roxburghe]] is at 49) # Arthur Balfour, [[Social Victorians/People/Balfour |the Right Hon. A. J. Balfour]] (Miss Balfour is at 486) # Algernon [[Social Victorians/People/Borthwick | Borthwick, Baron Glenesk]] (Lady Glenesk is at 88; Oliver Borthwick is at 89; Seymour Bathurst, [[Social Victorians/People/Bathurst |7th Earl Bathurst]], is at 82) # Alice [[Social Victorians/People/Borthwick | Borthwick]], Lady Glenesk (Baron Glenesk is at 87; Oliver Borthwick is at 89; Seymour Bathurst, [[Social Victorians/People/Bathurst |7th Earl Bathurst]], is at 82) # Hon. Oliver [[Social Victorians/People/Borthwick | Borthwick]] (Baron Glenesk is at 87; Lady Glenesk is at 88; Seymour Bathurst, [[Social Victorians/People/Bathurst |7th Earl Bathurst]], is at 82) # Minnie (Mary)[[Social Victorians/People/Paget Family | Paget]], Mrs. Arthur Paget (Arthur Paget is at 91) # Colonel Arthur [[Social Victorians/People/Paget Family | Paget]] (Minnie Paget is at 90) # Mrs. [[Social Victorians/People/Fanny Ronalds | Fanny Ronalds]] # The [[Social Victorians/People/Chamberlain |Right Hon. Joseph Chamberlain]] (Mrs. Mary Chamberlain is at 491; Miss Chamberlain is at 492) #[[Social Victorians/People/Harcourt |Lady Elizabeth Harcourt]] (Sir William Harcourt is at 128; Lewis Harcourt is at 664) # Mr. F. B. [[Social Victorians/People/Mildmay |(Francis Bingham) Mildmay]] #[[Social Victorians/People/Sarah Spencer-Churchill Wilson |Captain Gordon Wilson]] (Lady Sarah Wilson is at 392) # Sir John[[Social Victorians/People/Lister-Kaye | Lister Kaye, Bart.]] (Lady Maria Lister Kaye is at 499) #[[Social Victorians/People/Chaine |Colonel William Chaine]] (Maria Chaine is at 490) # Sir Samuel [[Social Victorians/People/Cadogan | Scott]], Bart. (Lady Sophie Scott, his wife, is at 57) # Mr. Gerald [[Social Victorians/People/Loder | Loder]], M.P. # Charles Chetwynd-Talbot, Earl of [[Social Victorians/People/Shrewsbury | Shrewsbury]] #[[Social Victorians/People/Salisbury |Lady Edward Cecil]] (Lord E. Cecil is at 411; Lord R. Cecil is at 126; Lady R. Cecil is at 450; Gwendolen Cecil is at 404) # [[Social Victorians/People/Cresswell |Addison Francis Baker-Cresswell]] (Mr. A. F. B. Cresswell) # Mr. Schomberg M'Donnell: [[Social Victorians/People/Antrim |Schomberg McDonnell]] # [[Social Victorians/People/Abercorn |Mr. Ronald Hamilton]] (possibly Ronald James Hamilton, nephew of the 1st Duke of Abercorn) (Lady Alexandra Hamilton is at 45; Lord Frederick Hamilton is at 83) # [[Social Victorians/People/Jarvis |Weston (Mr. A. W.) Jarvis]] # Mr. R. (possibly [[Social Victorians/People/Cavendish |Lord Richard) Cavendish]] (the Hon. Victor Cavendish is at 121; Lady E. Cavendish is at 164; Lady Edward Cavendish is at 393; Lady Moyra Cavendish is at 366) # [[Social Victorians/People/Gourko|Mr. Nicolas Gourko]] # Edward Marjoribanks, Baron [[Social Victorians/People/Tweedmouth | Tweedmouth]], as the Earl of Leicester (Fanny Marjoribanks, Lady Tweedmouth is at 85; son Dudley Marjoribanks is at 319; his cousin, Duke of Roxburghe is at 49) # Cyril Flower, [[Social Victorians/People/Rothschild Family#Cyril Flower, Lord Battersea and Constance de Rothschild Flower, Lady Battersea|Lord Battersea]] (Constance de Rothschild Flower, Lady Battersea, is at 328) # Sir [[Social Victorians/People/Hartopp |Charles Hartopp]] (Millicent, Lady Hartopp is at 488) # Emma Louise von Rothschild, [[Social Victorians/People/Rothschild Family#Emma, Lady Rothschild and Nathan Mayer, Lord Rothschild|Lady Rothschild]] (Nathan Mayer de Rothschild, Lord Rothschild is at 216) # Mr. [[Social Victorians/People/Portland | Cavendish-Bentinck]] (Mrs. Cavendish Bentinck is 263) # Sir [[Social Victorians/People/Donald Mackenzie Wallace | Donald Mackenzie Wallace]] # Mr. Montague [[Social Victorians/People/Guest | Guest]] (Ivor Bertie Guest, at 295; Frederick Guest, at 345) # Sir Henry [[Social Victorians/People/Meysey-Thompson|Meysey-Thompson]] (Lady Meysey Thompson is at 391) # Walter Hume [[Social Victorians/People/Long | Long]], the Right Hon. W. H. Long, M.P. (Lady Doreen Long is at 484) # Mr. [[Social Victorians/People/Arthur Stanley Wilson | Arthur Wilson]] # Lady [[Social Victorians/People/Lathom |Edith Wilbraham]] (Edward Bootle-Wilbraham, Earl Lathom, is at 125; Alice Bootle-Wilbraham, Countess Lathom, is at 213) # The [[Social Victorians/People/Alington|Hon. Humphrey Sturt, M.P.]] (Lady Alington is at 41) # The [[Social Victorians/People/Cavendish |Hon. Victor Cavendish]] (Lady E. Cavendish is at 164; Mr. R Cavendish is at 107; Lady Edward Cavendish is at 393; Lady Moyra Cavendish is at 366) # Lord [[Social Victorians/People/Henry James | James of Hereford]] (his niece, Miss James, is at 396) # [[Social Victorians/People/Talbot |Lord Edmund Talbot]] # Mr. C. Wyndham, M.P.: Colonel Sir Charles [[Social Victorians/People/Wyndham | Wyndham Murray]] # Edward Bootle-Wilbraham, the [[Social Victorians/People/Lathom |Earl of Lathom]] (The Countess of Lathom is at 213; Lady Edith Wilbraham is at 119) # [[Social Victorians/People/Salisbury |Lord Robert Cecil]] (Lady Edward Cecil is at 102; Lord E. Cecil is at 411; Lady Robert Cecil [Eleanor Lambton Gascoyne-Cecil] is at 450; Gwendolen Cecil is at 404). # Sir [[Social Victorians/People/Charles Hall | Charles Hall]], Q.C, M.P. # Sir [[Social Victorians/People/Harcourt |William Harcourt]] (Lady Elizabeth Harcourt is at 94; Lewis Harcourt is at 669) # Herbert Gardner, [[Social Victorians/People/Burghclere |Lord Burghclere]], as a Puritan (Lady Burghclere is at 437) # Edith Glyn, Lady [[Social Victorians/People/Wolverton | Wolverton]] (Lord Wolverton is at 79) # [[Social Victorians/People/Princess Louise | Princess Louise]] Marchioness of Lorne (the Marquis of Lorne is at 620; Elspeth Campbell is at 621) # [[Social Victorians/People/Churchill |Lady Randolph Churchill]] (her son Winston Churchill, is at 179; Jack Churchill is at 223) # Alphonse [[Social Victorians/People/de Courcel |Chodron de Courcel]] (Madame de Courcel is at 182; Mademoiselle Henriette de Courcel is at 371; Mademoiselle de Courcel is at 498) # Ernest Louis, the [[Social Victorians/People/Princess Alice | Grand Duke of Hesse]] (Princess Victoria, the Grand Duchess of Hesse, is at 138). # M. [[Social Victorians/People/de Soveral | de Soveral]] # Gwladys Robinson, [[Social Victorians/People/Ripon |Countess de Grey]] (Frederick Oliver Robinson, Earl de Grey is at 656) ## Ethiopian or Nubian attendant # [[Social Victorians/People/Georges de Staal | Georges de Staal]] # [[Social Victorians/People/Princess Alice | Princess Victoria]], the Grand Duchess of Hesse (the Grand Duke of Hesse is at 134). # Archibald Primrose, 5th [[Social Victorians/People/Rosebery |Earl of Rosebery]] # Louisa Acheson, [[Social Victorians/People/Gosford |Lady Gosford]] (the Earl of Gosford is at 143) # John Lambton, 3rd [[Social Victorians/People/Durham |Earl of Durham]] # Sunny (Charles Richard John) Spencer-Churchill, the [[Social Victorians/People/Marlborough |Duke of Marlborough]] (Consuelo, Duchess of Marlborough is at 174) # Archibald Acheson, 4th [[Social Victorians/People/Gosford |Earl of Gosford]] (Lady Gosford is at 140) # [[Social Victorians/People/Prince Charles of Denmark | Prince Charles of Denmark]] (Princess Charles of Denmark is at 159). The Prince and Princess Charles of Denmark were attended by ## Cecilia, [[Social Victorians/People/Suffield|Lady Suffield]] (at 536) ## [[Social Victorians/People/Knollys|Miss Charlotte Knollys]] (at 651) ## Major-General [[Social Victorians/People/Ellis|Arthur Ellis]] (at 654) # John Spencer, [[Social Victorians/People/Spencer |Earl Spencer]] (Charlotte, Countess Spencer is at 192) # Beatrix Herbert, the [[Social Victorians/People/Pembroke |Countess of Pembroke]] (the Earl of Pembroke is at 181; Lady Beatrix Herbert is at 648) # Hardinge Stanley Giffard, [[Social Victorians/People/Halsbury |Lord Halsbury]] (Lady Halsbury is at 515) # Ana, Countess de [[Social Victorians/People/Casa de Valencia | Casa Valencia]] (the Count is at 183) # [[Social Victorians/People/Francis Duke of Teck|Prince Adolphus of Teck]] # Kathleen Pelham-Clinton, the [[Social Victorians/People/Newcastle |Duchess of Newcastle]] (the Duke of Newcastle is at 564) # Mrs. White: [[Social Victorians/People/Henry White |Daisy (Margaret Stuyvesant Rutherford) White]] (Henry White is at 310) # [[Social Victorians/People/Cust |Sir Charles Cust]] , who accompanied the Duke and Duchess of York with Lady Mary Lygon # William Court [[Social Victorians/People/Gully Selby | Gully Selby]] (Mrs. Gully is at 441; Miss Gully at 442) # [[Social Victorians/People/John Milton Hay |Clara Stone Hay]] (John Milton Hay is at 187; Miss Helen Hay at 508) # Alice Anne Graham-Montgomery Temple-Nugent-Brydges-Chandos-Grenville Edgerton, [[Social Victorians/People/Buckingham and Chandos |Duchess of Buckingham]] (Lord Wilbraham Egerton of Tatton is at 591; Lady Gore-Langton is at 592) # [[Social Victorians/People/Gordon-Lennox |Princess Edward of Saxe-Weimar]] # Lady [[Social Victorians/People/Stanley |Alice Maude Olivia Montagu Stanley]] (her husband Lord Edward George Villiers Stanley is at 188) # Edwyn Scudamore-Stanhope, the [[Social Victorians/People/Chesterfield |Earl of Chesterfield]] # Princess [[Social Victorians/People/Prince Charles of Denmark | Charles of Denmark]] (Princess Maud of Wales) (Prince Charles of Denmark is at 144). The Prince and Princess Charles of Denmark were attended by ## Cecilia, [[Social Victorians/People/Suffield|Lady Suffield]] (at 536) ## [[Social Victorians/People/Knollys|Miss Charlotte Knollys]] (at 651) ## Major-General [[Social Victorians/People/Ellis|Arthur Ellis]] (at 654) # Lady Violet (Susan Violet) Erskine, [[Social Victorians/People/Mar and Kellie |Countess of Mar and Kellie]] (the Earl of Mar and Kellie is at 58) # Lord Charles Montagu, [[Social Victorians/People/Manchester | Charles William Augustus Montagu]] # Mildred Cadogan, [[Social Victorians/People/Cadogan |Viscountess Chelsea]] # Henry Arthur Cadogan, [[Social Victorians/People/Cadogan |Viscount Chelsea]] # Lady E., probably [[Social Victorians/People/Cavendish |Lady Evelyn, Cavendish]] (the Hon. Victor Cavendish is at 121; Mr. R. Cavendish is at 107; Lady Edward Cavendish is at 393; Lady Moyra Cavendish is at 366) # Lord William [[Social Victorians/People/Lurgan |Lurgan]] (Lady Lurgan is at 56) # Mary Louise Douglas-Hamilton, [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton |Duchess of Hamilton]] # Lord Kenyon, Baron [[Social Victorians/People/Lloyd Kenyon | Lloyd Tyrell-Kenyon]]. # Georgiana Elizabeth Spencer-Churchill Curzon, [[Social Victorians/People/Howe|Viscountess Curzon]] (Viscount Curzon is at 197) # Robert Crewe-Milnes, [[Social Victorians/People/Crewe-Milnes |Earl of Crewe]] # The [[Social Victorians/People/Montrose |Duke of Montrose]] (the Duchess of Montrose is at 186) # Viscount Garnet [[Social Victorians/People/Wolseley | Wolseley]] (Lady Wolseley is at 541; Miss Wolseley is at 542) # Lord Falmouth: Evelyn Edward Thomas Boscawen, [[Social Victorians/People/Falmouth |7th Viscount Falmouth]] (Lady Falmouth is at 471) # Hugh Grosvenor, [[Social Victorians/People/Westminster |Duke of Westminster]] (the Duchess of Westminster is at 34) #[[Social Victorians/People/Consuelo Vanderbilt Spencer-Churchill |Consuelo Vanderbilt Spencer-Churchill]], Duchess of [[Social Victorians/People/Marlborough | Marlborough]] (The Duke of Marlborough is at 142) # Consuelo, [[Social Victorians/People/Manchester|Duchess of Manchester]] (William, Duke of Manchester is at 21) # Earl [[Social Victorians/People/Cadogan | Cadogan]] (Countess Cadogan is at 55) # Princess Royal, Louise, [[Social Victorians/People/Fife |Duchess of Fife]] (the Duke of Fife is at 15) # M. de [[Social Victorians/People/Souza Correa | Souza Correa]] (João Arthur Souza Corrêa) #Winston [[Social Victorians/People/Churchill|Churchill]] (his mother, [[Social Victorians/People/Churchill|Lady Randolph Churchill]], is at 132; his brother, Jack Churchill, is at 223) # Albert, [[Social Victorians/People/Mensdorff |Count Mensdorff]] # Sidney Herbert, [[Social Victorians/People/Pembroke |14th Earl of Pembroke]] (the Countess of Pembroke is at 145; Lady Beatrix Herbert is at 648) # Madame [[Social Victorians/People/de Courcel | de Courcel]] (Alphonse Chodron de Courcel is at 133; Mademoiselle Henriette de Courcel is at 371; Mademoiselle de Courcel is at 498) # Count [[Social Victorians/People/Casa de Valencia | Casa de Valencia]] (the Countess is at 148) # Countess Torby: Sophia Nicholaievna, [[Social Victorians/People/Grand Duke Michael of Russia |Countess Torbi or Torby]] # Lord Ribblesdale: Thomas Lister, [[Social Victorians/People/Ribblesdale|4th Baron Ribblesdale]] (Lady Ribblesdale is at 206) # The [[Social Victorians/People/Montrose |Duchess of Montrose]] (the Duke of Montrose is at 170) # [[Social Victorians/People/John Milton Hay |John Milton Hay]] (Clara Stone Hay is at 154; Helen Hay at 508) # Lord Edward George Villiers [[Social Victorians/People/Stanley | Stanley]] (Lady A. Stanley [Lady Alice Maude Olivia Montagu Stanley] is at 157) # Lord Montagu: William Lowry-Corry, [[Social Victorians/People/Rowton |1st Baron Rowton]] #Lady H. Lennox: Lady [[Social Victorians/People/Richmond and Gordon|Amelia Gordon-Lennox]] # Countess Clary: Thérèse, [[Social Victorians/People/Clary Aldringen |Countess Clary-Aldringen]] (Count Siegfried Clary is at 205; [[Social Victorians/People/Kinsky|Count Charles Kinsky]] is at 575; [[Social Victorians/People/Kinsky|Countess Josephine Kinsky]] is at 394) # Charlotte, [[Social Victorians/People/Spencer |Countess Spencer]] (John, Earl Spencer is at 145) # Lily, [[Social Victorians/People/Marlborough|Duchess of Marlborough]] (William Beresford is at 581) # Adele Grant Cappell, [[Social Victorians/People/Essex |Countess Essex]] (George Capell, Earl of Essex is at 64) # The [[Social Victorians/People/Kapurthala|Maharajah of Kapurthala]] #Cicely Gascoyne-Cecil, [[Social Victorians/People/Salisbury|Viscountess Cranborne]] (Lord Cranborne is at 610) #Richard George Penn, [[Social Victorians/People/Curzon |Viscount Curzon]] (Georgiana, Viscountess Curzon is at 168; Countess Howe is at 489) #Georgina, [[Social Victorians/People/Dudley |Lady Dudley]] (Rachel, Countess of Dudley is at 31; William, Earl of Dudley is at 63; the Hon. Gerald Ward is at 271) #Windham, [[Social Victorians/People/Dunraven|Earl of Dunraven]] (Florence, [[Social Victorians/People/Dunraven|Countess of Dunraven]] is at 606) #[[Social Victorians/People/Grenfell |Ettie (Mrs. W. H.) Grenfell]] (Mr. W. H. Grenfell is at 222; Miss Mildred Grenfell is at 30) #Hugo Charteris, [[Social Victorians/People/Charteris|Lord Elcho]] (Mary Charteris, Lady Elcho is at 224) #Louise ([[Social Victorians/People/Arthur Sassoon |Mrs. Arthur) Sassoon]] (Mr. Arthur Sassoon is at 552), with nephews as attendants: ##Evelyn [[Social Victorians/People/Rothschild Family|de Rothschild]] (at 668 ##Anthony [[Social Victorians/People/Rothschild Family|de Rothschild]] (at 669) # Henry, [[Social Victorians/People/Suffolk|Earl of Suffolk]] (Lady Suffolk is at 538) # Lady Hastings: [[Social Victorians/People/Hastings |Elizabeth Evelyn Harbord Astley]] (Lord Hastings is at 425) # Count Clary, [[Social Victorians/People/Clary Aldringen |Siegfried Graf von Clary und Aldringen]] (Countess Thérèse Clary is at 191; [[Social Victorians/People/Kinsky|Count Charles Kinsky]] is at 575; [[Social Victorians/People/Kinsky|Countess Josephine Kinsky]] is at 394) # Lady Ribblesdale: [[Social Victorians/People/Ribblesdale|Charlotte, Baroness Ribblesdale]] (Lord Ribblesdale is at 185) # [[Social Victorians/People/Kilmorey |Nellie, Countess of Kilmorey]] # Lowry Egerton Cole, [[Social Victorians/People/Cole|4th Earl of Enniskillen]] (Charlotte, Countess of Enniskillen is at 597; Lady Florence Cole is at 239) # Susan St. Maur, [[Social Victorians/People/Somerset |Duchess of Somerset]] (Algernon St. Maur, Duke of Somerset is at 27) # Frederick Arthur Stanley, [[Social Victorians/People/Derby |16th Earl of Derby]] (Constance, Countess of Derby is at 36) # Grace, [[Social Victorians/People/Lowther |Countess of Lonsdale]] (Hugh Cecil Lowther, Earl of Lonsdale is at 225) # Mr. Goschen: [[Social Victorians/People/Goschen|George Joachim Goschen]] (Mrs. Lucy Goschen is at 423; Miss Goschen is at 424) # Lady Alice Villiers Bootle-Wilbraham, the [[Social Victorians/People/Lathom |Countess of Lathom]] (Edward Bootle-Wilbraham, Earl Lathom is at 125; Lady Edith Wilbraham is at 119) # The [[Social Victorians/People/Ribblesdale|Hon. Reginald Lister]] # Lady [[Social Victorians/People/Feversham | Helen Venetia Duncombe Vincent]] (Sir Edgar Vincent is at 226) # Nathan Mayer de Rothschild, [[Social Victorians/People/Rothschild Family#Emma, Lady Rothschild and Nathan Mayer, Lord Rothschild|Lord Rothschild]], as a Swiss Burgher (Emma Louise von Rothschild, Lady Rothschild is at 112) # [[Social Victorians/People/Asquith |Margot Asquith]] (Herbert Henry Asquith is at 381) # Colonel [[Social Victorians/People/Oliphant|Laurence Oliphant]] # Sybil Fane, [[Social Victorians/People/Westmorland |Countess of Westmorland]] (Anthony Mildmay Fane, Earl of Westmorland is at 257) # Lady Cynthia [[Social Victorians/People/Feversham|Graham of Netherby]] (Sir Richard Graham is at 464) # [[Social Victorians/People/Wyndham |Mr. George Wyndham]] #Mr. [[Social Victorians/People/Grenfell |William Henry Grenfell]] (Ethel Grenfell is at 200; Miss Mildred Grenfell is at 30) # [[Social Victorians/People/Churchill|Jack Churchill]] (his mother, Lady Randolph Churchill, is at 132; his brother, Winston Churchill, is at 179) #Mary Charteris, [[Social Victorians/People/Charteris|Lady Elcho]] (Hugo Charteris, Lord Elcho is at 201) # Hugh Cecil Lowther, [[Social Victorians/People/Lowther |5th Earl of Lonsdale]] (Grace, Countess of Lonsdale is at 211) # Sir [[Social Victorians/People/Feversham |Edgar Vincent]] (Lady Helen Vincent is at 215) #Miss West: Shelagh [[Social Victorians/People/Cornwallis-West |(Constance Edwina) Cornwallis-West]] # [[Social Victorians/People/Goelet |Mary Goelet]], Miss Ogden Göelet (Mr. Ogden Göelet is at 502; Mrs. May Göelet is at 503) #Lady [[Social Victorians/People/Westminster|C. Grosvenor]] (family of the [[Social Victorians/People/Westminster#Lady C. Grosvenor|Duke of Westminster]]) #Miss [[Social Victorians/People/Oppenheim|Rosalinda Oppenheim]] (Henry Oppenheim is at 397; Mrs. Isabel Oppenheim is at 408) #[[Social Victorians/People/Keppel |Alice Keppel]] (George Keppel is at 39). # [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]] #[[Social Victorians/People/Portman|Arthur B. Portman]] # Mr. [[Social Victorians/People/Halifax|Gordon Wood]] #The Hon. [[Social Victorians/People/Bourke |Algernon Bourke]] (Guendoline Bourke is at 236) #Hon. Mrs. [[Social Victorians/People/Bourke |A. (Guendoline) Bourke]] (Algernon Bourke is at 235) #[[Social Victorians/People/Paget Family|Gerald Paget Paget]]: likely Gerald Cecil Stewart Paget (Mrs. Arthur Paget is at 90; Arthur Paget is at 91) #Lady [[Social Victorians/People/de Trafford |Violet de Trafford]] # [[Social Victorians/People/Cole |Lady Florence Cole]] (Lowry, Earl of Inneskillen is at 208; Charlotte, Countess Inneskillen is at 597) #Hon. Mrs. [[Social Victorians/People/Peel Family |Julia Peel Maguire]] (Mr. Rochfort Maguire is at 241) #Mr. [[Social Victorians/People/Peel Family |Rochfort Maguire]] #Miss [[Social Victorians/People/Muriel Wilson | Muriel Wilson]] #[[Social Victorians/People/Fraser |Helena Violet Alice Fraser]] ("Miss Keith Fraser") (Captain Keith Fraser is at 244) #Captain Fraser: [[Social Victorians/People/Fraser |Keith Alexander Fraser]] (Helena Violet Alice Fraser is at 243) #[[Social Victorians/People/Hope-Vere |Marie Hope-Vere]] #Alexandra Harriet Paget, [[Social Victorians/People/Colebrooke | Lady Colebrooke]] # <!-- Unidentified still -->Mrs. Leo was in the Duchess procession. #<!-- [Unidentified still] -->[[Social Victorians/People/Stanley#E. Stanley|E. Stanley]] #Right Hon. [[Social Victorians/People/Stanley |George Frederick Stanley]] #Lady [[Social Victorians/People/Derby#Hon. J. Stanley|J. Stanley]] #Hon. F. C. Stanley: [[Social Victorians/People/Stanley |Ferdinand Charles Stanley]] #[[Social Victorians/People/Brassey|L. Brassey]] # Mr. [[Social Victorians/People/Brassey|Harold Brassey]] #Lady A. Acheson: Lady [[Social Victorians/People/Gosford |Alexandra Louise Elizabeth Acheson]] #Lord Acheson: Lord [[Social Victorians/People/Gosford |Archibald Charles Montagu Brabazon Acheson]] #Lady [[Social Victorians/People/Gerard |Mary Milner Gerard]] #Anthony Mildmay Julian Fane, [[Social Victorians/People/Westmorland |13th Earl of Westmorland]] (Sybil Fane, Countess of Westmorland is at 219) #Mrs. [[Social Victorians/People/Talbot |Talbot]] # Miss [[Social Victorians/People/Brienen|de Brienen]] (Baron Brienen is at 465; Baroness Brienen is at 466) # Mrs. [[Social Victorians/People/Leslie |Leonie Leslie]] (Col. John Leslie is at 261) # Colonel [[Social Victorians/People/Leslie |John Leslie]] (Leonie Leslie is at 260) # Lord [[Social Victorians/People/Cavendish Bentinck|Henry Cavendish Bentinck]] (Lady Olivia Cavendish Bentinck is at 263; Lady Ottoline Cavendish-Bentinck is at 543) # Lady [[Social Victorians/People/Cavendish Bentinck|Olivia Cavendish Bentinck]] (Lord Henry Cavendish Bentinck is at 262; Lady Ottoline Cavendish-Bentinck (is at 543) # Mrs. [[Social Victorians/People/Portland | Cavendish Bentinck]] (Mr. Cavendish Bentinck is at 112) # [[Social Victorians/People/Heeren|Count Heeren]] # <!-- Unidentified still. -->Mrs. [[Social Victorians/People/Barclay|H. T. Barclay]] # <!-- Unidentified still. -->Mr. [[Social Victorians/People/Barclay|H. T. Barclay]] # Mr. A. M. Biddulph, possibly [[Social Victorians/People/Myddleton-Biddulph |Algernon Myddleton Biddulph]] # Lord [[Social Victorians/People/Romilly|Romilly]], probably John Gaspard le Marchant Romilly, [[Social Victorians/People/Romilly|3rd Baron Romilly]] # <!-- Unidentified still. -->Captain [[Social Victorians/People/Cook|E. B. Cook]] # The [[Social Victorians/People/Dudley|Hon. Gerald Ward]] (the Countess of Dudley is at 31; William, Earl of Dudley is at 63; Georgina Lady Dudley is at 198) # The Hon. [[Social Victorians/People/Campbell |Cecil Campbell]] # Mr. [[Social Victorians/People/Forbes |James Stewart Forbes]] (Lady Angela Forbes is at 37) # Mr. [[Social Victorians/People/Arthur Stanley Wilson#Charles Henry Wellesley Wilson|C. H. Wellesley Wilson]] # Lord [[Social Victorians/People/Buchan |Shipley Cardross]] (Lady Rosalie Cardross is at 276; the Hon. Muriel Erskine is at 278) # Lady [[Social Victorians/People/Buchan |Rosalie Cardross]] (Lord Shipley Cardross is at 276; the Hon. Muriel Erskine is at 278) # Mr. [[Social Victorians/People/Stourton |Herbert Marmaduke Joseph Stourton]] # The Hon. [[Social Victorians/People/Buchan |Muriel Erskine]] (Lord Shipley Cardross is at 275; Lady Rosalie Cardross is at 276) # Mr. Elliot: the Right Hon. [[Social Victorians/People/Minto|Sir Henry Elliot]] (Lady Minto is at 544) # M. [[Social Victorians/People/Boulatzell | Boulatzell]] # Lady [[Social Victorians/People/Spicer |Margaret Spicer]] (Captain John Spicer is at 410) # Lady [[Social Victorians/People/Villiers |Edith Villiers]] (Lady May Julia Child-Villiers is at 372; Earl Clarendon is at 65; Lord Hyde is at 294) # Lady [[Social Victorians/People/Londesborough |Mildred Denison]] (Grace, Viscountess Raincliffe is at 75; William, Viscount Raincliffe is at 76) # Lady [[Social Victorians/People/Saint Oswald|St. Oswald]] (Lord St. Oswald is at 641) # Miss [[Social Victorians/People/Forbes |Blanche Forbes]] (Mr. James Stewart Forbes is at 273; Lady Angela Forbes is at 37) # Mr. [[Social Victorians/People/Schreiber|Schreiber, Charles Shuldham Schreiber]] # Mrs. [[Social Victorians/People/Higgins|Higgins]] # Mr. [[Social Victorians/People/Higgins|Higgins]] # Mrs. [[Social Victorians/People/Von Andre |Mary Von André]] (Herr Adolf Von André is at 386) # [[Social Victorians/People/Walter Murray Guthrie | Walter Murray Guthrie]] (Olive Guthrie is at 291) # Mrs. [[Social Victorians/People/Walter Murray Guthrie |Olive Guthrie]] (Walter Murray Guthrie is at 290) # [[Social Victorians/People/Montagu|Lady Alice Eleanor Louise Montagu]] (escorted by Lord Stavordale, at 78) # [[Social Victorians/People/Arthur Stanley Wilson|Miss Enid Wilson]] # [[Social Victorians/People/Villiers |George Herbert Hyde Villiers]], Lord Hyde (Earl Clarendon is at 65; Lady Edith Villiers is at 282) # Hon. [[Social Victorians/People/Guest |Ivor Guest]] (Montague Guest, at 115; Frederick Guest, at 345) # The Hon. [[Social Victorians/People/Fortescue |Seymour Fortescue]] # The [[Social Victorians/People/Warwick|Hon. Sidney Greville]] # The Hon. [[Social Victorians/People/Greville |Margaret (Mrs. Ronald) Greville]] (where was Ronald Greville?) # <!-- Still unidentified. -->The [[Social Victorians/People/Warwick|Hon. Mrs. Greville]] (probably not 298?) # [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Mr. Clarence Wilson]] # The Hon. Mrs. George Curzon: [[Social Victorians/People/Curzon |the Hon. Mary Curzon]] (The Hon. George Curzon is at 495) # The [[Social Victorians/People/Peel Family|Hon. George Peel]] (Arthur Wellesley Peel, [[Social Victorians/People/Peel Family|1st Viscount Peel]] is at 74) #The Hon. [[Social Victorians/People/Charteris |Evan Charteris]] # Lady [[Social Victorians/People/Westminster#Lady Lettice Grosvenor|Lettice Grosvenor]] (family of the [[Social Victorians/People/Westminster|Duke of Westminster]]) # Lord [[Social Victorians/People/Thynne|Alexander Thynne]] # Possibly [[Social Victorians/People/Lurgan|Hon. Francis Cecil Brownlow]], the Hon. Cecil Brownlow # [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Mr. Herbert Wilson]] # Mrs. [[Social Victorians/People/Leigh |Marion Leigh]] (Captain Gerard Leigh is at 570; Lady Rose Leigh is at 337; John Blundell Leigh is at 602) # Mrs. [[Social Victorians/People/Drummond |Katherine Mary Drummond]] # Mr. [[Social Victorians/People/Henry White | Henry White]] (Mrs. Daisy White is at 151) # <!-- Unidentified still -->Mr. Norton (MornPost Fancy 1897-07-03) or Mr. Morton (Times 1897-07-03) was dressed as Guyman di Silva in the 17th-century procession. # Mr. [[Social Victorians/People/Beraud|Jean Béraud]] # Mr. [[Social Victorians/People/Grimthorpe |Ernest William Beckett]] (Mr. Gervase Beckett is at 483; Mabel Beckett is at 359; Mr. Rupert Beckett is at 481; Muriel Beckett is at 482) # Mr. H. [[Social Victorians/People/Warrender | Warrender]]: probably Hugh Valdave Warrender (Captain Warrender, probably George John Scott Warrender, is at 519) # Sir [[Social Victorians/People/Jeune |Francis Jeune]] attended with (Lady Susan Jeune is at 550; Miss Madeline Stanley is at 551) # Violet [[Social Victorians/People/Powis|Countess of Powis]] # George [[Social Victorians/People/Powis|Earl of Powis]] # Mrs. [[Social Victorians/People/Cavendish Bentinck |Arthur (Mary Venetia) James]] (Mr. Arthur James is at 480) # Hon. [[Social Victorians/People/Tweedmouth |D. Marjoribanks]] (Fanny Lady Tweedmouth is at 85; Baron Tweedmouth is at 109; Henry Duke of Roxburghe is at 49; two "brother officers" are at 637 and 638) # Mr. [[Social Victorians/People/Ephrussi|Ephrussi]] # [[Social Victorians/People/Mann Thomson|Captain Mann Thomson]] # [[Social Victorians/People/Rose|Mr. Rose]] # [[Social Victorians/People/Edmonstone|Sir A. Edmonstone]] # [[Social Victorians/People/Edmonstone|Lady Edmonstone]] # Mr. [[Social Victorians/People/Holden |Henry Holden]] # Mr. [[Social Victorians/People/Villiers#Mr. E. Villiers|E. Villiers]] # Arthur, [[Social Victorians/People/Arran|Earl of Arran]] # Constance de Rothschild Flower, [[Social Victorians/People/Rothschild Family#Cyril Flower, Lord Battersea and Constance de Rothschild Flower, Lady Battersea|Lady Battersea]] (Cyril Flower, Lord Battersea is at 110) # Rosamond Fellowes, [[Social Victorians/People/de Ramsey |Lady de Ramsey]] # Baron [[Social Victorians/People/Rothschild Family#Baron Ferdinand de Rothschild|Ferdinand de Rothschild]] # Mr. [[Social Victorians/People/Webb|Godfrey Webb]] # The [[Social Victorians/People/Lyttelton |Hon. S. (George William Spencer) Lyttelton]] # Lady [[Social Victorians/People/Gordon-Lennox |Blanche Gordon-Lennox]] (Lord Algernon Gordon Lennox is at 623) # [[Social Victorians/People/Burton|Lady Harriet Burton]] # [[Social Victorians/People/Burton|Lord Michael Burton]] # Florence Canning, [[Social Victorians/People/Garvagh |Lady Garvagh]] # Lady [[Social Victorians/People/Leigh |Rose Leigh]] (John Blundell Leigh is at 602; Mrs. Marion Leigh is at 308; Captain Gerard Leigh is at 570) # Mrs. [[Social Victorians/People/Farquharson |Zoë Farquharson]] (Alexander Farquharson is at 458) # Miss [[Social Victorians/People/Naylor|Naylor]] # The Hon. Mrs. [[Social Victorians/People/Sackville West|Sackville West]] # Lord Camden: John Pratt, [[Social Victorians/People/Camden|4th Marquess Camden]] # Lord Annaly: Luke White, [[Social Victorians/People/Annaly|Baron Annaly]] # John George Stewart-Murray, [[Social Victorians/People/Atholl |Marquess of Tullibardine]] # Lord George [[Social Victorians/People/Atholl | Stewart-Murray]] # Hon. [[Social Victorians/People/Guest |Frederick Edward Guest]] # Captain [[Social Victorians/People/Durham|the Hon. W. Lambton]] # [[Social Victorians/People/Elliot|Captain Gilbert Elliot]] # Mr. [[Social Victorians/People/Warwick |Frank Dugdale]] (Lady Eva Dugdale is at 409) #Mr. [[Social Victorians/People/Arthur Stanley Wilson|Clive Wilson]] # Mr. [[Social Victorians/People/Lowe|W. M. Lowe]] # Mr. [[Social Victorians/People/Morley |Arnold Morley]] # Mr. [[Social Victorians/People/Gathorne-Hardy |Francis Gathorne-Hardy]] # Charles William Reginald Duncombe, [[Social Victorians/People/Helmsley |Viscount Helmsley]] # Muriel Duncombe Owen, [[Social Victorians/People/Helmsley |Viscountess Helmsley]] # Evelyn McGarel-Hogg, [[Social Victorians/People/Magheramorne|Lady Magheramorne]] #Lady [[Social Victorians/People/Beaumont|Aline Beaumont]] (Mr. Wentworth Beaumont is at 468) # [[Social Victorians/People/Hamilton Temple Blackwood|Earl of Ava]]: Archibald Hamilton-Temple-Blackwood # <!-- [Still unidentified?] -->Mr. [[Social Victorians/People/Ancaster|C. Willoughby]] # Mrs. G. Beckett: Mrs. [[Social Victorians/People/Grimthorpe |Mabel Beckett]] (Mr. Gervase Beckett is at 483) # Miss [[Social Victorians/People/Yznaga |Emilia Yznaga]] # [[Social Victorians/People/Hadik |Count Hadik]] # Lady [[Social Victorians/People/Midleton |Hilda Brodrick]] ([[Social Victorians/People/Midleton |St. John Brodrick]] is at 368) # Mr. [[Social Victorians/People/Arthur Stanley Wilson |Jack Graham Menzies]] # [[Social Victorians/People/William James |Evelyn Elizabeth Forbes James]] # Lady [[Social Victorians/People/Lansdowne#Edmond and Lady Caroline Fitzmaurice|C. (Caroline) FitzMaurice]] (Lord Edmond Fitzmaurice is at 626) # Lady [[Social Victorians/People/Cavendish |Moyra Cavendish]] (Mr. R. Cavendish: Richard Frederick Cavendish is at 107) # James Somerville, 2nd Baron [[Social Victorians/People/Athlumney | Athlumney]] # Mr. Brodrick: [[Social Victorians/People/Midleton |St. John Brodrick]] (Lady H. Brodrick is at 362) # [[Social Victorians/People/Connaught | Prince Arthur, Duke of Connaught]] (Princess Louise, Duchess of Connaught is at 9) # [[Social Victorians/People/Princess Victoria of Wales|Princess Victoria of Wales]] # Mademoiselle [[Social Victorians/People/de Courcel |Henriette de Courcel]] (Alphonse de Courcel is at 133; Marie-Elisabeth de Courcel is at 182; Mademoiselle de Courcel is at 498) # Lady [[Social Victorians/People/Jersey|May Julia Child-Villiers]] # Elizabeth Grosvenor Butler, the [[Social Victorians/People/Ormonde |Marchioness of Ormonde]] (Beatrice Butler is at 45; Constance Butler is at 374) # Constance [[Social Victorians/People/Ormonde | Butler]] (Beatrice Butler is at 45; the [[Social Victorians/People/Ormonde |Marchioness of Ormonde]] is at 373) # Mabel, Lady [[Social Victorians/People/Ashburton | Ashburton]] (Francis, Baron Ashburton is at 376) # Francis, Baron [[Social Victorians/People/Ashburton | Ashburton]] (Mabel, Lady Ashburton is at 375) # Lady Archibald [[Social Victorians/People/Argyll | Campbell]] # Mrs. Susannah Wilson [[Social Victorians/People/Arthur Stanley Wilson | Graham Menzies]] (Jack Graham Menzies is at 363) # Mr. Henry [[Social Victorians/People/Henry Chaplin | Chaplin]] (Hon. Edith Helen Chaplin is at 407; Eric Chaplin is at 616) # Sir [[Social Victorians/People/Farquhar |Horace Farquhar]], Bart. (Lady Emilie Farquhar is at 639) # The Right Hon. H. H. (Herbert Henry) [[Social Victorians/People/Asquith | Asquith]] (Margot Asquith is at 217) # Edward Cecil Guiness, [[Social Victorians/People/Iveagh |Lord Iveagh]] (Adelaide Guiness, Lady Iveagh is at 440) # Lady [[Social Victorians/People/Roxburghe#Lady Margaret Innes-Ker and Lady Victoria Innes-Kerr|Victoria Innes-Ker]] (the Duchess of Roxburghe is at 21) # Mr. [[Social Victorians/People/Beit |Alfred Beit]] # Captain [[Social Victorians/People/Holford|George Holford]] # Herr [[Social Victorians/People/Von Andre |Adolf Von André]] (Mrs. Mary Von André is at 289) # Pierre Louis Leopold d'Hautpoul, [[Social Victorians/People/Stonor |Marquis d'Hautpoul]] # Julia Caroline Stonor d'Hautpoul, the [[Social Victorians/People/Stonor |Marquise d'Hautpoul]] # Hon. [[Social Victorians/People/Stonor |Harry Julian Stonor]] # <!-- Unidentified still -->Mrs. [[Social Victorians/People/Adair|Adair]] # Lady [[Social Victorians/People/Meysey-Thompson |Ethel Meysey Thompson]] (Sir Henry Meysey-Thompson is at 116) # Lady [[Social Victorians/People/Sarah Spencer-Churchill Wilson | Sarah Wilson]] (Captain Gordon Wilson is at 96) # Lady [[Social Victorians/People/Cavendish |Edward Cavendish]] # Countess [[Social Victorians/People/Kinsky |Josephine Kinsky]] ([[Social Victorians/People/Clary Aldringen|Countess Thérèse Clary]] is at 191; [[Social Victorians/People/Clary Aldringen|Count Siegfried Clary]] is at 205; Count Charles Kinsky is at 575) # Mary ([[Social Victorians/People/Arthur Stanley Wilson |Mrs. Arthur) Wilson]] # Miss [[Social Victorians/People/Henry James | James]] (Lord James of Hereford is at 122) # [[Social Victorians/People/Oppenheim|Henry Maurice William Oppenheim]] (Mrs. Oppenheim is at 408; Miss Rosalina Oppenheim is at 230) # The Hon. [[Social Victorians/People/Suffield|Bridget Harbord]] (Lord Suffield is at 535; Lady Suffield is at 536) # Candida Hay, [[Social Victorians/People/Tweeddale |Marchioness of Tweeddale]] (the Marquis of Tweeddale is at 400), accompanied by two sons dressed as pages: ## Lord William George Montagu Hay ## Lord Arthur Vincent Hay # William Montagu Hay, the [[Social Victorians/People/Tweeddale |Marquis of Tweeddale]] (The Marchioness of Tweeddale is at 399) # Lady [[Social Victorians/People/Ancaster#Lady Evelyn Ewart|Evelyn Ewart]] (Sir Henry Ewart is at 430) # Lady Hilda FitzRoy, [[Social Victorians/People/Southampton |Baroness Southampton]] (Baron Southampton is at 569) # Lady Muriel [[Social Victorians/People/Ilchester | Fox Strangways]] (Giles Fox-Strangways, Lord Stavordale is at 78) # Lady [[Social Victorians/People/Salisbury |Gwendolen Cecil]] # Lord Alva: [[Social Victorians/People/Alva|Jacobo Fitz-James Stuart y Falcó]] (Carlos Duke Alba is at 32) # [[Social Victorians/People/Somerset|Miss Seymour]] # Miss Chaplin, probably Hon. Edith Helen [[Social Victorians/People/Henry Chaplin | Chaplin]] (Henry Chaplin is at 379; Eric Chaplin is at 616) #Mrs. Openheim: Mrs. [[Social Victorians/People/Oppenheim|Isabella Oppenheim]] (Mr. Henry Oppenheim is at 397; Miss Rosalina Oppenheim is at 230) # Lady [[Social Victorians/People/Warwick |Eva Dugdale]] (Mr. Frank Dugdale is at 348) # Captain [[Social Victorians/People/Spicer |John Spicer]] (Lady Margaret Spicer is at 281) # Lord [[Social Victorians/People/Salisbury |Edward Cecil]] (Edward Herbert [[Social Victorians/People/Salisbury | Gascoyne-Cecil]]) (Lady Edward Cecil is at 102; Lord R. Cecil is at 126). #Mr. C. Wilson: [[Social Victorians/People/Arthur Stanley Wilson|Charles Henry Wilson]] #Mrs. C. Wilson: [[Social Victorians/People/Arthur Stanley Wilson|Florence Wilson]] # Sir [[Social Victorians/People/Henry Irving | Henry Irving]] # Colonel [[Social Victorians/People/Swaine |Charles Edward Swaine]] # Lord Rosslyn: James, 5th [[Social Victorians/People/Forbes|Earl of Rosslyn]] # Lady Rosslyn: Violet, [[Social Victorians/People/Forbes|Countess of Rosslyn]] # Miss Constance [[Social Victorians/People/Ampthill | Russell]] (Lord Ampthill is at 77; Margaret Russell, Lady Ampthill is at 419; Emily, Lady Ampthill is at 420) # Margaret Russell, [[Social Victorians/People/Ampthill |Lady Ampthill]] (Lord Ampthill is at 77) # Emily, [[Social Victorians/People/Ampthill |Lady Ampthill]] (Lord Ampthill is at 77) # Mr. [[Social Victorians/People/Anstruther|Anstruther]] # Mrs. [[Social Victorians/People/Anstruther|Anstruther]] # [[Social Victorians/People/Goschen|Mrs. Goschen]]: Lucy Goschen (G. J. Goschen is at 212\) # [[Social Victorians/People/Goschen|Miss Goschen]] (G. J. Goschen is at 212) # Lord [[Social Victorians/People/Hastings | Hastings]]: George Manners Astley, 20th Baron Hastings (Lady Hastings is at 204) # Florence Chetwynd, [[Social Victorians/People/Florence Rawdon-Hastings Chetwynd |Marchioness of Hastings]] # [[Social Victorians/People/Florence Rawdon-Hastings Chetwynd|Miss Chetwynd]] # Mr. [[Social Victorians/People/Bischoffsheim |Henri Louis Bischoffsheim]] # Mrs. [[Social Victorians/People/Bischoffsheim |Clarissa Bischoffsheim]] # Sir [[Social Victorians/People/Ancaster |Henry Ewart]] (Lady Evelyn Ewart is at at 401) # Lord Jersey: Victor Child-Villiers, 7th [[Social Victorians/People/Jersey | Earl of Jersey]] # Lady Jersey: Margaret Child-Villiers, [[Social Victorians/People/Jersey | Countess of Jersey]] # Lady [[Social Victorians/People/Jersey |Margaret Villiers]] # Lord [[Social Victorians/People/Northampton |Alwyne Frederick Compton]] # Lady [[Social Victorians/People/Northampton |Mary Compton]] # Sir [[Social Victorians/People/Frere|Bartle Frere]] # Winifred Gardner, Lady [[Social Victorians/People/Burghclere | Burghclere]] (Lord Burghclere is at at 129) # Mr. [[Social Victorians/People/Burton|Hamar Bass]] (Lady Harriet Burton is at 334; Lord Michael Burton is at 335; Nellie Baillie is at 667) # [[Social Victorians/People/Burton|Mrs. Louisa Hamar Bass]] (Lady Harriet Burton is at 334; Lord Michael Burton is at 335; Nellie Baillie is at 667) # Adelaide Guiness, [[Social Victorians/People/Iveagh |Lady Iveagh]] (Edward Cecil Guiness, Lord Iveagh is at 382) # Elizabeth [[Social Victorians/People/Gully Selby |Selby Gully]] (William Court Gully is at 153) # Elizabeth Kate Shelley [[Social Victorians/People/Gully Selby | Gully]] (William Court Gully is at 153) # Lord Feversham: William Ernest Duncombe, 1st [[Social Victorians/People/Feversham | Earl of Feversham]] # Lady Feversham: Mabel Duncombe, [[Social Victorians/People/Feversham | Countess Feversham]] # Mr. [[Social Victorians/People/Tedeschi|Tadeschi]] # James McGarel-Hogg, [[Social Victorians/People/Magheramorne|Lord Magheramorne]] (Lady Magheramorne is at 355) # Lord Granby: [[Social Victorians/People/Marion Margaret Violet Lindsay Manners |Henry John Brinsley Manners]] # Lady Granby: [[Social Victorians/People/Marion Margaret Violet Lindsay Manners |Violet Manners]] # Sir Allen [[Social Victorians/People/Young|Young]] # Lady [[Social Victorians/People/Salisbury |R. Cecil]]: Eleanor Lambton [[Social Victorians/People/Salisbury |Gascoyne-Cecil]] (Lord Robert Cecil is at 126) #General Reginald Talbot: General Reginald [[Social Victorians/People/Shrewsbury|Chetwynd-Talbot]] (Mrs. Talbot, Margaret Jane Stuart-Wortley Chetwynd-Talbot is at 485) # Mr. [[Social Victorians/People/Neumann |Ludwig Neumann]] # [[Social Victorians/People/Duncombe|Lady Alicia Duncombe]] # [[Social Victorians/People/Duncombe |Mr. Alfred Duncombe]] (Lady Florence Duncombe is at 456) # George Godolphin Osborne, 10th [[Social Victorians/People/Leeds | Duke of Leeds]] (the duchess is at 35) # [[Social Victorians/People/Duncombe |Lady Florence Duncombe]] (Alfred Duncombe is at 454) # Mrs. [[Social Victorians/People/Williams|Owen Williams]]: Mrs. Nina Williams # Mr. Alexander [[Social Victorians/People/Farquharson | Farquharson]] (Zoë Farquharson is at 338) # Lord Dalkeith: John Charles Montagu Douglas Scott, [[Social Victorians/People/Dalkeith | Earl of Dalkeith]] # Lady Dalkeith: Margaret Montagu-Douglas-Scott, [[Social Victorians/People/Dalkeith | Countess of Dalkeith]] # The [[Social Victorians/People/Euston|Earl of Euston]]: Henry James FitzRoy # Mr. [[Social Victorians/People/Cassel |Ernest Joseph Cassel]] # Lady Cromer: [[Social Victorians/People/Maurice Baring#Edith, Countess Cromer|Edith, Countess of Cromer]] # Sir R. Graham: [[Social Victorians/People/Feversham#Lady Cynthia Graham and Sir Richard Graham|Sir Richard Graham]] (Lady Cynthia Graham is at 220) # [[Social Victorians/People/Brienen|Baron Brienen]] (Miss Brienen is at 259) # [[Social Victorians/People/Brienen|Baroness Brienen]] (Miss Brienen is at 259) #[[Social Victorians/People/Arran|Lady Esther Gore Smith]] # Mr. Beaumont: [[Social Victorians/People/Beaumont|Wentworth Canning Blackett Beaumont]] (Lady Aline Beaumont is at 356) # <!-- Identification uncertain. -->Lady M. Greville: possibly [[Social Victorians/People/Buckingham and Chandos#Mr. and Lady M. Grenville|Lady Mary Grenville]] # <!-- Identification uncertain. -->Mr. Greville: possibly Mr. [[Social Victorians/People/Buckingham and Chandos#Mr. and Lady M. Grenville|Luis Grenville]] # Lady Falmouth: Kathleen Douglas-Pennant Boscawen, [[Social Victorians/People/Falmouth | Viscountess Falmouth]] (Viscount Falmouth is at 172) # Lady Rodney: [[Social Victorians/People/Rodney |Corisande Rodney]] (Lord Rodney is at 80) # Lord W. Stanley: Lord [[Social Victorians/People/Stanley#Lord William Stanley and Lady Alexandra Stanley|Frederick William Stanley]] # <!-- [Unidentified still] -->Lady [[Social Victorians/People/Stanley#Lady W. Stanley|W. Stanley]] # Mr. C. Sykes: Mr. [[Social Victorians/People/Sykes|Christopher Sykes]] # Sir [[Social Victorians/People/Hicks-Beach|M. Hicks-Beach]] # Lady [[Social Victorians/People/Hicks-Beach|Lucy Hicks-Beach]] # Lord Leconfield: Henry Wyndham, [[Social Victorians/People/Wyndham|2nd Baron Leconfield]] # Lady Leconfield: Lady Constance Wyndham, [[Social Victorians/People/Wyndham#Lord and Lady Leconfield|Lady Leconfield]] # Mr. [[Social Victorians/People/Cavendish Bentinck |Arthur James]] (Mrs. [Mary Venetia] Arthur James is at 318) # Mr. R. Beckett: Mr. [[Social Victorians/People/Grimthorpe |Rupert Beckett]] # Muriel Beckett: Mrs. [[Social Victorians/People/Grimthorpe |R. Beckett]] # Mr. [[Social Victorians/People/Grimthorpe |Gervase Beckett]] (Mabel [Mrs. G.] Beckett is at 359) # Lady [[Social Victorians/People/Long |Doreen Long]] (Walter Hume Long is at 117) #Mrs. Talbot: [[Social Victorians/People/Shrewsbury |Margaret Jane Stuart-Wortley Chetwynd-Talbot]] (General Reginald Talbot is at 451) # Miss [[Social Victorians/People/Balfour | Balfour]] (Arthur Balfour is at 86) # <!-- Unidentified still -->Mr. Lu Rack [named in the ''Times'', spelling confirmed] # Millicent, [[Social Victorians/People/Hartopp |Lady Hartopp]] (Sir Charles Hartopp is at 111) # Lady Howe: Isabella,[[Social Victorians/People/Howe | Countess Howe]]) (Viscount Curzon is at 197) # [[Social Victorians/People/Chaine |Maria Chaine]] (William Chaine is at 97) # Mrs. Mary [[Social Victorians/People/Chamberlain | Chamberlain]] (Joseph Chamberlain is at 93; Miss Chamberlain is at 492) # Miss Beatrice (?) [[Social Victorians/People/Chamberlain | Chamberlain]] (Joseph Chamberlain is at 93) # Mr. R. Spencer ([[Social Victorians/People/Spencer|Charles Robert Spencer]]) # Mrs. R. Spencer ([[Social Victorians/People/Spencer|Margaret Baring Spencer]]) # Mr. [[Social Victorians/People/Curzon |George Curzon]] (The Hon. Mrs. George Curzon is at 301) # Lord [[Social Victorians/People/Herschell |Farrer Herschell]] # Lady [[Social Victorians/People/Herschell |Agnes Herschell]] # Mademoiselle [[Social Victorians/People/de Courcel | de Courcel]] (Alphonse de Courcel is at 133; Marie-Elisabeth de Courcel is at 182; Mademoiselle Henriette de Courcel is at 371) # Lady [[Social Victorians/People/Lister-Kaye |Natica (Maria) Lister Kaye]] (Sir John Lister Kaye is at 97) # Lord Milton: Viscount [[Social Victorians/People/Fitzwilliam |Billy Wentworth-Fitzwilliam]] # Lady Milton: [[Social Victorians/People/Fitzwilliam |Maud Wentworth-Fitzwilliam]] # Mr. [[Social Victorians/People/Goelet |Ogden Göelet]] (Mary Goelet, Miss Ogden Göelet is at 228) # Mrs. [[Social Victorians/People/Goelet |May Göelet]] (Mary Goelet, Miss Ogden Göelet is at 228) # Mr. [[Social Victorians/People/Cork and Orrery|W. Boyle]] # Mrs. Hartman: possibly Mrs. [[Social Victorians/People/Hartmann|Eliza Hartmann]] #Mr. [[Social Victorians/People/Rothschild Family#Mr. Lewis Flower|Lewis Flower]] #Major Drummond: [[Social Victorians/People/Drummond|Laurence Drummond]] # Miss Hay: [[Social Victorians/People/John Milton Hay |Helen Hay]] (Clara Stone Hay is at 154; John Milton Hay is at 187) # Hon. Mr. [[Social Victorians/People/Grosvenor#Hon. Catherine and Mr. Algernon Grosvenor|Algernon Grosvenor]] (family of the [[Social Victorians/People/Grosvenor|Baron of Ebury]]) # Mrs. [[Social Victorians/People/Grosvenor#Hon. Catherine and Mr. Algernon Grosvenor|Algernon (Catherine) Grosvenor]] (family of the [[Social Victorians/People/Grosvenor|Baron of Ebury]]) # The Marquis of Londonderry: Charles Vane-Tempest-Stewart, the [[Social Victorians/People/Londonderry | Marquis of Londonderry]] (the Marchioness of Londonderry is at 42) # Henry Strutt, [[Social Victorians/People/Belper | Baron Belper]] # Margaret, [[Social Victorians/People/Belper | Lady Belper]] # [[Social Victorians/People/Belper |Hon. Miss Strutt]], probably Norah Strutt (Margaret, Lady Belper is at 560) # Wilhelmina Giffard, Lady [[Social Victorians/People/Halsbury | Halsbury]] (Lord Halsbury is at 147) # The [[Social Victorians/People/Leicester|Countess of Leicester]]: Georgina Cavendish Coke # Lord Carnarvon: George Herbert, [[Social Victorians/People/Carnarvon|5th Earl of Carnarvon]] # Lady Carnarvon: Almina, [[Social Victorians/People/Carnarvon|Countess Carnarvon]] # Captain Warrender: [[Social Victorians/People/Warrender |George John Scott Warrender]] (Lady Maud Warrender is at 520) # Lady [[Social Victorians/People/Warrender |Maud Warrender]] (Captain George Warrender is at 519) # Major [[Social Victorians/People/Dawson |Vesey Dawson]] # Mr. [[Social Victorians/People/Walsh|Arthur Walsh]] # Lady [[Social Victorians/People/Walsh|Clementine Walsh]] # Lady Harewood: Florence Lascelles, [[Social Victorians/People/Harewood |Lady Harewood]] (the Earl of Harewood is at 62) # Francis, [[Social Victorians/People/Warwick | Earl of Warwick]] (Daisy, Countess of Warwick is at 53) # Lord [[Social Victorians/People/Buccleuch#Lord George Scott|George Scott]] # Mr. [[Social Victorians/People/Rothschild Family#Leopold de Rothschild and Marie Perugia Rothschild|Leopold Rothschild]] (Marie Perugia [Mrs. Leopold] Rothschild is at 528) # Mrs. L. ([[Social Victorians/People/Rothschild Family#Leopold de Rothschild and Marie Perugia Rothschild|Marie Perugia) Rothschild]] (sons Evelyn Achille de Rothschild, at 669, and Anthony Gustav de Rothschild, at 670) # Lawrence John Lumley Dundas, [[Social Victorians/People/Zetland | Earl of Ronaldshay]] #Mr. Brassey, [[Social Victorians/People/Brassey|Henry Leonard Campbell Brassey]] # [[Social Victorians/People/Brassey|Lady Violet Brassey]] # Mr. [[Social Victorians/People/Duberly|Grey Duberly]] # (Mr. R.) [[Social Victorians/People/Reuben David Sassoon | Reuben David Sassoon]] # [[Social Victorians/People/Reuben David Sassoon |Miss Sassoon]] # Charles, [[Social Victorians/People/Suffield|Lord Suffield]] # Cecilia, [[Social Victorians/People/Suffield|Lady Suffield]] # [[Social Victorians/People/Peel Family |Miss Peel]] (Arthur Wellesley Peel, 1st Viscount Peel is at 74; other family members are on the same page) # Lady Suffolk: Mary, [[Social Victorians/People/Suffolk|Countess of Suffolk]] (Henry, Earl of Suffolk is at 203) # The [[Social Victorians/People/Phipps|Hon. Harriet Phipps]] # The [[Social Victorians/People/Scarbrough|Earl of Scarbrough]] # Lady [[Social Victorians/People/Wolseley |Louisa Wolseley]] (Viscount Garnet Wolseley is at 171; Miss Frances Wolseley is at 542) # Miss Wolseley: [[Social Victorians/People/Wolseley |Frances Wolseley]] (Viscount Wolseley is at 171; Lady Louisa Wolseley is at 541) # Lady Ottoline [[Social Victorians/People/Cavendish Bentinck|Cavendish-Bentinck]] (Lord Henry Cavendish Bentinck is at 262; Lady Olivia Cavendish Bentinck is at 263) # Lady Minto: Mary Caroline Grey Elliot-Murray-Kynynmound, [[Social Victorians/People/Minto | Countess Minto]] # [[Social Victorians/People/Crawford and Balcarres|Lord Balcarres]]: David Alexander Edward Lindsay, Lord Balcarres # Sir [[Social Victorians/People/Poynter|Edward Poynter]] # Lady [[Social Victorians/People/Beauchamp |Mary Lygon]] (with Charles Cust, at 152, attended the Duke and Duchess of York) # Mr. B. Bathurst: Mr. [[Social Victorians/People/Bathurst#Mr. B. Bathurst|Benjamin Bathurst]] # Mr. [[Social Victorians/People/Portal |William Portal]] # Mrs. [[Social Victorians/People/Portal |Florence Portal]] # Lady Susan Mary Elizabeth ([[Social Victorians/People/Stanley | Stanley]]) [[Social Victorians/People/Jeune | Jeune]] (Sir Francis Jeune is at 315) # Miss Stanley: [[Social Victorians/People/Stanley#Madeline Stanley|Madeline Cecilia Carlyle Stanley]] (accompanying Sir Francis Jeune, at 314, and Lady Jeune, at 550) # Mr. [[Social Victorians/People/Arthur Sassoon | Arthur Sassoon]] (Louise [Mrs. Arthur] Sassoon is at 201) # Lady [[Social Victorians/People/Ellesmere |Mabel Egerton]] (with her father, the Earl of Ellesmere, at 68) # [[Social Victorians/People/Dyke|Sir W. Hart Dyke]] # [[Social Victorians/People/Dyke|Lady Emily Hart Dyke]] # Beatrix Palmer, [[Social Victorians/People/Selborne |Lady Selborne]] (the Earl of Selborne is at 70) #Prince [[Social Victorians/People/Duleep Singh |Victor Duleep Singh]] #Blanche, [[Social Victorians/People/Coventry | Countess of Coventry]] #Lady [[Social Victorians/People/Coventry |Anne Coventry]] #Lady [[Social Victorians/People/Coventry |Dorothy Coventry]] # Mr. [[Social Victorians/People/Hughes-Onslow|Somerset Hughes-Onslow]] # [[Social Victorians/People/Arthur|Sir George Arthur]] # Henry Pelham-Clinton,[[Social Victorians/People/Newcastle | Duke of Newcastle]] (the Duchess is at 150) # The [[Social Victorians/People/Dupplin#Hon. and Mrs. Claude Hay|Hon. Claude Hay]] # <!-- Unidentified still -->Mrs. Hay, attending with the [[Social Victorians/People/Dupplin#Hon. and Mrs. Claude Hay|Hon. Claude Hay]] #Monsieur [[Social Victorians/People/Baudon de Mony |Xavier Baudon de Mony]] #Madame [[Social Victorians/People/Baudon de Mony |de Courcel Baudon de Mony]] # Charles FitzRoy, [[Social Victorians/People/Southampton | Baron Southampton]] (Hilda FitzRoy, Lady Southampton is at 402) # Captain Gerard [[Social Victorians/People/Leigh | Leigh]] (Mrs. Marion Leigh is at 308) # Lady [[Social Victorians/People/Marlborough |Lilian Maud Spencer-Churchill]] # Lady [[Social Victorians/People/Marlborough |Norah Beatrice Henriette Spencer-Churchill]] # François, [[Social Victorians/People/De Jancourt|Marquis de Jancourt]] # Victoria Lina, [[Social Victorians/People/De Jancourt|Marchioness de Jancourt]] # [[Social Victorians/People/Kinsky | Count Charles Kinsky]] ([[Social Victorians/People/Clary Aldringen|Count Siegfried Clary]] is at 205; [[Social Victorians/People/Clary Aldringen|Countess Thérèse Clary]] is at 191; [[Social Victorians/People/Kinsky|Countess Josephine Kinsky]] is at 394) # Captain [[Social Victorians/People/Camden#Captain and Mrs. Philip Green|Philip Green]] # Mrs. [[Social Victorians/People/Camden#Captain and Mrs. Philip Green|Philip (Mabel) Green]] # [[Social Victorians/People/Montagliari|Marquis Paulac Montagliari]] # Mr. [[Social Victorians/People/Lyttelton |Alfred Lyttelton]] # Mrs. [[Social Victorians/People/Lyttelton |Edith Sophy Balfour Lyttelton]] # Lord William [[Social Victorians/People/Marlborough|Beresford]] (Lily, [[Social Victorians/People/Marlborough|Duchess of Marlborough]] is at 193) # Lord [[Social Victorians/People/Hamilton Temple Blackwood|Basil Blackwood]] # Mr. [[Social Victorians/People/Walker |Hall Walker]] # Mrs. [[Social Victorians/People/Walker |Sophie Walker]] # Lord Bingham: [[Social Victorians/People/Lucan |George Charles Bingham]] # Lady Bingham: [[Social Victorians/People/Lucan |Violet Bingham]] # [[Social Victorians/People/Farquhar#Mr. and Mrs. Almeric FitzRoy|Mr. Almeric FitzRoy]] # [[Social Victorians/People/Farquhar#Mr. and Mrs. Almeric FitzRoy|Mrs. Almeric (Katherine) FitzRoy]] #Colonel [[Social Victorians/People/Shrewsbury |Talbot]] (many Talbots attended; these are Chetwynd-Talbots) #Mrs. [[Social Victorians/People/Shrewsbury | Talbot]] (attending with Colonel Talbot) # Lord [[Social Victorians/People/Wilbraham Egerton of Tatton | Wilbraham Egerton of Tatton]] (Anne, Duchess of Buckingham is at 155) # Lady Gore-Langton: Lady Caroline Jemima Elizabeth [[Social Victorians/People/Buckingham and Chandos | Gore-Langton]] # Sir [[Social Victorians/People/Blois |Ralph Blois]] # [[Social Victorians/People/Mills|Lord Hillingdon]]: Charles Henry Mills, 1st Baron Hillingdon of Hillingdon # [[Social Victorians/People/Mills|Lady Hillingdon]]: Lady Louisa Isabella Lascelles Mills, Baroness Hillingdon # Miss Mills: the [[Social Victorians/People/Mills|Hon. Violet Mills]] # Charlotte, [[Social Victorians/People/Cole|Countess of Enniskillen]] (Lowry, Earl of Enniskillen is at 208; Lady Florence Cole is at 239) # Sir M. FitzGerald: Sir [[Social Victorians/People/Fitzgerald |Maurice FitzGerald]] # Lady FitzGerald: [[Social Victorians/People/Fitzgerald |Amelia Lady, FitzGerald]] # Mr. [[Social Victorians/People/Watson|Meyer Watson]] (identification highly uncertain) # The [[Social Victorians/People/Marlborough|Marchioness of Blandford]]: Albertha Spencer-Churchill # John Blundell [[Social Victorians/People/Leigh | Leigh]] (Lady Rose Leigh is at 337; Mrs. Marion Leigh is at 308; Captain Gerard Leigh is at 570) # Hon. Mr. Reginald Baliol [[Social Victorians/People/Brett | Brett]] # Hon. Mrs. Eleanor [[Social Victorians/People/Brett | Brett]] # Mr. [[Social Victorians/People/Rothschild Family |Alfred Rothschild]] #Florence, [[Social Victorians/People/Dunraven|Countess of Dunraven]] (Windham, [[Social Victorians/People/Dunraven|Earl of Dunraven]] is at 198) # Algernon Keith-Falconer, 9th [[Social Victorians/People/Kintore | Earl of Kintore]] (Sydney, Countess Kintore is at 607; Lady Hilda Madeleine Keith-Falconer is at 677) # Sydney, [[Social Victorians/People/Kintore | Countess Kintore]] # [[Social Victorians/People/Salmon|Mr. Arthur Salmon]] # [[Social Victorians/People/Salisbury|Lord Cranborne]]: James Edward Hubert Gascoyne-Cecil, [[Social Victorians/People/Salisbury|Viscount Cranborne]] (Lady Cranborne is at 196) # <!-- Identification uncertain. -->[[Social Victorians/People/Marlborough#Lord Churchill|Lord Churchill]] # Mr. H. Milner: [[Social Victorians/People/Milner|Harry (Marcus Henry) Milner]] # Mr. [[Social Victorians/People/Strong|Arthur Strong]] # [[Social Victorians/People/Peel Family|Captain R. Peel]] # [[Social Victorians/People/Tilney|Mr. Tilney]] # Mr. Eric [[Social Victorians/People/Henry Chaplin | Chaplin]] (Henry Chaplin is at 379; Hon. Edith Helen Chaplin is at 407) #Captain G. Milner: Captain [[Social Victorians/People/Milner|George Francis Milner]] # Lord [[Social Victorians/People/Westminster#Lord Gerald Grosvenor|Gerald Grosvenor]] (family of the [[Social Victorians/People/Westminster|Duke of Westminster]]) # Lord [[Social Victorians/People/Westminster#Lord Arthur Grosvenor|Arthur Grosvenor]] (family of the [[Social Victorians/People/Westminster|Duke of Westminster]]) # [[Social Victorians/People/Bagot|Lord William Bagot]] # John Campbell, [[Social Victorians/People/Princess Louise | Marquis of Lorne]], as a Tudor (Princess Louise, Marchioness of Lorne, is at 130) # Miss [[Social Victorians/People/Argyll |Elspeth Campbell]] # Lord Algernon [[Social Victorians/People/Gordon-Lennox | Gordon Lennox]] (Lady Blanche Gordon Lennox is at 333) # The [[Social Victorians/People/Sutherland | Duke of Sutherland]] (the Duchess of Sutherland is at 32) # [[Social Victorians/People/Burghclere#Mr. and Mrs. Alan Gardner|Colonel Alan Gardner]] # [[Social Victorians/People/Burghclere#Mr. and Mrs. Alan Gardner|Mrs. Alan Gardner]]: Mrs. Nora Gardner # [[Social Victorians/People/Lansdowne#Edmond and Lady Caroline Fitzmaurice|Edmond FitzMaurice]] (Lady C. FitzMaurice is at 364) # <!-- Still unidentified. -->The [[Social Victorians/People/Durham|Hon. Cecil Lambton]] # Lady Clementine [[Social Victorians/People/Tweeddale | Hay]] (William Hay, Marquis of Tweeddale is at 399; Candida Hay, Marchioness of Tweeddale is at 398) # Miss Tufnell: Gian, [[Social Victorians/People/Mount Stephen|Lady Mount Stephen]] #Mademoiselle [[Social Victorians/People/de Alcalo Galiano | de Alcalo Galiano]] # Mademoiselle [[Social Victorians/People/de Alcalo Galiano |Consuelo de Alcalo Galiano]] # Jesusa Murrieta del Campo Mello y Urritio (née Bellido), [[Social Victorians/People/Santurce | Marquisa de Santurce]] # Mr. F. Murrieta: possibly Don José Murrieta del Campo Mello y Urritio, [[Social Victorians/People/Santurce|Marques de Santurce]] # The Hon. Mrs. Reginald Fitzwilliam: Edith Isabella Georgina [[Social Victorians/People/Fitzwilliam | Wentworth Fitzwilliam]] #The Hon. Reginald Fitzwilliam: Hon. Reginald [[Social Victorians/People/Fitzwilliam | Wentworth Fitzwilliam]] # Lady Florence [[Social Victorians/People/Hamilton Temple Blackwood | Hamilton-Temple-Blackwood]] # Lord Terence [[Social Victorians/People/Hamilton Temple Blackwood | Hamilton-Temple-Blackwood]] # Lady [[Social Victorians/People/Farquhar |Emilie Farquhar]] (Sir Horace Farquhar, Bart., is at 380) # Geraldine ([[Social Victorians/People/Magniac |Sybil Aimée Geraldine) Magniac]] # Lord [[Social Victorians/People/Saint Oswald | St. Oswald]] (Lady St. Oswald is at 284) # The Hon. [[Social Victorians/People/Saint Oswald |Maud Julia Winn]] (with Lord and Lady St. Oswald, her mother, at 284) # Alice Emily White Coke, [[Social Victorians/People/Leicester | Viscountess Coke]] # Lady [[Social Victorians/People/Leicester|Mabel Coke]] # Lady [[Social Victorians/People/Stanley |Isobel Constance Mary Stanley]] # Lord Crichton: Henry William Crichton, [[Social Victorians/People/Crichton|Viscount Crichton]] # <!-- Unidentified still. -->Mr. [[Social Victorians/People/Crichton|Herbert Creighton]] # Lady [[Social Victorians/People/Pembroke |Beatrix Herbert]] (Beatrix Countess Pembroke is at 146; Sidney Herbert, Earl Pembroke is at 181) # Lt.-Col. John Dunville [[Social Victorians/People/Dunville | Dunville]] # Mrs. Violet [[Social Victorians/People/Dunville | Dunville]] # [[Social Victorians/People/Knollys#Miss Knollys|Miss Charlotte Knollys]] (attending Prince and Princess Charles of Denmark, at 159 and 144) # Mrs. Claud Cole-Hamilton: Lucy [[Social Victorians/People/Cole-Hamilton |Charlewood Cole-Hamilton]] # Claud George [[Social Victorians/People/Cole-Hamilton | Cole-Hamilton]] #General Ellis: Gen. Sir [[Social Victorians/People/Ellis#Major-General Ellis|Arthur Edward Augustus Ellis]], in attendance on Prince Charles of Denmark (at 143) # Miss [[Social Victorians/People/Ellis#Miss Alexandra Ellis|Alexandra Ellis]] # Frederick Oliver Robinson, [[Social Victorians/People/Ripon#Frederick Oliver Robinson, Earl de Grey|Earl de Grey]] (Gwladys Robinson, Countess de Grey is at 136) # James Albert Edward Hamilton, [[Social Victorians/People/Abercorn|Marquis of Hamilton]] # Mr. [[Social Victorians/People/Shaftesbury|W. W. Ashley]] #Lady [[Social Victorians/People/Durham|Anne Lambton]] #Captain [[Social Victorians/People/Durham|Hedworth Lambton]] # Lady [[Social Victorians/People/Dunraven |Aileen May Wyndham-Quin]] # Colonel [[Social Victorians/People/Burton|James Evan Bruce Baillie of Dochfour]] # [[Social Victorians/People/Burton|Nellie Bass Baillie]], Hon. Mrs. Baillie (Lady Harriet Burton is at 334) # Miss [[Social Victorians/People/Burton#Jane Thornewill|Jane Thornewill]] (or Miss Jane Thornville) # [[Social Victorians/People/Harcourt |Lewis Harcourt]] (Lady Elizabeth Harcourt is at 94; Sir William Harcourt is at 128) # [[Social Victorians/People/Portland#George Cavendish-Bentinck|George (William George) Cavendish-Bentinck]] # Mrs. Sneyd: [[Social Victorians/People/Sneyd|Mary Evelyn Ellis Sneyd]] # [[Social Victorians/People/Cadogan|Hon. Mrs. Cadogan]] #[[Social Victorians/People/Rothschild Family#Evelyn and Anthony de Rothschild|Evelyn Achille de Rothschild]] (Marie de Rothschild, his mother, at 527) # [[Social Victorians/People/Rothschild Family#Evelyn and Anthony de Rothschild|Anthony Gustav de Rothschild]] (Marie de Rothschild, his mother, at 527) # Mr. [[Social Victorians/People/Wombwell |Stephen Frederick Wombwell]] # The Hon. Mrs. Gwendoline [[Social Victorians/People/Lowther | Lowther]] # Col. [[Social Victorians/People/Dawson |Douglas Dawson]] # Louisa Montefiore, [[Social Victorians/People/Rothschild Family#Louisa, Lady de Rothschild|Lady de Rothschild]] # Hon. [[Social Victorians/People/Maurice Baring|John Baring]] # Hon. [[Social Victorians/People/Antrim |Alexander McDonnell]] # Lady [[Social Victorians/People/Kintore |Hilda Madeleine Keith-Falconer]] (Algernon Keith-Falconer, 9th Earl of Kintore is at 607) # [[Social Victorians/People/Maurice Baring|Hon. Maurice Baring]] # Hon. [[Social Victorians/People/Peel Family|W. G. Peel]] # Rose Towneley-Bertie, [[Social Victorians/People/Norreys | Lady Norreys]] # Major John Seymour [[Social Victorians/People/Peel Family | Wynne-Finch]] # Marie (Agnes Blanche Marie) [[Social Victorians/People/Dupplin | Hay-Drummond]] # Sir [[Social Victorians/People/Hamilton |Edward Walter Hamilton]] # Daisy (Marguerite Hyde) [[Social Victorians/People/Suffolk |Leiter]] # [[Social Victorians/People/Lukach |Joseph Harry Lukach]] # [[Social Victorians/People/William James | William Dodge James]] (Evelyn Forbes James is at 364) # Mrs. [[Social Victorians/People/Murray|Graham Murray]] # <!-- 688 Still unidentified. -->Mrs. Habington (mentioned as part of Queen Elizabeth's court by the ''Gentlewoman''.<ref name=":42" />{{rp|32, Col. 3c}} There is no doubt about the spelling in the ''Gentlewoman'' article.) # <!-- Unidentified still. -->Mr. [[Social Victorians/People/Longhurst|P. A. Longhurst]] #<!-- Unidentified still. -->Mr. [[Social Victorians/People/Foley|Foley]] #Carlo Ermes Visconti, [[Social Victorians/People/San Vito|Marquis of San Vito]] #[[Social Victorians/People/Malcolm|Mr. Ian Malcolm]], M.P. #Mr. E. [[Social Victorians/People/Crawley|Crawley]] #Mr. W. R. Chaine: Mr. [[Social Victorians/People/Chaine#Mr. W. R. Chaine|William Robert Chaine]] #The Hon. [[Social Victorians/People/Campbell|K. Campbell]] #The Hon. [[Social Victorians/People/Mar and Kellie|William Erskine]] #<!-- Highly uncertain ID -->Mr. [[Social Victorians/People/Carter|J. Carter]] #<!-- Still unidentified. -->Lord [[Social Victorians/People/Hamilton Temple Blackwood|J. Blackwood]] #<!-- Still unidentified. -->Lady [[Social Victorians/People/Hamilton Temple Blackwood|J. Blackwood]] #<!-- Still unidentified. -->[[Social Victorians/People/Cavendish |Mr. S. Cavendish]], possibly Mr. R. Cavendish (at 107) #<!-- 719 -->A "brother officer" of the [[Social Victorians/People/Roxburghe|Duke of Roxburghe]] in the Royal Horse Guards (see Fanny Marjoribanks, Lady Tweedmouth, at 85; the Duke of Roxburghe is at 49). #<!-- 720 -->A second "brother officer" of the [[Social Victorians/People/Roxburghe|Duke of Roxburghe]] in the Royal Horse Guards (see Fanny Marjoribanks, Lady Tweedmouth, at 85; the Duke of Roxburghe is at 49). #<!-- unidentified still? -->Mr. Bourke (the Hon. A. Bourke is at 235) #<!-- Unidentified still? -->Mrs. Bourke (the Hon. Mrs. A. Bourke is at 236) ===Attendants of the People Who Were Present=== A number of people present at the ball were not invited in their own right and were there as attendants. Listed in the descriptions of the people at the ball and their costumes are some people who were clearly there as attendants: # "Black attendants" followed the Court in the Empress Catherine II of Russia procession, preceding the Italian procession.<ref name=":0" /><ref name=":2">"Ball at Devonshire House." The ''Times'' Saturday 3 July 1897: 12, Cols. 1A–4C ''The Times Digital Archive''. Web. 28 Nov. 2015.</ref> # There were unnamed Imperial Trumpeters in the Court in the Empress Catherine II of Russia procession. They had to really be able to play the trumpet so perhaps were hired musicians? # Heralds led the Queen Elizabeth Procession, but they are not named, so they were probably not invited guests but servants or attendants of some kind? # According to the Leamington ''Spa Courier'', the Countess of Warwick's "four pages shared in the compliments."<ref>“Town Talk and Street Echoes.” ''Leamington Spa Courier'' 10 July 1897, Saturday: 5 [of 8], Col. 4B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000319/18970710/015/0005.</ref> According to the Guernsey ''Star'', Lady Warwick "was accompanied by four boys dressed in white satin, with three-cornered hats to match."<ref name=":1">"Duchess of Devonshire's Fancy-Dress Ball. Brilliant Spectacle." The [Guernsey] ''Star'' 6 July 1897, Tuesday: 1 [of 4], Col. 1–2. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000184/18970706/003/0001.</ref> # The Marchioness of Tweeddale also had two pages: "The Marchioness of Tweeddale was Joséphine, wife of Napoleon, in white satin, wrought with gold and a deep rose-coloured train, trimmed with ermine, and borne by two pages in mauve velvet, embroidered with gold."<ref name=":1" /> # Princess Henry of Pless had black and white pages: "As the Queen of Sheba, Princess Henry of Pless was attended by five black pages and five white, in gorgeous dresses, who carried her train."<ref name=":1" /> In the large list of people who were present for the ball, above, attendants are listed with the people for whom they worked; typically royals had attendants with them. ====Attendants of Color==== Clearly, some of these attendants were black people (especially at 1 and 6). The vocabulary the newspapers used ranged from "Black" to "Negro" to the actual n-word (for American Minnie Paget?). The Aberdeen ''Journal'' of 4 August 1897 ran a story, "Black Boys for London Ladies," that refers to the black attendants at the Duchess of Devonshire's ball: :Titian’s pictures (says London correspondent) have made us familiar with black boys forming part of the train of certain great ladies. The Prince of Wales brought a Nubian boy home, and for a time he was in the Marlborough House and Sandringham households. The Duchess of Marlborough is very often accompanied by a black boy in Oriental scarlet and gold, who seems '''but live''' to obey her grace’s behests; for his dark, piercing eyes follow her every movement, giving him a weird look, which is increased by the curious incision in his cheeks. At the Devonshire House fancy ball the glory of the great Oriental procession was much increased by the Nubian boys, who carried palm-leaves over some of the queenly heads.<ref>"Black Boys for London Ladies." ''Aberdeen Journal'' Wednesday 4 August 1897: 6 [of 8], Col. 5C. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000032/18970804/130/0006.</ref> We need to know more about these children. ==People Absent== The ''London Daily News'' and the ''Times'' reported as attending Lady Hindlip, who was not able to attend, according to the ''Morning Post'', suggesting that they may have gotten a list of people attending from something other than onsite reportage, perhaps from someone describing the costumes that had been made. Of the people who were not present but seem missing because their immediate family, for example, was present, some are women, the wives of the people named. So perhaps they did not court newspaper attention? Of the men who might have been there, logically, perhaps they did not dress in costume and thus did not receive mention? (We know some men attended the ball and were not in fancy dress.) # Samuel Allsopp, [[Social Victorians/People/Hindlip|Lord Hindlip]] and Georgina Allsopp, [[Social Victorians/People/Hindlip|Lady Hindlip]] were not present because Lord Hindlip was ill and died less than two weeks later. # Colonel Brabazon "unavoidably prevented" from attending.<ref>"The Queen's Sympathy." ''Morning Post'' Monday 05 July 1897: 7 [of 12], Col. 5B. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970705/070/0007.</ref> # Mrs. Hwfa Williams was reported in the Morning Post not to have attended because she was in mourning.<ref>“Arrangements for This Day.” ''Morning Post'' 2 July 1897, Friday: 5 [of 10], Col. 7B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970702/038/0005.</ref> Owen's and Hwfa Williams' sister Edith Peers-Williams had died. Although General or Mr. Owen Williams is not listed as having attended, his wife Mrs. Nina Williams (at 457) was said to have been present, but really it seems most likely that none of them attended. # Fanny Ronalds was there, but Arthur Sullivan's name is not listed; was he there but not in an interesting costume? Or not present? # Lady [[Social Victorians/People/de Trafford|Violet de Trafford]] was there (at 238, above), but her husband? or son?, Sir Humphrey Francis de Trafford, 3rd Baronet, is not listed. # Mrs. Henry White isn't listed as present, but Mr. Henry White is at 310, and Margaret "Daisy" Stuyvesant Rutherford White is now at 151. I believe she was present because both Whites were photographed in costume and that photograph is in the album at the NPG. # Even though Henry Maurice William Oppenheim and his daughter, Rosalinda Oppenheim were present, Mrs. Isabel Georgina Oppenheim (who does not appear to have been Rosalinda's mother) is not listed anywhere as being present. # Jesusa Murrieta del Campo Mello y Urritio (née Bellido), [[Social Victorians/People/Santurce|Marquisa de Santurce]] attended the Duchess of Devonshire's fancy-dress ball at Devonshire House. Mr. [[Social Victorians/People/Santurce|F. Murrieta]] (at 708) was present according to ''The Gentlewoman'', but who was he? Her husband, José Murrieta y del Campo Downey, 1st Marques de Santurce, is not listed as having been present although he was still alive. Possibly the F. is a mistake on the part of The Gentlewoman, and it was Don José who was there? # Baron [[Social Victorians/People/Gerard|William Cansfield Gerard]], Lady [[Social Victorians/People/Gerard|Mary Gerard]]'s husband: she was present (at 256) and represented in the album, but he's not mentioned. Was he there? # The Hon. Mrs. [[Social Victorians/People/Lowther|Gwendoline Lowther]] (at 672), was present, but her husband, whose brother was Hugh Cecil Lowther, 5th Earl of Lonsdale and who would be later in his own right, was not? # Rosamond Fellowes, [[Social Victorians/People/de Ramsey|Lady de Ramsey]] (at 329) was present, but William Fellowes, Baron de Ramsey was not? # Florence Canning, [[Social Victorians/People/Garvagh|Lady Garvagh]] (at 336) attended the ball. Where was Charles Canning, Lord Garvagh? Did he just not get mentioned? # Nellie, Countess of Kilmorey (at 207) attended the ball, but Francis Needham, Earl of Kilmorey did not? # Prince Leopold's wife, Helena, Duchess of Albany wasn't there? # Princess Beatrice didn't go? # [[Social Victorians/People/Bathurst|Lilias Bathurst]] is not listed has having attended the Duchess of Devonshire's ball, although her husband [[Social Victorians/People/Bathurst|Henry Bathurst, 7th Earl of Bathurst]], her parents [[Social Victorians/People/Borthwick|Algernon Borthwick, Lord Glenesk]] and [[Social Victorians/People/Borthwick|Alice, Lady Glenesk]] and her brother [[Social Victorians/People/Borthwick|Oliver Borthwick]] were there. A child was not born to her in 1897 as far as I can tell, although we may not be able to know about a miscarriage. Perhaps she was present and not reported on. # Mrs. [[Social Victorians/People/Loder|Louise Loder]] is not listed among the attendees at the ball; was she there and just not reported on? No child was born that year, but she was bearing children during this time. Gerald Loder is at 100. #Was [[Social Victorians/People/Talbot|Lady Mary Bertie Talbot]] at the ball? She is not mentioned. She isn't likely to be Mrs. Talbot because her father was an Earl? She would have been Lady Talbot? #Was [[Social Victorians/People/Hope-Vere|James Charles Hope-Vere]] present at the ball and just not mentioned? Marie Hope-Vere was not mentioned in the press, so without the Album of portraits of people in their costumes in the National Portrait Gallery, we might not know about her. #Did [[Social Victorians/People/Colebrooke|Ned (Edward Arthur) Colebrooke]] attend the ball? Alexandra Paget Colebrooke (at 246) did. #Was [[Social Victorians/People/Heeren|Countess Arthur de Heeren]] at the ball and not reported on? #Mrs. Margaret Greville (298) was there; was Ronald Greville but not mentioned in reports? #The wife of [[Social Victorians/People/Ephrussi|M. Ephrussi]], whichever one attended, is not mentioned as having been present; perhaps she was there but not recognized or described? #"The little daughter of Sir Francis and Lady Knollys"<ref name=":42">“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.</ref>{{rp|32, Col. 2a}} attended, as did her aunt, Hon. Charlotte Knollys, but were her parents not there? Francis Knollys was the Prince of Wales's private secretary at this point, as well as holding a number of other courtier positions in the Household at the same time. #Carlo Ermes Visconti, [[Social Victorians/People/San Vito|Marquis of San Vito]] (at 691) was present; was his wife? #If the Lord Churchill (at 610) is [[Social Victorians/People/Marlborough#Lord Churchill|Lord Edward Spencer-Churchill]], did his wife Lady Augusta Spencer-Churchill also attend? #Neither the [[Social Victorians/People/Leicester|Earl of Leicester]] nor [[Social Victorians/People/Leicester|Viscount Coke]] are listed as having attended the ball, but did they? #[[Social Victorians/People/Sneyd|Mary Evelyn Ellis Sneyd]] was present at the ball; where was Ralph de Tunstall Sneyd? #[[Social Victorians/People/Murray|Mary Graham Murray]] was present at the ball: where was Andrew Graham Murray? #Mr. [[Social Victorians/People/Strong|Arthur Strong]] was at the ball; was Eugénie Sellers, whom he married less than 6 months later? #Miss [[Social Victorians/People/Naylor|Mary Naylor]]'s sister, Mettie Lady Rossmore, is not listed as having attended the ball; where was she? #Was Juliette Gordon Low, wife of Mr. [[Social Victorians/People/Lowe|W. M. Low]], present and just not mentioned? #Was Maria del Rosario Falcó y Osorio, wife of [[Social Victorians/People/Alva|Carlos Duke of Alba]], present but not mentioned? #[[Social Victorians/People/Maurice Baring#Edith, Countess Cromer|Edith, Countess of Cromer]] (at 462) attended, but Evelyn, Earl of Cromer is not listed. He seems likely to have attended if she did? #Isabella, [[Social Victorians/People/Howe|Countess Howe]] (at 489) was present, but Richard, Earl Howe is not mentioned in any reports. Was he there? #Charles, [[Social Victorians/People/Carrington|Earl Carington]] was present, but his wife Cecilia, Countess Carington is not mentioned in any reports. Was she there? #If [[Social Victorians/People/Wyndham#Mr. George Wyndham|Mr. George Wyndham]] (at 221) is the Right Hon. George Wyndham, who married Sibell Mary [[Social Victorians/People/Scarbrough|Lumley]] Grosvenor, then was she at the ball? Her nephew Alfred Lumley, [[Social Victorians/People/Scarbrough|10th Earl Scarbrough]] attended. #Sir [[Social Victorians/People/Poynter|Edward Poynter]] (at 546) was at the ball, so where was Agnes Poynter? She attended other social events at this level with him. #Rose Towneley-Bertie, [[Social Victorians/People/Norreys|Lady Norreys]] was present at the ball, but Montagu Towneley-Bertie, [[Social Victorians/People/Norreys|Lord Norreys]] was not? #If [[Social Victorians/People/Reuben David Sassoon#Reuben David Sassoon|Reuben David Sassoon]] was at the ball, was his wife, Kate (Catherine Ezekiel) Sassoon? #Gilbert, [[Social Victorians/People/Minto#Mary, Countess of Minto|Earl of Minto]] was still alive; was he at the ball? #Anne Antrobus Elliot, wife of [[Social Victorians/People/Minto#The Right Hon. Henry George Elliot|Henry George Elliot]] (at 279), was still alive at this time; did she attend the ball? #George, [[Social Victorians/People/Coventry|Earl of Coventry]] was still alive at this point, and his wife and two daughters attended the ball. Where was he? #Sir [[Social Victorians/People/Fortescue|Seymour Fortescue]]'s wife Emily Ormsby-Gore Fortescue is not mentioned. Was she at the ball? #Was Lady [[Social Victorians/People/Kintore|Ethel Sydney Keith-Falconer]] at the ball? Her parents and younger sister were, assuming the Album's information is correct. #Neither [[Social Victorians/People/Norreys|Rose, Lady Norreys]] (at 680) nor Montagu, Lord Norreys was mentioned in any press reports, but her portrait was in the commemorative album of portraits. Was he present and just not mentioned? == Notes and Questions == # According to the ''Western Gazette'', three men dressed as Lorenzaccio, whom Sarah Bernhardt was performing at the Adelphi, appeared at the ball.<ref name=":5">"The Duchess of Devonshire's Great Ball. Remarkable Social Function. Crowds of Mimic Kings & Queens. Panorama of Historical Costume. An Array of Priceless Jewels." ''Western Gazette'' 9 July 1897: 2 [of 8], Col. 7A–C. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000407/18970709/009/0002.</ref>{{rp|p. 2, Col. 7C}} # Possibly another group of young women similarly dressed occurs here: "three young girls were noticeable as Reynolds's "Three Ladies Waldegrave"<ref>"The Duchess of Devonshire’s Historic Ball. Some of the Fancy Costumes." ''Leister Chronicle'' 10 July 1897: 11 [of 12], Col. 4a–b. ''British Newspaper Archive''.</ref>{{rp|11, 4a}} The 1780–81 Joshua Reynolds' ''The Ladies Walgrave'' shows 3 young women, probably in "Oriental cream satin," but no "coloured silk sashes" are apparent: https://en.wikipedia.org/wiki/The_Ladies_Waldegrave#/media/File:Sir_Joshua_Reynolds_-_The_Ladies_Waldegrave_-_Google_Art_Project.jpg. Cosway is not Reynolds, so unless one of the reports made a mistake, so these are not [[Social Victorians/People/Villiers|Villiers daughters]] or the [[Social Victorians/People/Roxburghe|Innes-Ker daughters]]. #Who was "Madame Rose" in the 25 June 1897 ''Northampton Mercury'' story<ref name=":6">"For Wives and Daughters." ''Northampton Mercury'' Friday 25 June 1897: 8 [of 10], Col. 3b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000317/18970625/078/0008.</ref> on the ball? A [[Social Victorians/People/Rose|Mr. Rose]] was present at the ball as one of the yeomen in the Queen Elizabeth procession, but she was a businesswoman and he must have been an oligarch or patrician. Madame Rose wrote a fashion column called "For Wives and Daughters" that was published in regional newspapers like the ''Sussex Express, Surrey Standard, Weald of Kent Mail, Hands and County Advertiser''; ''Northampton Mercury''; the ''Burnley Gazette''; and so on, as well as the story on the ball in the 25 June 1897 ''Northampton Mercury''.<ref name=":6" /> (1893–1897). In 1905, the column is called "Home and Fashion. A Letter for Mothers and Daughters," in similar papers as well as the ''Tottenham and Edmonton Herald''.<ref>"Home and Fashion. A Letter for Mothers and Daughters." Tottenham and Edmonton Weekly ''Herald'' 07 June 1905 Wednesday: 4 [of 4], Col. 6–7b–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001716/19050607/031/0004.</ref> A Madame Rose also advertised in the newspapers. For example, "Madame Rose, Court Dressmaker & Ladies' Taylor. Personally Superintends all orders and guarantees perfection in fit and elegance. Speciality in Evening Gowns. Mme. Rose, 30, Shaftesbury Avenue, Piccadilly, one door from Trocadore Restaurant, and 56, two doors from Wardocr-street [sic?]. Tel. 7341 Gerrard."<ref>"Madame Rose." ''The Referee'' 23 October 1904 Sunday: 10 [of 12], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002310/19041023/094/0010.</ref> #The report from the ''Western Gazette'' says some women were dressed as abbesses<ref name=":5" />; who were they? #The ''Westminster Gazette'' says that "There were two or three Napoleons."<ref name=":4" />{{rp|Col. 1}} #Several women came dressed as Princess Lamballe, one of Napoleon's sisters: [[Social Victorians/People/Gordon-Lennox|Lady Blanche (Algernon) Gordon-Lennox]] (at 333); [[Social Victorians/People/Ampthill|Emily, Lady Ampthill]] (at 420); [[Social Victorians/People/Deym|Countess Isabel Deym]] (at 67); [[Social Victorians/People/John Milton Hay|Clara Hay]] (at 153). #The Yeomen in the Queen Elizabeth procession are mostly not notable at this point in their lives though they were present at this event: Henry John Innes-Ker, 8th [[Social Victorians/People/Roxburghe|Duke of Roxburghe]], [[Social Victorians/People/Tweedmouth|Hon. D. (Dudley) Marjoribanks]], [[Social Victorians/People/Mann Thomson|Captain Mann Thomson]], Mr. Rose. According to the ''Gentlewoman'' Mr. E. Villiers, Mr. Harold Brassey were heralds.<ref name=":42" />{{rp|32, Col. 3c}} #The "eight officers of the Imperial Guard attending Catherine of Russia" were the following: "[[Social Victorians/People/Londesborough|Lord Raincliffe]], [[Social Victorians/People/Romilly|Lord Romilly]], Mr. [[Social Victorians/People/Barclay|H. T. Barclay]], Mr. [[Social Victorians/People/Forbes|J. Forbes]], Mr. [[Social Victorians/People/Arthur Stanley Wilson#Charles Henry Wellesley Wilson|C. H. Wellesley Wilson]], Captain [[Social Victorians/People/Cook|E. B. Cook]], the Hon. [[Social Victorians/People/Dudley#Hon. Gerald Ernest Francis Ward|Gerald Ward]], the Hon. [[Social Victorians/People/Campbell|Cecil Campbell]]."<ref name=":42" />{{rp|36, Col. 3b}} #According to the ''Morning Post'' and the ''Gentlewoman'', the Knights of the Round Table were George, [[Social Victorians/People/Rodney|Baron Rodney]]; [[Social Victorians/People/Grosvenor#Hon. R. Grosvenor|Hon. R. Grosvenor]]; Seymour Henry Bathurst, [[Social Victorians/People/Bathurst|7th Earl Bathurst]]; and Hon. Grosvenor [[Social Victorians/People/Hood|Hood]].<ref name=":0" />{{rp|8, Col. 1b}} <ref name=":42" />{{rp|40, Col. 1c}} According to the ''Daily News,'' the Knights of the Table Round were "[[Social Victorians/People/Ashburton|Lord Ashburton]], [[Social Victorians/People/Rodney|Lord Rodney]], [[Social Victorians/People/Bathurst|Lord Bathurst]], [[Social Victorians/People/Ampthill|Lord Ampthill]], and [[Social Victorians/People/Beauchamp|Lord Beauchamp]]."<ref name=":3">"Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses." ''London Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6A–6, Col. 1B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and http://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.</ref>{{rp|5, Col. 7a}} George, Baron Rodney was 40 years old at the time of the ball; [[Social Victorians/People/Grosvenor#Hon. R. Grosvenor|Hon. Robert Victor Grosvenor, 3rd Baron Ebury]] was 29; Seymour Henry Bathurst, [[Social Victorians/People/Bathurst|7th Earl Bathurst]] was nearly 33; Hon. Grosvenor [[Social Victorians/People/Hood|Hood]] was 29;  [[Social Victorians/People/Ashburton|Lord Francis Ashburton]] was nearly 31; [[Social Victorians/People/Ampthill|Lord Ampthill]] was 28; [[Social Victorians/People/Beauchamp|Lord Beauchamp]] was 25. ==References== {{reflist}} * [[Category:Lists]] 90jatllnw7gw7u7kuihlaji7p8lovw9 0 262713 2412346 2412178 2022-08-06T13:02:25Z Rwatson1955 2831054 /* Prevention */ slight change to sentence structure wikitext text/x-wiki {{Article info | journal = WikiJournal of Medicine | first1 = Siang Ching | last1 = Raymond Chieng | orcid1 = 0000-0003-1286-2196 |last2 = |first2 = |last3 = |first3 = |last4 = |first4 = |submitted = 2020-05-01 | affiliation1 = Klinik Kesihatan Bintangor, Sarawak, Malaysia | correspondence1 = by [[w:Special:EmailUser/Cerevisae|online form]] | w1 = Melioidosis | et_al = true | abstract = '''Melioidosis''' is an [[w:infectious disease|infectious disease]] caused by a [[w:gram-negative|gram-negative]] [[w:bacterium|bacterium]] called ''[[w:Burkholderia pseudomallei|Burkholderia pseudomallei]]''.<ref name="Joost 2018"/> Most people exposed to ''B. pseudomallei'' experience no symptoms; however, those who do experience symptoms have signs and symptoms that range from mild such as [[w:fever|fever]] and skin changes, to severe with [[w:pneumonia|pneumonia]], [[w:abscess|abscess]]es, and [[w:septic shock|septic shock]] that could cause death.<ref name="Joost 2018"/> Approximately 10% of people with melioidosis develop symptoms that last longer than two months, termed "chronic melioidosis".<ref name="Joost 2018"/> Humans are infected with ''B. pseudomallei'' by contact with contaminated soil or water. The bacteria enter the body through wounds, inhalation, or ingestion. Person-to-person or animal-to-human transmission is extremely rare.<ref name="Joost 2018"/> The infection is constantly present in Southeast Asia particularly in northeast [[w:Thailand|Thailand]] and northern Australia.<ref name="Joost 2018"/> In temperate countries such as Europe and the United States, melioidosis cases are usually imported from countries where melioidosis is endemic.<ref name="Currie 2015"/> The signs and symptoms of melioidosis resemble [[w:tuberculosis|tuberculosis]] and misdiagnosis is common.<ref name="Yi 2014"/> Diagnosis is usually confirmed by the growth of ''B. pseudomallei'' from an infected person's blood or other bodily fluid such as pus, sputum, and urine.<ref name="Joost 2018"/> Those with melioidosis are treated first with an "intensive phase" course of intravenous antibiotics (most commonly [[w:ceftazidime|ceftazidime]]) followed by a several-months treatment course of [[w:co-trimoxazole|co-trimoxazole]].<ref name="Joost 2018"/> In countries with the advanced healthcare system, approximately 10% of people with melioidosis die from the disease. In less developed countries, the death rate could reach 40%.<ref name="Joost 2018">{{cite journal |author= Wiersinga WJ |author2=Virk HS |author3=Torres AG |author4=Currie BJ et al |title=Melioidosis |journal=Nature Reviews Disease Primers |date=1 February 2018 |volume=4 |issue= |pages=17107 |doi=10.1038/nrdp.2017.107 |pmid=29388572 |pmc=6456913 }}</ref> Efforts to prevent melioidosis include: wearing protective gear while handling contaminated water or soil, practising hand hygiene, drinking boiled water, and avoiding direct contact with soil, water, or heavy rain.<ref name="Joost 2018"/> There is little evidence in supporting the use of melioidosis prophylaxis in humans. The [[w:antibiotic|antibiotic]] [[w:co-trimoxazole|co-trimoxazole]] is used as a preventative only for individuals at high risk for getting the disease after being exposed to the bacteria in laboratory settings.<ref name="Joost 2018"/> One study conducted in 2018 determined that the drug could be useful in preventing melioidosis in high-risk renal failure patients undergoing haemodylysis.<ref>{{cite journal |author=Majoni SW |author2=Hughes JT |author3=Heron B |author4=Currie BJ |title=Trimethoprim+Sulfamethoxazole Reduces Rates of Melioidosis in High-Risk Hemodialysis Patients |journal=Kidney International Reports |date=2018 |volume=3 |issue=1 |pages=160-167 |doi=10.1016/j.ekir.2017.09.005 |pmid=29340327 |pmcid=5762962 }}</ref> There is no approved vaccine for melioidosis.<ref name="Joost 2018"/> Approximately 165,000 people are infected by melioidosis per year, resulting in about 89,000 deaths, based on a mathematical model published in 2016.<ref name="Limmathurotsakul 2016">{{cite journal |author=Limmathurotsakul D |author2=Golding N |author3=Dance DAB |author4=Messina JP et al |title=Predicted global distribution of Burkholderia pseudomallei and burden of melioidosis |journal=Nature Microbiology |date=2016 |volume=1 |issue=1 |pages=15008 |doi=10.1038/nmicrobiol.2015.8 |pmid=26877885 |pmcid=4746747 }}</ref> [[w:Diabetes|Diabetes]] is a major risk factor for melioidosis; over half of melioidosis cases are in people with diabetes.<ref name="Joost 2018"/> Increased rainfall and severe weather events such as thunderstorm are associated with an increased number of melioidosis cases in [[w:Endemic (epidemiology)|endemic]] areas.<ref name="Yi 2014"/> }} ==Signs and symptoms== ===Acute=== {{fig|1 |Melioidosis PA and lateral X rays.jpg |Chest X-ray showing opacity of the left upper lobe of the lung of a patient with melioidosis complicated with pneumonia. |attribution=Samira Rahat Afroze et al, CC BY |size=285px }} {{fig|2 |CT and MRI scan of the brain with melioidosis.jpg |CT and MRI scans showing lesion of the right frontal lobe of the brain of a patient with melioidosis. |attribution=Wei-yuan Huang et al, CC BY |size=285px }} {{fig|3 |Septic arthritis of left hip joint with melioidosis.jpg |Septic arthritis of the left hip with joint destruction due to melioidosis. |attribution=N. P. Weerasinghe et al, CC BY |size=285px }} Most people exposed to ''[[w:Burkholderia pseudomallei|B. pseudomallei]]'' experience no symptoms.<ref name="Yi 2014"/><ref>{{cite journal |author=Mustafa M |author2=Balingi J |author3=Torresi J |author4=Menon J |title=Clinical manifestations, diagnosis, and treatment of Melioidosis |journal=IOSR Journal of Pharmacy |date=February 2015 |volume=5 |issue=2 |pages=2319-4219 |doi= |pmid= |url=https://web.archive.org/web/20220626050909/https://www.ums.edu.my/fpsk/files/12.-Dr.-Fredie-Robinson-IOSR-Journal-of-Pharmacy.pdf }}</ref> The mean [[w:incubation period|incubation period]] of acute melioidosis is 9 days (range 1&ndash;21 days).<ref name="Joost 2018"/> Nevertheless, symptoms of melioidosis can appear in 24 hours for those who experienced near drowning in water.<ref name="Bennett 2015"/> Those affected present with symptoms of [[w:sepsis|sepsis]] (predominantly fever) with or without [[w:pneumonia|pneumonia]], or localised [[w:abscess|abscess]] or other focus of infection. The presence of non-specific signs and symptoms has caused melioidosis to be nicknamed "the great mimicker".<ref name="Joost 2018"/> [[w:diabetes mellitus|Diabetes mellitus]] is one of the most important risk factors in developing melioidosis. The disease should be considered in anyone who has spent time in endemic areas who develops a fever, pneumonia, or abscesses in their liver, spleen, prostate, or parotid gland.<ref name="Joost 2018"/> The clinical manifestation of the disease can range from simple skin changes such as abscesses or ulcerations to severe organ problems.<ref>{{cite journal |author=Fertitta L |author2=Monsel G |author3=Torresi J |author4=Caumes E |title=Cutaneous melioidosis: a review of the literature |journal=The International Society of Dermatology |date=2018 |volume=58 |issue=2 |pages=221–227 |doi=10.1111/ijd.14167 |pmid=30132827 }}</ref> The commonest organs affected are liver, spleen, lungs, prostate, and kidneys. Among the most common features are [[w:bacteremia|bacteremia]] (in 40 to 60% of cases), pneumonia (50%), and [[w:septic shock|septic shock]] (20%).<ref name="Joost 2018"/><ref name="Currie 2021">{{cite journal |author=Currie BJ |author2=Mayo M |author3=Ward LM et al |title=The Darwin Prospective Melioidosis Study: a 30-year prospective, observational investigation |journal=The Lancet - Infectious Diseases |date=1 December 2021 |volume=21 |issue=2 |pages=1737-1746 |doi=10.1016/S1473-3099(21)00022-0 |pmid=34303419 |pmc= }}</ref> People with only pneumonia may have a prominent cough with sputum and shortness of breath. However, those with septic shock together with pneumonia may have minimal coughing.<ref name="Yi 2014"/> Results of a chest X-ray can range from diffuse nodular infiltrates in those with septic shock to progressive [[w:pulmonary consolidation|consolidation]] located most commonly in the [[w:Lung#Anatomy|upper lobes]] for those with pneumonia only. [[w:Pleural effusion|Pleural effusion]] and [[w:empyema|empyema]] are more common for melioidosis affecting lower lobes of the lungs.<ref name="Yi 2014"/> In 10% of cases, people develop secondary pneumonia caused by other bacteria after the primary infection.<ref name="Currie 2015"/> In northern Australia, 60% of the infected children presented with only skin lesions, while 20% presented with pneumonia.<ref name="Currie 2015"/> Depending on the course of infection, other severe manifestations develop. Approximately 1 to 5% of those infected develop [[w:encephalomyelitis|inflammation of the brain and brain covering]] or [[w:brain abscess|brain abscess]]; 14 to 28% develop [[w:acute pyelonephritis|pyelonephritis]], kidney abscess or prostatic abscesses; 0 to 30% develop neck or [[w:parotid gland|salivary gland]] abscesses; 10 to 33% develop liver, spleen, or paraintestinal abscesses; and 4 to 14% develop [[w:septic arthritis|septic arthritis]] and [[w:osteomyelitis|osteomyelitis]].<ref name="Joost 2018"/> Rare manifestations include [[w:lymphadenopathy|lymph node disease]] resembling tuberculosis,<ref name="Gassiep 2020">{{cite journal |author=Gassiep I |author2=Armstrong M |author3=Norton R |title=Human Melioidosis |journal=Clinical Microbiology Reviews |date=11 March 2020 |volume=33 |issue=2 |doi=10.1128/CMR.00006-19 |pmid=32161067 |pmc=7067580 }}</ref> [[w:mediastinum|mediastinal]] masses, [[w:pericardial effusion|pericardial effusion]],<ref name="Currie 2015"/> [[w:mycotic aneurysm|mycotic aneurysm]],<ref name="Joost 2018"/> and [[w:pancreatitis|inflammation of the pancreas]].<ref name="Currie 2015"/> In Australia, up to 20% of infected males develop prostatic abscess which may manifests clinically as [[w:dysuria|pain during urination]], difficulty in passing urine, and [[w:urinary retention|urinary retention]] requiring [[w:catheter|catheter]]isation.<ref name="Joost 2018"/> [[w:Rectal examination|Rectal examination]] may find enlarged [[w:prostate|prostate]].<ref name="Currie 2015"/> In Thailand, 30% of the infected children develop parotid abscesses.<ref name="Joost 2018"/> Encephalomyelitis not only happens in those with risk factors, but can also occur in healthy people without risk factors. Those with melioidosis encephomyelitis tend to have normal [[w:computed tomography|computed tomography]] (CT) scans but increased [[w:T2*-weighted imaging|T2 signal]] by [[w:magnetic resonance imaging|magnetic resonance imaging]] (MRI), extending to the [[w:brain stem|brain stem]] and [[w:spinal cord|spinal cord]]. Clinical signs include: unilateral [[w:upper motor neuron|upper motor neuron]] limb weakness, [[w:focal neurological signs|cerebellar signs]], and cranial nerve palsies ([[w:Sixth nerve palsy|VI]], [[w:Facial nerve paralysis|VII]] nerve palsies and [[w:bulbar palsy|bulbar palsy]]). Some cases presented with [[w:flaccid paralysis|flaccid paralysis]] alone.<ref name="Currie 2015"/> In northern Australia, all melioidosis with encephalomyelitis cases had elevated white cells in the [[w:cerebrospinal fluid|cerebrospinal fluid]] (CSF), mostly [[w:mononuclear cell|mononuclear cell]]s with elevated CSF protein.<ref name="Gassiep 2020"/> ===Chronic=== Chronic melioidosis is usually defined by symptoms lasting greater than two months and occurs in about 10% of patients.<ref name="Joost 2018"/> Clinical presentations include fever, weight loss, productive cough with or without bloody sputum which may mimic [[w:tuberculosis|tuberculosis]]. Additionally, long-standing abscesses at multiple body sites may also present.<ref name="Yi 2014"/> Tuberculosis should be considered for lymph nodes enlargement at the [[w:root of the lung|root of the lung]]. Additionally, pneumonia caused by melioidosis rarely causes scarring and calcification of the lungs, unlike tuberculosis.<ref name="Gassiep 2020"/> ===Latent=== The potential for prolonged incubation was recognized in US servicemen involved in the Vietnam War, and was referred to as the "Vietnam time-bomb".<ref name="Yi 2014"/> Initially, it was thought that the longest period between presumed exposure and clinical presentation is 62 years in a [[w:prisoner of war|prisoner of war]] in Burma-Thailand-Malaysia.<ref name="Ngauy 2005">{{cite journal |author=Ngauy V |author2=Lemeshev Y |author3=Sadkowski L |author4=Crawford G |title=Cutaneous Melioidosis in a Man Who Was Taken as a Prisoner of War by the Japanese during World War II |year=2005 |journal=Journal of Clinical Microbiology |volume=43 |issue=2 |pages=970&ndash;972 |pmid=15695721 |doi=10.1128/JCM.43.2.970-972.2005 |pmc=548040 }}</ref> However, subsequent genotyping of the bacteria isolate from the Vietnam veteran showed that the isolate may not come from [[w:Southeast Asia|Southeast Asia]], but from South America.<ref>{{cite journal |author=Gee JE |author2=Gulvick CA |author3=Elrod MG et al |title=Phylogeography of Burkholderia pseudomallei Isolates, Western Hemisphere |journal=Emergency Infectious Disease |date=July 2017 |volume=23 |issue=7 |pages=1133–1138 |doi=10.3201/eid2307.161978 |pmid=28628442 |pmc=5512505 }}</ref> This reinstates another report that put the longest latency period for melioidosis as 29 years.<ref>{{cite journal |author=Chodimella U |author2=Hoppes WL |author3=Whalen S |title=Septicemia and suppuration in a Vietnam veteran |journal=Hospital Practice |date=15 May 1997 |volume=32 |issue=5 |pages=219–221 |pmid=9153149 |doi=10.1080/21548331.1997.11443493 }}</ref> Patients with latent melioidosis may be symptom-free for decades.<ref name="Ngauy 2005"/> Less than 5% of all melioidosis cases have activation after a period of latency.<ref name="Joost 2018"/> Various comorbidities such as diabetes, renal failure, and alcoholism can predispose to reactivation of melioidosis.<ref name="Yi 2014"/> ==Cause== ===Bacteria=== {{fig|4 |Burkholderia pseudomallei gram stain safety pin apperance.jpg |''B. pseudomallei'' with bipolar gram staining showing safety pin appearance. |attribution=Neha Shrestha, CC BY |size=285px }} Melioidosis is caused by [[w:gram-negative|gram-negative]], [[w:motility|motile]], [[w:Saprotrophic nutrition|saprophytic]] bacteria named ''Burkholderia pseudomallei''.<ref name="Chakravorty 2019">{{cite journal |author= Chakravorty A |author2=Heath C |title=Melioidosis: An updated review |journal= Australian Journal of General Practice |date=5 May 2019 |volume=48 |issue=5 |pages=327-332 |doi=10.31128/AJGP-04-18-4558 |pmid=31129946 }}</ref> The bacteria are usually [[w:opportunistic infection|opportunistic]], [[w:Facultative parasite|facultative]] [[w:intracellular|intracellular]] pathogens.<ref name="Chakravorty 2019"/> It is also aerobic and [[w:oxidase test|oxidase test]] positive.<ref name="Yi 2014"/> A granule at the centre of the bacterium makes it resemble a “safety pin” when [[w:Gram stain|Gram stain]]ed.<ref name="Yi 2014"/> The bacteria emit a strong soil smell after 24 to 48 hours of growth in culture, however smelling for the identification of the bacteria is not recommended for routine laboratory practice. One of the factors causing ''B. pseudomallei'''s resistance to various kinds of antibiotics is because of its production of a [[w:glycocalyx|glycocalyx]] [[w:polysaccharide|polysaccharide]] capsule.<ref name="Allen C 2005">{{cite journal |author=Cheng AC |author2=Currie BJ |title=Melioidosis: Epidemiology, Pathophysiology, and Management |journal=Clinical Microbiology Reviews |date=April 2005 |volume=18 |issue=2 |pages=383–416 |doi=10.1128/CMR.18.2.383-416.2005 |pmid=15831829 |pmc=1082802 }}</ref> It is generally resistant to [[w:gentamicin|gentamicin]] and [[w:colistin|colistin]] but sensitive to [[w:amoxicillin/clavulanic acid|co-amoxiclav]]. ''B. pseudomallei'' is a [[w:biosafety level|biosafety level]] 3 pathogen which requires specialized laboratory handling.<ref name="Yi 2014"/> In humans and animals, another similar organism named ''[[w:Burkholderia mallei|Burkholderia mallei]]'' is the causative agent of the disease [[w:glanders|glanders]].<ref name="Joost 2018"/> ''B. pseudomallei'' can be differentiated from another closely related, but less pathogenic species ''B. thailandensis'' by its ability to assimilate [[w:arabinose|arabinose]].<ref name="Gassiep 2020"/> ''B. pseudomallei'' is highly adaptable to various host environments ranging from inside [[w:Mycorrhiza|mycorrhizal fungi]] spores to [[w:amoeba|amoeba]].<ref name="Yi 2014"/> Its adaptability may give it a survival advantage in the human body.<ref name="Joost 2018"/> The genome of ''B. pseudomallei'' consists of two [[w:replicon (genetics)|replicons]]: chromosome 1 encodes [[w:housekeeping gene|housekeeping functions]] of the bacteria such as cell wall synthesis, mobility, and metabolism; chromosome 2 encodes functions that allow the bacteria to adapt to various environments. [[w:Horizontal gene transfer|Horizontal gene transfer]] has resulted in highly variable genomes in ''B. pseudomallei''. Australia has been suggested as the origin for ''B. pseudomallei'' because of the high genetic variability of the bacteria found in this region. Bacteria that was introduced to Central and South America in the 17th to 19th centuries seem to have a common ancestor from Africa.<ref name="Chewapreecha 2017">{{cite journal |author= Chewapreecha C |author2=Holden MT |author3=Vehkala M |author4=Välimäki N et al |title=Global and regional dissemination and evolution of Burkholderia pseudomallei |journal= Nature Microbiology |date=23 January 2017 |volume=2 |issue=16263 |pages=1-8 |doi=10.1038/nmicrobiol.2016.263 |pmid=28112723 |pmcid=5300093 }}</ref> ''B. mallei'' is a clone of ''B. pseudomallei'' that has lost substantial portions of its genome as it adapted to live exclusively in mammals.<ref name="Currie 2015">{{cite journal |author=Currie BJ |title=Melioidosis: evolving concepts in epidemiology, pathogenesis, and treatment |journal=Seminars in Respiratory and Critical Care Medicine |date=February 2015 |volume=36 |issue=1 |pages=111–125 |doi=10.1055/s-0034-1398389 |pmid=25643275 }}</ref> This makes the ''B. mallei'' genome much smaller than ''B. pseudomallei''.<ref name="Nierman 2004">{{cite journal |author=Nierman WC |author2=DeShazer D |author3=Kim HS |title=Structural flexibility in the Burkholderia mallei genome |journal=Proceedings of National Academy of Science of United States of America |date=28 September 2004 |volume=101 |issue=39 |pages=14246-14251 |doi=10.1073/pnas.0403306101 |pmid=15377793 |pmc=521142 }}</ref> ===Transmission=== ''B. pseudomallei'' is normally found in soil and surface water, and is most abundant at soil depths of 10 to 90 cm.<ref name="Joost 2018"/> It has been found in soils, ponds, streams, pools, stagnant water, and rice paddy fields.<ref name="Yi 2014">{{cite journal |author=Foong YC |author2=Tan M |author3=Bradbury RS |title=Melioidosis: A Review |journal=Journal of Remote and Rural Health |date=30 October 2014 |volume=14 |issue=4 |pages=2763 |pmid=25359677|doi=10.22605/RRH2763 |url=https://www.rrh.org.au/journal/article/2763 }}</ref> ''B. pseudomallei'' can survive in nutrient-poor conditions such as distilled water, desert soil, and nutrient-depleted soil for more than 16 years.<ref name="Joost 2018"/> It can also survive in antiseptic and detergent solutions, acidic environments ([[w:pH|pH]] 4.5 for 70 days), and in environments at temperatures ranging from 24 °C (75.2 °F) to 32 °C (89.6 °F). However, the bacteria may be killed by the presence of ultraviolet light.<ref name="Joost 2018"/> Bacteria can enter the body through wounds, inhalation, and [[w:ingestion|ingestion]] of contaminated soil or water.<ref name="Joost 2018"/> Person-to-person transmission is extremely rare.<ref name="Yi 2014"/> Melioidosis is a recognised disease in animals including pigs, cats, dogs, goats, sheep, horses and others. Cattle, water buffalo, and crocodiles are considered to be relatively resistant to melioidosis despite their constant exposure to mud. Birds are also considered resistant to melioidosis although several cases had been reported in Australia and aquatic birds.<ref name="Gassiep 2020"/><ref name="Allen C 2005"/> [[w:zoonosis|Transmission from animals to humans]] is rare.<ref name="Joost 2018"/><ref name="Yi 2014"/> Inadequate [[w:Water chlorination|chlorination]] of water supply has been associated with ''B. pseudomallei'' outbreak in Northern and Western Australia.<ref name="Currie 2001">{{cite journal |author=Currie BJ |author2=Mayo M |author3=Anstey NM |author4=Donohoe P |author5=Haase A |author6=Kemp DJ |title=A cluster of melioidosis cases from an endemic region is clonal and is linked to the water supply using molecular typing of Burkholderia pseudomallei isolates |journal=American Society of Tropical Medicine and Hygiene |date=September 2001 |volume=65 |issue=3 |pages=177-179 |pmid=11561699 |doi=10.4269/ajtmh.2001.65.177 }}</ref><ref name="Inglis">{{cite journal |author=Inglis TJ |author2=Garrow SC |author3=Adams C |author4=Henderson M |author5=Mayo M |author6=Currie BJ |title=Acute melioidosis outbreak in Western Australia |journal=Epidemiology and Infections |date=December 1999 |volume=123 |issue=3 |pages=437-443 |pmid=10694154 |pmc= 2810777 | doi=10.1017/s0950268899002964 }}</ref> The were also several cases of where bacteria have also been found in unchlorinated water supply in rural Thailand.<ref name="Limmathurotsakul 2012">{{cite journal |author=Limmathurotsakul D |author2=Wongsuvan G |author3=Aanensen D |author4=Ngamwilai S |title=Melioidosis Caused by Burkholderia pseudomallei in Drinking Water, Thailand, 2012 |journal=Emerging Infectious Diseases |date=February 2014 |volume=20 |issue=2 |pages=265-268 |pmid=24447771 |pmc=3901481 |doi=10.3201/eid2002.121891 }}</ref> Based on the whole genome sequencing of the bacteria, the variety of the bacteria ''B. pseudomallei'' in Papua New Guinea is narrow due to limited movements of the indigenous people. This findings supports the hypothesis that humans play an important role in bacterial transmission.<ref>{{cite journal |author=Baker A |author2=Pearson T |author3=Price EP |author4=Dale J et al |title=Molecular Phylogeny of Burkholderia pseudomallei from a Remote Region of Papua New Guinea |journal=PLOS One |year=2011 |volume=6 |issue=3 |pages=e18343 |pmid=21483841 |pmc=3069084 |doi=10.1371/journal.pone.0018343 |bibcode=2011PLoSO...618343B }}</ref> ==Pathogenesis== {{fig|5 |Pathogenesis of melioidosis.svg |Ways of ''B. pseudomallei'' bacteria infecting human cells and blood stream. |attribution=Cerevisae, CC BY-SA |size=285px }} ''B. pseudomallei'' has the ability to infect various types of cells and to evade human immune responses. Bacteria first enter at a break in the skin or [[w:mucous membrane|mucous membrane]] and replicate in the epithelial cells. From there, they use [[w:flagella|flagella]]r motility to spread and infect various cell types.<ref name="Gassiep 2020"/> In the bloodstream, the bacteria can infect both [[w:phagocyte|phagocyte]]s and non-phagocytes.<ref name="Gassiep 2020"/> ''B. pseudomallei'' use their flagella to move near [[w:Host (biology)|host]] cells, then attach to the cells using various adhesion proteins, including the [[w:type IV pilus|type IV pilus]] protein PilA as well as adhesion proteins BoaA and BoaB.<ref name="Gassiep 2020"/> Additionally, adhesion of the bacteria partially depends on the presence of the host protein [[w:Coagulation factor II receptor|Protease-activated receptor-1]] which is present on the surface of [[w:endothelial cell|endothelial cell]]s, [[w:platelet|platelet]]s, and [[w:monocyte|monocyte]]s. Once bound, the bacteria enter host cells through [[w:endocytosis|endocytosis]], ending up inside an endocytic [[w:Vesicle (biology and chemistry)|vesicle]]. As the vesicle acidifies, ''B. pseudomallei'' uses its [[w:Bacterial secretion system#Type III secretion system (T3SS or TTSS)|Type 3 secretion system]] (T3SS) to inject effector proteins into the host cell, disrupting the vesicle and allowing the bacteria to escape into the host [[w:cytoplasm|cytoplasm]]. Within the host cytoplasm, the bacteria evade being killed by the host [[w:autophagy|autophagy]] using various T3SS effector proteins. The bacteria replicate in the host cytoplasm.<ref name="Joost 2018"/><ref name="Gassiep 2020"/> Inside the host cell, the bacteria move by inducing the polymerization of the host [[w:actin|actin]] behind them, propelling the bacteria forward.<ref name="Joost 2018"/> This actin-mediated motility is accomplished with the [[w:Secretion#Type V secretion system .28T5SS.29|autotransporter]] BimA which interacts with actin at the tail-end of the bacterium.<ref name="Joost 2018"/><ref name="Gassiep 2020"/> The bacteria that has BimABm [[w:allele|allele]] has higher possibility of causing neurological melioidosis, thus higher chance of death and residual disability to the host when compared to the bacteria that has BimABp variant.<ref>{{cite journal |author=Gora H |author2=Hasan T |author3=Smith S et al. |title=Melioidosis of the central nervous system; impact of the bimABm allele on patient presentation and outcome |journal=Clinical Infectious Diseases |date=7 February 2022 |volume |issue= |pages=ciac111 |doi=10.1093/cid/ciac111 |pmid=35137005 }}</ref> Propelled by actin, the bacteria push against the host membrane, creating protrusions that extend into neighbouring cells. These protrusions cause neighboring cells to fuse, leading to the formation of [[w:multinucleated giant cells|multinucleated giant cells]] (MNGCs). When MNGCs lyse, they form plaques (a central clear area with a ring of fused cells) that provide shelter for the bacteria for further replication or [[w:latent infection|latent infection]]. This same process in infected neurons can allow bacteria to travel through nerve roots in the spinal cord and brain, leading to [[w:encephalomyelitis|inflammation of the brain and spinal cord]]. In addition to spreading from cell to cell, the bacteria can also spread through the bloodstream, causing sepsis. The bacteria can survive in [[w:antigen-presenting cell|antigen-presenting cell]]s and [[w:dendritic cell|dendritic cell]]s. Thus, these cells act as vehicles that transport the bacteria into the lymphatic system, causing widespread dissemination of the bacteria in the human body.<ref name="Joost 2018"/><ref name="Gassiep 2020"/> While ''B. pseudomallei'' can survive in phagocytic cells, these cells can kill ''B. pseudomallei'' by several mechanisms. Macrophages activated by [[w:interferon gamma|interferon gamma]] (IFN) have improved the killing of ''B. pseudomallei'' via the production of [[w:Nitric oxide synthase#iNOS|inducible nitric oxide synthase]]. Acidification of the endosome and degradation of the bacteria is also possible, however, the bacterial capsule and LPS makes ''B. pseudomallei'' resistant to lysosomal degradation. Once ''B. pseudomallei'' escapes into the host cytosol it can be recognized by [[w:pattern recognition receptor|pattern recognition receptor]]s such as [[w:NOD-like receptor|NOD-like receptor]]s, triggering the formation of the [[w:inflammasome|inflammasome]] and activation of [[w:caspase 1|caspase 1]], which induces death of the host cell by [[w:pyroptosis|pyroptosis]] and further activation of the immune system. Several systemic host defenses also contribute to the immune response. ''B. pseudomallei'' triggers both the [[w:complement system|complement system]] and [[w:coagulation cascade|coagulation cascade]], however the thick bacterial capsule prevent the action of the [[w:complement membrane attack complex|complement membrane attack complex]].<ref name="Joost 2018"/><ref name="Gassiep 2020"/> Additional elements of the immune system are activated by the host [[w:toll-like receptor|toll-like receptor]]s such as TLR2, TLR4, and TLR5 that recognize the [[w:pathogen-associated molecular pattern|conserved piece]]s of the bacteria such as LPS and flagella. This activation results in the production of [[w:cytokine|cytokine]]s such as [[w:Interleukin 1 beta|Interleukin 1 beta]] (IL-1β) and [[w:Interleukin 18|Interleukin 18]] (IL-18). IL-18 increases IFN production through [[w:natural killer cell|natural killer cell]]s while IL-1beta reduces the IFN production. These immune molecules drive the recruitment of other immune cells such as [[w:neutrophil|neutrophil]]s, [[w:dendritic cell|dendritic cell]]s, [[w:B cell|B cell]]s, and [[w:T cell|T cell]]s to the site of infection. T cells seem to be particularly important for controlling ''B. pseudomallei''; T cell numbers are increased in survivors, and low T cell numbers are associated with a high risk of death from melioidosis. Despite this, HIV infection is not a risk factor for melioidosis. Although macrophages show deregulated [[w:cytokine|cytokine]] responses in individuals with HIV infection, bacterial internalization and intracellular killing are still effective. People infected with ''B. pseudomallei'' may develop antibodies against the bacteria, and people that live in endemic areas tend to have antibodies in their blood that recognize ''B. pseudomallei''. However, the effectiveness of these antibodies at preventing melioidosis is unclear.<ref name="Joost 2018"/><ref name="Gassiep 2020"/> ''B. pseudomallei'' can remain latent in the human body for up to 29 years until it is reactivated during human [[w:immunosuppression|immunosuppression]] or stress response. However, the site of bacteria during latent infection and the mechanism by which they avoid immune recognition for years are both unclear. Amongst mechanisms suggested are: residing in the nucleus of the cell to prevent being digested, entering a stage of slower growth, antibiotic resistance, and genetic adaption to the host environment. [[w:Granuloma|Granuloma]]s (containing neutrophils, macrophages, lymphocytes, and multinucleated giant cells) formed at the infection site in melioidosis have been associated with latent infection in humans.<ref name="Joost 2018"/> ==Diagnosis== {{fig|6 |Bps close.JPG |Appearance of ''B. pseudomallei'' colonies on Ashdown's medium after four days of incubation. |attribution=Gavin Koh, CC BY-SA |size=285px }} {{fig|7 |Immunofluorescent-stained sample of guinea pig tissue leads to positive diagnosis of melioidosis.png |Immunofluorescent microscopy showing the presence of rod-shaped ''B. pseudomallei'' (circled area) on a guinea pig tissue. |attribution=Dr. Biegeleisen, CDC, Public Domain |size=285px }} {{fig|8 |Latex agglutination test positive for melioidosis.jpg |Right most slide showing positive latex agglutination for melioidosis. Latex agglutination uses latex coated antibodies to detect melioidosis antigens. |attribution=Neha Shrestha, CC BY |size=285px }} ===Culture=== Bacterial culture has 60% sensitivity in diagnosing melioidosis.<ref name="Limmathurotsakul 2010">{{cite journal |author=Limmathurotsakul D |author2=Jamsen K |author3=Arayawichanont A |author4=Simpson JA et al |title=Defining the True Sensitivity of Culture for the Diagnosis of Melioidosis Using Bayesian Latent Class Models |journal=PLOS One |date=30 August 2010 |volume=5 |issue=8 |pages=e12485 |pmid=20830194 | pmc=2932979 | doi=10.1371/journal.pone.0012485 }}</ref> ''B. pseudomallei'' is never part of human flora. Therefore, any growth of the bacteria is diagnostic of melioidosis. Other samples such as throat, rectal swabs, pus from abscesses, and sputum can also be used for culture.<ref name="Joost 2018"/> However, culture from CSF is difficult because in one case series, only 29% of the neuromelioidosis cases are culture positive.<ref name="Gassiep 2020"/> When bacteria do not grow from people strongly suspected of having melioidosis, repeated cultures should be taken as subsequent cultures can become positive.<ref name="Joost 2018"/> ''B. pseudomallei'' can be grown on any blood agar, [[w:MacConkey agar|MacConkey agar]], and agar containing antibiotics such as [[w:Ashdown's medium|Ashdown's medium]] (containing [[w:gentamicin|gentamicin]]),<ref name="Gassiep 2020"/> and Ashdown's broth (containing [[w:colistin|colistin]])<ref name="Currie 2015"/> for better isolation of ''B. pseudomallei'' from other types of bacteria.<ref name="Gassiep 2020"/> Agar plates for melioidosis should be incubated at 37 °C (98.6 °F) in air <ref name="Yi 2014"/> and inspected daily for four days. On the agar plates, ''B. pseudomallei'' forms creamy, [[w:Hemolysis (microbiology)|non-haemolytic]], colonies after 2 days of incubation. After 4 days of incubation, colonies appear dry and wrinkled.<ref name="Joost 2018"/> Colonies of ''B. pseudomallei'' that are grown on Francis medium (a modification of Ashdown medium with gentamicin concentration increased to 8&nbsp;mg/L and neutral red indicator replaced with 0.2% bromocresol purple) are yellow.<ref name="Francis 2006">{{cite journal |author=Francis A |author2=Aiyar S |author3=Yean Yean C |author4=Naing L |author5=Ravichandran M |title=An improved selective and differential medium for the isolation of Burkholderia pseudomallei from clinical specimens |journal=Diagnostic Microbiology and Infectious Disease |date=28 November 2005 |volume=55 |issue=2 |pages=95-99 |pmid=16626918 | doi=10.1016/j.diagmicrobio.2005.11.008}}</ref> For laboratories located outside endemic areas, ''Burkholderia cepacia'' selective agar can be used if Ashdown's medium is not available.<ref name="Yi 2014"/> It is important not misinterpret the bacterial growth as ''[[w:Pseudomonas|Pseudomonas]]'' or ''[[w:Bacillus|Bacillus]]'' spp. Other biochemical screening tools can also be used for detecting ''B. pseudomallei'', including the [[w:analytical profile index|API 20NE or 20E biochemical kit]] combined with Gram stain, [[w:oxidase test|oxidase test]], typical growth characteristics, and resistance to certain antibiotics of the bacteria.<ref name="Currie 2015"/> API 20NE biochemical kit is 99% sensitive in identifying ''B. pseudomallei''.<ref name="Gassiep 2020"/> Molecular methods such as 16S rDNA sequencing, multiplex [[w:polymerase chain reaction|polymerase chain reaction]] (PCR), and real-time PCR can also be used to identify ''B. pseudomallei'' in culture.<ref name="Joost 2018"/><ref name="Fook Koh 2012">{{cite journal |author=Koh SF |author2=Tay ST |author3=Sermswan R |author4=Wongratanacheewin S et al |title=Development of a multiplex PCR assay for rapid identification of Burkholderia pseudomallei, Burkholderia thailandensis, Burkholderia mallei and Burkholderia cepacia complex |journal=Journal of Microbiological Methods |date=September 2012 |volume=90 |issue=3 |pages=305-308 |pmid=22705921 |doi=10.1016/j.mimet.2012.06.002 }}</ref><ref name="Gee 2003">{{cite journal |author=Gee JE |author2=Sacchi CT |author3=Glass MB |author4=Dee BK et al |title=Use of 16S rRNA gene sequencing for rapid identification and differentiation of Burkholderia pseudomallei and B. mallei |date=October 2003 |volume=41 |issue=10 |pages=4547-4654 |pmid=14532197 |pmc= 254370 |doi=10.1128/jcm.41.10.4647-4654.2003 }}</ref><ref name="Wang 2022"/> Other bacterial genes such as fliC genes encoding flagellin, rpsU gene encoding for ribosomal protein, and TTS genes encoding Type III secretion systems has also been employed for detection. Another method of gene detection namely [[w:multiple displacement amplification|multiple cross displacement amplification]] for the bacterial TTS1 gene detection produces results within an hour.<ref name="Wang 2022">{{cite journal |author=Wang X |author2=Wang L |author3=Zhu H et al |title=Reliable detection of Burkholderia pseudomallei using multiple cross displacement amplification label-based biosensor |date=10 March 2022 |volume=22 |issue=72 |pages= |pmid=35272632 |pmc= PMC8908694 |doi=10.1186/s12866-022-02485-2 }}</ref> ===Hematological and biochemical tests=== General blood tests in people with melioidosis show low white blood cell counts (indicates infection), raised liver enzymes, increased [[w:bilirubin|bilirubin]] levels (indicates liver dysfunction), and raised urea and creatinine levels (indicates kidney dysfunction). [[w:Hypoglycemia|Low blood glucose]] and [[w:acidosis|acidosis]] predicts a poorer prognosis in those with melioidosis. However, other tests such as [[w:C-reactive protein|C-reactive protein]] and [[w:procalcitonin|procalcitonin]] levels are not reliable in predicting the severity of melioidosis infection.<ref name="Allen C 2005"/> ===Serological tests=== [[w:serology|Serological test]]s such as indirect [[w:haemagglutination assay|haemagglutination]] assay (IHA) have been used to detect the presence of antibodies against ''B. pseudomallei''. However, different groups of people have widely different levels of antibodies, so interpretation of these tests depends on location. In Australia, less than 5% of people have ''B. pseudomallei'' antibodies, so the presence of even relatively low amounts of antibody is unusual and could suggest melioidosis. In Thailand, many people have antibodies against ''B. pseudomallei'' so the diagnosis of melioidosis should not be reliant entirely on the serological tests done in endemic areas.<ref name="Joost 2018"/><ref name="Currie 2015"/> Indirect immunofluorescent test (IFAT) uses either ''B. pseudomallei'' or ''B. thailandensis'' antigens to look for the total number of antibodies in human serum. Using IFAT is labour intensive and is not used in large scale investigations.<ref name="Suat Moi 2013">{{cite journal |author=Puah SM |author2=Puthucheary SD |author3=Chua KH |title=Potential Immunogenic Polypeptides of Burkholderia pseudomallei Identified by Shotgun Expression Library and Evaluation of Their Efficacy for Serodiagnosis of Melioidosis |journal=International Journal of Medical Sciences |date=2013 |volume=10 |issue=5 |pages=539-547 |pmid=23532805 |pmc=3607239 |doi=10.7150/ijms.5516 }}</ref> Antigen detect tests allow rapid detection of melioidosis. Examples of antigen detection tests are: latex agglutination test and [[w:ELISA|ELISA]]. [[w:Latex agglutination|Latex agglutination]] uses antibodies coated on latex beads to detect ''B. pseudomallei'' antigens in solid or liquid media, although not all the assays can detect different species of ''Burkholderia''.<ref name="Amornchai 2007">{{cite journal |author=Amornchai P |author2=Chierakul W |author3=Wuthiekanun V |author4=Mahakhunkijcharoen Y et al |title=Accuracy of Burkholderia pseudomallei Identification Using the API 20NE System and a Latex Agglutination Test |journal=Journal of Clinical Microbiology |date=2007 |volume=45 |issue=11 |pages=3774-3776 |pmid=17804660 | pmc=2168515 | doi=10.1128/JCM.00935-07 }}</ref> Latex agglutination is useful in screening for suspected ''B. pseudomallei'' colonies.<ref name="Joost 2018"/> IgG and IgM ELISAs has been used to detect lipopolysaccharide (LPS) antigens of ''B. pseudomallei'', but plagued with low sensitivity.<ref name="KP Lau 2015">{{cite journal |author=KP Lau S |author2=Sridhar S |author3=Chun Ho C et al |title=Laboratory diagnosis of melioidosis: Past, present and future |journal=Experimental Biology and Medicine |date=June 2015 |volume=240 |issue=6 |pages=742-751 |pmid=25908634 |pmc=PMC4935216 |doi=10.1177/1535370215583801 }}</ref> Commercial ELISA kits for melioidosis no longer available in the market due to low sensitivity to human antibodies detection.<ref name="Gassiep 2020"/> Nevertheless, antigen detection tests may be useful in severely ill patients because the bacterial load is high enough for detection. Other methods of antigen detection such as [[w:direct fluorescent antibody|direct immunofluorescence]], antibody-sandwich ELISAs, and [[w:lateral flow test|lateral flow immunoassays]] using [[w:monoclonal antibody|monoclonal antibody]].<ref name="KP Lau 2015"/> ===Microscopy=== By microscopy, ''B. pseudomallei'' is seen as [[w:Gram stain|gram-negative]] and rod-shaped, with a bipolar staining similar in appearance to a safety pin. Bacteria can sometimes be seen directly in clinical samples from infected people; however, identification by light microscopy is neither [[w:Sensitivity and specificity|specific]] nor [[w:Sensitivity and specificity|sensitive]]. [[w:Immunofluorescence microscopy|Immunofluorescence microscopy]] is highly specific for detecting bacteria directly from clinical specimens, but has less than 50% sensitivity.<ref name="Joost 2018"/><ref name="Currie 2015"/> ===Imaging=== Various imaging modalities can also help with the diagnosis of melioidosis. In acute melioidosis with the spreading of the bacteria through the bloodstream, the chest X-ray shows multifocal nodular lesions. It may also show merging nodules or [[w:cavitary pneumonia|cavitations]]. For those with acute melioidosis without the spread to the bloodstream, chest x-ray most commonly shows upper lobe [[w:Pulmonary consolidation|consolidation]] or cavitations.<ref name="Gassiep 2020"/> In chronic melioidosis, the slowly progressing of upper lobe consolidation of the lungs resembles tuberculosis.<ref name="Gassiep 2020"/> For abscesses located in other parts of the body apart from the lungs, especially in the liver and spleen, [[w:computed tomography|CT]] scan has higher sensitivity when compared with an ultrasound scan. In liver and splenic abscesses, an ultrasound scan shows "target-like" lesions while CT scan shows "honeycomb sign" (abscess with loculations separated by thin septa) in liver abscesses.<ref name="Gassiep 2020"/> For melioidosis involving the brain, MRI have higher sensitivity than a CT scan in diagnosing the lesion. MRI shows ring-enhancing lesions for brain melioidosis.<ref name="Gassiep 2020"/> ==Prevention== Melioidosis is a notifiable disease in Australia<ref name="Gassiep 2020"/> which enables the country to monitor disease burden and contain outbreaks. On the other hand, melioidosis is only a notifiable condition in Thailand since June 2016.<ref name="Gassiep 2020"/><ref name="Hantrakun 2019">{{cite journal |author=Hantrakun V |author2=Kongyu S |author3=Klaytong P |author4=Rongsumlee S et al |title=Clinical Epidemiology of 7126 Melioidosis Patients in Thailand and the Implications for a National Notifiable Diseases Surveillance System |journal= Open Forum Infectious Diseases |date=19 November 2019 |volume=6 |issue=12 |pages=ofz498 |pmid=32083145 | pmc=7020769 | doi=10.1093/ofid/ofz498 }}</ref> However, until recently, the official notification system in Thailand has significantly underestimated the incidence of culture-positive melioidosis and its mortality.<ref name="Hantrakun 2019"/> Nevertheless, Australia also embarked on awareness campaigns to increase the community's understanding of the disease.<ref name="Gassiep 2020"/> In the United Kingdom, where reporting by laboratories is mandatory, 41.3% of cases imported since 2010 were not notified.<ref name="Conor 2020">{{cite journal |author=Conor CO |author2=Kenna D |author3=Walsh A et al |title=Imported melioidosis in the United Kingdom: Increasing incidence but continued under-reporting |journal= Journal of Clinical Microbiology |date=October 2020 |volume=7 |issue= |pages=100051 |pmid= | pmc= | doi=10.1016/j.clinpr.2020.100051 }}</ref> In the United States, lab workers can handle clinical specimens of ''B. pseudomallei'' under [[w:BSL-2|BSL-2]] conditions, while mass production of such organisms requires [[w:BSL-3|BSL-3]] precautions.<ref>{{cite book |author=Centers for Disease Control and Prevention |title=Biosafety in Microbiological and Biomedical Laboratories |publisher=National Institutes of Health |location=Atlanta, Georgia |year=2009 |edition=5th }}</ref> On the other hand, in other endemic areas where the ''B. pseudomallei'' samples were handled less stringently, there has been no confirmed laboratory-acquired infection reported. This phenomenon may show that the risk of infection with ''B. pseudomallei'' is less than a typical biohazard type 3 agent.<ref name="Dance 2017">{{cite journal |author=Dance DAB |author2=Limmathurotsakul D |author3=Currie BJ |title=Burkholderia pseudomallei: Challenges for the Clinical Microbiology Laboratory—a Response from the Front Line |journal= Journal of Clinical Microbiology |date=February 2017 |volume=55 |issue=3 |pages=980-982 |pmid=28232503 | pmc=5328468 | doi=10.1128/JCM.02378-16 }}</ref> There are also several cases of hospital-acquired infection of melioidosis.<ref name="Joost 2018"/> Therefore, healthcare providers are recommended to practice hand hygiene and [[w:universal precautions|universal precautions]].<ref name="Joost 2018"/> Large-scale water chlorination has been successful at reducing ''B. pseudomallei'' in the water in Australia.<ref name="Howard 2003">{{cite journal |author=Howard K |author2=Inglis TJJ |title=The effect of free chlorine on Burkholderia pseudomallei in potable water |journal= Water Research |date=February 2017 |volume=37 |issue=18 |pages=4425-4432 |pmid=14511713 | doi=10.1016/S0043-1354(03)00440-8 }}</ref><ref name="Joost 2018"/> In middle to low-income countries, water should be boiled before consumption.<ref name="Joost 2018"/> In high income countries, water could be treated with ultraviolet light for those at risk of contracting melioidosis.<ref name="McRobb E 2013">{{cite journal |author=McRobb E |author2=Kaestli M |author3=Mayo M |author4=Price EP et al |title= Melioidosis from Contaminated Bore Water and Successful UV Sterilization |journal= American Journal of Tropical Medicine and Hygiene |date=7 August 2013 |volume=89 |issue=2 |pages=367-368 |pmid=23751401 | pmc=3741262 | doi=10.4269/ajtmh.13-0101 }}</ref><ref name="Joost 2018"/> Those who are at high risk of contact with the bacteria should wear protective gear (such as boots and gloves) during work.<ref name="Joost 2018"/> Those staying in endemic areas should avoid direct contact with soil, and outdoor exposure to heavy rain or dust clouds. Bottled water or boiled water are preferred as drinking water.<ref name="Limmathurotsakul 2013">{{cite journal |author=Limmathurotsakul D |author2=Kanoksil M |author3=Wuthiekanun V et al |title= Activities of daily living associated with acquisition of melioidosis in northeast Thailand: a matched case-control study |journal= PLOS Neglected Tropical Diseases |date= 2013 |volume=7 |issue=2 |pages=e2072 |pmid=23437412 | pmc=3578767 | doi=10.1371/journal.pntd.0002072 }}</ref><ref name="Joost 2018"/> A study conducted from 2014 to 2018, however showed no significant differences on whether behavioural changes can reduce the risk of contracting melioidosis. Modification of behavioural changes or more frequent interventions may be needed to ensure a definite reduction in risk of getting melioidosis.<ref name="Suntornsut 2021">{{cite journal |author=Suntornsut P |author2=Teparrukkul P |author3=Wongsuvan G et al |title= Effectiveness of a multifaceted prevention programme for melioidosis in diabetics (PREMEL): A stepped-wedge cluster-randomised controlled trial |date= June 2021 |volume=15 |issue=6 |pages=e0009060 |pmid=34170931 | pmc=PMC8266097 | doi=10.1371/journal.pntd.0009060 }}</ref> ===Antibiotic prophylaxis=== Administering cotrimoxazole three times a week throughout a wet season for dialysis patients has no obvious benefit of preventing melioidosis. Besides, high cost and side effects of this drug limits its use to only those with high risk of getting melioidosis.<ref name="Chau 2018">{{cite journal |author=Chau KWT |author2=Smith S |author3=Kang K et al |title=Antibiotic Prophylaxis for Melioidosis in Patients Receiving Hemodialysis in the Tropics? One Size Does Not Fit All |journal= The American Journal of Tropical Medicine and Hygiene |date=16 July 2018 |volume=99 |issue=3 |pages=597-600 |pmid=30014827 |pmc=PMC6169155 |doi=10.4269/ajtmh.18-0421 }}</ref> After exposure to ''B. pseudomallei'' (particularly following a laboratory accident, penetrating injuries, exposure of mouth and eyes to contaminated materials or aerosols), treatment with antibiotics is only given when in highly selected individuals after weighing the risk of adverse effects of the drugs against the benefits from contracting melioidosis. Cotrimoxazole can be used in this context. Alternatively, [[w:co-amoxiclav|co-amoxiclav]] and [[w:doxycycline|doxycycline]] can be used for those who are intolerant to co-trimoxazole. Low-risk individuals would receive frequent monitoring instead.<ref name="Lipsitz 2012">{{cite journal |author=Lipsitz R |author2=Garges S |author3=Aurigemma R et al |title=Workshop on treatment of and postexposure prophylaxis for Burkholderia pseudomallei and B. mallei Infection, 2010 |journal= Emerging Infectious Diseases |date=18 December 2012 |volume=18 |issue=12 |pages=e2 |pmid=23171644 |pmc=3557896 |doi=10.3201/eid1812.120638 }}</ref> ===Vaccination=== {{Further|w:Burkholderia_pseudomallei#Vaccine_candidates}} Several vaccine candidates have been tested in animal models. Nevertheless, no vaccine candidates have been tried in humans. Major hurdles of the vaccines are limited efficacy in animal models, establishing the best method of vaccine administration in humans and logistical and financial issues in establishing human trials in endemic areas.<ref name="Gassiep 2020"/> ==Treatment== The treatment of melioidosis is divided into two stages: an intravenous intensive phase and an eradication phase to prevent recurrence. The choice of antibiotics depends upon the susceptibility of the bacteria to various antibiotics. ''B. pesudomallei'' are generally susceptible to ceftazidime, meropenem, imipenem, and co-amoxiclav. These drugs generally kill bacteria. ''B. pseudomallei'' is also susceptible to doyxcycline, chloramphenicol, and co-trimoxazole. These drugs generally inhibit the growth of the bacteria. However, the bacteria are resistant to penicillin, ampicillin, 1st and 2nd generation [[w:cephalosporin|cephalosporin]], gentamicin, streptomycin, tobramycin, macrolides, and polymyxins.<ref name="Joost 2018"/> On the other hand, 86% of the ''B. pseudomallei'' isolates from the region of [[w:Sarawak|Sarawak]], [[w:Malaysia|Malaysia]] are susceptible to gentamicin and this has not been found elsewhere in other parts of the world.<ref name="Podin 2014">{{cite journal |author=Podin Y |author2=Sarovich DS |author3=Price EP et al |title=Burkholderia pseudomallei Isolates from Sarawak, Malaysian Borneo, Are Predominantly Susceptible to Aminoglycosides and Macrolides |journal= Antimicrobial agents and chemotherapy |date=January 2014 |volume=58 |issue=1 |pages=162-166 |pmid=24145517 | pmc=3910780 | doi=10.1128/AAC.01842-13 }}</ref> Prior to 1989, the standard treatment for acute melioidosis was a three-drug combination of [[w:chloramphenicol|chloramphenicol]], [[w:co-trimoxazole|co-trimoxazole]] and [[w:doxycycline|doxycycline]]; this regimen is associated with a mortality rate of 80% and is no longer used unless no other alternatives are available.<ref name="CAZ">{{cite journal |author=White NJ |author2=Dance DA |author3=Chaowagul W |author4=et al | title = Halving of mortality of severe melioidosis by ceftazidime | journal = Lancet | year = 1989 | volume = 2 | issue = 8665 | pages = 697&ndash;701 | pmid = 2570956 | doi = 10.1016/S0140-6736(89)90768-X }}</ref> All three drugs are bacteriostatic (they stop the bacterium from growing, but do not kill it) and the action of co-trimoxazole antagonizes both chloramphenicol and doxycycline.<ref name="Dance2006">{{cite journal |author=Dance DA |author2=Wuthiekanun V |author3=Chaowagul W |author4=White NJ |title=Interactions in vitro between agents used to treat melioidosis |journal=Journal of Antimicrobial Chemotherapy |year=1989 |volume=24 |pages=311&ndash;316 |pmid=2681117 |doi=10.1093/jac/24.3.311 |issue=3 }}</ref> ===Intensive phase=== [[w:Intravenous|Intravenous]] [[w:ceftazidime|ceftazidime]] is the current drug of choice for treatment of acute melioidosis and should be administered for at least 10 to 14 days. [[w:Meropenem|Meropenem]], [[w:imipenem|imipenem]] and the [[w:cefoperazone|cefoperazone]]-[[w:sulbactam|sulbactam]] combination (Sulperazone) are also effective.<ref name="Joost 2018"/> Intravenous amoxicillin-clavulanate ([[w:co-amoxiclav|co-amoxiclav]]) may be used if none of the above four drugs is available;<ref name="Joost 2018"/> co-amoxiclav prevents death from melioidosis as well as ceftazidime.<ref name="Bennett 2015">{{cite book |author=Bennett JE |author2=Dolin R |author3=Blaser MJ |title=Mandell, Douglas, and Bennett's Principles and Practice of Infectious Diseases |chapter=223 |date=2015 |publisher=Elsevier |isbn=978-1-4557-4801-3 |pages=2541–2549 |edition=Eighth }}</ref> Co-amoxiclav is also used if patient has allergy towards [[w:Sulfonamide (medicine)|sulfonamide]], unable to tolerate co-trimaxazole, in pregnant patients or in children. High dose of co-amoxiclav (20 mg/kg for amoxicillin and 5mg/kg for clavulanate) is recommended to prevent treatment failures.<ref name="Cheng 2008">{{cite journal |author=Cheng AC |author2=Chierakul W |author3=Chaowagul W et al |title=Consensus Guidelines for Dosing of Amoxicillin-Clavulanate in Melioidosis |journal= American Journal of Tropical Medicine and Hygiene |date=February 2008 |volume=78 |issue=2 |pages=208-209 |pmid=18256414 | pmc=PMC3034162 | doi=10.4269/ajtmh.2008.78.208 }}</ref><ref name="Suputtamongkol 1994">{{cite journal |author=Suputtamongkol Y |author2=Rajchanuwong A |author3=Chaowagul W et al |title=Ceftazidime vs. amoxicillin/clavulanate in the treatment of severe melioidosis |journal= Clinical Infectious Diseases |date=November 1994 |volume=19 |issue=5 |pages=846-853 |pmid=7893868 | pmc= | doi=10.1093/clinids/19.5.846 }}</ref> Intravenous [[w:antibiotic|antibiotic]]s are given for a minimum of 10 to 14 days. The median fever clearance time in melioidosis is 9 days.<ref name="Joost 2018"/> The treatment duration is in accordance with Darwin melioidosis treatment guidelines where there is low rate of [[w:recrudescence|recrudescence]] and [[w:relapse|relapse]].<ref name="Sullivan 2020">{{cite journal |author=Sullivan RP |author2=Marshall CS |author3=Anstey NM |author4=Ward L |author5=Currie BJ |title=2020 Review and revision of the 2015 Darwin melioidosis treatment guideline; paradigm drift not shift |journal= Plos Neglected Tropical Diseases |date=28 September 2020 |volume=14 |issue=9 |pages=e0008659 |pmid=32986699 | pmc=7544138 | doi=10.1371/journal.pntd.0008659 }}</ref> Meropenem is the preferred antibiotic therapy for neurological melioidosis and those with [[w:sepsis|septic shock]] admitted into [[w:intensive care unit|intensive care unit]]s. Co-trimoxazole is recommended in addition to ceftazidime for neurological melioidosis, osteomyelitis, septic arthritis, skin and gastrointestinal infection, and deeply seated abscess. For deep-seated infections such as abscesses of internal organs, osteomyelitis, septic arthritis, and neurological melioidosis, the duration of antibiotics given should be longer (up to 4 to 8 weeks). The time taken for the fever to be resolved can be more than 10 days in those with deep-seated infection. According to the 2020 Revised Royal Darwin Hospital Guideline, the dosage for intravenous ceftazidime is 2g 6-hourly in adults (50&nbsp;mg/kg up to 2g in children less than 15 years old). The dosage for meropenem is 1g 8-hourly in adults (25&nbsp;mg/kg up to 1g in children).<ref name="Sullivan 2020"/> Acquired resistance to ceftazidime, carbapenems, and co-amoxiclav is rare in the intensive phase but resistance to cotrimoxazole during eradication therapy is technically difficult to assess.<ref name="Dance 2014"/> There are no differences between using cefoperazone/sulbactam or ceftazidime to treat melioidosis as both shows similar death rates and disease progression following treatment. However, data are lacking to recommend cefoperazone/sulbactam usage.<ref name="Dance 2014">{{cite journal |author=Dance D |title=Treatment and prophylaxis of melioidosis |journal=International Journal of Anti-microbial agents |date=April 2014 |volume=43 |issue=4 |pages=310-318 |pmid=24613038 |doi=10.1016/j.ijantimicag.2014.01.005}}</ref><ref name="Apisarnthanarak 2002">{{cite journal |author1=Apisarnthanarak A |author2= Little JR |title=The role of cefoperazone-sulbactam for treatment of severe melioidosis |journal=International Journal of Anti-microbial agents |date=1 March 2002 |volume=34 |issue=5 |pages=721-722 |pmid=11823963 |doi=10.1086/338722}}</ref> For those with kidney impairment, the dosage of ceftazidime, meropenem, and co-trimoxazole should be lowered.<ref name="Currie 2015"/> Once the clinical condition improved, meropenem can be switched back to ceftazidime.<ref name="Joost 2018"/> ===Eradication phase=== Following the treatment of the acute disease, eradication treatment with [[w:co-trimoxazole|co-trimoxazole]] is the drug of choice and should be used for 3 months (12 weeks) as all-cause mortality was lower in 12 weeks group when compared to those receiving treatment for 20 weeks.<ref name="Anunnatsiri 2021">{{cite journal |author1=Anunnatsiri S |author2=Chaowagul W |author3=Teparrukkul P |title=A Comparison Between 12 Versus 20 Weeks of Trimethoprim-sulfamethoxazole as Oral Eradication Treatment for Melioidosis: An Open-label, Pragmatic, Multicenter, Non-inferiority, Randomized Controlled Trial |journal= Clinical Infectious Diseases |date=2021 |volume=73 |issue=11 |pages=e3627-e3633 |pmid=32725199 | pmc=PMC8662794 | doi=10.1093/cid/ciaa1084 }}</ref> For those with neurological melioidosis and [[w:osteomyelitis|osteomyelitis]], drugs should be given for more than 6 months. Co-amoxiclav and [[w:doxycycline|doxycycline]] are drugs of second choice. Co-trimoxazole should not be used in those with [[w:glucose-6-phosphate dehydrogenase|glucose-6-phosphate dehydrogenase]] deficiency as it can cause [[w:haemolytic anemia|haemolytic anemia]]. However, in Thailand, usage of co-trimoxazole does not accompany G6PD screening.<ref name="Joost 2018"/> Other side effects such as rash, [[w:hyperkalemia|hyperkalemia]], renal dysfunction, and gastrointestinal symptoms should prompt the reduction of co-trimoxazole doses. [[w:Chloramphenicol|Chloramphenicol]] is no longer routinely recommended for this purpose. Co-amoxiclav is an alternative for patients unable to take co-trimoxazole and [[w:doxycycline|doxycycline]] (e.g. pregnant women and children under the age of 12), but is not as effective and has a higher relapse rate. Single-agent treatment with [[w:fluoroquinolone|fluoroquinolone]] (e.g., [[w:ciprofloxacin|ciprofloxacin]]) or doxycycline for the oral eradication phase is ineffective.<ref name="Joost 2018"/> In Australia, co-trimoxazole is used with children and pregnant mothers after the first 12 weeks of pregnancy. Meanwhile, in Thailand, co-amoxiclav is the drug of choice for children and pregnant women.<ref name="Joost 2018"/> ''B. pseudomallei'' rarely acquires resistance when co-amoxiclav is used.<ref name="Dance 2014"/> The dosing regimen for co-trimoxazole (trimethoprim/sulfamethoxazole) in eradication phase is 6/30&nbsp;mg/kg, up to maximum 240/1200&nbsp;mg in children, 240/1200&nbsp;mg in adults weighing 40 to 60&nbsp;kg, and 320/1600&nbsp;mg in adults weighing more than 60&nbsp;kg, taken orally every 12 hours.<ref name="Sullivan 2020"/> In both Thailand and Australia, co-trimoxazole is taken together with [[w:folic acid|folic acid]] (0.1&nbsp;mg/kg up to 5&nbsp;mg in children).<ref name="Joost 2018"/><ref name="Sullivan 2020"/> There are also cases where melioidosis is successfully treated with co-trimoxazole for 3 months without going through intensive therapy provided that there is only skin manifestations without the involvement of internal organs or sepsis.<ref name="Joost 2018"/> Resistance to cotrimoxazole is rare in Asia.<ref name="Dance 2014 resistance">{{cite journal |author1=Dance DAB |author2=Davong V |author3=Soeng S |author4=Phetsouvanh R |author5=Newton PN |author6=Turner P |title=Trimethoprim/sulfamethoxazole resistance in Burkholderia pseudomallei |journal= International Journal of Antimicrobial Agents |date=October 2014 |volume=44 |issue=4 |pages=368-369 |pmid=25245211 | pmc=4195405 | doi=10.1016/j.ijantimicag.2014.06.003 }}</ref> Besides that, it is difficult to determine the resistance reliably because resistance to cotrimoxazole is defined when [[w:minimum inhibitory concentration|minimum inhibitory concentration]] (MIC) of more than 4 mg/L is required to completely inhibit the growth of 80% of the bacteria (80% inhibition point). Interpretation of 80% inhibition point is subjective and prone to human error.<ref name="Saiprom 2015">{{cite journal |author1=Saiprom N |author2=Amornchai P |author3=Wuthiekanun V et al |title=Trimethoprim/sulfamethoxazole resistance in clinical isolates of Burkholderia pseudomallei from Thailand |journal= International Journal of Antimicrobial Agents |date=May 2015 |volume=45 |issue=5 |pages=557-559 |pmid=25758020 | pmc=4537509 | doi=10.1016/j.ijantimicag.2015.01.006 }}</ref> In 2021, European Committee on Antimicrobial Susceptibility Testing (EUCAST) released a new guideline on interpreting the susceptibility of ''B pseudomallei'' towards various antibiotics on [[w:antibiotic sensitivity testing|disc susceptibility testing]]. The new guideline includes "S" for susceptible organism, "I" for susceptible organism only after increased exposure (when dosage or concentration of the drug increases) and "R" for resistant organism.<ref name="Dance 2021">{{cite journal |author1=Dance DAB |author2=Wuthiekanun P |author3=Baird W et al |title=Interpreting Burkholderia pseudomallei disc diffusion susceptibility test results by the EUCAST method |journal= Clinical Microbiology and Infection |date=June 2021 |volume=27 |issue=6 |pages=827-829 |pmid=33636339 | pmc= | doi=10.1016/j.cmi.2021.02.017 }}</ref> ===Surgery=== Surgical drainage is indicated for single, large abscesses in the liver, muscle, and prostate. However, for multiple abscesses in the liver, spleen, and kidney, surgical drainage may not be possible or necessary. For septic arthritis, [[w:arthrotomy|arthrotomy]] washout and drainage are required. Surgical [[w:debridement|debridement]] may be necessary.<ref name="Joost 2018"/> For those with [[w:mycotic aneurysm|mycotic aneurysm]], urgent surgery is required for prosthetic vascular grafts. Lifelong therapy with co-trimoxazole may be needed for those with prosthetic vascular grafts according to a review of case reports in 2005.<ref name="Hong Low 2005">{{cite journal |author=Low JGH |author2=Quek AML |author3=Sin YK |author4=Ang BSP |title=Mycotic aneurysm due to Burkholderia pseudomallei infection: case reports and literature review |journal= Clinical Infectious Diseases |date=January 2005 |volume=40 |issue=1 |pages=193-198 |pmid=15614712 | pmc= | doi=10.1086/426590 }}</ref> Other abscesses rarely need to be drained because most resolve with antibiotic treatment.<ref name="Joost 2018"/> Prostate abscess may require routine imaging. Antibiotics treatment for prostatic abscess may be enough except for abscesses more than 10 to 15 mm where surgical drainage is required.<ref name="Kozlowska 2018">{{cite journal |author=Kozlowska J |author2=Smith S |author3=Roberts J |author4=Pridgeon S |author5=Hanson J |title=Prostatic Abscess due to Burkholderia pseudomallei: Facilitating Diagnosis to Optimize Management |journal= American Journal of Tropical Medicine |date=January 2018 |volume=98 |issue=1 |pages=227-230 |pmid=29141724 | pmc= 5928742 | doi=10.4269/ajtmh.17-0633 }}</ref><ref name="Ng 2009">{{cite journal |author=Ng TH |author2=How SH |author3=Amran AR |author4=Razali MR |author5=Kuan YC |title=Melioidotic prostatic abscess in Pahang |journal= American Journal of Tropical Medicine |date=April 2009 |volume=50 |issue=4 |pages=385-389 |pmid=19421682 | pmc= | doi=10.4269/ajtmh.17-0633 }}</ref><ref name="Morse 2009">{{cite journal |author=Morese LP |author2=Moller CCB |author3=Harvey E |author4=Ward L et al |title=Prostatic Abscess Due to Burkholderia pseudomallei: 81 Cases From a 19-Year Prospective Melioidosis Study |journal= The Journal of Urology |date=1 August 2009 |volume=182 |issue=2 |pages=542-547 |pmid=19524969 | pmc= | doi=10.1016/j.juro.2009.04.010 }}</ref> ===Others=== Several immunomodulating therapies are suggested to boost the human body immune function against the bacteria because the pathogenesis of melioidosis is thought to be contributed by defects in [[w:neutrophil|neutrophils]].<ref name="Joost 2018"/> The Royal Darwin Hospital 2014 guidelines recommended [[w:granulocyte colony-stimulating factor|granulocyte colony-stimulating factor]] (G-CSF) as immunomodulating therapy for those with septic shock at 300ug daily as soon as the bacteriological laboratory flag the culture as possibly ''Burkholderia pseudomallei''. The main contraindication of starting (G-CSF) is a heart event. The G-CSF is continued for ten days depends on clinical response or a contraindication develops such as white cell count greater than >50,000 X106/litre.<ref name="Sullivan 2020"/> Anti-PDI ([[w:programmed cell death|programmed cell death]]) agents could be useful in melioidosis treatment especially for those with septic shock. This is because ''Burkholderia pseudomallei'' bacteria increases the expression of PDI-1 that regulates and inhibits the formation of T-cells that are essential for fighting against melioidosis.<ref name="Buddhisa 2015">{{cite journal |author=Buddhisa S |author2=Rinchai D |author3=Ato M et al |title=Programmed Death Ligand 1 on Burkholderia pseudomallei–Infected Human Polymorphonuclear Neutrophils Impairs T Cell Functions |journal= The Journal of Immunology |date=May 2015 |volume=194 |issue=9 |pages=4413-4421 |pmid=25801435 | pmc=3910780 | doi=10.4049/jimmunol.1402417 }}</ref> ==Prognosis== In well-resourced settings, where the disease can be detected and treated early, the risk of death is 10%. In resource-poor settings, the risk of death from the disease is more than 40%.<ref name="Joost 2018"/> Recurrent melioidosis can occur either due to re-infection or relapse after the completion of eradication therapy. Re-infection is due to a new strain of ''B. pseudomallei'' bacteria. Meanwhile, relapse is due to failure to clear infections after the eradication therapy. Recurrent melioidosis is rare since 2014 due to improved antibiotic therapy and prolongation of the intensive phase of therapy as evident in Darwin Prospective Melioidosis Study.<ref name="Sarovich 2014">{{cite journal |author=Sarovich DS |author2=Ward L |author3=Price EP |author4=Mayo M et al |title=Recurrent Melioidosis in the Darwin Prospective Melioidosis Study: Improving Therapies Mean that Relapse Cases Are Now Rare |journal=Journal of Clinical Microbiology |date=February 2014 |volume=52 |issue=2 |pages=650-653 |pmid=24478504 |pmc=3911345 | doi=10.1128/JCM.02239-13 }}</ref> On the other hand, [[w:recrudescence|recrudescence]] are those who present with symptoms during the eradication therapy. Recrudescence rates may be improved by ensuring adherence to a full course of eradication therapy e.g. by reducing self-discharge [[w:against medical advice|against medical advice]].<ref name="Pitman 2015">{{cite journal |author=Pitman MC |author2=Luck T |author3=Marshall CS |author4=Anstey NM et al |title=Intravenous Therapy Duration and Outcomes in Melioidosis: A New Treatment Paradigm |journal=Plos Neglected Tropical Diseases |date=26 March 2015 |volume=9 |issue=4 |pages=e0003737 |pmid=25811783 |pmc=4374799 | doi=10.1371/journal.pntd.0003586 }}</ref> Underlying medical conditions such as diabetes mellitus, chronic kidney disease, and cancer can worsen the long-term survival and disability of those who recover from infection. One of the complications of melioidosis is [[w:encephalomyelitis|encephalomyelitis]]. It can cause quadriparesis (muscle weakness in all the limbs), partial flaccid paraparesis (muscle weakness of both legs), or foot drop. For those with previous melioidosis-associated bone and joint infections, complications such as sinus tract infection, bone and joint deformities with limited range of motion can occur.<ref name="Joost 2018"/> ==Epidemiology== {{fig|9 |Melioidosis world map distribution.svg |Number of deaths by each country due to melioidosis in 2018. |attribution=Cerevisae, CC BY-SA |size=285px }} Melioidosis is an understudied disease that remains endemic in developing countries. In 2015, the International Melioidosis Society was formed to raise awareness of the disease.<ref name="Joost 2018"/> In 2016, a [[w:statistical model|statistical model]] was developed which predicted that the number is 165,000 cases per year with 138,000 of those occurring in East and South Asia and the Pacific.<ref>{{cite journal |author=Limmathurotsakul D |author2=Golding N |author3=Dance DA |author4=Messina JP |author5=Pigott DM |author6=Moyes CL |author7=Rolim DB |author8=Bertherat E |author9=Day NP |author10=Peacock SJ |author11=Hay SI |title=Predicted global distribution of Burkholderia pseudomallei and burden of melioidosis |journal=Nature Microbiology |date=11 January 2016 |volume=1 |issue=1 |pages=15008 |doi=10.1038/nmicrobiol.2015.8 |pmid=26877885 |pmc=4746747 }}</ref> In approximately half of those cases (54% or 89,000), people will die.<ref name="Joost 2018"/> Under-reporting is a common problem as only 1,300 cases were reported worldwide since 2010, which is less than 1% of the projected incidence based on the modelling.<ref name="Joost 2018"/> Lack of laboratory diagnostic capabilities and lack of disease awareness amongst health care providers also causes underdiagnosis. Even if bacterial cultures show positive result for ''B. pesudomallei'', they can be discarded as contaminants especially in laboratories in non-endemic areas.<ref name="Joost 2018"/> In 2015, it was estimated that the yearly [[w:disability-adjusted life year|disability-adjusted life year]] (DALY) was 84.3 per 100,000 people. As of 2022, melioidosis is not included in the WHO list of [[w:neglected tropical diseases|neglected tropical diseases]].<ref>{{cite journal |author=Birnie E |author2=Virk HS |author3=Savelkoel J |author4=Spijker R |author5=Bertherat E |title=Global burden of melioidosis in 2015: a systematic review and data synthesis |journal=Lancet Infectious Diseases |date=August 2019 |volume=19 |issue=8 |pages=892-902 |doi=10.1016/S1473-3099(19)30157-4 |pmid=31285144 |pmc=6867904 }}</ref><ref>{{cite journal |author=Savelkoel J |author2=Dance DAB |author3=Currie BJ et al |title=A call to action: time to recognise melioidosis as a neglected tropical disease |journal=Lancet Infectious Diseases |date=22 June 2022 |volume=22 |issue=6 |pages=e176-e182 |doi=10.1016/S1473-3099(21)00394-7 |pmid=34953519 |pmc= }}</ref> Melioidosis is endemic in parts of southeast Asia (including Thailand,<ref name="Hinjoy 2018">{{cite journal |author=Hinjoy S |author2=Hantrakun V |author3=Kongyu S |author4=Kaewrakmuk J |author5=Wangrangsimakul T et al |title=Melioidosis in Thailand: Present and Future |journal=Tropical Medicine and Infectious Disease |date=8 April 2018 |volume=3 |issue=2 |pages=38 |doi=10.3390/tropicalmed3020038 |pmid=29725623 |pmc=5928800 }}</ref> Laos,<ref>{{cite journal |author=Dance DAB |author2=Luangraj M |author3=Rattanavong S |author4=Sithivong N et al |title=Melioidosis in the Lao People's Democratic Republic |journal=Tropical Medicine and Infectious Disease |date=19 February 2018 |volume=3 |issue=1 |pages=21 |doi=10.3390/tropicalmed3010021 |pmid=30274419 |pmc=6136615 }}</ref> Singapore,<ref>{{cite journal |author=Sim SH |author2=Ong CEL |author3=Gan YH |author4=Wang D et al |title=Melioidosis in Singapore: Clinical, Veterinary, and Environmental Perspectives |journal=Tropical Medicine and Infectious Disease |date=12 March 2018 |volume=3 |issue=1 |pages=31 |doi=10.3390/tropicalmed3010031 |pmid=30274428 |pmc=6136607 }}</ref> Brunei,<ref>{{cite journal |author=Pande K |author2=Kadir KAA |author3=Asli R |author4=Chong VH |title=Melioidosis in Brunei Darussalam |journal=Tropical Medicine and Infectious Disease |date=19 February 2018 |volume=3 |issue=1 |pages=20 |doi=10.3390/tropicalmed3010020 |pmid=30274418 |pmc=6136610 }}</ref> Malaysia,<ref name="Nathan 2018">{{cite journal |author=Nathan S |author2=Chieng S |author3=Kingsley PV |author4=Mohan A |author5=Podin Y et al |title=Melioidosis in Malaysia: Incidence, Clinical Challenges, and Advances in Understanding Pathogenesis |journal=Tropical Medicine and Infectious Disease |date=27 February 2018 |volume=3 |issue=1 |pages=25 |doi=10.3390/tropicalmed3010025 |pmid=30274422 |pmc=6136604 }}</ref> Myanmar<ref>{{cite journal |author=Win MM |author2=Ashley EA |author3=Zin KN |author4=Aung MT |author5=Swee MMM et al |title=Melioidosis in Myanmar |journal=Tropical Medicine and Infectious Disease |date=1 March 2018 |volume=3 |issue=1 |pages=28 |doi=10.3390/tropicalmed3010028 |pmid=30274425 |pmc=6136617 }}</ref> and Vietnam<ref>{{cite journal |author=Trinh TT |author2=Nguyen LDN |author3=Nguyen TV |author4=Tran CX |author5=Le AV et al |title=Melioidosis in Vietnam: Recently Improved Recognition but still an Uncertain Disease Burden after Almost a Century of Reporting |journal=Tropical Medicine and Infectious Disease |date=9 April 2018 |volume=3 |issue=2 |pages=39 |doi=10.3390/tropicalmed3020039 |pmid=30274435 |pmc=6073866 }}</ref>), southern China,<ref>{{cite journal |author=Zheng X |author2=Xia Q |author3=Xia L |author4=Li W |title=Endemic Melioidosis in Southern China: Past and Present |journal=Tropical Medicine and Infectious Disease |date=25 February 2019 |volume=4 |issue=1 |pages=39 |doi=10.3390/tropicalmed4010039 |pmid=30823573 |pmc=6473618 }}</ref> Taiwan<ref>{{cite journal |author=Hsueh PT |author2=Huang WT |author3=Huseueh HK |author4=Chen YL |author5=Chen SY et al |title=Transmission Modes of Melioidosis in Taiwan |journal=Tropical Medicine and Infectious Disease |date=28 February 2018 |volume=3 |issue=1 |pages=26 |doi=10.3390/tropicalmed3010026 |pmid=30274423 |pmc=6136622 }}</ref> northern Australia.<ref name="Smith 2018">{{cite journal |author=Smith S |author2=Hanson J |author3=Currie BJ |title=Melioidosis: An Australian Perspective |journal=Tropical Medicine and Infectious Disease |date=1 March 2018 |volume=3 |issue=27 |pages=1 |doi=10.3390/tropicalmed3010027 |pmid=30274424 |pmc=6136632 }}</ref> India,<ref name="Mukhopadhyay 2018">{{cite journal |author=Mukhopadhyay C |author2=Shaw T |author3=Varghese GM |author4=Dance DAB |title=Melioidosis in South Asia (India, Nepal, Pakistan, Bhutan and Afghanistan) |journal=Tropical Medicine and Infectious Disease |date=22 May 2018 |volume=3 |issue=2 |pages=51 |doi=10.3390/tropicalmed3020051 |pmid=30274447 |pmc=6073985 }}</ref> and South America.<ref>{{cite journal |author=Rolim DB |author2=Lima RX |author3=Ribeiro AK |author4=Colares RM et al |title=Melioidosis in South America |journal=Tropical Medicine and Infectious Disease |date=5 June 2018 |volume=3 |issue=2 |pages=60 |doi=10.3390/tropicalmed3020060 |pmid=30274456 |pmc=6073846 }}</ref> Since 1991, a total of 583 cases were reported in India. Most Indian cases are located in [[w:Karnataka|Karnataka]] and [[w:Tamil Nadu|Tamil Nadu]].<ref name="Mukhopadhyay 2018"/> Fifty-one cases of melioidosis were reported in Bangladesh from 1961–2017. Nonetheless, lack of awareness and resources gives rise to underdiagnosis of the disease in the country.<ref>{{cite journal |author=Chowdhury FR |author2=Jilani MSA |author3=Barai L |author4=Rahman T et al |title=Melioidosis in Bangladesh: A Clinical and Epidemiological Analysis of Culture-Confirmed Cases |journal=Tropical Medicine and Infectious Disease |date=9 April 2018 |volume=3 |issue=2 |pages=40 |doi=10.3390/tropicalmed3020040 |pmid=30274436 |pmc=6073520 }}</ref> The true burden of melioidosis in Africa and Middle East remain unknown due to low amount of data. Several melioidosis cases were reported over the years. Although 24 African countries and three Middle Eastern countries predicted to be endemic with melioidosis, however not a single case was reported from these specific countries.<ref>{{cite journal |author=Steinmetz I |author2=Wagner GE |author3=Kanyala E et al |title=Melioidosis in Africa: Time to Uncover the True Disease Load |journal=Tropical Medicine and Infectious Disease |date=10 June 2018 |volume=3 |issue=2 |pages=62 |doi=10.3390/tropicalmed3020062 |pmid=30274458 |pmc=6073667 }}</ref> In the United States, two historical cases (1950 and 1971) and four recent cases (2010, 2011, 2013, 2020) have been reported amongst people that did not travel overseas.<ref name="Currie 2015"/><ref>{{cite journal |author=Cossaboom CM |author2=Marinova-Petkova A |author3=Strysko J et al |title=Melioidosis in a Resident of Texas with No Recent Travel History, United States |journal=Emerging Infectious Diseases |date=June 2020 |volume=26 |issue=6 |pages=1295-1299 |doi=10.3201/eid2606.190975 |pmid=32442394 |pmc=7258475 }}</ref> Despite extensive investigations, the source of melioidosis was never confirmed. One possible explanation is that importation of medicinal plant products or exotic reptiles could have resulted in the introduction of melioidosis in the United States.<ref name="Currie 2015"/> In 2021, there was a melioidosis outbreak in several states in the United States due to usage of contaminated aromatherapy spray imported from India.<ref>{{cite journal |author=Gee JE |author2=Bower WA |author3=Kunkel A et al |title=Multistate Outbreak of Melioidosis Associated with Imported Aromatherapy Spray |journal=New England Journal of Medicine |date=March 2022 |volume=386 |issue=9 |pages=861-868 |doi=10.1056/NEJMoa2116130 |pmid=35235727 }}</ref> There are also cases of infection through imported tropical fishes in home aquariums.<ref>{{cite journal |author=Dawson P |author2=Duwell MM |author3=Elrod MG et al |title=Human Melioidosis Caused by Novel Transmission of Burkholderia pseudomallei from Freshwater Home Aquarium, United States |journal=Emerging Infectious Diseases |date=December 2021 |volume=27 |issue=12 |pages=3030-3035 |doi=10.3201/eid2712.211756 |pmid=34570693 |pmc=8632198 }}</ref> In Europe, more than half of the melioidosis cases are imported from Thailand.<ref>{{cite journal |author=Tohic SL |author2=Montana M |author3=Koch L et al |title=A review of melioidosis cases imported into Europe |journal=European Journal of Clinical Microbiology & Infectious DIseases |date=25 March 2019 |volume=38 |issue=8 |pages=1395–1408 |doi=10.1007/s10096-019-03548-5 |pmid=30949898 }}</ref> Melioidosis is found in all age groups.<ref name="Joost 2018"/> For Australia and Thailand, the median age of infection is at 50 years; 5 to 10% of the patients are under 15 years.<ref name="Joost 2018"/> The single most important risk factor for developing melioidosis is [[w:diabetes mellitus|diabetes mellitus]], followed by hazardous alcohol use, chronic kidney disease, and chronic lung disease.<ref name="Suputtamongkol 1999">{{cite journal |author=Suputtamongkol Y |author2=Chaowagul W |author3=Chetchotisakd P |author4=Lertpatanasuwun N et al |year=1999 |title=Risk factors for melioidosis and bacteremic melioidosis |journal=Clinical Infectious Diseases |pmid=10476750 |volume=29 |issue=2 |pages=408&ndash;413 |doi=10.1086/520223 }}</ref> More than 50% of people with melioidosis have diabetes; diabetics have a 12-fold increased risk of contracting melioidosis. Diabetes decreases the ability of macrophages to fight the bacteria and reduced the [[w:T helper cell|T helper cell]] production. Excessive release of [[w:Tumor necrosis factor alpha|Tumor necrosis factor alpha]] and [[w:Interleukin 12|Interleukin 12]] by [[w:peripheral blood mononuclear cell|mononuclear cells]] increases the risk of septic shock.<ref name="Joost 2018"/> Other risk factors include [[w:thalassaemia|thalassaemia]], occupational exposure (e.g. [[w:rice paddy|rice paddy]] farmers),<ref name="Gassiep 2020"/> recreational exposure to soil, water, being male, age greater than 45 years, and prolonged steroid use/immunosuppression.<ref name="Joost 2018"/> However, 8% of children and 20% of adults with melioidosis have no risk factors.<ref name="Joost 2018"/> [[w:HIV|HIV]] infection does not appear to predispose to melioidosis, although several other co-infections have been reported.<ref name="Gassiep 2020"/> [[w:Infant|Infant]] cases have been reported possibly due to mother-to-child transmission, community-acquired infection, or healthcare-associated infection.<ref name="Joost 2018"/> Those who are well may also be infected with ''B. pseudomallei''. For example, 25% of children started [[w:seroconversion|producing antibodies]] against ''B. pseudomallei'' between 6 months to 4 years of staying in [[w:endemic (epidemiology)|endemic]] areas although they did not experience any melioidosis symptoms; suggesting they were exposed to it over this time. This means that many people without symptoms will test positive in serology tests in endemic areas.<ref name="Yi 2014"/> In Thailand, the seropositivity rate exceeds 50%, while in Australia the seropositivity rate is only 5%.<ref name="Currie 2015"/> The disease is clearly associated with increased rainfall, with the number of cases rising following increased precipitation. Severe rainfall increases the concentration of the bacteria in the topsoil, thus increasing thus of transmitting the bacteria through the air.<ref name="Gassiep 2020"/> A recent CDC Advisory indicated that the recent detection of the organism in the environment in Mississippi following the occurrence of two indigenous cases of melioidosis, confirms that parts of the southern USA should now be regarded as melioidosis-endemic.<ref>{{Cite web|url=https://www.emergency.cdc.gov/han/2022/pdf/CDC_HAN_470.pdf |title=Melioidosis Locally Endemic in Areas of the Mississippi Gulf Coast after Burkholderia pseudomallei Isolated in Soil and Water and Linked to Two Cases – Mississippi, 2020 and 2022|publisher=CDC|access-date=2022-08-05}}</ref> ==History== Pathologist [[w:Alfred Whitmore|Alfred Whitmore]] and his assistant Krishnaswami first reported melioidosis among beggars and morphine addicts at autopsy in Rangoon, present-day [[w:Burma|Myanmar]], in a report published in 1912.<ref name="Whitmore 1912">{{cite journal |author=Whitmore A |author2=Krishnaswami CS |title=A Hitherto Undescribed Infective Disease in Rangoon |journal=Indian Medical Gazette |date=1912 |volume=47 |issue=7 |pages=262–267 |pmid=29005374 |pmc=5168169 |doi= }}</ref> Whitmore was able to grow the organism in culture and its showed similarity with ''B. mallei'', another bacteria that was known causing glanders in animals. Therefore, he named the new organism ''Bacillus pseudomallei''. He did no further work on the organism.<ref name="Brightman 2020">{{cite journal |author=Brightman C |author2=Locum |title=Melioidosis, the Vietnamese time bomb |journal=Trends in Urology and Men's health |year=4 June 2020 |volume=11 |issue=3 |pages=30-32 |pmid= |pmc= |doi=10.1002/tre.753 }}</ref> [[w:Arthur Conan Doyle|Arthur Conan Doyle]] may have read Whitmore's report before writing a short story that involved the fictitious tropical disease "Tapanuli fever" in a [[w:Sherlock Holmes|Sherlock Holmes]] story<ref name="pmid11823558">{{cite journal |author=Vora SK |title=Sherlock Holmes and a biological weapon |journal=Journal of the Royal Society of Medicine |volume=95 |issue=2 |pages=101–103 |date=February 2002 |pmid=11823558 |pmc=1279324 |doi=10.1258/jrsm.95.2.101 |url=http://www.jrsm.org/cgi/pmidlookup?view=long&pmid=11823558 }}</ref> titled “[[w:The Adventure of the Dying Detective|The Adventure of the Dying Detective]]” published in 1913.<ref name="Allen C 2005"/> In the same year, melioidosis outbreak occurred inside the Institute for Medical Research (IMR), [[w:Kuala Lumpur|Kuala Lumpur]], [[w:Federated Malay States|Malaya]] after its laboratory animals such as guinea pigs and rabbits were infected.<ref name="Nathan 2018"/> William Fletcher and Ambrose Thomas Stanton, doctors who worked at the IMR, were the next ones to study the organism. They were unable identify the organism that caused the outbreak. It was only in 1917, when Fletcher isolated an organism similar to Whitmore's bacillus from a Tamil rubber estate worker, the presence of the new species of bacteria was confirmed.<ref name="Brightman 2020"/> The term “melioidosis” was first coined in 1921. The name melioidosis is derived from the Greek ''melis'' (μηλις) meaning "a distemper of asses" with the suffixes -oid meaning "similar to" and -osis meaning "a condition", that is, a condition similar to glanders.<ref name="Stanton 1921">{{cite book |author=Stanton AT |author2=Fletcher W |chapter=Melioidosis, a new disease of the tropics |title=Far Eastern Association of Tropical Medicine: Transactions of the Fourth Congress |location=Batavia, Dutch East Indies |publisher=Javasche Boekhandel en Drukkerij |year=1921 }}</ref> ''B pseudomallei'' is similar in clinical presentation and genome make-up with ''B. mallei''<ref name="Godoy 2003">{{cite journal |author=Godoy D |author2=Randle G |author3=Simpson AJ |author4=Aanensen DM et al |title=Multilocus sequence typing and evolutionary relationships among the causative agents of melioidosis and glanders, Burkholderia pseudomallei and Burkholderia mallei |journal=Journal of Clinical Microbiology |year=May 2003 |volume=41 |issue=5 |pages=2068-2079 |pmid=12734250 |pmc=154742 |doi=10.1128/jcm.41.5.2068-2079.2003 }}</ref> but is distinguished from it due to epidemiological and [[w:zoonosis|zoonotic]] characteristics.<ref name="Yabuuci 1992"/> The first human case of melioidosis in South Asia was reported in Sri Lanka in 1927.<ref name="Mukhopadhyay 2018"/> In 1932, Thomas and Fletcher collected 83 cases of melioidosis from literature. In this [[w:cases series|case series]], there were only two survivals. Since then, more case series of melioidosis were reported.<ref name="Khaira 1959">{{cite journal |author=Khaira BS |author2=Young WB |author3=Hart PdeV |title=Melioidosis |journal=British Medical Journal |volume=1 |issue=5127 |pages=949-952 |date=11 April 1959 |pmid=13638596 |pmc=1993315 |doi=10.1136/bmj.1.5127.949 }}</ref> Thomas and Fletcher also pioneered the use of serological methods in diagnosing the disease. Thomas and Fletcher incorrectly believed that melioidosis infection came from human contact with [[w:rondent|rodents]]. However, observations on the disease noted that humans usually got it after exposure to mud or contaminated water. Besides, the organism was never grown from rats. This led to a search of the bacteria in the environment.<ref name="Ketheesan 2012">{{cite book |author=Ketheesan N |chapter= VIII.1 - Melioidosis in animals |title=Melioidosis - A Century of Observation and Research |location=Townsville, Australia |publisher=Elsevier B.V. |year=2012 |pages=313 }}</ref> In 1936, the first animal (pig) case of melioidosis in Africa was reported in Madagascar.<ref name="Garin 2014">{{cite journal |author=Garin B |author2=Djaomazala I |author3=Dubois-Cauwelaert N et al |title=Autochthonous Melioidosis in Humans, Madagascar, 2012 and 2013 |journal=Emerging Infectious Diseases |volume=20 |issue=10 |pages=1739-1741 |date=October 2014 |pmid=25272365 |pmc=4193270 |doi=10.3201/eid2010.131524 }}</ref> In 1937, water was first identified as the habitat of ''B. pseudomallei''.<ref name="Limmathurotsakul review 2013 ">{{cite journal |author=Limmathurotsakul D |author2=Dance DAB |author3=Wuthiekanun V et al |title=Systematic Review and Consensus Guidelines for Environmental Sampling of Burkholderia pseudomallei |journal=PLoS Neglected Tropical Diseases |volume=7 |issue=3 |pages=e2105 |date=2013 |pmid=23556010 |pmc=3605150 |doi=10.1371/journal.pntd.0002105 }}</ref> The first case of Australian melioidosis was described in an outbreak in sheep in 1949 at [[w:North Queensland|North Queensland]]. This was followed by the first case of human melioidosis at [[w:Townsville|Townsville]] in 1950.<ref name="Currie 2000">{{cite journal |author=Currie BJ |author2=Fisher DA |author3=Howard DM et al |title=The epidemiology of melioidosis in Australia and Papua New Guinea |journal=Acta Tropica |volume=74 |issue=2 |pages=121-127 |date=February 2000 |pmid=10674639 |pmc= |doi=10.1016/s0001-706x(99)00060-1 }}</ref> Initially, the discovery of melioidosis in Australia had led to a debate on when and how the disease spread from Southeast Asia to a new distant environment.<ref name="Ketheesan 2012"/> However, this hypothesis was later disproved in 2017 when [[w:whole genome sequencing|whole genome sequencing]] of ''B. pseudomallei'' over 30 countries collected over 79 years suggested Australia as the early reservoir for melioidosis.<ref name="Chewapreecha 2017"/> In 1955, first case of local human melioidosis was reported in Thailand.<ref name="Hinjoy 2018"/> During the [[w:Vietnam War|Vietnam War]] from 1967 to 1973, 343 American soldiers were reported with melioidosis, with about 50 cases transmitted through inhalation.<ref name="Rubin 1963">{{cite journal |author=Rubin HL |author2=Alexander AD |author3=Yager RH |title=Melioidosis—a military medical problem? |journal=Military Medicine |volume=128 |issue= |pages=538-642 |date=1963 |pmid=13983001 |pmc= |doi=10.1093/milmed/128.6.538 }}</ref> An outbreak of melioidosis at the Paris Zoo in the 1970s (known as ''L’affaire du jardin des plantes'') was thought to have originated from an imported [[w:panda|panda]] or horses from Iran.<ref name="Allen C 2005"/><ref>{{cite journal |author=Mollaret HH |title=''"L'affaire du Jardin des plantes" ou comment le mélioïdose fit son apparition en France'' |journal=Médecine et Maladies Infectieuses |year=1988 |volume=18 |issue=Suppl 4 |pages=643&ndash;654 |doi=10.1016/S0399-077X(88)80175-6 }}</ref> It is unclear how imported melioidosis is able to persist in a completely new environment. Eventually, the outbreak terminated by itself after a period of time.<ref name="Ketheesan 2012"/> It was only during the 1980s, Infectious Disease Association of Thailand started took notice of this disease. First conference on melioidosis was held in 1985 in Thailand. It was during this meeting that collaboration between Sappasitprasong Hospital, Thailand, and Wellcome-Mahido-Oxford Tropical Medicine Research Programme was established. Such collaboration made Thailand a world leader in clinical and epidemiology research on melioidosis.<ref name="Ketheesan 2012"/> In 1989, several studies conducted in Thailand demonstrated ceftazidime as an effective antibiotic against melioidosis.<ref name="Ketheesan 2012"/> [[w:Ceftazidime|Ceftazidime]] had been shown to reduce the risk of death of melioidosis from 74% to 37%.<ref name="White 1989">{{cite journal |author=White NJ |author2=Dance DA |author3=Chaowagul W |author4=Wattanagoon Y et al |title=Halving of mortality of severe melioidosis by ceftazidime |journal=Lancet |year=1989 |volume=23 |issue=2 |pages=697-701 |pmid=2570956 |pmc= |doi=10.1016/s0140-6736(89)90768-x }}</ref> In 1990, a non-virulent ‘arabinose-positive B. pseudomallei’ was found by Vanaporn Wuthiekanun. The organism was later reclassified into a new species called ''B. thailandensis''. This species has become a useful tool in the laboratory for the studies of the pathogenesis of ''B. pseudomallei''.<ref name="Ketheesan 2012"/> ''B. pseudomallei'' was previously classified as part of the genus ''[[w:Pseudomonas|Pseudomonas]]''. In 1992, the pathogen was formally named ''B. pseudomallei''.<ref name="Yabuuci 1992">{{cite journal |author=Yabuuci E |author2=Kosako Y |author3=Oyaizu H |author4=Yano I et al |title=Proposal of Burkholderia gen. nov. and transfer of seven species of the genus Pseudomonas homology group II to the new genus, with the type species Burkholderia cepacia (Palleroni and Holmes 1981) comb. nov |journal=Microbiology and Immunology |year=1993 |volume=36 |issue=12 |pages=1251-1275 |pmid=1283774 |pmc=154742 |doi=10.1111/j.1348-0421.1992.tb02129.x }}</ref> In 1994, First International Symposium on melioidosis was held in Kuala Lumpur where 80 delegates attended. Papers were presented and later published as a book.<ref name="Ketheesan 2012"/> Subsequent congresses were held in Thailand, Australia, and Singapore once every three years.<ref name="Ketheesan 2012"/> In 2002, ''B. pseudomallei'' was classified as a "Category B agent".<ref name="Rotz 2002">{{cite journal |author=Rotz LD |author2=Khan AS |author3=Lillibridge SR |author4=Ostroff SM |author5=Hughes JM |title=Public Health Assessment of Potential Biological Terrorism Agents |journal=Emerging Infectious Diseases |year=February 2002 |volume=8 |issue=2 |pages=225-230 |pmid=11897082 |pmc=2732458 |doi=10.3201/eid0802.010164 }}</ref> In 2004, the complete genome of ''B. pseudomallei'' was published.<ref name="Ketheesan 2012"/> In 2012, ''B pseudomallei'' was classified as a "Tier 1 select agent" by the U.S. Centers for Disease Control.<ref name="McRobb 2015">{{cite journal |author=McRobb E |author2=Sarovich DS |author3=Price EP |author4=Kaestli M et al |title=Tracing melioidosis back to the source: using whole-genome sequencing to investigate an outbreak originating from a contaminated domestic water supply |journal=Journal of Clinical Microbiology |year=April 2015 |volume=53 |issue=4 |pages=1144-1148 |pmid=25631791 |pmc=4365233 |doi=10.1128/JCM.03453-14 }}</ref> In 2014, [[w:co-trimoxazole|co-trimoxazole]] was established as the only oral eradication therapy rather than combination therapy of co-trimoxazole with doxycycline.<ref name="Chetchotisakd 2014">{{cite journal |author=Chetchotisakd P |author2=Chierakul W |author3=Chaowagul W |author4=Anunnatsiri S et al |title=Trimethoprim-sulfamethoxazole versus trimethoprim-sulfamethoxazole plus doxycycline as oral eradicative treatment for melioidosis (MERTH): a multicentre, double-blind, non-inferiority, randomised controlled trial |journal=Lancet |year=1 March 2014 |volume=383 |issue=9919 |pages=807-814 |pmid=24284287 |pmc=3939931 |doi=10.1016/S0140-6736(13)61951-0 }}</ref> In 2016, a statistical model was developed to predict the occurrence of global melioidosis per year.<ref name="Limmathurotsakul 2016"/> ==Synonyms== *Pseudoglanders<ref>{{cite journal |author=Chai LYA |author2=Fisher D |title=Earth, wind, rain, and melioidosis |journal=The Lancet - Planetary Health |date=1 August 2018 |volume=2 |issue=8 |pages=329–330 |doi=10.1016/S2542-5196(18)30165-7 |pmid=30082045 }}</ref> *Whitmore's disease (after Captain [[w:Alfred Whitmore|Alfred Whitmore]], who first described the disease)<ref name="Whitmore 1912"/> *Nightcliff gardener's disease ([[w:Nightcliff|Nightcliff]] is a suburb of [[w:Darwin, Northern Territory|Darwin, Australia]] where melioidosis is endemic)<ref>{{cite web |url=http://www.abc.net.au/pm/content/2005/s1285014.htm |title=Rise in melioidosis rates in NT |author=Barker A |date=19 June 2005 |accessdate=2007-06-24 |publisher=Australian Broadcasting Corporation }}</ref> *Paddy-field disease<ref>{{cite journal |author=Orellana C |title=Melioidosis strikes Singapore |journal=Lancet Infect Dis |date=November 2004 |volume=4 |issue=11 |pages=655 |pmid=15534940 |doi=10.1016/S1473-3099(04)01190-9 }}</ref> *Morphia injector's septicaemia<ref name="Stevenson 1916">{{cite journal |author=Stevenson AC |title=Morphia injector's septicæmia (Whitmore's Disease) |journal=Transactions of The Royal Society of Tropical Medicine and Hygiene |date=June 1916 |volume=9 |issue=7 |pages=218-219 |pmid= |pmc= |doi=10.1016/S0035-9203(16)90035-X }}</ref> ==Biological warfare== Interest in melioidosis has been expressed because it has the potential to be developed as a [[w:biological warfare|biological weapon]]. Another similar bacterium, ''Burkholderia mallei'' was used by the Germans in [[w:World War I|World War I]] to infect livestock shipped to Allied countries.<ref name="Matthew 2018"/> Deliberate infection of human [[w:prisoners of war|prisoners of war]] and animals using ''B. mallei'' were carried out in China's [[w:Pingfang District|Pingfang District]] by the Japanese during World War II.<ref name="Allen C 2005"/> The [[w:Soviet Union|Soviet Union]] reportedly used ''B. mallei'' during the [[w:Soviet–Afghan War|Soviet–Afghan War]] in 1982 and 1984.<ref name="Matthew 2018"/> ''B. pseudomallei'', like ''B. mallei'', was studied by both the US<ref>{{cite book |editor=Withers MR |title=USAMRIID's Medical Management of Biological Casualties Handbook |edition=8th |publisher=U.S. Army Medical Institute of Infectious Diseases |location=Fort Detrick, Maryland |year=2014 |url=http://www.usamriid.army.mil/education/bluebookpdf/USAMRIID%20BlueBook%208th%20Edition%20-%20Sep%202014.pdf |pages=53 }}</ref> and Soviet Union as a potential biological warfare agent, but never weaponized.<ref name="Matthew 2018">{{cite journal |author=Nguyen HVN |author2=Smith ME |author3=Hayoun MA |title=Glanders and Melioidosis |date=27 October 2018 |pmid=28846298 |url=https://www.ncbi.nlm.nih.gov/books/NBK448110/ |accessdate=15 February 2019 |journal=StatPearls |publisher=StatPearls Publishing |id=NBK448110 }}</ref> Other countries such as Iran, Iraq, North Korea, and Syria may have investigated the properties of ''B. pseudomallei'' for biological weapons.<ref name="Yi 2014"/> The bacterium is readily available in the environment. It can also be aerosolized and transmitted via inhalation.<ref name="Yi 2014"/> However, the ''B. pseudomallei'' has never been used in biological warfare.<ref name="Yi 2014"/> The actual risk of the deliberate release of ''B. pseudomallei'' or ''B. mallei'' is unknown.<ref name="Gilad 1997">{{cite journal |author=Gilad J |author2=Harary I |author3=Dushnitsky T |author4=Schwartz D |author5=Amsalem Y |title=Burkholderia mallei and Burkholderia pseudomallei as bioterrorism agents: national aspects of emergency preparedness |journal=The Israel Medical Association Journal |year=1997 |volume=9 |issue=7 |pages=499-503 |pmid=17710778 }}</ref> ==Additional information== ===Acknowledgements=== All authors contributed to the article. ===Conflict of interest=== No funding was received for the preparation of this article. No financial competing interests declared. ===Ethics statement=== No ethical permission required. ==References== {{Reflist}} suh7onkzijm6qp3cucu8rlf85onucta 0 263444 2412392 2411425 2022-08-06T18:04:18Z Scogdill 1331941 wikitext text/x-wiki == Overview == Louise, Duchess of Devonshire was the subject of much comment and gossip in her life, arising in part from her prominence in society and in part from her conduct, which was not controlled by middle-class notions of "respectability." == Also Known As == *Louise, Duchess of Devonshire (15 January 1832 – 15 November 1911) *Louisa, Duchess of Manchester *Luise Friederike August Gräfin von Alten *Louisa Montagu *Louise Cavendish *The Double Duchess == Acquaintances, Friends and Enemies == === Friends === *[[Social Victorians/People/Albert Edward, Prince of Wales | Albert Edward, Prince of Wales]] (beginning about 1852) *[[Social Victorians/People/Spencer Compton Cavendish|Spencer Compton Cavendish]], Lord Hartington (later 8th Duke of Devonshire) *Daisy, Lady Warwick *Lady Mayoress, Mrs. Benjamin Samuel Faudel-Phillips, 2nd Baronet,<ref>{{Cite journal|date=2020-08-25|title=Faudel-Phillips baronets|url=https://en.wikipedia.org/w/index.php?title=Faudel-Phillips_baronets&oldid=974879290|journal=Wikipedia|language=en}}</ref> presented to Victoria by Louisa Cavendish at a Queen's Drawing-room on Wednesday, 24 February 1897 at Buckingham Palace.<ref name=":4">"The Queen's Drawing Room" ''Morning Post'' 25 February 1897 Thursday: 5 [of 10], Col. 5a–7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970225/047/0005.</ref>{{rp|p. 5, Col. 6c}} *Mrs. J. E. Mellor, presented to Victoria by Louisa Cavendish at a Queen's Drawing-room on Wednesday, 24 February 1897 at Buckingham Palace.<ref name=":4" />{{rp|p. 5, Col. 6c}} === Enemies === * Consuelo, Duchess of Marlborough (at least, in 1901)<ref name=":1">Murphy, Sophia. ''The Duchess of Devonshire's Ball''. London: Sidgwick & Jackson, 1984.</ref>{{rp|pp. 31–32}} == Organizations == == Timeline == '''1852 July 22''', Luise Friederike Auguste Gräfin von Alten and William Drogo Montagu married.<ref name=":2">"Luise Friederike Auguste Gräfin von Alten." {{Cite web|url=http://www.thepeerage.com/p10947.htm#i109469|title=Person Page|website=www.thepeerage.com|access-date=2020-09-25}}</ref> '''1863, early, or late 1862''', Louise and Spencer Compton Cavendish began a relationship.<ref name=":1" />{{rp|p. 26}} '''1873 December 10''', Mary Louise Elizabeth Montagu (daughter) and William Douglas-Hamilton married. '''1876 May 22''', Consuelo Iznaga y Clement and George Victor Drogo Montagu (son) married in Grace Church, New York City.<ref>{{Cite journal|date=2020-08-24|title=George Montagu, 8th Duke of Manchester|url=https://en.wikipedia.org/w/index.php?title=George_Montagu,_8th_Duke_of_Manchester&oldid=974659520|journal=Wikipedia|language=en}}</ref><ref>{{Cite journal|date=2020-07-27|title=Consuelo Montagu, Duchess of Manchester|url=https://en.wikipedia.org/w/index.php?title=Consuelo_Montagu,_Duchess_of_Manchester&oldid=969888488|journal=Wikipedia|language=en}}</ref> '''1876 August 10''', Louisa Augusta Beatrice Montagu (daughter) and Archibald Acheson married. '''1889 January 5''', Alice Maude Olivia Montagu (daughter) and Edward Stanley married. '''1890 March 22''', William Drogo Montagu (7th Duke) died.<ref name=":3">"William Drogo Montagu, 7th Duke of Manchester." {{Cite web|url=http://www.thepeerage.com/p10128.htm#i101274|title=Person Page|website=www.thepeerage.com|access-date=2020-09-25}}</ref> '''1890 November 14''', William Angus Drogo Montagu (grandson) and Helena Zimmerman married secretly, in London.<ref>"Helena Zimmerman." {{Cite web|url=http://www.thepeerage.com/p34555.htm#i345545|title=Person Page|website=www.thepeerage.com|access-date=2020-09-25}}</ref> '''1892 August 16''', Louise Friederike Auguste Gräfin von Alten Montagu and Spencer Compton Cavendish, her second husband, married.<ref name=":2" /> '''1897 July 2, Friday''', Louise Cavendish (#18 on the list of attendees) hosted her famous [[Social Victorians/1897 Fancy Dress Ball| fancy-dress ball]] at Devonshire House in London. '''1897 July 20''', Mary Louise Elizabeth Montagu Douglas-Hamilton and Robert Carnaby Foster married. '''1900 November 14''', William Angus Drogo Montagu and Helena Zimmerman married.<ref>{{Cite journal|date=2020-07-17|title=Helena, Countess of Kintore|url=https://en.wikipedia.org/w/index.php?title=Helena,_Countess_of_Kintore&oldid=968067371|journal=Wikipedia|language=en}}</ref> '''1901 Spring''', Paris, Consuelo Spencer-Churchill, Duchess of Marlborough, describes a meeting with Louise Cavendish in the spring following Queen Victoria's death at the horse racetrack, Longchamps:<blockquote>A renowned character and virtually dictator of what was known as the fast set as opposed to the Victorian, Her Grace was a German aristocrat by birth. She had first been married to the impoverished Duke of Manchester, and when he died had improved her status by marriage to the rich Duke of Devonshire, who waged an undisputed influence in politics. Rumour had her beautiful, but when I knew her she was a raddled old woman, covering her wrinkles with paint and her pate with a brown wig. Her mouth was a red gash and from it, when she saw me, issued a stream of abuse. How could I, she complained, pointing to my white gloves, show so little respect to the memory of a great Queen? What a carefree world we must have lived in, that etiquette even in such small matters could assume so much importance?<ref>Balsan, Consuelo Vanderbilt. ''The Glitter and the Gold: The American Duchess — In Her Own Words''. New York: St. Martin's, 1953.</ref>{{rp|p. 115}}</blockquote> === Annual Events === Every year, as Duchess of Devonshire, Louise held a dance on the night after the Derby at Epsom Downs, which at this point was held on Wednesdays after Easter. == The Duchess of Devonshire's 2 July 1897 Fancy-dress Ball == Louisa, Duchess of Devonshire and Spencer Compton, 98th Duke of Devonshire hosted the famous [[Social Victorians/Terminology#Fancy-dress ball|fancy-dress ball]], which took place on Friday night. According to ''House Style: Five Centuries of Fashion at Chatsworth'',<blockquote>Such an event required extensive planning and attention to detail. The housekeeper aided by two secretaries was in charge of organisation inside the house with precise instructions from the Duchess on menus and all arrangements.<ref name=":18" />(137)</blockquote> === The Devonshire House Staff at the Ball === The Dukes of Devonshire did not keep employment records of the staff working at their various properties. The Servants and Staff Database managed by Chatsworth House has a list of everyone ever named in any documents as a servant or staff member, and by 1891 census records included employment at places like the properties owned by the Duke of Devonshire.<ref name=":19" /> According to ''House Style: Five Centuries of Fashion at Chatsworth'', some of the staff who worked the ball were hired from the "outside," and some were already staff at Devonshire House.<blockquote>Then there was the mammoth task of organising costumes for the staff, as the Duchess had decided that they should all be in fancy dress. Those hired from outside were to wear Elizabethan and Egyptian costumes from a theatrical outfitter and, for the Devonshire House staff, the men were to be dressed in the blue and buff Devonshire livery of the eighteenth century and the maids in Elizabethan sprigged frocks.<ref name=":18" />(137)</blockquote> === Questions === # Who was housekeeper? Who were the secretaries? # Where did this info about the "precise instructions" come from? == The Duchess of Devonshire's Costume == [[File:Louise Frederica Augusta Cavendish (née von Alten), Duchess of Devonshire (formerly Duchess of Manchester) as Zenobia, Queen of Palmyra.jpg|thumb|Louise, Duchess of Devonshire as Zenobia, Queen of Palmyra|alt=Louise, Duchess of Devonshire in costume as Zenobia, Queen of Palmyra]] At their fancy-dress ball, Louisa, Duchess of Devonshire sat at Table 1 during the first seating for supper, escorted in to the table by the Prince of Wales.<ref name=":7">"Fancy Dress Ball at Devonshire House." ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.</ref>{{rp|p. 7, Col. 4c}} Her costume was designed by M. Comelli (Attillo Giuseppe Comelli, 1858–1925, artist and costumier for opera, ballet and theatre in London as well as Europe and the U.S.<ref name=":13">{{Cite book|url=https://books.google.com/books?id=SZh2DwAAQBAJ&pg=PT207&lpg=PT207&dq=Attilio+Comelli&source=bl&ots=lFB0If7CwV&sig=ACfU3U1_Ost_lhmMvzMMs6NvuhK5SlRhJw&hl=en&sa=X&ved=2ahUKEwjKlsTw2sH3AhXYAp0JHVIxDWA4KBDoAXoECBAQAw#v=onepage&q=Attilio%20Comelli&f=false|title=Forgotten Designers Costume Designers of American Broadway Revues and Musicals From 1900-1930|last=Unruh|first=Delbert|date=2018-11-06|publisher=Page Publishing Inc|isbn=978-1-64082-758-5|language=en}} N.P.</ref>)<ref name=":5">“The Devonshire House Ball.” The ''Man of Ross'' 10 July 1897, Saturday: 2 [of 8], Col. 4b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0001463/18970710/033/0002.</ref> <ref name=":8">"The Duchess of Devonshire's Fancy Dress Ball. Special Telegram." ''Belfast News-Letter'' Saturday 03 July 1897: 5 [of 8], Col. 9 [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000038/18970703/015/0005.</ref>{{rp|p. 5, Col. 9a}} <ref name=":9">"By One Who Was There." “The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref> and constructed by the House of Worth. Comelli seems to have designed [[Social Victorians/People/Louisa Montagu Cavendish#The Duchess and Her Entourage|the costumes of her retinue as well]]. According to Russell Harris,<blockquote>For her costume, the Duchess commissioned Monsieur Comelli (1858-1925), a well-known designer of opera costumes for the London theatre and opera stage, and then had the design made up by Worth of Paris. ''Munsey’s Magazine'' noted “it is safe to say that the Queen of Palmyra never owned such a sumptuous costume in her lifetime.”<ref>Harris, Russell. {{Cite web|url=http://www.rvondeh.dircon.co.uk/incalmprose/devonshiredss.html|title=Louise, Duchess of Devonshire, née Countess von Alten of Hanover (1832-1911), as Zenobia, Queen of Palmyra|website=www.rvondeh.dircon.co.uk|access-date=2022-05-05}} ''Narrated in Calm Prose: Photographs from the V&A's Lafayette Archive of Guests in Costume at the Duchess of Devonshire's Diamond Jubilee Ball, July 1897''. http://www.rvondeh.dircon.co.uk/incalmprose/devonshiredss.html.</ref></blockquote>Lafayette's portrait of "Louise Frederica Augusta Cavendish (née von Alten), Duchess of Devonshire (formerly Duchess of Manchester)" in costume is photogravure #5 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.<ref>"Devonshire House Fancy Dress Ball (1897): photogravures by Walker & Boutall after various photographers." 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.</ref> The printing on the portrait says, "The Duchess of Devonshire as Zenobia Queen of Palmyra," with a Long S in ''Duchess''.<ref>"Louise Frederica Augusta Cavendish (née von Alten), Duchess of Devonshire (formerly Duchess of Manchester) as Zenobia, Queen of Palmyra." Devonshire House Fancy Dress Ball Album. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158357/Louise-Frederica-Augusta-Cavendish-ne-von-Alten-Duchess-of-Devonshire-formerly-Duchess-of-Manchester-as-Zenobia-Queen-of-Palmyra.</ref> Often, the V&A Lafayette Archive contains more than one portrait of a sitter for this ball, but the uncropped portrait (above right), which shows the unfinished end of the balustrade in front of the Duchess and the edge of the painted flat behind it, seems to have been the only portrait taken by Lafayette of the Duchess in costume. The copy owned by the National Portrait Gallery in London and the copy included in the album are cropped so that those unfinished edges do not show, but they appear to be from the same photograph. === Newspaper Descriptions of the Duchess's Costume === Newspaper articles about the Duchess's presence at the ball focused on her hosting, her costume, [[Social Victorians/People/Louisa Montagu Cavendish#The Duchess's Jewelry|her jewelry]], and [[Social Victorians/People/Louisa Montagu Cavendish#The Duchess's Entourage|her entourage]], often in the same story. These almost exactly identical descriptions suggest [[Social Victorians/1897 Fancy Dress Ball/anthology#Scissors-and-Paste Journalism|scissors-and-paste journalism]] or a shared primary source: * The London ''Evening Standard'', ''Morning Post'' and ''Times'' published almost identical descriptions, varying only by the occasional punctuation mark or short phrase ("supplied by Worth, of Paris"). The fullest version is this one: "The Duchess of Devonshire, as Zenobia, Queen of Palmyra, wore a magnificent costume, supplied by Worth, of Paris. The skirt of gold tissue was embroidered all over in a star-like design in emeralds, sapphires, diamonds, and other jewels, outlined with gold, the corners where it opened in front being elaborately wrought in the same jewels and gold to represent peacocks' outspread tails. This opened to show an under-dress of cream crêpe de chine, delicately embroidered in silver, gold, and pearls, and sprinkled all over with diamonds. The train was attached to the shoulders by two slender points, and was fastened at the waist with a large diamond ornament. It was of green velvet of a lovely shade, and was superbly embroidered in Oriental designs, introducing the lotus flower in rubies, sapphires, amethysts, emeralds, and diamonds, in four borderings on contrasting grounds, separated with gold cord. The train was lined with turquoise satin. The bodice was composed of gold tissue to match the skirt, and the front was of crêpe de chine, hidden with a [[Social Victorians/Terminology#Stomacher|stomacher]] of real diamonds, rubies, and emeralds, and there was a jewelled belt."<ref name=":16">“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.</ref>{{rp|p. 3, Col. 2b}} <ref name=":7" />{{rp|p. 7, Col. 7a}} <ref name=":6">"Ball at Devonshire House." The ''Times'' Saturday 3 July 1897: 12, Cols. 1A–4C ''The Times Digital Archive''. Web. 28 Nov. 2015.</ref>{{rp|p. 12, Col. 3b}} *"The Duchess of Devonshire was a dazzling vision, dressed as 'Zenobia,' in a glistening gold gauze gown, elaborately ornamented with suns and discs, wrought in purple and green gems outlined with gold, and having a large diamond as centre. The space between was fluted with fine silver spangles. This robe was open in front over an under dress of white crépe de chine, delicately worked in crystals, and at each side of the opening on the gold robe were large fan-shaped groups of peacock feathers, worked in multicoloured jewels. The [[Social Victorians/Terminology#Corsage|corsage]] was to correspond, and had a magnificent [[Social Victorians/Terminology#Girdle|girdle]] of jewels, the train of bright green velvet, hung like a fan, without folds, being fastened at each side of the shoulders by diamond brooches, and caught at the waist with a similar ornament. It was a mass of gorgeous embroidery, carried out in heliotrope velvet, lotus flowers studded with tinted gems, and other devices in terra-cotta and electric blue velvet — all enriched with gold, diamond, and jewelled embroidery — and lined with pale blue satin. ... Attending the hostess were four children, four fan-bearers, and four trumpeters, all magnificently arrayed in artistically embroidered Assyrian robes, helmets, and other accessories, correct in every detail."<ref name=":15">"Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses." London ''Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6a–6, Col. 1b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and http://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.</ref>{{rp|p. 5, Col. 6a}} * According to the article in ''The Graphic'' written by [[Social Victorians/People/Lady Violet Greville|Lady Violet Greville]], though this caption to the Lafayette photograph may not be hers, the Duchess of Devonshire wore a "Skirt of gold tissue, embroidered all over with emeralds, sapphires, diamonds, and other jewels outlined with gold. This opened to show an underdress of crème crêpe de chine, embroidered in silver, gold, and pearls, and sprinkled all over with diamonds. The train was green velvet, superbly embroidered in Oriental designs. The bodice was composed of gold tissue, and the front was of crêpe de chine hidden with a stomacher of diamonds, rubies, and emeralds."<ref name=":10">Greville, Violet, Lady. "Devonshire House Ball." The ''Graphic'' Saturday 10 July 1897: 15 [of 24]: Col. 1a–16, Col. 1c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000057/18970710/019/0015.</ref>{{rp|p. 15, Col. 3b}} The photograph of the Duchess taken by Lafayette in her costume could not do justice to the colors of the costume, of course, because it is in black and white. Fortunately, this costume has survived and is held in Archives of the Duke of Devonshire (Devonshire Collections, Chatsworth). Published photographs of it '''show X'''.<ref name=":18">Burlington, Julia, and Hamish Bowles. ''House Style: Five Centuries of Fashion at Chatsworth''. Skira Rizzoli, 2017. Based on an exhibition 25 March to 22 October 2017.</ref> It has been worn by '''X, the xth duchess'''. Some accounts of her costume suggest that the reporter thought that all the jewels sewn onto the dress were actual precious or semiprecious stones, but the London ''Daily News'' says some of them were crystals.<ref name=":15" />(p. 5, Col. 6a) According to ''House Style: Five Centuries of Fashion at Chatsworth'',<blockquote>The skirt of gold gauze, appliquéd with tinsel medallions and peacock plumes worked in bright foils, wire coils and spangled with sequins, was worn over an ivory satin underskirt wrought over with silver thread and diamonds. Attached to the shoulders was a long graduated train in the most vivid emerald-green velvet, appliquéd with velvet and gold work in an eastern design and studied with jewels.<ref name=":18" />(128)</blockquote> === Observations on the Duchess's Costume === * The exhibitions of the dress show a different fit than what is shown in the Lafayette photograph of Louise, 8th Duchess. The 1897 bodice appears to be loose over the stomacher. * Recent photographs of the costume show that it may have been altered or adjusted to make the waist more defined and the line looks more Elizabethan (the wide, square neckline; the A-line, the split skirt with the petticoat in the middle). * The dress seems to have been designed to flatter the 8th Duchess's statuesque figure, especially her waist: the belt falls down to the hips, the A-line; the way what we can see of the under-dress is narrow at the top and widens toward the bottom. * The drape of the skirt is straighter on the 8th Duchess as well as the Dowager Duchess than on the mannequins. * The sleeve treatment on the 1897 photograph is caught up at the shoulder. On the Dowager Duchess and the mannequins, the sleeves are released. * The 1897 reports use different terminology for the parts of the dress than we would now: skirt, under-dress, bodice, stomacher as opposed to skirt, underskirt. * The train: very Victorian === The Historical Zenobia === Zenobia (240 – c. 274) was queen of the Syrian Palmyrene Empire, ruling as regent for her son after her husband's assassination.<ref>{{Cite journal|date=2022-05-03|title=Zenobia|url=https://en.wikipedia.org/w/index.php?title=Zenobia&oldid=1086005949|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Zenobia.</ref> She was the subject of much art in the 19th century, including literature, opera, sculpture, and paintings. Middle-eastern traveller Lady Hester Stanhope (1776–1839) discussed Zenobia in her memoirs, published in 1847.<ref>{{Cite journal|date=2022-03-07|title=Lady Hester Stanhope|url=https://en.wikipedia.org/w/index.php?title=Lady_Hester_Stanhope&oldid=1075838273|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Lady_Hester_Stanhope.</ref> == The Duchess's Jewelry == The Duchess was known for her jewelry, and as she aged and after her marriage to the 8th Duke in 1892, the jewelry she wore only increased in scale and notability. It is not surprising that her jewelry would make up copy for the newspapers. Gossipy newspaper reports before the ball '''reported''' on the jewelry associated with the costumes being developed. For example, according to the Edinburgh ''Evening News'' on 21 June 1897, less than two weeks before the party, "The ball being a fancy dress one, men as well as women will be able in certain characters to wear jewels. The Duchess of Devonshire, who is to appear as Zenobia, is getting her jewels reset after the antique style."<ref>“The Duchess of Devonshire’s Ball.” Edinburgh ''Evening News'' 21 June 1897, Monday: 4 [of 6], Col. 5c [of 7]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18970621/079/0004.</ref> While almost all descriptions of her mention her jewels because they were so much a topic of conversation and because they were sewn onto the costume itself, these emphasize her jewelry and most are very similar to each other: * "The Duchess was attired with great Oriental magnificence as Zenobia. Her dress was a tissue of silver, embroidered with gold and jewels, an overmantle of cloth of gold embroidered in the same manner hung from the shoulders, and she wore a bandeau of gold studded with gems, and surrounded by hanging chains of pearls over her elaborate headdress; strings and ropes of jewels and pearls were worn round the neck, and hung down almost to the knees."<ref>“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032. </ref>{{rp|p. 32, Cols. 1c–2a}} <ref name=":17">"Duchess of Devonshire's Fancy-Dress Ball. Brilliant Spectacle." The [Guernsey] ''Star'' 6 July 1897, Tuesday: 1 [of 4], Col. 1a–2b [of 7]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000184/18970706/003/0001.</ref>{{rp|p. 1, Col. 2a}} * "A wonderfully beautiful dress was that which was worn by the Duchess of Devonshire as Zenobia, Queen of Palmyra. It was of golden tissue, sewn with silver paillettes, and jewelled with diamonds and other precious stones. In front there were silk embroideries, in many vivid shades of colour, and here the golden draperies opened to show a petticoat of white crêpe de chine, embroidered with pearls and gold. The short train was of brilliant green velvet, exquisitely embroidered. One of the Duchess of Devonshire’s beautiful diamond and emerald tiaras had been taken to pieces to form a stomacher, the effect of which was dazzling in its brilliancy. Long chains of pearls and other wonderful jewels were worn with this beautiful dress."<ref>“The Devonshire House Ball. A Brilliant Gathering.” The ''Pall Mall Gazette'' 3 July 1897, Saturday: 7 [of 10], Col. 2a–3a [of 3]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18970703/019/0007.</ref>{{rp|p. 7, Col. 2b}} * In the article about the ball in the ''Graphic'', [[Social Victorians/People/Lady Violet Greville|Lady Violet Greville]] says, "The Ducal hostess herself elected to appear as Zenobia, Queen of Palmyra, with lavish magnificence, and wearing a corruscation of jewels which must have eclipsed the state of even the all-subduing majesty the Duchess impersonated."<ref name=":10" />{{rp|p. 16, Col. 1a}} *The Duchess was dressed "as Zenobia, Queen of Palmyra, her dress a marvel of soft tissues and exquisite ornament, and her tiara a still greater marvel of the jeweller's art."<ref name=":6" />{{rp|p. 12, Col. 2a}} <ref>"The Duchess of Devonshire’s Historic Ball. Some of the Fancy Costumes." Supplement. The ''Leicester Chronicle and Leicestershire Mercury'' 10 July 1897, Saturday: 11 [of 12], Cols. 4a–b [of 7]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000173/18970710/141/0011.</ref>{{rp|p. 11, 4a}} As with the colors, Lafayette's photograph of the Duchess in costume does not show the jewels very clearly. We cannot see the stomacher or the "long chains of pearls and other wonderful jewels" or the pearls that "hung down almost to the knees" (although, of course, any newspaper account can be wrong because reporters were not present at the ball). === Zenobia's Crown<ref name=":10" /> === The crown that the Duchess wore as Zenobia is difficult to see clearly in the Lafayette photograph (above right). It was lavish, "encrusted" with jewels and featuring pearls: * London ''Daily News'' says, "The crown worn with this was high, and of filigree gold, surmounted with two horns, each tipped with a large diamond. It was encrusted with large diamonds, rubies, and emeralds, and long chains of pearls fell under the chin and about the head — one magnificent pear-shaped pearl resting on the forehead."<ref name=":15" />(p. 5, Col. 6a) * These descriptions are all identical except for the addition or subtraction of an occasional comma: The London ''Evening Standard'' says, "A gold crown encrusted with emeralds, diamonds, and rubies, with a diamond drop at each curved end, and two upstanding white ostrich feathers in the centre, and round the front were festoons of pearls, with a large pear-shaped pearl in the centre falling on the forehead."<ref name=":16" />{{rp|p. 3, Col. 2b}} <ref name=":7" />{{rp|p. 7, Col. 7a}} <ref name=":6" />{{rp|p. 12, Col. 3b}} <ref name=":10" />{{rp|p. 15, Col. 3b}} * The Guernsey ''Star'' says, "Her Grace wore a bandeau of gold round her head, studded with diamonds, turquoise, and emeralds, and surrounded by hanging chains of superb pearls."<ref name=":17" />{{rp|p. 1, Col. 2a}} === Goldsmith, Pearl & Diamond Merchant, & Silversmith === The Duchess's pearls, which were an important feature of her costume, occasioned a great deal of direct commentary in the newspaper accounts. The Duchess's jewelry occasioned a great deal of reportage in the articles about the ball. '''It was reported that she had her jewels restrung to be used in the costume. stomacher and review of jewelry in more general articles''' An invoice and receipt in the Archives of the Duke of Devonshire (Devonshire Collections, Chatsworth) is from a concern whose preprinted stationery has a crown in the upper-left corner, suggesting that they had a royal warrant, and no name other than Goldsmith, Pearl & Diamond Merchant, & Silversmith. This document offers a unique view into the evolution of one necklace, at least, over the years. It lists what are apparently three restringing of some pearls of Louise, Duchess of Devonshire. The three restringings appear to be dated: The first necklace is a "Pearl Necklet in original 4 rows." The invoice is dated 20 October 1892 (but the stationery was printed to assume the invoice would be used in the 1880s, so the 9 is written over the second 8, and the 2 has been added).<ref name=":14">Invoice and receipt. Goldsmith, Pearl & Diamond Merchant & Silversmith. Date of itemized invoices for restringing pearls: 20 October 1892, 1 March 1897, 1909. The Devonshire Collections, Chatsworth, Reference number FIS/4/1/2.</ref>(p. 1) The necklet she brought in to be restrung contained a "Total [of] Total 224 large pearls": # 1st [row] 51 large pearls # 2nd 53 large pearls # 3rd 57 large pearls # 4th 63 large pearls The second necklace is a "Necklet as re-strung on October 15th 1892, with addition of small pearls supplied, now consists of 5 rows, containing" a total of "224 large pearls & 227 small"<ref name=":14" />(p. 1): # 1st 41 large pearls & 40 small # 2nd 42 large pearls & 42 small # 3rd 44 large pearls & 45 small # 4th 47 large pearls & 48 small # 5th 50 large pearls & 51 small The third necklace is a "Pearl Necklet as again re-strung with additional pearls supplied 1 March 1897, now consisting of 5 Rows containing" a total of "262 Large Pearls & 267 Small"<ref name=":14" />(p. 2): # 1st Row 45 Large Pearls & 44 Small # 2nd Row 48 large Pearls & 49 Small # 3rd Row 51 Large Pearls & 52 Small # 4th Row 56 Large Pearls & 65 small Possibly these pearls may have been restrung in 1909 into a coronet, but the handwriting is not clear enough to read.<ref name=":14" />(p. 2) If the Duchess wore one of these stringings of her pearls for the ball, then it must have been the second necklet, strung in 1892, a 5-strand necklace. None of the newspaper accounts refer to a 5-strand pearl necklace, although her pearls are often mentioned. == The Duchess's Entourage == Besides the Duke of Devonshire, the retinue of Louise, Duchess of Devonshire as Zenobia, Queen of Palmyra, included her grandson, [[Social Victorians/People/William Angus Drogo Montagu|William Angus Drago Montagu, 9th Duke of Manchester]], dressed as a Georgian courtier. Four newspapers say that the Duchess's entourage included three groups, all in costume: children, trumpeters and fan-bearers. The ''Westminster Gazette'' and the ''Man of Ross'' '''do not address''' the number of members of the groups. According to two sources, probably in error, the London ''Daily News''<ref name=":15" />(p. 5, Col. 6a) and the Belfast ''News-Letter,''<ref name=":8" />{{rp|p. 5, Col. 9a}} these groups each had four members. The London ''Daily News'' is likely the source (though not the only one) for the Belfast ''News-Letter'', which took part in [[Social Victorians/1897 Fancy Dress Ball/anthology#Scissors-and-Paste Journalism|scissors-and-paste journalism]], like so many other newspapers of the 19th century. ['''check this: which one was published earlier in the day, and on which day?'''] These four sources describe the Duchess's retinue and how the people in it were dressed: *"The Duchess of Devonshire was dazzingly [sic] magnificent as 'Zenobia,' arrayed in the glistening fabrics and massive jewels in which artists have delighted to depict the Warrior Queen, the costume in this case being specially designed by the clever French artist, M. Comelli, who was also responsible for the splendid attire of the Queen's suite. This was composed of four children in white Assyrian robes, draped with pink shawls; four trumpeters in white cloth robes, embroidered in subdued tones of silks, with a purple shawl draped over, beautifully ornamented with embroidery, and wearing fringed steel helmets and leather cuirasses embossed in steel; and four fan-bearers attired in pale blue robes, with crimson shawls, enriched with gold and jewelled embroidery, adorned with jewelled diadems, and holding long-handled fans of white feathers, mounted in blue and gold — a gloriously magnificent pageant."<ref name=":8" />{{rp|p. 5, Col. 9a}} *"Attending the hostess were four children, four fan-bearers, and four trumpeters, all magnificently arrayed in artistically embroidered Assyrian robes, helmets, and other accessories, correct in every detail."<ref name=":15" />{{rp|p. 5, Col. 6a}} *"The duchess was dressed as Zenobia, in gold cloth, gorgeously embroidered in gold, brilliants, and coloured stones, and opening over an under dress of white crêpe de Chine, worked finely in brilliants. The train of light green velvet was lined with blue, and sumptuously embroidered in jewels and gold, the colouring being particularly artistic. With this dress were worn splendid jewels, and a large horn crown, encrusted with diamonds, emeralds, and rubies. The duchess was attended by a suite of children, trumpeters, and fan-bearers, all picturesquely attired in Assyian [sic] costumes — the whole group being specially designed by M. Comelli."<ref name=":5" /> *"The host was dressed as Charles V. of Germany, in black velvet, satin, and fur; and the Duchess made the most gorgeous of Zenobias, in a gown of gold gauze, and a green velvet train — both a mass of exquisite oriental embroidery. The crown and hanging ropes of pearls, the jewelled girdle, and the train of children, fan-bearers, and trumpeters — all in Babylonish garb — as designed by M. Comelli, made a gloriously imposing and picturesque group."<ref name=":9" /> === Details of the Costumes in the Entourage === The Archives of the Duke of Devonshire (Devonshire Collections, Chatsworth) has "receipts" or invoices that functioned as receipts for several commercial concerns that were involved in making costumes or accessories for costumes for this ball. They are the following: * [[Social Victorians/People/Louisa Montagu Cavendish#M. (Attillo Giuseppe) Comelli|M. (Attillo Giuseppe) Comelli]] * [[Social Victorians/People/Louisa Montagu Cavendish#B. Burnet & Co.|B. Burnet & Co.]] * [[Social Victorians/People/Louisa Montagu Cavendish#Arthur Millward, Theatrical Jeweller|Arthur Millward, Theatrical Jeweller]] * [[Social Victorians/People/Louisa Montagu Cavendish#Liberty & Co., Ltd.|Liberty & Co., Ltd.]] * [[Social Victorians/People/Louisa Montagu Cavendish#Lafayette, Ltd.|Lafayette, Ltd.]] * [[Social Victorians/People/Louisa Montagu Cavendish#Goldsmith, Pearl & Diamond Merchant, & Silversmith|Goldsmith, Pearl & Diamond Merchant, & Silversmith]] This list of commercial concerns almost certainly cannot be the complete list of all concerns that contributed to the costumes. These are the only receipts or invoices about expenses for the ball, however, that the Chatsworth Archive contains; similar documents were likely not even kept or were destroyed with other papers not retained at some point in time. The business concerns listed above were specialized and likely used for different elements of the costumes. As a theatrical designer, Comelli would have depended on the suppliers he knew and arranged with them for the construction of these costumes. The Chatsworth Archive calls these documents ''receipts'', which indeed they are because they were returned to Devonshire House as receipts for payment. From our perspective, though, they are invoices that contain specifics about what was used to make the costumes. The analysis of these invoices has led to an understanding of what the people who attended the Duchess in her entourage wore and a clearer sense, perhaps, of how many people walked in that entourage. This analysis is based on the items listed on the invoices and their pricing, most of which is included in the section for each invoice, below. While the Belfast ''News-Letter'' says that each group contained four members,<ref name=":8" />{{rp|p. 5, Col. 9a}} the invoices and receipts suggest that the newspaper, the single source for this information, was wrong about the number of people in each group. It is theoretically possible, of course, that suppliers other than the ones in the Chatsworth Archive made some of these costumes and that other invoices and receipts must have existed at that time. But the [[Social Victorians/People/Louisa Montagu Cavendish#M. (Attillo Giuseppe) Comelli|Comelli memo, below]], seems definitive: he designed and seems to have overseen the construction of the costumes, which numbered six rather than twelve. '''[Collier discussion?]''' Besides providing welcome detail about the costumes of the people in the Duchess's entourage, which is available nowhere else, these invoices also raise at least as many questions as they answer. ==== M. (Attillo Giuseppe) Comelli ==== Attillo Giuseppe Comelli was a designer for opera, ballet and theatre in Europe, the UK and North America.<ref name=":13" /> The receipt in the Chatsworth Archive was sent from Covent Garden. The invoice lists £4 for "Making six costumes," 3''s'' for "Extras" and 12s for "Cab fares for men paid by the request of M. Comelli."<ref>M. Comelli, Covent Garden, to Duchess of Devonshire. Date of invoice 13 July 1897; postmarked 25 October 1897, for receipt of payment(?). The Devonshire Collections, Chatsworth, Reference number L/109/4(3).</ref> Three other names are on this invoice and receipt: * L. L[?] Collier [?], written under and perhaps as part of the direction to the Duchess of Devonshire * Mr. Strong ("Forwarded to Mr Strong. [sic] by the instructions of M. Comelli," written in the same hand as wrote the majority of the memo) * Floyd [?] Collier [??] ("Received with Thanks," presumably thanking for the payment, in a different hand) ==== B. Burnet & Co. ==== An invoice and receipt from B. Burnet & Co., held in the Archives of the Duke of Devonshire, has specific information about some of the fabrics, trims and accessories purchased for the costumes of the Duchess's retinue.<ref name=":11">B. Burnet & Co. to Louise, Duchess of Devonshire. Date of invoice 2 and 6 July 1897; postmarked 25 October 1897, for receipt of payment(?). The Devonshire Collections, Chatsworth, Reference number L/109/4(3).</ref> Besides itemizing some costume or accessory elements that seem clearly to be for the groups, the invoice also lists items not easy to associate with particular costumes, like the following: * 12 yards of White silk fringe 8in deep<ref name=":11" />{{rp|back left}} * 12 1/2 yards of "wht cloth"<ref name=":11" />{{rp|back left}} * 9 yards of "[[Social Victorians/Terminology#Selesia|Selesia]]"<ref name=":11" />{{rp|back left}} * 2 yards of Canvas<ref name=":11" />{{rp|back right}} * 4 Tan Wool Tights<ref name=":11" />{{rp|back right}} * 2 Tan Boys Tights<ref name=":11" />{{rp|back right}} At this time, we are not sure which costumes these elements were used for. Possibly the white silk fringe and the white cloth would have been used to construct the robes for the children and trumpeters in the entourage. The number of tights suggests that the six costumes on this invoice all included tights. With other elements of the trumpeters' costumes, the Burnet invoice also lists "6 prs Assyrian Buskins." Probably, to a late Victorian, buskins would have been "defensive leggings"<ref>Demmin, Auguste. An illustrated History of Arms and Armour: From the Earliest Period to the Present Time. George Bell, 1894. Google Books https://books.google.com/books?id=ArRCAAAAYAAJ: 106.</ref> laced together and covering the lower leg and often feet of a soldier. To a clothing and military historian, buskins (or greaves) were worn by people in a number of cultures over millennia and varied widely in style and construction. Buskins appear in Assyrian art held at the time by the British Museum. Listing six pairs of buskins suggests that every costume in the Duchess's entrourage included buskins, possibly worn over the tan tights. The Burnet invoice lists "4 Broad Belts," which may have held "4 Skins Fleshers."<ref name=":11" />{{rp|p. 1, front of invoice}} (A skin flesher is a kind of knife used to separate the skin from the meat in animals.) If each group included only two members, then perhaps the belts and fleshers were worn not only by the trumpeters but also by the fan-bearers. The Millward invoice (specifics in the section on the Millward invoice below) lists "8 Doz 'Plaques' for Belts'" with a drawing of an upright rectangle with a circle in the middle, which might have been a jewel. Double lines around the rectangle suggest that the plaques were not flat or the metal was not thin. The drawing does not give any ideas about how the plaques were attached to the belts, if they were. It is impossible to tell if the plaques were attached to the "4 Broad Belts" (likely for the trumpeters and fan-bearers), but unless they were quite tiny, "8 Doz 'Plaques'" would be far too many for the belts of only the two children. A different hand, probably "[L.??] L. Collier," wrote the following sentence at the end of the invoice and receipt, above the postmark:<blockquote>All the above named articles were used for the six [?] dresses made for the Devonshire Ball.<ref name=":11" />(back right)</blockquote>This same hand, signing what is possibly "Floyd Collier," also signed the postmark of the Comelli invoice and receipt. On the Burnet document, this writer, possibly an assistant or employee of the Duchess of Devonshire, says that "six dresses" were made (if in fact, that word is ''six''). (No "Collier" is listed among the staff or servants of the Duke of Devonshire at the end of the 19th century.<ref name=":19">"Servants A-H." ''Historic Servants and Staff. Servants and Staff Database''. Retrieved 18 July 2022 https://www.chatsworth.org/media/11528/servants-a-h.pdf.</ref> The invoice appears to itemize materials used for six costumes: two children, two trumpeters and two fan-bearers. ==== Arthur Millward, Theatrical Jeweller ==== An invoice and request for payment from Arthur Millward, Theatrical Jeweller, held in the Archives of Chatsworth House, has more specifics about some of the fabrics, trims and accessories for the costumes of the Duchess's retinue.<ref name=":12">Memorandum. Arthur Millward, Theatrical Jeweller, to Louise, Duchess of Devonshire. Date of itemized invoice 1 July 1897; date of request for payment(?) 27 August 1897. The Devonshire Collections, Chatsworth, Reference number L/109/4(?).</ref> This invoice lists the following, which could have been used in any of the costumes for the entourage: * 8 Doz 'Plaques' for Belts [discussed with the belts in the section on the Burnet invoice, above] * 4 Large Armlets * 4 Bracelets * 8 Armlets<ref name=":12" />{{rp|p. 2, back}} Because Millward was a Theatrical Jeweller, it seems likely that most (if not all) of the items listed on the invoice were made of metal and the jewels mentioned were artificial, made of glass or paste. Other items on the invoice seem to belong to the costumes of the trumpeters, which the Belfast ''News-Letter'' says included helmets: * 2 Helmets * 2 Centre pieces The Millward invoice shows tiny line drawings next to the words ''2 Helmets'' and ''2 Centre pieces''. These drawings suggest that the Centre pieces were attached to the helmets rather than being anything that would have been put on a table as decoration. Other items seem to belong to the costumes of the fan-bearers: * 2 Pearl & Gold Headdresses * 2 Fan properties with Feathers The "Pearl & Gold Headdresses" were likely the "jewelled diadems" mentioned in the Belfast ''News-Letter''. The "Fan properties with Feathers" are likely to have been the "long-handled fans of white feathers, mounted in blue and gold" mentioned in the newspaper report.<ref name=":8" />{{rp|p. 5, Col. 9a}} At the end of the Millward invoice, a "reduction as agreed with M [Mr?] Commelli [sic]" of £1 10''s'' is subtracted from a total of £22 3''s''. No reason for this reduction is given.<ref name=":12" />{{rp|p. 2, back}} ==== Liberty & Co., Ltd. ==== One invoice and receipt from the Chatsworth Archive, dated 12 July, to the Duchess of Devonshire, lists "13 yds S&W Satin[?]," 7 yards of blue and 6 of purple.<ref>Invoice and receipt. Liberty & Co. Ltd. To Her Grace, The Duchess of Devonshire. Date of itemized invoice 12 July [1897]. The Devonshire Collections, Chatsworth, Reference number L/109/4(?).</ref> Because the fabric is satin and from Liberty, it is possible that it was not used in the costumes of the people in the entourage but perhaps for the costume of the Duchess herself??? ==== Lafayette, Ltd. ==== The invoice and receipt from Lafayette, Ltd., the photographer that set up a temporary studio in the garden to take portraits of people at the ball in their costumes, may not be related to the ball at all.<ref>Invoice and receipt. Lafayette, Ltd. To His Grace The Duke of Devonshire. Date of itemized invoice 12 April 1897; addressed to the Duke, 18 February 1898; receipt and thanks for payment, 7 April 1898. The Devonshire Collections, Chatsworth, Reference number L/109/4(?).</ref> Three dates are written on the preprinted stationery: # 18/2/98 (18 February 1898), under the direction to "His Grace The Duke of Devonshire" # 4/12/97 (4 December 1897), next to the single item on the invoice for which a charge is listed: "6 [??] £1.10.0" # 7/4/98 (7 April 1898), in a different hand, with "Recd by cheque 7/4/98 Lafayette Ltd pp[?] [??] thanks" At the bottom of the page, in the hand that wrote all of the invoice except the receipt and thanks, is "With Lafayette Ltds Compliments." ==== Details for the Children in the Entourage ==== According to the ''Belfast News-Letter'', four children were "in white Assyrian robes, draped with pink shawls."<ref name=":8" />{{rp|p. 5, Col. 9a}} According to the B. Burnet invoice, the following was purchased for "White Cloth Dresses":<ref name=":11" />{{rp|p. 2, back left of invoice}} * "2 Terra Gown draperies with Stars 200 in all" * "2 Cloth fronts embroidered with Square Medallions down centre" * "2 do do [ditto ditto, that is, cloth fronts] embroidered double border down front each side and collar" * "4 Sleeves embroidered Small Medallions" The Burnet & Co. invoice lists 6 yards of "Terra" Silk Fringe, which perhaps was used to trim the "terra draperies," or shawls, made from 3 1/4 yards of "Light Terra Satinette" worn by the children? ==== Details for the Trumpeters in the Entourage ==== According to the ''Belfast News-Letter'', four trumpeters were "in white cloth robes, embroidered in subdued tones of silks, with a purple shawl draped over, beautifully ornamented with embroidery, and wearing fringed steel helmets and leather cuirasses embossed in steel."<ref name=":8" />{{rp|p. 5, Col. 9a}} The trumpeters appear to have been dressed as soldiers or military men. According to the B. Burnet invoice, the following was purchased for the trumpeters' costumes:<ref name=":11" />{{rp|p. 1, front of invoice}} * 7 '''units (yards?)''' of purple silk [probably used for shawls?] * "2 skirt fronts with border alround [sic]" * "2 sets of Leather Cuarasses [sic] Embroidered front & back" * "4 Sleeves embroidered loop stitch" The Millward invoice lists * 2 Helmets * 2 Centre Pieces [probably for helmets rather than table decorations] ==== Details for the Fan-bearers in the Entourage ==== According to the ''Belfast News-Letter'', four fan-bearers were "attired in pale blue robes, with crimson shawls, enriched with gold and jewelled embroidery, adorned with jewelled diadems, and holding long-handled fans of white feathers, mounted in blue and gold."<ref name=":8" />{{rp|p. 5, Col. 9a}} According to the B. Burnet invoice, the following was purchased for the fan bearers's costumes:<ref name=":11" />{{rp|pp. 1–2, front and left-back of invoice}} * "Embroidering 2 Crimson draperies with Stars 334 in all" * "2 Top [?] fronts embroidered & round necks" * "4 Sleeves embroidered long stitch"The Millward invoice lists * 2 Pearl & Gold Headdresses * 2 Fan properties with Feathers<ref name=":12" />{{rp|p. 2, back}} The Burnet & Co. invoice lists 12 yards of "Red Silk Fringe," which perhaps was used to trim the "crimson shawls" or "Crimson draperies," which may have been made from the 5 yards of "Red Satinette." Again, this list suggests two rather than four costumes. == Demographics == *Nationality: born in Hanover, in what is now Germany<ref name=":0">{{Cite journal|date=2020-07-27|title=Louisa Cavendish, Duchess of Devonshire|url=https://en.wikipedia.org/w/index.php?title=Louisa_Cavendish,_Duchess_of_Devonshire&oldid=969824214|journal=Wikipedia|language=en}}</ref> === Residences === ==== As Duchess of Manchester ==== *Kimbolton Castle, Huntingdonshire *Manchester House, London ==== As Duchess of Devonshire ==== *Devonshire House, London (mid-April until mid-July, for the Season) *Compton Place, Eastbourne (mid-July until 12 August<ref name=":1" />{{rp|p. 32}}) *Bolton Abbey, Yorkshire (12 August until the middle of September<ref name=":1" />{{rp|p. 32}}) *Chatsworth, Derbyshire (middle of September until early Spring<ref name=":1" />{{rp|p. 32}}) *Lismore Castle, County Waterford (early Spring until the middle of April<ref name=":1" />{{rp|p. 32}}) == Family == *Louisa (or Luise) Friederike Auguste Gräfin von Alten Montagu Cavendish (15 January 1832 – 15 November 1911)<ref name=":2" /><ref name=":0" /> *William Drogo Montagu, 7th Duke of Manchester (15 October 1823 – 22 March 1890)<ref name=":3" /><ref>{{Cite journal|date=2020-09-07|title=William Montagu, 7th Duke of Manchester|url=https://en.wikipedia.org/w/index.php?title=William_Montagu,_7th_Duke_of_Manchester&oldid=977197445|journal=Wikipedia|language=en}}</ref> #George Victor Drogo Montagu, 8th Duke of Manchester (17 June 1853 – 18 August 1892) #Mary Louise [Louisa?] Elizabeth Montagu Douglas-Hamilton Forster (27 December 1854 – 10 February 1934) #Louisa Augusta Beatrice Montagu Acheson (c. 1856 – 3 March 1944) #Charles William Augustus Montagu (23 November 1860 – 10 November 1939) #Alice Maude Olivia Montagu Stanley (15 August 1862 – 23 July 1957) *[[Social Victorians/People/Spencer Compton Cavendish|Spencer Compton Cavendish]], 8th Duke of Devonshire (23 July 1833 – 24 March 1908) == Notes and Questions == #As Duchess of Manchester Luise was not invited to the wedding between Bertie and Alix, Victoria's punishment for Luise's having gotten the Duke of Derby to promise her the position of Mistress of the Robes (and then exacting that promise).<ref>Leslie, Anita. ''The Marlborough House Set''. New York: Doubleday, 1973.</ref>{{rp|pp. 47–48}} #"As a young woman she was extremely beautiful; Princess Catherine Radziwill saw her at a reception given by the Empress of Germany and recalls on being introduced to her 'how she struck me as the loveliest creature I had ever set eyes upon. Indeed I have only met three women in my whole existence who could be compared to her.'"<ref name=":1" />{{rp|p. 21}} == Footnotes == {{reflist}} twb3cv70j19m4h027n6d8rtjw23klka 0 267591 2412499 2411864 2022-08-07T09:36:27Z D.H 52339 /* Translation in the hyperbolic plane */ wikitext text/x-wiki {{../Lorentz transformation (header)}} ==Lorentz transformation via hyperbolic functions== ===Translation in the hyperbolic plane=== The case of a Lorentz transformation without spatial rotation is called a [[w:Lorentz boost]]. The simplest case can be given, for instance, by setting ''n=1'' in the [[../Lorentz transformation (general)#math_1a|E:most general Lorentz transformation '''(1a)''']]: {{NumBlk|:|<math>\begin{matrix}-x_{0}^{2}+x_{1}^{2}=-x_{0}^{\prime2}+x_{1}^{\prime2}\\ \hline \begin{align}x_{0}^{\prime} & =x_{0}g_{00}+x_{1}g_{01}\\ x_{1}^{\prime} & =x_{0}g_{10}+x_{1}g_{11}\\ \\ x_{0} & =x_{0}^{\prime}g_{00}-x_{1}^{\prime}g_{10}\\ x_{1} & =-x_{0}^{\prime}g_{01}+x_{1}^{\prime}g_{11} \end{align} \left|\begin{align}g_{01}^{2}-g_{00}^{2} & =-1\\ g_{11}^{2}-g_{10}^{2} & =1\\ g_{01}g_{11}-g_{00}g_{10} & =0\\ g_{10}^{2}-g_{00}^{2} & =-1\\ g_{11}^{2}-g_{01}^{2} & =1\\ g_{10}g_{11}-g_{00}g_{01} & =0 \end{align} \rightarrow\begin{align}g_{00}^{2} & =g_{11}^{2}\\ g_{01}^{2} & =g_{10}^{2} \end{align} \right. \end{matrix}</math> or in matrix notation <math>\left.\begin{align}\mathbf{x}' & =\begin{bmatrix}g_{00} & g_{01}\\ g_{10} & g_{11} \end{bmatrix}\cdot\mathbf{x}\\ \mathbf{x} & =\begin{bmatrix}g_{00} & -g_{10}\\ -g_{01} & g_{11} \end{bmatrix}\cdot\mathbf{x}' \end{align} \quad\right|\quad\det\begin{bmatrix}g_{00} & g_{01}\\ g_{10} & g_{11} \end{bmatrix}=1</math>|{{equationRef|3a}}}} which resembles precisely the relations of [[w:hyperbolic function]]s in terms of [[w:hyperbolic angle]] <math>\eta</math>. Thus a Lorentz boost or [[w:hyperbolic rotation]] (being the same as a rotation around an imaginary angle <math>i\eta=\phi</math> in [[../Lorentz transformation (imaginary)#math_2b|E:'''(2b)''']] or a [[w:Translation (geometry)|translation]] in the hyperbolic plane in terms of the hyperboloid model) is given by {{NumBlk|:|<math>\begin{matrix}-x_{0}^{2}+x_{1}^{2}+x_{2}^{2}=-x_{0}^{\prime2}+x_{1}^{\prime2}+x_{2}^{\prime2}\\ \hline g_{00}=g_{11}=\cosh\eta,\ g_{01}=g_{10}=-\sinh\eta\\ \hline \left.\begin{align} & \quad\quad(A) & & \quad\quad(B) & & \quad\quad(C)\\ x_{0}^{\prime} & =x_{0}\cosh\eta-x_{1}\sinh\eta & & =\frac{x_{0}-x_{1}\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & & =\frac{x_{0}-x_{1}v}{\sqrt{1-v^{2}}}\\ x_{1}^{\prime} & =-x_{0}\sinh\eta+x_{1}\cosh\eta & & =\frac{x_{1}-x_{0}\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & & =\frac{x_{1}-x_{0}v}{\sqrt{1-v^{2}}}\\ x_{2}^{\prime} & =x_{2} & & =x_{2} & & =x_{2}\\ \\ x_{0} & =x_{0}^{\prime}\cosh\eta+x_{1}^{\prime}\sinh\eta & & =\frac{x_{0}^{\prime}-x_{1}^{\prime}\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & & =\frac{x_{0}^{\prime}-x_{1}^{\prime}v}{\sqrt{1-v^{2}}}\\ x_{1} & =x_{0}^{\prime}\sinh\eta+x_{1}^{\prime}\cosh\eta & & =\frac{x_{1}^{\prime}-x_{0}^{\prime}\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & & =\frac{x_{1}^{\prime}-x_{0}^{\prime}v}{\sqrt{1-v^{2}}}\\ x_{2} & =x_{2}^{\prime} & & =x_{2}^{\prime} & & =x_{2}^{\prime} \end{align} \right|{\scriptstyle \begin{align}\sinh^{2}\eta-\cosh^{2}\eta & =-1 & (a)\\ \cosh^{2}\eta-\sinh^{2}\eta & =1 & (b)\\ \frac{\sinh\eta}{\cosh\eta} & =\tanh\eta=v & (c)\\ \frac{1}{\sqrt{1-\tanh^{2}\eta}} & =\cosh\eta & (d)\\ \frac{\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & =\sinh\eta & (e)\\ \frac{\tanh q\pm\tanh\eta}{1\pm\tanh q\tanh\eta} & =\tanh\left(q\pm\eta\right) & (f) \end{align} } \end{matrix}</math> or in matrix notation <math>\left.\begin{align}\mathbf{x}' & =\begin{bmatrix}\cosh\eta & -\sinh\eta\\ -\sinh\eta & \cosh\eta \end{bmatrix}\cdot\mathbf{x}\\ \mathbf{x} & =\begin{bmatrix}\cosh\eta & \sinh\eta\\ \sinh\eta & \cosh\eta \end{bmatrix}\cdot\mathbf{x}' \end{align} \quad\right|\quad\det\begin{bmatrix}\cosh\eta & -\sinh\eta\\ -\sinh\eta & \cosh\eta \end{bmatrix}=1</math>|{{equationRef|3b}}}} Hyperbolic identities (a,b) on the right of ({{equationNote|3b}}) were given by [[#Riccati|Riccati (1757)]], all identities (a,b,c,d,e,f) by [[#Lambert|Lambert (1768–1770)]]. Lorentz transformations ({{equationNote|3b}}-A) were given by [[#Laisant|Laisant (1874)]], [[#Cox|Cox (1882)]], [[#Lindemann|Lindemann (1890/91)]], [[#Gerard|Gérard (1892)]], [[#Killing2|Killing (1893, 1897/98)]], [[#Whitehead|Whitehead (1897/98)]], [[#Woods2|Woods (1903/05)]], [[#Elliott|Elliott (1903)]] and [[#Liebmann|Liebmann (1904/05)]] in terms of Weierstrass coordinates of the [[w:hyperboloid model]], while transformations similar to ({{equationNote|3b}}-C) have been used by [[#Lipschitz1|Lipschitz (1885/86)]]. Rapidity can be composed of arbitrary many rapidities <math>\eta_{1},\eta_{2}\dots</math> as per the [[w:Hyperbolic functions#Sums of arguments|w:angle sum laws of hyperbolic sines and cosines]], so that one hyperbolic rotation can represent the sum of many other hyperbolic rotations, analogous to the relation between [[w:List of trigonometric identities#Angle sum and difference identities|w:angle sum laws of circular trigonometry]] and spatial rotations. Alternatively, the hyperbolic angle sum laws ''themselves'' can be interpreted as Lorentz boosts, as demonstrated by using the parameterization of the [[w:unit hyperbola]]: {{NumBlk|:|<math>\begin{matrix}-x_{0}^{2}+x_{1}^{2}=-x_{0}^{\prime2}+x_{1}^{\prime2}=1\\ \hline \left[\eta=\eta_{2}-\eta_{1}\right]\\ {\scriptstyle \begin{align}x_{0}^{\prime} & =\sinh\eta_{1} & & =\sinh\left(\eta_{2}-\eta\right) & & =\sinh\eta_{2}\cosh\eta-\cosh\eta_{2}\sinh\eta & & =x_{0}\cosh\eta-x_{1}\sinh\eta\\ x_{1}^{\prime} & =\cosh\eta_{1} & & =\cosh\left(\eta_{2}-\eta\right) & & =-\sinh\eta_{2}\sinh\eta+\cosh\eta_{2}\cosh\eta & & =-x_{0}\sinh\eta+x_{1}\cosh\eta\\ \\ x_{0} & =\sinh\eta_{2} & & =\sinh\left(\eta_{1}+\eta\right) & & =\sinh\eta_{1}\cosh\eta+\cosh\eta_{1}\sinh\eta & & =x_{0}^{\prime}\cosh\eta+x_{1}^{\prime}\sinh\eta\\ x_{1} & =\cosh\eta_{2} & & =\cosh\left(\eta_{1}+\eta\right) & & =\sinh\eta_{1}\sinh\eta+\cosh\eta_{1}\cosh\eta & & =x_{0}^{\prime}\sinh\eta+x_{1}^{\prime}\cosh\eta \end{align} } \end{matrix}</math> or in matrix notation <math>{\scriptstyle \begin{align} & \begin{bmatrix}x_{0}^{\prime}\\ x_{1}^{\prime} \end{bmatrix}=\begin{bmatrix}\sinh\eta_{1}\\ \cosh\eta_{1} \end{bmatrix}=\begin{bmatrix}\sinh\left(\eta_{2}-\eta\right)\\ \cosh\left(\eta_{2}-\eta\right) \end{bmatrix}=\begin{bmatrix}\cosh\eta & -\sinh\eta\\ -\sinh\eta & \cosh\eta \end{bmatrix}\cdot\begin{bmatrix}\sinh\eta_{2}\\ \cosh\eta_{2} \end{bmatrix} & & =\begin{bmatrix}\cosh\eta & -\sinh\eta\\ -\sinh\eta & \cosh\eta \end{bmatrix}\cdot\begin{bmatrix}x_{0}\\ x_{1} \end{bmatrix}\\ & \begin{bmatrix}x_{0}\\ x_{1} \end{bmatrix}=\begin{bmatrix}\sinh\eta_{2}\\ \cosh\eta_{2} \end{bmatrix}=\begin{bmatrix}\sinh\left(\eta_{1}+\eta\right)\\ \cosh\left(\eta_{1}+\eta\right) \end{bmatrix}=\begin{bmatrix}\cosh\eta & \sinh\eta\\ \sinh\eta & \cosh\eta \end{bmatrix}\cdot\begin{bmatrix}\sinh\eta_{1}\\ \cosh\eta_{1} \end{bmatrix} & & =\begin{bmatrix}\cosh\eta & \sinh\eta\\ \sinh\eta & \cosh\eta \end{bmatrix}\cdot\begin{bmatrix}x_{0}^{\prime}\\ x_{1}^{\prime} \end{bmatrix} \end{align} }</math>|{{equationRef|3c}}}} Hyperbolic angle sum laws equivalent to Lorentz boost ({{equationNote|3c}}) were given by [[#Riccati|Riccati (1757)]] and [[#Lambert|Lambert (1768–1770)]], while the matrix representation was given by [[#Glaisher|Glaisher (1878)]] and [[#Gunther2|Günther (1880/81)]]. In special relativity, hyperbolic functions were used by [[#Frank|Frank (1909)]] and [[#Varicak|Varićak (1910)]]. Finally, because of <math>\cosh\eta+\sinh\eta=e^{\eta}</math>, Lorentz boost ({{equationNote|3b}}) assumes a simple form by using [[w:squeeze mapping]]s in analogy to Euler's formula in [[../Lorentz transformation (imaginary)#math_2c|E:'''(2c)''']]:<ref name=rind>Rindler (1969), p. 45</ref> {{NumBlk|:|<math>\begin{matrix}-x_{0}^{2}+x_{1}^{2}+x_{2}^{2}=-x_{0}^{\prime2}+x_{1}^{\prime2}+x_{2}^{\prime2}\\ \hline \begin{matrix}\begin{aligned}x_{1}^{\prime}-x_{0}^{\prime} & =k\left(x_{1}-x_{0}\right)\\ x_{1}^{\prime}+x_{0}^{\prime} & =\frac{1}{k}\left(x_{1}+x_{0}\right)\\ x_{2}^{\prime} & =x_{2} \end{aligned} & \Rightarrow & \begin{aligned}x_{1}^{\prime}-x_{0}^{\prime} & =e^{\eta}\left(x_{1}-x_{0}\right)\\ x_{1}^{\prime}+x_{0}^{\prime} & =e^{-\eta}\left(x_{1}+x_{0}\right)\\ x_{2}^{\prime} & =x_{2} \end{aligned} \end{matrix}\\ \hline k=e^{\eta}=\cosh\eta+\sinh\eta=\sqrt{\frac{1+\tanh\eta}{1-\tanh\eta}}=\sqrt{\frac{1+v}{1-v}} \end{matrix}</math>|{{equationRef|3d}}}} Lorentz transformations ({{equationNote|3d}}) for arbitrary ''k'' were given by many authors (see [[../Lorentz transformation (squeeze)|E:Lorentz transformations via squeeze mappings]]), while the exponential form was explicitly used by [[#Lindemann|Lindemann (1890/91)]], [[#Elliott|Elliott (1903)]], [[#Herglotz1|Herglotz (1909)]]. ===Hyperbolic law of cosines=== In line with equation [[../Lorentz transformation (general)#math_1b|E:'''(1b)''']] one can use coordinates <math>[u_{1},\ u_{2}]=\left[\tfrac{x_{1}}{x_{0}},\ \tfrac{x_{2}}{x_{0}}\right]</math> inside the [[w:unit circle]] <math>u_{1}^{2}+u_{2}^{2}=1</math>, thus the corresponding Lorentz transformations ({{equationNote|3b}}) obtain the form: {{NumBlk|:|<math>\begin{align} & \quad\quad(A) & & \quad\quad(B) & & \quad\quad(C)\\ u_{1}^{\prime} & =\frac{-\sinh\eta+u_{1}\cosh\eta}{\cosh\eta-u_{1}\sinh\eta} & & =\frac{u_{1}-\tanh\eta}{1-u_{1}\tanh\eta} & & =\frac{u_{1}-v}{1-u_{1}v}\\ u_{2}^{\prime} & =\frac{u_{2}}{\cosh\eta-u_{1}\sinh\eta} & & =\frac{u_{2}\sqrt{1-\tanh^{2}\eta}}{1-u_{1}\tanh\eta} & & =\frac{u_{2}\sqrt{1-v^{2}}}{1-u_{1}v}\\ \\ u_{1} & =\frac{\sinh\eta+u_{1}^{\prime}\cosh\eta}{\cosh\eta+u_{1}^{\prime}\sinh\eta} & & =\frac{u_{1}^{\prime}+\tanh\eta}{1+u_{1}^{\prime}\tanh\eta} & & =\frac{u_{1}^{\prime}+v}{1+u_{1}^{\prime}v}\\ u_{2} & =\frac{u_{2}^{\prime}}{\cosh\eta+u_{1}^{\prime}\sinh\eta} & & =\frac{u_{2}^{\prime}\sqrt{1-\tanh^{2}\eta}}{1+u_{1}^{\prime}\tanh\eta} & & =\frac{u_{2}^{\prime}\sqrt{1-v^{2}}}{1+u_{1}^{\prime}v} \end{align} </math>|{{equationRef|3e}}}} Transformations (A) were given by [[#Escherich|Escherich (1874)]] and [[#Killing2|Killing (1898)]], and transformations (C) by [[#Beltrami|Beltrami (1868)]] and [[#Schur|Schur (1885/86, 1900/02)]] in terms of [[w:Beltrami–Klein model|Beltrami coordinates]]<ref>Rosenfeld (1988), p. 231</ref> of hyperbolic geometry. By using the scalar product of <math>\left[u_{1},u_{2}\right]</math>, the resulting Lorentz transformation can be seen as equivalent to the [[w:hyperbolic law of cosines]]:<ref name=pau>Pauli (1921), p. 561</ref><ref group=R name=var>Varićak (1912), p. 108</ref><ref name=barr>Barrett (2006), chapter 4, section 2</ref> {{NumBlk|:|<math>\begin{matrix} & \begin{matrix}u^{2}=u_{1}^{2}+u_{2}^{2}\\ u'^{2}=u_{1}^{\prime2}+u_{2}^{\prime2} \end{matrix}\left|\begin{matrix}u_{1}=u\cos\alpha\\ u_{2}=u\sin\alpha\\ \\ u_{1}^{\prime}=u'\cos\alpha'\\ u_{2}^{\prime}=u'\sin\alpha' \end{matrix}\right|\begin{align}u\cos\alpha & =\frac{u'\cos\alpha'+v}{1+vu'\cos\alpha'}, & u'\cos\alpha' & =\frac{u\cos\alpha-v}{1-vu\cos\alpha}\\ u\sin\alpha & =\frac{u'\sin\alpha'\sqrt{1-v^{2}}}{1+vu'\cos\alpha'}, & u'\sin\alpha' & =\frac{u\sin\alpha\sqrt{1-v^{2}}}{1-vu\cos\alpha}\\ \tan\alpha & =\frac{u'\sin\alpha'\sqrt{1-v^{2}}}{u'\cos\alpha'+v}, & \tan\alpha' & =\frac{u\sin\alpha\sqrt{1-v^{2}}}{u\cos\alpha-v} \end{align} \\ \Rightarrow & u=\frac{\sqrt{v^{2}+u^{\prime2}+2vu'\cos\alpha'-\left(vu'\sin\alpha'\right){}^{2}}}{1+vu'\cos\alpha'},\quad u'=\frac{\sqrt{-v^{2}-u^{2}+2vu\cos\alpha+\left(vu\sin\alpha\right){}^{2}}}{1-vu\cos\alpha}\\ \Rightarrow & \frac{1}{\sqrt{1-u^{\prime2}}}=\frac{1}{\sqrt{1-v^{2}}}\frac{1}{\sqrt{1-u^{2}}}-\frac{v}{\sqrt{1-v^{2}}}\frac{u}{\sqrt{1-u^{2}}}\cos\alpha & (b)\\ \Rightarrow & \frac{1}{\sqrt{1-\tanh^{2}\xi}}=\frac{1}{\sqrt{1-\tanh^{2}\eta}}\frac{1}{\sqrt{1-\tanh^{2}\zeta}}-\frac{\tanh\eta}{\sqrt{1-\tanh^{2}\eta}}\frac{\tanh\zeta}{\sqrt{1-\tanh^{2}\zeta}}\cos\alpha\\ \Rightarrow & \cosh\xi=\cosh\eta\cosh\zeta-\sinh\eta\sinh\zeta\cos\alpha & (a) \end{matrix}</math>|{{equationRef|3f}}}} The hyperbolic law of cosines (a) was given by [[#Taurinus|Taurinus (1826) and Lobachevsky (1829/30)]] and others, while variant (b) was given by [[#Schur|Schur (1900/02)]]. By further setting ''u=u′'' it follows: {{NumBlk|:|<math>\begin{matrix}\cos\alpha=\frac{\cos\alpha'+v}{1+v\cos\alpha'},\ \sin\alpha=\frac{\sin\alpha'\sqrt{1-v^{2}}}{1+v\cos\alpha'},\ \tan\alpha=\frac{\sin\alpha'\sqrt{1-v^{2}}}{\cos\alpha'+v},\ \tan\frac{\alpha}{2}=\sqrt{\frac{1-v}{1+v}}\tan\frac{\alpha'}{2}\\ \cos\alpha'=\frac{\cos\alpha-v}{1-v\cos\alpha},\ \sin\alpha'=\frac{\sin\alpha\sqrt{1-v^{2}}}{1-v\cos\alpha},\ \tan\alpha'=\frac{\sin\alpha\sqrt{1-v^{2}}}{\cos\alpha-v},\ \tan\frac{\alpha'}{2}=\sqrt{\frac{1+v}{1-v}}\tan\frac{\alpha}{2} \end{matrix}</math>|{{equationRef|3g}}}} Formulas (3b) resemble the equations of an [[w:ellipse]] of [[w:Orbital eccentricity|eccentricity]] ''v/c'', [[w:eccentric anomaly]] α' and [[w:true anomaly]] α, first geometrically formulated by [[#Euler|Kepler (1609)]] and explicitly written down by [[#Euler|Euler (1735, 1748), Lagrange (1770)]] and many others in relation to planetary motions. They were also used by [[../Lorentz transformation (conformal)#Darboux|E:Darboux (1873)]] as a sphere transformation. In special relativity, these formulas describes the aberration of light, see [[../Lorentz transformation (velocity)#Velocity addition and aberration|E:velocity addition and aberration]]. ==Historical notation== ==={{anchor|Euler}} Euler (1735) – True and eccentric anomaly=== [[w:Johannes Kepler]] (1609) geometrically formulated [[w:Kepler's equation]] and the relations between the [[w:mean anomaly]], [[w:true anomaly]], and [[w:eccentric anomaly]].<ref group=M>Kepler (1609), chapter 60. The editors of Kepler's collected papers remark (p. 482), that Kepler's relations correspond to <math>{\scriptstyle \alpha=\beta+e\sin\beta}</math> and <math>{\scriptstyle \cos\nu=\frac{e+\cos\beta}{1+e\cos\beta}}</math> and <math>{\scriptstyle \cos\beta=\frac{\cos\nu-e}{1-e\cos\nu}}</math></ref><ref>Volk (1976), p. 366</ref> The relation between the true anomaly ''z'' and the eccentric anomaly ''P'' was algebraically expressed by [[w:Leonhard Euler]] (1735/40) as follows:<ref group=M>Euler (1735/40), § 19</ref> :<math>\cos z=\frac{\cos P+v}{1+v\cos P},\ \cos P=\frac{\cos z-v}{1-v\cos z},\ \int P=\frac{\int z\sqrt{1-v^{2}}}{1-v\cos z}</math> and in 1748:<ref group=M>Euler (1748a), section VIII</ref> :<math>\cos z=\frac{n+\cos y}{1+n\cos y},\ \sin z=\frac{\sin y\sqrt{1-n^{2}}}{1+n\cos y},\ \tan z=\frac{\sin y\sqrt{1-n^{2}}}{n+\cos y}</math> while [[w:Joseph-Louis Lagrange]] (1770/71) expressed them as follows<ref group=M>Lagrange (1770/71), section I</ref> :<math>\sin u=\frac{m\sin x}{1+n\cos x},\ \cos u=\frac{n+\cos x}{1+n\cos x},\ \operatorname{tang}\frac{1}{2}u=\frac{m}{1+n}\operatorname{tang}\frac{1}{2}x,\ \left(m^{2}=1-n^{2}\right)</math> <p style="background-color:Beige;border:1px solid black"> These relations resemble formulas ({{equationNote|3g}}), while ({{equationNote|3f}}) follows by setting <math>[\cos z,\sin z]=\left[u_{x},u_{y}\right]</math> in Euler's formulas or <math>[\cos u,\sin u]=\left[u_{x},u_{y}\right]</math> in Lagrange's formulas.</p> ==={{anchor|Riccati}} Riccati (1757) – hyperbolic addition=== [[w:Vincenzo Riccati]] introduced hyperbolic functions in 1757,<ref group=M>Riccati (1757), p. 71</ref><ref group=M>Günther (1880/81), pp. 7–13</ref> in particular he formulated the angle sum laws for hyperbolic sine and cosine: :<math>\begin{matrix}\mathrm{Ch}(\varphi+\pi)=\frac{\mathrm{Ch}\varphi\mathrm{Ch}\pi+\mathrm{Sh}\varphi\mathrm{Sh}\pi}{r}\\ \mathrm{Sh}(\varphi+\pi)=\frac{\mathrm{Ch}\varphi\mathrm{Sh}\pi+\mathrm{Ch}\pi\mathrm{Sh}\varphi}{r}\\ \left[\mathrm{Ch}^{2}-\mathrm{Sh}^{2}=rr\right] \end{matrix}</math> He furthermore showed that <math>\mathrm{Ch}(\varphi-\pi)</math> and <math>\mathrm{Sh}(\varphi-\pi)</math> follow by setting <math>\mathrm{Ch}(\pi)\Rightarrow\mathrm{Ch}(-\pi)</math> and <math>\mathrm{Sh}(\pi)\Rightarrow\mathrm{Sh}(-\pi)</math> in the above formulas. <p style="background-color:Beige;border:1px solid black">The angle sum laws for hyperbolic sine and cosine can be interpreted as hyperbolic rotations of points on a hyperbola, as in Lorentz boost ({{equationNote|3c}}). (In modern publications, Riccati's additional factor ''r'' is set to unity.)</p> ==={{anchor|Lambert}} Lambert (1768–1770) – hyperbolic addition=== While [[#Riccati|Riccati (1757)]] discussed the hyperbolic sine and cosine, [[w:Johann Heinrich Lambert]] (read 1767, published 1768) introduced the expression ''tang φ'' or abbreviated ''tφ'' as the [[w:tangens hyperbolicus]] <math>{\scriptstyle \frac{e^{u}-e^{-u}}{e^{u}+e^{-u}}}</math> of a variable ''u'', or in modern notation ''tφ=tanh(u)'':<ref group=M>Lambert (1761/68), pp. 309–318</ref><ref>Barnett (2004), pp. 22–23</ref> :<math>\left.\begin{align}\xi\xi-1 & =\eta\eta & (a)\\ 1+\eta\eta & =\xi\xi & (b)\\ \frac{\eta}{\xi} & =tang\ \phi=t\phi & (c)\\ \xi & =\frac{1}{\sqrt{1-t\phi^{2}}} & (d)\\ \eta & =\frac{t\phi}{\sqrt{1-t\phi^{2}}} & (e)\\ t\phi'' & =\frac{t\phi+t\phi'}{1+t\phi\cdot t\phi'} & (f)\\ t\phi' & =\frac{t\phi''-t\phi}{1-t\phi\cdot t\phi''} & (g) \end{align} \right|\begin{align}2u & =\log\frac{1+t\phi}{1-t\phi}\\ \xi & =\frac{e^{u}+e^{-u}}{2}\\ \eta & =\frac{e^{u}-e^{-u}}{2}\\ t\phi & =\frac{e^{u}-e^{-u}}{e^{u}+e^{-u}}\\ e^{u} & =\xi+\eta\\ e^{-u} & =\xi-\eta \end{align}</math> In (1770) he rewrote the addition law for the hyperbolic tangens (f) or (g) as:<ref group=M>Lambert (1770), p. 335</ref> :<math>\begin{align}t(y+z) & =(ty+tz):(1+ty\cdot tz) & (f)\\ t(y-z) & =(ty-tz):(1-ty\cdot tz) & (g) \end{align} </math> <p style="background-color:Beige;border:1px solid black">The hyperbolic relations (a,b,c,d,e,f) are equivalent to the hyperbolic relations on the right of ({{equationNote|3b}}). Relations (f,g) can also be found in ({{equationNote|3e}}). By setting ''tφ=v/c'', formula (c) becomes the relative velocity between two frames, (d) the [[w:Lorentz factor]], (e) the [[w:proper velocity]], (f) or (g) becomes the Lorentz transformation of velocity (or relativistic [[w:velocity addition formula]]) for collinear velocities in [[../Lorentz transformation (velocity)#math_4a|E:'''(4a)''']] and [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']].</p> Lambert also formulated the addition laws for the hyperbolic cosine and sine (Lambert's "cos" and "sin" actually mean "cosh" and "sinh"): :<math>\begin{align}\sin(y+z) & =\sin y\cos z+\cos y\sin z\\ \sin(y-z) & =\sin y\cos z-\cos y\sin z\\ \cos(y+z) & =\cos y\cos z+\sin y\sin z\\ \cos(y-z) & =\cos y\cos z-\sin y\sin z \end{align} </math> <p style="background-color:Beige;border:1px solid black">The angle sum laws for hyperbolic sine and cosine can be interpreted as hyperbolic rotations of points on a hyperbola, as in Lorentz boost ({{equationNote|3c}}).</p> ==={{Anchor|Taurinus}} Taurinus (1826) – Hyperbolic law of cosines=== After the addition theorem for the tangens hyperbolicus was given by [[#Lambert|Lambert (1768)]], [[w:hyperbolic geometry]] was used by [[w:Franz Taurinus]] (1826), and later by [[w:Nikolai Lobachevsky]] (1829/30) and others, to formulate the [[w:hyperbolic law of cosines]]:<ref group=M>Taurinus (1826), p. 66; see also p. 272 in the translation by Engel and Stäckel (1899)</ref><ref>Bonola (1912), p. 79</ref><ref>Gray (1979), p. 242</ref> :<math>A=\operatorname{arccos}\frac{\cos\left(\alpha\sqrt{-1}\right)-\cos\left(\beta\sqrt{-1}\right)\cos\left(\gamma\sqrt{-1}\right)}{\sin\left(\beta\sqrt{-1}\right)\sin\left(\gamma\sqrt{-1}\right)}</math> <p style="background-color:Beige;border:1px solid black">When solved for <math>\cos\left(\alpha\sqrt{-1}\right)</math> it corresponds to the Lorentz transformation in Beltrami coordinates ({{equationNote|3f}}), and by defining the rapidities <math>{\scriptstyle \left(\left[\frac{U}{c},\ \frac{v}{c},\ \frac{u}{c}\right]=\left[\tanh\alpha,\ \tanh\beta,\ \tanh\gamma\right]\right)}</math> it corresponds to the relativistic velocity addition formula [[../Lorentz transformation (velocity)#math_4e|E:'''(4e)''']].</p> ==={{anchor|Beltrami}} Beltrami (1868) – Beltrami coordinates=== [[w:Eugenio Beltrami]] (1868a) introduced coordinates of the [[w:Beltrami–Klein model]] of hyperbolic geometry, and formulated the corresponding transformations in terms of homographies:<ref group=M>Beltrami (1868a), pp. 287-288; Note I; Note II</ref> :<math>\begin{matrix}ds^{2}=R^{2}\frac{\left(a^{2}+v^{2}\right)du^{2}-2uv\,du\,dv+\left(a^{2}+v^{2}\right)dv^{2}}{\left(a^{2}+u^{2}+v^{2}\right)^{2}}\\ u^{2}+v^{2}=a^{2}\\ \hline u''=\frac{aa_{0}\left(u'-r_{0}\right)}{a^{2}-r_{0}u'},\ v''=\frac{a_{0}w_{0}v'}{a^{2}-r_{0}u'},\\ \left(r_{0}=\sqrt{u_{0}^{2}+v_{0}^{2}},\ w_{0}=\sqrt{a^{2}-r_{0}^{2}}\right)\\ \hline ds^{2}=R^{2}\frac{\left(a^{2}-v^{2}\right)du^{2}+2uv\,du\,dv+\left(a^{2}-v^{2}\right)dv^{2}}{\left(a^{2}-u^{2}-v^{2}\right)^{2}}\\ (R=R\sqrt{-1},\ a=a\sqrt{-1}) \end{matrix}</math> (where the disk radius ''a'' and the [[w:radius of curvature]] ''R'' are real in spherical geometry, in hyperbolic geometry they are imaginary), and for arbitrary dimensions in (1868b)<ref group=M>Beltrami (1868b), pp. 232, 240–241, 253–254</ref> :<math>\begin{matrix}ds=R\frac{\sqrt{dx^{2}+dx_{1}^{2}+dx_{2}^{2}+\cdots+dx_{n}^{2}}}{x}\\ x^{2}+x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=a^{2}\\ \hline y_{1}=\frac{ab\left(x_{1}-a_{1}\right)}{a^{2}-a_{1}x_{1}}\ \text{or}\ x_{1}=\frac{a\left(ay_{1}+a_{1}b\right)}{ab+a_{1}y_{1}},\ x_{r}=\pm\frac{ay_{r}\sqrt{a^{2}-a_{1}^{2}}}{ab+a_{1}y_{1}}\ (r=2,3,\dots,n)\\ \hline ds=R\frac{\sqrt{dx_{1}^{2}+dx_{2}^{2}+\cdots+dx_{n}^{2}-dx^{2}}}{x}\\ x^{2}=a^{2}+x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}\\ \left(R=R\sqrt{-1},\ x=x\sqrt{-1},\ a=a\sqrt{-1}\right) \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">Setting ''a=a₀'' Beltrami's (1868a) formulas become formulas ({{equationNote|3e}}), or in his (1868b) formulas one sets ''a=b'' for arbitrary dimensions.</p> === {{anchor|Laisant2}} Laisant (1874) – Equipollences=== In his French translation of [[w:Giusto Bellavitis]]' principal work on [[w:Equipollence (geometry)|w:equipollences]], [[w:Charles-Ange Laisant]] (1874) added a chapter related to hyperbolas. The equipollence OM and its tangent MT of a hyperbola is defined by Laisant as<ref group=M>Laisant (1874b), pp. 134–135</ref> :(1) <math>\begin{matrix} & \mathrm{OM}\bumpeq x\mathrm{OA}+y\mathrm{OB}\\ & \mathrm{MT}\bumpeq y\mathrm{OA}+x\mathrm{OB}\\ & \left[x^{2}-y^{2}=1;\ x=\cosh t,\ y=\sinh t\right]\\ \Rightarrow & \mathrm{OM}\bumpeq\cosh t\cdot\mathrm{OA}+\sinh t\cdot\mathrm{OB} \end{matrix}</math> Here, OA and OB are [[w:Conjugate diameters|conjugate semi-diameters]] of a hyperbola with OB being imaginary, both of which he related to two other conjugated semi-diameters OC and OD by the following transformation: :<math>\begin{matrix}\begin{align}\mathrm{OC} & \bumpeq c\mathrm{OA}+d\mathrm{OB} & \qquad & & \mathrm{OA} & \bumpeq c\mathrm{OC}-d\mathrm{OD}\\ \mathrm{OD} & \bumpeq d\mathrm{OA}+c\mathrm{OB} & & & \mathrm{OB} & \bumpeq-d\mathrm{OC}+c\mathrm{OD} \end{align} \\ \left[c^{2}-d^{2}=1\right] \end{matrix}</math> producing the invariant relation :<math>(\mathrm{OC})^{2}-(\mathrm{OD})^{2}\bumpeq(\mathrm{OA})^{2}-(\mathrm{OB})^{2}</math>. Substituting into (1), he showed that OM retains its form :<math>\begin{matrix}\mathrm{OM}\bumpeq(cx-dy)\mathrm{OC}+(cy-dx)\mathrm{OD}\\ \left[(cx-dy)^{2}-(cy-dx)^{2}=1\right] \end{matrix}</math> He also defined velocity and acceleration by differentiation of (1). <p style="background-color:Beige;border:1px solid black">These relations are equivalent to several Lorentz boosts or hyperbolic rotations producing the invariant Lorentz interval in line with ({{equationNote|3b}}).</p> ==={{anchor|Escherich}} Escherich (1874) – Beltrami coordinates=== [[w:Gustav von Escherich]] (1874) discussed the plane of constant negative curvature<ref>Sommerville (1911), p. 297</ref> based on the [[w:Beltrami–Klein model]] of hyperbolic geometry by [[#Beltrami|Beltrami (1868)]]. Similar to [[w:Christoph Gudermann]] (1830)<ref name=guder group=M>Gudermann (1830), §1–3, §18–19</ref> who introduced axial coordinates ''x''=tan(a) and ''y''=tan(b) in sphere geometry in order to perform coordinate transformations in the case of rotation and translation, Escherich used hyperbolic functions ''x''=tanh(a/k) and ''y''=tanh(b/k)<ref group=M>Escherich (1874), p. 508</ref> in order to give the corresponding coordinate transformations for the hyperbolic plane, which for the case of translation have the form:<ref group=M name=escher>Escherich (1874), p. 510</ref> :<math>x=\frac{\sinh\frac{a}{k}+x'\cosh\frac{a}{k}}{\cosh\frac{a}{k}+x'\sinh\frac{a}{k}}</math> and <math>y=\frac{y'}{\cosh\frac{a}{k}+x'\sinh\frac{a}{k}}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz transformation ({{equationNote|3e}}), also equivalent to the relativistic velocity addition [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']] by setting <math>\tfrac{a}{k}=\operatorname{atanh}\tfrac{v}{c}</math> and multiplying ''[x,y,x′,y′]'' by 1/''c'', and equivalent to Lorentz boost ({{equationNote|3b}}) by setting <math>\scriptstyle (x,\ y,\ x',\ y')=\left(\frac{x_{1}}{x_{0}},\ \frac{x_{2}}{x_{0}},\ \frac{x_{1}^{\prime}}{x_{0}^{\prime}},\ \frac{x_{2}^{\prime}}{x_{0}^{\prime}}\right)</math>. This is the relation between the [[w:Beltrami–Klein model|Beltrami coordinates]] in terms of Gudermann-Escherich coordinates, and the Weierstrass coordinates of the [[w:hyperboloid model]] introduced by [[../Lorentz transformation (general)#Killing1|E:Killing (1878–1893)]], [[../Lorentz transformation (general)#Poincare|E:Poincaré (1881)]], and [[../Lorentz transformation (general)#Cox|E:Cox (1881)]]. Both coordinate systems were compared by Cox (1881).<ref group=M>Cox (1881), p. 186</ref></p> ==={{anchor|Glaisher}} Glaisher (1878) – hyperbolic addition=== It was shown by [[w:James Whitbread Lee Glaisher]] (1878) that the hyperbolic addition laws can be written as matrix multiplication<ref group=M>Glaisher (1878), p. 30</ref> :<math>\begin{matrix}\begin{vmatrix}\cosh x, & \sinh x\\ \sinh x, & \cosh x \end{vmatrix}=1,\ \begin{vmatrix}\cosh y, & \sinh y\\ \sinh y, & \cosh y \end{vmatrix}=1\\ \left[c_{1},c_{2},c_{3},c_{4}\right]=\left[\cosh x,\cosh y,\sinh x,\sinh y\right]\\ \Rightarrow\begin{vmatrix}c_{1}c_{2}+s_{1}s_{2}, & s_{1}c_{2}+c_{1}s_{2}\\ c_{1}s_{2}+s_{1}c_{2}, & s_{1}s_{2}+c_{1}c_{2} \end{vmatrix}=1\ \Rightarrow\begin{vmatrix}\cosh(x+y), & \sinh(x+y)\\ \sinh(x+y), & \cosh(x+y) \end{vmatrix}=1 \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3c}}).</p> ==={{anchor|Gunther1}} Günther (1880/81) – hyperbolic addition === Following [[#Glaisher|Glaisher (1878)]], [[w:Siegmund Günther]] (1880/81) formulated the hyperbolic addition laws in matrix form as<ref group=M>Günther (1880/81), p. 405</ref> :<math>\begin{matrix}\begin{vmatrix}\mathfrak{Cos}x, & \mathfrak{Sin}x\\ \mathfrak{Sin}x, & \mathfrak{Cos}x \end{vmatrix}\cdot\begin{vmatrix}\mathfrak{Cos}y, & \mathfrak{Sin}y\\ \mathfrak{Sin}y, & \mathfrak{Cos}y \end{vmatrix}\\ =\begin{vmatrix}\mathfrak{Cos}x\mathfrak{Cos}y+\mathfrak{Sin}x\mathfrak{Sin}y, & \mathfrak{Cos}x\mathfrak{Sin}y+\mathfrak{Sin}x\mathfrak{Cos}y\\ \mathfrak{Sin}x\mathfrak{Cos}y+\mathfrak{Cos}x\mathfrak{Sin}y, & \mathfrak{Sin}x\mathfrak{Sin}y+\mathfrak{Cos}x\mathfrak{Cos}y \end{vmatrix}\\ =\begin{vmatrix}\mathfrak{Cos}(x+y), & \mathfrak{Sin}(x+y)\\ \mathfrak{Sin}(x+y), & \mathfrak{Cos}(x+y) \end{vmatrix}=1 \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3c}}).</p> ==={{anchor|Lipschitz1}} Lipschitz (1885/86) === [[w:Rudolf Lipschitz]] (1885/86) formulated transformations leaving invariant the sum of squares <math>x_{1}^{2}+x_{2}^{2}\dots+x_{n}^{2}=y_{1}^{2}+y_{2}^{2}+\dots+y_{n}^{2}</math>, which he rewrote as <math>x_{1}^{2}-y_{1}^{2}+x_{2}^{2}-y_{2}^{2}+\dots+x_{n}^{2}-y_{n}^{2}=0</math>. This led to the problem of finding transformations leaving invariant the pairs <math>x_{a}^{2}-y_{a}^{2}</math> (''a''=1...n) for which he gave the following solution:<ref group=M>Lipschitz (1886), pp. 90–92</ref> :<math>\begin{matrix}x_{a}^{2}-y_{a}^{2}=\mathfrak{x}_{a}^{2}-\mathfrak{y}_{a}^{2}\\ \hline \begin{align}x_{a}-y_{a} & =\left(\mathfrak{x}_{a}-\mathfrak{y}_{a}\right)r_{a}\\ x_{a}+y_{a} & =\left(\mathfrak{x}_{a}+\mathfrak{y}_{a}\right)\frac{1}{r_{a}} \end{align} \quad(a)\\ \hline \begin{matrix}\begin{align}2\mathfrak{x}_{a} & =\left(r_{a}+\frac{1}{r_{a}}\right)x_{a}+\left(r_{a}-\frac{1}{r_{a}}\right)y_{a}\\ 2\mathfrak{y}_{a} & =\left(r_{a}-\frac{1}{r_{a}}\right)x_{a}+\left(r_{a}+\frac{1}{r_{a}}\right)y_{a} \end{align} \quad(b)\end{matrix}\\ \hline \left\{ \begin{matrix}r_{a}=\frac{\sqrt{s_{a}+1}}{\sqrt{s_{a}-1}}\\ s_{a}>1 \end{matrix}\right\}\Rightarrow\begin{align}\mathfrak{x}_{a} & =\frac{s_{a}x_{a}+y_{a}}{\sqrt{s_{a}-1}\sqrt{s_{a}+1}}\\ \mathfrak{y}_{a} & =\frac{x_{a}+s_{a}y_{a}}{\sqrt{s_{a}-1}\sqrt{s_{a}+1}} \end{align} \quad(c) \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">Equation (a) is identical to Lorentz boost ({{equationNote|3d}}), while (c) is similar, though not identical, to Lorentz boost ({{equationNote|3b}}-C). The difference stems from his definition<br><math>\qquad\left\{ \begin{matrix}r_{a}=\frac{\sqrt{s_{a}+1}}{\sqrt{s_{a}-1}}\\ s_{a}>1 \end{matrix}\right\}</math><br>whereas in accordance to expression <math>\sqrt{\tfrac{1+v}{1-v}}</math> in ({{equationNote|3d}}) he should have stated <br><math>\qquad\left\{ \begin{matrix}r_{a}=\frac{\sqrt{1+s_{a}}}{\sqrt{1-s_{a}}}\\ s_{a}<1 \end{matrix}\right\}</math>.<br>Using the latter choice, equations (c) would assume a form equivalent to ({{equationNote|3b}}):<br><math>\qquad\begin{align}\mathfrak{x}_{a} & =\frac{x_{a}+s_{a}y_{a}}{\sqrt{1-s_{a}}\sqrt{1+s_{a}}}\\ \mathfrak{y}_{a} & =\frac{s_{a}x_{a}+y_{a}}{\sqrt{1-s_{a}}\sqrt{1+s_{a}}}\end{align}</math></p> ==={{Anchor|Schur}} Schur (1885/86, 1900/02) – Beltrami coordinates=== [[w:Friedrich Schur]] (1885/86) discussed spaces of constant Riemann curvature, and by following [[#Beltrami|Beltrami (1868)]] he used the transformation<ref group=M>Schur (1885/86), p. 167</ref> :<math>x_{1}=R^{2}\frac{y_{1}+a_{1}}{R^{2}+a_{1}y_{1}},\ x_{2}=R\sqrt{R^{2}-a_{1}^{2}}\frac{y_{2}}{R^{2}+a_{1}y_{1}},\dots,\ x_{n}=R\sqrt{R^{2}-a_{1}^{2}}\frac{y_{n}}{R^{2}+a_{1}y_{1}}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz transformation ({{equationNote|3e}}) and therefore also equivalent to the relativistic velocity addition [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']] in arbitrary dimensions by setting ''R=c'' as the speed of light and ''a₁=v'' as relative velocity.</p> In (1900/02) he derived basic formulas of non-Eucliden geometry, including the case of translation for which he obtained the transformation similar to his previous one:<ref group=M>Schur (1900/02), p. 290; (1909), p. 83</ref> :<math>x'=\frac{x-a}{1-\mathfrak{k}ax},\quad y'=\frac{y\sqrt{1-\mathfrak{k}a^{2}}}{1-\mathfrak{k}ax}</math> where <math>\mathfrak{k}</math> can have values >0, <0 or ∞. <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz transformation ({{equationNote|3e}}) and therefore also equivalent to the relativistic velocity addition [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']] by setting ''a=v'' and <math>\mathfrak{k}=\tfrac{1}{c^{2}}</math>.</p> He also defined the triangle<ref group=M>Schur (1900/02), p. 291; (1909), p. 83</ref> :<math>\frac{1}{\sqrt{1-\mathfrak{k}c^{2}}}=\frac{1}{\sqrt{1-\mathfrak{k}a^{2}}}\cdot\frac{1}{\sqrt{1-\mathfrak{k}b^{2}}}-\frac{a}{\sqrt{1-\mathfrak{k}a^{2}}}\cdot\frac{b}{\sqrt{1-\mathfrak{k}b^{2}}}\cos\gamma</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to the hyperbolic law of cosines and the relativistic velocity addition ({{equationNote|3f}}, b) or [[../Lorentz transformation (velocity)#math_4e|E:'''(4e)''']] by setting <math>[\mathfrak{k},\ c,\ a,\ b]=\left[\tfrac{1}{c^{2}},\ \sqrt{u_{x}^{\prime2}+u_{y}^{\prime2}},\ v,\ \sqrt{u_{x}^{2}+u_{y}^{2}}\right]</math>.</p> ==={{anchor|Lindemann}} Lindemann (1890–91) – Weierstrass coordinates and Cayley absolute=== [[w:Ferdinand von Lindemann]] discussed hyperbolic geometry in terms of the [[w:Cayley–Klein metric]] in his (1890/91) edition of the lectures on geometry of [[w:Alfred Clebsch]]. Citing [[../Lorentz transformation (general)#Killing|E:Killing (1885)]] and [[../Lorentz transformation (general)#Poincare|Poincaré (1887)]] in relation to the hyperboloid model in terms of Weierstrass coordinates for the hyperbolic plane and space, he set<ref group=M>Lindemann & Clebsch (1890/91), pp. 477–478, 524</ref> :<math>\begin{matrix}\Omega_{xx}=x_{1}^{2}+x_{2}^{2}-4k^{2}x_{3}^{2}=-4k^{2}\ \text{and}\ ds^{2}=dx_{1}^{2}+dx_{2}^{2}-4k^{2}dx_{3}^{2}\\ \Omega_{xx}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-4k^{2}x_{4}^{2}=-4k^{2}\ \text{and}\ ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-4k^{2}dx_{4}^{2} \end{matrix}</math> and used the following transformation<ref group=M>Lindemann & Clebsch (1890/91), pp. 361–362</ref> :<math>\begin{matrix}X_{1}X_{4}+X_{2}X_{3}=0\\ X_{1}X_{4}+X_{2}X_{3}=\Xi_{1}\Xi_{4}+\Xi_{2}\Xi_{3}\\ \hline \begin{align}X_{1} & =\left(\lambda+\lambda_{1}\right)U_{4} & \Xi_{1} & =\left(\lambda-\lambda_{1}\right)U_{4} & X_{1} & =\frac{\lambda+\lambda_{1}}{\lambda-\lambda_{1}}\Xi_{1}\\ X_{2} & =\left(\lambda+\lambda_{3}\right)U_{4} & \Xi_{2} & =\left(\lambda-\lambda_{3}\right)U_{4} & X_{2} & =\frac{\lambda+\lambda_{3}}{\lambda-\lambda_{3}}\Xi_{2}\\ X_{3} & =\left(\lambda-\lambda_{3}\right)U_{2} & \Xi_{3} & =\left(\lambda+\lambda_{3}\right)U_{2} & X_{3} & =\frac{\lambda-\lambda_{3}}{\lambda+\lambda_{3}}\Xi_{3}\\ X_{4} & =\left(\lambda-\lambda_{1}\right)U_{1} & \Xi_{4} & =\left(\lambda+\lambda_{1}\right)U_{1} & X_{4} & =\frac{\lambda-\lambda_{1}}{\lambda+\lambda_{1}}\Xi_{4} \end{align} \end{matrix}</math> into which he put<ref group=M name=linde>Lindemann & Clebsch (1890/91), p. 496</ref> :<math>\begin{align}X_{1} & =x_{1}+2kx_{4}, & X_{2} & =x_{2}+ix_{3}, & \lambda+\lambda_{1} & =\left(\lambda-\lambda_{1}\right)e^{a},\\ X_{4} & =x_{1}-2kx_{4}, & X_{3} & =x_{2}-ix_{3}, & \lambda+\lambda_{3} & =\left(\lambda-\lambda_{3}\right)e^{\alpha i}, \end{align} </math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3d}}) with <math>e^{\alpha i}=1</math> and ''2k=1'' .</p> From that, he obtained the following Cayley absolute and the corresponding most general motion in hyperbolic space comprising ordinary rotations (''a''=0) or translations (α=0):<ref group=M name=linde /> :<math>\begin{matrix}x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-4k^{2}x_{4}^{2}=0\\ \hline \begin{align}x_{2} & =\xi_{2}\cos\alpha+\xi_{3}\sin\alpha, & x_{1} & =\xi_{1}\cos\frac{a}{i}+2ki\xi_{4}\sin\frac{a}{i},\\ x_{3} & =-\xi_{2}\sin\alpha+\xi_{3}\cos\alpha, & 2kx_{4} & =i\xi_{1}\sin\frac{a}{i}+2k\xi_{4}\cos\frac{a}{i}. \end{align} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) with α=0 and ''2k=1''.</p> ==={{anchor|Gerard}} Gérard (1892) – Weierstrass coordinates=== [[w:Louis Gérard]] (1892) – in a thesis examined by Poincaré – discussed Weierstrass coordinates (without using that name) in the plane and gave the case of translation as follows:<ref group=M name=gerard>Gérard (1892), pp. 40–41</ref> :<math>\begin{align}X & =Z_{0}X'+X_{0}Z'\\ Y & =Y'\\ Z & =X_{0}X'+Z_{0}Z' \end{align} \ \text{with}\ \begin{align}X_{0} & =\operatorname{sh}OO'\\ Z_{0} & =\operatorname{ch}OO' \end{align} </math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> ==={{anchor|Killing2}} Killing (1893,97) – Weierstrass coordinates=== [[w:Wilhelm Killing]] (1878–1880) gave case of translation in the form<ref group=M name=killtra>Killing (1893), p. 331</ref> :<math>y_{0}=x_{0}\operatorname{Ch}a+x_{1}\operatorname{Sh}a,\quad y_{1}=x_{0}\operatorname{Sh}a+x_{1}\operatorname{Ch}a,\quad y_{2}=x_{2}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> In 1898, Killing wrote that relation in a form similar to [[#Escherich|Escherich (1874)]], and derived the corresponding Lorentz transformation for the two cases were ''v'' is unchanged or ''u'' is unchanged:<ref group=M name=kill98>Killing (1898), p. 133</ref> :<math>\begin{matrix}\xi'=\frac{\xi\operatorname{Ch}\frac{\mu}{l}+l\operatorname{Sh}\frac{\mu}{l}}{\frac{\xi}{l}\operatorname{Sh}\frac{\mu}{l}+\operatorname{Ch}\frac{\mu}{l}},\ \eta'=\frac{\eta}{\frac{\xi}{l}\operatorname{Sh}\frac{\mu}{l}+\operatorname{Ch}\frac{\mu}{l}}\\ \hline \frac{u}{p}=\xi,\ \frac{v}{p}=\eta\\ \hline p'=p\operatorname{Ch}\frac{\mu}{l}+\frac{u}{l}\operatorname{Sh}\frac{\mu}{l},\quad u'=pl\operatorname{Sh}\frac{\mu}{l}+u\operatorname{Ch}\frac{\mu}{l},\quad v'=v\\ \text{or}\\ p'=p\operatorname{Ch}\frac{\nu}{l}+\frac{v}{l}\operatorname{Sh}\frac{\nu}{l},\quad u'=u,\quad v'=pl\operatorname{Sh}\frac{\nu}{l}+v\operatorname{Ch}\frac{\nu}{l} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">The upper transformation system is equivalent to Lorentz transformation ({{equationNote|3e}}) and the velocity addition [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']] with ''l=c'' and <math>\mu=c\operatorname{atanh}\tfrac{v}{c}</math>, the system below is equivalent to Lorentz boost ({{equationNote|3b}}).</p> ==={{anchor|Whitehead}} Whitehead (1897/98) – Universal algebra=== [[w:Alfred North Whitehead]] (1898) discussed the kinematics of hyperbolic space as part of his study of [[w:universal algebra]], and obtained the following transformation:<ref group=M name=white>Whitehead (1898), pp. 459–460</ref> :<math>\begin{align}x' & =\left(\eta\cosh\frac{\delta}{\gamma}+\eta_{1}\sinh\frac{\delta}{\gamma}\right)e+\left(\eta\sinh\frac{\delta}{\gamma}+\eta_{1}\cosh\frac{\delta}{\gamma}\right)e_{1}\\ & \qquad+\left(\eta_{2}\cos\alpha+\eta_{3}\sin\alpha\right)e_{2}+\left(\eta_{3}\cos\alpha-\eta_{2}\sin\alpha\right)e_{3} \end{align} </math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) with α=0.</p> ==={{anchor|Elliott}} Elliott (1903) – Invariant theory === [[w:Edwin Bailey Elliott]] (1903) discussed a special cyclical subgroup of ternary linear transformations for which the (unit) determinant of transformation is resoluble into three ordinary algebraical factors, which he pointed out is in direct analogy to a subgroup formed by the following transformations:<ref group=M>Elliott (1903), p. 109</ref> :<math>\begin{matrix}x=X\cosh\phi+Y\sinh\phi,\quad y=X\sinh\phi+Y\cosh\phi\\ \hline X+Y=e^{-\phi}(x+y),\quad X-Y=e^{\phi}(x-y) \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) and ({{equationNote|3d}}). The mentioned subgroup corresponds to the one-parameter subgroup generated by Lorentz boosts.</p> ==={{anchor|Woods2}} Woods (1903) – Weierstrass coordinates === [[w:Frederick S. Woods]] (1903, published 1905) gave the case of translation in hyperbolic space:<ref group=M>Woods (1903/05), p. 55</ref> :<math>x_{1}^{\prime}=x_{1}\cos kl+x_{0}\frac{\sin kl}{k},\quad x_{2}^{\prime}=x_{2},\quad x_{2}^{\prime}=x_{3},\quad x_{0}^{\prime}=-x_{1}k\sin kl+x_{0}\cos kl</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) with ''k''²=-1.</p> and the loxodromic substitution for hyperbolic space:<ref group=M>Woods (1903/05), p. 72</ref> :<math>\begin{matrix}\begin{align}x_{1}^{\prime} & =x_{1}\cosh\alpha-x_{0}\sinh\alpha\\ x_{2}^{\prime} & =x_{2}\cos\beta-x_{3}\sin\beta\\ x_{3}^{\prime} & =x_{2}\sin\beta+x_{3}\cos\beta\\ x_{0}^{\prime} & =-x_{1}\sinh\alpha+x_{0}\cosh\alpha \end{align} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) with β=0.</p> ==={{anchor|Liebmann}} Liebmann (1904–05) – Weierstrass coordinates=== [[w:Heinrich Liebmann]] (1904/05) – citing Killing (1885), Gérard (1892), Hausdorff (1899) – gave the case of translation in the hyperbolic plane:<ref group=M name=lieb>Liebmann (1904/05), p. 174</ref> :<math>x_{1}^{\prime}=x'\operatorname{ch}a+p'\operatorname{sh}a,\quad y_{1}^{\prime}=y',\quad p_{1}^{\prime}=x'\operatorname{sh}a+p'\operatorname{ch}a</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> ==={{anchor|Frank}} Frank (1909) – Special relativity=== In special relativity, hyperbolic functions were used by [[w:Philipp Frank]] (1909), who derived the Lorentz transformation using ''ψ'' as rapidity:<ref group=R>Frank (1909), pp. 423-425</ref> :<math>\begin{matrix}x'=x\varphi(a)\,{\rm ch}\,\psi+t\varphi(a)\,{\rm sh}\,\psi\\ t'=-x\varphi(a)\,{\rm sh}\,\psi+t\varphi(a)\,{\rm ch}\,\psi\\ \hline {\rm th}\,\psi=-a,\ {\rm sh}\,\psi=\frac{a}{\sqrt{1-a^{2}}},\ {\rm ch}\,\psi=\frac{1}{\sqrt{1-a^{2}}},\ \varphi(a)=1\\ \hline x'=\frac{x-at}{\sqrt{1-a^{2}}},\ y'=y,\ z'=z,\ t'=\frac{-ax+t}{\sqrt{1-a^{2}}} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> === {{anchor|Herglotz1}} Herglotz (1909/10) – Special relativity=== In special relativity, [[w:Gustav Herglotz]] (1909/10) classified the one-parameter Lorentz transformations as loxodromic, hyperbolic, parabolic and elliptic, with the hyperbolic case being:<ref group=R>Herglotz (1909/10), pp. 404-408</ref> :<math>\begin{matrix}Z=Z'e^{\vartheta}\\ \begin{aligned}x & =x', & t-z & =(t'-z')e^{\vartheta}\\ y & =y', & t+z & =(t'+z')e^{-\vartheta} \end{aligned} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3d}}).</p> ==={{anchor|Varicak}} Varićak (1910) – Special relativity=== In special relativity, hyperbolic functions were used by [[w:Vladimir Varićak]] in several papers starting from 1910, who represented the equations of special relativity on the basis of [[w:hyperbolic geometry]] in terms of Weierstrass coordinates. For instance, by setting ''l=ct'' and ''v/c=tanh(u)'' with ''u'' as rapidity he wrote the Lorentz transformation in agreement with ({{equationNote|4b}}):<ref group=R name=var1>Varićak (1910), p. 93</ref> :<math>\begin{align}l' & =-x\operatorname{sh}u+l\operatorname{ch}u,\\ x' & =x\operatorname{ch}u-l\operatorname{sh}u,\\ y' & =y,\quad z'=z,\\ \operatorname{ch}u & =\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^{2}}} \end{align} </math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> He showed the relation of rapidity to the [[w:Gudermannian function]] and the [[w:angle of parallelism]]:<ref group=R name=var1 /> :<math>\frac{v}{c}=\operatorname{th}u=\operatorname{tg}\psi=\sin\operatorname{gd}(u)=\cos\Pi(u)</math> He also related the velocity addition to the [[w:hyperbolic law of cosines]]:<ref group=R>Varićak (1910), p. 94</ref> :<math>\begin{matrix}\operatorname{ch}{u}=\operatorname{ch}{u_{1}}\operatorname ch{u_{2}}+\operatorname{sh}{u_{1}}\operatorname{sh}{u_{2}}\cos\alpha\\ \operatorname{ch}{u_{i}}=\frac{1}{\sqrt{1-\left(\frac{v_{i}}{c}\right)^{2}}},\ \operatorname{sh}{u_{i}}=\frac{v_{i}}{\sqrt{1-\left(\frac{v_{i}}{c}\right)^{2}}}\\ v=\sqrt{v_{1}^{2}+v_{2}^{2}-\left(\frac{v_{1}v_{2}}{c}\right)^{2}}\ \left(a=\frac{\pi}{2}\right) \end{matrix}</math> ==References== ===Historical mathematical sources=== {{reflist|3|group=M}} *{{#section:History of Topics in Special Relativity/mathsource|bel68sag}} *{{#section:History of Topics in Special Relativity/mathsource|bel68fond}} *{{#section:History of Topics in Special Relativity/mathsource|cox81hom}} *{{#section:History of Topics in Special Relativity/mathsource|cox82hom}} *{{#section:History of Topics in Special Relativity/mathsource|eli03}} *{{#section:History of Topics in Special Relativity/mathsource|esch74}} *{{#section:History of Topics in Special Relativity/mathsource|eul35}} *{{#section:History of Topics in Special Relativity/mathsource|eul48a}} *{{#section:History of Topics in Special Relativity/mathsource|ger92}} *{{#section:History of Topics in Special Relativity/mathsource|glai78}} *{{#section:History of Topics in Special Relativity/mathsource|gud30}} *{{#section:History of Topics in Special Relativity/mathsource|guen80}} *{{#section:History of Topics in Special Relativity/mathsource|kep09}} *{{#section:History of Topics in Special Relativity/mathsource|kil93}} *{{#section:History of Topics in Special Relativity/mathsource|kil97}} *{{#section:History of Topics in Special Relativity/mathsource|lag70}} *{{#section:History of Topics in Special Relativity/mathsource|lais74b}} *{{#section:History of Topics in Special Relativity/mathsource|lam67}} *{{#section:History of Topics in Special Relativity/mathsource|lam70}} *{{#section:History of Topics in Special Relativity/mathsource|lieb04}} *{{#section:History of Topics in Special Relativity/mathsource|lind90}} *{{#section:History of Topics in Special Relativity/mathsource|lip86}} *{{#section:History of Topics in Special Relativity/mathsource|ric57}} *{{#section:History of Topics in Special Relativity/mathsource|schu85}} *{{#section:History of Topics in Special Relativity/mathsource|schu00}} *{{#section:History of Topics in Special Relativity/mathsource|schu09}} *{{#section:History of Topics in Special Relativity/mathsource|tau26}} *{{#section:History of Topics in Special Relativity/mathsource|whit98}} *{{#section:History of Topics in Special Relativity/mathsource|woo01}} *{{#section:History of Topics in Special Relativity/mathsource|woo03}} ===Historical relativity sources=== {{reflist|3|group=R}} *{{#section:History of Topics in Special Relativity/relsource|frank09a}} *{{#section:History of Topics in Special Relativity/relsource|herg10}} *{{#section:History of Topics in Special Relativity/relsource|var10}} *{{#section:History of Topics in Special Relativity/relsource|var12}} ===Secondary sources=== {{reflist|3}} {{#section:History of Topics in Special Relativity/secsource|L3}} [[Category:Special Relativity]] [[Category:History of Physics]] tctw757rh19hfmz1xz1nwws19uq7ze5 2412502 2412499 2022-08-07T11:25:28Z D.H 52339 /* Translation in the hyperbolic plane */ wikitext text/x-wiki {{../Lorentz transformation (header)}} ==Lorentz transformation via hyperbolic functions== ===Translation in the hyperbolic plane=== The case of a Lorentz transformation without spatial rotation is called a [[w:Lorentz boost]]. The simplest case can be given, for instance, by setting ''n=1'' in the [[../Lorentz transformation (general)#math_1a|E:most general Lorentz transformation '''(1a)''']]: {{NumBlk|:|<math>\begin{matrix}-x_{0}^{2}+x_{1}^{2}=-x_{0}^{\prime2}+x_{1}^{\prime2}\\ \hline \begin{align}x_{0}^{\prime} & =x_{0}g_{00}+x_{1}g_{01}\\ x_{1}^{\prime} & =x_{0}g_{10}+x_{1}g_{11}\\ \\ x_{0} & =x_{0}^{\prime}g_{00}-x_{1}^{\prime}g_{10}\\ x_{1} & =-x_{0}^{\prime}g_{01}+x_{1}^{\prime}g_{11} \end{align} \left|\begin{align}g_{01}^{2}-g_{00}^{2} & =-1\\ g_{11}^{2}-g_{10}^{2} & =1\\ g_{01}g_{11}-g_{00}g_{10} & =0\\ g_{10}^{2}-g_{00}^{2} & =-1\\ g_{11}^{2}-g_{01}^{2} & =1\\ g_{10}g_{11}-g_{00}g_{01} & =0 \end{align} \rightarrow\begin{align}g_{00}^{2} & =g_{11}^{2}\\ g_{01}^{2} & =g_{10}^{2} \end{align} \right. \end{matrix}</math> or in matrix notation <math>\left.\begin{align}\mathbf{x}' & =\begin{bmatrix}g_{00} & g_{01}\\ g_{10} & g_{11} \end{bmatrix}\cdot\mathbf{x}\\ \mathbf{x} & =\begin{bmatrix}g_{00} & -g_{10}\\ -g_{01} & g_{11} \end{bmatrix}\cdot\mathbf{x}' \end{align} \quad\right|\quad\det\begin{bmatrix}g_{00} & g_{01}\\ g_{10} & g_{11} \end{bmatrix}=1</math>|{{equationRef|3a}}}} which resembles precisely the relations of [[w:hyperbolic function]]s in terms of [[w:hyperbolic angle]] <math>\eta</math>. Thus a Lorentz boost or [[w:hyperbolic rotation]] (being the same as a rotation around an imaginary angle <math>i\eta=\phi</math> in [[../Lorentz transformation (imaginary)#math_2b|E:'''(2b)''']] or a [[w:Translation (geometry)|translation]] in the hyperbolic plane in terms of the hyperboloid model) is given by {{NumBlk|:|<math>\begin{matrix}-x_{0}^{2}+x_{1}^{2}=-x_{0}^{\prime2}+x_{1}^{\prime2}\\ \hline g_{00}=g_{11}=\cosh\eta,\ g_{01}=g_{10}=-\sinh\eta\\ \hline \left.\begin{align} & \quad\quad(A) & & \quad\quad(B) & & \quad\quad(C)\\ x_{0}^{\prime} & =x_{0}\cosh\eta-x_{1}\sinh\eta & & =\frac{x_{0}-x_{1}\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & & =\frac{x_{0}-x_{1}v}{\sqrt{1-v^{2}}}\\ x_{1}^{\prime} & =-x_{0}\sinh\eta+x_{1}\cosh\eta & & =\frac{x_{1}-x_{0}\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & & =\frac{x_{1}-x_{0}v}{\sqrt{1-v^{2}}}\\ \\ x_{0} & =x_{0}^{\prime}\cosh\eta+x_{1}^{\prime}\sinh\eta & & =\frac{x_{0}^{\prime}+x_{1}^{\prime}\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & & =\frac{x_{0}^{\prime}+x_{1}^{\prime}v}{\sqrt{1-v^{2}}}\\ x_{1} & =x_{0}^{\prime}\sinh\eta+x_{1}^{\prime}\cosh\eta & & =\frac{x_{1}^{\prime}+x_{0}^{\prime}\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & & =\frac{x_{1}^{\prime}+x_{0}^{\prime}v}{\sqrt{1-v^{2}}} \end{align} \right|{\scriptstyle \begin{align}\sinh^{2}\eta-\cosh^{2}\eta & =-1 & (a)\\ \cosh^{2}\eta-\sinh^{2}\eta & =1 & (b)\\ \frac{\sinh\eta}{\cosh\eta} & =\tanh\eta=v & (c)\\ \frac{1}{\sqrt{1-\tanh^{2}\eta}} & =\cosh\eta & (d)\\ \frac{\tanh\eta}{\sqrt{1-\tanh^{2}\eta}} & =\sinh\eta & (e)\\ \frac{\tanh q\pm\tanh\eta}{1\pm\tanh q\tanh\eta} & =\tanh\left(q\pm\eta\right) & (f) \end{align} } \end{matrix}</math> or in matrix notation <math>\left.\begin{align}\mathbf{x}' & =\begin{bmatrix}\cosh\eta & -\sinh\eta\\ -\sinh\eta & \cosh\eta \end{bmatrix}\cdot\mathbf{x}\\ \mathbf{x} & =\begin{bmatrix}\cosh\eta & \sinh\eta\\ \sinh\eta & \cosh\eta \end{bmatrix}\cdot\mathbf{x}' \end{align} \quad\right|\quad\det\begin{bmatrix}\cosh\eta & -\sinh\eta\\ -\sinh\eta & \cosh\eta \end{bmatrix}=1</math>|{{equationRef|3b}}}} Hyperbolic identities (a,b) on the right of ({{equationNote|3b}}) were given by [[#Riccati|Riccati (1757)]], all identities (a,b,c,d,e,f) by [[#Lambert|Lambert (1768–1770)]]. Lorentz transformations ({{equationNote|3b}}-A) were given by [[#Laisant|Laisant (1874)]], [[#Cox|Cox (1882)]], [[#Lindemann|Lindemann (1890/91)]], [[#Gerard|Gérard (1892)]], [[#Killing2|Killing (1893, 1897/98)]], [[#Whitehead|Whitehead (1897/98)]], [[#Woods2|Woods (1903/05)]], [[#Elliott|Elliott (1903)]] and [[#Liebmann|Liebmann (1904/05)]] in terms of Weierstrass coordinates of the [[w:hyperboloid model]], while transformations similar to ({{equationNote|3b}}-C) have been used by [[#Lipschitz1|Lipschitz (1885/86)]]. Rapidity can be composed of arbitrary many rapidities <math>\eta_{1},\eta_{2}\dots</math> as per the [[w:Hyperbolic functions#Sums of arguments|w:angle sum laws of hyperbolic sines and cosines]], so that one hyperbolic rotation can represent the sum of many other hyperbolic rotations, analogous to the relation between [[w:List of trigonometric identities#Angle sum and difference identities|w:angle sum laws of circular trigonometry]] and spatial rotations. Alternatively, the hyperbolic angle sum laws ''themselves'' can be interpreted as Lorentz boosts, as demonstrated by using the parameterization of the [[w:unit hyperbola]]: {{NumBlk|:|<math>\begin{matrix}-x_{0}^{2}+x_{1}^{2}=-x_{0}^{\prime2}+x_{1}^{\prime2}=1\\ \hline \left[\eta=\eta_{2}-\eta_{1}\right]\\ {\scriptstyle \begin{align}x_{0}^{\prime} & =\sinh\eta_{1} & & =\sinh\left(\eta_{2}-\eta\right) & & =\sinh\eta_{2}\cosh\eta-\cosh\eta_{2}\sinh\eta & & =x_{0}\cosh\eta-x_{1}\sinh\eta\\ x_{1}^{\prime} & =\cosh\eta_{1} & & =\cosh\left(\eta_{2}-\eta\right) & & =-\sinh\eta_{2}\sinh\eta+\cosh\eta_{2}\cosh\eta & & =-x_{0}\sinh\eta+x_{1}\cosh\eta\\ \\ x_{0} & =\sinh\eta_{2} & & =\sinh\left(\eta_{1}+\eta\right) & & =\sinh\eta_{1}\cosh\eta+\cosh\eta_{1}\sinh\eta & & =x_{0}^{\prime}\cosh\eta+x_{1}^{\prime}\sinh\eta\\ x_{1} & =\cosh\eta_{2} & & =\cosh\left(\eta_{1}+\eta\right) & & =\sinh\eta_{1}\sinh\eta+\cosh\eta_{1}\cosh\eta & & =x_{0}^{\prime}\sinh\eta+x_{1}^{\prime}\cosh\eta \end{align} } \end{matrix}</math> or in matrix notation <math>{\scriptstyle \begin{align} & \begin{bmatrix}x_{0}^{\prime}\\ x_{1}^{\prime} \end{bmatrix}=\begin{bmatrix}\sinh\eta_{1}\\ \cosh\eta_{1} \end{bmatrix}=\begin{bmatrix}\sinh\left(\eta_{2}-\eta\right)\\ \cosh\left(\eta_{2}-\eta\right) \end{bmatrix}=\begin{bmatrix}\cosh\eta & -\sinh\eta\\ -\sinh\eta & \cosh\eta \end{bmatrix}\cdot\begin{bmatrix}\sinh\eta_{2}\\ \cosh\eta_{2} \end{bmatrix} & & =\begin{bmatrix}\cosh\eta & -\sinh\eta\\ -\sinh\eta & \cosh\eta \end{bmatrix}\cdot\begin{bmatrix}x_{0}\\ x_{1} \end{bmatrix}\\ & \begin{bmatrix}x_{0}\\ x_{1} \end{bmatrix}=\begin{bmatrix}\sinh\eta_{2}\\ \cosh\eta_{2} \end{bmatrix}=\begin{bmatrix}\sinh\left(\eta_{1}+\eta\right)\\ \cosh\left(\eta_{1}+\eta\right) \end{bmatrix}=\begin{bmatrix}\cosh\eta & \sinh\eta\\ \sinh\eta & \cosh\eta \end{bmatrix}\cdot\begin{bmatrix}\sinh\eta_{1}\\ \cosh\eta_{1} \end{bmatrix} & & =\begin{bmatrix}\cosh\eta & \sinh\eta\\ \sinh\eta & \cosh\eta \end{bmatrix}\cdot\begin{bmatrix}x_{0}^{\prime}\\ x_{1}^{\prime} \end{bmatrix} \end{align} }</math>|{{equationRef|3c}}}} Hyperbolic angle sum laws equivalent to Lorentz boost ({{equationNote|3c}}) were given by [[#Riccati|Riccati (1757)]] and [[#Lambert|Lambert (1768–1770)]], while the matrix representation was given by [[#Glaisher|Glaisher (1878)]] and [[#Gunther2|Günther (1880/81)]]. In special relativity, hyperbolic functions were used by [[#Frank|Frank (1909)]] and [[#Varicak|Varićak (1910)]]. Finally, because of <math>\cosh\eta+\sinh\eta=e^{\eta}</math>, Lorentz boost ({{equationNote|3b}}) assumes a simple form by using [[w:squeeze mapping]]s in analogy to Euler's formula in [[../Lorentz transformation (imaginary)#math_2c|E:'''(2c)''']]:<ref name=rind>Rindler (1969), p. 45</ref> {{NumBlk|:|<math>\begin{matrix}-x_{0}^{2}+x_{1}^{2}=-x_{0}^{\prime2}+x_{1}^{\prime2}\\ \hline \begin{matrix}\begin{aligned}x_{1}^{\prime}-x_{0}^{\prime} & =k\left(x_{1}-x_{0}\right)\\ x_{1}^{\prime}+x_{0}^{\prime} & =\frac{1}{k}\left(x_{1}+x_{0}\right) \end{aligned} & \Rightarrow & \begin{aligned}x_{1}^{\prime}-x_{0}^{\prime} & =e^{\eta}\left(x_{1}-x_{0}\right)\\ x_{1}^{\prime}+x_{0}^{\prime} & =e^{-\eta}\left(x_{1}+x_{0}\right) \end{aligned} \end{matrix}\\ \hline k=e^{\eta}=\cosh\eta+\sinh\eta=\sqrt{\frac{1+\tanh\eta}{1-\tanh\eta}}=\sqrt{\frac{1+v}{1-v}} \end{matrix}</math>|{{equationRef|3d}}}} Lorentz transformations ({{equationNote|3d}}) for arbitrary ''k'' were given by many authors (see [[../Lorentz transformation (squeeze)|E:Lorentz transformations via squeeze mappings]]), while the exponential form was explicitly used by [[#Lindemann|Lindemann (1890/91)]], [[#Elliott|Elliott (1903)]], [[#Herglotz1|Herglotz (1909)]]. ===Hyperbolic law of cosines=== In line with equation [[../Lorentz transformation (general)#math_1b|E:'''(1b)''']] one can use coordinates <math>[u_{1},\ u_{2}]=\left[\tfrac{x_{1}}{x_{0}},\ \tfrac{x_{2}}{x_{0}}\right]</math> inside the [[w:unit circle]] <math>u_{1}^{2}+u_{2}^{2}=1</math>, thus the corresponding Lorentz transformations ({{equationNote|3b}}) obtain the form: {{NumBlk|:|<math>\begin{align} & \quad\quad(A) & & \quad\quad(B) & & \quad\quad(C)\\ u_{1}^{\prime} & =\frac{-\sinh\eta+u_{1}\cosh\eta}{\cosh\eta-u_{1}\sinh\eta} & & =\frac{u_{1}-\tanh\eta}{1-u_{1}\tanh\eta} & & =\frac{u_{1}-v}{1-u_{1}v}\\ u_{2}^{\prime} & =\frac{u_{2}}{\cosh\eta-u_{1}\sinh\eta} & & =\frac{u_{2}\sqrt{1-\tanh^{2}\eta}}{1-u_{1}\tanh\eta} & & =\frac{u_{2}\sqrt{1-v^{2}}}{1-u_{1}v}\\ \\ u_{1} & =\frac{\sinh\eta+u_{1}^{\prime}\cosh\eta}{\cosh\eta+u_{1}^{\prime}\sinh\eta} & & =\frac{u_{1}^{\prime}+\tanh\eta}{1+u_{1}^{\prime}\tanh\eta} & & =\frac{u_{1}^{\prime}+v}{1+u_{1}^{\prime}v}\\ u_{2} & =\frac{u_{2}^{\prime}}{\cosh\eta+u_{1}^{\prime}\sinh\eta} & & =\frac{u_{2}^{\prime}\sqrt{1-\tanh^{2}\eta}}{1+u_{1}^{\prime}\tanh\eta} & & =\frac{u_{2}^{\prime}\sqrt{1-v^{2}}}{1+u_{1}^{\prime}v} \end{align} </math>|{{equationRef|3e}}}} Transformations (A) were given by [[#Escherich|Escherich (1874)]] and [[#Killing2|Killing (1898)]], and transformations (C) by [[#Beltrami|Beltrami (1868)]] and [[#Schur|Schur (1885/86, 1900/02)]] in terms of [[w:Beltrami–Klein model|Beltrami coordinates]]<ref>Rosenfeld (1988), p. 231</ref> of hyperbolic geometry. By using the scalar product of <math>\left[u_{1},u_{2}\right]</math>, the resulting Lorentz transformation can be seen as equivalent to the [[w:hyperbolic law of cosines]]:<ref name=pau>Pauli (1921), p. 561</ref><ref group=R name=var>Varićak (1912), p. 108</ref><ref name=barr>Barrett (2006), chapter 4, section 2</ref> {{NumBlk|:|<math>\begin{matrix} & \begin{matrix}u^{2}=u_{1}^{2}+u_{2}^{2}\\ u'^{2}=u_{1}^{\prime2}+u_{2}^{\prime2} \end{matrix}\left|\begin{matrix}u_{1}=u\cos\alpha\\ u_{2}=u\sin\alpha\\ \\ u_{1}^{\prime}=u'\cos\alpha'\\ u_{2}^{\prime}=u'\sin\alpha' \end{matrix}\right|\begin{align}u\cos\alpha & =\frac{u'\cos\alpha'+v}{1+vu'\cos\alpha'}, & u'\cos\alpha' & =\frac{u\cos\alpha-v}{1-vu\cos\alpha}\\ u\sin\alpha & =\frac{u'\sin\alpha'\sqrt{1-v^{2}}}{1+vu'\cos\alpha'}, & u'\sin\alpha' & =\frac{u\sin\alpha\sqrt{1-v^{2}}}{1-vu\cos\alpha}\\ \tan\alpha & =\frac{u'\sin\alpha'\sqrt{1-v^{2}}}{u'\cos\alpha'+v}, & \tan\alpha' & =\frac{u\sin\alpha\sqrt{1-v^{2}}}{u\cos\alpha-v} \end{align} \\ \Rightarrow & u=\frac{\sqrt{v^{2}+u^{\prime2}+2vu'\cos\alpha'-\left(vu'\sin\alpha'\right){}^{2}}}{1+vu'\cos\alpha'},\quad u'=\frac{\sqrt{-v^{2}-u^{2}+2vu\cos\alpha+\left(vu\sin\alpha\right){}^{2}}}{1-vu\cos\alpha}\\ \Rightarrow & \frac{1}{\sqrt{1-u^{\prime2}}}=\frac{1}{\sqrt{1-v^{2}}}\frac{1}{\sqrt{1-u^{2}}}-\frac{v}{\sqrt{1-v^{2}}}\frac{u}{\sqrt{1-u^{2}}}\cos\alpha & (b)\\ \Rightarrow & \frac{1}{\sqrt{1-\tanh^{2}\xi}}=\frac{1}{\sqrt{1-\tanh^{2}\eta}}\frac{1}{\sqrt{1-\tanh^{2}\zeta}}-\frac{\tanh\eta}{\sqrt{1-\tanh^{2}\eta}}\frac{\tanh\zeta}{\sqrt{1-\tanh^{2}\zeta}}\cos\alpha\\ \Rightarrow & \cosh\xi=\cosh\eta\cosh\zeta-\sinh\eta\sinh\zeta\cos\alpha & (a) \end{matrix}</math>|{{equationRef|3f}}}} The hyperbolic law of cosines (a) was given by [[#Taurinus|Taurinus (1826) and Lobachevsky (1829/30)]] and others, while variant (b) was given by [[#Schur|Schur (1900/02)]]. By further setting ''u=u′'' it follows: {{NumBlk|:|<math>\begin{matrix}\cos\alpha=\frac{\cos\alpha'+v}{1+v\cos\alpha'},\ \sin\alpha=\frac{\sin\alpha'\sqrt{1-v^{2}}}{1+v\cos\alpha'},\ \tan\alpha=\frac{\sin\alpha'\sqrt{1-v^{2}}}{\cos\alpha'+v},\ \tan\frac{\alpha}{2}=\sqrt{\frac{1-v}{1+v}}\tan\frac{\alpha'}{2}\\ \cos\alpha'=\frac{\cos\alpha-v}{1-v\cos\alpha},\ \sin\alpha'=\frac{\sin\alpha\sqrt{1-v^{2}}}{1-v\cos\alpha},\ \tan\alpha'=\frac{\sin\alpha\sqrt{1-v^{2}}}{\cos\alpha-v},\ \tan\frac{\alpha'}{2}=\sqrt{\frac{1+v}{1-v}}\tan\frac{\alpha}{2} \end{matrix}</math>|{{equationRef|3g}}}} Formulas (3b) resemble the equations of an [[w:ellipse]] of [[w:Orbital eccentricity|eccentricity]] ''v/c'', [[w:eccentric anomaly]] α' and [[w:true anomaly]] α, first geometrically formulated by [[#Euler|Kepler (1609)]] and explicitly written down by [[#Euler|Euler (1735, 1748), Lagrange (1770)]] and many others in relation to planetary motions. They were also used by [[../Lorentz transformation (conformal)#Darboux|E:Darboux (1873)]] as a sphere transformation. In special relativity, these formulas describes the aberration of light, see [[../Lorentz transformation (velocity)#Velocity addition and aberration|E:velocity addition and aberration]]. ==Historical notation== ==={{anchor|Euler}} Euler (1735) – True and eccentric anomaly=== [[w:Johannes Kepler]] (1609) geometrically formulated [[w:Kepler's equation]] and the relations between the [[w:mean anomaly]], [[w:true anomaly]], and [[w:eccentric anomaly]].<ref group=M>Kepler (1609), chapter 60. The editors of Kepler's collected papers remark (p. 482), that Kepler's relations correspond to <math>{\scriptstyle \alpha=\beta+e\sin\beta}</math> and <math>{\scriptstyle \cos\nu=\frac{e+\cos\beta}{1+e\cos\beta}}</math> and <math>{\scriptstyle \cos\beta=\frac{\cos\nu-e}{1-e\cos\nu}}</math></ref><ref>Volk (1976), p. 366</ref> The relation between the true anomaly ''z'' and the eccentric anomaly ''P'' was algebraically expressed by [[w:Leonhard Euler]] (1735/40) as follows:<ref group=M>Euler (1735/40), § 19</ref> :<math>\cos z=\frac{\cos P+v}{1+v\cos P},\ \cos P=\frac{\cos z-v}{1-v\cos z},\ \int P=\frac{\int z\sqrt{1-v^{2}}}{1-v\cos z}</math> and in 1748:<ref group=M>Euler (1748a), section VIII</ref> :<math>\cos z=\frac{n+\cos y}{1+n\cos y},\ \sin z=\frac{\sin y\sqrt{1-n^{2}}}{1+n\cos y},\ \tan z=\frac{\sin y\sqrt{1-n^{2}}}{n+\cos y}</math> while [[w:Joseph-Louis Lagrange]] (1770/71) expressed them as follows<ref group=M>Lagrange (1770/71), section I</ref> :<math>\sin u=\frac{m\sin x}{1+n\cos x},\ \cos u=\frac{n+\cos x}{1+n\cos x},\ \operatorname{tang}\frac{1}{2}u=\frac{m}{1+n}\operatorname{tang}\frac{1}{2}x,\ \left(m^{2}=1-n^{2}\right)</math> <p style="background-color:Beige;border:1px solid black"> These relations resemble formulas ({{equationNote|3g}}), while ({{equationNote|3f}}) follows by setting <math>[\cos z,\sin z]=\left[u_{x},u_{y}\right]</math> in Euler's formulas or <math>[\cos u,\sin u]=\left[u_{x},u_{y}\right]</math> in Lagrange's formulas.</p> ==={{anchor|Riccati}} Riccati (1757) – hyperbolic addition=== [[w:Vincenzo Riccati]] introduced hyperbolic functions in 1757,<ref group=M>Riccati (1757), p. 71</ref><ref group=M>Günther (1880/81), pp. 7–13</ref> in particular he formulated the angle sum laws for hyperbolic sine and cosine: :<math>\begin{matrix}\mathrm{Ch}(\varphi+\pi)=\frac{\mathrm{Ch}\varphi\mathrm{Ch}\pi+\mathrm{Sh}\varphi\mathrm{Sh}\pi}{r}\\ \mathrm{Sh}(\varphi+\pi)=\frac{\mathrm{Ch}\varphi\mathrm{Sh}\pi+\mathrm{Ch}\pi\mathrm{Sh}\varphi}{r}\\ \left[\mathrm{Ch}^{2}-\mathrm{Sh}^{2}=rr\right] \end{matrix}</math> He furthermore showed that <math>\mathrm{Ch}(\varphi-\pi)</math> and <math>\mathrm{Sh}(\varphi-\pi)</math> follow by setting <math>\mathrm{Ch}(\pi)\Rightarrow\mathrm{Ch}(-\pi)</math> and <math>\mathrm{Sh}(\pi)\Rightarrow\mathrm{Sh}(-\pi)</math> in the above formulas. <p style="background-color:Beige;border:1px solid black">The angle sum laws for hyperbolic sine and cosine can be interpreted as hyperbolic rotations of points on a hyperbola, as in Lorentz boost ({{equationNote|3c}}). (In modern publications, Riccati's additional factor ''r'' is set to unity.)</p> ==={{anchor|Lambert}} Lambert (1768–1770) – hyperbolic addition=== While [[#Riccati|Riccati (1757)]] discussed the hyperbolic sine and cosine, [[w:Johann Heinrich Lambert]] (read 1767, published 1768) introduced the expression ''tang φ'' or abbreviated ''tφ'' as the [[w:tangens hyperbolicus]] <math>{\scriptstyle \frac{e^{u}-e^{-u}}{e^{u}+e^{-u}}}</math> of a variable ''u'', or in modern notation ''tφ=tanh(u)'':<ref group=M>Lambert (1761/68), pp. 309–318</ref><ref>Barnett (2004), pp. 22–23</ref> :<math>\left.\begin{align}\xi\xi-1 & =\eta\eta & (a)\\ 1+\eta\eta & =\xi\xi & (b)\\ \frac{\eta}{\xi} & =tang\ \phi=t\phi & (c)\\ \xi & =\frac{1}{\sqrt{1-t\phi^{2}}} & (d)\\ \eta & =\frac{t\phi}{\sqrt{1-t\phi^{2}}} & (e)\\ t\phi'' & =\frac{t\phi+t\phi'}{1+t\phi\cdot t\phi'} & (f)\\ t\phi' & =\frac{t\phi''-t\phi}{1-t\phi\cdot t\phi''} & (g) \end{align} \right|\begin{align}2u & =\log\frac{1+t\phi}{1-t\phi}\\ \xi & =\frac{e^{u}+e^{-u}}{2}\\ \eta & =\frac{e^{u}-e^{-u}}{2}\\ t\phi & =\frac{e^{u}-e^{-u}}{e^{u}+e^{-u}}\\ e^{u} & =\xi+\eta\\ e^{-u} & =\xi-\eta \end{align}</math> In (1770) he rewrote the addition law for the hyperbolic tangens (f) or (g) as:<ref group=M>Lambert (1770), p. 335</ref> :<math>\begin{align}t(y+z) & =(ty+tz):(1+ty\cdot tz) & (f)\\ t(y-z) & =(ty-tz):(1-ty\cdot tz) & (g) \end{align} </math> <p style="background-color:Beige;border:1px solid black">The hyperbolic relations (a,b,c,d,e,f) are equivalent to the hyperbolic relations on the right of ({{equationNote|3b}}). Relations (f,g) can also be found in ({{equationNote|3e}}). By setting ''tφ=v/c'', formula (c) becomes the relative velocity between two frames, (d) the [[w:Lorentz factor]], (e) the [[w:proper velocity]], (f) or (g) becomes the Lorentz transformation of velocity (or relativistic [[w:velocity addition formula]]) for collinear velocities in [[../Lorentz transformation (velocity)#math_4a|E:'''(4a)''']] and [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']].</p> Lambert also formulated the addition laws for the hyperbolic cosine and sine (Lambert's "cos" and "sin" actually mean "cosh" and "sinh"): :<math>\begin{align}\sin(y+z) & =\sin y\cos z+\cos y\sin z\\ \sin(y-z) & =\sin y\cos z-\cos y\sin z\\ \cos(y+z) & =\cos y\cos z+\sin y\sin z\\ \cos(y-z) & =\cos y\cos z-\sin y\sin z \end{align} </math> <p style="background-color:Beige;border:1px solid black">The angle sum laws for hyperbolic sine and cosine can be interpreted as hyperbolic rotations of points on a hyperbola, as in Lorentz boost ({{equationNote|3c}}).</p> ==={{Anchor|Taurinus}} Taurinus (1826) – Hyperbolic law of cosines=== After the addition theorem for the tangens hyperbolicus was given by [[#Lambert|Lambert (1768)]], [[w:hyperbolic geometry]] was used by [[w:Franz Taurinus]] (1826), and later by [[w:Nikolai Lobachevsky]] (1829/30) and others, to formulate the [[w:hyperbolic law of cosines]]:<ref group=M>Taurinus (1826), p. 66; see also p. 272 in the translation by Engel and Stäckel (1899)</ref><ref>Bonola (1912), p. 79</ref><ref>Gray (1979), p. 242</ref> :<math>A=\operatorname{arccos}\frac{\cos\left(\alpha\sqrt{-1}\right)-\cos\left(\beta\sqrt{-1}\right)\cos\left(\gamma\sqrt{-1}\right)}{\sin\left(\beta\sqrt{-1}\right)\sin\left(\gamma\sqrt{-1}\right)}</math> <p style="background-color:Beige;border:1px solid black">When solved for <math>\cos\left(\alpha\sqrt{-1}\right)</math> it corresponds to the Lorentz transformation in Beltrami coordinates ({{equationNote|3f}}), and by defining the rapidities <math>{\scriptstyle \left(\left[\frac{U}{c},\ \frac{v}{c},\ \frac{u}{c}\right]=\left[\tanh\alpha,\ \tanh\beta,\ \tanh\gamma\right]\right)}</math> it corresponds to the relativistic velocity addition formula [[../Lorentz transformation (velocity)#math_4e|E:'''(4e)''']].</p> ==={{anchor|Beltrami}} Beltrami (1868) – Beltrami coordinates=== [[w:Eugenio Beltrami]] (1868a) introduced coordinates of the [[w:Beltrami–Klein model]] of hyperbolic geometry, and formulated the corresponding transformations in terms of homographies:<ref group=M>Beltrami (1868a), pp. 287-288; Note I; Note II</ref> :<math>\begin{matrix}ds^{2}=R^{2}\frac{\left(a^{2}+v^{2}\right)du^{2}-2uv\,du\,dv+\left(a^{2}+v^{2}\right)dv^{2}}{\left(a^{2}+u^{2}+v^{2}\right)^{2}}\\ u^{2}+v^{2}=a^{2}\\ \hline u''=\frac{aa_{0}\left(u'-r_{0}\right)}{a^{2}-r_{0}u'},\ v''=\frac{a_{0}w_{0}v'}{a^{2}-r_{0}u'},\\ \left(r_{0}=\sqrt{u_{0}^{2}+v_{0}^{2}},\ w_{0}=\sqrt{a^{2}-r_{0}^{2}}\right)\\ \hline ds^{2}=R^{2}\frac{\left(a^{2}-v^{2}\right)du^{2}+2uv\,du\,dv+\left(a^{2}-v^{2}\right)dv^{2}}{\left(a^{2}-u^{2}-v^{2}\right)^{2}}\\ (R=R\sqrt{-1},\ a=a\sqrt{-1}) \end{matrix}</math> (where the disk radius ''a'' and the [[w:radius of curvature]] ''R'' are real in spherical geometry, in hyperbolic geometry they are imaginary), and for arbitrary dimensions in (1868b)<ref group=M>Beltrami (1868b), pp. 232, 240–241, 253–254</ref> :<math>\begin{matrix}ds=R\frac{\sqrt{dx^{2}+dx_{1}^{2}+dx_{2}^{2}+\cdots+dx_{n}^{2}}}{x}\\ x^{2}+x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=a^{2}\\ \hline y_{1}=\frac{ab\left(x_{1}-a_{1}\right)}{a^{2}-a_{1}x_{1}}\ \text{or}\ x_{1}=\frac{a\left(ay_{1}+a_{1}b\right)}{ab+a_{1}y_{1}},\ x_{r}=\pm\frac{ay_{r}\sqrt{a^{2}-a_{1}^{2}}}{ab+a_{1}y_{1}}\ (r=2,3,\dots,n)\\ \hline ds=R\frac{\sqrt{dx_{1}^{2}+dx_{2}^{2}+\cdots+dx_{n}^{2}-dx^{2}}}{x}\\ x^{2}=a^{2}+x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}\\ \left(R=R\sqrt{-1},\ x=x\sqrt{-1},\ a=a\sqrt{-1}\right) \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">Setting ''a=a₀'' Beltrami's (1868a) formulas become formulas ({{equationNote|3e}}), or in his (1868b) formulas one sets ''a=b'' for arbitrary dimensions.</p> === {{anchor|Laisant2}} Laisant (1874) – Equipollences=== In his French translation of [[w:Giusto Bellavitis]]' principal work on [[w:Equipollence (geometry)|w:equipollences]], [[w:Charles-Ange Laisant]] (1874) added a chapter related to hyperbolas. The equipollence OM and its tangent MT of a hyperbola is defined by Laisant as<ref group=M>Laisant (1874b), pp. 134–135</ref> :(1) <math>\begin{matrix} & \mathrm{OM}\bumpeq x\mathrm{OA}+y\mathrm{OB}\\ & \mathrm{MT}\bumpeq y\mathrm{OA}+x\mathrm{OB}\\ & \left[x^{2}-y^{2}=1;\ x=\cosh t,\ y=\sinh t\right]\\ \Rightarrow & \mathrm{OM}\bumpeq\cosh t\cdot\mathrm{OA}+\sinh t\cdot\mathrm{OB} \end{matrix}</math> Here, OA and OB are [[w:Conjugate diameters|conjugate semi-diameters]] of a hyperbola with OB being imaginary, both of which he related to two other conjugated semi-diameters OC and OD by the following transformation: :<math>\begin{matrix}\begin{align}\mathrm{OC} & \bumpeq c\mathrm{OA}+d\mathrm{OB} & \qquad & & \mathrm{OA} & \bumpeq c\mathrm{OC}-d\mathrm{OD}\\ \mathrm{OD} & \bumpeq d\mathrm{OA}+c\mathrm{OB} & & & \mathrm{OB} & \bumpeq-d\mathrm{OC}+c\mathrm{OD} \end{align} \\ \left[c^{2}-d^{2}=1\right] \end{matrix}</math> producing the invariant relation :<math>(\mathrm{OC})^{2}-(\mathrm{OD})^{2}\bumpeq(\mathrm{OA})^{2}-(\mathrm{OB})^{2}</math>. Substituting into (1), he showed that OM retains its form :<math>\begin{matrix}\mathrm{OM}\bumpeq(cx-dy)\mathrm{OC}+(cy-dx)\mathrm{OD}\\ \left[(cx-dy)^{2}-(cy-dx)^{2}=1\right] \end{matrix}</math> He also defined velocity and acceleration by differentiation of (1). <p style="background-color:Beige;border:1px solid black">These relations are equivalent to several Lorentz boosts or hyperbolic rotations producing the invariant Lorentz interval in line with ({{equationNote|3b}}).</p> ==={{anchor|Escherich}} Escherich (1874) – Beltrami coordinates=== [[w:Gustav von Escherich]] (1874) discussed the plane of constant negative curvature<ref>Sommerville (1911), p. 297</ref> based on the [[w:Beltrami–Klein model]] of hyperbolic geometry by [[#Beltrami|Beltrami (1868)]]. Similar to [[w:Christoph Gudermann]] (1830)<ref name=guder group=M>Gudermann (1830), §1–3, §18–19</ref> who introduced axial coordinates ''x''=tan(a) and ''y''=tan(b) in sphere geometry in order to perform coordinate transformations in the case of rotation and translation, Escherich used hyperbolic functions ''x''=tanh(a/k) and ''y''=tanh(b/k)<ref group=M>Escherich (1874), p. 508</ref> in order to give the corresponding coordinate transformations for the hyperbolic plane, which for the case of translation have the form:<ref group=M name=escher>Escherich (1874), p. 510</ref> :<math>x=\frac{\sinh\frac{a}{k}+x'\cosh\frac{a}{k}}{\cosh\frac{a}{k}+x'\sinh\frac{a}{k}}</math> and <math>y=\frac{y'}{\cosh\frac{a}{k}+x'\sinh\frac{a}{k}}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz transformation ({{equationNote|3e}}), also equivalent to the relativistic velocity addition [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']] by setting <math>\tfrac{a}{k}=\operatorname{atanh}\tfrac{v}{c}</math> and multiplying ''[x,y,x′,y′]'' by 1/''c'', and equivalent to Lorentz boost ({{equationNote|3b}}) by setting <math>\scriptstyle (x,\ y,\ x',\ y')=\left(\frac{x_{1}}{x_{0}},\ \frac{x_{2}}{x_{0}},\ \frac{x_{1}^{\prime}}{x_{0}^{\prime}},\ \frac{x_{2}^{\prime}}{x_{0}^{\prime}}\right)</math>. This is the relation between the [[w:Beltrami–Klein model|Beltrami coordinates]] in terms of Gudermann-Escherich coordinates, and the Weierstrass coordinates of the [[w:hyperboloid model]] introduced by [[../Lorentz transformation (general)#Killing1|E:Killing (1878–1893)]], [[../Lorentz transformation (general)#Poincare|E:Poincaré (1881)]], and [[../Lorentz transformation (general)#Cox|E:Cox (1881)]]. Both coordinate systems were compared by Cox (1881).<ref group=M>Cox (1881), p. 186</ref></p> ==={{anchor|Glaisher}} Glaisher (1878) – hyperbolic addition=== It was shown by [[w:James Whitbread Lee Glaisher]] (1878) that the hyperbolic addition laws can be written as matrix multiplication<ref group=M>Glaisher (1878), p. 30</ref> :<math>\begin{matrix}\begin{vmatrix}\cosh x, & \sinh x\\ \sinh x, & \cosh x \end{vmatrix}=1,\ \begin{vmatrix}\cosh y, & \sinh y\\ \sinh y, & \cosh y \end{vmatrix}=1\\ \left[c_{1},c_{2},c_{3},c_{4}\right]=\left[\cosh x,\cosh y,\sinh x,\sinh y\right]\\ \Rightarrow\begin{vmatrix}c_{1}c_{2}+s_{1}s_{2}, & s_{1}c_{2}+c_{1}s_{2}\\ c_{1}s_{2}+s_{1}c_{2}, & s_{1}s_{2}+c_{1}c_{2} \end{vmatrix}=1\ \Rightarrow\begin{vmatrix}\cosh(x+y), & \sinh(x+y)\\ \sinh(x+y), & \cosh(x+y) \end{vmatrix}=1 \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3c}}).</p> ==={{anchor|Gunther1}} Günther (1880/81) – hyperbolic addition === Following [[#Glaisher|Glaisher (1878)]], [[w:Siegmund Günther]] (1880/81) formulated the hyperbolic addition laws in matrix form as<ref group=M>Günther (1880/81), p. 405</ref> :<math>\begin{matrix}\begin{vmatrix}\mathfrak{Cos}x, & \mathfrak{Sin}x\\ \mathfrak{Sin}x, & \mathfrak{Cos}x \end{vmatrix}\cdot\begin{vmatrix}\mathfrak{Cos}y, & \mathfrak{Sin}y\\ \mathfrak{Sin}y, & \mathfrak{Cos}y \end{vmatrix}\\ =\begin{vmatrix}\mathfrak{Cos}x\mathfrak{Cos}y+\mathfrak{Sin}x\mathfrak{Sin}y, & \mathfrak{Cos}x\mathfrak{Sin}y+\mathfrak{Sin}x\mathfrak{Cos}y\\ \mathfrak{Sin}x\mathfrak{Cos}y+\mathfrak{Cos}x\mathfrak{Sin}y, & \mathfrak{Sin}x\mathfrak{Sin}y+\mathfrak{Cos}x\mathfrak{Cos}y \end{vmatrix}\\ =\begin{vmatrix}\mathfrak{Cos}(x+y), & \mathfrak{Sin}(x+y)\\ \mathfrak{Sin}(x+y), & \mathfrak{Cos}(x+y) \end{vmatrix}=1 \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3c}}).</p> ==={{anchor|Lipschitz1}} Lipschitz (1885/86) === [[w:Rudolf Lipschitz]] (1885/86) formulated transformations leaving invariant the sum of squares <math>x_{1}^{2}+x_{2}^{2}\dots+x_{n}^{2}=y_{1}^{2}+y_{2}^{2}+\dots+y_{n}^{2}</math>, which he rewrote as <math>x_{1}^{2}-y_{1}^{2}+x_{2}^{2}-y_{2}^{2}+\dots+x_{n}^{2}-y_{n}^{2}=0</math>. This led to the problem of finding transformations leaving invariant the pairs <math>x_{a}^{2}-y_{a}^{2}</math> (''a''=1...n) for which he gave the following solution:<ref group=M>Lipschitz (1886), pp. 90–92</ref> :<math>\begin{matrix}x_{a}^{2}-y_{a}^{2}=\mathfrak{x}_{a}^{2}-\mathfrak{y}_{a}^{2}\\ \hline \begin{align}x_{a}-y_{a} & =\left(\mathfrak{x}_{a}-\mathfrak{y}_{a}\right)r_{a}\\ x_{a}+y_{a} & =\left(\mathfrak{x}_{a}+\mathfrak{y}_{a}\right)\frac{1}{r_{a}} \end{align} \quad(a)\\ \hline \begin{matrix}\begin{align}2\mathfrak{x}_{a} & =\left(r_{a}+\frac{1}{r_{a}}\right)x_{a}+\left(r_{a}-\frac{1}{r_{a}}\right)y_{a}\\ 2\mathfrak{y}_{a} & =\left(r_{a}-\frac{1}{r_{a}}\right)x_{a}+\left(r_{a}+\frac{1}{r_{a}}\right)y_{a} \end{align} \quad(b)\end{matrix}\\ \hline \left\{ \begin{matrix}r_{a}=\frac{\sqrt{s_{a}+1}}{\sqrt{s_{a}-1}}\\ s_{a}>1 \end{matrix}\right\}\Rightarrow\begin{align}\mathfrak{x}_{a} & =\frac{s_{a}x_{a}+y_{a}}{\sqrt{s_{a}-1}\sqrt{s_{a}+1}}\\ \mathfrak{y}_{a} & =\frac{x_{a}+s_{a}y_{a}}{\sqrt{s_{a}-1}\sqrt{s_{a}+1}} \end{align} \quad(c) \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">Equation (a) is identical to Lorentz boost ({{equationNote|3d}}), while (c) is similar, though not identical, to Lorentz boost ({{equationNote|3b}}-C). The difference stems from his definition<br><math>\qquad\left\{ \begin{matrix}r_{a}=\frac{\sqrt{s_{a}+1}}{\sqrt{s_{a}-1}}\\ s_{a}>1 \end{matrix}\right\}</math><br>whereas in accordance to expression <math>\sqrt{\tfrac{1+v}{1-v}}</math> in ({{equationNote|3d}}) he should have stated <br><math>\qquad\left\{ \begin{matrix}r_{a}=\frac{\sqrt{1+s_{a}}}{\sqrt{1-s_{a}}}\\ s_{a}<1 \end{matrix}\right\}</math>.<br>Using the latter choice, equations (c) would assume a form equivalent to ({{equationNote|3b}}):<br><math>\qquad\begin{align}\mathfrak{x}_{a} & =\frac{x_{a}+s_{a}y_{a}}{\sqrt{1-s_{a}}\sqrt{1+s_{a}}}\\ \mathfrak{y}_{a} & =\frac{s_{a}x_{a}+y_{a}}{\sqrt{1-s_{a}}\sqrt{1+s_{a}}}\end{align}</math></p> ==={{Anchor|Schur}} Schur (1885/86, 1900/02) – Beltrami coordinates=== [[w:Friedrich Schur]] (1885/86) discussed spaces of constant Riemann curvature, and by following [[#Beltrami|Beltrami (1868)]] he used the transformation<ref group=M>Schur (1885/86), p. 167</ref> :<math>x_{1}=R^{2}\frac{y_{1}+a_{1}}{R^{2}+a_{1}y_{1}},\ x_{2}=R\sqrt{R^{2}-a_{1}^{2}}\frac{y_{2}}{R^{2}+a_{1}y_{1}},\dots,\ x_{n}=R\sqrt{R^{2}-a_{1}^{2}}\frac{y_{n}}{R^{2}+a_{1}y_{1}}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz transformation ({{equationNote|3e}}) and therefore also equivalent to the relativistic velocity addition [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']] in arbitrary dimensions by setting ''R=c'' as the speed of light and ''a₁=v'' as relative velocity.</p> In (1900/02) he derived basic formulas of non-Eucliden geometry, including the case of translation for which he obtained the transformation similar to his previous one:<ref group=M>Schur (1900/02), p. 290; (1909), p. 83</ref> :<math>x'=\frac{x-a}{1-\mathfrak{k}ax},\quad y'=\frac{y\sqrt{1-\mathfrak{k}a^{2}}}{1-\mathfrak{k}ax}</math> where <math>\mathfrak{k}</math> can have values >0, <0 or ∞. <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz transformation ({{equationNote|3e}}) and therefore also equivalent to the relativistic velocity addition [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']] by setting ''a=v'' and <math>\mathfrak{k}=\tfrac{1}{c^{2}}</math>.</p> He also defined the triangle<ref group=M>Schur (1900/02), p. 291; (1909), p. 83</ref> :<math>\frac{1}{\sqrt{1-\mathfrak{k}c^{2}}}=\frac{1}{\sqrt{1-\mathfrak{k}a^{2}}}\cdot\frac{1}{\sqrt{1-\mathfrak{k}b^{2}}}-\frac{a}{\sqrt{1-\mathfrak{k}a^{2}}}\cdot\frac{b}{\sqrt{1-\mathfrak{k}b^{2}}}\cos\gamma</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to the hyperbolic law of cosines and the relativistic velocity addition ({{equationNote|3f}}, b) or [[../Lorentz transformation (velocity)#math_4e|E:'''(4e)''']] by setting <math>[\mathfrak{k},\ c,\ a,\ b]=\left[\tfrac{1}{c^{2}},\ \sqrt{u_{x}^{\prime2}+u_{y}^{\prime2}},\ v,\ \sqrt{u_{x}^{2}+u_{y}^{2}}\right]</math>.</p> ==={{anchor|Lindemann}} Lindemann (1890–91) – Weierstrass coordinates and Cayley absolute=== [[w:Ferdinand von Lindemann]] discussed hyperbolic geometry in terms of the [[w:Cayley–Klein metric]] in his (1890/91) edition of the lectures on geometry of [[w:Alfred Clebsch]]. Citing [[../Lorentz transformation (general)#Killing|E:Killing (1885)]] and [[../Lorentz transformation (general)#Poincare|Poincaré (1887)]] in relation to the hyperboloid model in terms of Weierstrass coordinates for the hyperbolic plane and space, he set<ref group=M>Lindemann & Clebsch (1890/91), pp. 477–478, 524</ref> :<math>\begin{matrix}\Omega_{xx}=x_{1}^{2}+x_{2}^{2}-4k^{2}x_{3}^{2}=-4k^{2}\ \text{and}\ ds^{2}=dx_{1}^{2}+dx_{2}^{2}-4k^{2}dx_{3}^{2}\\ \Omega_{xx}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-4k^{2}x_{4}^{2}=-4k^{2}\ \text{and}\ ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}-4k^{2}dx_{4}^{2} \end{matrix}</math> and used the following transformation<ref group=M>Lindemann & Clebsch (1890/91), pp. 361–362</ref> :<math>\begin{matrix}X_{1}X_{4}+X_{2}X_{3}=0\\ X_{1}X_{4}+X_{2}X_{3}=\Xi_{1}\Xi_{4}+\Xi_{2}\Xi_{3}\\ \hline \begin{align}X_{1} & =\left(\lambda+\lambda_{1}\right)U_{4} & \Xi_{1} & =\left(\lambda-\lambda_{1}\right)U_{4} & X_{1} & =\frac{\lambda+\lambda_{1}}{\lambda-\lambda_{1}}\Xi_{1}\\ X_{2} & =\left(\lambda+\lambda_{3}\right)U_{4} & \Xi_{2} & =\left(\lambda-\lambda_{3}\right)U_{4} & X_{2} & =\frac{\lambda+\lambda_{3}}{\lambda-\lambda_{3}}\Xi_{2}\\ X_{3} & =\left(\lambda-\lambda_{3}\right)U_{2} & \Xi_{3} & =\left(\lambda+\lambda_{3}\right)U_{2} & X_{3} & =\frac{\lambda-\lambda_{3}}{\lambda+\lambda_{3}}\Xi_{3}\\ X_{4} & =\left(\lambda-\lambda_{1}\right)U_{1} & \Xi_{4} & =\left(\lambda+\lambda_{1}\right)U_{1} & X_{4} & =\frac{\lambda-\lambda_{1}}{\lambda+\lambda_{1}}\Xi_{4} \end{align} \end{matrix}</math> into which he put<ref group=M name=linde>Lindemann & Clebsch (1890/91), p. 496</ref> :<math>\begin{align}X_{1} & =x_{1}+2kx_{4}, & X_{2} & =x_{2}+ix_{3}, & \lambda+\lambda_{1} & =\left(\lambda-\lambda_{1}\right)e^{a},\\ X_{4} & =x_{1}-2kx_{4}, & X_{3} & =x_{2}-ix_{3}, & \lambda+\lambda_{3} & =\left(\lambda-\lambda_{3}\right)e^{\alpha i}, \end{align} </math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3d}}) with <math>e^{\alpha i}=1</math> and ''2k=1'' .</p> From that, he obtained the following Cayley absolute and the corresponding most general motion in hyperbolic space comprising ordinary rotations (''a''=0) or translations (α=0):<ref group=M name=linde /> :<math>\begin{matrix}x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-4k^{2}x_{4}^{2}=0\\ \hline \begin{align}x_{2} & =\xi_{2}\cos\alpha+\xi_{3}\sin\alpha, & x_{1} & =\xi_{1}\cos\frac{a}{i}+2ki\xi_{4}\sin\frac{a}{i},\\ x_{3} & =-\xi_{2}\sin\alpha+\xi_{3}\cos\alpha, & 2kx_{4} & =i\xi_{1}\sin\frac{a}{i}+2k\xi_{4}\cos\frac{a}{i}. \end{align} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) with α=0 and ''2k=1''.</p> ==={{anchor|Gerard}} Gérard (1892) – Weierstrass coordinates=== [[w:Louis Gérard]] (1892) – in a thesis examined by Poincaré – discussed Weierstrass coordinates (without using that name) in the plane and gave the case of translation as follows:<ref group=M name=gerard>Gérard (1892), pp. 40–41</ref> :<math>\begin{align}X & =Z_{0}X'+X_{0}Z'\\ Y & =Y'\\ Z & =X_{0}X'+Z_{0}Z' \end{align} \ \text{with}\ \begin{align}X_{0} & =\operatorname{sh}OO'\\ Z_{0} & =\operatorname{ch}OO' \end{align} </math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> ==={{anchor|Killing2}} Killing (1893,97) – Weierstrass coordinates=== [[w:Wilhelm Killing]] (1878–1880) gave case of translation in the form<ref group=M name=killtra>Killing (1893), p. 331</ref> :<math>y_{0}=x_{0}\operatorname{Ch}a+x_{1}\operatorname{Sh}a,\quad y_{1}=x_{0}\operatorname{Sh}a+x_{1}\operatorname{Ch}a,\quad y_{2}=x_{2}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> In 1898, Killing wrote that relation in a form similar to [[#Escherich|Escherich (1874)]], and derived the corresponding Lorentz transformation for the two cases were ''v'' is unchanged or ''u'' is unchanged:<ref group=M name=kill98>Killing (1898), p. 133</ref> :<math>\begin{matrix}\xi'=\frac{\xi\operatorname{Ch}\frac{\mu}{l}+l\operatorname{Sh}\frac{\mu}{l}}{\frac{\xi}{l}\operatorname{Sh}\frac{\mu}{l}+\operatorname{Ch}\frac{\mu}{l}},\ \eta'=\frac{\eta}{\frac{\xi}{l}\operatorname{Sh}\frac{\mu}{l}+\operatorname{Ch}\frac{\mu}{l}}\\ \hline \frac{u}{p}=\xi,\ \frac{v}{p}=\eta\\ \hline p'=p\operatorname{Ch}\frac{\mu}{l}+\frac{u}{l}\operatorname{Sh}\frac{\mu}{l},\quad u'=pl\operatorname{Sh}\frac{\mu}{l}+u\operatorname{Ch}\frac{\mu}{l},\quad v'=v\\ \text{or}\\ p'=p\operatorname{Ch}\frac{\nu}{l}+\frac{v}{l}\operatorname{Sh}\frac{\nu}{l},\quad u'=u,\quad v'=pl\operatorname{Sh}\frac{\nu}{l}+v\operatorname{Ch}\frac{\nu}{l} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">The upper transformation system is equivalent to Lorentz transformation ({{equationNote|3e}}) and the velocity addition [[../Lorentz transformation (velocity)#math_4d|E:'''(4d)''']] with ''l=c'' and <math>\mu=c\operatorname{atanh}\tfrac{v}{c}</math>, the system below is equivalent to Lorentz boost ({{equationNote|3b}}).</p> ==={{anchor|Whitehead}} Whitehead (1897/98) – Universal algebra=== [[w:Alfred North Whitehead]] (1898) discussed the kinematics of hyperbolic space as part of his study of [[w:universal algebra]], and obtained the following transformation:<ref group=M name=white>Whitehead (1898), pp. 459–460</ref> :<math>\begin{align}x' & =\left(\eta\cosh\frac{\delta}{\gamma}+\eta_{1}\sinh\frac{\delta}{\gamma}\right)e+\left(\eta\sinh\frac{\delta}{\gamma}+\eta_{1}\cosh\frac{\delta}{\gamma}\right)e_{1}\\ & \qquad+\left(\eta_{2}\cos\alpha+\eta_{3}\sin\alpha\right)e_{2}+\left(\eta_{3}\cos\alpha-\eta_{2}\sin\alpha\right)e_{3} \end{align} </math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) with α=0.</p> ==={{anchor|Elliott}} Elliott (1903) – Invariant theory === [[w:Edwin Bailey Elliott]] (1903) discussed a special cyclical subgroup of ternary linear transformations for which the (unit) determinant of transformation is resoluble into three ordinary algebraical factors, which he pointed out is in direct analogy to a subgroup formed by the following transformations:<ref group=M>Elliott (1903), p. 109</ref> :<math>\begin{matrix}x=X\cosh\phi+Y\sinh\phi,\quad y=X\sinh\phi+Y\cosh\phi\\ \hline X+Y=e^{-\phi}(x+y),\quad X-Y=e^{\phi}(x-y) \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) and ({{equationNote|3d}}). The mentioned subgroup corresponds to the one-parameter subgroup generated by Lorentz boosts.</p> ==={{anchor|Woods2}} Woods (1903) – Weierstrass coordinates === [[w:Frederick S. Woods]] (1903, published 1905) gave the case of translation in hyperbolic space:<ref group=M>Woods (1903/05), p. 55</ref> :<math>x_{1}^{\prime}=x_{1}\cos kl+x_{0}\frac{\sin kl}{k},\quad x_{2}^{\prime}=x_{2},\quad x_{2}^{\prime}=x_{3},\quad x_{0}^{\prime}=-x_{1}k\sin kl+x_{0}\cos kl</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) with ''k''²=-1.</p> and the loxodromic substitution for hyperbolic space:<ref group=M>Woods (1903/05), p. 72</ref> :<math>\begin{matrix}\begin{align}x_{1}^{\prime} & =x_{1}\cosh\alpha-x_{0}\sinh\alpha\\ x_{2}^{\prime} & =x_{2}\cos\beta-x_{3}\sin\beta\\ x_{3}^{\prime} & =x_{2}\sin\beta+x_{3}\cos\beta\\ x_{0}^{\prime} & =-x_{1}\sinh\alpha+x_{0}\cosh\alpha \end{align} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}) with β=0.</p> ==={{anchor|Liebmann}} Liebmann (1904–05) – Weierstrass coordinates=== [[w:Heinrich Liebmann]] (1904/05) – citing Killing (1885), Gérard (1892), Hausdorff (1899) – gave the case of translation in the hyperbolic plane:<ref group=M name=lieb>Liebmann (1904/05), p. 174</ref> :<math>x_{1}^{\prime}=x'\operatorname{ch}a+p'\operatorname{sh}a,\quad y_{1}^{\prime}=y',\quad p_{1}^{\prime}=x'\operatorname{sh}a+p'\operatorname{ch}a</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> ==={{anchor|Frank}} Frank (1909) – Special relativity=== In special relativity, hyperbolic functions were used by [[w:Philipp Frank]] (1909), who derived the Lorentz transformation using ''ψ'' as rapidity:<ref group=R>Frank (1909), pp. 423-425</ref> :<math>\begin{matrix}x'=x\varphi(a)\,{\rm ch}\,\psi+t\varphi(a)\,{\rm sh}\,\psi\\ t'=-x\varphi(a)\,{\rm sh}\,\psi+t\varphi(a)\,{\rm ch}\,\psi\\ \hline {\rm th}\,\psi=-a,\ {\rm sh}\,\psi=\frac{a}{\sqrt{1-a^{2}}},\ {\rm ch}\,\psi=\frac{1}{\sqrt{1-a^{2}}},\ \varphi(a)=1\\ \hline x'=\frac{x-at}{\sqrt{1-a^{2}}},\ y'=y,\ z'=z,\ t'=\frac{-ax+t}{\sqrt{1-a^{2}}} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> === {{anchor|Herglotz1}} Herglotz (1909/10) – Special relativity=== In special relativity, [[w:Gustav Herglotz]] (1909/10) classified the one-parameter Lorentz transformations as loxodromic, hyperbolic, parabolic and elliptic, with the hyperbolic case being:<ref group=R>Herglotz (1909/10), pp. 404-408</ref> :<math>\begin{matrix}Z=Z'e^{\vartheta}\\ \begin{aligned}x & =x', & t-z & =(t'-z')e^{\vartheta}\\ y & =y', & t+z & =(t'+z')e^{-\vartheta} \end{aligned} \end{matrix}</math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3d}}).</p> ==={{anchor|Varicak}} Varićak (1910) – Special relativity=== In special relativity, hyperbolic functions were used by [[w:Vladimir Varićak]] in several papers starting from 1910, who represented the equations of special relativity on the basis of [[w:hyperbolic geometry]] in terms of Weierstrass coordinates. For instance, by setting ''l=ct'' and ''v/c=tanh(u)'' with ''u'' as rapidity he wrote the Lorentz transformation in agreement with ({{equationNote|4b}}):<ref group=R name=var1>Varićak (1910), p. 93</ref> :<math>\begin{align}l' & =-x\operatorname{sh}u+l\operatorname{ch}u,\\ x' & =x\operatorname{ch}u-l\operatorname{sh}u,\\ y' & =y,\quad z'=z,\\ \operatorname{ch}u & =\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^{2}}} \end{align} </math> <p style="background-color:Beige;border:1px solid black">This is equivalent to Lorentz boost ({{equationNote|3b}}).</p> He showed the relation of rapidity to the [[w:Gudermannian function]] and the [[w:angle of parallelism]]:<ref group=R name=var1 /> :<math>\frac{v}{c}=\operatorname{th}u=\operatorname{tg}\psi=\sin\operatorname{gd}(u)=\cos\Pi(u)</math> He also related the velocity addition to the [[w:hyperbolic law of cosines]]:<ref group=R>Varićak (1910), p. 94</ref> :<math>\begin{matrix}\operatorname{ch}{u}=\operatorname{ch}{u_{1}}\operatorname ch{u_{2}}+\operatorname{sh}{u_{1}}\operatorname{sh}{u_{2}}\cos\alpha\\ \operatorname{ch}{u_{i}}=\frac{1}{\sqrt{1-\left(\frac{v_{i}}{c}\right)^{2}}},\ \operatorname{sh}{u_{i}}=\frac{v_{i}}{\sqrt{1-\left(\frac{v_{i}}{c}\right)^{2}}}\\ v=\sqrt{v_{1}^{2}+v_{2}^{2}-\left(\frac{v_{1}v_{2}}{c}\right)^{2}}\ \left(a=\frac{\pi}{2}\right) \end{matrix}</math> ==References== ===Historical mathematical sources=== {{reflist|3|group=M}} *{{#section:History of Topics in Special Relativity/mathsource|bel68sag}} *{{#section:History of Topics in Special Relativity/mathsource|bel68fond}} *{{#section:History of Topics in Special Relativity/mathsource|cox81hom}} *{{#section:History of Topics in Special Relativity/mathsource|cox82hom}} *{{#section:History of Topics in Special Relativity/mathsource|eli03}} *{{#section:History of Topics in Special Relativity/mathsource|esch74}} *{{#section:History of Topics in Special Relativity/mathsource|eul35}} *{{#section:History of Topics in Special Relativity/mathsource|eul48a}} *{{#section:History of Topics in Special Relativity/mathsource|ger92}} *{{#section:History of Topics in Special Relativity/mathsource|glai78}} *{{#section:History of Topics in Special Relativity/mathsource|gud30}} *{{#section:History of Topics in Special Relativity/mathsource|guen80}} *{{#section:History of Topics in Special Relativity/mathsource|kep09}} *{{#section:History of Topics in Special Relativity/mathsource|kil93}} *{{#section:History of Topics in Special Relativity/mathsource|kil97}} *{{#section:History of Topics in Special Relativity/mathsource|lag70}} *{{#section:History of Topics in Special Relativity/mathsource|lais74b}} *{{#section:History of Topics in Special Relativity/mathsource|lam67}} *{{#section:History of Topics in Special Relativity/mathsource|lam70}} *{{#section:History of Topics in Special Relativity/mathsource|lieb04}} *{{#section:History of Topics in Special Relativity/mathsource|lind90}} *{{#section:History of Topics in Special Relativity/mathsource|lip86}} *{{#section:History of Topics in Special Relativity/mathsource|ric57}} *{{#section:History of Topics in Special Relativity/mathsource|schu85}} *{{#section:History of Topics in Special Relativity/mathsource|schu00}} *{{#section:History of Topics in Special Relativity/mathsource|schu09}} *{{#section:History of Topics in Special Relativity/mathsource|tau26}} *{{#section:History of Topics in Special Relativity/mathsource|whit98}} *{{#section:History of Topics in Special Relativity/mathsource|woo01}} *{{#section:History of Topics in Special Relativity/mathsource|woo03}} ===Historical relativity sources=== {{reflist|3|group=R}} *{{#section:History of Topics in Special Relativity/relsource|frank09a}} *{{#section:History of Topics in Special Relativity/relsource|herg10}} *{{#section:History of Topics in Special Relativity/relsource|var10}} *{{#section:History of Topics in Special Relativity/relsource|var12}} ===Secondary sources=== {{reflist|3}} {{#section:History of Topics in Special Relativity/secsource|L3}} [[Category:Special Relativity]] [[Category:History of Physics]] h1pfxqt2h7vdpdz3qwokfqfrux7l0hr 0 268193 2412388 2372762 2022-08-06T16:23:44Z Saltrabook 1417466 /* Methods */ wikitext text/x-wiki [https://es.wikiversity.org/wiki/GHQ12-protocolo ->Español] == GHQ12-cohort protocol == The psycho-social study environment in the maritime universities and on board the ships. <br> ==ABSTRACT== ====Background==== Stress among students is well known but a suspected excess study related to stress and the GHQ12 has not so far been used to evaluate the stress among maritime students. The GHQ12 survey in the maritime schools completes part of the diagnostics of a global mental health program at the schools and workplaces, also related to the WHO program: [https://learningportal.iiep.unesco.org/en/library/the-who-health-promoting-school-framework-for-improving-the-health-and-well-being-of?back_url=/en/library/search/occupational%20health%20research The WHO health promoting school-framework for improving the health and well being]. ====Objectives==== =====For the maritime students===== To evaluate the well-being of the maritime students and the evaluation of the precautions taken by the maritime schools =====For the seafarers===== To evaluate the well-being of the seafarers and the evaluation of the precautions taken by the shipping companies. It is very important to correctly assess the stress risk of these sea workers. In fact, the role of the bio-humoral influences of stress on the immune system and not only on the psychological structure of workers and therefore on the organization of work is well known. ====Methods==== A sample of seafarers is asked to complete the General Health Questionnaire (GHQ) and to evaluate the stress precautions taken on board. This is a pilot study and lays the foundations for further larger studies, always based on questionnaires, or even on other methods of assessing work-related stress, also with the search for laboratory-level stress markers. ====Expected results==== Seafarers have increased work-related stress levels compared to shore workers due to the specific work situation. However, we expect that someone needs more support, not only in terms of security measures but also on a psychological level. if the situation of excess risk-related work stress is confirmed, it would be interesting in the future to investigate the stress of mariners also from a bio-humoral point of view to have a more objective point of view. There is a need to integrate stress prevention in the maritime universities and these surveys will be part of the learning program. == BACKGROUND == This protocol under development is intended to be used as a standard protocol for the completion of the GHQ12 cross-sectional studies in MAHRE-NET. The GHQ12 survey in the maritime schools is part of the diagnostics in a global mental health program at the maritime workplaces [https://www.dropbox.com/s/y2dhnx9e2pnhpyf/2017%20The%20global%20mental%20health%20IJCFM-134.pdf?dl=0 Jensen O, Canals M & A Bygvraa D. 2017] and [https://www.dropbox.com/s/aa1lmtf4juxws17/2019%20Mental%20health%20promotion%20program%20apmh-aid1004-F.pdf?dl=0 Jensen et al. 2019] The seafaring employees often face more difficult working conditions in the sea than the employees working on the land. Their mental health is affected by the environment in which they live, often coupled with long working hours that contribute to stress, anxiety, loneliness, depression, and suicide. This proposal seeks to improve the seafarers’ mental health by introducing a comprehensive, evidence-based global maritime mental health promotion program that attracts the youngest seafarers to choose and to stay in the job. Methods: The theories on empowerment, life-long- and problem-oriented learning with the inclusion of all stakeholders form the theoretical background. Our main task is to create responsibility among all stakeholders to help to create a comprehensive occupational- and public health program at sea that includes the whole maritime industry. The specific physical, chemical and psychological working environment factors on board also relate to the seafarer's health conditions (1)(2)(3). The quality of the mental work environment is dependent on several factors which have been carefully described in the past approx. 30 years (4) (5) (1). Ships with ongoing replacement of crew present great challenges for both the manager and the employees and the culture at the workplace (6). During navigation, the sailors are often moved to very small working groups, where conflict management can be difficult. The requirements are very variable, the nature of the work requires considerable discipline and thus less self-control. Support from superiors and colleagues can be made difficult by the fact that crews come from many different nationalities. These conditions can lead to experienced stress and burnout (7) (1). Fatigue is considered a significant health and safety problem [14]. Jet lag after long flights for joining is described as part of this (8). (12) In the latest research Helen Sampson, director of Cardiff University's Seafarers International Research Centre, said that seafarers working on cargo ships "experience very little happiness on board". (9) She said there was evidence recent-onset psychological disorders were increasing among serving seafarers but 55% of employers said they had not introduced any policies or practices to address mental health for a decade. Seafarers' mental health and well-being found that internet access would make the most significant contribution to improving mental health and well-being together with other key recommendations underscored in the report and the BBC News (Seafarers Mental Health and Well-being Nov. 2019). Jensen and Oldenburg conclude that because of many stressors on board, and the lacking respective education, there is a strong need to integrate stress management in the maritime educations especially for officers <ref>Jensen H-J, Oldenburg M. Training seafarers to deal with multicultural crew members and stress on board. International maritime health. 2020;71(3):174–180. </ref> Guidelines for prevention https://www.copsoq-network.org/assets/Uploads/COPSOQ-network-guidelines-an-questionnaire-COPSOQ-III-131119-signed.pdf Authors "soft guidelines" page 7, start with: "Never start a psychosocial risk assessment unless there is a clear intention of taking action if indicated". The psychological stress in seafarers resulting from the Covid pandemic has already been investigated by our MAHRE group with GHQ 12 test. In a small pilot study, it emerged that the category of seafarers did not suffer additional stress from the international situation and that they feel safe at work (10). =====For the schools===== The European community underscores the need to take more attention to mental health in all parts of the communities. For the youth and the adults the policy recommendations include <ref> https://ec.europa.eu/health/sites/health/files/mental_health/docs/2017_mh_schools_en.pdf </ref> 1. Strengthen information and research on mental health and well-being among children and adolescents. a. Establish a solid information base to have a detailed epidemiological frame of the mental health among children and adolescents and evidence on interventions. b. Provide information on coverage and outcomes of interventions, including for groups at higher risk as well as on the size, impact, cost, and potential economic savings of appropriate interventions. c. Carry out a mapping and analysis of existing screening tools for early identification, from the first developmental stages, of mental health disorders and poor well-being among children and school populations. d. Examine the potential to increase access to information and services through the use of web-based technologies (e-mental health) to promote mental well-being and the prevention of mental and behavioral disorders. The surveys in the maritime schools complete part of the diagnostics of a global mental health program at the schools and workplaces in the WHO health-promoting school-framework for improving the health and well being<ref> [https://learningportal.iiep.unesco.org/en/library/the-who-health-promoting-school-framework-for-improving-the-health-and-well-being-of?back_url=/en/library/search/occupational%20health%20research The WHO health-promoting school-framework for improving the health and well being]</ref>,<ref>https://pubmed.ncbi.nlm.nih.gov/24737131/</ref> <ref>https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-015-1360-y</ref> == Objectives == To provide systematic and current knowledge about the psychosocial working environment for students at the maritime universities. To use scientific methods that are well tested on land and which are supposed to be useful on the ships and thus can ensure relevant and valid results. == Scientific aims == The aim is to help to create an evidence-based Health Promotion Program for maritime workers and the schools. The goal is for everyone to benefit from the project, both for the seafarers and for the company. The project focuses on good psycho-social wellbeing at the University, onboard and in the company with the benefits for all parties the students, teachers, workers, shipping companies, and the community. The scientific aim is to produce data and publications that convey new knowledge of high validity based on the newest scientific principles for the conduct of studies in peer-reviewed publications. ==Occupational stress and depression etiological models== Due to the high prevalence and severe consequences, stress and depressive disorders provide an important challenge to occupational and public health. The literature about etiological models for the development of occupational stress and depression is scarce specifically for GHQ12. More in general for occupational stress and depression, the classical model is the Karasek job control and demand model<ref>Hatami, Ali, Shahram Vosoughi, Agha F. Hosseini, and Hossein Ebrahimi. ‘Effect of Co-Driver on Job Content and Depression of Truck Drivers’. Safety and Health at Work 10, no. 1 (March 2019): 75–79 https://doi.org/10.1016/j.shaw.2018.06.001</ref> Occupational stress and depression has been described in terms of an interaction between the predisposing, precipitating, and perpetuating factors <ref>Kumar, Shailesh, Simon Hatcher, and Peter Huggard. ‘Burnout in Psychiatrists: An Etiological Model’. International Journal of Psychiatry in Medicine 35, no. 4 (2005): 405–16. https://doi.org/10.2190/8XWB-AJF4-KPRR-LWMF </ref>. Danasekaran, Raja, and Ravivarman Govindasamy have given a list of suspected etiological risk factors for anxiety and depression <ref>Danasekaran, Raja, and Ravivarman Govindasamy. ‘Better Psychosocial Work Environment: For Well-Being of the Worker and the Organization’. Indian Journal of Occupational and Environmental Medicine 23, no. 1 (2019): 57–58. https://doi.org/10.4103/ijoem.IJOEM_183_18 </ref> According to Siegrist chronic psychosocial stress at work, demand-control, and effort-reward imbalance, is a modifiable risk factor. Findings from 12 reports indicate a rather consistently elevated odds ratio of about 1.8 of depression among men and women who were exposed to high demand and low control at work or who spent high efforts in combination with low rewards received in turn<ref>Johannes Siegrist European archives of psychiatry and clinical neuroscience 258 (5), 115-119, 2008</ref>. == Methods== An epidemiological, cross-sectional-based study will be performed by the use of mail distributed general Health Questionnaires (GHQ12) are used. The content of the questionnaires is demographic information about the person, questions about the psychosocial work environment, about the way your work affects your private life and family, It is in line with the Danish Maritime Leaders' wishes. Maritime Schools are invited to participate. Standardized questionnaires are sent to the students about smoking, alcohol, mental health, bullying, sexual harassment and suggestions for improving of the education. The students can use it as their final study thesis. The managers can together with the students, use the results to propose concrete improvements to the education and contribute to creating interest among young people in entering the maritime profession. The same model can be used on the ships. If the survey seems to indicate problems with the psychosocial work environment, the work environment committee or other relevant actors at the university should discuss how to act on the basis of the results. If help from the outside is needed, the workplace may contact consultants, the Labour Inspection, or relevant organizations. [https://docs.google.com/forms/d/1HgdA6yBIdQ567ydHjxc5RLo66p9ihwah4kML0vCdR5A/edit GHQ12 For maritime students] [https://docs.google.com/forms/d/1rSGz_J7VuZfV8jT9gHSFVcgQNqt2_VfPCFvhtvHR6LY/edit GHQ12 For seafarers and practicants] == Pilot studies == A pilot study is carried out among 20 students in each of the participating maritime universities == Long-term follow-up of the cohort == After a successful baseline study, follow-up will be done in 1-4-year intervals of the same participants. A low participation rate can be a problem. Further, the aim is to collaborate with other countries. Iceland that have shown interest for the same type of study. An identical questionnaire will be used with the possibility to compare between the countries. == Data processing == Data is transferred to electronic processing during the investigation. Standardized statistical methods will be used using the latest data processing SPSS program. Data will be handled under strict confidentiality in an anonymous form. All data will be stored in a special database to use data up following studies later. The current legislation is complied with. == Data analysis == Each of the Goldberg’s General Health Questionnaire (GHQ12) items has four answer options: 1) more than usual, 2) as usual, 3) less than usual, and 4) much less than usual describing mood states. Using the Likert code method 0-1-2-3 gives a total score range of 0–36. The Likert sum scores were classified as 0–14 (no problems), 15–19 (starting problems), and 19–36 (serious problems). Analyses of the Likert scores can be divided into two groups: group 1: Likert score 0–14 no problems, (no action needed) and group 2: Likert score 15–19 starting problems (included 2 with Likert score 20–36: serious problem).<ref>Giuliano Pesel, Maria Luisa Canals, Matteo Sandrin, Olaf Jensen Wellbeing of a selection of seafarers in Eastern Adriatic Sea during the COVID-19 pandemic 2020 Giuliano Pesel, Maria Luisa Canals, Matteo Sandrin, Olaf Jensen DOI: 10.5603/IMH.2020.0033·Pubmed: 33001430·International Maritime Health 2020;71(3):184-190 https://journals.viamedica.pl/international_maritime_health/article/view/IMH.2020.0033</ref> Cut-off-point of Likert scores for the GHQ-12 has been proposed in mental health studies of working people. The optimal cut-off points that can serve as a tool for identifying persons with a mental disorder were established at the level of 2/3 points for GHQ-12 <ref>Makowska, Zofia, Dorota Meretz, Agnieszka Mościcka, and Wojciech Kolasa. ‘The Validity of General Health Questionnaires, GHQ-12, and GHQ-28, in Mental Health Studies of Working People’. International Journal of Occupational Medicine and Environmental Health 15, no. 4 (2002): 353–62 </ref> The explanation is that 2/3 of maximum scores = 36 in the Likert code method 0-1-2-3 with a cut-off point of 24. Lundin et al. y Pesel et al. estimated the beginning of problems at 12+ and 14+, respectively<ref>Lundin, A., M. Hallgren, H. Theobald, C. Hellgren, and M. Torgén. ‘Validity of the 12-Item Version of the General Health Questionnaire in Detecting Depression in the General Population. Public Health 136 (July 2016): 66–74. https://doi.org/10.1016/j.puhe.2016.03.005.</ref> <ref>Pesel, Giuliano, Maria Luisa Canals, Matteo Sandrin, and Olaf Jensen. ‘Wellbeing of a Selection of Seafarers in Eastern Adriatic Sea during the COVID-19 Pandemic 2020’. International Maritime Health 71, no. 3 (2020): 184–90. https://doi.org/10.5603/IMH.2020.0033</ref> Excel methods to recode the questions <ref>https://www.dropbox.com/s/tvn59dnghigwby6/olafGHQ12%20%20Recode%20repsonses%20example.xlsx?dl=0</ref> == Ethical requirements == Since the study does not involve blood sampling, and since participation in the study is completely voluntary after informed consent, the study does not involve ethical problems. All data are treated according to the Act on the duty of confidentiality, and the guidelines for good epidemiological practice will be followed. The participants' anonymity will be ensured in all ways and this will be apparent from the project description and the form. It will be ensured that the electronic form is locked so that the information cannot be seen by anyone other than the researchers. [https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET#Ethical_requirements More detailed information] [https://www.sdu.dk/da/om_sdu/fakulteterne/sundhedsvidenskab/om_sund/gdpr_sund SDU Guide for data safety ] == Dissemination of results == The students finish his/her Thesis which will also be handed over to the UMIP. The results will also be presented in the Maritime News and at conferences and be available on relevant websites from e.g. In case the student wants to go further support to write a scientific article will be given. == Work plan == # Agreement with the universities and the students # Questionnaire translations and development # Pilot test # Mail lists # Mail send out with link to the questionnaire # Data analysed and tables ready # Thesis prepared (and possibly an article) # Prevention plan == References == 78t31nwlm0ilwdxphgs71c5go8mef5o 0 271693 2412469 2412324 2022-08-07T03:10:09Z 2402:7500:942:36DD:9962:A44F:536A:30BC /* Unsolved families */ wikitext text/x-wiki A '''quasi-minimal prime''' is a [[w:Prime number|prime number]] for which there is no shorter [[w:Subsequence|subsequence]] of its [[w:Numerical digit|digit]]s in a given [[w:Radix|base]] ''b'' that form a prime > ''b''. For example, 857 is a quasi-minimal prime in [[w:Decimal|decimal]] because there is no prime > 10 among the shorter subsequences of the digits: 8, 5, 7, 85, 87, 57. The subsequence does not have to consist of consecutive digits, so 149 is not a quasi-minimal prime in decimal (because 19 is prime and 19 > 10). But it does have to be in the same order; so, for example, 991 is still a quasi-minimal prime in decimal even though a subset of the digits can form the shorter prime 19 > 10 by changing the order. (using A−Z to represent digit values 10 to 35) For the quasi-minimal primes in bases up to 36, I have only solved (found all quasi-minimal primes and proved that these are all such primes) bases 2~12, 14~15, 18, 20, 22, 24, 30 (bases 11, 22, 30 need primality proving of the probable primes). For the remain bases 13, 16~17, 19, 21, 23, 25~29, 31~36, there are some ''x''{''d''}''y'' (with ''x'', ''y'' strings (may be [[w:Empty string|empty]]) with digits in base ''b'', ''d'' digit in base ''b'') families which are not solved (not even a probable prime is known nor can be ruled out as only contain composites (only count the numbers > base (''b'')). I left as a challenge to readers the task of solving (finding all quasi-minimal primes and proving that these are all such primes) bases 13, 16~17, 19, 21, 23, 25~29, 31~36 (this will be a hard problem, e.g. base 23 has a quasi-minimal prime 9E₈₀₀₈₇₃, and base 36 has quasi-minimal prime P₈₁₉₉₃SZ). Proving the set of the quasi-minimal primes in base ''b'' is ''S'', is equivalent to: * Prove that all elements in ''S'', when read as base ''b'' representation, are primes > ''b''. * Prove that all [[w:Proper subset|proper]] subsequence of all elements in ''S'', when read as base ''b'' representation, which are > ''b'', are composite. * Prove that all primes > ''b'', when written in base ''b'', contain at least one element in ''S'' as subsequence (equivalently, prove that all strings not containing any element in ''S'' as subsequence, when read as base ''b'' representation, which are > ''b'', are composite). e.g. proving the set of the quasi-minimal primes in base ''b'' = 10 is {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}, is equivalent to: * Prove that all of 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 are primes > 10. * Prove that all proper subsequence of all elements in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} which are > 10 are composite. * Prove that all primes > 10 contain at least one element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence (equivalently, prove that all numbers > 10 not containing any element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence are composite). ==Condensed table== {|class=wikitable |''b''||number of quasi-minimal primes base ''b''||base-''b'' form of largest known quasi-minimal prime base ''b''||length of largest known quasi-minimal prime base ''b''||algebraic ((''a''×''b''^''n''+''c'')/''d'') form of largest known quasi-minimal prime base ''b'' |- |2||1||11||2||3 |- |3||3||111||3||13 |- |4||5||221||3||41 |- |5||22||10₉₃13||96||5⁹⁵+8 |- |6||11||40041||5||5209 |- |7||71||3₁₆1||17||(7¹⁷−5)/2 |- |8||75||4₂₂₀7||221||(4×8²²¹+17)/7 |- |9||151||30₁₁₅₈11||1161||3×9¹¹⁶⁰+10 |- |10||77||50₂₈27||31||5×10³⁰+27 |- |11^*||1068||57₆₂₆₆₈||62669||(57×11⁶²⁶⁶⁸−7)/10 |- |12||106||40₃₉77||42||4×12⁴¹+91 |- |13^*||3195~3197||80₃₂₀₁₇111||32021||8×13³²⁰²⁰+183 |- |14||650||4D₁₉₆₉₈||19699||5×14¹⁹⁶⁹⁸−1 |- |15||1284||7₁₅₅97||157||(15¹⁵⁷+59)/2 |- |16^*||2346~2347||4₇₂₇₈₅DD||72787||(4×16⁷²⁷⁸⁷+2291)/15 |- |17^*||10409~10428||F70₁₈₆₇₆₇1||186770||262×17¹⁸⁶⁷⁶⁸+1 |- |18||549||C0₆₂₆₈C5||6271||12×18⁶²⁷⁰+221 |- |20||3314||G0₆₂₆₉D||6271||16×20⁶²⁷⁰+13 |- |21^*||13375~13395||CF₄₇₉₁₄₇0K||479150||(51×21⁴⁷⁹¹⁴⁹−1243)/4 |- |22^*||8003||BK₂₂₀₀₁5||22003||(251×22²²⁰⁰²−335)/21 |- |24||3409||N00N₈₁₂₉LN||8134||13249×24⁸¹³¹−49 |- |30^*||2619||OT₃₄₂₀₅||34206||25×30³⁴²⁰⁵−1 |- |36^*||35257~35263||P₈₁₉₉₃SZ||81995||(5×36⁸¹⁹⁹⁵+821)/7 |} ^* Data assumes the primality of the [[w:probable prime|probable prime]]s. Except bases ''b'' = 13, 16, 17, 21, all bases in this table are completely solved (if we allow strong probable primes > 10²⁵⁰⁰⁰), also, except bases ''b'' = 11, 13, 16, 17, 21, 22, 30, 36, all bases in this table are completely solved even if we only allow definitely primes (thus, we can complete the classification of the quasi-minimal primes in these bases, i.e. the “quasi-minimal problems” in these bases are now theorems), for the quasi-minimal primes see the data below. Base ''b'' = 13 has 3195 known quasi-minimal primes (or PRPs), see the data below, and if there are more quasi-minimal primes in base 13, then they must be of the form 9{5} or A{3}A (we are unable to determine if these two families contain a prime or not, i.e. these two families have no known prime members, nor can these two families be ruled out as only containing composites), and must have at least 111000 digits in base 13, besides, since these two families can contain at most one quasi-minimal prime, there are at most 3197 quasi-minimal primes in base 13. (i.e. the quasi-minimal primes in base 13 are the 3195 known quasi-minimal primes in base 13 (they are given in the data section) plus the smallest prime in the family 9{5} in base 13 (if exists) plus the smallest prime in the family A{3}A in base 13 (if exists)) Base ''b'' = 16 has 2346 known quasi-minimal primes (or PRPs), see the data below, and if there are more quasi-minimal primes in base 16, then they must be of the form {3}AF (we are unable to determine if this family contains a prime or not, i.e. this family have no known prime members, nor can this family be ruled out as only containing composites), and must have at least 98000 digits in base 16, besides, since this family can contain at most one quasi-minimal prime, there are at most 2347 quasi-minimal primes in base 16. (i.e. the quasi-minimal primes in base 16 are the 2346 known quasi-minimal primes in base 16 (they are given in the data section) plus the smallest prime in the family {3}AF in base 16 (if exists)) ==Data for quasi-minimal primes== ===Base 2=== 11 ===Base 3=== 12, 21, 111 ===Base 4=== 11, 13, 23, 31, 221 ===Base 5=== 12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013 ===Base 6=== 11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041 ===Base 7=== 14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331 ===Base 8=== 13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 ===Base 9=== 12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011 ===Base 10=== 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 ===Base 11=== 12, 16, 18, 21, 27, 29, 34, 38, 3A, 43, 49, 54, 56, 61, 65, 67, 72, 76, 81, 89, 92, 94, 98, 9A, A3, 10A, 115, 117, 133, 139, 153, 155, 171, 193, 197, 199, 1AA, 225, 232, 236, 25A, 263, 315, 319, 331, 335, 351, 353, 362, 373, 379, 391, 395, 407, 414, 452, 458, 478, 47A, 485, 4A5, 4A7, 502, 508, 511, 513, 533, 535, 539, 551, 571, 579, 588, 595, 623, 632, 70A, 711, 715, 731, 733, 737, 755, 759, 775, 791, 797, 7AA, 803, 847, 858, 85A, 874, 885, 887, 913, 919, 931, 937, 957, 959, 975, 995, A07, A1A, A25, A45, A74, A7A, A85, AA1, AA7, 1101, 11A9, 1305, 1451, 1457, 15A7, 175A, 17A5, 17A9, 2023, 2045, 2052, 2083, 20A5, 2333, 2A05, 2A52, 3013, 3026, 3059, 3097, 3206, 3222, 3233, 3307, 3332, 3505, 4025, 4151, 4157, 4175, 4405, 4445, 4487, 450A, 4575, 5017, 5031, 5059, 5075, 5097, 5099, 5105, 515A, 517A, 520A, 5301, 5583, 5705, 577A, 5853, 5873, 5909, 5A17, 5A57, 5A77, 5A8A, 6683, 66A9, 7019, 7073, 7079, 7088, 7093, 7095, 7309, 7451, 7501, 7507, 7578, 757A, 75A7, 7787, 7804, 7844, 7848, 7853, 7877, 78A4, 7A04, 7A57, 7A79, 7A95, 8078, 8245, 8333, 8355, 8366, 8375, 8425, 8553, 8663, 8708, 8777, 878A, 8A05, 9053, 9101, 9107, 9305, 9505, 9703, A052, A119, A151, A175, A515, A517, A575, A577, A5A8, A719, A779, A911, AAA9, 10011, 10075, 10091, 10109, 10411, 10444, 10705, 10709, 10774, 10901, 11104, 11131, 11144, 11191, 1141A, 114A1, 13757, 1411A, 14477, 144A4, 14A04, 14A11, 17045, 17704, 1774A, 17777, 177A4, 17A47, 1A091, 1A109, 1A114, 1A404, 1A411, 1A709, 20005, 20555, 22203, 25228, 25282, 25552, 25822, 28522, 30037, 30701, 30707, 31113, 33777, 35009, 35757, 39997, 40045, 4041A, 40441, 4045A, 404A1, 4111A, 411A1, 42005, 44401, 44474, 444A1, 44555, 44577, 445AA, 44744, 44A01, 47471, 47477, 47701, 5057A, 50903, 5228A, 52A22, 52A55, 52A82, 55007, 550A9, 55205, 55522, 55557, 55593, 55805, 57007, 57573, 57773, 57807, 5822A, 58307, 58505, 58A22, 59773, 59917, 59973, 59977, 59999, 5A015, 5A2A2, 5AA99, 60836, 60863, 68636, 6A609, 6A669, 6A696, 6A906, 6A966, 70048, 70103, 70471, 70583, 70714, 71474, 717A4, 71A09, 74084, 74444, 74448, 74477, 744A8, 74747, 74774, 7488A, 74A48, 75773, 77144, 77401, 77447, 77799, 77A09, 78008, 78783, 7884A, 78888, 788A8, 79939, 79993, 79999, 7A051, 7A444, 7A471, 80005, 80252, 80405, 80522, 80757, 80AA5, 83002, 84045, 85307, 86883, 88863, 8A788, 90073, 90707, 90901, 95003, 97779, 97939, 99111, 99177, 99973, A0111, A0669, A0966, A0999, A0A09, A1404, A4177, A4401, A4717, A5228, A52AA, A5558, A580A, A5822, A58AA, A5A59, A5AA2, A6096, A6966, A6999, A7051, A7778, A7808, A9055, A9091, A9699, A9969, AA52A, AA58A, 100019, 100079, 101113, 101119, 101911, 107003, 140004, 144011, 144404, 1A0019, 1A0141, 1A5001, 1A7005, 1A9001, 222223, 222823, 300107, 300202, 300323, 303203, 307577, 310007, 332003, 370777, 400555, 401A11, 404001, 404111, 405AAA, 41A011, 440A41, 441011, 451777, 455555, 470051, 470444, 474404, 4A0401, 4A4041, 500015, 500053, 500077, 500507, 505577, 522A2A, 525223, 528A2A, 531707, 550777, 553707, 5555A9, 555A99, 557707, 55A559, 5807A7, 580A0A, 580A55, 58A0AA, 590007, 599907, 5A2228, 5A2822, 5A2AAA, 5A552A, 5AA22A, 5AAA22, 60A069, 683006, 6A0096, 6A0A96, 6A9099, 6A9909, 700778, 701074, 701777, 704408, 704417, 704457, 704484, 707041, 707441, 707708, 707744, 707784, 710777, 717044, 717077, 740008, 74484A, 770441, 770744, 770748, 770771, 777017, 777071, 777448, 777484, 777701, 7778A8, 777A19, 777A48, 778883, 78A808, 790003, 7A1009, 7A4408, 7A7708, 80A555, 828283, 828883, 840555, 850505, 868306, 873005, 883202, 900701, 909739, 909979, 909991, 970771, 977701, 979909, 990739, 990777, 990793, 997099, 999709, 999901, A00009, A00599, A01901, A05509, A0A058, A0A955, A10114, A555A2, A55999, A59991, A5A222, A5A22A, A60609, A66069, A66906, A69006, A79005, A87888, A90099, A90996, A96006, A96666, A97177, A97771, AA0A58, AA5A22, AAA522, 1000501, 1011141, 1030007, 1070047, 111114A, 1111A14, 1111A41, 1144441, 14A4444, 1700005, 1700474, 1A44444, 2555505, 2845055, 3030023, 3100003, 3333397, 4000111, 4011111, 41A1111, 4411111, 444441A, 4444771, 4470004, 4505005, 4744417, 4774441, 4777404, 4777417, 4777747, 4A11111, 4A40001, 5000093, 50005A7, 5005777, 5050553, 5055503, 5070777, 5222222, 5222AAA, 52AAAA2, 52AAAAA, 5505053, 5552AAA, 5555599, 5555A58, 5558A0A, 5558A55, 5558AAA, 55A0009, 55AAA52, 580000A, 5822222, 58AAAAA, 5A2222A, 5AA2222, 6000A69, 6000A96, 6A00069, 7000417, 7000741, 7000835, 7000857, 7007177, 7008305, 7014447, 7017444, 7074177, 7077477, 7077741, 7077747, 7100447, 7174404, 717444A, 7400404, 7700717, 7701077, 7701707, 7707778, 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DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD ===Base 15=== 12, 14, 18, 1E, 21, 27, 2B, 2D, 32, 38, 3E, 41, 47, 4B, 4D, 54, 58, 5E, 67, 6B, 6D, 72, 74, 78, 87, 8B, 92, 94, 9E, A1, A7, AD, B2, B8, BE, C1, CB, CD, D2, D4, E1, ED, 111, 11B, 131, 137, 13B, 13D, 157, 15B, 15D, 171, 177, 197, 19D, 1B7, 1BB, 1D1, 1DB, 1DD, 234, 298, 311, 31B, 337, 33D, 344, 351, 357, 35B, 364, 377, 391, 39B, 39D, 3A4, 3BD, 3C4, 3D7, 3DB, 3DD, 452, 51B, 51D, 531, 53B, 551, 55D, 562, 571, 577, 5A2, 5B1, 5B7, 5BB, 5BD, 5C2, 5D1, 5D7, 634, 652, 681, 698, 717, 71B, 731, 737, 757, 75D, 77D, 79B, 79D, 7B1, 7B7, 7BD, 7D7, 7DD, 801, 852, 88D, 8D8, 91D, 93B, 93D, 95B, 95D, 971, 977, 97B, 97D, 988, 991, 9BD, 9C8, 9D1, A98, AAB, B1D, B31, B3B, B44, B51, B57, B7B, B7D, B97, B9B, BB7, BC4, BD1, BD7, BDD, C07, C34, C52, C7E, C98, CC7, CE7, D0E, D1D, D31, D51, D5B, D68, D77, D7B, D91, D97, DA8, DAE, DCE, DD1, EB4, EEB, 107B, 1091, 10B1, 1107, 110D, 1561, 1651, 1691, 1B01, 2052, 2502, 2522, 303B, 307D, 3097, 30BB, 30D1, 3107, 3361, 3701, 3907, 3B01, 3B0B, 3C97, 4434, 4498, 4834, 4898, 49A8, 4E34, 5037, 507D, 5091, 509B, 5107, 5161, 5202, 53C7, 5552, 570B, 590B, 590D, 59C7, 5A5B, 5C97, 5D0D, 5DAB, 6061, 6151, 6191, 6511, 6601, 6911, 707B, 7091, 7097, 70AE, 70BB, 70CE, 70DB, 7561, 760E, 7691, 76CE, 7907, 7961, 7A0E, 7A3B, 7AEE, 7B0B, 7BAB, 7C0E, 7C77, 7CAE, 7D0B, 7D61, 7DAB, 7E5B, 7E6E, 7E7B, 7EBB, 8098, 811D, 8191, 835D, 853D, 8881, 8908, 8951, 8968, 899D, 8D3D, 8D5D, 8D6E, 8DDD, 8E98, 9011, 9037, 9097, 90D7, 9301, 93C7, 95C7, 9611, 9631, 96A8, 9811, 9851, 989D, 990B, 990D, 998D, 99AB, 99C7, 99D8, 9A08, 9A9B, 9AA8, 9ABB, 9B61, 9BC7, 9D0B, 9DAB, 9DC7, 9DD8, A052, A304, A502, A55B, A9BB, AB04, AB64, B09D, B107, B10B, B161, B1AB, B1C7, B30D, B3C7, B50B, B664, B691, B6A4, B707, B761, B90D, B961, BA5B, BABB, BBAB, BBB4, BC37, BC77, C777, C937, C997, D011, D03D, D05D, D09B, D0B1, D0BD, D101, D10B, D30D, D3AB, D507, D50D, D66E, D761, D7DE, D811, D85D, D86E, D89D, D8C8, D8E8, D9AB, D9D8, DA3B, DA9B, DABB, DB01, DB61, DBAB, DC88, DD07, DD0B, DD7E, DD8D, DDE7, DE6E, E252, E33B, E522, E57B, E7AE, E7CE, E898, E997, E9A8, E9BB, EA34, EB5B, EE98, EEC7, 10017, 10B0D, 170AB, 17A0B, 19001, 19601, 1A09B, 1D0C7, 22E52, 2EA52, 30017, 3001D, 300B1, 301C7, 30334, 30631, 307AB, 3300B, 3333B, 36031, 36301, 37A0B, 37BBB, 39997, 3A30B, 3B0C7, 3D001, 3D601, 40034, 40968, 43334, 49668, 49998, 50022, 5009D, 501C7, 50222, 50507, 505C7, 50611, 50C57, 53007, 53997, 55537, 5555B, 5557B, 5599B, 56101, 56691, 56961, 5700D, 5755B, 59001, 59557, 59997, 5999D, 599DB, 59DDD, 5D99B, 5DD3D, 5DD9D, 60931, 63031, 65691, 66951, 69031, 69361, 69561, 70011, 70051, 7005B, 7006E, 7030D, 703AB, 70501, 70701, 707C7, 71601, 71951, 7300D, 7333B, 75001, 7555B, 75911, 76011, 76051, 766EE, 76EEE, 7700B, 77191, 77661, 7776E, 77771, 777BB, 77911, 77BBB, 79001, 7A05B, 7A66E, 7AA6E, 7AAAE, 7ACCE, 7C6EE, 7CCEE, 7CECE, 7CEEE, 7D3BB, 7E7C7, 7EECE, 80034, 80304, 80434, 809DD, 80A34, 84A34, 850DD, 85961, 86661, 88151, 88331, 88511, 88591, 88898, 890DD, 89998, 89D0D, 8D90D, 8E434, 90017, 90051, 900A8, 900DB, 901C7, 90C57, 90D8D, 91007, 91061, 9199B, 95997, 96068, 96561, 99397, 99537, 9999B, 999B7, 999D7, 999DB, 999DD, 99BBB, 99DBB, 99DD7, 99DDD, 9B007, 9B00B, 9B0AB, 9BB11, 9BBBB, 9D007, 9D08D, 9D537, 9D9BB, 9D9DB, 9DD57, 9DDB7, 9DDDB, 9DDDD, A0A34, A0B5B, A0BBB, A0E34, A2E52, A330B, A8434, A8834, A8E34, A909B, AAA34, AAE52, AB0BB, AB334, ABB34, AE034, AE834, AE99B, AEA52, AEE52, B0011, B0071, B0077, B00B1, B0611, B0A64, B500D, B599D, B6101, B7771, B7911, BA064, BAAA4, BAB34, BB061, BB304, BB53D, BB601, BBB91, BBB9D, BBBBD, BDA0B, BDBBB, D0088, D00D7, D0307, D05C7, D070D, D0888, D0B07, D0BC7, D0C08, D0DC7, D0DD8, D1661, D59DD, D5D3D, D5DDD, D6611, D700D, D8D0D, D900B, D9908, D999D, D9BBB, D9D9D, D9DDB, DB007, DB00D, DB1B1, DB53D, DB59D, DB99D, DBBB1, DD0D8, DD33B, DD3B7, DD3BB, DD57D, DD898, DD9DD, DDB37, DDBDB, DDD08, DDD3D, DDD5D, DDD7D, DDD88, DDD9D, DDDB7, DDDC8, DDDD7, DDE98, DE037, DE998, DEB07, E0098, E00C7, E0537, E0557, E077B, E0834, E0968, E3334, E37AB, E39C7, E4034, E5307, E55AB, E705B, E750B, E766E, E76EE, E8304, E8434, E9608, E9C37, EAE52, EBB0B, EC557, EC597, EC957, 1000BD, 1009AB, 10A90B, 1900AB, 190661, 19099B, 190A0B, 1A900B, 222A52, 2AAA52, 31000D, 330331, 333334, 3733AB, 373ABB, 3BBB61, 430004, 490068, 490608, 5000DB, 500D0B, 505557, 505A0B, 50D00B, 50DDDB, 50DDDD, 522222, 5500AB, 5500C7, 550957, 550A0B, 555A9B, 559057, 560011, 590661, 633331, 666331, 666591, 666661, 7050AB, 705A0B, 706101, 70A50B, 7300AB, 761661, 76666E, 777011, 777101, 77750B, 777A5B, 777CEE, 779051, 791501, 7E7797, 7ECCCE, 7EEE97, 800D9D, 808834, 836631, 83D661, 843004, 856611, 884034, 884304, 888E34, 88A434, 88AE34, 8A4034, 8AEE34, 8E8034, 8E8E34, 8EEE34, 9000BB, 9001AB, 900B07, 900D98, 903661, 905661, 906651, 9080DD, 9099A8, 909D9B, 90A668, 90DD9B, 90DDBB, 910001, 9100AB, 91A00B, 930007, 950001, 956661, 9909A8, 995907, 999068, 999507, 999907, 9B0B1B, 9B0BB1, 9BB01B, 9C5597, 9C5957, 9D09DD, 9D0D9D, 9D800D, 9DB307, 9DD09D, A00034, A0033B, A033B4, A2A252, AAAA52, ABBBBB, B00004, B0001B, B0003D, B00A04, B0555B, B07191, B07711, B07777, B0B911, B0BDBB, B77011, B777C7, BB0001, BB0034, BB035D, BB055B, BB0BDB, BB9101, BBB0DB, BBB50D, BBBB01, BBD0BB, C55397, C55557, C55597, D0003B, D00057, D0007D, D000B7, D000C8, D008DD, D00DAB, D0333B, D05537, D099DD, D09DDD, D0DDBB, D555C7, D5C537, D88008, D88088, D888EE, D909DD, D9D0DD, D9DD0D, DB0BBB, DBBB0B, DBBB0D, DC0008, DC5537, DDDDD8, DDDEBB, DDE99B, DE0808, DE0C57, DE300B, DE5537, DE8888, DEE088, DEE307, DEE888, DEEE37, DEEE57, DEEEC8, E0000B, E007BB, E00A52, E03BC7, E07ABB, E09B07, E0A99B, E0C397, E0E76E, E50057, E55007, E55597, E55937, E730AB, E73A0B, E80E34, E88834, E8E034, E90008, E95557, EA099B, EE4304, EE5057, EE5507, EE8E34, EE9307, EEE434, 100001D, 1000A9B, 1000DC7, 22AA252, 3000BC7, 3033301, 3076661, 333B304, 33B3034, 3B33304, 3D66661, 50007AB, 5005957, 5500597, 5550057, 5559007, 5559597, 5595007, 5966661, 5DDDDDB, 6366631, 7010001, 7066651, 7100061, 733BBBB, 766A6AE, 77505AB, 7776501, 777775B, 777AACE, 777ECCE, 777EEAE, 7CCCCCE, 7E30A0B, 7EEEEAE, 8300004, 8363331, 8693331, 880E834, 8833304, 8888034, 8888434, 888A034, 88A3334, 88E8834, 88EE034, 88EE304, 8AA3334, 8D0009D, 8EE8834, 9000361, 9000668, 9003331, 9005557, 9006008, 9008D0D, 9083331, 9090968, 90BBB01, 90D0908, 9500661, 9555597, 9555957, 9660008, 9900968, 9995597, 9996008, 9999557, 9999597, 9999908, 9A66668, A003B34, A003BB4, AA22252, B00B034, B00B35D, B033334, B0B6661, B0BB01B, B100001, B333304, B777777, B99999D, BA60004, BAA0334, BBB001B, BBB6611, BBBBB11, BBBD00B, BD000AB, D0000DB, D009098, D00CCC8, D00D908, D00D99D, D03000B, D0BB0BB, D0D9008, D0D9998, D1000C7, D800008, D8DDEEE, D90080D, DBBBBBB, DD09998, DDD5557, DDDDBBB, DDDDDBD, DDDE8EE, DECC008, DECCCC8, DEE0CC8, DEEC0C8, E000397, E0003BB, E000434, E00076E, E000937, E007A5B, E00909B, E0090B7, E009307, E00B077, E00E434, E00E797, E00E937, E05999B, E09009B, E0900B7, E0E0937, E0E7E97, E0EAA52, E0EEA52, E555057, E5555C7, E7777C7, E77E797, E88EE34, E999998, EA5999B, EB000BB, EB0BBBB, EE00434, EE0E797, EEE076E, EEE706E, EEE8834, EEEE557, EEEE797, 30333331, 30B66661, 33000034, 33030004, 33B33004, 500575AB, 55000007, 5500075B, 55500907, 55555057, 55555907, 55559507, 60003301, 60033001, 60330001, 7000003D, 70106661, 70666611, 77000001, 7777770B, 777777C7, 77777ACE, 77777EAE, 777E30AB, 777E3A0B, 7CCCC66E, 800005DD, 88AA0834, 90000008, 900008DD, 90099668, 90500557, 90555007, 90666668, 90909998, 90990998, 90996668, 9099999D, 90D00098, 90D90998, 95500057, 99099098, 99555057, 99900998, 99966608, 99966668, 99999668, 99999998, 9D009008, 9D090998, A0803334, A2222252, AAA52222, B00005AB, B000B55B, B0BBBB5B, B3330034, BB0BBB1B, BBAA3334, BBB0BB1B, BBB0BB5B, BBDB000B, D000BBBB, D00100C7, D8888888, D900008D, D9000098, DBB000BB, DC0CCCC8, DCC0CCC8, DCCCC008, DD000908, DD09009D, DDDDDDAB, DDDDDEEE, DDDEEE8E, DDDEEEE8, DEE80008, E0777E97, E0E0E397, E0E77797, E0EE0397, E7777797, E9066668, EE00E397, EE077797, EE0E0397, EEE00797, EEE07E97, EEE0AA52, EEE55397, EEE55557, EEEAAA52, EEEEE834, EEEEEA52, 300003331, 300007661, 300330031, 333000004, 333300001, 333B00034, 3700000AB, 3B3300034, 500000057, 555555007, 555555557, 5DDDDDDDD, 600000331, 7500000AB, 75000A00B, 75A00000B, 761000001, 77000E0C7, 777700EC7, 7777730AB, 7777777AE, 77777EE97, 7777E7E97, 777999997, 7A500000B, 7BBBBBB5B, 88888A834, 900000031, 900666608, 909990098, 90D009998, 950000557, 966666008, 990000007, 990555507, 999999997, A000000B4, A0005999B, AAEEEEE34, B000AA334, BBBBB005B, BBBBBBB5B, D09999998, D0D90009D, D800000DD, D90009998, DCCCC0CC8, DE88EEEEE, DEEEEEE88, E000B7777, E000BBBBB, E003ABBBB, EE0000797, EE0EEE397, EE5555557, EE777EE97, EEEEEE537, EEEEEE937, 2222222252, 3000000071, 3330030001, 3333303001, 3333330001, 500000007B, 5555555097, 7000000071, 77000000C7, 8333333331, 8888883334, 8888888834, 888888AA34, 900000009B, 900000009D, 900000DD9D, 9000099998, 9955555507, 9D0000099D, 9D05555557, AB0000005B, B000000DAB, B00000BBDB, BB00BB0B5B, BB0BB00B5B, D000099998, D00090008D, D0D000909D, D0DDDDDDDB, D300000007, D88EEEEEEE, D900999998, DD00900008, DDD6EEEEEE, DDDDDDD6EE, DDDDDDDDDE, DDDEEEEEEE, DEEEEE8008, E000000797, 7777777CCCE, 88888830004, 90000009D9D, 99955555557, 9999999999D, B00000D00AB, BB000BBB05B, BBBB0000B5B, D000009080D, D000090800D, D090800000D, DDDDDDD999B, DDDDDDDDD9B, EEEEEE00397, EEEEEEE0397, 333000000301, 5000000000DD, 73A00000000B, 9000000000B7, 903333333331, ABB00000000B, D000000001C7, DCCCCCCCCCC8, E0EEEEEEE397, 19A000000000B, 3333333333331, 3BBBBBBBBBBBB, 9333333333331, A00000000099B, B00000000050D, EEEEEEEEEE76E, 1000000000999B, 71000000000001, 908D000000000D, BBBBBBBBBB6661, 77777777777777B, BB00000000BBB5B, DEEEEEEEEEEEEEE, 7777777777777E97, B0BBBBBBBBBBBB1B, BB0000000000DB0B, D000000000000998, D908000000000000D, DDDDDDDDDDDDDDDDB, E9666666666666668, 3330000000000000031, D00000000000000908D, E0BBBBBBBBBBBBBBBBB, 2EEEEEEEEEEEEEEEEE52, 77777777777777777ECE, 5000000000000000005AB, 777777777777777777997, 7BBBBBBBBBBBBBBBBBBBB, BB0000000000000000DBB, DD000000000000000909D, D900000000000000000DDD, DD0000000000000000099D, BBBBBBBBBBBBBBBBBBBBBB1, B00000000000000000000005B, B0700000000000000000000001, B70000000000000000000000001, 705000000000000000000000000B, 633000000000000000000000000001, EBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB, 500000000000000000000000000000000017, 77777777777777777777777777777777777777777777777777777777777CCE, 7777777777777777777777777777777777777777777777777777777777777777777777777CE, 96666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666608, EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE397, 7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777797 ===Base 16=== 11, 13, 17, 1D, 1F, 25, 29, 2B, 2F, 35, 3B, 3D, 43, 47, 49, 4F, 53, 59, 61, 65, 67, 6B, 6D, 71, 7F, 83, 89, 8B, 95, 97, 9D, A3, A7, AD, B3, B5, BF, C1, C5, C7, D3, DF, E3, E5, E9, EF, F1, FB, 14B, 15B, 185, 199, 1A5, 1BB, 1C9, 1EB, 223, 22D, 233, 241, 277, 281, 287, 28D, 2A1, 2D7, 2DD, 2E7, 301, 337, 373, 377, 38F, 3A1, 3A9, 41B, 42D, 445, 455, 45D, 481, 4B1, 4BD, 4CD, 4D5, 4E1, 4EB, 50B, 515, 51B, 527, 551, 557, 55D, 577, 581, 58F, 5AB, 5CB, 5CF, 5D1, 5D5, 5DB, 5E7, 623, 709, 727, 737, 745, 74B, 755, 757, 773, 779, 78D, 7BB, 7C3, 7C9, 7CD, 7DB, 7EB, 7ED, 805, 80F, 815, 821, 827, 841, 851, 85D, 85F, 8A5, 8DD, 8E1, 8F5, 923, 98F, 99B, 9A9, 9EB, A21, A6F, A81, A85, A99, A9F, AA9, AAB, ACF, B1B, B2D, B7B, B8D, B99, B9B, BB7, BB9, BCB, BDD, BE1, C0B, CB9, CBB, CEB, D01, D21, D2D, D55, D69, D79, D81, D85, D87, D8D, DAB, DB7, DBD, DC9, DCD, DD5, DDB, DE7, E21, E27, E4B, E7D, E87, EB1, EB7, ED1, EDB, EED, F07, F0D, F4D, FD9, FFD, 1069, 1505, 1609, 1669, 16A9, 19AB, 1A69, 1AB9, 2027, 204D, 2063, 207D, 20C3, 20ED, 2221, 22E1, 2327, 244D, 26C3, 274D, 2E01, 2E0D, 2ECD, 3023, 3079, 3109, 3263, 3341, 36AF, 3941, 3991, 39AF, 3E41, 3E81, 3EE1, 3EE7, 3F79, 4021, 40DB, 440B, 444B, 44A1, 44AB, 44DB, 4541, 45BB, 4A41, 4B0B, 4BBB, 4C4B, 4D41, 4DED, 5045, 50A1, 50ED, 540D, 5441, 555B, 556F, 5585, 560F, 56FF, 5705, 574D, 580D, 582D, 5855, 588D, 5A01, 5AA1, 5B01, 5B4B, 5B87, 5BB1, 5BEB, 5C4D, 5CDD, 5CED, 5DD7, 5DDD, 5E0D, 5E2D, 5EBB, 68FF, 6A69, 6AC9, 6C8F, 6CA9, 6CAF, 6F8F, 6FAF, 7033, 7063, 7075, 7087, 70A5, 70AB, 7303, 7393, 74DD, 754D, 7603, 7633, 7663, 7669, 7705, 772D, 775D, 77D5, 7807, 7877, 7885, 7939, 7969, 7993, 79AB, 7A05, 7A69, 7A9B, 7AA5, 7B77, 7BA9, 7D4D, 7D75, 7D77, 8077, 808D, 80D7, 80E7, 8587, 86CF, 8777, 8785, 8885, 88CF, 88ED, 88FD, 8C6F, 8C8F, 8E8D, 8EE7, 8F2D, 8F8D, 9031, 9041, 90AF, 90B9, 9221, 9319, 9401, 944B, 9881, 9931, 9941, 9991, 99AF, 9A0F, 9A1B, 9A4B, 9AFF, 9BA1, 9BB1, 9CAF, 9E81, 9EA1, 9FAF, A001, A05B, A0C9, A105, A10B, A4CB, A55B, A6C9, A88F, A91B, A9B1, A9BB, AA15, AB01, AB0B, AB19, ABBB, AC09, AF09, B041, B04B, B069, B07D, B087, B0B1, B0ED, B1A9, B201, B40B, B40D, B609, B70D, B7A9, B807, B9A1, BA41, BAA1, BB4B, BBB1, BBDB, BBED, BD19, BD41, BDBB, BDEB, BE07, BEE7, C0D9, C203, C24D, C6A9, C88D, C88F, C8CF, C8ED, C9AF, C9CB, CA09, CA4B, CA69, CAC9, CC0D, CC23, CC4D, CC9B, CD09, CDD9, CE4D, CEDD, CFA9, CFCD, D04B, D099, D405, D415, D44B, D4A5, D4DD, D50D, D70B, D74D, D77B, D7CB, D91B, D991, DA05, DA09, DA15, DA51, DB91, DBEB, DD7D, DDA1, DDED, DE0B, DE41, DE4D, DEA1, E02D, E07B, E0D7, E1CB, E2CD, E401, E801, EABB, EACB, EAEB, EBAB, EC4D, ECDD, ED07, EDD7, EE7B, EE81, EEAB, EEE1, F08F, F0A9, F227, F2ED, F3AF, F485, F58D, F72D, F763, F769, F787, F7A5, F7E7, F82D, F86F, F877, F88D, F8D7, F8E7, F8FF, FCCD, FED7, FF85, FF8F, FFA9, 100AB, 10BA9, 1A0CB, 1BA09, 200E1, 2C603, 2CC03, 30227, 303AF, 30AAF, 32003, 32207, 32CC3, 330AF, 33169, 33221, 33391, 33881, 33AFF, 38807, 38887, 3AFFF, 3F203, 3F887, 3FAFF, 400BB, 4084D, 40A4B, 42001, 44221, 44401, 444D1, 4480D, 4488D, 44CCB, 44D4D, 44E8D, 4804D, 4840D, 4A0CB, 4A54B, 4CACB, 4D0DD, 4D40D, 4D44D, 5004D, 50075, 502CD, 5044D, 50887, 50EE1, 5448D, 548ED, 55A45, 55F45, 5844D, 5A4A5, 5AE41, 5B0CD, 5B44D, 5BBCD, 5D4ED, 5E0E1, 5EB4D, 5EC8D, 5ECCD, 5EE41, 5F06F, 5F7DD, 5F885, 5F8CD, 5FC8D, 5FF75, 6088F, 60AFF, 630AF, 633AF, 660A9, 668CF, 669AF, 66A09, 66A0F, 66FA9, 6886F, 6A00F, 6A0FF, 6A8AF, 6AFFF, 7002D, 7024D, 70B0D, 70B7D, 7200D, 73363, 73999, 7444D, 770B7, 777D7, 77B07, 77D7D, 77DD7, 79003, 79999, 7B00D, 7D05D, 7D7DD, 8007D, 800D1, 8074D, 82CCD, 82E4D, 8448D, 8484D, 8704D, 8724D, 87887, 88001, 8800D, 880CD, 88507, 88555, 8866F, 8872D, 8877D, 888D1, 888D7, 88AA1, 88C2D, 88D57, 88D75, 88D77, 8AFAF, 8C2CD, 8C40D, 8C8CD, 8CCED, 8CE2D, 8CFED, 8E007, 8E20D, 8E24D, 8F6FF, 8FAAF, 900CB, 901AB, 90901, 909A1, 90AB1, 90AE1, 90EE1, 910AB, 93331, 940AB, 963AF, 966AF, 99019, 99109, 99A01, 9AAE1, 9B00B, 9B0AB, 9B441, 9BABB, 9BBBB, 9E441, A00BB, A0405, A044B, A08AF, A0A51, A0B91, A0C4B, A1B09, A54A5, A5B41, A6609, A904B, A94A1, A9C4B, A9E01, A9E41, AA0A1, AA441, AA501, AA8AF, AAEE1, AAF45, AAF8F, ABBA1, ACC69, AE0BB, AE0EB, AEAE1, AEE0B, AEEA1, AEECB, AF045, AF4A5, AFA8F, B00A1, B00D7, B044D, B0777, B0A0B, B0A91, B0BBD, B0BCD, B0C09, B0DA9, B0EAB, B2207, B4001, B6669, B7707, B7D07, B8081, B9021, BA091, BA109, BA4BB, BB001, BB0EB, BB8A1, BBBEB, BBE0B, BBEBB, BC009, BCECD, BD0A9, BE44D, BEB0D, BEBBB, BEEBB, C0263, C02C3, C02ED, C040D, C0CA9, C0CCD, C2663, C2CED, C32C3, C3323, C400D, C40ED, C44CB, C44ED, C480D, C484D, C4CAB, C60AF, C686F, C6A0F, C86FF, C8C2D, CAA0F, CAFAF, CBCED, CC0AF, CC44B, CC82D, CC8FF, CCAF9, CCAFF, CCCFD, CCFAF, CD00D, CD4CB, CD4ED, CDDDD, CF2C3, CFC8F, CFE8D, D0045, D07DD, D09BB, D0D4D, D0DD7, D0EBB, D0EEB, D1009, D1045, D10B9, D1BA9, D54BB, D54ED, D5AE1, D5D07, D5EE1, D70DD, D7707, D7777, D77DD, D7DD7, D9441, D9AE1, D9B0B, DA9A1, DA9E1, DAA41, DAAA1, DBB0B, DBBA1, DC4CB, DD227, DD44D, DDDD7, E0081, E00E1, E010B, E088D, E08CD, E0B0D, E0BBD, E100B, E4D0D, E777B, E77AB, E7CCB, E844D, E848D, E884D, E88A1, EB0BB, EBB4D, EBBEB, EBEEB, EC8CD, ECBCD, ECC8D, ED04D, EE001, EE0EB, EE4A1, EEEBB, F0085, F09AF, F0C23, F0CAF, F2663, F2C03, F3799, F3887, F4A05, F4AA5, F506F, F5845, F5885, F5C2D, F5ECD, F5F45, F66A9, F688F, F6AFF, F7399, F777D, F8545, F8555, F8AAF, F8F87, F9AAF, FA0F9, FA405, FA669, FAFF9, FC263, FCA0F, FCAFF, FCE8D, FCF23, FD777, FDDDD, FDEDD, FEC2D, FEC8D, FF545, FF6AF, FF739, FF775, FF9AF, FFC23, 100055, 100555, 10A9CB, 1A090B, 1A900B, 1CACCB, 1CCACB, 20DEE1, 266003, 3000AF, 300A0F, 300AFF, 308087, 308E07, 3323E1, 333A0F, 339331, 33CA0F, 33CF23, 33CFAF, 33F323, 380087, 3A00AF, 3A0F0F, 3AA0FF, 3AAF0F, 3C33AF, 3C3A0F, 3C3FAF, 3CCAAF, 3F0FAF, 3F32C3, 3FF0AF, 3FFAAF, 4004CB, 400A05, 4048ED, 404DDD, 40AA05, 40D04D, 40DD4D, 40E0DD, 40E48D, 440041, 44008D, 44044D, 4404DD, 44440D, 4448ED, 4484ED, 448E4D, 44E44D, 48888D, 4AA005, 4DD00D, 4DD04D, 4DDD0D, 4E048D, 4E448D, 4E880D, 5000DD, 500201, 50066F, 5008CD, 500C2D, 500D7D, 50C20D, 520C0D, 544EDD, 54AA05, 54AAA5, 54ED4D, 566AAF, 57D00D, 580087, 5A5545, 5C20CD, 5C8CCD, 5CC2CD, 5D000D, 5D070D, 5F666F, 5FAA45, 5FFF45, 60008F, 600A0F, 603AAF, 6060AF, 6066AF, 60A0AF, 63AA0F, 6663AF, 66668F, 666AAF, 668A8F, 66AFF9, 68888F, 693AAF, 7007B7, 70404D, 70770B, 70770D, 707BE7, 70DD0D, 733339, 733699, 74004D, 74040D, 77007B, 770CCB, 777B4D, 777BE7, 777CCB, 77ACCB, 77B74D, 77D0DD, 7A0CCB, 7B744D, 7CACCB, 7DDD99, 80044D, 800807, 80200D, 8044ED, 80C04D, 80CC2D, 80E44D, 8404ED, 84888D, 84E04D, 84E40D, 86686F, 8668AF, 8686AF, 86F66F, 86FFFF, 87000D, 87744D, 880807, 886AFF, 88824D, 88870D, 888787, 88884D, 88886F, 88887D, 88888D, 888C4D, 888FAF, 88AA8F, 88CC8D, 88F6AF, 88F8AF, 88FA8F, 88FF6F, 88FF87, 88FFAF, 8A8FFF, 8C0C2D, 8C802D, 8CCFFF, 8CE00D, 8CE0CD, 8CFCCF, 8E00CD, 8E044D, 8E0CCD, 8EC0CD, 8F68AF, 8F88F7, 8FCFCF, 8FF887, 8FFCCF, 8FFF6F, 9002E1, 9004AB, 9008A1, 900919, 900ABB, 900B21, 90B801, 90CCCB, 9332E1, 944441, 94ACCB, 990001, 9900A1, 9A4441, 9A4AA1, 9AA4A1, 9AAA41, 9AAAAF, 9B66C9, 9BBA0B, 9BC0C9, 9BC669, 9BC6C9, 9C4ACB, A0094B, A00ECB, A09441, A0A08F, A0E0CB, A0ECCB, A0F669, A40A05, A4AAA5, A50E41, A5AA45, A60069, A8FAFF, A9AA41, AA5E41, AAA4A5, AAA545, AC6669, ACCC4B, ACCCC9, AEAA41, AFF405, AFF669, AFFA45, AFFFF9, B00921, B00BEB, B00CC9, B00D91, B08801, B0D077, B70077, B70E77, B77E77, B88877, B88881, B94421, BAE00B, BB00AB, BB0DA1, BB444D, BB44D1, BB8881, BBBBBD, BBBC4D, BBCCCD, BC0CC9, BC66C9, BCC669, BCC6C9, BCCC09, BE000D, BE00BD, BE0B4D, BE0CCD, BEA00B, BECCCD, C0084D, C00A0F, C0608F, C0668F, C0844D, C0A0FF, C0AFF9, C0C3AF, C0C68F, C0CAAF, C0CDED, C0D0ED, C0E80D, C0EC2D, C0EC8D, C0FA0F, C0FAAF, C2CC63, C30CAF, C333AF, C3CAAF, C3CCAF, C4048D, C40D4D, C4404D, C4408D, C4440D, C44DDD, C4ACCB, C4DCCB, C4DD4D, C6068F, C66AAF, C68AAF, C6AA8F, C8044D, C8440D, C8666F, CA00FF, CA0FFF, CAAAAF, CAAFFF, CAFF0F, CBE0CD, CC008F, CC0C8F, CC3CAF, CC4ACB, CC608F, CC66AF, CCBECD, CCC4AB, CCCA0F, CCCC8F, CCCE8D, CE0C8D, CF0F23, CF0FAF, CFAFFF, CFCAAF, CFFAFF, D0005D, D00BA9, D05EDD, D077D7, D10CCB, D22207, D4000B, D4040D, D4044D, D40CCB, D70077, D7D00D, D90009, D900BB, DB00BB, DB4441, DD400D, DDD109, DDD1A9, DDD919, DDD941, DED00D, E00D4D, E00EEB, E0AAE1, E0AE41, E0AEA1, E0B44D, E0BCCD, E0BEBB, E0D0DD, E0E441, E4048D, E4448D, E800CD, E8200D, EA0E41, EAA0E1, EBB00B, ECCCAB, EDDDDD, EEBE0B, F00263, F0056F, F00A45, F02C63, F03F23, F05405, F060AF, F08585, F0A4A5, F0F2C3, F0F323, F2CCC3, F33203, F33C23, F5F66F, F5FF6F, F68CCF, F6AA8F, F888AF, FA0F45, FAA045, FAA545, FAFC69, FC0AAF, FC66AF, FCCCAF, FCFFAF, FF0323, FF056F, FF3203, FF7903, FFA045, FFA4A5, FFAA45, FFC0AF, FFF4A5, FFF575, FFFA45, FFFCAF, 10A009B, 20000D1, 2CCC663, 30A00FF, 30CCCAF, 30FA00F, 30FCCAF, 3333C23, 333C2C3, 33C3AAF, 33FCAAF, 33FFFAF, 3A0A00F, 3AAAA0F, 3AF000F, 3AFAAAF, 3C0CA0F, 3CCC3AF, 3CFF323, 3F33F23, 3FAA00F, 3FF3323, 4004441, 400DDD1, 400E00D, 400ED0D, 404404D, 404448D, 404E4DD, 440EDDD, 4440EDD, 44444ED, 4444E4D, 44DDDDD, 4A000A5, 4CCCCAB, 4D0CCCB, 4E4404D, 4E4444D, 4E4DDDD, 5000021, 5004221, 5006AAF, 500FF6F, 5042201, 508CCCD, 5400005, 5400AA5, 5555405, 5808007, 5AA4005, 5C0008D, 5CCC8CD, 5D4444D, 5EEEEEB, 5F40005, 5F554A5, 5F6AAAF, 60000AF, 60006A9, 600866F, 6008AAF, 600AA8F, 600F6A9, 606608F, 606686F, 608666F, 60AA08F, 60AAA8F, 66000AF, 66666A9, 6666AF9, 6866A8F, 6AAAAAF, 70070D7, 70077DD, 700DDDD, 707077D, 707D007, 70D00DD, 770077D, 770400D, 770740D, 7777775, 77777B7, 77777DD, 7777ACB, 77B88E7, 77DD00D, 77DDDDD, 7D0D00D, 7DD0D07, 7DDD00D, 800002D, 8000CED, 80C0E0D, 80CECCD, 840400D, 844000D, 844E00D, 868688F, 880444D, 884404D, 887D007, 8888801, 8888881, 8888E07, 8888F77, 8888FE7, 88A8AFF, 88AAAFF, 88FAFFF, 8A8AAAF, 8A8AAFF, 8AAA8FF, 8C00ECD, 8C8444D, 8E4400D, 8FCCCCF, 900BBAB, 90CC4AB, 9908AA1, 99E0E01, 9B00801, 9B6CCC9, A000FF9, A006069, A00A8FF, A01CCCB, A05F545, A0BEEEB, A0E4AA1, AA0008F, AA08FFF, AA40AA5, AA8FFFF, AAAA405, AE04AA1, AE44441, AE4AAA1, AECCCCB, AF40005, AFA5A45, AFFFC69, B000BAB, B000EBB, B0D0007, B222227, B6CCCC9, B8880A1, BA000EB, BA0BEEB, BAEEEEB, BB000CD, BB00C0D, BB0B00D, BC6CC69, BC6CCC9, BCCCC69, BCCCCED, C0000A9, 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4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444DD ===Base 17=== 12, 16, 1C, 1E, 23, 27, 29, 2D, 32, 38, 3A, 3G, 43, 45, 4B, 4F, 54, 5C, 5G, 61, 65, 67, 6B, 78, 7C, 81, 83, 8D, 8F, 94, 9A, 9E, A3, A9, AB, B4, B6, BA, BC, C7, D2, D6, D8, DC, E1, E3, ED, F2, F8, FE, FG, G5, G9, GB, 104, 111, 115, 117, 11B, 137, 139, 13D, 14A, 14G, 155, 159, 15F, 171, 17B, 17D, 188, 191, 197, 19F, 1A4, 1A8, 1B3, 1BB, 1BF, 1DB, 1DD, 1F3, 1FD, 1G8, 1GA, 1GG, 20F, 214, 221, 225, 241, 25A, 25E, 285, 2B8, 2C5, 2CF, 2E5, 2EB, 2F6, 30E, 313, 331, 33B, 346, 34C, 351, 35F, 36E, 375, 37B, 391, 39B, 39D, 3B7, 3B9, 3BF, 3D3, 3D5, 3D9, 3DF, 3E4, 3EC, 3F1, 3F7, 407, 418, 447, 44D, 472, 474, 47E, 47G, 489, 49C, 4A1, 4C1, 4CD, 4D4, 4G1, 502, 506, 508, 50E, 519, 522, 528, 52A, 52E, 533, 53F, 551, 55D, 562, 566, 573, 577, 57F, 582, 593, 599, 59B, 59F, 5A6, 5B5, 5D1, 5D3, 5EA, 5EE, 5F9, 60D, 62F, 634, 649, 689, 692, 6CD, 6EF, 6F4, 6FA, 704, 706, 70G, 71D, 726, 737, 739, 73D, 73F, 753, 755, 764, 766, 76G, 771, 77B, 793, 7AA, 7AE, 7B3, 7BB, 7D7, 7E6, 7F3, 7F9, 7FF, 7G2, 7GE, 7GG, 825, 82B, 849, 852, 85E, 869, 876, 87A, 87G, 88B, 892, 898, 89C, 8C5, 8E7, 8G7, 908, 90G, 913, 91F, 92C, 935, 937, 93B, 951, 953, 957, 95D, 968, 96G, 979, 97B, 98C, 98G, 99D, 9B1, 9B3, 9B9, 9BD, 9BF, 9DB, 9DF, 9F1, 9F5, 9G6, A07, A0D, A1A, A2F, A4D, A72, A7A, A7E, AA1, AA7, ACF, ADA, AG1, AG7, B02, B08, B17, B1D, B28, B2G, B57, B71, B73, B79, B7F, B88, B8E, B8G, B9B, B9F, BB5, BB7, BD7, BDD, BEG, BFF, BGG, C01, C2F, C3E, C56, C6D, C89, C92, C9G, CA5, CBG, CC1, CC5, CF4, CFA, D04, D0A, D15, D3D, D3F, D55, D59, D5B, D71, D75, D7D, D91, D97, D99, D9D, DA4, DAG, DB3, DDB, DF1, DF7, DF9, DFF, E05, E0B, E2B, E52, E58, E69, E92, E9C, EAF, EB8, EC9, ECB, EE5, F04, F15, F1B, F35, F3B, F46, F51, F53, F64, F6A, F73, F79, F95, FAC, FB1, FCA, FD5, FDB, FF1, FF7, FFD, G0D, G0F, G18, G1A, G1G, G2F, G34, G63, G7G, GA7, GC3, GDG, GEF, GFA, GG7, GGD, 1013, 101D, 1033, 1035, 1051, 105B, 105D, 1077, 108A, 109B, 10AG, 10B1, 10B7, 10BD, 10FB, 1149, 1189, 11AF, 11G3, 1303, 130B, 1314, 1341, 1479, 14D9, 1501, 1503, 15A1, 15B8, 1734, 1749, 17AF, 17G3, 1844, 185B, 1875, 1877, 18AG, 18B5, 1903, 1909, 1958, 19BG, 19G3, 1A5D, 1A75, 1A7F, 1ADF, 1AF1, 1B01, 1B09, 1B18, 1B85, 1B89, 1BDG, 1BGD, 1D07, 1D49, 1D9G, 1DF4, 1F09, 1F47, 1F5A, 1F74, 1F7A, 1FA1, 1FAF, 2018, 201G, 202B, 208B, 20G1, 215B, 218G, 21AG, 21B1, 222F, 22AF, 22BG, 22EF, 22F4, 22GF, 251B, 2526, 25F1, 266F, 26FC, 280B, 2A05, 2A58, 2AFC, 2AGF, 2B1B, 2B1F, 2BGE, 2C1G, 2C2B, 2C8B, 2CG1, 2E2F, 2EGF, 2F0C, 2F55, 2FAA, 2FC4, 2FFF, 2GA1, 2GFC, 2GG1, 2GGF, 301B, 301F, 3037, 3053, 3057, 3079, 3095, 30B3, 30BD, 30C4, 31F4, 330D, 3334, 333E, 3349, 3376, 337E, 33CD, 33EF, 3411, 3417, 3499, 3503, 3505, 3509, 353E, 35E5, 35EB, 3604, 36FD, 3701, 3741, 374D, 376F, 3796, 37D4, 37F4, 3956, 3B03, 3B05, 3B0B, 3BBE, 3C04, 3C15, 3C19, 3C4E, 3C59, 3C64, 3CB3, 3CDB, 3CE6, 3D07, 3D14, 3DDE, 3E77, 3E79, 3E7F, 3E99, 3EEE, 3EFB, 3F05, 3F0D, 3FCB, 3FF4, 4009, 4021, 4069, 4098, 40DG, 40GD, 419D, 4201, 4401, 4492, 46AD, 46C9, 46DA, 4719, 476A, 4779, 479D, 47A6, 4906, 4911, 4917, 4919, 491D, 492G, 4982, 4988, 49D7, 49D9, 49GG, 4ADE, 4AE7, 4C49, 4C96, 4CC9, 4D79, 4DAE, 4DEG, 4E7A, 4E96, 4EG7, 4G6D, 4G87, 501B, 5037, 5059, 507D, 50BB, 50BF, 50D7, 50DD, 50F1, 5105, 51A7, 51AD, 521B, 525F, 52FB, 5307, 5356, 53BE, 53DE, 53E9, 5507, 550B, 5587, 5598, 55EF, 560A, 568E, 56AA, 56F3, 5709, 5725, 572B, 575A, 575E, 5769, 57A1, 57B2, 5868, 586E, 58AE, 58B9, 590D, 5918, 5952, 5958, 596D, 5A17, 5A1F, 5ADD, 5ADF, 5AE8, 5B07, 5B21, 5B2F, 5B3E, 5BEF, 5DA7, 5DEB, 5E57, 5E5F, 5E86, 5E97, 5EB9, 5EBF, 5EF5, 5F01, 5F1A, 5F6F, 5FA7, 5FDA, 60AF, 60G3, 64AD, 64DE, 64DG, 663E, 666D, 66AF, 693D, 69CG, 69D3, 69D9, 69G8, 69GC, 6ADE, 6AGD, 6C98, 6D33, 6D4E, 6D93, 6D9F, 6DDD, 6DEE, 6DF3, 6DFD, 6DGE, 6E09, 6G36, 6G4D, 6G6D, 6GD4, 6GDE, 6GFC, 702E, 7057, 705B, 7073, 7079, 7095, 70B5, 70BD, 70D1, 70E2, 70F5, 7107, 7149, 719G, 71BG, 71F4, 724E, 724G, 725F, 72A2, 72BF, 72EE, 72GA, 7314, 733E, 7341, 7363, 73EB, 7419, 742A, 742G, 7442, 74EG, 7501, 750F, 751A, 756D, 757E, 75A1, 75A7, 75BE, 75DA, 75E9, 75F6, 7622, 769F, 76EA, 7734, 773E, 776D, 779G, 77AF, 7905, 790B, 7976, 79B2, 79F6, 79GD, 7A1F, 7A5D, 7AD5, 7ADF, 7AF1, 7AFD, 7B01, 7B09, 7B2F, 7B52, 7B72, 7BE5, 7D01, 7D05, 7D9G, 7DAF, 7DBG, 7E0A, 7E75, 7EA2, 7EA4, 7EB5, 7EBF, 7EE2, 7EF7, 7EG4, 7F0B, 7F14, 7F5A, 7F76, 7FA7, 7G1F, 7G46, 7GA6, 7GD3, 7GDF, 8009, 8058, 80B8, 80E9, 84A7, 850A, 8557, 857B, 85A8, 870E, 8744, 8777, 879B, 87B5, 87B7, 87EE, 8805, 8872, 8887, 8889, 88E9, 8906, 8959, 8966, 89GG, 8A87, 8AE5, 8B0G, 8B59, 8B95, 8B97, 8CB2, 8CB8, 8CE9, 8E56, 8EE9, 9026, 9031, 903D, 907F, 9091, 909B, 90FB, 9101, 910D, 9118, 917G, 9185, 9189, 91B8, 9202, 9288, 92B5, 92FB, 92GG, 93C1, 9505, 950B, 950F, 952B, 956F, 9592, 9596, 9598, 9602, 96D9, 96FD, 971G, 9725, 9752, 97DG, 9855, 9862, 9895, 9899, 98B7, 98BB, 9901, 990B, 9921, 992F, 99G3, 9B0B, 9B2B, 9B8B, 9BB8, 9BBG, 9C19, 9C1B, 9C31, 9C59, 9C95, 9CD5, 9CFB, 9CGC, 9D03, 9D07, 9D7G, 9DG1, 9DGD, 9F0B, 9F76, 9FCB, 9G11, 9G1D, 9G28, 9G3F, 9G7D, 9GCC, 9GD7, 9GF7, 9GFD, 9GG8, A025, A041, A058, A0C5, A0F6, A0GF, A11F, A184, A1F7, A21G, A258, A401, A421, A476, A511, A517, A57D, A5A8, A5E8, A6AD, A6FC, A6GF, A751, A77F, A7F5, A7FD, A7G6, A847, AACD, AC1G, AC41, AC58, AC5E, ACGD, AD0E, AD0G, AD1F, AD51, ADD5, ADE4, ADF5, ADGE, AE56, AE74, AEF6, AEFA, AF77, AF7D, AFA4, AFCC, AFD7, AFDD, AGAF, AGF4, B00G, B037, B055, B05B, B075, B0D5, B0FD, B10F, B198, B25F, B2F1, B2F5, B307, B309, B35E, B3EF, B50D, B589, B7BE, B7BG, B7E7, B875, B952, B958, B97G, B99G, B9G7, B9GD, BB01, BB2F, BB3E, BB89, BB98, BBDE, BD03, BD09, BD5E, BDE5, BDEB, BDG1, BE5F, BF01, BF0D, BG13, BG1F, BG3F, BGD1, BGE2, BGE8, C00B, C034, C05A, C0AF, C0EF, C0GF, C153, C15B, C199, C1B9, C1D1, C1D5, C1F9, C205, C21A, C21G, C252, C258, C2B2, C335, C33D, C35D, C364, C395, C3B3, C3F5, C3FB, C3FD, C414, C41A, C469, C496, C4DA, C4GD, C535, C55B, C5B1, C5BD, C5D9, C5DF, C5E8, C5F3, C5F5, C6E9, C85A, C885, C8B8, C8BE, C8CB, C8E5, C919, C931, C959, C95F, C9D3, CA0F, CA18, CA1G, CAD4, CADE, CAEF, CAGD, CB22, CB33, CB35, CB3F, CB5D, CB82, CB99, CBB1, CBFB, CC49, CCCB, CCDE, CD11, CD1D, CD39, CD4A, CD53, CD93, CDAE, CDD5, CDF3, CDFD, CDG4, CE49, CE5A, CE8B, CF13, CF19, CF5D, CF5F, CFB9, CFBF, CFD9, CFDF, CG14, CG41, CG6F, CGCF, CGF6, CGG1, D01F, D039, D079, D09B, D09F, D0B7, D0BB, D0D1, D0EG, D0GG, D10D, D19G, D1G3, D30B, D347, D3BE, D4E4, D50D, D57E, D5AD, D5FA, D707, D73E, D7E7, D7GF, DA1F, DA57, DAAE, DB01, DB09, DB0D, DB7E, DB9G, DD05, DD7E, DDA5, DDFA, DDG3, DE0G, DE44, DE4A, DE77, DEAE, DEB9, DEBB, DF03, DF05, DG0E, DGDF, E009, E06F, E072, E07G, E089, E0CF, E0E9, E0G7, E47A, E498, E4E7, E50A, E559, E55F, E575, E5B9, E5BF, E5F5, E5F7, E6FC, E722, E724, E72A, E72E, E744, E746, E75B, E76E, E79B, E7A4, E7A6, E7AG, E7B5, E7B7, E7EG, E7G4, E887, E89G, E8E9, E906, E955, E95B, E95F, E988, E99F, E9F9, E9G8, E9GG, EA25, EA7G, EAC5, EAE7, EB7B, EBF5, EBF7, EBFB, EC6F, ECCF, ECEF, EE72, EE76, EE89, EE9G, EF0A, EF44, EF77, EF97, EFA4, EFB5, EFC6, EFFF, EG6F, EG74, EGE7, EGFC, EGGF, F019, F01F, F075, F091, F09B, F0BF, F0FB, F10F, F1A7, F1AD, F1D4, F376, F3CD, F3F4, F40A, F411, F444, F44A, F497, F499, F49D, F4D7, F509, F57A, F5AD, F5F6, F6D3, F6D9, F70D, F741, F747, F76D, F7F6, F7FA, F907, F976, F9CB, FA11, FA7D, FADD, FB09, FC4C, FC5D, FC5F, FC91, FCB9, FD1A, FD41, FD47, FDF4, FF0B, FF56, G021, G07A, G0A1, G0E7, G11F, G17F, G1DF, G1F1, G1F7, G201, G2A1, G306, G311, G36C, G377, G37F, G3CC, G3CE, G3D1, G476, G487, G4DE, G6AF, G6D4, G6F6, G6GF, G713, G724, G731, G742, G74E, G76E, G7A2, G872, G874, GA21, GAC1, GC6F, GCAF, GCD4, GCDA, GCG1, GD73, GD7F, GDAE, GDDF, GDEA, GDFD, GE47, GE7E, GF13, GF33, GF3F, GF4C, GF71, GF7F, GFDD, GG01, GG21, GGAF, GGC1, 1000G, 10053, 100AA, 100B9, 100F1, 100FF, 10301, 10587, 10705, 1075A, 107GF, 10895, 108B9, 10985, 1099G, 10B98, 10B9G, 10D03, 10D0F, 10D7A, 10DG3, 10DG7, 10G1F, 10G3F, 110GF, 1140D, 11D93, 11DG4, 11F0A, 11G4D, 11GD4, 13333, 133FF, 13F44, 14109, 14499, 150A7, 153B1, 1570A, 17005, 17799, 177AG, 17995, 17A7G, 17G47, 18079, 18507, 185A7, 18B07, 18B9G, 19333, 199B5, 1A00A, 1A00G, 1A0F5, 1AAAA, 1AAAG, 1AF05, 1AFFA, 1B07G, 1B10G, 1B807, 1D001, 1D1AA, 1D7G4, 1DG03, 1DG41, 1F001, 1F00F, 1F01A, 1F0A7, 1F199, 1F1F9, 1F414, 1F449, 1F7F5, 1F999, 1FF0A, 1FFAA, 1FFB5, 1G073, 1G14D, 1G1F4, 1G301, 1G477, 1GD01, 1GD47, 1GF07, 1GFF4, 20005, 200A1, 2010A, 20586, 20588, 20A01, 20B11, 20B15, 20BEE, 20C1A, 20CBE, 210B5, 21A1F, 21A51, 21F1A, 21G1F, 21GFF, 222BE, 228B2, 228BE, 22BE2, 22C0B, 22F0A, 252BB, 25505, 25552, 26GAF, 2A001, 2A1FF, 2A55F, 2AEEF, 2AF44, 2B051, 2B20E, 2BB2B, 2BBBG, 2BE22, 2BEE2, 2BEEE, 2BF0B, 2C0BE, 2C18A, 2F101, 2F1FA, 2F44C, 2FCBB, 2G1FF, 2GA6F, 2GF44, 30035, 300B1, 300FB, 30101, 303C5, 30444, 30497, 304D1, 304D7, 30703, 30714, 30734, 30763, 30774, 30CF5, 30CFD, 30D41, 30FC5, 3100B, 31779, 31F5B, 31FB5, 31FFF, 330C5, 330F4, 33357, 33373, 33379, 33555, 33557, 33777, 3379F, 337FD, 33997, 33D44, 33D4E, 33F3D, 33FF5, 34019, 34044, 340D1, 353DD, 35535, 355B3, 355E6, 35BB3, 35DDD, 3636D, 364DD, 3663D, 36DD4, 37003, 3700F, 3717F, 373EE, 37609, 3774E, 37773, 37797, 37977, 3797F, 37EEF, 39007, 390C5, 39777, 39973, 3B355, 3B553, 3BBDB, 3BDB1, 3C03D, 3C0F5, 3C10F, 3C141, 3C444, 3CBE5, 3CD0D, 3CE5B, 3CEBB, 3CEF9, 3D401, 3DEBE, 3E006, 3E066, 3E57E, 3E5E9, 3E666, 3E90F, 3EF6F, 3F33D, 3F3C4, 3F5BB, 3FB33, 3FDDD, 3FF59, 4006D, 400DE, 4011D, 401D9, 40414, 4041G, 404C9, 40966, 40D11, 40D19, 40D1D, 40E49, 41019, 411DA, 41AAG, 4210A, 44049, 4410G, 44144, 441G4, 44441, 444E9, 446E9, 44986, 44E49, 4609G, 460E9, 466DE, 469DD, 46E9G, 4711A, 476D9, 4770D, 47A77, 47D09, 49099, 490D1, 49226, 49622, 49699, 496DD, 49996, 4999G, 499G7, 49G22, 49G77, 4A7DD, 4AA6D, 4ADD7, 4C0E9, 4C999, 4D1DA, 4DADD, 4DD01, 4DD1G, 4DD7A, 4DDA7, 4DDE9, 4DG0G, 4DGAA, 4DGGA, 4DGGE, 4E049, 4E449, 4E49G, 4E4E9, 4E797, 4G7DD, 4GDAA, 4GDD7, 50011, 50079, 50095, 500B1, 500F3, 501A5, 501AF, 50503, 507A5, 50AF7, 50F03, 50F7A, 510A1, 510DA, 511AA, 511DF, 5135B, 515B7, 5180B, 51A0F, 51F0A, 520B1, 53005, 531BD, 53559, 53609, 53B11, 55205, 55357, 553E6, 5555B, 5556E, 55588, 5558A, 555F3, 555FB, 556AF, 556E9, 55759, 5575B, 55805, 55885, 55896, 558B8, 55926, 55BE2, 55E8B, 55F57, 560FF, 5700D, 570A5, 570DA, 575B9, 576AD, 576DA, 579D5, 57A05, 57A52, 57B9D, 57DBD, 58057, 58509, 5855A, 585A7, 587EB, 58857, 588E8, 58A75, 58B0B, 58B87, 58BBE, 58BEB, 58E5B, 591D5, 59201, 59256, 59715, 59807, 5A88A, 5AA88, 5AFAD, 5B001, 5B00B, 5B1F1, 5B31B, 5B7E2, 5B80B, 5BB13, 5BBE8, 5BBFB, 5BE87, 5BE8B, 5BF37, 5BFBD, 5D00F, 5DA05, 5DA5A, 5DAE5, 5DBBD, 5DD95, 5DDAA, 5DFDD, 5E879, 5E8B7, 5E8BB, 5F07A, 5F0AD, 5F37D, 5F70A, 5F7BD, 5FB7B, 5FBBB, 5FBF3, 5FFF3, 6003E, 60098, 603E6, 606GF, 60986, 609C8, 60G6F, 60GCF, 6336D, 633E9, 63CCE, 63E06, 63E66, 6609G, 660E9, 66AD4, 66D4A, 66DG4, 66DGG, 66E98, 66FD9, 66GF6, 69806, 69866, 69C86, 69CC8, 6A66F, 6AAGF, 6AF06, 6AF66, 6AGGF, 6C6G3, 6C6GF, 6CCGF, 6CG03, 6DA0E, 6DAEA, 6DD9G, 6DDE9, 6DEGA, 6DGD3, 6E986, 6EEE9, 6F69D, 6F6DF, 6F96D, 6FD03, 6FD09, 6G003, 6G3F3, 6G3FF, 6G6CF, 6GAAF, 6GCCF, 70031, 70099, 700BF, 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777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777F ====Additional known quasi-minimal primes (not necessarily the next)==== 570₅₁₃₁₀1, 49₁₁₁₃₃₃, 970₁₆₆₀₄₇1, F70₁₈₆₇₆₇1 ===Base 18=== 11, 15, 1B, 1D, 21, 25, 27, 2B, 2H, 35, 37, 3D, 3H, 41, 47, 4B, 4H, 57, 5B, 5D, 5H, 61, 65, 71, 75, 7B, 7D, 85, 87, 8D, 91, 95, 9B, 9H, A1, AB, AD, AH, B1, BD, C7, CB, CD, CH, D5, D7, DH, E5, EB, EH, F1, F7, FB, FD, G5, H1, H5, H7, HB, 107, 167, 16H, 177, 17H, 1G7, 1HH, 20D, 24D, 26D, 29D, 30B, 36B, 381, 3BB, 405, 445, 44D, 49D, 4A5, 4DD, 4F5, 4GD, 501, 545, 5E1, 607, 62D, 64D, 66B, 66H, 67H, 68B, 697, 6A7, 6BB, 6E7, 6G7, 6GB, 6HH, 767, 76H, 77H, 797, 7HH, 801, 80H, 831, 83B, 86B, 88H, 8BB, 8FH, 8GH, 94D, 96D, 977, 9DD, 9ED, 9GD, A77, AC5, AE7, B07, B0H, B55, B77, B8B, B97, BB5, BB7, BBH, BE7, BFH, BGB, C01, C31, CA5, CG1, D2D, D4D, D81, DBB, DD1, DDB, DGD, E0D, E17, E31, E4D, E67, E6D, EA7, EDD, EE1, EED, EG7, F0H, F45, F8H, FC5, FFH, G0D, G17, G2D, G6B, G6H, GBB, GBH, GD1, GDD, GE1, GE7, GED, GFH, GG7, GGB, GHD, GHH, H0D, H2D, H8H, H9D, HGH, HHD, 100H, 19E7, 1A97, 1EE7, 1G8H, 1GGH, 22ED, 22GD, 2DED, 2E2D, 3001, 3031, 30C1, 30E1, 3331, 33G1, 3CC1, 40ED, 45C5, 46ED, 4CC5, 5331, 5551, 55G1, 5C05, 608H, 60ED, 60FH, 60HD, 666D, 66ED, 699D, 6B67, 6BGH, 6D0D, 6DDD, 6E9D, 6EGD, 6G0H, 6G9D, 6HGD, 700H, 70A7, 7A07, 7FGH, 7G77, 808B, 8881, 88G1, 88GB, 8BHH, 8EG1, 8GC1, 8H6H, 900D, 90E7, 90G7, 9667, 9907, 999D, 99E7, 9A67, 9A97, 9E97, 9EE7, 9G07, 9G67, 9GA7, AA45, AA97, AGA7, B005, B03B, B06B, B0C5, B60B, B63B, BAA5, BAA7, BCC5, BFA5, BG8H, C045, C055, C555, C5C1, C5F5, CC05, CC81, CCC5, D06D, D09D, D0ED, D38B, D3E1, D60D, D6DD, D8GB, DD6D, DE9D, DG01, E001, E097, E0G1, E8C1, EDC1, EE97, EGC1, EGG1, EGGD, FH6H, G007, G00B, G00H, G03B, G067, G097, G0C1, G0G1, G1GH, G33B, G38B, G3G1, G70H, G777, G88B, GA67, GAA7, GG81, GGC1, GGGH, H0FH, H66D, HEGD, HFHH, 1AAA7, 222DD, 30GG1, 3388B, 33E01, 38G8B, 3G3C1, 3GGG1, 4002D, 500C5, 50C55, 50CF5, 53GG1, 558C1, 55CC5, 55CF5, 58GG1, 5C8C1, 5CFF5, 5G881, 5GG31, 6000H, 6003B, 6006D, 600DB, 6033B, 606GD, 60D0B, 66GGD, 6D03B, 6D33B, 6H6DD, 6HD6D, 6HDED, 70G07, 70GGH, 777A7, 7AAG7, 7G0GH, 80G0B, 8888B, 8CCE1, 90067, 90097, 9022D, 99967, 99997, 9A007, 9A0A7, 9AA07, 9AAA7, 9E007, A0045, A0455, A0667, A09G7, A0A07, A0G07, A0G97, A9997, AA0A7, AAG67, B0AF5, B6GGH, B7GGH, B8HHH, BA045, BAF05, BG667, C0F05, C5005, C5581, C88C1, C8CC1, C8CE1, CCF55, D03C1, D060B, D080B, D0CC1, D0G0B, D0G8B, D3G3B, D600B, DDDED, DG331, DG80B, E8G81, E9007, F6GGH, G018H, G0301, G0331, G466D, G6667, G66GD, GD08B, GG18H, GG6GD, GGG4D, H060H, HGGGD, HHH6H, 199AA7, 40006D, 40600D, 46600D, 5055C5, 5505C5, 55CCC1, 588CC1, 58CCC1, 60000D, 60009D, 7077G7, 7707G7, 777G07, 88000B, 9099A7, A000A7, A009A7, A09067, A099A7, A0AAA7, A90AA7, A99AA7, AA0007, AA6667, AAAG07, BFFF05, BFFFF5, C0FFF5, CCECC1, CECCC1, CF0FF5, CFF005, D0008B, D0033B, D0088B, D0333B, D033GB, D03G31, D0633B, DD990D, DGGG31, FHHHHH, G00081, G6GGGD, G8GGG1, GGG001, GGG331, GGGGG1, GGGGGD, H0006H, H00H6H, HH600H, 222222D, 22DDDDD, 333333B, 5CCCCC1, 70007G7, 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CDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD, 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71D, 73D, 73H, 73J, 75B, 75H, 768, 77H, 77J, 7B1, 7B5, 7BB, 7BD, 7C8, 7D1, 7DB, 7DD, 7E8, 7F5, 7FB, 7H5, 7HD, 7HH, 7HJ, 7J5, 7JD, 801, 80J, 832, 841, 86H, 86J, 881, 89G, 8E1, 8F4, 8F8, 8FA, 8FK, 8H4, 8IH, 8J4, 8JG, 90K, 91B, 91D, 91H, 93H, 93J, 955, 95H, 95J, 96G, 97B, 97D, 97H, 991, 99J, 9B1, 9BB, 9BH, 9BJ, 9CK, 9D1, 9DB, 9DH, 9DJ, 9EK, 9F5, 9FD, 9H1, 9HB, 9HD, 9IG, 9J5, 9KK, A0B, ABG, AF4, AF8, AG5, B15, B1H, B35, B3H, B3J, B4G, B51, B5B, B5D, B5H, B6G, B71, B75, B7B, B7D, B9B, B9J, BB5, BBH, BBJ, BC4, BCG, BF1, BF5, BFD, BH1, BHJ, BI4, BJB, C2D, C9K, CCD, CDG, CID, D0G, D2G, D35, D3B, D3H, D51, D55, D5B, D5D, D5J, D62, D71, D7H, D91, D95, D9H, DBH, DC2, DD1, DD5, DE2, DEG, DF5, DFJ, DH1, DHB, DI2, DJ1, DJB, DJJ, E14, E4B, E5K, E78, E81, E9G, EA5, EBG, EC1, EE1, EE5, EK5, F04, F11, F1H, F31, F3B, F3D, F44, F4A, F4K, F5D, F5H, F6K, F71, F7H, F7J, F88, F8A, F8K, F9J, FA4, FA8, FBB, FBH, FC4, FDB, FDJ, FE8, FFH, FFJ, FH5, FHB, FHJ, FI4, FI8, FIK, FJ5, FJD, FK4, FK8, G32, G5G, G78, G8J, 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====Additional known quasi-minimal primes (not necessarily the next)==== 40₄₇₃₃₃9G, CF₄₇₉₁₄₇0K ===Base 22=== 11, 17, 19, 1F, 1J, 1L, 23, 29, 2F, 2H, 31, 35, 37, 3D, 3H, 41, 49, 4D, 4F, 4J, 4L, 53, 5H, 5L, 65, 67, 6H, 6J, 73, 79, 7D, 7J, 83, 85, 8F, 8H, 8L, 91, 9D, A3, A7, A9, AD, AJ, AL, B9, BF, BL, C5, C7, CD, CH, CJ, D7, DL, E3, E5, E9, F1, F7, FH, FJ, G1, G7, GF, GL, H5, H9, HF, I1, I5, ID, J1, J3, JD, JF, JL, K3, K9, KH, KL, L1, L5, LH, 103, 12D, 145, 155, 15D, 163, 18D, 1A5, 1BD, 1BH, 1C3, 1D3, 1DH, 1EH, 1G3, 1GH, 1I3, 1K5, 1KD, 221, 227, 22J, 22L, 245, 247, 25D, 25J, 271, 277, 287, 28J, 2A5, 2B7, 2BD, 2BJ, 2D5, 2E1, 2E7, 2ED, 2EL, 2K1, 2KJ, 2LL, 30J, 343, 389, 39J, 3B3, 3GJ, 3IJ, 3J9, 3JJ, 3KF, 3LJ, 427, 443, 445, 457, 4A5, 4C3, 4E7, 4G5, 4I7, 4K5, 4K7, 515, 52D, 551, 559, 55D, 55J, 575, 58D, 59F, 5B1, 5C9, 5CF, 5D1, 5D5, 5DD, 5E1, 5ED, 5G5, 5GJ, 5J5, 5JJ, 5K1, 5KJ, 60D, 61D, 62L, 661, 66D, 689, 6C1, 6D1, 6DD, 6G3, 6KF, 701, 721, 751, 76L, 775, 77F, 77H, 787, 7A5, 7AF, 7B1, 7B7, 7CL, 7E1, 7FF, 7FL, 7H7, 7HH, 7K5, 809, 81D, 821, 827, 82D, 847, 869, 871, 881, 889, 899, 8A1, 8BD, 8BJ, 8D1, 8DJ, 8GJ, 8J7, 907, 90H, 92L, 93J, 943, 947, 95F, 977, 997, 9AF, 9B5, 9EF, 9F5, 9H3, 9HL, 9I7, 9J9, 9JJ, 9K5, A25, A45, A51, A61, A6F, AAH, AB5, ABH, ACF, AG5, AGH, AHH, AK1, B15, B2D, B2J, B33, B45, B47, B57, B71, B75, B81, B87, B8J, BB3, BB7, BC3, BDD, BE7, BEJ, BGD, BGH, BH3, BHD, BHJ, BIH, BJ7, BKJ, CA1, CAF, CB3, CC1, CEF, CG3, CKF, D09, D0J, D13, D21, D33, D39, D3F, D4H, D5J, D63, D81, D8D, DAH, DBD, DBH, DBJ, DCF, DD3, DEJ, DFF, DG9, DGH, DHD, DI3, DIF, DJ9, DK1, DK5, E0F, E0H, E27, E2D, E2L, E47, E7H, E87, E8J, EA1, EAH, EB1, EDH, EEJ, EFF, EFL, EH1, EIF, EIL, EJH, EJJ, EKD, ELF, F25, F43, FB5, FD3, FDD, FDF, FEF, FEL, FFD, FG9, G09, G0D, G25, G3J, G5D, G5J, G63, G8D, G99, GC3, GC9, GD9, GEH, GG5, GJ5, GJ9, GJH, H03, H1D, H21, H2J, H2L, H33, H63, H77, H8J, HCL, HDD, HE1, HE7, HGH, HGJ, HH7, HHL, HI3, HIH, HJH, HK1, HKD, HL3, I07, I0J, I43, I47, I7L, I9J, IBH, IEL, IG3, 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7KC1, 7L27, 7LCF, 7LK7, 802J, 80B1, 80GD, 80JJ, 80KJ, 820J, 86E1, 880D, 882J, 88E7, 88I7, 892J, 89EJ, 8B61, 8BI7, 8CI9, 8CK1, 8D6D, 8DD9, 8DGD, 8E01, 8E07, 8EE1, 8EI7, 8EK1, 8EKJ, 8I77, 8I87, 8IC9, 8IK7, 8J0J, 8K6D, 8KI7, 8KIJ, 8KK7, 9025, 9055, 9089, 9275, 92EJ, 92G5, 92GJ, 93EL, 9455, 9505, 9557, 9599, 96B3, 970L, 976F, 97G5, 982J, 98E7, 98I9, 98K7, 9905, 990J, 9925, 9995, 999H, 99BH, 99EL, 99G9, 99GJ, 99LJ, 9A55, 9B03, 9B27, 9BGJ, 9BH7, 9BK7, 9CG9, 9E6L, 9EHJ, 9EKJ, 9ELL, 9G39, 9G45, 9G4H, 9GA5, 9GAH, 9GBJ, 9GEJ, 9GHH, 9GHJ, 9GI9, 9GIJ, 9H7H, 9H87, 9HAH, 9HB7, 9I89, 9I9H, 9IB3, 9IEH, 9IKF, 9J7H, 9J87, 9JB7, 9JGH, 9K0F, 9K27, 9KGJ, 9KKF, 9L89, 9L9J, 9LG9, 9LGJ, 9LIJ, 9LKF, A081, A14H, A1IH, A201, A2C1, AA15, AA81, AAIF, ABC1, AC01, AHC1, AIIF, AKEF, B005, B01D, B01H, B051, B05D, B0A5, B0B1, B0BJ, B0DH, B0E1, B0GJ, B0H1, B0JH, B143, B16D, B255, B2B5, B2C1, B2G5, B2K7, B4EH, B4G3, B501, B5A5, B5BJ, B5C1, B5IJ, B5K5, B621, B663, B6I3, B6K1, B777, B7I7, B80D, B88D, B8ED, B8KD, BB01, BB0J, BB21, BB25, BB4H, BB6D, BBD5, BBE1, BBEH, BBH1, BBIJ, BBJH, BCK1, BD61, BDB5, BDGJ, BEE1, BG55, BGB5, BGGJ, BGIJ, BH27, BH7H, BHC1, BHH1, BHK7, BI77, BIGJ, BJ0H, BJBH, BJIJ, BJJJ, BK25, BK27, BK55, BKA5, BKK1, C043, C143, C2B1, C32L, C3G9, C601, C6EL, C6G9, C8B1, CBK1, CC2L, CC89, CE21, CECL, CF2L, CF89, CG69, CIG9, D003, D015, D045, D05D, D06D, D06F, D0DH, D0H1, D1D5, D1GD, D205, D26D, D2DJ, D32J, D38J, D403, D525, D561, D56D, D5AF, D5F5, D5GD, D6C9, D6D9, D6DF, D6E1, D6ED, D6F9, D6FD, D8IJ, D8JJ, D945, D993, D99F, D9C9, D9F3, D9G5, D9KJ, DA15, DAA5, DAE1, DAKF, DB25, DB61, DBC1, DBG3, DC43, DC99, DCE1, DD0F, DD1D, DD2D, DD2J, DD5D, DD9H, DDA5, DDD5, DDDJ, DDED, DDH1, DDHJ, DDI9, DDJ5, DE0D, DED1, DEDF, DEFD, DF03, DF45, DF55, DF5D, DF6D, DG05, DGGJ, DH0H, DH43, DHC1, DHEH, DHH3, DHJJ, DI8J, DIC9, DII9, DIJH, DJG5, DJHJ, DJKJ, DK6D, DKAF, DKDD, DKGD, E081, E0BJ, E0DD, E0DJ, E0E1, E0ED, E0J7, E0K7, E0KJ, E1GD, E1IH, E201, E281, E66F, E6BD, E6ED, E6K1, E6LL, E7EF, E861, E86D, E88D, EB0D, EB4H, EBHH, EBI7, EC6F, ECEL, ED0D, ED1D, ED6D, EDAF, EDDD, EDFD, EE01, EE0D, EE1H, EE21, EECF, EEE1, EEGH, EEH7, EF8D, EGGD, EGHH, EGIH, EGIJ, EH07, EH0L, EH8D, EHBH, EHBJ, EHK7, EHL7, EI4H, EIK7, EIKJ, EJ77, EK07, EK0J, EKC1, EKIJ, EKK1, EKK7, EL6L, ELBD, ELCL, ELDJ, ELK7, F059, F20L, F26L, F28D, F2GD, F2KD, F32L, F3AF, F3G3, F455, F56F, F595, F5KD, F6AF, F6GD, F88D, F8I9, F955, F995, F9B3, F9G3, F9KF, FB03, FB8D, FBI3, FC89, FD99, FDA5, FDI9, FEGD, FF59, FG2D, FGI3, FGKD, FI89, FIB3, FIKF, FK2D, FK45, FKD5, FL6D, FLG3, G003, G04H, G055, G0BH, G0HH, G0HJ, G0I3, G0K5, G0KJ, G26D, G2DJ, G2GJ, G303, G333, G393, G3G9, G3I3, G403, G40H, G433, G4AH, G4GH, G4H3, G4IH, G589, G5G9, G80J, G89J, G94H, G9G3, GAA5, GAIH, GB0H, GB43, GB6D, GBB5, GBG3, GBGJ, GBJJ, GD0H, GD45, GDD5, GDKD, GG2D, GG39, GG8J, GG9H, GGAH, GGDJ, GGEJ, GGGH, GGH3, GGKJ, GH0H, GHG3, GHH3, GHHH, GHJJ, GI03, GI2J, GI93, GIAH, GIEJ, GIG9, GII3, GJJJ, GJKJ, GK05, GKDD, GKGD, GKGJ, GKIJ, H081, H087, H0AH, H0BJ, 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5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000BB5, J000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000BIJ, C4IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII3, F0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000066B3, G0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000A5, D5KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKF, HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHBH, L0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000IKF, 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LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLKE7, 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80BN, 80FH, 80LN, 80MN, 840N, 848N, 866B, 86FB, 880B, 880N, 884N, 88CB, 88FB, 88LN, 88MN, 8BBB, 8BLB, 8C6B, 8CCH, 8CFH, 8F0B, 8FHH, 8FLB, 8H0H, 8HCH, 8IGN, 8ILN, 8KKH, 8L8B, 8LBB, 8LFB, 8LIN, 8M8N, 8MLN, 8N0N, 8NGN, 8NLN, 9061, 9091, 90EJ, 90F1, 90GJ, 90K1, 940J, 9501, 95F1, 9CC1, 9E0J, 9E95, 9F61, 9FI5, 9G3J, 9II5, 9K01, 9KK1, 9M01, A007, A05D, A0AD, A33D, A3AD, A3F5, A44J, A727, A9EJ, AA0D, AAAD, AAAJ, ACM7, AD8D, ADKD, AE27, AE9J, AEAJ, AEE7, AIAD, AIDD, AIID, AJ9J, AK5D, AM07, AM27, AM35, AMK5, B08B, B0CB, B0GB, B18B, B1CB, B80B, B8CB, BB21, BB4N, BBCB, BBF1, BBFB, BBK1, BC8B, BCF1, BCLB, BF1B, BF8B, BFB1, BFM1, BGC1, BGF1, BK21, BL8B, BLFB, BM1B, BM3N, BMB1, BMMN, BNF1, C00D, C06B, C077, C0D7, C0H7, C0L7, C0LB, C0M1, C60H, C6LB, C76H, C7E7, CAID, CC01, CCFH, CCKH, CDLB, CGE7, CH07, CHE7, CI8D, CIAD, CK0D, CL8B, CLDB, CLE7, CM01, CM07, CME7, CMM1, D007, D08D, D0C7, D0HH, D0LN, D0M7, D0NN, D207, D2KH, D2M7, D777, D7E7, D80H, D8LD, DA27, DAC7, DAM7, DBFB, DBMB, DC77, DCLB, DDL7, DE77, DF0H, DF2H, DFFH, DFMB, DH27, DH8H, DHC7, DHHH, DILN, DK0H, DK2H, DK8H, DKHH, DLIN, DLL7, DLM7, DLMB, DM07, DMH7, DMMB, DNGN, E07J, E09J, E335, E355, E555, E5A5, E5K5, E79J, E93J, E995, EA35, EE95, EKE5, F00B, F00H, F06H, F08B, F0I5, F11B, F18B, F1L1, F20H, F26H, F2FH, F355, F661, F6K1, F80B, F86B, F8BB, FBGB, FBK1, FBLB, FC0B, FC6H, FCLB, FEK5, FGB1, FH05, FH0H, FH35, FH6H, FHCH, FHF5, FHHH, FI05, FK91, FKK1, FL1B, FLB1, FLBB, FM61, FMBB, FMK1, G00J, G021, G027, G0EJ, G0JJ, G0M1, G0M7, G1CB, G2E7, G40J, G4AJ, G4IJ, G4JJ, G6C1, G701, G94J, G9IJ, GAEJ, GAJJ, GB21, GBM1, GC01, GCF1, GCLB, GE0J, GEAJ, GEE7, GEG7, GEIJ, GEL7, GFM1, GGE7, GGMB, GI0J, GIIJ, GIIN, GJ9J, GM27, GMB1, GNM7, H005, H0K5, H0M5, H207, H2E7, H335, H3I5, H595, H5K5, H60H, H68H, H76H, H80H, H8HH, HAAJ, HE7J, HEC7, HGE7, HGM7, HH35, HI55, HIM5, I00J, I035, I08D, I0CD, I4JJ, IC0D, ICID, II0D, II0J, II35, IIAD, IILD, IIM5, IIMN, IJ9J, ILCD, IM05, IM35, IMNN, INLD, J03J, J0HJ, J0JH, J2CH, J39J, J3ID, J60H, J62H, J8CH, J9IJ, JGAJ, JGJJ, JH9J, JI0J, JIDD, JJ0H, JJCD, JJJD, JJLD, JL3D, JLCD, K0E5, K0I5, K0K1, K0KH, K191, K211, K2F1, K2G1, K591, K5AD, K6F1, K6G1, K9I5, KA0D, KAAD, KAM5, KCCH, KCHH, KD8D, KDDD, KFI5, KG01, KG61, KH0H, KHHH, KI55, KIDD, KK21, KK8H, KKF1, KKK1, KKKD, KM8H, KMHH, KMK5, L027, L0M7, L1C1, L1MB, L211, L727, L8BB, L8BN, L8FB, L8LN, L9C1, L9M1, LB8B, LBC1, LBM1, LCAD, LD77, LDIN, LDL7, LDM7, LF8B, LG21, LIIN, LLLN, LLN7, LM07, LM1B, LM77, LMG1, LN77, LNM1, M00N, M01B, M03N, M055, M077, M08B, M0B1, M0C1, M0GB, M0K1, M0M7, M0N7, M18B, M1BB, M1MB, M26H, M335, M3GN, M3M5, M3MN, M3NN, M501, M53N, M5M1, M5NN, M6BB, M6C1, M6G1, M6KH, M88B, M88N, M8BB, M8NN, MBB1, MC01, MCC1, MCKH, MCM1, ME07, ME35, MEK5, MGGB, MGMB, MH35, MH8H, MHE7, MHM5, MK8H, MKC1, MKG1, MKHH, MKK5, ML8N, MM01, MM8B, MMC1, MMLN, MMM5, MMMN, MMN1, MN0N, MN27, MNGN, MNLN, N007, N027, N077, N0C7, N0DN, N0IN, N1M1, N227, N2M7, N661, N707, N727, N8LD, NA27, NA3D, NC07, ND0D, ND0N, NDLD, NF11, NF61, NGG7, NILN, 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5M0M1, 5MNNN, 5N03D, 5N3LD, 5NA8D, 5NADD, 5NDGN, 5NNGN, 600KH, 61661, 616L1, 61MM1, 66161, 66611, 666B1, 666L1, 666LB, 66BB1, 66BG1, 66BLB, 66G61, 66KF1, 66LBB, 66LG1, 6BBBB, 6BFCB, 6CC11, 6F1M1, 6F66B, 6F6B1, 6F6L1, 6FBCB, 6FLMB, 6FMCB, 6FMM1, 6FMMB, 6GCM1, 6GM61, 6GMC1, 6K1C1, 6K1K1, 6KK11, 6KKL1, 6KL11, 6L1G1, 6LBFB, 6LCC1, 6LFMB, 6MM61, 6MM6B, 70291, 702C1, 702G1, 72CF1, 72EE7, 7433J, 7443J, 77A07, 79901, 799F1, 7AAEJ, 7EE27, 7H9EJ, 7K2KH, 7KK2H, 7KKKH, 7KKMH, 7L2C1, 800NN, 806BB, 808BB, 808LB, 80F8B, 80IIN, 833ID, 860KH, 8886B, 888NN, 8BG4N, 8CH6H, 8CKHH, 8FC0H, 8FFCH, 8HHHH, 8IIIN, 8K0HH, 8LL4N, 8M0NN, 8MNNN, 8NNND, 9000J, 900M1, 9034J, 90IIJ, 94IIJ, 96CM1, 96KF1, 96MM1, 990C1, 990M1, 99591, 99961, 999C1, 99F91, 99FM1, 99KF1, 99M61, 99MK1, 9AAA5, 9FEE5, 9FFA5, 9FFF5, 9II4J, 9K6C1, 9K9C1, 9K9F1, 9KF91, 9M6M1, 9MK61, A02M7, A0A35, A0AM5, A0C77, A0D0D, A0DDD, A0EC7, A0M55, A0MM7, A2ME7, A3335, A33M5, A3555, A3MM5, A550D, A58ID, A5D0D, A5DDD, A74AJ, A7E07, AA0M5, AA3ID, AA3M5, AA83D, AA8ID, AAAM5, AACID, AAICD, AAM05, AC08D, AC0ID, AC0KD, AC8ID, ACA8D, AFA35, AIC8D, AJAJJ, AK0KD, AKI0D, AKKM5, AKM05, AM505, B00FB, B00LB, B0LBB, B1MBB, B1MMB, B2GM1, B3MGN, B88BB, BB3MN, BBB3N, BBB8B, BBBBN, BBBMN, BBCC1, BBGB1, BBGLB, BBMC1, BBMGB, BBNM1, BFB0B, BFBMB, BFGLB, BFGMB, BGGLB, BGMM1, BLMMB, BMC0B, BMGM1, BMMK1, BMNM1, C006H, C00CH, C00M7, C0C11, C0CC1, C0E07, C0F6H, C0GG7, C0K8D, C0KDH, C0KHH, C1CC1, C1CM1, C1MC1, C70F1, C886B, CC06H, CCCCH, CCCF1, CCCM1, CDHH7, CE707, CE7L7, CEE77, CEEG7, CEL07, CFFHH, CGLL7, CHC6H, CHCCH, CHH7H, CHHH7, CHHM7, CI0LD, CK0HH, CKHCH, CL007, CLD07, CLLL7, CM777, CMMM7, D008H, D07L7, D0DE7, D0EL7, D0L77, D0M8H, D0NA7, D22E7, D70A7, D7227, DBLBB, DCL07, DD7A7, DDAE7, DDD8D, DDE07, DDK0D, DDM77, DEE27, DKK8D, DL227, DL707, DLBBB, DLDFB, DLE27, DM2E7, DMM77, DMME7, DN0A7, DNIIN, DNLLN, E000J, E0227, E02E7, E0AAJ, E0GL7, E0I0J, E2E07, E7AAJ, E7E27, EAA55, EAK55, EC777, ECEE7, ECEL7, ECGL7, ECL77, EEC77, EECL7, EEEC7, EEG27, EEGG7, EG0E7, EG0L7, EG207, EGE07, EGG07, EGG27, EGL07, EI9IJ, F02HH, F06LB, F0C6B, F0CCH, F0CHH, F0E55, F0EA5, F0FH5, F0GGB, F0M2H, F0MGB, F0MMB, F1BMB, F3FF5, F3I35, F3II5, F6BCB, FA035, FB1MB, FBBM1, FBBMB, FBM8B, FC0HH, FC88B, FCFHH, FFC0H, FFCFH, FFCHH, FFF0H, FFF6H, FFFH5, FFHI5, FFI55, FG1MB, FGGCB, FGM1B, FHK55, FI5I5, FKEA5, FKKI5, FKL11, FM16B, FM1CB, FM62H, FM6CB, FMBG1, FMM0B, G0001, G00E7, G039J, G06F1, G07C1, G07F1, G0A9J, G0G07, G0GG7, G0I4J, G0I9J, G0LL7, G22M7, G2M07, G339J, G433J, G62M1, G6M61, G6MM1, G903J, G933J, GAA9J, GBCC1, GE007, GGGGB, GGGL7, GJ0IJ, GL007, GL2M7, GLL07, GLLM7, GMGCB, GMM07, GMM1B, H007H, H05I5, H0CCH, H0CM7, H0GG7, H0H27, H0H8H, H0HC7, H0HH5, H0I35, H0MM7, H3555, H35F5, H3F55, H3FF5, H5055, H50F5, H7HEJ, H9995, H9GEJ, HCC0H, HCC6H, HCGG7, HCHM7, HE027, HE0G7, HEE07, HEEG7, HEG27, HF0F5, HF505, HF555, HFF05, HFKF5, HG0G7, HH06H, HH08H, HH0H5, HH5I5, HH7HJ, HH9EJ, HH9I5, HHCHH, HHE07, HHGG7, HHH05, HHH7H, HHH9J, HHKI5, HHM05, HHM07, HHM27, HI0I5, HJ86H, HJC0H, HK055, HK9F5, HKF05, HKFF5, HKFK5, HKII5, HKK95, HM2M7, HME27, HMKM5, HMM05, HMM27, HMM55, HMMM7, I00DD, I00M5, I044J, I0505, I09IJ, I0AAD, I0D0D, I0DDD, I0I05, I0IDD, I0II5, I0IJJ, I0JIJ, I33M5, I4I4J, I5INN, I888N, I8NND, I8NNN, I904J, I94IJ, IA8ID, IAADD, IAI8D, IDDDD, IDINN, II88N, II8NN, IID8D, IIDIN, III8N, IIIDD, IIIID, IIIIN, IIIND, IIN8D, IINDD, IJJ0J, IJJJJ, ILILN, ILLIN, IMM8N, INA0D, INDNN, INGIN, INNDN, INNND, J000H, J002H, J00AJ, J00GJ, J00KH, J02KH, J068H, J080H, J090J, J0A9J, J0AAJ, J0C0H, J0G0J, J0IIJ, J0JGJ, J0JIJ, J0K8H, J2K0H, J2KKH, J6K8H, J86KH, JC00H, JC0KH, JCCCH, JCK0H, JCKCH, JDDLD, JG93J, JIIJJ, JJ0IJ, JJ2KH, JJ9GJ, JJCCH, JJG9J, JJGIJ, JJJ9J, JJJJH, JJK8H, JK08H, JK0CH, JK8KH, JKC0H, JKKKH, K0001, K0091, K020H, K02C1, K03ID, K0611, K06L1, K083D, K08HH, K0961, K09C1, K0CF1, K0F91, K0KM5, K0LG1, K1G21, K20HH, K29K1, K2KHH, K5001, K500D, K58ID, K5D0D, K5L11, K6621, K6C11, K6LC1, K8CKH, K8KCH, K96C1, K99E5, K9F91, K9FA5, K9FE5, K9K91, KA55D, KC011, KCF11, KD02H, KD0MH, KD20H, KDM2H, KEA55, KEAA5, KEK95, KEKK5, KF1G1, KF1K1, KF611, KF6L1, KFEA5, KH8CH, KI005, KIMM5, KK05D, KK0AD, KK0DH, KK2CH, KK2KH, KK33D, KK961, KK9C1, KKA5D, KKD0D, KKE55, KKI0D, KKIID, KKIM5, KKK0H, KKKM5, KLGC1, KMK2H, L188B, L1991, L2007, L22M7, L2EE7, L2MM7, L333D, L3LIN, L7291, L72G1, L88IN, L8C8B, L9991, LBB1B, LBBBB, LBBBN, LD0E7, LDBBN, LE207, LFMCB, LGCC1, LL227, LL3IN, LL48N, LLM27, LLMM7, LMBCB, LME27, LMMBB, LMMM7, LN33D, LN3AD, LNAAD, LNACD, M0007, M0061, M00K5, M0207, M066B, M0BCB, M0EE5, M0G01, M0GM1, M0M8N, M27KH, M2E27, M2M07, M2M27, M5005, M5555, M66CB, M66K1, M6K61, M6MCB, M7007, M7EE7, M8C0B, M8KCH, M8MGN, MBBGB, MBGM1, MCCCH, MCHCH, MEE55, MGBC1, MGMM1, MH227, MH2M7, MHH7H, MKM55, ML3LN, MM0CB, MM16B, MM227, MM661, MM6K1, MME55, MMEE7, MMKE5, MMM07, MMM6B, MMMB1, MMMGB, MMMM7, MNM61, MNN3N, N00CD, N00KD, N03LN, N0A8D, N0AM7, N0D8D, N0KKD, N0L3N, N0LAD, N0NDD, N16L1, N3GIN, N3LAD, N3LIN, N3NNN, N61L1, N96M1, N9M61, NA0CD, NAK0D, NAKKD, NCA8D, NCM77, NDGIN, NDIIN, NDLLN, NF991, NGM07, NIIIN, NINNN, NKKDD, NLNAD, NN0LN, NN191, NN3NN, NN6L1, NN83D, NNAAD, NNDIN, NNGIN, NNL3N, NNLND, NNM61, NNNIN, 166G21, 16G621, 19MMM1, 1BBBMB, 1BBGM1, 1GCCC1, 1GCCM1, 1MMM1B, 200E27, 2E0027, 2HH0HH, 2HHC0H, 2KK0HH, 2M0E27, 2M22E7, 30NNNN, 3333M5, 333AID, 333I35, 33I555, 3F5FF5, 3I3MM5, 3I88GN, 3II8LN, 3IIII5, 400IJJ, 40J00J, 40JJ3J, 40JJJJ, 44403J, 444I0J, 44IJJJ, 44J0JJ, 44JJIJ, 48I8IN, 4I440J, 4II8IN, 4IJ0IJ, 4JIIIJ, 4JJ0JJ, 4JJJ0J, 50033D, 5003AD, 5008ID, 500D8D, 500G01, 500L11, 500LAD, 500MG1, 503LAD, 508ILD, 50DDLD, 50ILAD, 50M001, 516G61, 519MM1, 538NNN, 53NNNN, 55005D, 5508ID, 550D8D, 558ILD, 55F5I5, 56G661, 58333D, 58NNNN, 5999F5, 59AAF5, 5DNNNN, 5F55I5, 5FMMM1, 5G6661, 5K9AA5, 5KK9F5, 5KKK95, 5M0001, 5NDD8D, 5NDINN, 5NN33D, 5NNLAD, 5NNNAD, 5NNNDN, 608K0H, 61CCM1, 61G621, 661G21, 666621, 6666CB, 6666F1, 66K661, 6BCCC1, 6BKKC1, 6F6BBB, 6G6621, 6GCCC1, 6GMMM1, 6K6K61, 6M666B, 70A077, 70L991, 7722E7, 772E27, 7772E7, 777A27, 777L27, 77A777, 77EL27, 7A7077, 7A7777, 7E7227, 7L2E27, 7LEL27, 7LL2E7, 7LLE27, 7LLL27, 800GIN, 80NINN, 80NNNN, 8BBMGN, 8C888B, 8C88LB, 8MM0GN, 900001, 90043J, 959MM1, 96K661, 9999F1, 9999K1, 999AF5, 999FF5, 99EEE5, 99K991, 99MMM1, 9AAFF5, 9EIIIJ, 9F9991, 9F9MM1, 9FEAA5, 9G444J, 9K9991, 9M6661, A000CD, A000KD, A000M5, A0083D, A00I0D, A00M05, A022E7, A07E77, A0FF35, A0K3ID, A0K83D, A4AJJJ, A77777, AA0035, AA0355, AAA035, ADDD0D, ADDDDD, AF0035, AFFF35, AKK8ID, AM0M05, AM7777, B0F0MB, BBBBM1, BBLBMB, BFBBBB, BFM0MB, BFMMMB, BLBBMB, BLMBBB, C00071, C000E7, C007C1, C00G07, C07KKH, C0CC6H, C0CH6H, C0EEE7, C0HHHH, C777L7, C77L77, C7L777, C7LL07, C8088B, CAAK8D, CAKKAD, CC000H, CC0CHH, CD000H, CD0KKH, CE0007, CEE0E7, CELL77, CG0007, CGGL07, CH0CHH, CHCH0H, CHHH6H, CK0C0H, CKAK8D, CKKA8D, CL7707, D002FH, D0D0KD, D0DA77, D0DKKD, D0IIIN, D0K0DD, D0KDKD, D0KKDD, D0KKKH, DC0EE7, DCEEE7, DD0227, DD0D27, DD0DKD, DD0KKD, DD2E27, DDD0D7, DDD0LD, DDD227, DDDA77, DDDBCB, DDDCE7, DDDDFB, DDDMM7, DDEEE7, DDMBCB, DEEC07, DH000H, DHMEE7, DIIIGN, DK0KDD, DKMKKH, DMBBBB, DMEEE7, DMMM27, E00G27, E07727, E0C707, E0CE77, E0E027, E0EEG7, E0EGE7, E0EL27, E0GE27, E0L207, E0LE27, E0LL27, E2E2E7, E7L2E7, E900IJ, E9EEE5, EAAKK5, EC00E7, EC0G07, EC7007, ECEG07, EE0G07, EE0GE7, EE72E7, EE7L27, EECE07, EECEG7, EEEEE5, EEEK55, EEEKA5, EEEL27, EEGLL7, EELE27, EGLLL7, EKK595, EKKA55, EKKAK5, EKKKK5, F000E5, F0AA35, F0F035, F0FFFH, F0HKK5, F0KKE5, F16BB1, F16MM1, F1BBBB, F1MC6B, F666BB, F66BBB, F6GMM1, FB0BBB, FB1BBB, FBBB0B, FBMMG1, FC0FFH, FCFCCH, FEEE55, FEEEA5, FF03F5, FF0FFH, FF3F35, FFEE35, FFF2CH, FFFCCH, FFFFE5, FFI335, FFKFE5, FGLMMB, FK55I5, FKFE55, FLM8CB, FMC66B, FMMC6B, G0AA4J, G0CCC1, G0LE07, G666F1, GG0007, GG00G7, GG0L07, GGLLL7, GGLMM7, GI444J, GJJ33J, GLLE27, GLMMCB, GM0661, GMMM61, H00G07, H05555, H09FF5, H0C0E7, H0CE07, H0CEE7, H0E227, H0H007, H0H5F5, H0H995, H0HHE7, H0HHH7, H55505, H55II5, H5FII5, H99FF5, HEG007, HFFK55, HH0007, HH02M7, HH0C0H, HH7AEJ, HHC0E7, HHE227, HHH0C7, HHH0M7, HHH995, HHHC0H, HHHE27, HHHEAJ, HHHH07, HHHH8H, HHHHE7, HHHHI5, HHHHJH, HHHJ8H, HHHJCH, HHJ00H, HHK095, HHKKM5, HKK0F5, HKK5F5, HKKK55, HKKKK5, HKM555, HMEEE7, I00555, I05555, I0I94J, I333I5, I33555, I444IJ, I55055, I55505, I55555, IAAC8D, ID000D, IDD0LD, II9I4J, III4IJ, III505, IIIC8D, IIJIJJ, IJIIIJ, IM8LLN, IN00AD, INAACD, INCAAD, ININGN, J00CCH, J0IJJJ, J0J09J, J3333D, JIJIIJ, JJ68KH, JJIJIJ, JJJAJJ, JJJHGJ, JJJJAJ, JJJJGJ, JJJJIJ, K0008H, K00161, K001G1, K001L1, K002CH, K002HH, K00521, K00AKD, K00C0H, K00GF1, K00I0D, K00K95, K00M05, K01621, K05021, K0505D, K051G1, K059F5, K05K95, K0C0C1, K0L291, K0M005, K0M505, K1K661, K2CK0H, K33IAD, K3IIID, K5550D, K56121, K59AA5, K612K1, K61CC1, K66661, K6K611, K900C1, K99661, K9AFF5, K9C001, KAKI8D, KC00C1, KDK00D, KF9991, KI0IID, KK000D, KK01L1, KK0661, KK0I8D, KK0L11, KK0M2H, KK5661, KK59F5, KK61C1, KK9995, KK9EE5, KKA3ID, KKA83D, KKAI8D, KKC001, KKC0C1, KKC1C1, KKCCC1, KKD2HH, KKK595, KKK9A5, KKKK95, KKKKKH, KKKMCH, KKM505, KKMEE5, KKMKCH, KM0005, L222E7, L33AAD, L38I8N, LCCC11, LDFBCB, LEL2E7, LELE27, LELL27, LGMMM1, LLE2E7, LM2ME7, M000M5, M006MB, M00E27, M00MM1, M02227, M06M61, M06MM1, M0E227, M0EE27, M0KME5, M0M5GN, M0MM61, M0MMCB, M0MNNN, M0NNM1, M38LLN, M5K505, M77707, M7E227, M7E727, M8CHHH, MBMMCB, MBMMM1, MEEE77, MHH027, MHH505, MHHC6H, MHHH6H, MHHK05, MKK001, MM2ME7, MM7707, MM7E77, MMBMK1, MMM2E7, MMMC0B, MMMK61, N0003D, N0008D, N0030N, N030NN, N0C0AD, N0CKAD, N0DKDD, N0N3GN, N0NN3N, N333AD, N777A7, N77A77, NAACKD, NAAKDD, NACAKD, NACKAD, NC0AKD, NC0KAD, NCA0KD, NCKAKD, NDNNLN, NNNLAD, NNNNLD, 1BBBBBB, 1BBBBG1, 1M6MMMB, 1MMBBBB, 1MMMMK1, 2000227, 2000EE7, 20EEEE7, 2C0FFFH, 2E2EEE7, 2KKKHCH, 2MEE227, 2MEEE27, 333333D, 3333355, 3335555, 333FFF5, 333IIID, 388NNNN, 38INNNN, 3INNNNN, 4000IMN, 4000JJJ, 400IIIN, 444444J, 44JJJJJ, 488888N, 4IIJIIJ, 4JJJ33J, 50002M1, 5001G21, 5006621, 500LGM1, 555083D, 55555I5, 5616G21, 59MMMM1, 5K999A5, 61CCCC1, 66666K1, 6K0000H, 6K0080H, 70000A7, 70077A7, 70700A7, 7070A77, 77700A7, 77770A7, 7777227, 7777E27, 77L2227, 7LE22E7, 888888B, 888888N, 8888BBN, 8888IIN, 888B88B, 888I8IN, 88IINNN, 88NIINN, 88NNIIN, 8INNNNN, 90444IJ, 904I44J, 9666661, 9666FK1, 9666K61, 9966FK1, A00KK0D, A0K000D, AAAAA35, AAKKI8D, BB8888B, BBB0BLB, BBBB1BB, BBBBBB1, BBBBBGB, BBBBBLB, BBBLMBB, C0007KH, C000F11, C00FFFH, C00HH0H, C00K00H, C0C0HHH, C0CCHHH, C0CHH0H, C0CHHCH, C0FFFFH, C0H0H0H, C0KKC0H, CC0HH0H, CCCCC11, CCCCCC1, CCHHHHH, CDKKKKH, CEL7777, CGGG0G7, CGGGGG7, CH00HHH, CHGGGG7, CHHHH0H, CHHHHCH, CHHHHHH, CK0000H, CKDKKKH, D00DDKD, DD0DDD7, DDBBBLB, DDD2EE7, DDDBBLB, DDDDD27, DDDDDBB, DDDDDC7, DDDDDKD, DDDDDMB, DDDDEE7, DDDDKKD, DDDDLDB, DDDFBBB, DDDLFCB, DDDMEE7, DDM2227, DHHEEE7, DK000KD, DK00D0D, DK0D00D, DNN000N, E000CL7, E000EG7, E000GE7, E00C0G7, E00CE07, E00EE27, E0C00G7, E0C0EG7, E0CE007, E0EC0G7, E0EE207, E0G0007, E20EE27, E22EEE7, E2EE227, E2EEE27, E772227, E77LL27, E7L2227, E9IIIIJ, EAKKKA5, EC000G7, ECG00G7, EE00L27, EE0E0G7, EE20EE7, EEE0EG7, EEE22E7, EEEE727, EEEEE27, EEEEG07, EEEEGE7, EEEKKK5, EELLL27, EI0IIIJ, EKKKAA5, ELLLE27, F00FA35, F0333F5, F0F0FE5, F333335, FAAFF35, FCF0FCH, FEEEE35, FF03335, FF0FA35, FF0FE35, FF0FMCH, FFF0A35, FFF0F35, FFFAF35, FFFF5I5, FFFFM2H, FFFI3I5, FFFIII5, FFH5555, FH55555, FL1MMM1, G0000G7, G0000L7, GGGG007, GLE2227, GLLLLE7, GLLLLL7, H000007, H0000C7, H000HCH, H000HM7, H000M27, H000ME7, H00G227, H00HHM7, H02M227, H0C0HHH, H0CH00H, H0E0007, H0FFF35, H0FFFF5, H0H0ME7, H0HFII5, H0HHHCH, H0M0227, H555555, H5F5FF5, HC000G7, HC00H0H, HCCHHCH, HCHHHCH, HCHHHHH, HEEEE27, HFF5FF5, HFF5FI5, HFKKK05, HG00007, HH00E27, HH0G227, HHH2MM7, HHH55F5, HHH9FF5, HHHFFK5, HHHFK55, HHHH7EJ, HHHHCM7, HHHHHAJ, HHHHHF5, HHHHHHJ, HKK5505, I000055, I00A0ID, I0I4IIJ, I0IIIIJ, I88NIIN, III0055, III0I55, III444J, IINNLIN, J000IJJ, K0000DH, K0000KD, K00033D, K000A5D, K000K5D, K00555D, K009995, K00K00D, K00K8ID, K00KI8D, K00KIAD, K01GCC1, K05033D, K0999F5, K2KKKCH, K53333D, K956661, K999991, KCCC1C1, KFFFE55, KFFKKE5, KFKFKE5, KK009A5, KK00C11, KK01GC1, KK99001, KKIII05, KKK09F5, KKKE9E5, KKKEAK5, KKKKI05, KKKKKE5, KMMEEE5, L1BBBG1, LBMMMCB, LBMMMMB, LDEEE07, LEE22E7, LEE2E27, LEEE2E7, LLLLE27, M0000CB, M000C6B, M02EEE7, M0K0005, M0M0005, M2CHHHH, M2HHHHH, M6MMMM1, MC0000B, MCHHHHH, ME7E777, MEE7777, MEEE2E7, MG06661, MHHHCCH, MHHHH27, MHHHHH7, MHM0027, MM6666B, MM77777, MMC000B, MMM7727, MMNM777, N000NLN, N00333D, N003AAD, N0A00DD, N0NN33D, N0NNLLN, N30000N, N777777, NDNNNNN, NN0N0GN, NN0N30N, NNN300N, NNN333D, NNN3LLN, NNNDDDD, NNNNN3N, NNNNNND, 33333F35, 33FFFF35, 3555FFF5, 3FFFFF55, 3NNNNNLN, 40000I0J, 40I0IIIJ, 444440IJ, 4J0000IJ, 500006G1, 5D00DDDD, 5L1MMMM1, 5MMMMMG1, 5NNDDDDD, 5NNNNDDD, 5NNNNN8D, 6000080H, 777777A7, 77777A77, 7944444J, 800000IN, 996666K1, 999999I5, 9999FEA5, A00003ID, AAAAFF35, BBBGMMMB, C0000011, C000007H, C0CC0H0H, C666666B, CCCH0HHH, CCHH0HCH, CE777777, CEEEEE07, CHH0H00H, D00000GN, D000D0LD, D000IIGN, D0DDDDD7, DDD0E2E7, DDDDDDDB, DDDDDME7, DEEEELE7, DEEELEE7, DEELEEE7, DELEE0E7, E00000C7, E00000G7, E0000CG7, E000C0E7, E000G007, E00CG007, E00E0CG7, E0C00007, E0CGGGG7, E0GGGGG7, E20000E7, EAAKAAA5, EAKKAAA5, EE00E727, EE020007, EEEE2027, ELEE2227, F00003F5, F0000A35, F0003335, F0FFFA35, F1999991, F1999MM1, FAAAAF35, FBBBBBG1, FEAAAAA5, FF000A35, FF00FF35, FF0KEEE5, FFAAAF35, FFF555I5, FFFF33I5, FFFFF035, FFFFF3F5, FFFFFKI5, FFFFFMHH, FKFKEEE5, FKKFEEE5, FMMMMMCB, FMMMMMM1, G2000007, GGGGGMM7, GJJJJJ0J, GJJJJJ3J, H0000E27, H0000G27, H000C0G7, H000CEG7, H000CHH7, H000E0E7, H000EE27, H00CHHG7, H00EEE27, H00M0EE7, H05FF5F5, H0E00EE7, H55FF5F5, HCHH0H0H, HE000EE7, HFFIIII5, HGGG2227, HH00CEG7, HH00H0CH, HH0EEEE7, HH0FFFI5, HHEEEEE7, HHH000CH, HHH00EG7, HHHC00G7, HHHFFFF5, HHHHHKK5, HHHK5F55, HK5555F5, I4IIIIIJ, IA0000ID, II0005I5, III000I5, III055I5, III5NNNN, IIIII9IJ, IIIIIII5, IIINNNGN, JAJJJJJJ, JJAJJJJJ, K000005D, K00009A5, K0000M55, K000M555, K008IIID, K00D0K0D, K00III8D, K00K550D, K00LCC11, K0999951, K0D0000H, K0K00595, K0K9AAF5, K0KK0095, K0KK9FF5, K3333IID, KFKFEEE5, KFKKEEE5, KK00000H, KK0000M5, KK099991, KK55583D, KKKEEEA5, KKKKKKI5, LEEEE227, LLLEEE27, LLLL2E07, M000006B, M000M6CB, M0MMMMM1, M222EEE7, M777E777, M7E77777, ME222EE7, ME2EEEE7, MEE222E7, MM0NNNNN, MME77727, MMM6MMM1, N00003GN, N0000ADD, N000N0GN, N000NNND, N033333D, N0NN0NGN, NDDDDKDD, NN000N3N, NN00N03N, NN03000N, NNN003GN, NNNNDNLN, NNNNNADD, 199999MM1, 200FFFFFH, 222MEEEE7, 2FFFFFFCH, 30000000N, 30N00000N, 400000J3J, 500000M01, 5000166G1, 5000666G1, 50DDDDDDD, 8NN33333D, 999999991, C000000FH, C00000K0H, C000H00HH, C77777707, CH00H000H, CHH0000HH, D00000DKD, D00000DLD, D0000200H, D0000KK0D, D000KK00D, D00D0DDLD, D0D00DDLD, D0LEEEEE7, DDBBBBBBB, DDD000KDD, DDDDDDDE7, DK00000DD, DNNNNNNNN, E00000E27, E00007L27, E0000E727, E0E000C07, E20000027, EAAAAKAA5, EAKAAAAK5, EE0000C07, EEE000E27, EEEEEEGL7, F00FFFF35, F0FFFFF35, FF0000035, FF0FFFF35, FF5555FI5, FFFFFFA35, FFFFFFF35, FFFFFFFI5, FKKKKEEE5, FMMMMMMMB, GGGGG2227, GGGGGG207, GJJJJJJJJ, GLMMMMMMB, H000022M7, H000222M7, H000EEEE7, H0EEEEEE7, H0H0000CH, H0IIIIII5, HCH00000H, HE0EEEEE7, HFFFFFI35, HFFFFKKK5, HHHHHHG27, HHHHHHH55, HHHHHHHH7, HHHHHHM55, HHHKK5555, HHIIIII05, HIIIIII05, HKK5555I5, I000000AD, I000000ID, I000A000D, I00A0000D, IIIII0555, IIIIIII9J, K000000AD, K00000595, K000009F5, K0000550D, K099999A5, K0C00000H, K0I00000D, KK0000595, KK0000HCH, KKK000095, KKKFKFFE5, KKKIIIII5, M77777777, MEEEE2227, MMMMMMMM1, N0000000D, N0000003N, N000003NN, N00000N3N, N00000NGN, N00N000GN, N00NNNN8D, N0NNN00GN, N0NNNN3AD, N0NNNNNGN, N999999M1, NN0NNNNGN, NNN000NGN, NNNNNDD8D, NNNNNN0GN, 16MMMMMMMB, 1MMMMMMBCB, 3333333335, 33333333I5, 400000000N, 40IIIIIIJJ, 4IIIIIIIJJ, 4IIIIIIJIJ, 50000000M1, 70F9999991, 777E777727, 9999995MM1, ADD000000D, C00000088B, C000000CF1, C00000F0HH, CH00000H0H, D00KD0000D, D0D0DDDDLD, D0E2EEEEE7, D2EEEEEEE7, DBBBBBBBBB, DD000000KD, DD0000DDLD, DLE0EEEEE7, EEE0000727, EEEAAAAAA5, EEEEEE00G7, EEEEEEE0G7, F000000F35, F00FFKEEE5, F00KFFEEE5, F0M666666B, FCFFFFFFFH, FFFFFFF2HH, FFFKKKEEE5, GGGGGGG227, H00000C06H, H0000HHH6H, H555FFFFF5, H55FFFFF55, H5FFFFFF55, HF5FFFFFF5, HHHH0H0HCH, HHHHH0HHCH, HHHHHH0HCH, HHHHHHHHM5, HHHIIIIII5, IIDNNNNNLN, IIIIIJJIIJ, IIINNNNNLN, IINNNNNNGN, INNNNNNNLN, J0000000IJ, K0000II8ID, K099999995, K0I0000AID, K0K0009FF5, K9999999F5, KK00000095, KKFFFKEEE5, LLLLLLLME7, LLLMEEEEE7, LMEEEEEEE7, M000000005, MHHHHHHHH5, MK00000005, MMMMMMMBCB, NN000000GN, NN0000NNGN, NN99999991, 2HHHHHHHHHH, 38NNNNNNNNN, 3MNNNNNNNNN, 40IIIIIIIIJ, 4AJJJJJJJJJ, 4J000000J0J, 4JJJJJJJJJJ, 506666666G1, 5DDDDDDDDLD, 999999999F5, 99999999EA5, 99999999FE5, A0000000035, C0000000007, C00000000G7, C00000000KH, CEEEEEEEEL7, D0000000FMH, D000DDDDDLD, D0KD000000D, DDDD00000KD, DEEE0EEEEE7, DEL0EEEEEE7, DELEEEEEE07, E0000E20007, E7777777727, EE000000207, EEE20000007, FFFFFFFFMCH, FM66666666B, GGGGGGGG2M7, HFFFFFFFF55, HHHHHHHHH6H, HHHHHHHHHCH, HHHHHK55555, I9IIIIIIIIJ, IIIIIIII44J, IIIIIIIJJIJ, IINNNNNNNNN, JDDDDDDDDDD, JJIIIIIIIIJ, K00000I8IID, LLLLLLLLL27, 9999999EEAA5, AI000000000D, C77700000007, CH0HH000000H, D00D000000LD, DEEEEEEE0EE7, DN000000000N, EAKAAAAAAAA5, EKAAAAAAAAK5, F6666666666B, H000HHHHHH6H, H55FFFFFFFF5, HFFFFFFFFKK5, K00000000I8D, K999999999A5, 3555555555FF5, 5000000000001, 6G66666666661, 99999999999A5, C00000000000H, CFFFFFFFFFFCH, CHHH00000000H, D00000000K0KD, D0000000K00KD, D0D00000000LD, DEEEEEEEEEL07, E000E20000007, E00E200000007, EEE0000000027, GGGGGGGGGGGM7, GGGGGGGGGGM07, H00000000CHHH, H00HC0000000H, HFFFFFFFFFFK5, I0A000000000D, J000000000J9J, K000000000095, K000000000M2H, M0000000000M1, M0EEEEEEEEEE7, MHHHHHHHHHHHH, MMNNNNNNNNNNN, MNNNNNNNNNNNN, N000000DDDDDD, N000DDDDDDDDD, NNDDDDDDDDDDD, 22EEEEEEEEEEE7, 35FFFFFFFFFFF5, 400000000000JJ, 800000000000GN, DDDDDDDDDDD077, DDDDDDDDDDDDD7, E0000000000L27, EAAAAAAAAAAKA5, EEG00000000007, H0000000000C6H, I5500000000005, II0000000000I5, M0666666666661, M6MMMMMMMMMMMB, 4JJ00000000000J, 506666666666661, BGMMMMMMMMMMMCB, CFFFFFFFFFFFFFH, D0000000000KD0D, D0HEEEEEEEEEEE7, F0BBBBBBBBBBBBB, HGGGGGGGGGGGGG7, K0000000000000D, K00000000000MCH, M0M6MMMMMMMMMMB, 5DDDDDDDDDDDDDDD, C00000000000008B, D00000000000000H, DEEEEEEEEEEEE0L7, DEEEEEEEEEEEEEL7, EEE2EEEEEEEEEEE7, GM66666666666661, H5FFFFFFFFFFFFF5, IIIIIIIIIIIIIJJJ, BGMMMMMMMMMMMMMMB, DLEEEEEEEEEEEEEE7, H0000000000000CHH, H000000000C0000HH, I000000000000000D, IIIIIIIIIIIIIIIJJ, INNNNNNNNNNNNNNNN, J000000000000009J, M666666666666666B, N0000000000000LLN, N00DDDDDDDDDDDDDD, 355555555555555555, 60000000000000008H, 6M6666666666666661, C000000000000000F1, N0DDDDDDDDDDDDDDDD, 666666666666666666B, 800000000000000000N, AD000000000000000DD, DEEEEEEEEEEEEEEEEE7, I500000000000000005, 20000000000000000027, 4000000000000000003J, 400000000000000000IJ, 99999999999999999995, DD00DDDDDDDDDDDDDDLD, E2EEEEEEEEEEEEEEEEE7, N00000000000000000LN, 500000000066666666661, EE0000000000000000727, GGGGGGGGGGGGGGGGGGG07, H0000000000000000006H, 40000000000000IIIIIIIJ, AD0000000000000000000D, K0000000000000000000M5, CL777777777777777777777, D000000000000000000000N, D0000000000000000000IIN, HHHHHHHHHHHHHHHHHHHHHK5, NDDDDDDDDDDDDDDDDDDDDDD, 1MMMMMMMMMMMMMMMMMMMMMBB, D00DDDDDDDDDDDDDDDDDDDLD, FFFFFFFFFFFFFFFFFFFFFFFH, 4J0000000000000000000000J, 566666666666666666666666G1, EKKAAAAAAAAAAAAAAAAAAAAAA5, 6666666666666666666666666G1, AJJJJJJJJJJJJJJJJJJJJJJJJJJJ, H00000000000000000000000008H, N0000000000000000000000000GN, DD0000000000000000000000000LD, IIIIIIIIIIIIIIIIIIIIIIIIIIIIJ, G0666666666666666666666666666661, GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG7, K000000000000000000000000000000000H, EAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA5, LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLM7, M2EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE7, C000000000000000000000000000000000000000001, MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMCB, E00000000000000000000000000000000000000000000727, 777777777777777777777777777777777777777777777777727, EG000000000000000000000000000000000000000000000000000007, D000000000000000000000000000000000000000000000000000000000LD, 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===Base 36=== 11, 15, 17, 1B, 1H, 1N, 1P, 1V, 1Z, 21, 27, 2B, 2H, 2P, 2T, 2V, 2Z, 31, 35, 3J, 3N, 3T, 3V, 45, 47, 4D, 4J, 4N, 4T, 4Z, 51, 5B, 5D, 5H, 5J, 5V, 67, 6B, 6D, 6H, 6N, 6P, 6Z, 75, 7B, 7H, 7J, 7P, 7T, 7V, 85, 8J, 8N, 8P, 8T, 97, 9D, 9N, 9P, 9T, 9Z, A7, AD, AJ, AN, AT, B1, B5, BD, BN, BP, BZ, C1, C7, CB, CH, CP, CT, CV, CZ, DB, DJ, DN, DV, DZ, E5, EH, EJ, F1, F7, FH, FN, FT, FV, G1, GB, GH, GN, GP, GV, H1, H5, H7, HJ, HT, HV, HZ, I5, IB, ID, IP, IT, IZ, J7, JH, JP, JZ, K7, KD, KJ, KN, KV, L1, L5, LD, LH, LV, M5, MH, MJ, MT, MV, MZ, N1, NB, NP, NT, NV, NZ, OD, OH, OJ, ON, P7, PB, PJ, PT, Q1, Q5, QB, QH, QV, QZ, R5, RB, RJ, RP, S1, S5, SB, SD, SN, SP, SV, T5, T7, TH, TJ, TP, U7, UB, UD, UH, UN, UT, V1, V7, VD, VZ, W1, WB, WJ, WT, WZ, X5, XD, XP, XT, XZ, Y5, Y7, YD, YP, YZ, ZH, ZJ, ZN, ZT, ZV, 12D, 16J, 18D, 1CD, 1CJ, 1DD, 1GT, 1JD, 1JJ, 1LT, 1QJ, 1RD, 1RT, 1ST, 1XJ, 1YJ, 1YT, 22D, 22J, 22N, 23D, 255, 2A5, 2CD, 2ED, 2EN, 2F5, 2GD, 2GJ, 2IJ, 2JN, 2LN, 2MN, 2ND, 2O5, 2QD, 2QJ, 2U5, 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MYMU1, MYRK1, MYUU1, MYXR1, N000D, N0055, N006J, N007N, N00CN, N00IH, N00O7, N00S7, N029J, N02DD, N0307, N044H, N049H, N0505, N05M7, N05Q7, N06LJ, N070N, N0A55, N0CEN, N0CNN, N0CYN, N0DMD, N0DRD, N0F05, N0FF5, N0FMD, N0GED, N0HNN, N0I4H, N0IS7, N0IXJ, N0JLN, N0JNN, N0K4H, N0KIH, N0L6J, N0LI7, N0LLN, N0M0N, N0MQ7, N0NEN, N0O07, N0O77, N0Q0N, N0QEN, N0RRH, N0S07, N0SS7, N0U0J, N0ULJ, N0W77, N0WC5, N0WL7, N0XO7, N26JJ, N29XJ, N2CNN, N2CYN, N2MMD, N2N6J, N2N9J, N2NLJ, N2YYN, N30ED, N32RD, N33GD, N33MD, N3GGD, N3IW7, N3MR7, N3MX7, N3RGD, N3RI7, N3W2D, N3W77, N3X07, N3X77, N400H, N409H, N44YH, N494H, N49YH, N4AYH, N50K5, N5307, N5537, N5577, N57Q7, N5FK5, N5KK5, N5Q77, N5SQ7, N69LJ, N6L9J, N6U0J, N700D, N7077, N70EN, N70FD, N73RD, N7777, N777N, N7DMD, N7E2N, N7FED, N7M3D, N7MWD, N7SR7, N7WMD, N92LJ, N9XXJ, NA505, NA5F5, NAFK5, NAK05, NAKF5, NARYH, NAWW5, NC00N, NC0EN, NC0NN, NCE0N, NCN0N, NCNQN, NCW05, ND3GD, ND7DD, NDAW5, NDDGD, NDDRD, NDE3D, NDWM7, NDWW7, NE0GD, NED3D, NEDDD, NEL2N, NEMMD, NEMRD, NF0F5, NFEMD, NFKF5, NFWC5, NFWW5, NGDED, NGW2D, NH00H, NH2NN, NHH0H, NHMCN, NHMMD, NHNNN, NI00H, NI0EN, NI0MN, NI0NH, NI0NJ, NI0XJ, NI44H, NI7R7, NI7S7, NII77, NIIM7, NIIMN, NIIYN, NIM0N, NIN0H, NIN0J, NINJJ, NIW37, NIWM7, NIX77, NIXW7, NJ0EN, NJ0NN, NJ30D, NJ33D, NJFMD, NJIEN, NJJ2N, NJJIN, NJJJJ, NJJJN, NJL0J, NJLNN, NJN0N, NJSJJ, NK005, NK04H, NK3KH, NK5F5, NKA05, NKFK5, NKK55, NKKF5, NL09J, NL2IN, NLCNN, NLII7, NLIIN, NLJLN, NLL2J, NLLNJ, NLLNN, NLNCN, NLNIN, NLNLJ, NLNLN, NM00N, NM73D, NM7DD, NM7RD, NME0N, NMELN, NMLL7, NMLQ7, NMMRD, NMQEN, NMRD7, NMRR7, NMWWD, NN02J, NN0AH, NN0EN, NN30H, NN525, NN6UJ, NN92J, NNA55, NNASH, NNCLN, NNCMN, NNELN, NNF25, NNHHN, NNJ2J, NNJJJ, NNLNN, NNN55, NNN9J, NNNMN, NNNNJ, NNNSH, NNNXJ, NNQYN, NNS3H, NNU9J, NNW55, NNXJJ, NO077, NO0W7, NO777, NOI77, NOIM7, NOWL7, NQ00N, NQ0YN, NQ77N, NQ7EN, NQLLN, NQLNN, NQQQN, NQQYN, NRARH, NRAYH, NRDI7, NRHYH, NRQL7, NRRHH, NRW2D, NS0L7, NSA3H, NSHHH, NSIIJ, NSIJJ, NSS07, NSSJJ, NSSL7, NSSS7, NSULJ, NU00J, NUL6J, NUSIJ, NW0C5, NW3W7, NW5W5, NWI77, NWIM7, NWIO7, NWW55, NWWM7, NX0I7, NX0O7, NX3R7, NX9XJ, NXIM7, NXRL7, NXSSJ, NXWI7, NXWW7, NXXSJ, NY44H, NY94H, NYYIN, O0057, O005T, O0077, O0091, O009B, O00BT, O00EV, O00OV, O00TT, O00WP, O00WV, O040V, O0507, O056T, O065T, O08AV, O08E7, O0901, O09AB, O09I1, O09K1, O09WV, O0A4V, O0AI1, O0E9V, O0EAB, O0EAV, O0EFP, O0EKB, O0EOB, O0EU1, O0FMP, O0K6T, O0K91, O0MM1, O0O9B, O0OAB, O0OI1, O0OOB, O0OT1, O0OUV, O0OW7, O0OYT, O0T8V, O0TOT, O0TOV, O0TTV, O0TUV, O0TX1, O0U91, O0UE1, O0W87, O0WOV, O0YOT, O100T, O1EET, O4PAV, O4U0V, O5005, O50EP, O50I7, O50K5, O555P, O55FP, O55UP, O5EFP, O5I07, O5K05, O5KK5, O5OYT, O6LGT, O77E7, O7Q77, O80E7, O8AAZ, O8AFZ, O8AOV, O8FFZ, O8FKB, O8FZB, O8IM7, O8ZRZ, O8ZZB, O900V, O90WV, O96OV, O99LB, O9K01, O9OU1, O9R6V, O9U01, O9UI1, OA091, OA0O1, OA4AV, OA4IV, OA68V, OA8AZ, OA9I1, OAA4V, OAAFZ, OAAO1, OAAOV, OAAZZ, OAFAZ, OAFYB, OAI0V, OAI91, OAOAV, OAOE1, OAOU1, OAUE1, OAUI1, OAY01, OAY0B, OAYI1, OAZZZ, OB66T, OBE0T, OBEET, OE0BT, OE0FB, OE4AV, OE6ET, OE8AV, OE9EB, OEA8V, OEAA1, OEAFB, OEBET, OEBI7, OEEO7, OEFFP, OEFLP, OEKA1, OEKAB, OEKU1, OELMP, OEML7, OEO07, OEO0B, OEO4V, OEO6V, OEOAV, OEOO7, OEOOB, OEOVB, OEPU1, OERET, OERRV, OETY1, OEUK1, OEUU1, OEV9B, OEVFP, OEW8V, OEWW7, OF0FP, OF0OB, OFFFP, OFFMP, OFFZP, OFFZZ, OFMMP, OFMWP, OFOQP, OFPFZ, OFPUZ, OFZ0P, OFZFZ, OFZOB, OFZZZ, OG065, OG0YT, OI0EV, OI7Q7, OI9WV, OIIE7, OIQ77, OIQW7, OIR6V, OIYO1, OK8KB, OKAE1, OKAY1, OKE6T, OKEU1, OKFYB, OKIY1, OKYA1, OKYI1, OL08B, OL4EP, OL777, OL8E7, OLBI7, OLEL7, OLFOP, OLGYT, OLIW7, OLLSZ, OLLZZ, OLOUP, OLR6T, OLUMP, OMAU1, OMOU1, OMXM1, OO0AB, OO0I7, OO0T1, OO1ET, OO4AV, OO4MP, OO4QP, OO6KT, OO6LT, OO6OV, OO7O7, OOA0B, OOAIV, OOAOV, OOBGT, OOEMP, OOERT, OOET1, OOEU1, OOEY1, OOGTT, OOI4V, OOIRV, OOKET, OOLBT, OOMMP, OOMQ7, OOMU1, OOMWP, OOO0B, OOO6T, OOO77, OOOE7, OOOKT, OOOOV, OOORT, OOOW7, OOPY1, OOQ77, OOT01, OOT91, OOTAV, OOTOV, OOTUV, OOU91, OOUUV, OOWIV, OOWMP, OOWVP, OOY01, OOY0B, OOYKB, OOYU1, OOYYB, OP0EV, OP44V, OP8FZ, OPA91, OPAAZ, OPAOV, OPEAV, OPI4V, OPO4V, OPOIV, OPOUV, OPOY1, OPUAZ, OPUEV, OPWUV, OPYU1, OQ7W7, OQ8E7, OQLE7, OQQL7, OR8AZ, ORA8Z, ORKLT, ORS8Z, OS8RZ, OSR8Z, OSS8Z, OT09V, OT0K1, OT66T, OTT8V, OTUOV, OU091, OU0E1, OU0MP, OU4LP, OUAAZ, OUASZ, OUL4P, OUP8Z, OUP91, OUPAZ, OUPY1, OUU0P, OUUPZ, OUYM1, OUZ91, OV0FB, OV0LB, OV54P, OV5WP, OV9K5, OVALB, OVB6T, OVKFB, OVLEB, OVLFP, OVQWP, OW0EV, OW7O7, OW7Q7, OW7W7, OW90V, OWEEP, OWIWV, OWLW7, OWOM7, OWOVP, OWQ87, OWU0V, OWW9V, OWWL7, OWWOV, OXAA1, OXU01, OXUI1, OXXI1, OXXX1, OY00T, OY0E1, OY0RT, OY0U1, OY0YB, OY98B, OYE0T, OYFKB, OYKFB, OYLYB, OYYYB, OZ0OB, OZ0WP, OZ0YB, OZ9EB, OZ9K1, OZ9O1, OZALB, OZAYB, OZEAB, OZEOB, OZFEB, OZFFP, OZFFZ, OZFRZ, OZFZP, OZO0B, OZO91, OZOYB, OZPRZ, OZR8Z, OZUUP, OZZYB, P00W5, P02G5, P049V, P04YV, P0A0V, P0AW5, P0CC5, P0CU5, P0E9V, P0EWV, P0F25, P0FC5, P0G25, P0K3Z, P0KOZ, P0KRH, P0O55, P0OEV, P0PG5, P0PO5, P0PW5, P0R0H, P0ROZ, P0U25, P0UIV, P0UVP, P0V0P, P0VKP, P0W9V, P0YIV, P13WD, P22K5, P2D95, P2NC5, P33ZZ, P38DD, P3GGD, P3SAH, P409V, P444V, P44O1, P44Y1, P4AIV, P4AYV, P4E0V, P4OA1, P4OK1, P4OO1, P4U81, P4UEV, P4UR1, P55EP, P5GZ5, P6A41, P803H, P80AZ, P838D, P8AAZ, P8D8D, P8FKZ, P8K0Z, P8KKZ, P8KXH, P8OE1, P8UE1, P8X0H, P8X3H, P8XKH, P909V, P9941, P99EV, P99U1, P9E9V, P9K91, P9OE1, P9OK1, P9W9V, P9X9H, PA00H, PA441, PA5G5, PA8FZ, PA9O1, PAA8Z, PAI4V, PAI9V, PAMKP, PAOEV, PAR8H, PAUM1, PAVKP, PAZEP, PC0W5, PCAG5, PCAU5, PCCA5, PCWN5, PD0QP, PD0SH, PD33D, PD3AH, PD3MD, PDGC5, PDK3H, PDK8H, PDSAH, PDUAP, PE99V, PEA91, PEAEP, PEEA1, PEEE1, PEER1, PEI9V, PEK61, PEQQP, PERE1, PERK1, PEUY1, PEY0V, PF2K5, PF3CD, PF83D, PFC2D, PFCWD, PFDAP, PFEKP, PFMCD, PFMMD, PFO55, PFR2D, PFZEP, PG295, PG2WD, PG8CD, PGCD5, PGDC5, PGF5Z, PGG8D, PGKF5, PGKK5, PGO95, PGW8D, PH2MD, PHD8D, PK0O5, PK441, PK53Z, PK5GZ, PK83H, PK8KZ, PKAA1, PKAU1, PKKO5, PKP3Z, PKRXH, PKSIH, PMAA1, PMAAP, PMAU1, PMF3D, PMFCD, PMMAP, PMMMD, PMMMP, PMMPD, PMRR1, PMUO1, PN2D5, PN2W5, PNA3H, PNAF5, PNFK5, PNHFD, PNK55, PNKF5, PNSKH, PO09V, PO0EV, PO4AV, PO90V, POAY1, POI4V, POOE1, POUEV, POUY1, POWUV, POWWV, POYA1, POZAZ, POZFZ, PP0QP, PP2CN, PP2MD, PP33D, PP595, PP5W5, PP8CD, PPCNN, PPCRD, PPCU5, PPCW5, PPCWD, PPD05, PPDUP, PPECN, PPF8D, PPFC5, PPFW5, PPGC5, PPGF5, PPGFZ, PPKGZ, PPMCD, PPMCN, PPMEN, PPMND, PPNF5, PPNMN, PPNWD, PPP3Z, PPP95, PPPC5, PPPRZ, PPPZD, PPQKP, PPS0Z, PPW2N, PPWND, PPWWN, PPZC5, PPZSZ, PQQQP, PR1GD, PR8AH, PRA0H, PREK1, PRKO1, PRMM1, PRNFD, PRRM1, PRRRH, PRW2N, PS0ZZ, PS80H, PS80Z, PS8AH, PS8ZZ, PSIKH, PSR3Z, PU025, PU0IV, PU49V, PU4YV, PU8AZ, PU9EV, PUE91, PUE9V, PUI9V, PURK1, PUUM1, PUUR1, PUVAP, PUYIV, PUYO1, PUZMP, PV00P, PV2CN, PV2RN, PVAKP, PVFAP, PVFFP, PVFKP, PVK0P, PVKAP, PVNCN, PVNEN, PW005, PW0C5, PWCWD, PWF8D, PWNC5, PWO9V, PWOWV, PWWOV, PWWWN, PWWWV, PX0IH, PXAIH, PXIAH, PXIKH, PYKE1, PYKO1, PYRK1, PYRM1, PZ0G5, PZ1WD, PZ295, PZ2C5, PZ2G5, PZ481, PZ641, PZE61, PZEAP, PZG25, PZK61, PZKOZ, PZOFZ, PZOO1, PZR41, PZRZZ, PZS0Z, PZSUZ, PZUMP, Q00DT, Q00JD, Q00QT, Q00YN, Q020J, Q03RD, Q0CQN, Q0DRD, Q0FRD, Q0JTT, Q0Q3D, Q0QRN, Q0QXN, Q0XEN, Q0XIJ, Q0XLN, Q0XQN, Q0YYN, Q20RD, Q2D0D, Q32WD, Q3D3D, Q4EKP, Q4PQP, Q7777, Q77Q7, Q7ER7, Q7EW7, Q7LR7, Q7LS7, Q7LW7, Q7QQN, Q7QR7, Q7QYN, Q7RE7, Q7SS7, QAAPP, QAOOP, QAOWP, QAUAP, QAUWP, QAWEP, QAWLP, QCEQN, QCNYN, QCQEN, QD0GD, QD0RD, QD20D, QD33D, QD3DD, QDAWP, QDRET, QDWKP, QE7QN, QECLN, QEEL7, QEES7, QELCN, QEQCN, QEQTT, QERE7, QESR7, QF2WD, QFGUJ, QFR2D, QG00J, QG0IJ, QG7Q7, QG7R7, QGDDD, QGGGD, QGGQD, QGJ2J, QGMQ7, QGOO7, QGQQ7, QGRR7, QJ02J, QJ03D, QJ0SJ, QJ33D, QJ3WD, QJD0D, QJI0J, QK44P, QKPKP, QL7W7, QLES7, QLLL7, QLNNN, QLQ77, QLQL7, QLQM7, QLQPN, QLR87, QLSRT, QMLR7, QMQQ7, QN0YN, QN70N, QNCYN, QNLW7, QNNQN, QNNYN, QNQNN, QO777, QO7E7, QO8M7, QOUWP, QP3RD, QPDAP, QPEEP, QPFRD, QPGGD, QPPQP, QPR2D, QPRGD, QQ0RN, QQ0YN, QQ4LP, QQ4QP, QQAEP, QQCYN, QQELT, QQEPN, QQEQP, QQGDD, QQGGD, QQGO7, QQGQD, QQKKP, QQLAP, QQLPN, QQLRT, QQMR7, QQN77, QQNNN, QQNQN, QQPDD, QQPEN, QQPGD, QQPQP, QQPWD, QQQ0N, QQQ3D, QQQ87, QQQKP, QQQL7, QQQM7, QQQPD, QQQQN, QQQWD, QQRL7, QQRN7, QQRYN, QQSST, QQTDT, QQTQT, QQU4P, QQUAP, QQUUP, QQWPD, QQXEN, QQXQN, QQYXN, QR00N, QR0XN, QR2FD, QR32D, QREKT, QRN0N, QRNL7, QRQQD, QRRE7, QRXXN, QSES7, QSS2J, QSSE7, QSSS7, QSSSJ, QTDET, QTQ2D, QTQLT, QUAAP, QUAWP, QUPPP, QUUAP, QW7G7, QWG77, QWGM7, QWLEP, QWOEP, QWOLP, QX77N, QX7EN, QXELN, QXEQN, QXLLN, QXLQN, QXNQN, QXOE7, QXQXN, QXXNN, R0061, R008D, R00IH, R00NN, R00XN, R013D, R02YN, R030D, R04R1, R06E1, R06ET, R07M1, R08AH, R0A8H, R0AYH, R0D07, R0DDT, R0EK1, R0EYT, R0F3D, R0G8D, R0GDD, R0GGD, R0GQ7, R0H0N, R0KE1, R0LQ7, R0N0N, R0RYN, R0T2N, R0TLT, R0TNN, R0TYN, R0X0N, R0YST, R100T, R130D, R13WD, R166T, R1E0T, R1F3D, R1GFD, R1TGD, R200N, R28WD, R2W8D, R2WFD, R32DD, R330D, R332D, R3W8D, R44XV, R4AAV, R4AYV, R4MO1, R4OI1, R4RO1, R4U4V, R4X9V, R6001, R60K1, R66LT, R66YV, R6E01, R6EE1, R6MK1, R6SST, R6X01, R6X9V, R6XE1, R6XYV, R6Y6V, R7OO1, R7XE1, R80G7, R88FD, R8F8D, R8IE7, R8X8H, R9OAV, R9UVV, R9VOV, R9X6V, RA08H, RAA9V, RAS8Z, RAX0H, RD00D, RD8I7, RD8IH, RDA0H, RDDQT, RDQDT, RE061, RE6KT, RE6LT, REEK1, REEKT, RER01, RERK1, RERR1, RF0DD, RFD0D, RG28D, RGGFD, RGGWD, RGRM7, RGWQD, RH00H, RH0EN, RH8HH, RH9HH, RH9XH, RHH9H, RHHIN, RHHNN, RHIWN, RHNEN, RHWIN, RHWWN, RHX8H, RHXEN, RHY9H, RI00H, RI2IN, RIHEN, RIIWN, RIMRN, RK00T, RKEE1, RKELT, RKL0T, RKQLT, RLEI7, RLQM7, RLR07, RLRE7, RLSSZ, RLSYT, RLZE7, RLZI7, RLZLZ, RM0G7, RM0Q7, RMIWN, RMKO1, RMLQ7, RMOX1, RMR07, RMRR1, RN2YN, RN30D, RND3D, RNI2N, RNIMN, RNMEN, RNW2D, RO0TT, RO66T, RO6KT, ROAAV, ROOKT, ROOOT, ROU9V, ROXM1, ROZK1, RQK0T, RQLKT, RQLST, RQMR7, RQQLT, RQQQT, RQQWD, RQRE7, RQTQD, RR44V, RR4YV, RR601, RR66V, RR6WV, RR9HH, RR9UV, RRA9V, RRAYV, RRE01, RREE1, RRGM7, RRGR7, RRI2N, RRIIN, RRIN7, RRIXN, RRKE1, RRL07, RRLM7, RRM07, RRMG7, RRML7, RRMM1, RRMO1, RRMWN, RRNR7, RRO01, RROI1, RROK1, RRR0N, RRRE1, RRRG7, RRRIN, RRRL7, RRRM1, RRRO1, RRROV, RRRWV, RRU6V, RRV9H, RRVUV, RRVYH, RRWWV, RRXRN, RRY4V, RRY9H, RRYHH, RRYIN, RRYRN, RS8FZ, RSSSZ, RSSYT, RSYST, RT3ZZ, 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====Additional known quasi-minimal primes (not necessarily the next)==== P₈₁₉₉₃SZ ==Unsolved families== Families for which not even a probable prime is known nor can be ruled out as only contain composites (only count the numbers > base (''b'')) by covering congruence, algebraic factorization, or combine of them. {|class=wikitable |base (''b'')||unsolved family (base-''b'' form)||unsolved family (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||current search limit of length||factorization of numbers in this family |- |13||9{5}||(113×13^''n''−5)/12||116000||[http://factordb.com/index.php?query=%28113*13%5En-5%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |13||A{3}A||(41×13^''n''+1+27)/4||111000||[http://factordb.com/index.php?query=%2841*13%5E%28n%2B1%29%2B27%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |16||{3}AF||(16^''n''+2+619)/5||98000||[http://factordb.com/index.php?query=%2816%5E%28n%2B2%29%2B619%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||1{7}||(23×17^''n''−7)/16||32074||[http://factordb.com/index.php?query=%2823*17%5En-7%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||1F{0}7||32×17^''n''+1+7||32074||[http://factordb.com/index.php?query=32*17%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||4{7}A||(71×17^''n''+1+41)/16||32074||[http://factordb.com/index.php?query=%2871*17%5E%28n%2B1%29%2B41%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||51{0}D||86×17^''n''+1+13||32074||[http://factordb.com/index.php?query=86*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||70F{0}D||2038×17^''n''+1+13||32074||[http://factordb.com/index.php?query=2038*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||8{B}9||(139×17^''n''+1−43)/16||32074||[http://factordb.com/index.php?query=%28139*17%5E%28n%2B1%29-43%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||9{5}9||(149×17^''n''+1+59)/16||32074||[http://factordb.com/index.php?query=%28149*17%5E%28n%2B1%29%2B59%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||95{F}||(2543×17^''n''−15)/16||32074||[http://factordb.com/index.php?query=%282543*17%5En-15%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||A{D}F||(173×17^''n''+1+19)/16||32074||[http://factordb.com/index.php?query=%28173*17%5E%28n%2B1%29%2B19%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||B{0}B3||11×17^''n''+2+190||32074||[http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B190&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||B{0}DB||11×17^''n''+2+232||32074||[http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B232&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}2BE||(11×17^''n''+3−41579)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B3%29-41579%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}2E||(11×17^''n''+2−2411)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29-2411%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}E9||(11×17^''n''+2+773)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B773%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}EE||(11×17^''n''+2+853)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B853%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||D0G{D}||(60381×17^''n''−13)/16||32074||[http://factordb.com/index.php?query=%2860381*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||E9{B}||(3963×17^''n''−11)/16||32074||[http://factordb.com/index.php?query=%283963*17%5En-11%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||F1{9}||(4105×17^''n''−9)/16||1000000||[http://factordb.com/index.php?query=%284105*17%5En-9%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||FD0{D}||(72909×17^''n''−13)/16||32074||[http://factordb.com/index.php?query=%2872909*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||2{7}9D||(47×21^''n''+2+953)/20||20000||[http://factordb.com/index.php?query=%2847*21%5E%28n%2B2%29%2B953%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||2F{C}A||(288×21^''n''+1−13)/5||20000||[http://factordb.com/index.php?query=%28288*21%5E%28n%2B1%29-13%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||4{3}B||(83×21^''n''+1+157)/20||20000||[http://factordb.com/index.php?query=%2883*21%5E%28n%2B1%29%2B157%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||5{0}DJ||5×21^''n''+2+292||20000||[http://factordb.com/index.php?query=5*21%5E%28n%2B2%29%2B292&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{5}FEK||(21^''n''+3+18455)/4||20000||[http://factordb.com/index.php?query=%2821%5E%28n%2B3%29%2B18455%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{7}ID||(7×21^''n''+2+4733)/20||20000||[http://factordb.com/index.php?query=%287*21%5E%28n%2B2%29%2B4733%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||99{0}99H||198×21^''n''+3+4175||20000||[http://factordb.com/index.php?query=198*21%5E%28n%2B3%29%2B4175&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{9}0D||(9×21^''n''+2−3709)/20||20000||[http://factordb.com/index.php?query=%289*21%5E%28n%2B2%29-3709%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{9}D||(9×21^''n''+1+71)/20||20000||[http://factordb.com/index.php?query=%289*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B3{0}EB||234×21^''n''+2+305||20000||[http://factordb.com/index.php?query=234*21%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B9{0}E5||240×21^''n''+2+299||20000||[http://factordb.com/index.php?query=240*21%5E%28n%2B2%29%2B299&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B{D}B||(233×21^''n''+1−53)/20||20000||[http://factordb.com/index.php?query=%28233*21%5E%28n%2B1%29-53%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B{H}6H||(237×21^''n''+2−4637)/20||20000||[http://factordb.com/index.php?query=%28237*21%5E%28n%2B2%29-4637%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||DH{D}||(5813×21^''n''−13)/20||20000||[http://factordb.com/index.php?query=%285813*21%5En-13%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||F{9}D||(309×21^''n''+1+71)/20||20000||[http://factordb.com/index.php?query=%28309*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{F}35||(3×21^''n''+2−1051)/4||20000||[http://factordb.com/index.php?query=%283*21%5E%28n%2B2%29-1051%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||G{0}FK||16×21^''n''+2+335||506000||[http://factordb.com/index.php?query=16*21%5E%28n%2B2%29%2B335&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||H{0}7771||17×21^''n''+4+68062||20000||[http://factordb.com/index.php?query=17*21%5E%28n%2B4%29%2B68062&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||H{D}||(353×21^''n''−13)/20||20000||[http://factordb.com/index.php?query=%28353*21%5En-13%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{J}6J||(19×21^''n''+2−5479)/20||20000||[http://factordb.com/index.php?query=%2819*21%5E%28n%2B2%29-5479%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||7{K}Z||(53×36^''n''+1+101)/7||20000||[http://factordb.com/index.php?query=%2853*36%5E%28n%2B1%29%2B101%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||B{0}EUV||11×36^''n''+3+19255||20000||[http://factordb.com/index.php?query=11*36%5E%28n%2B3%29%2B19255&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||HM{0}N||634×36^''n''+1+23||20000||[http://factordb.com/index.php?query=634*36%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||N{0}YYN||23×36^''n''+3+45311||20000||[http://factordb.com/index.php?query=23*36%5E%28n%2B3%29%2B45311&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||O{L}Z||(123×36^''n''+1+67)/5||100000||[http://factordb.com/index.php?query=%28123*36%5E%28n%2B1%29%2B67%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||S{0}8H||28×36^''n''+2+305||20000||[http://factordb.com/index.php?query=28*36%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |} For base 17, the smallest prime in family {B}2BE may or may not be quasi-minimal prime, since another unsolved family is {B}2E For base 21, the smallest prime in families {9}0D and F{9}D may or may not be quasi-minimal primes, since another unsolved family is {9}D, and the smallest prime in family DH{D} may or may not be quasi-minimal prime, since another unsolved family is H{D} === Base 17 === All searched to length 32074 * 1{7} * 1F{0}7 * 4{7}A * 51{0}D * 70F{0}D * 8{B}9 * 9{5}9 * 95{F} * A{D}F * B{0}B3 * B{0}DB * {B}2BE * {B}2E * {B}E9 * {B}EE * D0G{D} * E9{B} * F1{9} * FD0{D} === Base 21 === All searched to length 20000 * 2{7}9D * 2F{C}A * 4{3}B * 5{0}DJ * {5}FEK * {7}ID * 99{0}99H * {9}0D * {9}D * B3{0}EB * B9{0}E5 * B{D}B * B{H}6H * DH{D} * F{9}D * {F}35 * G{0}FK * H{0}7771 * H{D} * {J}6J === Base 36 === All searched to length 20000 * 7{K}Z * B{0}EUV * HM{0}N * N{0}YYN * O{L}Z * S{0}8H ==Primality certificates for the proven primes > 10²⁹⁹== See also: [[w:Primality certificate|Primality certificate]] and [[w:Elliptic curve primality|Elliptic curve primality]] {|class=wikitable |base (''b'')||index of this quasi-minimal prime in base ''b''||quasi-minimal prime (base-''b'' form)||quasi-minimal prime (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||factordb entry of this prime||primality certificate of this prime |- |9||149||76₃₂₉2||(31×9³³⁰−19)/4||[http://factordb.com/index.php?id=1100000002359003642]||[http://factordb.com/cert.php?id=1100000002359003642] |- |9||150||27₆₈₆07||(23×9⁶⁸⁸−511)/8||[http://factordb.com/index.php?id=1100000002495467486]||[http://factordb.com/cert.php?id=1100000002495467486] |- |9||151||30₁₁₅₈11||3×9¹¹⁶⁰+10||[http://factordb.com/index.php?id=1100000002376318423]||[http://factordb.com/cert.php?id=1100000002376318423] |- |11||1065||A₇₁₃58||11⁷¹⁵−58||[http://factordb.com/index.php?id=1100000003576826487]||[http://factordb.com/cert.php?id=1100000003576826487] |- |11||1066||7₇₅₉44||(7×11⁷⁶¹−367)/10||[http://factordb.com/index.php?id=1100000002505568840]||[http://factordb.com/cert.php?id=1100000002505568840] |- |11||1067||557₁₀₁₁||(607×11¹⁰¹¹−7)/10||[http://factordb.com/index.php?id=1100000002361376522]||[http://factordb.com/cert.php?id=1100000002361376522] |- |13||3165||50₂₇₀44||5×13²⁷²+56||[http://factordb.com/index.php?id=1100000002632397005]||[http://factordb.com/cert.php?id=1100000002632397005] |- |13||3166||9₂₇₁095||(3×13²⁷⁴−6103)/4||[http://factordb.com/index.php?id=1100000003590431654]||[http://factordb.com/cert.php?id=1100000003590431654] |- |13||3167||10₂₈₆7771||13²⁹⁰+16654||[http://factordb.com/index.php?id=1100000003590431633]||[http://factordb.com/cert.php?id=1100000003590431633] |- |13||3168||9₃₀₈1||(3×13³⁰⁹−35)/4||[http://factordb.com/index.php?id=1100000000840126705]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=308&c0=-&EN= 13³⁰⁸−1] |- |13||3169||B₃₄₁C4||(11×13³⁴³+61)/12||[http://factordb.com/index.php?id=1100000003590431618]||[http://factordb.com/cert.php?id=1100000003590431618] |- |13||3170||8B₃₄₃||(107×13³⁴³−11)/12||[http://factordb.com/index.php?id=1100000002321018736]||[http://factordb.com/cert.php?id=1100000002321018736] |- |13||3171||710₃₇₁111||92×13³⁷⁴+183||[http://factordb.com/index.php?id=1100000003590431609]||[http://factordb.com/cert.php?id=1100000003590431609] |- |13||3172||75₃₇₅7||(89×13³⁷⁶+19)/12||[http://factordb.com/index.php?id=1100000003590431596]||[http://factordb.com/cert.php?id=1100000003590431596] |- |13||3173||9B0₃₉₁9||128×13³⁹²+9||[http://factordb.com/index.php?id=1100000002632396790]||[http://factordb.com/cert.php?id=1100000002632396790] |- |13||3174||7B0B₃₉₇||(15923×13³⁹⁷−11)/12||[http://factordb.com/index.php?id=1100000003590431574]||[http://factordb.com/cert.php?id=1100000003590431574] |- |13||3175||10₄₁₄93||13⁴¹⁶+120||[http://factordb.com/index.php?id=1100000002523249240]||[http://factordb.com/cert.php?id=1100000002523249240] |- |13||3176||81010₄₁₅1||17746×13⁴¹⁶+1||[http://factordb.com/index.php?id=1100000003590431555]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3177||8110₄₃₅1||1366×13⁴³⁶+1||[http://factordb.com/index.php?id=1100000002373259109]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3178||B7₄₈₆||(139×13⁴⁸⁶−7)/12||[http://factordb.com/index.php?id=1100000002321015892]||[http://factordb.com/cert.php?id=1100000002321015892] |- |13||3179||B₅₆₃C||(11×13⁵⁶⁴+1)/12||[http://factordb.com/index.php?id=1100000000000217927]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=564&c0=-&EN= 13⁵⁶⁴−1] |- |13||3180||1B₅₇₆||(23×13⁵⁷⁶−11)/12||[http://factordb.com/index.php?id=1100000002321021456]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=576&c0=-&EN= 13⁵⁷⁶−1] |- |13||3181||80₆₉₃87||8×13⁶⁹⁵+111||[http://factordb.com/index.php?id=1100000002615636527]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 has a large prime factor, factordb entry of this prime factor is [http://factordb.com/index.php?id=1100000002615636532], and primality certificate of this prime factor is [http://factordb.com/cert.php?id=1100000002615636532] |- |13||3182||CC5₇₁₃||(2021×13⁷¹³−5)/12||[http://factordb.com/index.php?id=1100000002615627353]||[http://factordb.com/cert.php?id=1100000002615627353] |- |13||3183||B₈₃₄74||(11×13⁸³⁶−719)/12||[http://factordb.com/index.php?id=1100000003590430871]||[http://factordb.com/cert.php?id=1100000003590430871] |- |13||3184||9₉₆₈B||(3×13⁹⁶⁹+5)/4||[http://factordb.com/index.php?id=1100000000258566244]||[http://factordb.com/cert.php?id=1100000000258566244] |- |13||3185||10₁₂₉₅181||13¹²⁹⁸+274||[http://factordb.com/index.php?id=1100000002615445013]||[http://factordb.com/cert.php?id=1100000002615445013] |- |13||3186||9₁₃₆₂5||(3×13¹³⁶³−19)/4||[http://factordb.com/index.php?id=1100000002321017776]||[http://factordb.com/cert.php?id=1100000002321017776] |- |13||3187||7₁₅₀₄1||(7×13¹⁵⁰⁵−79)/12||[http://factordb.com/index.php?id=1100000002320890755]||[http://factordb.com/cert.php?id=1100000002320890755] |- |13||3188||930₁₅₅₁1||120×13¹⁵⁵²+1||[http://factordb.com/index.php?id=1100000000765961452]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3189||720₂₂₉₇2||93×13²²⁹⁸+2||[http://factordb.com/index.php?id=1100000002632396910]||[http://factordb.com/cert.php?id=1100000002632396910] |- |13||3190||1770₂₇₀₃17||267×13²⁷⁰⁵+20||[http://factordb.com/index.php?id=1100000003590430825]||[http://factordb.com/cert.php?id=1100000003590430825] |- |13||3191||390₆₂₆₆1||48×13⁶²⁶⁷+1||[http://factordb.com/index.php?id=1100000000765961441]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3192||B0₆₅₄₀BBA||11×13⁶⁵⁴³+2012||[http://factordb.com/index.php?id=1100000002616382906]||[http://factordb.com/cert.php?id=1100000002616382906] |- |13||3193||C₁₀₆₃₁92||13¹⁰⁶³³−50||[http://factordb.com/index.php?id=1100000003590493750]||[http://factordb.com/cert.php?id=1100000003590493750] |- |14||649||34D₇₀₈||47×14⁷⁰⁸−1||[http://factordb.com/index.php?id=1100000001540144903]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |14||650||4D₁₉₆₉₈||5×14¹⁹⁶⁹⁸−1||[http://factordb.com/index.php?id=1100000000884560233]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |16||2328||880₂₄₆7||136×16²⁴⁷+7||[http://factordb.com/index.php?id=1100000002468140199]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has a large prime factor, and this prime factor is < 10²⁹⁹ |- |16||2329||D4₂₆₃D||(199×16²⁶⁴+131)/15||[http://factordb.com/index.php?id=1100000002468170238]||[http://factordb.com/cert.php?id=1100000002468170238] |- |16||2330||E0₂₆₁4DD||14×16²⁶⁴+1245||[http://factordb.com/index.php?id=1100000003588388352]||[http://factordb.com/cert.php?id=1100000003588388352] |- |16||2331||8C0₂₉₀ED||140×16²⁹²+237||[http://factordb.com/index.php?id=1100000003588388307]||[http://factordb.com/cert.php?id=1100000003588388307] |- |16||2332||DA₃₀₅5||(41×16³⁰⁶−17)/3||[http://factordb.com/index.php?id=1100000003588388284]||[http://factordb.com/cert.php?id=1100000003588388284] |- |16||2333||CE80₄₂₂D||3304×16⁴²³+13||[http://factordb.com/index.php?id=1100000003588388257]||[http://factordb.com/cert.php?id=1100000003588388257] |- |16||2334||5F₅₄₄6F||6×16⁵⁴⁶−145||[http://factordb.com/index.php?id=1100000002604723967]||[http://factordb.com/cert.php?id=1100000002604723967] |- |16||2335||88F₅₄₅||137×16⁵⁴⁵−1||[http://factordb.com/index.php?id=1100000000413679658]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |16||2336||BE0₇₉₂BB||190×16⁷⁹⁴+187||[http://factordb.com/index.php?id=1100000003588387938]||[http://factordb.com/cert.php?id=1100000003588387938] |- |16||2337||D9₁₀₅₂||(68×16¹⁰⁵²−3)/5||[http://factordb.com/index.php?id=1100000002321036020]||[http://factordb.com/cert.php?id=1100000002321036020] |- |16||2338||FAF₁₀₆₂45||251×16¹⁰⁶⁴−187||[http://factordb.com/index.php?id=1100000003588387610]||[http://factordb.com/cert.php?id=1100000003588387610] |- |16||2339||F8₁₅₁₇F||(233×16¹⁵¹⁸+97)/15||[http://factordb.com/index.php?id=1100000000633744824]||[http://factordb.com/cert.php?id=1100000000633744824] |- |16||2340||20₁₇₁₃321||2×16¹⁷¹⁶+801||[http://factordb.com/index.php?id=1100000003588386735]||[http://factordb.com/cert.php?id=1100000003588386735] |- |16||2341||300F₁₉₆₀AF||769×16¹⁹⁶²−81||[http://factordb.com/index.php?id=1100000003588368750]||[http://factordb.com/cert.php?id=1100000003588368750] |- |16||2342||90₃₅₄₂91||9×16³⁵⁴⁴+145||[http://factordb.com/index.php?id=1100000000633424191]||[http://factordb.com/cert.php?id=1100000000633424191] |- |16||2343||5BC₃₇₀₀D||(459×16³⁷⁰¹+1)/5||[http://factordb.com/index.php?id=1100000000993764322]||[http://factordb.com/cert.php?id=1100000000993764322] |- |16||2344||D0B₁₇₈₀₄||(3131×16¹⁷⁸⁰⁴−11)/15||[http://factordb.com/index.php?id=1100000003589278511]||[http://factordb.com/cert.php?id=1100000003589278511] |- |18||547||80₂₉₈B||8×18²⁹⁹+11||[http://factordb.com/index.php?id=1100000002355574745]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has sum-of-two-cubes algebraic factorization, 6×18⁹⁹+1 is an algebraic factor of ''N''+1, factordb entry of 6×18⁹⁹+1 is [http://factordb.com/index.php?id=1100000000900149167] |- |18||548||H₇₆₆FH||18⁷⁶⁸−37||[http://factordb.com/index.php?id=1100000003590430490]||[http://factordb.com/cert.php?id=1100000003590430490] |- |18||549||C0₆₂₆₈C5||12×18⁶²⁷⁰+221||[http://factordb.com/index.php?id=1100000003590442437]||[http://factordb.com/cert.php?id=1100000003590442437] |- |20||3301||H₂₄₇A0H||(17×20²⁵⁰−59677)/19||[http://factordb.com/index.php?id=1100000003590502619]||[http://factordb.com/cert.php?id=1100000003590502619] |- |20||3302||7₂₄₉A7||(7×20²⁵¹+1133)/19||[http://factordb.com/index.php?id=1100000003590502602]||[http://factordb.com/cert.php?id=1100000003590502602] |- |20||3303||J7₂₇₀||(368×20²⁷⁰−7)/19||[http://factordb.com/index.php?id=1100000002325395462]||[http://factordb.com/cert.php?id=1100000002325395462] |- |20||3304||J₃₃₀CCC7||20³³⁴−58953||[http://factordb.com/index.php?id=1100000003590502572]||[http://factordb.com/cert.php?id=1100000003590502572] |- |20||3305||40₃₈₇404B||4×20³⁹¹+32091||[http://factordb.com/index.php?id=1100000003590502563]||[http://factordb.com/cert.php?id=1100000003590502563] |- |20||3306||EC0₄₂₉7||292×20⁴³⁰+7||[http://factordb.com/index.php?id=1100000002633348702]||[http://factordb.com/cert.php?id=1100000002633348702] |- |20||3307||G₄₄₇99||(16×20⁴⁴⁹−2809)/19||[http://factordb.com/index.php?id=1100000000840126753]||[http://factordb.com/cert.php?id=1100000000840126753] |- |20||3308||3A₅₂₇3||(67×20⁵²⁸−143)/19||[http://factordb.com/index.php?id=1100000003590502531]||[http://factordb.com/cert.php?id=1100000003590502531] |- |20||3309||E₅₆₆C7||(14×20⁵⁶⁸−907)/19||[http://factordb.com/index.php?id=1100000003590502516]||[http://factordb.com/cert.php?id=1100000003590502516] |- |20||3310||JCJ₆₂₉||393×20⁶²⁹−1||[http://factordb.com/index.php?id=1100000001559454258]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |20||3311||J₆₅₅05J||20⁶⁵⁸−7881||[http://factordb.com/index.php?id=1100000003590502490]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has a large prime factor, factordb entry of this prime factor is [http://factordb.com/index.php?id=1100000003591067052], and primality certificate of this prime factor is [http://factordb.com/cert.php?id=1100000003591067052] |- |20||3312||50₁₁₆₃AJ||5×20¹¹⁶⁵+219||[http://factordb.com/index.php?id=1100000003590502412]||[http://factordb.com/cert.php?id=1100000003590502412] |- |20||3313||CD₂₄₄₉||(241×20²⁴⁴⁹−13)/19||[http://factordb.com/index.php?id=1100000002325393915]||[http://factordb.com/cert.php?id=1100000002325393915] |- |20||3314||G0₆₂₆₉D||16×20⁶²⁷⁰+13||[http://factordb.com/index.php?id=1100000003590539457]||[http://factordb.com/cert.php?id=1100000003590539457] |- |22||7984||I7G0₂₅₄H||8882×22²⁵⁵+17||[http://factordb.com/index.php?id=1100000003591372788]||[http://factordb.com/cert.php?id=1100000003591372788] |- |22||7985||D0₂₅₅5EEF||13×22²⁵⁹+60339||[http://factordb.com/index.php?id=1100000003591371932]||[http://factordb.com/cert.php?id=1100000003591371932] |- |22||7986||IK₃₂₂F||(398×22³²³−125)/21||[http://factordb.com/index.php?id=1100000000840384145]||[http://factordb.com/cert.php?id=1100000000840384145] |- |22||7987||C0₃₄₀G9||12×22³⁴²+361||[http://factordb.com/index.php?id=1100000000840384159]||[http://factordb.com/cert.php?id=1100000000840384159] |- |22||7988||77E₃₄₈K7||(485×22³⁵⁰+373)/3||[http://factordb.com/index.php?id=1100000003591369779]||[http://factordb.com/cert.php?id=1100000003591369779] |- |22||7989||J₃₇₉KJ||(19×22³⁸¹+443)/21||[http://factordb.com/index.php?id=1100000003591369027]||[http://factordb.com/cert.php?id=1100000003591369027] |- |22||7990||J₃₈₈EJ||(19×22³⁹⁰−2329)/21||[http://factordb.com/index.php?id=1100000003591367729]||[http://factordb.com/cert.php?id=1100000003591367729] |- |22||7991||DJ₄₀₀||(292×22⁴⁰⁰−19)/21||[http://factordb.com/index.php?id=1100000002325880110]||[http://factordb.com/cert.php?id=1100000002325880110] |- |22||7992||E₄₀₄K7||(2×22⁴⁰⁶+373)/3||[http://factordb.com/index.php?id=1100000003591366298]||[http://factordb.com/cert.php?id=1100000003591366298] |- |22||7993||66F₄₅₃B3||(971×22⁴⁵⁵−705)/7||[http://factordb.com/index.php?id=1100000003591365809]||[http://factordb.com/cert.php?id=1100000003591365809] |- |22||7994||L0₄₅₄B63||21×22⁴⁵⁷+5459||[http://factordb.com/index.php?id=1100000003591365331]||[http://factordb.com/cert.php?id=1100000003591365331] |- |22||7995||L₄₈₃G3||22⁴⁸⁵−129||[http://factordb.com/index.php?id=1100000003591364730]||[http://factordb.com/cert.php?id=1100000003591364730] |- |22||7996||E60₄₉₆L||314×22⁴⁹⁷+21||[http://factordb.com/index.php?id=1100000000632703239]||[http://factordb.com/cert.php?id=1100000000632703239] |- |22||7997||I₆₂₆AF||(6×22⁶²⁸−1259)/7||[http://factordb.com/index.php?id=1100000000632724334]||[http://factordb.com/cert.php?id=1100000000632724334] |- |22||7998||K0₇₆₀EC1||20×22⁷⁶³+7041||[http://factordb.com/index.php?id=1100000000632724415]||[http://factordb.com/cert.php?id=1100000000632724415] |- |22||7999||J0₇₆₇IGGJ||19×22⁷⁷¹+199779||[http://factordb.com/index.php?id=1100000003591362567]||[http://factordb.com/cert.php?id=1100000003591362567] |- |22||8000||7₉₅₉K7||(22⁹⁶¹+857)/3||[http://factordb.com/index.php?id=1100000003591361817]||[http://factordb.com/cert.php?id=1100000003591361817] |- |22||8001||L₂₃₈₅KE7||22²³⁸⁸−653||[http://factordb.com/index.php?id=1100000003591360774]||[http://factordb.com/cert.php?id=1100000003591360774] |- |22||8002||7₃₈₁₅2L||(22³⁸¹⁷−289)/3||[http://factordb.com/index.php?id=1100000003591359839]||[http://factordb.com/cert.php?id=1100000003591359839] |- |24||3400||I0₂₄₁I5||18×24²⁴³+437||[http://factordb.com/index.php?id=1100000002633360037]||[http://factordb.com/cert.php?id=1100000002633360037] |- |24||3401||D0₂₅₉KKD||13×24²⁶²+12013||[http://factordb.com/index.php?id=1100000003593270725]||[http://factordb.com/cert.php?id=1100000003593270725] |- |24||3402||C7₂₉₈||(283×24²⁹⁸−7)/23||[http://factordb.com/index.php?id=1100000002326181235]||[http://factordb.com/cert.php?id=1100000002326181235] |- |24||3403||20₃₁₃7||2×24³¹⁴+7||[http://factordb.com/index.php?id=1100000002355610241]||[http://factordb.com/cert.php?id=1100000002355610241] |- |24||3404||BC0₃₃₁B||276×24³³²+11||[http://factordb.com/index.php?id=1100000002633359842]||[http://factordb.com/cert.php?id=1100000002633359842] |- |24||3405||N₂₆₄₄LLN||24²⁶⁴⁷−1201||[http://factordb.com/index.php?id=1100000003593270089]||[http://factordb.com/cert.php?id=1100000003593270089] |- |24||3406||D₂₆₉₈LD||(13×24²⁷⁰⁰+4403)/23||[http://factordb.com/index.php?id=1100000003593269876]||[http://factordb.com/cert.php?id=1100000003593269876] |- |24||3407||A0₂₉₅₁8ID||10×24²⁹⁵⁴+5053||[http://factordb.com/index.php?id=1100000003593269654]||[http://factordb.com/cert.php?id=1100000003593269654] |- |24||3408||88N₅₉₅₁||201×24⁵⁹⁵¹−1||[http://factordb.com/index.php?id=1100000003593275880]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |24||3409||N00N₈₁₂₉LN||13249×24⁸¹³¹−49||[http://factordb.com/index.php?id=1100000003593391606]||[http://factordb.com/cert.php?id=1100000003593391606] |- |30||2613||AN₂₀₆||(313×30²⁰⁶−23)/29||[http://factordb.com/index.php?id=1100000002327651073]||[http://factordb.com/cert.php?id=1100000002327651073] |- |30||2614||M₂₄₁QB||(22×30²⁴³+3139)/29||[http://factordb.com/index.php?id=1100000003593408295]||[http://factordb.com/cert.php?id=1100000003593408295] |- |30||2615||M0₅₄₇SS7||22×30⁵⁵⁰+26047||[http://factordb.com/index.php?id=1100000003593407988]||[http://factordb.com/cert.php?id=1100000003593407988] |- |30||2616||C0₁₀₂₂1||12×30¹⁰²³+1||[http://factordb.com/index.php?id=1100000000785448736]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |30||2617||5₄₈₈₂J||(5×30⁴⁸⁸³+401)/29||[http://factordb.com/index.php?id=1100000002327649423]||[http://factordb.com/cert.php?id=1100000002327649423] |- |30||2619||OT₃₄₂₀₅||25×30³⁴²⁰⁵−1||[http://factordb.com/index.php?id=1100000000800812865]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |} ==Unproven PRPs== {|class=wikitable |base (''b'')||index of this quasi-minimal prime in base ''b'' (assuming the primality of all PRP in base ''b'')||unproven PRP (base-''b'' form)||unproven PRP (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||factordb entry of this PRP |- |11||1068||57₆₂₆₆₈||(57×11⁶²⁶⁶⁸−7)/10||[http://factordb.com/index.php?id=1100000003573679860] |- |13||3194||C5₂₃₇₅₅C||(149×13²³⁷⁵⁶+79)/12||[http://factordb.com/index.php?id=1100000003590647776] |- |13||3195||80₃₂₀₁₇111||8×13³²⁰²⁰+183||[http://factordb.com/index.php?id=1100000000490878060] |- |16||2345||DB₃₂₂₃₄||(206×16³²²³⁴−11)/15||[http://factordb.com/index.php?id=1100000002383583629] |- |16||2346||4₇₂₇₈₅DD||(4×16⁷²⁷⁸⁷+2291)/15||[http://factordb.com/index.php?id=1100000003615909841] |- |22||8003||BK₂₂₀₀₁5||(251×22²²⁰⁰²−335)/21||[http://factordb.com/index.php?id=1100000003594696838] |- |30||2618||I0₂₄₆₀₈D||18×30²⁴⁶⁰⁹+13||[http://factordb.com/index.php?id=1100000003593967511] |} All these PRPs pass the [[w:Miller–Rabin primality test|Miller–Rabin primality test]] to bases 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and 61, and pass the [[w:Lucas pseudoprime#Strong Lucas pseudoprimes|strong Lucas primality test]] with parameters (''P'', ''Q'') defined by Selfridge's Method ''A'', and [[w:Trial division|trial factored]] to 10¹⁶. (Thus, they pass the [[w:Baillie–PSW primality test|Baillie–PSW primality test]]) ==Proof== ===Base 2=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. ===Base 3=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (2,1), (2,2) * Case (1,1): ** Since 12, 21, 111 are primes, we only need to consider the family 1{0}1 (since any digits 1, 2 between them will produce smaller primes) *** All numbers of the form 1{0}1 are divisible by 2, thus cannot be prime. * Case (1,2): ** 12 is prime, and thus the only minimal prime in this family. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,2): ** Since 21, 12 are primes, we only need to consider the family 2{0,2}2 (since any digits 1 between them will produce smaller primes) *** All numbers of the form 2{0,2}2 are divisible by 2, thus cannot be prime. ===Base 4=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (2,1), (2,3), (3,1), (3,3) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 11, 31, 221 are primes, we only need to consider the family 2{0}1 (since any digits 1, 2, 3 between them will produce smaller primes) *** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 31, 13, 23 are primes, we only need to consider the family 3{0,3}3 (since any digits 1, 2 between them will produce smaller primes) *** All numbers of the form 3{0,3}3 are divisible by 3, thus cannot be prime. ===Base 5=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4) * Case (1,1): ** Since 12, 21, 111, 131 are primes, we only need to consider the family 1{0,4}1 (since any digits 1, 2, 3 between them will produce smaller primes) *** All numbers of the form 1{0,4}1 are divisible by 2, thus cannot be prime. * Case (1,2): ** 12 is prime, and thus the only minimal prime in this family. * Case (1,3): ** Since 12, 23, 43, 133 are primes, we only need to consider the family 1{0,1}3 (since any digits 2, 3, 4 between them will produce smaller primes) *** Since 111 is prime, we only need to consider the families 1{0}3 and 1{0}1{0}3 (since any digit combo 11 between (1,3) will produce smaller primes) **** All numbers of the form 1{0}3 are divisible by 2, thus cannot be prime. **** For the 1{0}1{0}3 family, since 10103 is prime, we only need to consider the families 1{0}13 and 11{0}3 (since any digit combo 010 between (1,3) will produce smaller primes) ***** The smallest prime of the form 1{0}13 is 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013, which can be written as 1(0^93)13 and equal the prime 5^95+8 ([http://factordb.com/index.php?id=1100000000034686071 factordb]) ***** All numbers of the form 11{0}3 are divisible by 3, thus cannot be prime. * Case (1,4): ** Since 12, 34, 104 are primes, we only need to consider the family 1{1,4}4 (since any digits 0, 2, 3 between them will produce smaller primes) *** Since 111, 414 are primes, we only need to consider the families 1{4}4 and 11{4}4 (since any digit combo 11 or 41 between them will produce smaller primes) **** The smallest prime of the form 1{4}4 is 14444. **** All numbers of the form 11{4}4 are divisible by 2, thus cannot be prime. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,2): ** Since 21, 23, 12, 32 are primes, we only need to consider the family 2{0,2,4}2 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 2{0,2,4}2 are divisible by 2, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,4): ** Since 21, 23, 34 are primes, we only need to consider the family 2{0,2,4}4 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 2{0,2,4}4 are divisible by 2, thus cannot be prime. * Case (3,1): ** Since 32, 34, 21 are primes, we only need to consider the family 3{0,1,3}1 (since any digits 2, 4 between them will produce smaller primes) *** Since 313, 111, 131, 3101 are primes, we only need to consider the families 3{0,3}1 and 3{0,3}11 (since any digit combo 10, 11, 13 between (3,1) will produce smaller primes) **** For the 3{0,3}1 family, we can separate this family to four families: ***** For the 30{0,3}01 family, we have the prime 30301, and the remain case is the family 30{0}01. ****** All numbers of the form 30{0}01 are divisible by 2, thus cannot be prime. ***** For the 30{0,3}31 family, note that there must be an even number of 3's between (30,31), or the result number will be divisible by 2 and cannot be prime. ****** Since 33331 is prime, any digit combo 33 between (30,31) will produce smaller primes. ******* Thus, the only possible prime is the smallest prime in the family 30{0}31, and this prime is 300031. ***** For the 33{0,3}01 family, note that there must be an even number of 3's between (33,01), or the result number will be divisible by 2 and cannot be prime. ****** Since 33331 is prime, any digit combo 33 between (33,01) will produce smaller primes. ******* Thus, the only possible prime is the smallest prime in the family 33{0}01, and this prime is 33001. ***** For the 33{0,3}31 family, we have the prime 33331, and the remain case is the family 33{0}31. ****** All numbers of the form 33{0}31 are divisible by 2, thus cannot be prime. **** All numbers of the form 3{0,3}11 are divisible by 3, thus cannot be prime. * Case (3,2): ** 32 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 32, 34, 23, 43, 313 are primes, we only need to consider the family 3{0,3}3 (since any digits 1, 2, 4 between them will produce smaller primes) *** All numbers of the form 3{0,3}3 are divisible by 3, thus cannot be prime. * Case (3,4): ** 34 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 43, 21, 401 are primes, we only need to consider the family 4{1,4}1 (since any digits 0, 2, 3 between them will produce smaller primes) *** Since 414, 111 are primes, we only need to consider the families 4{4}1 and 4{4}11 (since any digit combo 14 or 11 between them will produce smaller primes) **** The smallest prime of the form 4{4}1 is 44441. **** All numbers of the form 4{4}11 are divisible by 2, thus cannot be prime. * Case (4,2): ** Since 43, 12, 32 are primes, we only need to consider the family 4{0,2,4}2 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 4{0,2,4}2 are divisible by 2, thus cannot be prime. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,4): ** Since 43, 34, 414 are primes, we only need to consider the family 4{0,2,4}4 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 4{0,2,4}4 are divisible by 2, thus cannot be prime. ===Base 6=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,5), (2,1), (2,5), (3,1), (3,5), (4,1), (4,5), (5,1), (5,5) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 11, 21, 31, 51 are primes, we only need to consider the family 4{0,4}1 (since any digits 1, 2, 3, 5 between them will produce smaller primes) *** Since 4401 and 4441 are primes, we only need to consider the families 4{0}1 and 4{0}41 (since any digits combo 40 and 44 between them will produce smaller primes) **** All numbers of the form 4{0}1 are divisible by 5, thus cannot be prime. **** The smallest prime of the form 4{0}41 is 40041 * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 15, 25, 35, 45 are primes, we only need to consider the family 5{0,5}5 (since any digits 1, 2, 3, 4 between them will produce smaller primes) *** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. ===Base 7=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) * Case (1,1): ** Since 14, 16, 41, 61, 131 are primes, we only need to consider the family 1{0,1,2,5}1 (since any digits 3, 4, 6 between them will produce smaller primes) *** Since the digit sum of primes must be odd (otherwise the number will be divisible by 2, thus cannot be prime), there is an odd total number of 1 and 5 in the {} **** If there are >=3 number of 1 and 5 in the {}: ***** If there is 111 in the {}, then we have the prime 11111 ***** If there is 115 in the {}, then the prime 115 is a subsequence ***** If there is 151 in the {}, then the prime 115 is a subsequence ***** If there is 155 in the {}, then the prime 155 is a subsequence ***** If there is 511 in the {}, then the current number is 15111, which has digit sum = 12, but digit sum divisible by 3 will cause the number divisible by 3 and cannot be prime, and we cannot add more 1 or 5 to this number (to avoid 11111, 155, 515, 551 as subsequence), thus we must add at least one 2 to this number, but then the number has both 2 and 5, and will have either 25 or 52 as subsequence, thus cannot be minimal prime ***** If there is 515 in the {}, then the prime 515 is a subsequence ***** If there is 551 in the {}, then the prime 551 is a subsequence ***** If there is 555 in the {}, then the prime 551 is a subsequence **** Thus there is only one 1 (and no 5) or only one 5 (and no 1) in the {}, i.e. we only need to consider the families 1{0,2}1{0,2}1 and 1{0,2}5{0,2}1 ***** For the 1{0,2}1{0,2}1 family, since 1211 is prime, we only need to consider the family 1{0}1{0,2}1 ****** Since all numbers of the form 1{0}1{0}1 are divisible by 3 and cannot be prime, we only need to consider the family 1{0}1{0}2{0}1 ******* Since 11201 is prime, we only need to consider the family 1{0}1{0}21 ******** The smallest prime of the form 11{0}21 is 1100021 ******** All numbers of the form 101{0}21 are divisible by 5, thus cannot be prime ******** The smallest prime of the form 1001{0}21 is 100121 ********* Since this prime has no 0 between 1{0}1 and 21, we do not need to consider more families ***** For the 1{0,2}5{0,2}1 family, since 25 and 52 are primes, we only need to consider the family 1{0}5{0}1 ****** Since 1051 is prime, we only need to consider the family 15{0}1 ******* The smallest prime of the form 15{0}1 is 150001 * Case (1,2): ** Since 14, 16, 32, 52 are primes, we only need to consider the family 1{0,1,2}2 (since any digits 3, 4, 5, 6 between them will produce smaller primes) *** Since 1112 and 1222 are primes, there is at most one 1 and at most one 2 in {} **** If there are one 1 and one 2 in {}, then the digit sum is 6, and the number will be divisible by 6 and cannot be prime. **** If there is one 1 but no 2 in {}, then the digit sum is 4, and the number will be divisible by 2 and cannot be prime. **** If there is no 1 but one 2 in {}, then the form is 1{0}2{0}2 ***** Since 1022 and 1202 are primes, we only need to consider the number 122 ****** 122 is not prime. **** If there is no 1 and no 2 in {}, then the digit sum is 3, and the number will be divisible by 3 and cannot be prime. * Case (1,3): ** Since 14, 16, 23, 43, 113, 133 are primes, we only need to consider the family 1{0,5}3 (since any digits 1, 2, 3, 4, 6 between them will produce smaller primes) *** Since 155 is prime, we only need to consider the family 1{0}3 and 1{0}5{0}3 **** All numbers of the form 1{0}3 are divisible by 2, thus cannot be prime. **** All numbers of the form 1{0}5{0}3 are divisible by 3, thus cannot be prime. * Case (1,4): ** 14 is prime, and thus the only minimal prime in this family. * Case (1,5): ** Since 14, 16, 25, 65, 115, 155 are primes, we only need to consider the family 1{0,3}5 (since any digits 1, 2, 4, 5, 6 between them will produce smaller primes) *** All numbers of the form 1{0,3}5 are divisible by 3, thus cannot be prime. * Case (1,6): ** 16 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 25, 41, 61, 221 are primes, we only need to consider the family 2{0,1}1 (since any digits 2, 3, 4, 5, 6 between them will produce smaller primes) *** Since 2111 is prime, we only need to consider the families 2{0}1 and 2{0}1{0}1 **** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. **** All numbers of the form 2{0}1{0}1 are divisible by 2, thus cannot be prime. * Case (2,2): ** Since 23, 25, 32, 52, 212 are primes, we only need to consider the family 2{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,4): ** Since 23, 25, 14 are primes, we only need to consider the family 2{0,2,4,6}4 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}4 are divisible by 2, thus cannot be prime. * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (2,6): ** Since 23, 25, 16, 56 are primes, we only need to consider the family 2{0,2,4,6}6 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}6 are divisible by 2, thus cannot be prime. * Case (3,1): ** Since 32, 41, 61 are primes, we only need to consider the family 3{0,1,3,5}1 (since any digits 2, 4, 6 between them will produce smaller primes) *** Since 551 is prime, we only need to consider the family 3{0,1,3}1 and 3{0,1,3}5{0,1,3}1 (since any digits combo 55 between (3,1) will produce smaller primes) **** For the 3{0,1,3}1 family, since 3031 and 131 are primes, we only need to consider the families 3{0,1}1 and 3{3}3{0,1}1 (since any digits combo 03, 13 between (3,1) will produce smaller primes, thus for the digits between (3,1), all 3's must be before all 0's and 1's, and thus we can let the red 3 in 3{3}3{0,1}1 be the rightmost 3 between (3,1), all digits before this 3 must be 3's, and all digits after this 3 must be either 0's or 1's) ***** For the 3{0,1}1 family: ****** If there are >=2 0's and >=1 1's between (3,1), then at least one of 30011, 30101, 31001 will be a subsequence. ****** If there are no 1's between (3,1), then the form will be 3{0}1 ******* All numbers of the form 3{0}1 are divisible by 2, thus cannot be prime. ****** If there are no 0's between (3,1), then the form will be 3{1}1 ******* The smallest prime of the form 3{1}1 is 31111 ****** If there are exactly 1 0's between (3,1), then there must be <3 1's between (3,1), or 31111 will be a subsequence. ******* If there are 2 1's between (3,1), then the digit sum is 6, thus the number is divisible by 6 and cannot be prime. ******* If there are 1 1's between (3,1), then the number can only be either 3101 or 3011 ******** Neither 3101 nor 3011 is prime. ******* If there are no 1's between (3,1), then the number must be 301 ******** 301 is not prime. ***** For the 3{3}3{0,1}1 family: ****** If there are at least one 3 between (3,3{0,1}1) and at least one 1 between (3{3}3,1), then 33311 will be a subsequence. ****** If there are no 3 between (3,3{0,1}1), then the form will be 33{0,1}1 ******* If there are at least 3 1's between (33,1), then 31111 will be a subsequence. ******* If there are exactly 2 1's between (33,1), then the digit sum is 12, thus the number is divisible by 3 and cannot be prime. ******* If there are exactly 1 1's between (33,1), then the digit sum is 11, thus the number is divisible by 2 and cannot be prime. ******* If there are no 1's between (33,1), then the form will be 33{0}1 ******** The smallest prime of the form 33{0}1 is 33001 ****** If there are no 1 between (3{3}3,1), then the form will be 3{3}3{0}1 ******* If there are at least 2 0's between (3{3}3,1), then 33001 will be a subsequence. ******* If there are exactly 1 0's between (3{3}3,1), then the form is 3{3}301 ******** The smallest prime of the form 3{3}301 is 33333301 ******* If there are no 0's between (3{3}3,1), then the form is 3{3}31 ******** The smallest prime of the form 3{3}31 is 33333333333333331 **** For the 3{0,1,3}5{0,1,3}1 family, since 335 is prime, we only need to consider the family 3{0,1}5{0,1,3}1 ***** Numbers containing 3 between (3{0,1}5,1): ****** The form is 3{0,1}5{0,1,3}3{0,1,3}1 ******* Since 3031 and 131 are primes, we only need to consider the family 35{3}3{0,1,3}1 (since any digits combo 03, 13 between (3,1) will produce smaller primes) ******** Since 533 is prime, we only need to consider the family 353{0,1}1 (since any digits combo 33 between (35,1) will produce smaller primes) ********* Since 5011 is prime, we only need to consider the family 353{1}{0}1 (since any digits combo 01 between (353,1) will produce smaller primes) ********** If there are at least 3 1's between (353,{0}1), then 31111 will be a subsequence. ********** If there are exactly 2 1's between (353,{0}1), then the digit sum is 20, thus the number is divisible by 2 and cannot be prime. ********** If there are exactly 1 1's between (353,{0}1), then the form is 3531{0}1 *********** The smallest prime of the form 3531{0}1 is 3531001, but it is not minimal prime since 31001 is prime. ********** If there are no 1's between (353,{0}1), then the digit sum is 15, thus the number is divisible by 6 and cannot be prime. ***** Numbers not containing 3 between (3{0,1}5,1): ****** The form is 3{0,1}5{0,1}1 ******* If there are >=2 0's and >=1 1's between (3,1), then at least one of 30011, 30101, 31001 will be a subsequence. ******* If there are no 1's between (3,1), then the form will be 3{0}5{0}1 ******** All numbers of the form 3{0}5{0}1 are divisible by 3, thus cannot be prime. ******* If there are no 0's between (3,1), then the form will be 3{1}5{1}1 ******** If there are >=3 1's between (3,1), then 31111 will be a subsequence. ******** If there are exactly 2 1's between (3,1), then the number can only be 31151, 31511, 35111 ********* None of 31151, 31511, 35111 are primes. ******** If there are exactly 1 1's between (3,1), then the digit sum is 13, thus the number is divisible by 2 and cannot be prime. ******** If there are no 1's between (3,1), then the number is 351 ********* 351 is not prime. ******* If there are exactly 1 0's between (3,1), then the form will be 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1 ******** No matter 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1, if there are >=3 1's between (3,1), then 31111 will be a subsequence. ******** If there are exactly 2 1's between (3,1), then the number can only be 311051, 310151, 310511, 301151, 301511, 305111, 311501, 315101, 315011, 351101, 351011, 350111 ********* Of these numbers, 311051, 301151, 311501, 351101, 350111 are primes. ********** However, 311051, 301151, 311501 have 115 as subsequence, and 350111 has 5011 as subsequence, thus only 351101 is minimal prime. ******** No matter 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1, if there are exactly 1 1's between (3,1), then the digit sum is 13, thus the number is divisible by 2 and cannot be prime. ******** If there are no 1's between (3,1), then the number is 3051 for 3{1}0{1}5{1}1 or 3501 for 3{1}5{1}0{1}1 ********* Neither 3051 nor 3501 is prime. * Case (3,2): ** 32 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 32, 23, 43, 313 are primes, we only need to consider the family 3{0,3,5,6}3 (since any digits 1, 2, 4 between them will produce smaller primes) *** If there are >=2 5's in {}, then 553 will be a subsequence. *** If there are no 5's in {}, then the family will be 3{0,3,6}3 **** All numbers of the form 3{0,3,6}3 are divisible by 3, thus cannot be prime. *** If there are exactly 1 5's in {}, then the family will be 3{0,3,6}5{0,3,6}3 **** Since 335, 65, 3503, 533, 56 are primes, we only need to consider the family 3{0}53 (since any digit 3, 6 between (3,5{0,3,6}3) and any digit 0, 3, 6 between (3{0,3,6}5,3) will produce smaller primes) ***** The smallest prime of the form 3{0}53 is 300053 * Case (3,4): ** Since 32, 14, 304, 344, 364 are primes, we only need to consider the family 3{3,5}4 (since any digits 0, 1, 2, 4, 6 between them will produce smaller primes) *** Since 3334 and 335 are primes, we only need to consider the family 3{5}4 and 3{5}34 (since any digits combo 33, 35 between them will produce smaller primes) **** The smallest prime of the form 3{5}4 is 35555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555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with 9234 5's, which can be written as 3(5^9234)4 and equal the prime (23*7^9235-11)/6 ([http://factordb.com/index.php?id=1100000002766595757 factordb]) ([http://factordb.com/cert.php?id=1100000002766595757 primality certificate]) (not minimal prime, since 35555 and 5554 are primes) **** The smallest prime of the form 3{5}34 is 355555555555555555555555555555555555555555555555555555555555555534 (not minimal prime, since 35555, 553, and 5554 are primes) * Case (3,5): ** Since 32, 25, 65, 335 are primes, we only need to consider the family 3{0,1,4,5}5 (since any digits 2, 3, 6 between them will produce smaller primes) *** If there are at least one 1's and at least one 5's in {}, then either 155 or 515 will be a subsequence. *** If there are at least one 1's and at least one 4's in {}, then either 14 or 41 will be a subsequence. *** If there are at least two 1's in {}, then 115 will be a subsequence. *** If there are exactly one 1's and no 4's or 5's in {}, then the family will be 3{0}1{0}5 **** All numbers of the form 3{0}1{0}5 are divisible by 3, thus cannot be prime. *** If there is no 1's in {}, then the family will be 3{0,4,5}5 **** If there are at least to 4's in {}, then 344 and 445 will be subsequences. **** If there is no 4's in {}, then the family will be 3{0,5}5 ***** Since 3055 and 3505 are primes, we only need to consider the families 3{0}5 and 3{5}5 ****** All numbers of the form 3{0}5 are divisible by 2, thus cannot be prime. ****** The smallest prime of the form 3{5}5 is 35555 **** If there is exactly one 4's in {}, then the family will be 3{0,5}4{0,5}5 ***** Since 304, 3545 are primes, we only need to consider the families 34{0,5}5 (since any digits 0 or 5 between (3,4{0,5}5) will produce small primes) ****** All numbers of the form 34{0,5}5 are divisible by 5, thus cannot be prime. * Case (3,6): ** Since 32, 16, 56, 346 are primes, we only need to consider the family 3{0,3,6}6 (since any digits 1, 2, 4, 5 between them will produce smaller primes) *** All numbers of the form 3{0,3,6}6 are divisible by 3, thus cannot be prime. * Case (4,1): ** 41 is prime, and thus the only minimal prime in this family. * Case (4,2): ** Since 41, 43, 32, 52 are primes, we only need to consider the family 4{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 4{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,4): ** Since 41, 43, 14 are primes, we only need to consider the family 4{0,2,4,5,6}4 (since any digits 1, 3 between them will produce smaller primes) *** If there is no 5's in {}, then the family will be 4{0,2,4,6}4 **** All numbers of the form 4{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there is at least one 5's in {}, then there cannot be 2 in {} (since if so, then either 25 or 52 will be a subsequence) and there cannot be 6 in {} (since if so, then either 65 or 56 will be a subsequence), thus the family is 4{0,4,5}5{0,4,5}4 **** Since 445, 4504, 544 are primes, we only need to consider the family 4{0,5}5{5}4 (since any digit 4 between (4,5{0,4,5}4) and any digit 0, 4 between (4{0,4,5}5,4) will produce smaller primes) ***** If there are at least two 0's between (4,5{0,4,5}4), then 40054 will be a subsequence. ***** If there is no 0's between (4,5{0,4,5}4), then the family will be 4{5}5{5}4, which is equivalent to 4{5}4 ****** The smallest prime of the form 4{5}4 is 45555555555555554 (not minimal prime, since 4555 and 5554 are primes) ***** If there is exactly one 0's between (4,5{0,4,5}4), then the family will be 4{5}0{5}5{5}4 ****** Since 4504 is prime, we only need to consider the family 40{5}5{5}4 (since any digit 5 between (4,0{5}5{5}4) will produce small primes), which is equivalent to 40{5}4 ******* The smallest prime of the form 40{5}4 is 405555555555555554 (not minimal prime, since 4555 and 5554 are primes) * Case (4,5): ** Since 41, 43, 25, 65, 445 are primes, we only need to consider the family 4{0,5}5 (since any digits 1, 2, 3, 4, 6 between them will produce smaller primes) *** If there are at least two 5's in {}, then 4555 will be a subsequence. *** If there is exactly one 5's in {}, then the digit sum is 20, and the number will be divisible by 2 and cannot be prime. *** If there is no 5's in {}, then the family will be 4{0}5 **** All numbers of the form 4{0}5 are divisible by 3, thus cannot be prime. * Case (4,6): ** Since 41, 43, 16, 56 are primes, we only need to consider the family 4{0,2,4,6}6 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 4{0,2,4,6}6 are divisible by 2, thus cannot be prime. * Case (5,1): ** Since 52, 56, 41, 61, 551 are primes, we only need to consider the family 5{0,1,3}1 (since any digits 2, 4, 5, 6 between them will produce smaller primes) *** If there are at least two 3's in {}, then 533 will be a subsequence. *** If there is no 3's in {}, then the family will be 5{0,1}1 **** Since 5011 is prime, we only need to consider the family 5{1}{0}1 ***** Since 11111 is prime, we only need to consider the families 5{0}1, 51{0}1, 511{0}1, 5111{0}1 (since any digits combo 1111 between (5,1) will produce small primes) ****** All numbers of the form 5{0}1 are divisible by 6, thus cannot be prime. ****** The smallest prime of the form 51{0}1 is 5100000001 ****** All numbers of the form 511{0}1 are divisible by 2, thus cannot be prime. ****** All numbers of the form 5111{0}1 are divisible by 3, thus cannot be prime. *** If there is exactly one 3's in {}, then the family will be 5{0,1}3{0,1}1 **** If there is at least one 1's between (5,3{0,1}1), then 131 will be a subsequence. ***** Thus we only need to consider the family 5{0}3{0,1}1 ****** If there are no 1's between (5{0}3,1), then the digit sum is 12, and the number will be divisible by 3 and cannot be prime. ****** If there are exactly one 1's between (5{0}3,1), then the digit sum is 13, and the number will be divisible by 2 and cannot be prime. ****** If there are exactly three 1's between (5{0}3,1), then the digit sum is 15, and the number will be divisible by 6 and cannot be prime. ****** If there are at least four 1's between (5{0}3,1), then 11111 will be a subsequence. ****** If there are exactly two 1's between (5{0}3,1), then the family will be 5{0}3{0}1{0}1{0}1 ******* Since 5011 is prime, we only need to consider the family 5311{0}1 (since any digit 0 between (5,1{0}1) will produce small primes, this includes the leftmost three {} in 5{0}3{0}1{0}1{0}1, and thus only the rightmost {} can contain 0) ******** The smallest prime of the form 5311{0}1 is 531101 * Case (5,2): ** 52 is prime, and thus the only minimal prime in this family. * Case (5,3): ** Since 52, 56, 23, 43, 533, 553 are primes, we only need to consider the family 5{0,1}3 (since any digits 2, 3, 4, 5, 6 between them will produce smaller primes) *** If there are at least two 1's in {}, then 113 will be a subsequence. *** If there is exactly one 1's in {}, then the digit sum is 12, and the number will be divisible by 3 and cannot be prime. *** If there is no 1's in {}, then the digit sum is 11, and the number will be divisible by 2 and cannot be prime. * Case (5,4): ** Since 52, 56, 14, 544 are primes, we only need to consider the family 5{0,3,5}4 (since any digits 1, 2, 4, 6 between them will produce smaller primes) *** If there are no 5's in {}, then the family will be 5{0,3}4 **** All numbers of the form 5{0,3}4 are divisible by 3, thus cannot be prime. *** If there are at least one 5's and at least one 3's in {}, then either 535 or 553 will be a subsequence. *** If there are exactly one 5's and no 3's in {}, then the digit sum is 20, and the number will be divisible by 2 and cannot be prime. *** If there are at least two 5's in {}, then 5554 will be a subsequence. * Case (5,5): ** Since 52, 56, 25, 65, 515, 535 are primes, we only need to consider the family 5{0,4,5}5 (since any digits 1, 2, 3, 6 between them will produce smaller primes) *** If there are no 4's in {}, then the family will be 5{0,5}5 **** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. *** If there are no 5's in {}, then the family will be 5{0,4}5 **** All numbers of the form 5{0,4}5 are divisible by 2, thus cannot be prime. *** If there are at least one 4's and at least one 5's in {}, then either 5455 or 5545 will be a subsequence. * Case (5,6): ** 56 is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,2): ** Since 61, 65, 32, 52 are primes, we only need to consider the family 6{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 6{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (6,3): ** Since 61, 65, 23, 43 are primes, we only need to consider the family 6{0,3,6}3 (since any digits 1, 2, 4, 5 between them will produce smaller primes) *** All numbers of the form 6{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (6,4): ** Since 61, 65, 14 are primes, we only need to consider the family 6{0,2,3,4,6}4 (since any digits 1, 5 between them will produce smaller primes) *** If there is no 3's in {}, then the family will be 6{0,2,4,6}4 **** All numbers of the form 6{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there are exactly two 3's in {}, then the family will be 6{0,2,4,6}3{0,2,4,6}3{0,2,4,6}4 **** All numbers of the form 6{0,2,4,6}3{0,2,4,6}3{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there are at least three 3's in {}, then 3334 will be a subsequence. *** If there is exactly one 3's in {}, then the family will be 6{0,2,4,6}3{0,2,4,6}4 **** If there is 0 between (6,3{0,2,4,6}4), then 6034 will be a subsequence. **** If there is 2 between (6,3{0,2,4,6}4), then 23 will be a subsequence. **** If there is 4 between (6,3{0,2,4,6}4), then 43 will be a subsequence. **** If there is 6 between (6,3{0,2,4,6}4), then 6634 will be a subsequence. **** If there is 0 between (6{0,2,4,6}3,4), then 304 will be a subsequence. **** If there is 2 between (6{0,2,4,6}3,4), then 32 will be a subsequence. **** If there is 4 between (6{0,2,4,6}3,4), then 344 will be a subsequence. **** If there is 6 between (6{0,2,4,6}3,4), then 364 will be a subsequence. **** Thus the number can only be 634 ***** 634 is not prime. * Case (6,5): ** 65 is prime, and thus the only minimal prime in this family. * Case (6,6): ** Since 61, 65, 16, 56 are primes, we only need to consider the family 6{0,2,3,4,6}6 (since any digits 1, 5 between them will produce smaller primes) *** If there is no 3's in {}, then the family will be 6{0,2,4,6}6 **** All numbers of the form 6{0,2,4,6}6 are divisible by 2, thus cannot be prime. *** If there is no 2's and no 4's in {}, then the family will be 6{0,3,6}6 **** All numbers of the form 6{0,3,6}6 are divisible by 3, thus cannot be prime. *** If there is at least one 3's and at least one 2's in {}, then either 32 or 23 will be a subsequence. *** If there is at least one 3's and at least one 4's in {}, then either 346 or 43 will be a subsequence. ===Base 8=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (1,5), (1,7), (2,1), (2,3), (2,5), (2,7), (3,1), (3,3), (3,5), (3,7), (4,1), (4,3), (4,5), (4,7), (5,1), (5,3), (5,5), (5,7), (6,1), (6,3), (6,5), (6,7), (7,1), (7,3), (7,5), (7,7) * Case (1,1): ** Since 13, 15, 21, 51, 111, 141, 161 are primes, we only need to consider the family 1{0,7}1 (since any digits 1, 2, 3, 4, 5, 6 between them will produce smaller primes) *** Since 107, 177, 701 are primes, we only need to consider the number 171 and the family 1{0}1 (since any digits combo 07, 70, 77 between them will produce smaller primes) **** 171 is not prime. **** All numbers of the form 1{0}1 factored as 10^n+1 = (2^n+1) * (4^n-2^n+1) (n≥1) (and since if n≥1, 2^n+1 ≥ 2^1+1 = 3 > 1, 4^n-2^n+1 ≥ 4^1-2^1+1 = 3 > 1, this factorization is nontrivial), thus cannot be prime. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (1,7): ** Since 13, 15, 27, 37, 57, 107, 117, 147, 177 are primes, we only need to consider the family 1{6}7 (since any digits 0, 1, 2, 3, 4, 5, 7 between them will produce smaller primes) *** The smallest prime of the form 1{6}7 is 16667 (not minimal prime, since 667 is prime) * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,5): ** Since 21, 23, 27, 15, 35, 45, 65, 75, 225, 255 are primes, we only need to consider the family 2{0}5 (since any digits 1, 2, 3, 4, 5, 6, 7 between them will produce smaller primes) *** All numbers of the form 2{0}5 are divisible by 7, thus cannot be prime. * Case (2,7): ** 27 is prime, and thus the only minimal prime in this family. * Case (3,1): ** Since 35, 37, 21, 51, 301, 361 are primes, we only need to consider the family 3{1,3,4}1 (since any digits 0, 2, 5, 6, 7 between them will produce smaller primes) *** Since 13, 343, 111, 131, 141, 431, 3331, 3411 are primes, we only need to consider the families 3{3}11, 33{1,4}1, 3{3,4}4{4}1 (since any digits combo 11, 13, 14, 33, 41, 43 between them will produce smaller primes) **** All numbers of the form 3{3}11 are divisible by 3, thus cannot be prime. **** For the 33{1,4}1 family, since 111 and 141 are primes, we only need to consider the families 33{4}1 and 33{4}11 (since any digits combo 11, 14 between them will produce smaller primes) ***** The smallest prime of the form 33{4}1 is 3344441 ***** All numbers of the form 33{4}11 are divisible by 301, thus cannot be prime. **** For the 3{3,4}4{4}1 family, since 3331 and 3344441 are primes, we only need to consider the families 3{4}1, 3{4}31, 3{4}341, 3{4}3441, 3{4}34441 (since any digits combo 33 or 34444 between (3,1) will produce smaller primes) ***** All numbers of the form 3{4}1 are divisible by 31, thus cannot be prime. ***** Since 4443 is prime, we only need to consider the numbers 3431, 34431, 34341, 344341, 343441, 3443441, 3434441, 34434441 (since any digit combo 444 between (3,3{4}1) will produce smaller primes) ****** None of 3431, 34431, 34341, 344341, 343441, 3443441, 3434441, 34434441 are primes. * Case (3,3): ** Since 35, 37, 13, 23, 53, 73, 343 are primes, we only need to consider the family 3{0,3,6}3 (since any digits 1, 2, 4, 5, 7 between them will produce smaller primes) *** All numbers of the form 3{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 21, 51, 401, 431, 471 are primes, we only need to consider the family 4{1,4,6}1 (since any digits 0, 2, 3, 5, 7 between them will produce smaller primes) *** Since 111, 141, 161, 661, 4611 are primes, we only need to consider the families 4{4}11, 4{4,6}4{1,4,6}1, 4{4}6{4}1 (since any digits combo 11, 14, 16, 61, 66 between them will produce smaller primes) **** The smallest prime of the form 4{4}11 is 44444444444444411 (not minimal prime, since 444444441 is prime) **** For the 4{4,6}4{1,4,6}1 family, we can separate this family to 4{4,6}41, 4{4,6}411, 4{4,6}461 ***** For the 4{4,6}41 family, since 661 and 6441 are primes, we only need to consider the families 4{4}41 and 4{4}641 (since any digits combo 64 or 66 between (4,41) will produce smaller primes) ****** The smallest prime of the form 4{4}41 is 444444441 ****** The smallest prime of the form 4{4}641 is 444641 ***** For the 4{4,6}411 family, since 661 and 6441 are primes, we only need to consider the families 4{4}411 and 4{4}6411 (since any digits combo 64 or 66 between (4,411) will produce smaller primes) ****** The smallest prime of the form 4{4}411 is 444444441 ****** The smallest prime of the form 4{4}6411 is 4444444444444446411 (not minimal prime, since 444444441 and 444641 are primes) ***** For the 4{4,6}461 family, since 661 is prime, we only need to consider the family 4{4}461 ****** The smallest prime of the form 4{4}461 is 4444444461 (not minimal prime, since 444444441 is prime) **** For the 4{4}6{4}1 family, since 6441 is prime, we only need to consider the families 4{4}61 and 4{4}641 (since any digits combo 44 between (4{4}6,1) will produce smaller primes) ***** The smallest prime of the form 4{4}61 is 4444444461 (not minimal prime, since 444444441 is prime) ***** The smallest prime of the form 4{4}641 is 444641 * Case (4,3): ** Since 45, 13, 23, 53, 73, 433, 463 are primes, we only need to consider the family 4{0,4}3 (since any digits 1, 2, 3, 5, 6, 7 between them will produce smaller primes) *** Since 4043 and 4443 are primes, we only need to consider the families 4{0}3 and 44{0}3 (since any digits combo 04, 44 between them will produce smaller primes) **** All numbers of the form 4{0}3 are divisible by 7, thus cannot be prime. **** All numbers of the form 44{0}3 are divisible by 3, thus cannot be prime. * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (4,7): ** Since 45, 27, 37, 57, 407, 417, 467 are primes, we only need to consider the family 4{4,7}7 (since any digits 0, 1, 2, 3, 5, 6 between them will produce smaller primes) *** Since 747 is prime, we only need to consider the families 4{4}7, 4{4}77, 4{7}7, 44{7}7 (since any digits combo 74 between (4,7) will produce smaller primes) **** The smallest prime of the form 4{4}7 is 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447, with 220 4's, which can be written as (4^220)7 and equal the prime (4*8^221+17)/7 ([http://factordb.com/index.php?id=1100000000416605822 factordb]) **** The smallest prime of the form 4{4}77 is 4444477 **** The smallest prime of the form 4{7}7 is 47777 **** The smallest prime of the form 44{7}7 is 4477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777, with 851 7's, which can be written as 44(7^851) and equal the prime 37*8^851-1 ([http://factordb.com/index.php?id=1100000000413677646 factordb]) (not minimal prime, since 47777 is prime) * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,3): ** 53 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 53, 57, 15, 35, 45, 65, 75 are primes, we only need to consider the family 5{0,2,5}5 (since any digits 1, 3, 4, 6, 7 between them will produce smaller primes) *** Since 225, 255, 5205 are primes, we only need to consider the families 5{0,5}5 and 5{0,5}25 (since any digits combo 20, 22, 25 between them will produce smaller primes) **** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. **** For the 5{0,5}25 family, since 500025 and 505525 are primes, we only need to consider the number 500525 the families 5{5}25, 5{5}025, 5{5}0025, 5{5}0525, 5{5}00525, 5{5}05025 (since any digits combo 000, 055 between (5,25) will produce smaller primes) ***** 500525 is not prime. ***** The smallest prime of the form 5{5}25 is 555555555555525 ***** The smallest prime of the form 5{5}025 is 55555025 ***** The smallest prime of the form 5{5}0025 is 5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555550025, with 184 5's, which can be written as (5^183)0025 and equal the prime (5*8^187-20333)/7 ([http://factordb.com/index.php?id=1100000002350205912 factordb]) (not minimal prime, since 55555025 and 555555555555525 are primes) ***** The smallest prime of the form 5{5}0525 is 5550525 ***** The smallest prime of the form 5{5}00525 is 5500525 ***** The smallest prime of the form 5{5}05025 is 5555555555555555555555505025 (not minimal prime, since 5550525, 55555025, and 555555555555525 are primes) * Case (5,7): ** 57 is prime, and thus the only minimal prime in this family. * Case (6,1): ** Since 65, 21, 51, 631, 661 are primes, we only need to consider the family 6{0,1,4,7}1 (since any digits 2, 3, 5, 6 between them will produce smaller primes) *** Numbers containing 4: (note that the number cannot contain two or more 4's, or 6441 will be a subsequence) **** The form is 6{0,1,7}4{0,1,7}1 ***** Since 141, 401, 471 are primes, we only need to consider the family 6{0,7}4{1}1 ****** Since 111 is prime, we only need to consider the families 6{0,7}41 and 6{0,7}411 ******* For the 6{0,7}41 family, since 60741 is prime, we only need to consider the family 6{7}{0}41 ******** Since 6777 is prime, we only need to consider the families 6{0}41, 67{0}41, 677{0}41 ********* All numbers of the form 6{0}41 are divisible by 3, thus cannot be prime. ********* All numbers of the form 67{0}41 are divisible by 13, thus cannot be prime. ********* All numbers of the form 677{0}41 are divisible by 3, thus cannot be prime. ******* For the 6{0,7}411 family, since 60411 is prime, we only need to consider the family 6{7}411 ******** The smallest prime of the form 6{7}411 is 67777411 (not minimal prime, since 6777 is prime) *** Numbers not containing 4: **** The form is 6{0,1,7}1 ***** Since 111 is prime, we only need to consider the families 6{0,7}1 and 6{0,7}1{0,7}1 ****** All numbers of the form 6{0,7}1 are divisible by 7, thus cannot be prime. ****** For the 6{0,7}1{0,7}1 family, since 711 and 6101 are primes, we only need to consider the family 6{0}1{7}1 ******* Since 60171 is prime, we only need to consider the families 6{0}11 and 61{7}1 ******** All numbers of the form 6{0}11 are divisible by 3, thus cannot be prime. ******** The smallest prime of the form 61{7}1 is 617771 (not minimal prime, since 6777 is prime) * Case (6,3): ** Since 65, 13, 23, 53, 73, 643 are primes, we only need to consider the family 6{0,3,6}3 (since any digits 1, 2, 4, 5, 7 between them will produce smaller primes) *** All numbers of the form 6{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (6,5): ** 65 is prime, and thus the only minimal prime in this family. * Case (6,7): ** Since 65, 27, 37, 57, 667 are primes, we only need to consider the family 6{0,1,4,7}7 (since any digits 2, 3, 5, 6 between them will produce smaller primes) *** Since 107, 117, 147, 177, 407, 417, 717, 747, 6007, 6477, 6707, 6777 are primes, there cannot be digits combo 00, 10, 11, 14, 17, 40, 41, 47, 70, 71, 74, 77 between them **** If there is 1 between them, then there cannot be 1, 4, 7 before it and cannot be 0, 1, 4, 7 after it, thus the form will be 6{0}17 ***** All numbers of the form 6{0}17 are divisible by 3, thus cannot be prime. **** If there is 7 between them, then there cannot be 1, 4, 7 before it and cannot be 0, 1, 4, 7 after it, thus the form will be 6{0}77 ***** All numbers of the form 6{0}77 are divisible by 3, thus cannot be prime. **** If there is neither 1 nor 7 between them, then the form is 6{0,4}7 ***** Since 6007, 407 at primes, we only need to consider the families 6{4}7 and 60{4}7 (since any digits combo 00, 40 between them will produce smaller primes) ****** All numbers of the form 6{4}7 are divisible by 3, 5, or 15, thus cannot be prime. ****** All numbers of the form 60{4}7 are divisible by 21, thus cannot be prime. * Case (7,1): ** Since 73, 75, 21, 51, 701, 711 are primes, we only need to consider the family 7{4,6,7}1 (since any digits 0, 1, 2, 3, 5 between them will produce smaller primes) *** Since 747, 767, 471, 661, 7461, 7641 are primes, we only need to consider the families 7{4,7}4{4}1, 7{7}61, 7{7}7{4,6,7}1 (since any digits combo 46, 47, 64, 66, 67 between them will produce smaller primes) **** For the 7{4,7}4{4}1 family, since 747, 471 are primes, we only need to consider the family 7{7}{4}1 (since any digits combo 47 between (7,4{4}1) will produce smaller primes) ***** The smallest prime of the form 7{7}1 is 7777777777771 ***** The smallest prime of the form 7{7}41 is 777777777777777777777777777777777777777777777777777777777777777777777777777777741, with 79 7's, which can be written as (7^79)41 and equal the prime 8^81-31 ([http://factordb.com/index.php?id=1100000000294462449 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}441 is 777777777777777777777777777777777777777777777777777777777777777777777777777777777777441, with 84 7's, which can be written as (7^84)441 and equal the prime 8^87-223 ([http://factordb.com/index.php?id=1100000000294462776 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}4441 is 777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777774441, with 233 7's, which can be written as (7^233)4441 and equal the prime 8^237-1759 ([http://factordb.com/index.php?id=1100000002352073382 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}44441 is 7777777777777777777777777777777777777777777777777777777744441, with 56 7's, which can be written as (7^56)44441 and equal the prime 8^61-14047 ([http://factordb.com/index.php?id=1100000002350250002 factordb]) (not minimal prime, since 7777777777771 is prime) ***** All numbers of the form 7{7}444441 are divisible by 7, thus cannot be prime. ***** The smallest prime of the form 7{7}4444441 is 77774444441 ****** Since this prime has just 4 7's, we only need to consider the families with <=3 7's ******* The smallest prime of the form 7{4}1 is 744444441 ******* All numbers of the form 77{4}1 are divisible by 5, thus cannot be prime. ******* The smallest prime of the form 777{4}1 is 777444444444441 (not minimal prime, since 444444441 and 744444441 are primes) * Case (7,3): ** 73 is prime, and thus the only minimal prime in this family. * Case (7,5): ** 75 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 73, 75, 27, 37, 57, 717, 747, 767 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6 between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. ===Base 10=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (1,7), (1,9), (2,1), (2,3), (2,7), (2,9), (3,1), (3,3), (3,7), (3,9), (4,1), (4,3), (4,7), (4,9), (5,1), (5,3), (5,7), (5,9), (6,1), (6,3), (6,7), (6,9), (7,1), (7,3), (7,7), (7,9), (8,1), (8,3), (8,7), (8,9), (9,1), (9,3), (9,7), (9,9) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (1,7): ** 17 is prime, and thus the only minimal prime in this family. * Case (1,9): ** 19 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 29, 11, 31, 41, 61, 71, 251, 281 are primes, we only need to consider the family 2{0,2}1 (since any digits 1, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 2221 and 20201 are primes, we only need to consider the families 2{0}1, 2{0}21, 22{0}1 (since any digits combo 22 or 020 between them will produce smaller primes) **** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. **** The smallest prime of the form 2{0}21 is 20021 **** The smallest prime of the form 22{0}1 is 22000001 * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,7): ** Since 23, 29, 17, 37, 47, 67, 97, 227, 257, 277 are primes, we only need to consider the family 2{0,8}7 (since any digits 1, 2, 3, 4, 5, 6, 7, 9 between them will produce smaller primes) *** Since 887 and 2087 are primes, we only need to consider the families 2{0}7 and 28{0}7 (since any digit combo 08 or 88 between them will produce smaller primes) **** All numbers of the form 2{0}7 are divisible by 3, thus cannot be prime. **** All numbers of the form 28{0}7 are divisible by 7, thus cannot be prime. * Case (2,9): ** 29 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 31, 37, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 3{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 3{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (3,9): ** Since 31, 37, 19, 29, 59, 79, 89, 349 are primes, we only need to consider the family 3{0,3,6,9}9 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 3{0,3,6,9}9 are divisible by 3, thus cannot be prime. * Case (4,1): ** 41 is prime, and thus the only minimal prime in this family. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,7): ** 47 is prime, and thus the only minimal prime in this family. * Case (4,9): ** Since 41, 43, 47, 19, 29, 59, 79, 89, 409, 449, 499 are primes, we only need to consider the family 4{6}9 (since any digits 0, 1, 2, 3, 4, 5, 7, 8, 9 between them will produce smaller primes) *** All numbers of the form 4{6}9 are divisible by 7, thus cannot be prime. * Case (5,1): ** Since 53, 59, 11, 31, 41, 61, 71, 521 are primes, we only need to consider the family 5{0,5,8}1 (since any digits 1, 2, 3, 4, 6, 7, 9 between them will produce smaller primes) *** Since 881 is prime, we only need to consider the families 5{0,5}1 and 5{0,5}8{0,5}1 (since any digit combo 88 between them will produce smaller primes) **** For the 5{0,5}1 family, since 5051 and 5501 are primes, we only need to consider the families 5{0}1 and 5{5}1 (since any digit combo 05 or 50 between them will produce smaller primes) ***** All numbers of the form 5{0}1 are divisible by 3, thus cannot be prime. ***** The smallest prime of the form 5{5}1 is 555555555551 **** For the 5{0,5}8{0,5}1 family, since 5081, 5581, 5801, 5851 are primes, we only need to consider the number 581 ***** 581 is not prime. * Case (5,3): ** 53 is prime, and thus the only minimal prime in this family. * Case (5,7): ** Since 53, 59, 17, 37, 47, 67, 97, 557, 577, 587 are primes, we only need to consider the family 5{0,2}7 (since any digits 1, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 227 and 50207 are primes, we only need to consider the families 5{0}7, 5{0}27, 52{0}7 (since any digits combo 22 or 020 between them will produce smaller primes) **** All numbers of the form 5{0}7 are divisible by 3, thus cannot be prime. **** The smallest prime of the form 5{0}27 is 5000000000000000000000000000027 **** The smallest prime of the form 52{0}7 is 5200007 * Case (5,9): ** 59 is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,3): ** Since 61, 67, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 6{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 6{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (6,7): ** 67 is prime, and thus the only minimal prime in this family. * Case (6,9): ** Since 61, 67, 19, 29, 59, 79, 89 are primes, we only need to consider the family 6{0,3,4,6,9}9 (since any digits 1, 2, 5, 7, 8 between them will produce smaller primes) *** Since 449 is prime, we only need to consider the families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9 (since any digit combo 44 between them will produce smaller primes) **** All numbers of the form 6{0,3,6,9}9 are divisible by 3, thus cannot be prime. **** For the 6{0,3,6,9}4{0,3,6,9}9 family, since 409, 43, 6469, 499 are primes, we only need to consider the family 6{0,3,6,9}49 ***** Since 349, 6949 are primes, we only need to consider the family 6{0,6}49 ****** Since 60649 is prime, we only need to consider the family 6{6}{0}49 (since any digits combo 06 between {6,49} will produce smaller primes) ******* The smallest prime of the form 6{6}49 is 666649 ******** Since this prime has just 4 6's, we only need to consider the families with <=3 6's ********* The smallest prime of the form 6{0}49 is 60000049 ********* The smallest prime of the form 66{0}49 is 66000049 ********* The smallest prime of the form 666{0}49 is 66600049 * Case (7,1): ** 71 is prime, and thus the only minimal prime in this family. * Case (7,3): ** 73 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 71, 73, 79, 17, 37, 47, 67, 97, 727, 757, 787 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6, 8, 9 between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. * Case (7,9): ** 79 is prime, and thus the only minimal prime in this family. * Case (8,1): ** Since 83, 89, 11, 31, 41, 61, 71, 821, 881 are primes, we only need to consider the family 8{0,5}1 (since any digits 1, 2, 3, 4, 6, 7, 8, 9 between them will produce smaller primes) *** Since 8501 is prime, we only need to consider the family 8{0}{5}1 (since any digits combo 50 between them will produce smaller primes) **** Since 80051 is prime, we only need to consider the families 8{0}1, 8{5}1, 80{5}1 (since any digits combo 005 between them will produce smaller primes) ***** All numbers of the form 8{0}1 are divisible by 3, thus cannot be prime. ***** The smallest prime of the form 8{5}1 is 8555555555555555555551 (not minimal prime, since 555555555551 is prime) ***** The smallest prime of the form 80{5}1 is 80555551 * Case (8,3): ** 83 is prime, and thus the only minimal prime in this family. * Case (8,7): ** Since 83, 89, 17, 37, 47, 67, 97, 827, 857, 877, 887 are primes, we only need to consider the family 8{0}7 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** All numbers of the form 8{0}7 are divisible by 3, thus cannot be prime. * Case (8,9): ** 89 is prime, and thus the only minimal prime in this family. * Case (9,1): ** Since 97, 11, 31, 41, 61, 71, 991 are primes, we only need to consider the family 9{0,2,5,8}1 (since any digits 1, 3, 4, 6, 7, 9 between them will produce smaller primes) *** Since 251, 281, 521, 821, 881, 9001, 9221, 9551, 9851 are primes, we only need to consider the families 9{2,5,8}0{2,5,8}1, 9{0}2{0}1, 9{0}5{0,8}1, 9{0,5}8{0}1 (since any digits combo 00, 22, 25, 28, 52, 55, 82, 85, 88 between them will produce smaller primes) **** For the 9{2,5,8}0{2,5,8}1 family, since any digits combo 22, 25, 28, 52, 55, 82, 85, 88 between (9,1) will produce smaller primes, we only need to consider the numbers 901, 9021, 9051, 9081, 9201, 9501, 9801, 90581, 95081, 95801 ***** 95801 is the only prime among 901, 9021, 9051, 9081, 9201, 9501, 9801, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. **** For the 9{0}2{0}1 family, since 9001 is prime, we only need to consider the numbers 921, 9201, 9021 ***** None of 921, 9201, 9021 are primes. **** For the 9{0}5{0,8}1 family, since 9001 and 881 are primes, we only need to consider the numbers 951, 9051, 9501, 9581, 90581, 95081, 95801 ***** 95801 is the only prime among 951, 9051, 9501, 9581, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. **** For the 9{0,5}8{0}1 family, since 9001 and 5581 are primes, we only need to consider the numbers 981, 9081, 9581, 9801, 90581, 95081, 95801 ***** 95801 is the only prime among 981, 9081, 9581, 9801, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. * Case (9,3): ** Since 97, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 9{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 9{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (9,7): ** 97 is prime, and thus the only minimal prime in this family. * Case (9,9): ** Since 97, 19, 29, 59, 79, 89 are primes, we only need to consider the family 9{0,3,4,6,9}9 (since any digits 1, 2, 5, 7, 8 between them will produce smaller primes) *** Since 449 is prime, we only need to consider the families 9{0,3,6,9}9 and 9{0,3,6,9}4{0,3,6,9}9 (since any digit combo 44 between them will produce smaller primes) **** All numbers of the form 9{0,3,6,9}9 are divisible by 3, thus cannot be prime. **** For the 9{0,3,6,9}4{0,3,6,9}9 family, since 9049, 349, 9649, 9949 are primes, we only need to consider the family 94{0,3,6,9}9 ***** Since 409, 43, 499 are primes, we only need to consider the family 94{6}9 (since any digits 0, 3, 9 between (94,9) will produce smaller primes) ****** The smallest prime of the form 94{6}9 is 946669 ===Base 12=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,5), (1,7), (1,B), (2,1), (2,5), (2,7), (2,B), (3,1), (3,5), (3,7), (3,B), (4,1), (4,5), (4,7), (4,B), (5,1), (5,5), (5,7), (5,B), (6,1), (6,5), (6,7), (6,B), (7,1), (7,5), (7,7), (7,B), (8,1), (8,5), (8,7), (8,B), (9,1), (9,5), (9,7), (9,B), (A,1), (A,5), (A,7), (A,B), (B,1), (B,5), (B,7), (B,B) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (1,7): ** 17 is prime, and thus the only minimal prime in this family. * Case (1,B): ** 1B is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 25, 27, 11, 31, 51, 61, 81, 91, 221, 241, 2A1, 2B1 are primes, we only need to consider the family 2{0}1 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B between them will produce smaller primes) *** The smallest prime of the form 2{0}1 is 2001 * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (2,7): ** 27 is prime, and thus the only minimal prime in this family. * Case (2,B): ** Since 25, 27, 1B, 3B, 4B, 5B, 6B, 8B, AB, 2BB are primes, we only need to consider the family 2{0,2,9}B (since any digits 1, 3, 4, 5, 6, 7, 8, A, B between them will produce smaller primes) *** Since 90B, 200B, 202B, 222B, 229B, 292B, 299B are primes, we only need to consider the numbers 20B, 22B, 29B, 209B, 220B (since any digits combo 00, 02, 22, 29, 90, 92, 99 between them will produce smaller primes) **** None of 20B, 22B, 29B, 209B, 220B are primes. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (3,B): ** 3B is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 4B, 11, 31, 51, 61, 81, 91, 401, 421, 471 are primes, we only need to consider the family 4{4,A}1 (since any digit 0, 1, 2, 3, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since A41 and 4441 are primes, we only need to consider the families 4{A}1 and 44{A}1 (since any digit combo 44, A4 between them will produce smaller primes) **** All numbers of the form 4{A}1 are divisible by 5, thus cannot be prime. **** The smallest prime of the form 44{A}1 is 44AAA1 * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (4,7): ** Since 45, 4B, 17, 27, 37, 57, 67, 87, A7, B7, 447, 497 are primes, we only need to consider the family 4{0,7}7 (since any digit 1, 2, 3, 4, 5, 6, 8, 9, A, B between them will produce smaller primes) *** Since 4707 and 4777 are primes, we only need to consider the families 4{0}7 and 4{0}77 (since any digit combo 70, 77 between them will produce smaller primes) **** All numbers of the form 4{0}7 are divisible by B, thus cannot be prime. **** The smallest prime of the form 4{0}77 is 400000000000000000000000000000000000000077 * Case (4,B): ** 4B is prime, and thus the only minimal prime in this family. * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 57, 5B, 15, 25, 35, 45, 75, 85, 95, B5, 565 are primes, we only need to consider the family 5{0,5,A}5 (since any digits 1, 2, 3, 4, 6, 7, 8, 9, B between them will produce smaller primes) *** All numbers of the form 5{0,5,A}5 are divisible by 5, thus cannot be prime. * Case (5,7): ** 57 is prime, and thus the only minimal prime in this family. * Case (5,B): ** 5B is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,5): ** Since 61, 67, 6B, 15, 25, 35, 45, 75, 85, 95, B5, 655, 665 are primes, we only need to consider the family 6{0,A}5 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since 6A05 and 6AA5 are primes, we only need to consider the families 6{0}5 and 6{0}A5 (since any digit combo A0, AA between them will produce smaller primes) **** All numbers of the form 6{0}5 are divisible by B, thus cannot be prime. **** The smallest prime of the form 6{0}A5 is 600A5 * Case (6,7): ** 67 is prime, and thus the only minimal prime in this family. * Case (6,B): ** 6B is prime, and thus the only minimal prime in this family. * Case (7,1): ** Since 75, 11, 31, 51, 61, 81, 91, 701, 721, 771, 7A1 are primes, we only need to consider the family 7{4,B}1 (since any digits 0, 1, 2, 3, 5, 6, 7, 8, 9, A between them will produce smaller primes) *** Since 7BB, 7441 and 7B41 are primes, we only need to consider the numbers 741, 7B1, 74B1 **** None of 741, 7B1, 74B1 are primes. * Case (7,5): ** 75 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 75, 17, 27, 37, 57, 67, 87, A7, B7, 747, 797 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6, 8, 9, A, B between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. * Case (7,B): ** Since 75, 1B, 3B, 4B, 5B, 6B, 8B, AB, 70B, 77B, 7BB are primes, we only need to consider the family 7{2,9}B (since any digits 0, 1, 3, 4, 5, 6, 7, 8, A, B between them will produce smaller primes) *** Since 222B, 729B is prime, we only need to consider the families 7{9}B, 7{9}2B, 7{9}22B (since any digits combo 222, 29 between them will produce smaller primes) **** The smallest prime of the form 7{9}B is 7999B **** The smallest prime of the form 7{9}2B is 79992B (not minimal prime, since 992B and 7999B are primes) **** The smallest prime of the form 7{9}22B is 79922B (not minimal prime, since 992B is prime) * Case (8,1): ** 81 is prime, and thus the only minimal prime in this family. * Case (8,5): ** 85 is prime, and thus the only minimal prime in this family. * Case (8,7): ** 87 is prime, and thus the only minimal prime in this family. * Case (8,B): ** 8B is prime, and thus the only minimal prime in this family. * Case (9,1): ** 91 is prime, and thus the only minimal prime in this family. * Case (9,5): ** 95 is prime, and thus the only minimal prime in this family. * Case (9,7): ** Since 91, 95, 17, 27, 37, 57, 67, 87, A7, B7, 907 are primes, we only need to consider the family 9{4,7,9}7 (since any digit 0, 1, 2, 3, 5, 6, 8, A, B between them will produce smaller primes) *** Since 447, 497, 747, 797, 9777, 9947, 9997 are primes, we only need to consider the numbers 947, 977, 997, 9477, 9977 (since any digits combo 44, 49, 74, 77, 79, 94, 99 between them will produce smaller primes) **** None of 947, 977, 997, 9477, 9977 are primes. * Case (9,B): ** Since 91, 95, 1B, 3B, 4B, 5B, 6B, 8B, AB, 90B, 9BB are primes, we only need to consider the family 9{2,7,9}B (since any digit 0, 1, 3, 4, 5, 6, 8, A, B between them will produce smaller primes) *** Since 27, 77B, 929B, 992B, 997B are primes, we only need to consider the families 9{2,7}2{2}B, 97{2,9}B, 9{7,9}9{9}B (since any digits combo 27, 29, 77, 92, 97 between them will produce smaller primes) **** For the 9{2,7}2{2}B family, since 27 and 77B are primes, we only need to consider the families 9{2}2{2}B and 97{2}2{2}B (since any digits combo 27, 77 between (9,2{2}B) will produce smaller primes) ***** The smallest prime of the form 9{2}2{2}B is 9222B (not minimal prime, since 222B is prime) ***** The smallest prime of the form 97{2}2{2}B is 9722222222222B (not minimal prime, since 222B is prime) **** For the 97{2,9}B family, since 729B and 929B are primes, we only need to consider the family 97{9}{2}B (since any digits combo 29 between (97,B) will produce smaller primes) ***** Since 222B is prime, we only need to consider the families 97{9}B, 97{9}2B, 97{9}22B (since any digit combo 222 between (97,B) will produce smaller primes) ****** All numbers of the form 97{9}B are divisible by 11, thus cannot be prime. ****** The smallest prime of the form 97{9}2B is 979999992B (not minimal prime, since 9999B is prime) ****** All numbers of the form 97{9}22B are divisible by 11, thus cannot be prime. **** For the 9{7,9}9{9}B family, since 77B and 9999B are primes, we only need to consider the numbers 99B, 999B, 979B, 9799B, 9979B ***** None of 99B, 999B, 979B, 9799B, 9979B are primes. * Case (A,1): ** Since A7, AB, 11, 31, 51, 61, 81, 91, A41 are primes, we only need to consider the family A{0,2,A}1 (since any digits 1, 3, 4, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since 221, 2A1, A0A1, A201 are primes, we only need to consider the families A{A}{0}1 and A{A}{0}21 (since any digits combo 0A, 20, 22, 2A between them will produce smaller primes) **** For the A{A}{0}1 family: ***** All numbers of the form A{0}1 are divisible by B, thus cannot be prime. ***** The smallest prime of the form AA{0}1 is AA000001 ***** The smallest prime of the form AAA{0}1 is AAA0001 ***** The smallest prime of the form AAAA{0}1 is AAAA1 ****** Since this prime has no 0's, we do not need to consider the families {A}1, {A}01, {A}001, etc. **** All numbers of the form A{A}{0}21 are divisible by 5, thus cannot be prime. * Case (A,5): ** Since A7, AB, 15, 25, 35, 45, 75, 85, 95, B5 are primes, we only need to consider the family A{0,5,6,A}5 (since any digits 1, 2, 3, 4, 7, 8, 9, B between them will produce smaller primes) *** Since 565, 655, 665, A605, A6A5, AA65 are primes, we only need to consider the families A{0,5,A}5 and A{0}65 (since any digits combo 56, 60, 65, 66, 6A, A6 between them will produce smaller primes) **** All numbers of the form A{0,5,A}5 are divisible by 5, thus cannot be prime. **** The smallest prime of the form A{0}65 is A00065 * Case (A,7): ** A7 is prime, and thus the only minimal prime in this family. * Case (A,B): ** AB is prime, and thus the only minimal prime in this family. * Case (B,1): ** Since B5, B7, 11, 31, 51, 61, 81, 91, B21 are primes, we only need to consider the family B{0,4,A,B}1 (since any digits 1, 2, 3, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 4B, AB, 401, A41, B001, B0B1, BB01, BB41 are primes, we only need to consider the families B{A}0{4,A}1, B{0,4}4{4,A}1, B{0,4,A,B}A{0,A}1, B{B}B{A,B}1 (since any digits combo 00, 0B, 40, 4B, A4, AB, B0, B4 between them will produce smaller primes) **** For the B{A}0{4,A}1 family, since A41 is prime, we only need consider the families B0{4}{A}1 and B{A}0{A}1 ***** For the B0{4}{A}1 family, since B04A1 is prime, we only need to consider the families B0{4}1 and B0{A}1 ****** The smallest prime of the form B0{4}1 is B04441 (not minimal prime, since 4441 is prime) ****** The smallest prime of the form B0{A}1 is B0AAAAA1 (not minimal prime, since AAAA1 is prime) ***** For the B{A}0{A}1 family, since A0A1 is prime, we only need to consider the families B{A}01 and B0{A}1 ****** The smallest prime of the form B{A}01 is BAA01 ****** The smallest prime of the form B0{A}1 is B0AAAAA1 (not minimal prime, since AAAA1 is prime) **** For the B{0,4}4{4,A}1 family, since 4441 is prime, we only need to consider the families B{0}4{4,A}1 and B{0,4}4{A}1 ***** For the B{0}4{4,A}1 family, since B001 is prime, we only need to consider the families B4{4,A}1 and B04{4,A}1 ****** For the B4{4,A}1 family, since A41 is prime, we only need to consider the family B4{4}{A}1 ******* Since 4441 and BAAA1 are primes, we only need to consider the numbers B41, B441, B4A1, B44A1, B4AA1, B44AA1 ******** None of B41, B441, B4A1, B44A1, B4AA1, B44AA1 are primes. ****** For the B04{4,A}1 family, since B04A1 is prime, we only need to consider the family B04{4}1 ******* The smallest prime of the form B04{4}1 is B04441 (not minimal prime, since 4441 is prime) ***** For the B{0,4}4{A}1 family, since 401, 4441, B001 are primes, we only need to consider the families B4{A}1, B04{A}1, B44{A}1, B044{A}1 (since any digits combo 00, 40, 44 between (B,4{A}1) will produce smaller primes) ****** The smallest prime of the form B4{A}1 is B4AAA1 (not minimal prime, since BAAA1 is prime) ****** The smallest prime of the form B04{A}1 is B04A1 ****** The smallest prime of the form B44{A}1 is B44AAAAAAA1 (not minimal prime, since BAAA1 is prime) ****** The smallest prime of the form B044{A}1 is B044A1 (not minimal prime, since B04A1 is prime) **** For the B{0,4,A,B}A{0,A}1 family, since all numbers in this family with 0 between (B,1) are in the B{A}0{4,A}1 family, and all numbers in this family with 4 between (B,1) are in the B{0,4}4{4,A}1 family, we only need to consider the family B{A,B}A{A}1 ***** Since BAAA1 is prime, we only need to consider the families B{A,B}A1 and B{A,B}AA1 ****** For the B{A,B}A1 family, since AB and BAAA1 are primes, we only need to consider the families B{B}A1 and B{B}AA1 ******* All numbers of the form B{B}A1 are divisible by B, thus cannot be prime. ******* The smallest prime of the form B{B}AA1 is BBBAA1 ****** For the B{A,B}AA1 family, since BAAA1 is prime, we only need to consider the families B{B}AA1 ******* The smallest prime of the form B{B}AA1 is BBBAA1 **** For the B{B}B{A,B}1 family, since AB and BAAA1 are primes, we only need to consider the families B{B}B1, B{B}BA1, B{B}BAA1 (since any digits combo AB or AAA between (B{B}B,1) will produce smaller primes) ***** The smallest prime of the form B{B}B1 is BBBB1 ***** All numbers of the form B{B}BA1 are divisible by B, thus cannot be prime. ***** The smallest prime of the form B{B}BAA1 is BBBAA1 * Case (B,5): ** B5 is prime, and thus the only minimal prime in this family. * Case (B,7): ** B7 is prime, and thus the only minimal prime in this family. * Case (B,B): ** Since B5, B7, 1B, 3B, 4B, 5B, 6B, 8B, AB, B2B are primes, we only need to consider the family B{0,9,B}B (since any digits 1, 2, 3, 4, 5, 6, 7, 8, A between them will produce smaller primes) *** Since 90B and 9BB are primes, we only need to consider the families B{0,B}{9}B **** Since 9999B is prime, we only need to consider the families B{0,B}B, B{0,B}9B, B{0,B}99B, B{0,B}999B ***** All numbers of the form B{0,B}B are divisible by B, thus cannot be prime. ***** For the B{0,B}9B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}9B and B{B}9B (since any digits combo 0B, B0 between (B,9B) will produce smaller primes) ******* The smallest prime of the form B{0}9B is B0000000000000000000000000009B ******* All numbers of the from B{B}9B is either divisible by 11 (if totally number of B's is even) or factored as 10^(2*n)-21 = (10^n-5) * (10^n+5) (if totally number of B's is odd number 2*n-1 (n≥1)) (and since if n≥1, 10^n-5 ≥ 10^1-5 = 7 > 1, 10^n+5 ≥ 10^1+5 = 15 > 1, this factorization is nontrivial), thus cannot be prime. ***** For the B{0,B}99B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}99B and B{B}99B (since any digits combo 0B, B0 between (B,99B) will produce smaller primes) ******* The smallest prime of the form B{0}99B is B00099B ******* The smallest prime of the form B{B}99B is BBBBBB99B ***** For the B{0,B}999B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}999B and B{B}999B (since any digits combo 0B, B0 between (B,999B) will produce smaller primes) ******* The smallest prime of the form B{0}999B is B0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000999B, with 1765 0's, which can be written as B(0^1765)999B and equal the prime 11*12^1769+16967 ([http://factordb.com/index.php?id=1100000002378273165 factordb]) ([http://factordb.com/cert.php?id=1100000002378273165 primality certificate]) (not minimal prime, since B00099B and B0000000000000000000000000009B are primes) ******* The smallest prime of the form B{B}999B is BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB999B, with 245 B's, which can be written as (B^244)999B and equal the prime 12^248-3769 ([http://factordb.com/index.php?id=1100000002378270237 factordb]) (not minimal prime, since BBBBBB99B is prime) == Examples of families which can be ruled out as contain no primes > ''b'' == It is not known if this problem is solvable: Problem: Given strings ''x'', ''y'', ''z'', and a base ''b'', does there exist a prime number whose base-''b'' expansion is of the form ''x''{''y''}''z''? It will be necessary for our algorithm to determine if families of the form ''x''{''y''}''z'' contain a prime > ''b'' or not. We use two different heuristic strategies to show that such families contain no primes > ''b''. In the first strategy, we mimic the well-known technique of “covering congruences”, by finding some finite set ''S'' of primes ''p'' such that every number in a given family is divisible by some element of ''S''. In the second strategy, we attempt to find an algebraic factorization, such as difference-of-squares factorization, difference-of-cubes factorization, and Aurifeuillian factorization for numbers of the form ''x''⁴+4''y''⁴. Examples of first strategy: (we can show that the corresponding numbers are > all elements in ''S'', if ''n'' makes corresponding numbers > ''b'' (i.e. ''n''≥1 for 5{1} in base 9 and 2{5} in base 11 and {4}D in base 16 and {8}F in base 16, ''n''≥0 for other examples), thus these factorizations are nontrivial) * In base 10, all numbers of the form 4{6}9 are divisible by 7 * In base 6, all numbers of the form 4{0}1 are divisible by 5 * In base 15, all numbers of the form 9{6}8 are divisible by 11 * In base 9, all numbers of the form 5{1} are divisible by some element of {2, 5} * In base 11, all numbers of the form 2{5} are divisible by some element of {2, 3} * In base 14, all numbers of the form B{0}1 are divisible by some element of {3, 5} * In base 8, all numbers of the form 6{4}7 are divisible by some element of {3, 5, 13} * In base 13, all numbers of the form 3{0}95 are divisible by some element of {5, 7, 17} * In base 16, all numbers of the form {4}D are divisible by some element of {3, 7, 13} * In base 16, all numbers of the form {8}F are divisible by some element of {3, 7, 13} Examples of second strategy: (we can show that both factors are > 1, if ''n'' makes corresponding numbers > ''b'' (i.e. ''n''≥2 for {1} in base 9, ''n''≥0 for 1{0}1 in base 8 and B{4}1 in base 16, ''n''≥1 for other examples), thus these factorizations are nontrivial) * In base 9, all numbers of the form {1} factored as difference of squares * In base 8, all numbers of the form 1{0}1 factored as sum of cubes * In base 9, all numbers of the form 3{8} factored as difference of squares * In base 16, all numbers of the form 8{F} factored as difference of squares * In base 16, all numbers of the form {F}7 factored as difference of squares * In base 9, all numbers of the form 3{1} factored as difference of squares * In base 16, all numbers of the form {4}1 factored as difference of squares * In base 16, all numbers of the form 1{5} factored as difference of squares * In base 16, all numbers of the from {C}D factored as ''x''⁴+4''y''⁴ * In base 16, all numbers of the form B{4}1 factored as difference of squares Examples of combine of the two strategies: (we can show that for the part of the first strategy, the corresponding numbers are > all elements in S, and for the part of the second strategy, both factors are > 1, if n makes corresponding numbers > b, thus these factorizations are nontrivial) * In base 14, numbers of the form 8{D} are divisible by 5 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 12, numbers of the form {B}9B are divisible by 13 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 14, numbers of the form {D}5 are divisible by 5 if ''n'' is even and factored as difference of squares if ''n'' is odd * In base 17, numbers of the form 1{9} are divisible by 2 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 19, numbers of the form 1{6} are divisible by 5 if ''n'' is odd and factored as difference of squares if ''n'' is even == Bases 2≤''b''≤1024 such that these families can be ruled out as contain no primes > ''b'' == (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) === 1{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-powers factorization === 1{0}2 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 1{0}3 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} === 1{0}4 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ === 1{0}5 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 0 mod 5: Finite covering set {5} === 1{0}6 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 7: Finite covering set {7} === 1{0}7 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 7: Finite covering set {7} === 1{0}z === (none) === 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === * ''b'' == 1 mod 3: Finite covering set {3} === 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) === (none) === 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === * ''b'' == 1 mod 3: Finite covering set {3} === {1}0z (not quasi-minimal prime if there is smaller prime of the form {1} or {1}z) === * ''b'' such that ''b'' and 2''b''−1 are both squares: Difference-of-squares factorization (such bases are 25, 841) === {1} === * ''b'' = ''m''^''r'' with ''r''>1: Difference-of-''r''th-powers factorization (some bases still have primes, since for the corresponding length this factorization is trivial, but they only have this prime, they are 4 (length 2), 8 (length 3), 16 (length 2), 27 (length 3), 36 (length 2), 100 (length 2), 128 (length 7), 196 (length 2), 256 (length 2), 400 (length 2), 512 (length 3), 576 (length 2), 676 (length 2)) === {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}) === * ''b'' == 0 mod 2: Finite covering set {2} === 1{2} === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' such that ''b'' and 2(''b''+1) are both squares: Difference-of-squares factorization (such bases are 49) === 1{3} === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' such that ''b'' and 3(''b''+2) are both squares: Difference-of-squares factorization (such bases are 25, 361) * ''b'' == 1 mod 2 such that 3(''b''+2) is square: Combine of finite covering set {2} (when length is even) and difference-of-squares factorization (when length is odd) (such bases are 25, 73, 145, 241, 361, 505, 673, 865) === 1{4} === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' such that ''b'' and 4(''b''+3) are both squares: Difference-of-squares factorization === 1{z} === (none) === 2{0}1 === * ''b'' == 1 mod 3: Finite covering set {3} === 2{0}3 === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 5: Finite covering set {5} === 2{1} (not quasi-minimal prime if there is smaller prime of the form {1}) === * ''b'' such that ''b'' and 2''b''−1 are both squares: Difference-of-squares factorization (such bases are 25, 841) === {2}1 === * ''b'' such that ''b'' and 2(''b''+1) are both squares: Difference-of-squares factorization (such bases are 49) === 2{z} === * ''b'' == 1 mod 2: Finite covering set {2} === 3{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} === 3{0}2 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} === 3{0}4 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 7: Finite covering set {7} === {3}1 === * ''b'' such that ''b'' and 3(2''b''+1) are both squares: Difference-of-squares factorization (such bases are 121) === 3{z} === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === 4{0}1 === * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ === 4{0}3 === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 7: Finite covering set {7} === {4}1 === * ''b'' such that ''b'' and 4(3''b''+1) are both squares: Difference-of-squares factorization (such bases are 16, 225) === 4{z} === * ''b'' == 1 mod 2: Finite covering set {2} === 5{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 5{z} === * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 34 mod 35: Finite covering set {5, 7} * ''b'' = 6''m''² with ''m'' == 2 or 3 mod 5: Combine of finite covering set {5} (when length is odd) and difference-of-squares factorization (when length is even) (such bases are 24, 54, 294, 384, 864, 1014) === 6{0}1 === * ''b'' == 1 mod 7: Finite covering set {7} * ''b'' == 34 mod 35: Finite covering set {5, 7} === 6{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 7{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} === 7{z} === * ''b'' == 1 mod 7: Finite covering set {7} * ''b'' == 20 mod 21: Finite covering set {3, 7} * ''b'' == 83, 307 mod 455: Finite covering set {5, 7, 13} (such bases are 83, 307, 538, 762, 993) * ''b'' = ''m''³: Difference-of-cubes factorization === 8{0}1 === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 20 mod 21: Finite covering set {3, 7} * ''b'' == 47, 83 mod 195: Finite covering set {3, 5, 13} (such bases are 47, 83, 242, 278, 437, 473, 632, 668, 827, 863, 1022) * ''b'' = 467: Finite covering set {3, 5, 7, 19, 37} * ''b'' = 722: Finite covering set {3, 5, 13, 73, 109} * ''b'' = ''m''³: Sum-of-cubes factorization * ''b'' = 128: Cannot have primes since 7''n''+3 cannot be power of 2 === 8{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === 9{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} === 9{z} === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 32 mod 33: Finite covering set {3, 11} === A{0}1 === * ''b'' == 1 mod 11: Finite covering set {11} * ''b'' == 32 mod 33: Finite covering set {3, 11} === A{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} === B{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} === B{z} === * ''b'' == 1 mod 11: Finite covering set {11} * ''b'' == 142 mod 143: Finite covering set {11, 13} * ''b'' = 307: Finite covering set {5, 11, 29} * ''b'' = 901: Finite covering set {7, 11, 13, 19} === C{0}1 === * ''b'' == 1 mod 13: Finite covering set {13} * ''b'' == 142 mod 143: Finite covering set {11, 13} * ''b'' = 296, 901: Finite covering set {7, 11, 13, 19} * ''b'' = 562, 828, 900: Finite covering set {7, 13, 19} * ''b'' = 563: Finite covering set {5, 7, 13, 19, 29} * ''b'' = 597: Finite covering set {5, 13, 29} === {#}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3) === (none) === {#}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) === * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-power factorization === #{z} (for even bases b, # = b/2−1) === (none) === y{z} === (none) === {y}z === (none) === z{0}1 === (none) === {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family) === * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-power factorization (some bases still have primes, since for the corresponding length this factorization is trivial, but they only have this prime, they are 128 (length 7), 216 (length 3), 343 (length 3), 729 (length 3)) * ''b'' = 4''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ (base 4 still have primes, since for the corresponding length this factorization is trivial, but it only have this prime, at length 2) === {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y) === (none) === {z}1 === (none) === {z}t === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 0 mod 7: Finite covering set {7} === {z}u === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 34 mod 35: Finite covering set {5, 7} === {z}v === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 5: Finite covering set {5} === {z}w === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === {z}x === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} === {z}y === * ''b'' == 0 mod 2: Finite covering set {2} == Large known (probable) primes (length ≥10000) in these families (for bases 2≤''b''≤1024) == Format: base (length) (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) === 1{0}1 === (none) === 1{0}2 === (none) === 1{0}3 === (none) === 1{0}4 === 53 (13403) 113 (10647) === 1{0}z === 113 (20089) 123 (64371) === 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === (none) === 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) === 208 (26682) 607 (11032) 828 (19659) === 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === 201 (31276) 222 (52727) 227 (36323) 327 (135983) 425 (11231) 710 (24112) 717 (37508) 719 (13420) === {1} === 152 (270217) 184 (16703) 200 (17807) 311 (36497) 326 (26713) 331 (25033) 371 (15527) 485 (99523) 629 (32233) 649 (43987) 670 (18617) 684 (22573) 691 (62903) 693 (41189) 731 (15427) 752 (32833) 872 (10093) 932 (20431) === {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}) === (none) === 1{z} === 107 (21911) 170 (166429) 278 (43909) 303 (40175) 383 (20957) 515 (58467) 522 (62289) 578 (129469) 590 (15527) 647 (21577) 662 (16591) 698 (127559) 704 (62035) 845 (39407) 938 (40423) 969 (24097) 989 (26869) === 2{0}1 === 101 (192276) 206 (46206) 218 (333926) 236 (161230) 257 (12184) 305 (16808) 467 (126776) 578 (44166) 626 (174204) 695 (94626) 752 (26164) 788 (72918) 869 (49150) 887 (27772) 899 (15732) 932 (13644) === 2{z} === 432 (16003) === 3{0}1 === 912 (132174) === 3{z} === 72 (1119850) 212 (34414) 218 (23050) 270 (89662) 303 (198358) 312 (51566) 422 (21738) 480 (93610) 513 (38032) 527 (46074) 566 (23874) 650 (498102) 686 (16584) 758 (15574) 783 (12508) 800 (33838) 921 (98668) 947 (10056) === 4{0}1 === 107 (32587) 227 (13347) 257 (160423) 355 (10990) 410 (144079) 440 (56087) 452 (14155) 482 (30691) 542 (15983) 579 (67776) 608 (20707) 635 (11723) 650 (96223) 679 (69450) 737 (269303) 740 (58043) 789 (149140) 797 (468703) 920 (103687) 934 (101404) 962 (84235) === 4{z} === 14 (19699) 68 (13575) 254 (15451) 800 (20509) === 5{0}1 === 326 (400786) 350 (20392) 554 (10630) 662 (13390) 926 (40036) === 5{z} === 258 (212135) 272 (148427) 299 (64898) 307 (26263) 354 (25566) 433 (283919) 635 (36163) 678 (40859) 692 (45447) 719 (20552) 768 (70214) 857 (23083) 867 (61411) 972 (36703) === 6{0}1 === 108 (16318) 129 (16797) 409 (369833) 522 (52604) 587 (24120) 643 (164916) 762 (11152) 789 (27297) 986 (21634) === 6{z} === 68 (25396) 332 (15222) 338 (42868) 362 (146342) 488 (33164) 566 (164828) 980 (50878) 986 (12506) 1016 (23336) === 7{0}1 === 398 (17473) 1004 (54849) === 7{z} === 97 (192336) 170 (15423) 194 (38361) 202 (155772) 282 (21413) 283 (164769) 332 (13205) 412 (29792) 560 (19905) 639 (10668) 655 (53009) 811 (31784) 814 (17366) 866 (108591) 908 (61797) 962 (31841) 992 (10605) 997 (15815) === 8{0}1 === 23 (119216) 53 (227184) 158 (123476) 254 (67716) 320 (52004) 410 (279992) 425 (94662) 513 (19076) 518 (11768) 596 (148446) 641 (87702) 684 (23387) 695 (39626) 785 (900326) 788 (11408) 893 (86772) 908 (243440) 920 (107822) 962 (47222) 998 (81240) 1013 (43872) === 8{z} === 138 (35686) 412 (12154) 788 (11326) 990 (23032) === 9{0}1 === 248 (39511) 592 (96870) === 9{z} === 431 (43574) 446 (152028) 458 (126262) 599 (11776) 846 (12781) === A{0}1 === 173 (264235) 198 (47665) 311 (314807) 341 (106009) 449 (18507) 492 (42843) 605 (12395) 708 (17563) 710 (31039) 743 (285479) 744 (137056) 786 (68169) 800 (15105) 802 (149320) 879 (25004) 929 (13065) 977 (125873) 986 (48279) 1004 (10645) === A{z} === 368 (10867) 488 (10231) 534 (80328) 662 (13307) 978 (14066) === B{0}1 === 710 (15272) 740 (33520) 878 (227482) === B{z} === 153 (21660) 186 (112718) 439 (18752) 593 (16064) 602 (36518) 707 (10573) 717 (67707) === C{0}1 === 68 (656922) 219 (29231) 230 (94751) 312 (21163) 334 (83334) 353 (20262) 359 (61295) 457 (10024) 481 (45941) 501 (20140) 593 (42779) 600 (11242) 604 (17371) 641 (26422) 700 (91953) 887 (13961) 919 (45359) 923 (64365) 992 (10300) === {#}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3) === (none) === {#}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) === (none) === #{z} (for even bases b, # = b/2−1) === (none) === y{z} === 38 (136212) 83 (21496) 113 (286644) 188 (13508) 401 (103670) 417 (21003) 458 (46900) 494 (21580) 518 (129372) 527 (65822) 602 (17644) 608 (36228) 638 (74528) 663 (47557) 723 (24536) 758 (50564) 833 (12220) 904 (13430) 938 (50008) 950 (16248) === z{0}1 === 202 (46774) 251 (102979) 272 (16681) 297 (14314) 298 (60671) 326 (64757) 347 (69661) 363 (142877) 452 (71941) 543 (10042) 564 (38065) 634 (84823) 788 (13541) 869 (12289) 890 (37377) 953 (60995) 1004 (29685) === {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family) === 53 (21942) 124 (16426) 175 (31626) 188 (22036) 316 (48538) 365 (25578) 373 (24006) 434 (10090) 530 (11086) 545 (12346) 560 (15072) 596 (12762) 701 (12576) 706 (10656) 821 (13536) 833 (17116) 966 (14820) 983 (11272) === {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y) === (none) === {z}1 === (none) === {z}y === 317 (13896) == Bases 2≤''b''≤1024 which have these families as unsolved families == Unsolved families are families which are neither primes (>''b'') found nor can be ruled out as contain no primes > ''b'' (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) 1{0}1: 38, 50, 62, 68, 86, 92, 98, 104, 122, 144, 168, 182, 186, 200, 202, 212, 214, 218, 244, 246, 252, 258, 286, 294, 298, 302, 304, 308, 322, 324, 338, 344, 354, 356, 362, 368, 380, 390, 394, 398, 402, 404, 410, 416, 422, 424, 446, 450, 454, 458, 468, 480, 482, 484, 500, 514, 518, 524, 528, 530, 534, 538, 552, 558, 564, 572, 574, 578, 580, 590, 602, 604, 608, 620, 622, 626, 632, 638, 648, 650, 662, 666, 668, 670, 678, 684, 692, 694, 698, 706, 712, 720, 722, 724, 734, 744, 746, 752, 754, 762, 766, 770, 792, 794, 802, 806, 812, 814, 818, 836, 840, 842, 844, 848, 854, 868, 870, 872, 878, 888, 896, 902, 904, 908, 922, 924, 926, 932, 938, 942, 944, 948, 954, 958, 964, 968, 974, 978, 980, 988, 994, 998, 1002, 1006, 1014, 1016 (length limit: ≥8388608) 1{0}2: 167, 257, 323, 353, 383, 527, 557, 563, 623, 635, 647, 677, 713, 719, 803, 815, 947, 971, 1013 (length limit: 2000) 1{0}3: 646, 718, 998 (length limit: 2000) 1{0}4: 139, 227, 263, 315, 335, 365, 485, 515, 647, 653, 683, 773, 789, 797, 815, 857, 875, 893, 939, 995, 1007 (length limit: 2000) 1{0}5 1{0}6 1{0}7 1{0}8 1{0}9 1{0}A 1{0}B 1{0}C 1{0}D 1{0}E 1{0}F 1{0}G 1{0}z: 173, 179, 257, 277, 302, 333, 362, 392, 422, 452, 467, 488, 512, 527, 545, 570, 575, 614, 622, 650, 677, 680, 704, 707, 734, 740, 827, 830, 851, 872, 886, 887, 902, 904, 908, 929, 932, 942, 947, 949, 962, 973, 1022 (length limit: 2000) 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1): 198, 213, 318, 327, 353, 375, 513, 591, 647, 732, 734, 738, 759, 948, 951, 957, 1013, 1014 (length limit: 2000) 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}): 575 (length limit: 247000) 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1): 813, 863, 962, 1017 (length limit: ≥100000) {1}0z (not quasi-minimal prime if there is smaller prime of the form {1} or {1}z): 137, 161, 167, 217, 229, 232, 253, 261, 317, 325, 337, 347, 355, 375, 403, 411, 421, 427, 457, 479, 483, 505, 507, 537, 547, 577, 597, 599, 601, 613, 627, 631, 632, 641, 643, 649, 657, 679, 688, 697, 707, 711, 729, 733, 737, 742, 762, 773, 787, 793, 797, 817, 819, 841, 843, 853, 859, 861, 874, 877, 895, 899, 907, 913, 916, 917, 927, 957, 959, 997, 1003, 1009, 1015, 1017 (length limit: 2000) {1}: 185, 269, 281, 380, 384, 385, 394, 452, 465, 511, 574, 601, 631, 632, 636, 711, 713, 759, 771, 795, 861, 866, 881, 938, 948, 951, 956, 963, 1005, 1015 (length limit: ≥100000) 11{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}): 31, 61, 91, 93, 143, 247, 253, 293, 313, 329, 371, 383, 391, 393, 403, 415, 435, 443, 451, 491, 493, 513, 523, 527, 537, 541, 553, 565, 581, 587, 601, 613, 615, 623, 627, 635, 663, 729, 735, 757, 763, 775, 783, 823, 843, 865, 873, 877, 883, 897, 931, 941, 943, 955, 983, 1013, 1015, 1021, 1023 (length limit: 2000) {1}z 1{2}: 265, 355, 379, 391, 481, 649, 661, 709, 745, 811, 877, 977 (length limit: 2000) 1{3}: 107, 133, 179, 281, 305, 365, 473, 485, 487, 491, 535, 541, 601, 617, 665, 737, 775, 787, 802, 827, 905, 911, 928, 953, 955, 995 1{4}: 83, 143, 185, 239, 269, 293, 299, 305, 319, 325, 373, 383, 395, 431, 471, 503, 551, 577, 581, 593, 605, 617, 631, 659, 743, 761, 773, 781, 803, 821, 857, 869, 897, 911, 917, 923, 935, 983, 1019 (length limit: 2000) 1{z}: 581, 992, 1019 (length limit: ≥100000) 2{0}1: 365, 383, 461, 512, 542, 647, 773, 801, 836, 878, 908, 914, 917, 947, 1004 (length limit: ≥100000) 2{0}3: 79, 149, 179, 254, 359, 394, 424, 434, 449, 488, 499, 532, 554, 578, 664, 683, 694, 749, 794, 839, 908, 944, 982 (length limit: 2000) 2{1} (not quasi-minimal prime if there is smaller prime of the form {1}): 109, 117, 137, 147, 157, 175, 177, 201, 227, 235, 256, 269, 271, 297, 310, 331, 335, 397, 417, 427, 430, 437, 442, 451, 465, 467, 481, 502, 517, 547, 557, 567, 572, 577, 591, 597, 607, 627, 649, 654, 655, 667, 679, 687, 691, 697, 715, 727, 739, 759, 766, 782, 787, 796, 797, 808, 817, 821, 829, 841, 852, 877, 881, 899, 903, 907, 937, 947, 955, 1007, 1011, 1021 (length limit: 2000) {2}1: 106, 238, 262, 295, 364, 382, 391, 397, 421, 458, 463, 478, 517, 523, 556, 601, 647, 687, 754, 790, 793, 832, 872, 898, 962, 1002, 1021 (length limit: 2000) 2{z}: 588, 972 (length limit: ≥100000) 3{0}1: 718 (length limit: ≥100000) 3{0}2: 223, 283, 359, 489, 515, 529, 579, 619, 669, 879, 915, 997 (length limit: 2000) 3{0}4: 167, 391, 447, 487, 529, 653, 657, 797, 853, 913, 937 (length limit: 2000) {3}1: 79, 101, 189, 215, 217, 235, 243, 253, 255, 265, 313, 338, 341, 378, 379, 401, 402, 413, 489, 498, 499, 508, 525, 535, 589, 591, 599, 611, 621, 635, 667, 668, 681, 691, 711, 717, 719, 721, 737, 785, 804, 805, 813, 831, 835, 837, 849, 873, 911, 915, 929, 933, 941, 948, 959, 999, 1013, 1019 (length limit: 2000) 3{z}: 275, 438, 647, 653, 812, 927, 968 (length limit: ≥100000) 4{0}1: 32, 53, 155, 174, 204, 212, 230, 332, 334, 335, 395, 467, 512, 593, 767, 803, 848, 875, 1024 (length limit: ≥100000) 4{0}3: 83, 88, 97, 167, 188, 268, 289, 293, 412, 419, 425, 433, 503, 517, 529, 548, 613, 620, 622, 650, 668, 692, 706, 727, 763, 818, 902, 913, 937, 947, 958 (length limit: 2000) {4}1: 46, 77, 103, 107, 119, 152, 198, 203, 211, 217, 229, 257, 263, 291, 296, 305, 332, 371, 374, 407, 413, 416, 440, 445, 446, 464, 467, 500, 542, 545, 548, 557, 566, 586, 587, 605, 611, 614, 632, 638, 641, 653, 659, 698, 701, 731, 733, 736, 755, 786, 812, 820, 821, 827, 830, 887, 896, 899, 901, 922, 923, 935, 941, 953, 977, 983, 991, 1004 (length limit: 2000) 4{z}: 338, 998 (length limit: ≥100000) 5{0}1: 308, 512, 824 (length limit: ≥100000) 5{z}: 234, 412, 549, 553, 573, 619, 750, 878, 894, 954 (length limit: ≥100000) 6{0}1: 212, 509, 579, 625, 774, 794, 993, 999 (length limit: ≥100000) 6{z}: 308, 392, 398, 518, 548, 638, 662, 878 (length limit: ≥100000) 7{0}1: (none) 7{z}: 321, 328, 374, 432, 665, 697, 710, 721, 727, 728, 752, 800, 815, 836, 867, 957, 958, 972 (length limit: ≥100000) 8{0}1: 86, 140, 182, 263, 353, 368, 389, 395, 422, 426, 428, 434, 443, 488, 497, 558, 572, 575, 593, 606, 698, 710, 746, 758, 770, 773, 824, 828, 866, 911, 930, 953, 957, 983, 993, 1014 (length limit: ≥100000) 8{z}: 378, 438, 536, 566, 570, 592, 636, 688, 718, 830, 852, 926, 1010 (length limit: ≥100000) 9{0}1: 724, 884 (length limit: ≥100000) 9{z}: 80, 233, 530, 551, 611, 899, 912, 980 (length limit: ≥100000) A{0}1: 185, 338, 417, 432, 614, 668, 773, 863, 935, 1000 (length limit: ≥100000) A{z}: 214, 422, 444, 452, 458, 542, 638, 668, 804, 872, 950, 962 (length limit: ≥100000) B{0}1: 560, 770, 968 (length limit: ≥100000) B{z}: 263, 615, 912, 978 (length limit: ≥100000) C{0}1: 163, 207, 354, 362, 368, 480, 620, 692, 697, 736, 753, 792, 978, 998, 1019, 1022 (length limit: ≥100000) C{z} D{0}1 D{z} E{0}1 E{z} F{0}1 F{z} G{0}1 {&#35;}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3): 808, 829, 859, 1006 (length limit: 2000) {&#35;}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2): 31, 37, 55, 63, 67, 77, 83, 89, 91, 93, 97, 99, 107, 109, 117, 123, 127, 133, 135, 137, 143, 147, 149, 151, 155, 161, 177, 179, 183, 189, 193, 197, 207, 211, 213, 215, 217, 223, 225, 227, 233, 235, 241, 247, 249, 255, 257, 263, 265, 269, 273, 277, 281, 283, 285, 287, 291, 293, 297, 303, 307, 311, 319, 327, 347, 351, 355, 357, 359, 361, 367, 369, 377, 381, 383, 385, 387, 389, 393, 397, 401, 407, 411, 413, 417, 421, 423, 437, 439, 443, 447, 457, 465, 467, 469, 473, 475, 481, 483, 489, 493, 495, 497, 509, 511, 515, 533, 541, 547, 549, 555, 563, 591, 593, 597, 601, 603, 611, 615, 619, 621, 625, 627, 629, 633, 635, 637, 645, 647, 651, 653, 655, 659, 663, 667, 671, 673, 675, 679, 683, 687, 691, 693, 697, 707, 709, 717, 731, 733, 735, 737, 741, 743, 749, 753, 755, 757, 759, 765, 767, 771, 773, 775, 777, 783, 785, 787, 793, 797, 801, 807, 809, 813, 817, 823, 825, 849, 851, 853, 865, 867, 873, 877, 887, 889, 893, 897, 899, 903, 907, 911, 915, 923, 927, 933, 937, 939, 941, 943, 945, 947, 953, 957, 961, 967, 975, 977, 983, 987, 993, 999, 1003, 1005, 1009, 1017 (length limit: ≥262143) &#35;{z} (for even bases ''b'', # = ''b''/2−1): 108, 278, 296, 338, 386, 494, 626, 920 (length limit: 2000) ${&#35;} (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) x{z} y{z}: 128, 233, 268, 383, 478, 488, 533, 554, 665, 698, 779, 863, 878, 932, 941, 1010 (length limit: ≥200000) z{0}1: 123, 342, 362, 422, 438, 479, 487, 512, 542, 602, 757, 767, 817, 830, 872, 893, 932, 992, 997, 1005, 1007 (length limit: ≥100000) {y}z: 143, 173, 176, 213, 235, 248, 253, 279, 327, 343, 353, 358, 373, 383, 401, 413, 416, 427, 439, 448, 453, 463, 481, 513, 522, 527, 535, 547, 559, 565, 583, 591, 598, 603, 621, 623, 653, 659, 663, 679, 691, 698, 711, 743, 745, 757, 768, 785, 793, 796, 801, 808, 811, 821, 835, 845, 847, 853, 856, 883, 898, 903, 927, 955, 961, 971, 973, 993, 1005, 1013, 1019, 1021 (length limit: 2000) {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family): 97, 103, 113, 186, 187, 220, 304, 306, 309, 335, 414, 416, 428, 433, 445, 459, 486, 498, 539, 550, 557, 587, 592, 597, 598, 617, 624, 637, 659, 665, 671, 677, 696, 717, 726, 730, 740, 754, 766, 790, 851, 873, 890, 914, 923, 929, 943, 944, 965, 984, 985, 996, 1004, 1005 (length limit: ≥17326) zy{z} (not quasi-minimal prime if there is smaller prime of the form y{z}) {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y): 215, 353, 517, 743, 852, 899, 913 (length limit: 2000) {z}01 (not quasi-minimal prime if there is smaller prime of the form {z}1) {z}1: 93, 113, 152, 158, 188, 217, 218, 226, 227, 228, 233, 240, 275, 278, 293, 312, 338, 350, 353, 383, 404, 438, 464, 471, 500, 533, 576, 614, 641, 653, 704, 723, 728, 730, 758, 779, 788, 791, 830, 878, 881, 899, 908, 918, 929, 944, 953, 965, 968, 978, 983, 986, 1013 (length limit: 2000) {z}k {z}l {z}m {z}n {z}o {z}p {z}q {z}r {z}s {z}t {z}u {z}v {z}w: 207, 221, 293, 375, 387, 533, 633, 647, 653, 687, 701, 747, 761, 785, 863, 897, 905, 965, 1017 (length limit: 2000) {z}x: (none) {z}y: 305, 353, 397, 485, 487, 535, 539, 597, 641, 679, 731, 739, 755 (length limit: 2000) == List of lengths for quasi-minimal primes in some simple families == [https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml list of lengths for quasi-minimal primes in some simple families for bases 2≤''b''≤1024] NB: this family is not interpretable in this base (e.g. family 7{0}1 and 7{z} in bases <=7, family {z}x in bases <=3) (including the case which this family has either leading zeros (leading zeros do not count) or ending zeros (numbers ending in zero cannot be prime > base) in this base) RC: this family can be proven to only contain composite numbers (only count numbers > base) unknown: this family has no primes or PRPs found, nor can this family be proven to only contain composite numbers (only count numbers > base) Background color: red for title (bases or families), green for length > 10000, orange for 2500 < length ≤ 10000, white for length ≤ 2500, cyan for "RC", pink for "NB", yellow for "unknown". Search limit for lengths: ≥8388608 for 1{0}1, ≥200000 for y{z}, ≥100000 for ''d''{0}1 (''d'' = one of digits in {2, 3, 4, 5, 6, 7, 8, 9, A, B, C}) and ''d''{z} (''d'' = one of digits in {1, 2, 3, 4, 5, 6, 7, 8, 9, A, B}) and z{0}1 and {1}, ≥5000 for 1{0}2, {z}y, 1{0}z, {z}1, {y}z, ≥2500 for other families. == References == * [https://mersenneforum.org/showthread.php?t=24972 mersenneforum thread of this problem] * [https://docs.google.com/document/d/e/2PACX-1vQct6Hx-IkJd5-iIuDuOKkKdw2teGmmHW-P75MPaxqBXB37u0odFBml5rx0PoLa0odTyuW67N_vn96J/pub Minimal elements for the base ''b'' representations of the primes which are > ''b'' for bases ''b''≤16] * [https://primes.utm.edu/glossary/xpage/MinimalPrime.html article “minimal prime” in The Prime Glossary] * [https://en.wikipedia.org/wiki/Minimal_prime_(recreational_mathematics article “minimal prime” in Wikipedia] * [https://www.primepuzzles.net/puzzles/puzz_178.htm the puzzle of minimal primes (when the restriction of prime>base is not required) in The Prime Puzzles & Problems Connection] * [https://www.primepuzzles.net/problems/prob_083.htm the problem of minimal primes in The Prime Puzzles & Problems Connection] * [https://github.com/xayahrainie4793/non-single-digit-primes my data for these M(Lb) sets for 2 ≤ b ≤ 16] * [http://www.cs.uwaterloo.ca/~shallit/Papers/minimal5.pdf Shallit’s proof of base 10 minimal primes, when the restriction of prime>base is not required] * [https://scholar.colorado.edu/downloads/hh63sw661 proofs of minimal primes in bases b≤10, when the restriction of prime>base is not required] * [https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://cs.uwaterloo.ca/~cbright/talks/minimal-slides.pdf the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://doi.org/10.1080/10586458.2015.1064048 the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://github.com/curtisbright/mepn-data data for these M(Lb) sets and unsolved families for 2 ≤ b ≤ 30, when the restriction of prime>base is not required, search limits of lengths: 1000000 for b=17, 707000 for b=19, 506000 for b=21, 292000 for b=25, 486000 for b=26, 543000 for b=28, 233000 for b=29] * [https://github.com/RaymondDevillers/primes data for these M(Lb) sets and unsolved families for 2 ≤ b ≤ 50, when the restriction of prime>base is not required, search limits of lengths: 10000 for all b] * [http://www.bitman.name/math/article/730 article for minimal primes, when the restriction of prime>base is not required] * [http://www.bitman.name/math/table/497 data for minimal primes in bases 2 ≤ b ≤ 16, when the restriction of prime>base is not required] * [http://www.prothsearch.com/sierp.html the Sierpinski problem] * [http://www.prothsearch.com/rieselprob.html the Riesel problem] * [https://oeis.org/A076336/a076336c.html the dual Sierpinski problem] * [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm generalized Sierpinski conjectures in bases b≤1030, some primes found in these conjectures are minimal primes in base b, especially, all primes for k&lt;b (if exist for a (k,b) combo) are always minimal primes in the base b) (also some examples for simple families contain no primes &gt; b] * [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm generalized Riesel conjectures in bases b≤1030, some primes found in these conjectures are minimal primes in base b, especially, all primes for k&lt;b (if exist for a (k,b) combo) are always minimal primes in the base b) (also some examples for simple families contain no primes &gt; b] * [http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm list for the status of the generalized Sierpinski conjectures and the generalized Riesel conjectures in bases b≤1030] * [https://www.utm.edu/staff/caldwell/preprints/2to100.pdf article for generalized Sierpinski conjectures in bases b≤100] * [http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf article for the mixed (original+dual) Sierpinski problem] * [http://www.fermatquotient.com/PrimSerien/GenRepu.txt generalized repunit primes (primes of the form (bn−1)/(b−1)) in bases b≤160, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html generalized repunit primes (primes of the form (bn−1)/(b−1)) in bases b≤1000, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://jeppesn.dk/generalized-fermat.html generalized Fermat primes (primes of the form b2^n+1) in even bases b≤1000, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://www.noprimeleftbehind.net/crus/GFN-primes.htm generalized Fermat primes (primes of the form b2^n+1) in even bases b≤1030, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt list of generalized half Fermat primes (primes of the form (b2^n+1)/2) sorted by n, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://harvey563.tripod.com/wills.txt primes of the form (b−1)*bn−1 for bases b≤2049, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Williams_prime_MM_least the smallest primes of the form (b−1)*bn−1 for bases b≤2049, these primes (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Williams_prime_MP_least the smallest primes of the form (b−1)*bn+1 for bases b≤1024, these primes (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n the smallest primes of the form k*bn−1 for k≤12 and bases b≤1024, these primes (if exists) is always minimal prime in base b if b>k] * [https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n the smallest primes of the form k*bn+1 for k≤12 and bases b≤1024, these primes (if exists) is always minimal prime in base b if b>k] * [https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml list for the smallest primes in given simple family in bases b≤1024] * [https://www.rose-hulman.edu/~rickert/Compositeseq/ a problem related to this project] * [http://www.worldofnumbers.com/Appending%201s%20to%20n.txt a problem related to this project] * [https://stdkmd.net/nrr/prime/primecount.txt near- and quasi- repdigit (probable) primes sorted by count] * [https://stdkmd.net/nrr/prime/primedifficulty.txt near- and quasi- repdigit (probable) primes sorted by difficulty] * [http://www.prothsearch.com/fermat.html factoring status of Fermat numbers] * [http://www.rieselprime.de/dl/CRUS_pack.zip srsieve, sr1sieve, sr2sieve, pfgw, and llr softwares] * [https://www.bc-team.org/app.php/dlext/?cat=3 srsieve, sr1sieve, sr2sieve, sr5sieve software] * [https://sourceforge.net/projects/openpfgw/ pfgw software] * [http://jpenne.free.fr/index2.html llr software] * [http://www.ellipsa.eu/public/primo/primo.html PRIMO software] * [https://primes.utm.edu/prove/index.html website for primality proving] * [https://primes.utm.edu/curios/page.php?number_id=22380 the largest base 10 minimal prime in Prime Curios!] * [https://oeis.org/A071062 OEIS sequence for base 10 minimal primes, when the restriction of prime>base is not required] * [https://oeis.org/A326609 OEIS sequence for the largest base b minimal prime, when the restriction of prime>base is not required] * [https://primes.utm.edu/primes/lists/all.txt top proven primes] * [http://www.primenumbers.net/prptop/prptop.php top PRPs] * [http://factordb.com online factor database, including many primes which are minimal primes in a small base] 9il5qtk133yky04vzk1hbvgdcjckrzh 2412470 2412469 2022-08-07T03:10:36Z 2402:7500:942:36DD:9962:A44F:536A:30BC /* Unsolved families */ wikitext text/x-wiki A '''quasi-minimal prime''' is a [[w:Prime number|prime number]] for which there is no shorter [[w:Subsequence|subsequence]] of its [[w:Numerical digit|digit]]s in a given [[w:Radix|base]] ''b'' that form a prime > ''b''. For example, 857 is a quasi-minimal prime in [[w:Decimal|decimal]] because there is no prime > 10 among the shorter subsequences of the digits: 8, 5, 7, 85, 87, 57. The subsequence does not have to consist of consecutive digits, so 149 is not a quasi-minimal prime in decimal (because 19 is prime and 19 > 10). But it does have to be in the same order; so, for example, 991 is still a quasi-minimal prime in decimal even though a subset of the digits can form the shorter prime 19 > 10 by changing the order. (using A−Z to represent digit values 10 to 35) For the quasi-minimal primes in bases up to 36, I have only solved (found all quasi-minimal primes and proved that these are all such primes) bases 2~12, 14~15, 18, 20, 22, 24, 30 (bases 11, 22, 30 need primality proving of the probable primes). For the remain bases 13, 16~17, 19, 21, 23, 25~29, 31~36, there are some ''x''{''d''}''y'' (with ''x'', ''y'' strings (may be [[w:Empty string|empty]]) with digits in base ''b'', ''d'' digit in base ''b'') families which are not solved (not even a probable prime is known nor can be ruled out as only contain composites (only count the numbers > base (''b'')). I left as a challenge to readers the task of solving (finding all quasi-minimal primes and proving that these are all such primes) bases 13, 16~17, 19, 21, 23, 25~29, 31~36 (this will be a hard problem, e.g. base 23 has a quasi-minimal prime 9E₈₀₀₈₇₃, and base 36 has quasi-minimal prime P₈₁₉₉₃SZ). Proving the set of the quasi-minimal primes in base ''b'' is ''S'', is equivalent to: * Prove that all elements in ''S'', when read as base ''b'' representation, are primes > ''b''. * Prove that all [[w:Proper subset|proper]] subsequence of all elements in ''S'', when read as base ''b'' representation, which are > ''b'', are composite. * Prove that all primes > ''b'', when written in base ''b'', contain at least one element in ''S'' as subsequence (equivalently, prove that all strings not containing any element in ''S'' as subsequence, when read as base ''b'' representation, which are > ''b'', are composite). e.g. proving the set of the quasi-minimal primes in base ''b'' = 10 is {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}, is equivalent to: * Prove that all of 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 are primes > 10. * Prove that all proper subsequence of all elements in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} which are > 10 are composite. * Prove that all primes > 10 contain at least one element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence (equivalently, prove that all numbers > 10 not containing any element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence are composite). ==Condensed table== {|class=wikitable |''b''||number of quasi-minimal primes base ''b''||base-''b'' form of largest known quasi-minimal prime base ''b''||length of largest known quasi-minimal prime base ''b''||algebraic ((''a''×''b''^''n''+''c'')/''d'') form of largest known quasi-minimal prime base ''b'' |- |2||1||11||2||3 |- |3||3||111||3||13 |- |4||5||221||3||41 |- |5||22||10₉₃13||96||5⁹⁵+8 |- |6||11||40041||5||5209 |- |7||71||3₁₆1||17||(7¹⁷−5)/2 |- |8||75||4₂₂₀7||221||(4×8²²¹+17)/7 |- |9||151||30₁₁₅₈11||1161||3×9¹¹⁶⁰+10 |- |10||77||50₂₈27||31||5×10³⁰+27 |- |11^*||1068||57₆₂₆₆₈||62669||(57×11⁶²⁶⁶⁸−7)/10 |- |12||106||40₃₉77||42||4×12⁴¹+91 |- |13^*||3195~3197||80₃₂₀₁₇111||32021||8×13³²⁰²⁰+183 |- |14||650||4D₁₉₆₉₈||19699||5×14¹⁹⁶⁹⁸−1 |- |15||1284||7₁₅₅97||157||(15¹⁵⁷+59)/2 |- |16^*||2346~2347||4₇₂₇₈₅DD||72787||(4×16⁷²⁷⁸⁷+2291)/15 |- |17^*||10409~10428||F70₁₈₆₇₆₇1||186770||262×17¹⁸⁶⁷⁶⁸+1 |- |18||549||C0₆₂₆₈C5||6271||12×18⁶²⁷⁰+221 |- |20||3314||G0₆₂₆₉D||6271||16×20⁶²⁷⁰+13 |- |21^*||13375~13395||CF₄₇₉₁₄₇0K||479150||(51×21⁴⁷⁹¹⁴⁹−1243)/4 |- |22^*||8003||BK₂₂₀₀₁5||22003||(251×22²²⁰⁰²−335)/21 |- |24||3409||N00N₈₁₂₉LN||8134||13249×24⁸¹³¹−49 |- |30^*||2619||OT₃₄₂₀₅||34206||25×30³⁴²⁰⁵−1 |- |36^*||35257~35263||P₈₁₉₉₃SZ||81995||(5×36⁸¹⁹⁹⁵+821)/7 |} ^* Data assumes the primality of the [[w:probable prime|probable prime]]s. Except bases ''b'' = 13, 16, 17, 21, all bases in this table are completely solved (if we allow strong probable primes > 10²⁵⁰⁰⁰), also, except bases ''b'' = 11, 13, 16, 17, 21, 22, 30, 36, all bases in this table are completely solved even if we only allow definitely primes (thus, we can complete the classification of the quasi-minimal primes in these bases, i.e. the “quasi-minimal problems” in these bases are now theorems), for the quasi-minimal primes see the data below. Base ''b'' = 13 has 3195 known quasi-minimal primes (or PRPs), see the data below, and if there are more quasi-minimal primes in base 13, then they must be of the form 9{5} or A{3}A (we are unable to determine if these two families contain a prime or not, i.e. these two families have no known prime members, nor can these two families be ruled out as only containing composites), and must have at least 111000 digits in base 13, besides, since these two families can contain at most one quasi-minimal prime, there are at most 3197 quasi-minimal primes in base 13. (i.e. the quasi-minimal primes in base 13 are the 3195 known quasi-minimal primes in base 13 (they are given in the data section) plus the smallest prime in the family 9{5} in base 13 (if exists) plus the smallest prime in the family A{3}A in base 13 (if exists)) Base ''b'' = 16 has 2346 known quasi-minimal primes (or PRPs), see the data below, and if there are more quasi-minimal primes in base 16, then they must be of the form {3}AF (we are unable to determine if this family contains a prime or not, i.e. this family have no known prime members, nor can this family be ruled out as only containing composites), and must have at least 98000 digits in base 16, besides, since this family can contain at most one quasi-minimal prime, there are at most 2347 quasi-minimal primes in base 16. (i.e. the quasi-minimal primes in base 16 are the 2346 known quasi-minimal primes in base 16 (they are given in the data section) plus the smallest prime in the family {3}AF in base 16 (if exists)) ==Data for quasi-minimal primes== ===Base 2=== 11 ===Base 3=== 12, 21, 111 ===Base 4=== 11, 13, 23, 31, 221 ===Base 5=== 12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013 ===Base 6=== 11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041 ===Base 7=== 14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331 ===Base 8=== 13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 ===Base 9=== 12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011 ===Base 10=== 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 ===Base 11=== 12, 16, 18, 21, 27, 29, 34, 38, 3A, 43, 49, 54, 56, 61, 65, 67, 72, 76, 81, 89, 92, 94, 98, 9A, A3, 10A, 115, 117, 133, 139, 153, 155, 171, 193, 197, 199, 1AA, 225, 232, 236, 25A, 263, 315, 319, 331, 335, 351, 353, 362, 373, 379, 391, 395, 407, 414, 452, 458, 478, 47A, 485, 4A5, 4A7, 502, 508, 511, 513, 533, 535, 539, 551, 571, 579, 588, 595, 623, 632, 70A, 711, 715, 731, 733, 737, 755, 759, 775, 791, 797, 7AA, 803, 847, 858, 85A, 874, 885, 887, 913, 919, 931, 937, 957, 959, 975, 995, A07, A1A, A25, A45, A74, A7A, A85, AA1, AA7, 1101, 11A9, 1305, 1451, 1457, 15A7, 175A, 17A5, 17A9, 2023, 2045, 2052, 2083, 20A5, 2333, 2A05, 2A52, 3013, 3026, 3059, 3097, 3206, 3222, 3233, 3307, 3332, 3505, 4025, 4151, 4157, 4175, 4405, 4445, 4487, 450A, 4575, 5017, 5031, 5059, 5075, 5097, 5099, 5105, 515A, 517A, 520A, 5301, 5583, 5705, 577A, 5853, 5873, 5909, 5A17, 5A57, 5A77, 5A8A, 6683, 66A9, 7019, 7073, 7079, 7088, 7093, 7095, 7309, 7451, 7501, 7507, 7578, 757A, 75A7, 7787, 7804, 7844, 7848, 7853, 7877, 78A4, 7A04, 7A57, 7A79, 7A95, 8078, 8245, 8333, 8355, 8366, 8375, 8425, 8553, 8663, 8708, 8777, 878A, 8A05, 9053, 9101, 9107, 9305, 9505, 9703, A052, A119, A151, A175, A515, A517, A575, A577, A5A8, A719, A779, A911, AAA9, 10011, 10075, 10091, 10109, 10411, 10444, 10705, 10709, 10774, 10901, 11104, 11131, 11144, 11191, 1141A, 114A1, 13757, 1411A, 14477, 144A4, 14A04, 14A11, 17045, 17704, 1774A, 17777, 177A4, 17A47, 1A091, 1A109, 1A114, 1A404, 1A411, 1A709, 20005, 20555, 22203, 25228, 25282, 25552, 25822, 28522, 30037, 30701, 30707, 31113, 33777, 35009, 35757, 39997, 40045, 4041A, 40441, 4045A, 404A1, 4111A, 411A1, 42005, 44401, 44474, 444A1, 44555, 44577, 445AA, 44744, 44A01, 47471, 47477, 47701, 5057A, 50903, 5228A, 52A22, 52A55, 52A82, 55007, 550A9, 55205, 55522, 55557, 55593, 55805, 57007, 57573, 57773, 57807, 5822A, 58307, 58505, 58A22, 59773, 59917, 59973, 59977, 59999, 5A015, 5A2A2, 5AA99, 60836, 60863, 68636, 6A609, 6A669, 6A696, 6A906, 6A966, 70048, 70103, 70471, 70583, 70714, 71474, 717A4, 71A09, 74084, 74444, 74448, 74477, 744A8, 74747, 74774, 7488A, 74A48, 75773, 77144, 77401, 77447, 77799, 77A09, 78008, 78783, 7884A, 78888, 788A8, 79939, 79993, 79999, 7A051, 7A444, 7A471, 80005, 80252, 80405, 80522, 80757, 80AA5, 83002, 84045, 85307, 86883, 88863, 8A788, 90073, 90707, 90901, 95003, 97779, 97939, 99111, 99177, 99973, A0111, A0669, A0966, A0999, A0A09, A1404, A4177, A4401, A4717, A5228, A52AA, A5558, A580A, A5822, A58AA, A5A59, A5AA2, A6096, A6966, A6999, A7051, A7778, A7808, A9055, A9091, A9699, A9969, AA52A, AA58A, 100019, 100079, 101113, 101119, 101911, 107003, 140004, 144011, 144404, 1A0019, 1A0141, 1A5001, 1A7005, 1A9001, 222223, 222823, 300107, 300202, 300323, 303203, 307577, 310007, 332003, 370777, 400555, 401A11, 404001, 404111, 405AAA, 41A011, 440A41, 441011, 451777, 455555, 470051, 470444, 474404, 4A0401, 4A4041, 500015, 500053, 500077, 500507, 505577, 522A2A, 525223, 528A2A, 531707, 550777, 553707, 5555A9, 555A99, 557707, 55A559, 5807A7, 580A0A, 580A55, 58A0AA, 590007, 599907, 5A2228, 5A2822, 5A2AAA, 5A552A, 5AA22A, 5AAA22, 60A069, 683006, 6A0096, 6A0A96, 6A9099, 6A9909, 700778, 701074, 701777, 704408, 704417, 704457, 704484, 707041, 707441, 707708, 707744, 707784, 710777, 717044, 717077, 740008, 74484A, 770441, 770744, 770748, 770771, 777017, 777071, 777448, 777484, 777701, 7778A8, 777A19, 777A48, 778883, 78A808, 790003, 7A1009, 7A4408, 7A7708, 80A555, 828283, 828883, 840555, 850505, 868306, 873005, 883202, 900701, 909739, 909979, 909991, 970771, 977701, 979909, 990739, 990777, 990793, 997099, 999709, 999901, A00009, A00599, A01901, A05509, A0A058, A0A955, A10114, A555A2, A55999, A59991, A5A222, A5A22A, A60609, A66069, A66906, A69006, A79005, A87888, A90099, A90996, A96006, A96666, A97177, A97771, AA0A58, AA5A22, AAA522, 1000501, 1011141, 1030007, 1070047, 111114A, 1111A14, 1111A41, 1144441, 14A4444, 1700005, 1700474, 1A44444, 2555505, 2845055, 3030023, 3100003, 3333397, 4000111, 4011111, 41A1111, 4411111, 444441A, 4444771, 4470004, 4505005, 4744417, 4774441, 4777404, 4777417, 4777747, 4A11111, 4A40001, 5000093, 50005A7, 5005777, 5050553, 5055503, 5070777, 5222222, 5222AAA, 52AAAA2, 52AAAAA, 5505053, 5552AAA, 5555599, 5555A58, 5558A0A, 5558A55, 5558AAA, 55A0009, 55AAA52, 580000A, 5822222, 58AAAAA, 5A2222A, 5AA2222, 6000A69, 6000A96, 6A00069, 7000417, 7000741, 7000835, 7000857, 7007177, 7008305, 7014447, 7017444, 7074177, 7077477, 7077741, 7077747, 7100447, 7174404, 717444A, 7400404, 7700717, 7701077, 7701707, 7707778, 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DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD ===Base 15=== 12, 14, 18, 1E, 21, 27, 2B, 2D, 32, 38, 3E, 41, 47, 4B, 4D, 54, 58, 5E, 67, 6B, 6D, 72, 74, 78, 87, 8B, 92, 94, 9E, A1, A7, AD, B2, B8, BE, C1, CB, CD, D2, D4, E1, ED, 111, 11B, 131, 137, 13B, 13D, 157, 15B, 15D, 171, 177, 197, 19D, 1B7, 1BB, 1D1, 1DB, 1DD, 234, 298, 311, 31B, 337, 33D, 344, 351, 357, 35B, 364, 377, 391, 39B, 39D, 3A4, 3BD, 3C4, 3D7, 3DB, 3DD, 452, 51B, 51D, 531, 53B, 551, 55D, 562, 571, 577, 5A2, 5B1, 5B7, 5BB, 5BD, 5C2, 5D1, 5D7, 634, 652, 681, 698, 717, 71B, 731, 737, 757, 75D, 77D, 79B, 79D, 7B1, 7B7, 7BD, 7D7, 7DD, 801, 852, 88D, 8D8, 91D, 93B, 93D, 95B, 95D, 971, 977, 97B, 97D, 988, 991, 9BD, 9C8, 9D1, A98, AAB, B1D, B31, B3B, B44, B51, B57, B7B, B7D, B97, B9B, BB7, BC4, BD1, BD7, BDD, C07, C34, C52, C7E, C98, CC7, CE7, D0E, D1D, D31, D51, D5B, D68, D77, D7B, D91, D97, DA8, DAE, DCE, DD1, EB4, EEB, 107B, 1091, 10B1, 1107, 110D, 1561, 1651, 1691, 1B01, 2052, 2502, 2522, 303B, 307D, 3097, 30BB, 30D1, 3107, 3361, 3701, 3907, 3B01, 3B0B, 3C97, 4434, 4498, 4834, 4898, 49A8, 4E34, 5037, 507D, 5091, 509B, 5107, 5161, 5202, 53C7, 5552, 570B, 590B, 590D, 59C7, 5A5B, 5C97, 5D0D, 5DAB, 6061, 6151, 6191, 6511, 6601, 6911, 707B, 7091, 7097, 70AE, 70BB, 70CE, 70DB, 7561, 760E, 7691, 76CE, 7907, 7961, 7A0E, 7A3B, 7AEE, 7B0B, 7BAB, 7C0E, 7C77, 7CAE, 7D0B, 7D61, 7DAB, 7E5B, 7E6E, 7E7B, 7EBB, 8098, 811D, 8191, 835D, 853D, 8881, 8908, 8951, 8968, 899D, 8D3D, 8D5D, 8D6E, 8DDD, 8E98, 9011, 9037, 9097, 90D7, 9301, 93C7, 95C7, 9611, 9631, 96A8, 9811, 9851, 989D, 990B, 990D, 998D, 99AB, 99C7, 99D8, 9A08, 9A9B, 9AA8, 9ABB, 9B61, 9BC7, 9D0B, 9DAB, 9DC7, 9DD8, A052, A304, A502, A55B, A9BB, AB04, AB64, B09D, B107, B10B, B161, B1AB, B1C7, B30D, B3C7, B50B, B664, B691, B6A4, B707, B761, B90D, B961, BA5B, BABB, BBAB, BBB4, BC37, BC77, C777, C937, C997, D011, D03D, D05D, D09B, D0B1, D0BD, D101, D10B, D30D, D3AB, D507, D50D, D66E, D761, D7DE, D811, D85D, D86E, D89D, D8C8, D8E8, D9AB, D9D8, DA3B, DA9B, DABB, DB01, DB61, DBAB, DC88, DD07, DD0B, DD7E, DD8D, DDE7, DE6E, E252, E33B, E522, E57B, E7AE, E7CE, E898, E997, E9A8, E9BB, EA34, EB5B, EE98, EEC7, 10017, 10B0D, 170AB, 17A0B, 19001, 19601, 1A09B, 1D0C7, 22E52, 2EA52, 30017, 3001D, 300B1, 301C7, 30334, 30631, 307AB, 3300B, 3333B, 36031, 36301, 37A0B, 37BBB, 39997, 3A30B, 3B0C7, 3D001, 3D601, 40034, 40968, 43334, 49668, 49998, 50022, 5009D, 501C7, 50222, 50507, 505C7, 50611, 50C57, 53007, 53997, 55537, 5555B, 5557B, 5599B, 56101, 56691, 56961, 5700D, 5755B, 59001, 59557, 59997, 5999D, 599DB, 59DDD, 5D99B, 5DD3D, 5DD9D, 60931, 63031, 65691, 66951, 69031, 69361, 69561, 70011, 70051, 7005B, 7006E, 7030D, 703AB, 70501, 70701, 707C7, 71601, 71951, 7300D, 7333B, 75001, 7555B, 75911, 76011, 76051, 766EE, 76EEE, 7700B, 77191, 77661, 7776E, 77771, 777BB, 77911, 77BBB, 79001, 7A05B, 7A66E, 7AA6E, 7AAAE, 7ACCE, 7C6EE, 7CCEE, 7CECE, 7CEEE, 7D3BB, 7E7C7, 7EECE, 80034, 80304, 80434, 809DD, 80A34, 84A34, 850DD, 85961, 86661, 88151, 88331, 88511, 88591, 88898, 890DD, 89998, 89D0D, 8D90D, 8E434, 90017, 90051, 900A8, 900DB, 901C7, 90C57, 90D8D, 91007, 91061, 9199B, 95997, 96068, 96561, 99397, 99537, 9999B, 999B7, 999D7, 999DB, 999DD, 99BBB, 99DBB, 99DD7, 99DDD, 9B007, 9B00B, 9B0AB, 9BB11, 9BBBB, 9D007, 9D08D, 9D537, 9D9BB, 9D9DB, 9DD57, 9DDB7, 9DDDB, 9DDDD, A0A34, A0B5B, A0BBB, A0E34, A2E52, A330B, A8434, A8834, A8E34, A909B, AAA34, AAE52, AB0BB, AB334, ABB34, AE034, AE834, AE99B, AEA52, AEE52, B0011, B0071, B0077, B00B1, B0611, B0A64, B500D, B599D, B6101, B7771, B7911, BA064, BAAA4, BAB34, BB061, BB304, BB53D, BB601, BBB91, BBB9D, BBBBD, BDA0B, BDBBB, D0088, D00D7, D0307, D05C7, D070D, D0888, D0B07, D0BC7, D0C08, D0DC7, D0DD8, D1661, D59DD, D5D3D, D5DDD, D6611, D700D, D8D0D, D900B, D9908, D999D, D9BBB, D9D9D, D9DDB, DB007, DB00D, DB1B1, DB53D, DB59D, DB99D, DBBB1, DD0D8, DD33B, DD3B7, DD3BB, DD57D, DD898, DD9DD, DDB37, DDBDB, DDD08, DDD3D, DDD5D, DDD7D, DDD88, DDD9D, DDDB7, DDDC8, DDDD7, DDE98, DE037, DE998, DEB07, E0098, E00C7, E0537, E0557, E077B, E0834, E0968, E3334, E37AB, E39C7, E4034, E5307, E55AB, E705B, E750B, E766E, E76EE, E8304, E8434, E9608, E9C37, EAE52, EBB0B, EC557, EC597, EC957, 1000BD, 1009AB, 10A90B, 1900AB, 190661, 19099B, 190A0B, 1A900B, 222A52, 2AAA52, 31000D, 330331, 333334, 3733AB, 373ABB, 3BBB61, 430004, 490068, 490608, 5000DB, 500D0B, 505557, 505A0B, 50D00B, 50DDDB, 50DDDD, 522222, 5500AB, 5500C7, 550957, 550A0B, 555A9B, 559057, 560011, 590661, 633331, 666331, 666591, 666661, 7050AB, 705A0B, 706101, 70A50B, 7300AB, 761661, 76666E, 777011, 777101, 77750B, 777A5B, 777CEE, 779051, 791501, 7E7797, 7ECCCE, 7EEE97, 800D9D, 808834, 836631, 83D661, 843004, 856611, 884034, 884304, 888E34, 88A434, 88AE34, 8A4034, 8AEE34, 8E8034, 8E8E34, 8EEE34, 9000BB, 9001AB, 900B07, 900D98, 903661, 905661, 906651, 9080DD, 9099A8, 909D9B, 90A668, 90DD9B, 90DDBB, 910001, 9100AB, 91A00B, 930007, 950001, 956661, 9909A8, 995907, 999068, 999507, 999907, 9B0B1B, 9B0BB1, 9BB01B, 9C5597, 9C5957, 9D09DD, 9D0D9D, 9D800D, 9DB307, 9DD09D, A00034, A0033B, A033B4, A2A252, AAAA52, ABBBBB, B00004, B0001B, B0003D, B00A04, B0555B, B07191, B07711, B07777, B0B911, B0BDBB, B77011, B777C7, BB0001, BB0034, BB035D, BB055B, BB0BDB, BB9101, BBB0DB, BBB50D, BBBB01, BBD0BB, C55397, C55557, C55597, D0003B, D00057, D0007D, D000B7, D000C8, D008DD, D00DAB, D0333B, D05537, D099DD, D09DDD, D0DDBB, D555C7, D5C537, D88008, D88088, D888EE, D909DD, D9D0DD, D9DD0D, DB0BBB, DBBB0B, DBBB0D, DC0008, DC5537, DDDDD8, DDDEBB, DDE99B, DE0808, DE0C57, DE300B, DE5537, DE8888, DEE088, DEE307, DEE888, DEEE37, DEEE57, DEEEC8, E0000B, E007BB, E00A52, E03BC7, E07ABB, E09B07, E0A99B, E0C397, E0E76E, E50057, E55007, E55597, E55937, E730AB, E73A0B, E80E34, E88834, E8E034, E90008, E95557, EA099B, EE4304, EE5057, EE5507, EE8E34, EE9307, EEE434, 100001D, 1000A9B, 1000DC7, 22AA252, 3000BC7, 3033301, 3076661, 333B304, 33B3034, 3B33304, 3D66661, 50007AB, 5005957, 5500597, 5550057, 5559007, 5559597, 5595007, 5966661, 5DDDDDB, 6366631, 7010001, 7066651, 7100061, 733BBBB, 766A6AE, 77505AB, 7776501, 777775B, 777AACE, 777ECCE, 777EEAE, 7CCCCCE, 7E30A0B, 7EEEEAE, 8300004, 8363331, 8693331, 880E834, 8833304, 8888034, 8888434, 888A034, 88A3334, 88E8834, 88EE034, 88EE304, 8AA3334, 8D0009D, 8EE8834, 9000361, 9000668, 9003331, 9005557, 9006008, 9008D0D, 9083331, 9090968, 90BBB01, 90D0908, 9500661, 9555597, 9555957, 9660008, 9900968, 9995597, 9996008, 9999557, 9999597, 9999908, 9A66668, A003B34, A003BB4, AA22252, B00B034, B00B35D, B033334, B0B6661, B0BB01B, B100001, B333304, B777777, B99999D, BA60004, BAA0334, BBB001B, BBB6611, BBBBB11, BBBD00B, BD000AB, D0000DB, D009098, D00CCC8, D00D908, D00D99D, D03000B, D0BB0BB, D0D9008, D0D9998, D1000C7, D800008, D8DDEEE, D90080D, DBBBBBB, DD09998, DDD5557, DDDDBBB, DDDDDBD, DDDE8EE, DECC008, DECCCC8, DEE0CC8, DEEC0C8, E000397, E0003BB, E000434, E00076E, E000937, E007A5B, E00909B, E0090B7, E009307, E00B077, E00E434, E00E797, E00E937, E05999B, E09009B, E0900B7, E0E0937, E0E7E97, E0EAA52, E0EEA52, E555057, E5555C7, E7777C7, E77E797, E88EE34, E999998, EA5999B, EB000BB, EB0BBBB, EE00434, EE0E797, EEE076E, EEE706E, EEE8834, EEEE557, EEEE797, 30333331, 30B66661, 33000034, 33030004, 33B33004, 500575AB, 55000007, 5500075B, 55500907, 55555057, 55555907, 55559507, 60003301, 60033001, 60330001, 7000003D, 70106661, 70666611, 77000001, 7777770B, 777777C7, 77777ACE, 77777EAE, 777E30AB, 777E3A0B, 7CCCC66E, 800005DD, 88AA0834, 90000008, 900008DD, 90099668, 90500557, 90555007, 90666668, 90909998, 90990998, 90996668, 9099999D, 90D00098, 90D90998, 95500057, 99099098, 99555057, 99900998, 99966608, 99966668, 99999668, 99999998, 9D009008, 9D090998, A0803334, A2222252, AAA52222, B00005AB, B000B55B, B0BBBB5B, B3330034, BB0BBB1B, BBAA3334, BBB0BB1B, BBB0BB5B, BBDB000B, D000BBBB, D00100C7, D8888888, D900008D, D9000098, DBB000BB, DC0CCCC8, DCC0CCC8, DCCCC008, DD000908, DD09009D, DDDDDDAB, DDDDDEEE, DDDEEE8E, DDDEEEE8, DEE80008, E0777E97, E0E0E397, E0E77797, E0EE0397, E7777797, E9066668, EE00E397, EE077797, EE0E0397, EEE00797, EEE07E97, EEE0AA52, EEE55397, EEE55557, EEEAAA52, EEEEE834, EEEEEA52, 300003331, 300007661, 300330031, 333000004, 333300001, 333B00034, 3700000AB, 3B3300034, 500000057, 555555007, 555555557, 5DDDDDDDD, 600000331, 7500000AB, 75000A00B, 75A00000B, 761000001, 77000E0C7, 777700EC7, 7777730AB, 7777777AE, 77777EE97, 7777E7E97, 777999997, 7A500000B, 7BBBBBB5B, 88888A834, 900000031, 900666608, 909990098, 90D009998, 950000557, 966666008, 990000007, 990555507, 999999997, A000000B4, A0005999B, AAEEEEE34, B000AA334, BBBBB005B, BBBBBBB5B, D09999998, D0D90009D, D800000DD, D90009998, DCCCC0CC8, DE88EEEEE, DEEEEEE88, E000B7777, E000BBBBB, E003ABBBB, EE0000797, EE0EEE397, EE5555557, EE777EE97, EEEEEE537, EEEEEE937, 2222222252, 3000000071, 3330030001, 3333303001, 3333330001, 500000007B, 5555555097, 7000000071, 77000000C7, 8333333331, 8888883334, 8888888834, 888888AA34, 900000009B, 900000009D, 900000DD9D, 9000099998, 9955555507, 9D0000099D, 9D05555557, AB0000005B, B000000DAB, B00000BBDB, BB00BB0B5B, BB0BB00B5B, D000099998, D00090008D, D0D000909D, D0DDDDDDDB, D300000007, D88EEEEEEE, D900999998, DD00900008, DDD6EEEEEE, DDDDDDD6EE, DDDDDDDDDE, DDDEEEEEEE, DEEEEE8008, E000000797, 7777777CCCE, 88888830004, 90000009D9D, 99955555557, 9999999999D, B00000D00AB, BB000BBB05B, BBBB0000B5B, D000009080D, D000090800D, D090800000D, DDDDDDD999B, DDDDDDDDD9B, EEEEEE00397, EEEEEEE0397, 333000000301, 5000000000DD, 73A00000000B, 9000000000B7, 903333333331, ABB00000000B, D000000001C7, DCCCCCCCCCC8, E0EEEEEEE397, 19A000000000B, 3333333333331, 3BBBBBBBBBBBB, 9333333333331, A00000000099B, B00000000050D, EEEEEEEEEE76E, 1000000000999B, 71000000000001, 908D000000000D, BBBBBBBBBB6661, 77777777777777B, BB00000000BBB5B, DEEEEEEEEEEEEEE, 7777777777777E97, B0BBBBBBBBBBBB1B, BB0000000000DB0B, D000000000000998, D908000000000000D, DDDDDDDDDDDDDDDDB, E9666666666666668, 3330000000000000031, D00000000000000908D, E0BBBBBBBBBBBBBBBBB, 2EEEEEEEEEEEEEEEEE52, 77777777777777777ECE, 5000000000000000005AB, 777777777777777777997, 7BBBBBBBBBBBBBBBBBBBB, BB0000000000000000DBB, DD000000000000000909D, D900000000000000000DDD, DD0000000000000000099D, BBBBBBBBBBBBBBBBBBBBBB1, B00000000000000000000005B, B0700000000000000000000001, B70000000000000000000000001, 705000000000000000000000000B, 633000000000000000000000000001, EBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB, 500000000000000000000000000000000017, 77777777777777777777777777777777777777777777777777777777777CCE, 7777777777777777777777777777777777777777777777777777777777777777777777777CE, 96666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666608, EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE397, 7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777797 ===Base 16=== 11, 13, 17, 1D, 1F, 25, 29, 2B, 2F, 35, 3B, 3D, 43, 47, 49, 4F, 53, 59, 61, 65, 67, 6B, 6D, 71, 7F, 83, 89, 8B, 95, 97, 9D, A3, A7, AD, B3, B5, BF, C1, C5, C7, D3, DF, E3, E5, E9, EF, F1, FB, 14B, 15B, 185, 199, 1A5, 1BB, 1C9, 1EB, 223, 22D, 233, 241, 277, 281, 287, 28D, 2A1, 2D7, 2DD, 2E7, 301, 337, 373, 377, 38F, 3A1, 3A9, 41B, 42D, 445, 455, 45D, 481, 4B1, 4BD, 4CD, 4D5, 4E1, 4EB, 50B, 515, 51B, 527, 551, 557, 55D, 577, 581, 58F, 5AB, 5CB, 5CF, 5D1, 5D5, 5DB, 5E7, 623, 709, 727, 737, 745, 74B, 755, 757, 773, 779, 78D, 7BB, 7C3, 7C9, 7CD, 7DB, 7EB, 7ED, 805, 80F, 815, 821, 827, 841, 851, 85D, 85F, 8A5, 8DD, 8E1, 8F5, 923, 98F, 99B, 9A9, 9EB, A21, A6F, A81, A85, A99, A9F, AA9, AAB, ACF, B1B, B2D, B7B, B8D, B99, B9B, BB7, BB9, BCB, BDD, BE1, C0B, CB9, CBB, CEB, D01, D21, D2D, D55, D69, D79, D81, D85, D87, D8D, DAB, DB7, DBD, DC9, DCD, DD5, DDB, DE7, E21, E27, E4B, E7D, E87, EB1, EB7, ED1, EDB, EED, F07, F0D, F4D, FD9, FFD, 1069, 1505, 1609, 1669, 16A9, 19AB, 1A69, 1AB9, 2027, 204D, 2063, 207D, 20C3, 20ED, 2221, 22E1, 2327, 244D, 26C3, 274D, 2E01, 2E0D, 2ECD, 3023, 3079, 3109, 3263, 3341, 36AF, 3941, 3991, 39AF, 3E41, 3E81, 3EE1, 3EE7, 3F79, 4021, 40DB, 440B, 444B, 44A1, 44AB, 44DB, 4541, 45BB, 4A41, 4B0B, 4BBB, 4C4B, 4D41, 4DED, 5045, 50A1, 50ED, 540D, 5441, 555B, 556F, 5585, 560F, 56FF, 5705, 574D, 580D, 582D, 5855, 588D, 5A01, 5AA1, 5B01, 5B4B, 5B87, 5BB1, 5BEB, 5C4D, 5CDD, 5CED, 5DD7, 5DDD, 5E0D, 5E2D, 5EBB, 68FF, 6A69, 6AC9, 6C8F, 6CA9, 6CAF, 6F8F, 6FAF, 7033, 7063, 7075, 7087, 70A5, 70AB, 7303, 7393, 74DD, 754D, 7603, 7633, 7663, 7669, 7705, 772D, 775D, 77D5, 7807, 7877, 7885, 7939, 7969, 7993, 79AB, 7A05, 7A69, 7A9B, 7AA5, 7B77, 7BA9, 7D4D, 7D75, 7D77, 8077, 808D, 80D7, 80E7, 8587, 86CF, 8777, 8785, 8885, 88CF, 88ED, 88FD, 8C6F, 8C8F, 8E8D, 8EE7, 8F2D, 8F8D, 9031, 9041, 90AF, 90B9, 9221, 9319, 9401, 944B, 9881, 9931, 9941, 9991, 99AF, 9A0F, 9A1B, 9A4B, 9AFF, 9BA1, 9BB1, 9CAF, 9E81, 9EA1, 9FAF, A001, A05B, A0C9, A105, A10B, A4CB, A55B, A6C9, A88F, A91B, A9B1, A9BB, AA15, AB01, AB0B, AB19, ABBB, AC09, AF09, B041, B04B, B069, B07D, B087, B0B1, B0ED, B1A9, B201, B40B, B40D, B609, B70D, B7A9, B807, B9A1, BA41, BAA1, BB4B, BBB1, BBDB, BBED, BD19, BD41, BDBB, BDEB, BE07, BEE7, C0D9, C203, C24D, C6A9, C88D, C88F, C8CF, C8ED, C9AF, C9CB, CA09, CA4B, CA69, CAC9, CC0D, CC23, CC4D, CC9B, CD09, CDD9, CE4D, CEDD, CFA9, CFCD, D04B, D099, D405, D415, D44B, D4A5, D4DD, D50D, D70B, D74D, D77B, D7CB, D91B, D991, DA05, DA09, DA15, DA51, DB91, DBEB, DD7D, DDA1, DDED, DE0B, DE41, DE4D, DEA1, E02D, E07B, E0D7, E1CB, E2CD, E401, E801, EABB, EACB, EAEB, EBAB, EC4D, ECDD, ED07, EDD7, EE7B, EE81, EEAB, EEE1, F08F, F0A9, F227, F2ED, F3AF, F485, F58D, F72D, F763, F769, F787, F7A5, F7E7, F82D, F86F, F877, F88D, F8D7, F8E7, F8FF, FCCD, FED7, FF85, FF8F, FFA9, 100AB, 10BA9, 1A0CB, 1BA09, 200E1, 2C603, 2CC03, 30227, 303AF, 30AAF, 32003, 32207, 32CC3, 330AF, 33169, 33221, 33391, 33881, 33AFF, 38807, 38887, 3AFFF, 3F203, 3F887, 3FAFF, 400BB, 4084D, 40A4B, 42001, 44221, 44401, 444D1, 4480D, 4488D, 44CCB, 44D4D, 44E8D, 4804D, 4840D, 4A0CB, 4A54B, 4CACB, 4D0DD, 4D40D, 4D44D, 5004D, 50075, 502CD, 5044D, 50887, 50EE1, 5448D, 548ED, 55A45, 55F45, 5844D, 5A4A5, 5AE41, 5B0CD, 5B44D, 5BBCD, 5D4ED, 5E0E1, 5EB4D, 5EC8D, 5ECCD, 5EE41, 5F06F, 5F7DD, 5F885, 5F8CD, 5FC8D, 5FF75, 6088F, 60AFF, 630AF, 633AF, 660A9, 668CF, 669AF, 66A09, 66A0F, 66FA9, 6886F, 6A00F, 6A0FF, 6A8AF, 6AFFF, 7002D, 7024D, 70B0D, 70B7D, 7200D, 73363, 73999, 7444D, 770B7, 777D7, 77B07, 77D7D, 77DD7, 79003, 79999, 7B00D, 7D05D, 7D7DD, 8007D, 800D1, 8074D, 82CCD, 82E4D, 8448D, 8484D, 8704D, 8724D, 87887, 88001, 8800D, 880CD, 88507, 88555, 8866F, 8872D, 8877D, 888D1, 888D7, 88AA1, 88C2D, 88D57, 88D75, 88D77, 8AFAF, 8C2CD, 8C40D, 8C8CD, 8CCED, 8CE2D, 8CFED, 8E007, 8E20D, 8E24D, 8F6FF, 8FAAF, 900CB, 901AB, 90901, 909A1, 90AB1, 90AE1, 90EE1, 910AB, 93331, 940AB, 963AF, 966AF, 99019, 99109, 99A01, 9AAE1, 9B00B, 9B0AB, 9B441, 9BABB, 9BBBB, 9E441, A00BB, A0405, A044B, A08AF, A0A51, A0B91, A0C4B, A1B09, A54A5, A5B41, A6609, A904B, A94A1, A9C4B, A9E01, A9E41, AA0A1, AA441, AA501, AA8AF, AAEE1, AAF45, AAF8F, ABBA1, ACC69, AE0BB, AE0EB, AEAE1, AEE0B, AEEA1, AEECB, AF045, AF4A5, AFA8F, B00A1, B00D7, B044D, B0777, B0A0B, B0A91, B0BBD, B0BCD, B0C09, B0DA9, B0EAB, B2207, B4001, B6669, B7707, B7D07, B8081, B9021, BA091, BA109, BA4BB, BB001, BB0EB, BB8A1, BBBEB, BBE0B, BBEBB, BC009, BCECD, BD0A9, BE44D, BEB0D, BEBBB, BEEBB, C0263, C02C3, C02ED, C040D, C0CA9, C0CCD, C2663, C2CED, C32C3, C3323, C400D, C40ED, C44CB, C44ED, C480D, C484D, C4CAB, C60AF, C686F, C6A0F, C86FF, C8C2D, CAA0F, CAFAF, CBCED, CC0AF, CC44B, CC82D, CC8FF, CCAF9, CCAFF, CCCFD, CCFAF, CD00D, CD4CB, CD4ED, CDDDD, CF2C3, CFC8F, CFE8D, D0045, D07DD, D09BB, D0D4D, D0DD7, D0EBB, D0EEB, D1009, D1045, D10B9, D1BA9, D54BB, D54ED, D5AE1, D5D07, D5EE1, D70DD, D7707, D7777, D77DD, D7DD7, D9441, D9AE1, D9B0B, DA9A1, DA9E1, DAA41, DAAA1, DBB0B, DBBA1, DC4CB, DD227, DD44D, DDDD7, E0081, E00E1, E010B, E088D, E08CD, E0B0D, E0BBD, E100B, E4D0D, E777B, E77AB, E7CCB, E844D, E848D, E884D, E88A1, EB0BB, EBB4D, EBBEB, EBEEB, EC8CD, ECBCD, ECC8D, ED04D, EE001, EE0EB, EE4A1, EEEBB, F0085, F09AF, F0C23, F0CAF, F2663, F2C03, F3799, F3887, F4A05, F4AA5, F506F, F5845, F5885, F5C2D, F5ECD, F5F45, F66A9, F688F, F6AFF, F7399, F777D, F8545, F8555, F8AAF, F8F87, F9AAF, FA0F9, FA405, FA669, FAFF9, FC263, FCA0F, FCAFF, FCE8D, FCF23, FD777, FDDDD, FDEDD, FEC2D, FEC8D, FF545, FF6AF, FF739, FF775, FF9AF, FFC23, 100055, 100555, 10A9CB, 1A090B, 1A900B, 1CACCB, 1CCACB, 20DEE1, 266003, 3000AF, 300A0F, 300AFF, 308087, 308E07, 3323E1, 333A0F, 339331, 33CA0F, 33CF23, 33CFAF, 33F323, 380087, 3A00AF, 3A0F0F, 3AA0FF, 3AAF0F, 3C33AF, 3C3A0F, 3C3FAF, 3CCAAF, 3F0FAF, 3F32C3, 3FF0AF, 3FFAAF, 4004CB, 400A05, 4048ED, 404DDD, 40AA05, 40D04D, 40DD4D, 40E0DD, 40E48D, 440041, 44008D, 44044D, 4404DD, 44440D, 4448ED, 4484ED, 448E4D, 44E44D, 48888D, 4AA005, 4DD00D, 4DD04D, 4DDD0D, 4E048D, 4E448D, 4E880D, 5000DD, 500201, 50066F, 5008CD, 500C2D, 500D7D, 50C20D, 520C0D, 544EDD, 54AA05, 54AAA5, 54ED4D, 566AAF, 57D00D, 580087, 5A5545, 5C20CD, 5C8CCD, 5CC2CD, 5D000D, 5D070D, 5F666F, 5FAA45, 5FFF45, 60008F, 600A0F, 603AAF, 6060AF, 6066AF, 60A0AF, 63AA0F, 6663AF, 66668F, 666AAF, 668A8F, 66AFF9, 68888F, 693AAF, 7007B7, 70404D, 70770B, 70770D, 707BE7, 70DD0D, 733339, 733699, 74004D, 74040D, 77007B, 770CCB, 777B4D, 777BE7, 777CCB, 77ACCB, 77B74D, 77D0DD, 7A0CCB, 7B744D, 7CACCB, 7DDD99, 80044D, 800807, 80200D, 8044ED, 80C04D, 80CC2D, 80E44D, 8404ED, 84888D, 84E04D, 84E40D, 86686F, 8668AF, 8686AF, 86F66F, 86FFFF, 87000D, 87744D, 880807, 886AFF, 88824D, 88870D, 888787, 88884D, 88886F, 88887D, 88888D, 888C4D, 888FAF, 88AA8F, 88CC8D, 88F6AF, 88F8AF, 88FA8F, 88FF6F, 88FF87, 88FFAF, 8A8FFF, 8C0C2D, 8C802D, 8CCFFF, 8CE00D, 8CE0CD, 8CFCCF, 8E00CD, 8E044D, 8E0CCD, 8EC0CD, 8F68AF, 8F88F7, 8FCFCF, 8FF887, 8FFCCF, 8FFF6F, 9002E1, 9004AB, 9008A1, 900919, 900ABB, 900B21, 90B801, 90CCCB, 9332E1, 944441, 94ACCB, 990001, 9900A1, 9A4441, 9A4AA1, 9AA4A1, 9AAA41, 9AAAAF, 9B66C9, 9BBA0B, 9BC0C9, 9BC669, 9BC6C9, 9C4ACB, A0094B, A00ECB, A09441, A0A08F, A0E0CB, A0ECCB, A0F669, A40A05, A4AAA5, A50E41, A5AA45, A60069, A8FAFF, A9AA41, AA5E41, AAA4A5, AAA545, AC6669, ACCC4B, ACCCC9, AEAA41, AFF405, AFF669, AFFA45, AFFFF9, B00921, B00BEB, B00CC9, B00D91, B08801, B0D077, B70077, B70E77, B77E77, B88877, B88881, B94421, BAE00B, BB00AB, BB0DA1, BB444D, BB44D1, BB8881, BBBBBD, BBBC4D, BBCCCD, BC0CC9, BC66C9, BCC669, BCC6C9, BCCC09, BE000D, BE00BD, BE0B4D, BE0CCD, BEA00B, BECCCD, C0084D, C00A0F, C0608F, C0668F, C0844D, C0A0FF, C0AFF9, C0C3AF, C0C68F, C0CAAF, C0CDED, C0D0ED, C0E80D, C0EC2D, C0EC8D, C0FA0F, C0FAAF, C2CC63, C30CAF, C333AF, C3CAAF, C3CCAF, C4048D, C40D4D, C4404D, C4408D, C4440D, C44DDD, C4ACCB, C4DCCB, C4DD4D, C6068F, C66AAF, C68AAF, C6AA8F, C8044D, C8440D, C8666F, CA00FF, CA0FFF, CAAAAF, CAAFFF, CAFF0F, CBE0CD, CC008F, CC0C8F, CC3CAF, CC4ACB, CC608F, CC66AF, CCBECD, CCC4AB, CCCA0F, CCCC8F, CCCE8D, CE0C8D, CF0F23, CF0FAF, CFAFFF, CFCAAF, CFFAFF, D0005D, D00BA9, D05EDD, D077D7, D10CCB, D22207, D4000B, D4040D, D4044D, D40CCB, D70077, D7D00D, D90009, D900BB, DB00BB, DB4441, DD400D, DDD109, DDD1A9, DDD919, DDD941, DED00D, E00D4D, E00EEB, E0AAE1, E0AE41, E0AEA1, E0B44D, E0BCCD, E0BEBB, E0D0DD, E0E441, E4048D, E4448D, E800CD, E8200D, EA0E41, EAA0E1, EBB00B, ECCCAB, EDDDDD, EEBE0B, F00263, F0056F, F00A45, F02C63, F03F23, F05405, F060AF, F08585, F0A4A5, F0F2C3, F0F323, F2CCC3, F33203, F33C23, F5F66F, F5FF6F, F68CCF, F6AA8F, F888AF, FA0F45, FAA045, FAA545, FAFC69, FC0AAF, FC66AF, FCCCAF, FCFFAF, FF0323, FF056F, FF3203, FF7903, FFA045, FFA4A5, FFAA45, FFC0AF, FFF4A5, FFF575, FFFA45, FFFCAF, 10A009B, 20000D1, 2CCC663, 30A00FF, 30CCCAF, 30FA00F, 30FCCAF, 3333C23, 333C2C3, 33C3AAF, 33FCAAF, 33FFFAF, 3A0A00F, 3AAAA0F, 3AF000F, 3AFAAAF, 3C0CA0F, 3CCC3AF, 3CFF323, 3F33F23, 3FAA00F, 3FF3323, 4004441, 400DDD1, 400E00D, 400ED0D, 404404D, 404448D, 404E4DD, 440EDDD, 4440EDD, 44444ED, 4444E4D, 44DDDDD, 4A000A5, 4CCCCAB, 4D0CCCB, 4E4404D, 4E4444D, 4E4DDDD, 5000021, 5004221, 5006AAF, 500FF6F, 5042201, 508CCCD, 5400005, 5400AA5, 5555405, 5808007, 5AA4005, 5C0008D, 5CCC8CD, 5D4444D, 5EEEEEB, 5F40005, 5F554A5, 5F6AAAF, 60000AF, 60006A9, 600866F, 6008AAF, 600AA8F, 600F6A9, 606608F, 606686F, 608666F, 60AA08F, 60AAA8F, 66000AF, 66666A9, 6666AF9, 6866A8F, 6AAAAAF, 70070D7, 70077DD, 700DDDD, 707077D, 707D007, 70D00DD, 770077D, 770400D, 770740D, 7777775, 77777B7, 77777DD, 7777ACB, 77B88E7, 77DD00D, 77DDDDD, 7D0D00D, 7DD0D07, 7DDD00D, 800002D, 8000CED, 80C0E0D, 80CECCD, 840400D, 844000D, 844E00D, 868688F, 880444D, 884404D, 887D007, 8888801, 8888881, 8888E07, 8888F77, 8888FE7, 88A8AFF, 88AAAFF, 88FAFFF, 8A8AAAF, 8A8AAFF, 8AAA8FF, 8C00ECD, 8C8444D, 8E4400D, 8FCCCCF, 900BBAB, 90CC4AB, 9908AA1, 99E0E01, 9B00801, 9B6CCC9, A000FF9, A006069, A00A8FF, A01CCCB, A05F545, A0BEEEB, A0E4AA1, AA0008F, AA08FFF, AA40AA5, AA8FFFF, AAAA405, AE04AA1, AE44441, AE4AAA1, AECCCCB, AF40005, AFA5A45, AFFFC69, B000BAB, B000EBB, B0D0007, B222227, B6CCCC9, B8880A1, BA000EB, BA0BEEB, BAEEEEB, BB000CD, BB00C0D, BB0B00D, BC6CC69, BC6CCC9, BCCCC69, BCCCCED, C0000A9, 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4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444DD ===Base 17=== 12, 16, 1C, 1E, 23, 27, 29, 2D, 32, 38, 3A, 3G, 43, 45, 4B, 4F, 54, 5C, 5G, 61, 65, 67, 6B, 78, 7C, 81, 83, 8D, 8F, 94, 9A, 9E, A3, A9, AB, B4, B6, BA, BC, C7, D2, D6, D8, DC, E1, E3, ED, F2, F8, FE, FG, G5, G9, GB, 104, 111, 115, 117, 11B, 137, 139, 13D, 14A, 14G, 155, 159, 15F, 171, 17B, 17D, 188, 191, 197, 19F, 1A4, 1A8, 1B3, 1BB, 1BF, 1DB, 1DD, 1F3, 1FD, 1G8, 1GA, 1GG, 20F, 214, 221, 225, 241, 25A, 25E, 285, 2B8, 2C5, 2CF, 2E5, 2EB, 2F6, 30E, 313, 331, 33B, 346, 34C, 351, 35F, 36E, 375, 37B, 391, 39B, 39D, 3B7, 3B9, 3BF, 3D3, 3D5, 3D9, 3DF, 3E4, 3EC, 3F1, 3F7, 407, 418, 447, 44D, 472, 474, 47E, 47G, 489, 49C, 4A1, 4C1, 4CD, 4D4, 4G1, 502, 506, 508, 50E, 519, 522, 528, 52A, 52E, 533, 53F, 551, 55D, 562, 566, 573, 577, 57F, 582, 593, 599, 59B, 59F, 5A6, 5B5, 5D1, 5D3, 5EA, 5EE, 5F9, 60D, 62F, 634, 649, 689, 692, 6CD, 6EF, 6F4, 6FA, 704, 706, 70G, 71D, 726, 737, 739, 73D, 73F, 753, 755, 764, 766, 76G, 771, 77B, 793, 7AA, 7AE, 7B3, 7BB, 7D7, 7E6, 7F3, 7F9, 7FF, 7G2, 7GE, 7GG, 825, 82B, 849, 852, 85E, 869, 876, 87A, 87G, 88B, 892, 898, 89C, 8C5, 8E7, 8G7, 908, 90G, 913, 91F, 92C, 935, 937, 93B, 951, 953, 957, 95D, 968, 96G, 979, 97B, 98C, 98G, 99D, 9B1, 9B3, 9B9, 9BD, 9BF, 9DB, 9DF, 9F1, 9F5, 9G6, A07, A0D, A1A, A2F, A4D, A72, A7A, A7E, AA1, AA7, ACF, ADA, AG1, AG7, B02, B08, B17, B1D, B28, B2G, B57, B71, B73, B79, B7F, B88, B8E, B8G, B9B, B9F, BB5, BB7, BD7, BDD, BEG, BFF, BGG, C01, C2F, C3E, C56, C6D, C89, C92, C9G, CA5, CBG, CC1, CC5, CF4, CFA, D04, D0A, D15, D3D, D3F, D55, D59, D5B, D71, D75, D7D, D91, D97, D99, D9D, DA4, DAG, DB3, DDB, DF1, DF7, DF9, DFF, E05, E0B, E2B, E52, E58, E69, E92, E9C, EAF, EB8, EC9, ECB, EE5, F04, F15, F1B, F35, F3B, F46, F51, F53, F64, F6A, F73, F79, F95, FAC, FB1, FCA, FD5, FDB, FF1, FF7, FFD, G0D, G0F, G18, G1A, G1G, G2F, G34, G63, G7G, GA7, GC3, GDG, GEF, GFA, GG7, GGD, 1013, 101D, 1033, 1035, 1051, 105B, 105D, 1077, 108A, 109B, 10AG, 10B1, 10B7, 10BD, 10FB, 1149, 1189, 11AF, 11G3, 1303, 130B, 1314, 1341, 1479, 14D9, 1501, 1503, 15A1, 15B8, 1734, 1749, 17AF, 17G3, 1844, 185B, 1875, 1877, 18AG, 18B5, 1903, 1909, 1958, 19BG, 19G3, 1A5D, 1A75, 1A7F, 1ADF, 1AF1, 1B01, 1B09, 1B18, 1B85, 1B89, 1BDG, 1BGD, 1D07, 1D49, 1D9G, 1DF4, 1F09, 1F47, 1F5A, 1F74, 1F7A, 1FA1, 1FAF, 2018, 201G, 202B, 208B, 20G1, 215B, 218G, 21AG, 21B1, 222F, 22AF, 22BG, 22EF, 22F4, 22GF, 251B, 2526, 25F1, 266F, 26FC, 280B, 2A05, 2A58, 2AFC, 2AGF, 2B1B, 2B1F, 2BGE, 2C1G, 2C2B, 2C8B, 2CG1, 2E2F, 2EGF, 2F0C, 2F55, 2FAA, 2FC4, 2FFF, 2GA1, 2GFC, 2GG1, 2GGF, 301B, 301F, 3037, 3053, 3057, 3079, 3095, 30B3, 30BD, 30C4, 31F4, 330D, 3334, 333E, 3349, 3376, 337E, 33CD, 33EF, 3411, 3417, 3499, 3503, 3505, 3509, 353E, 35E5, 35EB, 3604, 36FD, 3701, 3741, 374D, 376F, 3796, 37D4, 37F4, 3956, 3B03, 3B05, 3B0B, 3BBE, 3C04, 3C15, 3C19, 3C4E, 3C59, 3C64, 3CB3, 3CDB, 3CE6, 3D07, 3D14, 3DDE, 3E77, 3E79, 3E7F, 3E99, 3EEE, 3EFB, 3F05, 3F0D, 3FCB, 3FF4, 4009, 4021, 4069, 4098, 40DG, 40GD, 419D, 4201, 4401, 4492, 46AD, 46C9, 46DA, 4719, 476A, 4779, 479D, 47A6, 4906, 4911, 4917, 4919, 491D, 492G, 4982, 4988, 49D7, 49D9, 49GG, 4ADE, 4AE7, 4C49, 4C96, 4CC9, 4D79, 4DAE, 4DEG, 4E7A, 4E96, 4EG7, 4G6D, 4G87, 501B, 5037, 5059, 507D, 50BB, 50BF, 50D7, 50DD, 50F1, 5105, 51A7, 51AD, 521B, 525F, 52FB, 5307, 5356, 53BE, 53DE, 53E9, 5507, 550B, 5587, 5598, 55EF, 560A, 568E, 56AA, 56F3, 5709, 5725, 572B, 575A, 575E, 5769, 57A1, 57B2, 5868, 586E, 58AE, 58B9, 590D, 5918, 5952, 5958, 596D, 5A17, 5A1F, 5ADD, 5ADF, 5AE8, 5B07, 5B21, 5B2F, 5B3E, 5BEF, 5DA7, 5DEB, 5E57, 5E5F, 5E86, 5E97, 5EB9, 5EBF, 5EF5, 5F01, 5F1A, 5F6F, 5FA7, 5FDA, 60AF, 60G3, 64AD, 64DE, 64DG, 663E, 666D, 66AF, 693D, 69CG, 69D3, 69D9, 69G8, 69GC, 6ADE, 6AGD, 6C98, 6D33, 6D4E, 6D93, 6D9F, 6DDD, 6DEE, 6DF3, 6DFD, 6DGE, 6E09, 6G36, 6G4D, 6G6D, 6GD4, 6GDE, 6GFC, 702E, 7057, 705B, 7073, 7079, 7095, 70B5, 70BD, 70D1, 70E2, 70F5, 7107, 7149, 719G, 71BG, 71F4, 724E, 724G, 725F, 72A2, 72BF, 72EE, 72GA, 7314, 733E, 7341, 7363, 73EB, 7419, 742A, 742G, 7442, 74EG, 7501, 750F, 751A, 756D, 757E, 75A1, 75A7, 75BE, 75DA, 75E9, 75F6, 7622, 769F, 76EA, 7734, 773E, 776D, 779G, 77AF, 7905, 790B, 7976, 79B2, 79F6, 79GD, 7A1F, 7A5D, 7AD5, 7ADF, 7AF1, 7AFD, 7B01, 7B09, 7B2F, 7B52, 7B72, 7BE5, 7D01, 7D05, 7D9G, 7DAF, 7DBG, 7E0A, 7E75, 7EA2, 7EA4, 7EB5, 7EBF, 7EE2, 7EF7, 7EG4, 7F0B, 7F14, 7F5A, 7F76, 7FA7, 7G1F, 7G46, 7GA6, 7GD3, 7GDF, 8009, 8058, 80B8, 80E9, 84A7, 850A, 8557, 857B, 85A8, 870E, 8744, 8777, 879B, 87B5, 87B7, 87EE, 8805, 8872, 8887, 8889, 88E9, 8906, 8959, 8966, 89GG, 8A87, 8AE5, 8B0G, 8B59, 8B95, 8B97, 8CB2, 8CB8, 8CE9, 8E56, 8EE9, 9026, 9031, 903D, 907F, 9091, 909B, 90FB, 9101, 910D, 9118, 917G, 9185, 9189, 91B8, 9202, 9288, 92B5, 92FB, 92GG, 93C1, 9505, 950B, 950F, 952B, 956F, 9592, 9596, 9598, 9602, 96D9, 96FD, 971G, 9725, 9752, 97DG, 9855, 9862, 9895, 9899, 98B7, 98BB, 9901, 990B, 9921, 992F, 99G3, 9B0B, 9B2B, 9B8B, 9BB8, 9BBG, 9C19, 9C1B, 9C31, 9C59, 9C95, 9CD5, 9CFB, 9CGC, 9D03, 9D07, 9D7G, 9DG1, 9DGD, 9F0B, 9F76, 9FCB, 9G11, 9G1D, 9G28, 9G3F, 9G7D, 9GCC, 9GD7, 9GF7, 9GFD, 9GG8, A025, A041, A058, A0C5, A0F6, A0GF, A11F, A184, A1F7, A21G, A258, A401, A421, A476, A511, A517, A57D, A5A8, A5E8, A6AD, A6FC, A6GF, A751, A77F, A7F5, A7FD, A7G6, A847, AACD, AC1G, AC41, AC58, AC5E, ACGD, AD0E, AD0G, AD1F, AD51, ADD5, ADE4, ADF5, ADGE, AE56, AE74, AEF6, AEFA, AF77, AF7D, AFA4, AFCC, AFD7, AFDD, AGAF, AGF4, B00G, B037, B055, B05B, B075, B0D5, B0FD, B10F, B198, B25F, B2F1, B2F5, B307, B309, B35E, B3EF, B50D, B589, B7BE, B7BG, B7E7, B875, B952, B958, B97G, B99G, B9G7, B9GD, BB01, BB2F, BB3E, BB89, BB98, BBDE, BD03, BD09, BD5E, BDE5, BDEB, BDG1, BE5F, BF01, BF0D, BG13, BG1F, BG3F, BGD1, BGE2, BGE8, C00B, C034, C05A, C0AF, C0EF, C0GF, C153, C15B, C199, C1B9, C1D1, C1D5, C1F9, C205, C21A, C21G, C252, C258, C2B2, C335, C33D, C35D, C364, C395, C3B3, C3F5, C3FB, C3FD, C414, C41A, C469, C496, C4DA, C4GD, C535, C55B, C5B1, C5BD, C5D9, C5DF, C5E8, C5F3, C5F5, C6E9, C85A, C885, C8B8, C8BE, C8CB, C8E5, C919, C931, C959, C95F, C9D3, CA0F, CA18, CA1G, CAD4, CADE, CAEF, CAGD, CB22, CB33, CB35, CB3F, CB5D, CB82, CB99, CBB1, CBFB, CC49, CCCB, CCDE, CD11, CD1D, CD39, CD4A, CD53, CD93, CDAE, CDD5, CDF3, CDFD, CDG4, CE49, CE5A, CE8B, CF13, CF19, CF5D, CF5F, CFB9, CFBF, CFD9, CFDF, CG14, CG41, CG6F, CGCF, CGF6, CGG1, D01F, D039, D079, D09B, D09F, D0B7, D0BB, D0D1, D0EG, D0GG, D10D, D19G, D1G3, D30B, D347, D3BE, D4E4, D50D, D57E, D5AD, D5FA, D707, D73E, D7E7, D7GF, DA1F, DA57, DAAE, DB01, DB09, DB0D, DB7E, DB9G, DD05, DD7E, DDA5, DDFA, DDG3, DE0G, DE44, DE4A, DE77, DEAE, DEB9, DEBB, DF03, DF05, DG0E, DGDF, E009, E06F, E072, E07G, E089, E0CF, E0E9, E0G7, E47A, E498, E4E7, E50A, E559, E55F, E575, E5B9, E5BF, E5F5, E5F7, E6FC, E722, E724, E72A, E72E, E744, E746, E75B, E76E, E79B, E7A4, E7A6, E7AG, E7B5, E7B7, E7EG, E7G4, E887, E89G, E8E9, E906, E955, E95B, E95F, E988, E99F, E9F9, E9G8, E9GG, EA25, EA7G, EAC5, EAE7, EB7B, EBF5, EBF7, EBFB, EC6F, ECCF, ECEF, EE72, EE76, EE89, EE9G, EF0A, EF44, EF77, EF97, EFA4, EFB5, EFC6, EFFF, EG6F, EG74, EGE7, EGFC, EGGF, F019, F01F, F075, F091, F09B, F0BF, F0FB, F10F, F1A7, F1AD, F1D4, F376, F3CD, F3F4, F40A, F411, F444, F44A, F497, F499, F49D, F4D7, F509, F57A, F5AD, F5F6, F6D3, F6D9, F70D, F741, F747, F76D, F7F6, F7FA, F907, F976, F9CB, FA11, FA7D, FADD, FB09, FC4C, FC5D, FC5F, FC91, FCB9, FD1A, FD41, FD47, FDF4, FF0B, FF56, G021, G07A, G0A1, G0E7, G11F, G17F, G1DF, G1F1, G1F7, G201, G2A1, G306, G311, G36C, G377, G37F, G3CC, G3CE, G3D1, G476, G487, G4DE, G6AF, G6D4, G6F6, G6GF, G713, G724, G731, G742, G74E, G76E, G7A2, G872, G874, GA21, GAC1, GC6F, GCAF, GCD4, GCDA, GCG1, GD73, GD7F, GDAE, GDDF, GDEA, GDFD, GE47, GE7E, GF13, GF33, GF3F, GF4C, GF71, GF7F, GFDD, GG01, GG21, GGAF, GGC1, 1000G, 10053, 100AA, 100B9, 100F1, 100FF, 10301, 10587, 10705, 1075A, 107GF, 10895, 108B9, 10985, 1099G, 10B98, 10B9G, 10D03, 10D0F, 10D7A, 10DG3, 10DG7, 10G1F, 10G3F, 110GF, 1140D, 11D93, 11DG4, 11F0A, 11G4D, 11GD4, 13333, 133FF, 13F44, 14109, 14499, 150A7, 153B1, 1570A, 17005, 17799, 177AG, 17995, 17A7G, 17G47, 18079, 18507, 185A7, 18B07, 18B9G, 19333, 199B5, 1A00A, 1A00G, 1A0F5, 1AAAA, 1AAAG, 1AF05, 1AFFA, 1B07G, 1B10G, 1B807, 1D001, 1D1AA, 1D7G4, 1DG03, 1DG41, 1F001, 1F00F, 1F01A, 1F0A7, 1F199, 1F1F9, 1F414, 1F449, 1F7F5, 1F999, 1FF0A, 1FFAA, 1FFB5, 1G073, 1G14D, 1G1F4, 1G301, 1G477, 1GD01, 1GD47, 1GF07, 1GFF4, 20005, 200A1, 2010A, 20586, 20588, 20A01, 20B11, 20B15, 20BEE, 20C1A, 20CBE, 210B5, 21A1F, 21A51, 21F1A, 21G1F, 21GFF, 222BE, 228B2, 228BE, 22BE2, 22C0B, 22F0A, 252BB, 25505, 25552, 26GAF, 2A001, 2A1FF, 2A55F, 2AEEF, 2AF44, 2B051, 2B20E, 2BB2B, 2BBBG, 2BE22, 2BEE2, 2BEEE, 2BF0B, 2C0BE, 2C18A, 2F101, 2F1FA, 2F44C, 2FCBB, 2G1FF, 2GA6F, 2GF44, 30035, 300B1, 300FB, 30101, 303C5, 30444, 30497, 304D1, 304D7, 30703, 30714, 30734, 30763, 30774, 30CF5, 30CFD, 30D41, 30FC5, 3100B, 31779, 31F5B, 31FB5, 31FFF, 330C5, 330F4, 33357, 33373, 33379, 33555, 33557, 33777, 3379F, 337FD, 33997, 33D44, 33D4E, 33F3D, 33FF5, 34019, 34044, 340D1, 353DD, 35535, 355B3, 355E6, 35BB3, 35DDD, 3636D, 364DD, 3663D, 36DD4, 37003, 3700F, 3717F, 373EE, 37609, 3774E, 37773, 37797, 37977, 3797F, 37EEF, 39007, 390C5, 39777, 39973, 3B355, 3B553, 3BBDB, 3BDB1, 3C03D, 3C0F5, 3C10F, 3C141, 3C444, 3CBE5, 3CD0D, 3CE5B, 3CEBB, 3CEF9, 3D401, 3DEBE, 3E006, 3E066, 3E57E, 3E5E9, 3E666, 3E90F, 3EF6F, 3F33D, 3F3C4, 3F5BB, 3FB33, 3FDDD, 3FF59, 4006D, 400DE, 4011D, 401D9, 40414, 4041G, 404C9, 40966, 40D11, 40D19, 40D1D, 40E49, 41019, 411DA, 41AAG, 4210A, 44049, 4410G, 44144, 441G4, 44441, 444E9, 446E9, 44986, 44E49, 4609G, 460E9, 466DE, 469DD, 46E9G, 4711A, 476D9, 4770D, 47A77, 47D09, 49099, 490D1, 49226, 49622, 49699, 496DD, 49996, 4999G, 499G7, 49G22, 49G77, 4A7DD, 4AA6D, 4ADD7, 4C0E9, 4C999, 4D1DA, 4DADD, 4DD01, 4DD1G, 4DD7A, 4DDA7, 4DDE9, 4DG0G, 4DGAA, 4DGGA, 4DGGE, 4E049, 4E449, 4E49G, 4E4E9, 4E797, 4G7DD, 4GDAA, 4GDD7, 50011, 50079, 50095, 500B1, 500F3, 501A5, 501AF, 50503, 507A5, 50AF7, 50F03, 50F7A, 510A1, 510DA, 511AA, 511DF, 5135B, 515B7, 5180B, 51A0F, 51F0A, 520B1, 53005, 531BD, 53559, 53609, 53B11, 55205, 55357, 553E6, 5555B, 5556E, 55588, 5558A, 555F3, 555FB, 556AF, 556E9, 55759, 5575B, 55805, 55885, 55896, 558B8, 55926, 55BE2, 55E8B, 55F57, 560FF, 5700D, 570A5, 570DA, 575B9, 576AD, 576DA, 579D5, 57A05, 57A52, 57B9D, 57DBD, 58057, 58509, 5855A, 585A7, 587EB, 58857, 588E8, 58A75, 58B0B, 58B87, 58BBE, 58BEB, 58E5B, 591D5, 59201, 59256, 59715, 59807, 5A88A, 5AA88, 5AFAD, 5B001, 5B00B, 5B1F1, 5B31B, 5B7E2, 5B80B, 5BB13, 5BBE8, 5BBFB, 5BE87, 5BE8B, 5BF37, 5BFBD, 5D00F, 5DA05, 5DA5A, 5DAE5, 5DBBD, 5DD95, 5DDAA, 5DFDD, 5E879, 5E8B7, 5E8BB, 5F07A, 5F0AD, 5F37D, 5F70A, 5F7BD, 5FB7B, 5FBBB, 5FBF3, 5FFF3, 6003E, 60098, 603E6, 606GF, 60986, 609C8, 60G6F, 60GCF, 6336D, 633E9, 63CCE, 63E06, 63E66, 6609G, 660E9, 66AD4, 66D4A, 66DG4, 66DGG, 66E98, 66FD9, 66GF6, 69806, 69866, 69C86, 69CC8, 6A66F, 6AAGF, 6AF06, 6AF66, 6AGGF, 6C6G3, 6C6GF, 6CCGF, 6CG03, 6DA0E, 6DAEA, 6DD9G, 6DDE9, 6DEGA, 6DGD3, 6E986, 6EEE9, 6F69D, 6F6DF, 6F96D, 6FD03, 6FD09, 6G003, 6G3F3, 6G3FF, 6G6CF, 6GAAF, 6GCCF, 70031, 70099, 700BF, 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777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777F ====Additional known quasi-minimal primes (not necessarily the next)==== 570₅₁₃₁₀1, 49₁₁₁₃₃₃, 970₁₆₆₀₄₇1, F70₁₈₆₇₆₇1 ===Base 18=== 11, 15, 1B, 1D, 21, 25, 27, 2B, 2H, 35, 37, 3D, 3H, 41, 47, 4B, 4H, 57, 5B, 5D, 5H, 61, 65, 71, 75, 7B, 7D, 85, 87, 8D, 91, 95, 9B, 9H, A1, AB, AD, AH, B1, BD, C7, CB, CD, CH, D5, D7, DH, E5, EB, EH, F1, F7, FB, FD, G5, H1, H5, H7, HB, 107, 167, 16H, 177, 17H, 1G7, 1HH, 20D, 24D, 26D, 29D, 30B, 36B, 381, 3BB, 405, 445, 44D, 49D, 4A5, 4DD, 4F5, 4GD, 501, 545, 5E1, 607, 62D, 64D, 66B, 66H, 67H, 68B, 697, 6A7, 6BB, 6E7, 6G7, 6GB, 6HH, 767, 76H, 77H, 797, 7HH, 801, 80H, 831, 83B, 86B, 88H, 8BB, 8FH, 8GH, 94D, 96D, 977, 9DD, 9ED, 9GD, A77, AC5, AE7, B07, B0H, B55, B77, B8B, B97, BB5, BB7, BBH, BE7, BFH, BGB, C01, C31, CA5, CG1, D2D, D4D, D81, DBB, DD1, DDB, DGD, E0D, E17, E31, E4D, E67, E6D, EA7, EDD, EE1, EED, EG7, F0H, F45, F8H, FC5, FFH, G0D, G17, G2D, G6B, G6H, GBB, GBH, GD1, GDD, GE1, GE7, GED, GFH, GG7, GGB, GHD, GHH, H0D, H2D, H8H, H9D, HGH, HHD, 100H, 19E7, 1A97, 1EE7, 1G8H, 1GGH, 22ED, 22GD, 2DED, 2E2D, 3001, 3031, 30C1, 30E1, 3331, 33G1, 3CC1, 40ED, 45C5, 46ED, 4CC5, 5331, 5551, 55G1, 5C05, 608H, 60ED, 60FH, 60HD, 666D, 66ED, 699D, 6B67, 6BGH, 6D0D, 6DDD, 6E9D, 6EGD, 6G0H, 6G9D, 6HGD, 700H, 70A7, 7A07, 7FGH, 7G77, 808B, 8881, 88G1, 88GB, 8BHH, 8EG1, 8GC1, 8H6H, 900D, 90E7, 90G7, 9667, 9907, 999D, 99E7, 9A67, 9A97, 9E97, 9EE7, 9G07, 9G67, 9GA7, AA45, AA97, AGA7, B005, B03B, B06B, B0C5, B60B, B63B, BAA5, BAA7, BCC5, BFA5, BG8H, C045, C055, C555, C5C1, C5F5, CC05, CC81, CCC5, D06D, D09D, D0ED, D38B, D3E1, D60D, D6DD, D8GB, DD6D, DE9D, DG01, E001, E097, E0G1, E8C1, EDC1, EE97, EGC1, EGG1, EGGD, FH6H, G007, G00B, G00H, G03B, G067, G097, G0C1, G0G1, G1GH, G33B, G38B, G3G1, G70H, G777, G88B, GA67, GAA7, GG81, GGC1, GGGH, H0FH, H66D, HEGD, HFHH, 1AAA7, 222DD, 30GG1, 3388B, 33E01, 38G8B, 3G3C1, 3GGG1, 4002D, 500C5, 50C55, 50CF5, 53GG1, 558C1, 55CC5, 55CF5, 58GG1, 5C8C1, 5CFF5, 5G881, 5GG31, 6000H, 6003B, 6006D, 600DB, 6033B, 606GD, 60D0B, 66GGD, 6D03B, 6D33B, 6H6DD, 6HD6D, 6HDED, 70G07, 70GGH, 777A7, 7AAG7, 7G0GH, 80G0B, 8888B, 8CCE1, 90067, 90097, 9022D, 99967, 99997, 9A007, 9A0A7, 9AA07, 9AAA7, 9E007, A0045, A0455, A0667, A09G7, A0A07, A0G07, A0G97, A9997, AA0A7, AAG67, B0AF5, B6GGH, B7GGH, B8HHH, BA045, BAF05, BG667, C0F05, C5005, C5581, C88C1, C8CC1, C8CE1, CCF55, D03C1, D060B, D080B, D0CC1, D0G0B, D0G8B, D3G3B, D600B, DDDED, DG331, DG80B, E8G81, E9007, F6GGH, G018H, G0301, G0331, G466D, G6667, G66GD, GD08B, GG18H, GG6GD, GGG4D, H060H, HGGGD, HHH6H, 199AA7, 40006D, 40600D, 46600D, 5055C5, 5505C5, 55CCC1, 588CC1, 58CCC1, 60000D, 60009D, 7077G7, 7707G7, 777G07, 88000B, 9099A7, A000A7, A009A7, A09067, A099A7, A0AAA7, A90AA7, A99AA7, AA0007, AA6667, AAAG07, BFFF05, BFFFF5, C0FFF5, CCECC1, CECCC1, CF0FF5, CFF005, D0008B, D0033B, D0088B, D0333B, D033GB, D03G31, D0633B, DD990D, DGGG31, FHHHHH, G00081, G6GGGD, G8GGG1, GGG001, GGG331, GGGGG1, GGGGGD, H0006H, H00H6H, HH600H, 222222D, 22DDDDD, 333333B, 5CCCCC1, 70007G7, 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CDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD, 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71D, 73D, 73H, 73J, 75B, 75H, 768, 77H, 77J, 7B1, 7B5, 7BB, 7BD, 7C8, 7D1, 7DB, 7DD, 7E8, 7F5, 7FB, 7H5, 7HD, 7HH, 7HJ, 7J5, 7JD, 801, 80J, 832, 841, 86H, 86J, 881, 89G, 8E1, 8F4, 8F8, 8FA, 8FK, 8H4, 8IH, 8J4, 8JG, 90K, 91B, 91D, 91H, 93H, 93J, 955, 95H, 95J, 96G, 97B, 97D, 97H, 991, 99J, 9B1, 9BB, 9BH, 9BJ, 9CK, 9D1, 9DB, 9DH, 9DJ, 9EK, 9F5, 9FD, 9H1, 9HB, 9HD, 9IG, 9J5, 9KK, A0B, ABG, AF4, AF8, AG5, B15, B1H, B35, B3H, B3J, B4G, B51, B5B, B5D, B5H, B6G, B71, B75, B7B, B7D, B9B, B9J, BB5, BBH, BBJ, BC4, BCG, BF1, BF5, BFD, BH1, BHJ, BI4, BJB, C2D, C9K, CCD, CDG, CID, D0G, D2G, D35, D3B, D3H, D51, D55, D5B, D5D, D5J, D62, D71, D7H, D91, D95, D9H, DBH, DC2, DD1, DD5, DE2, DEG, DF5, DFJ, DH1, DHB, DI2, DJ1, DJB, DJJ, E14, E4B, E5K, E78, E81, E9G, EA5, EBG, EC1, EE1, EE5, EK5, F04, F11, F1H, F31, F3B, F3D, F44, F4A, F4K, F5D, F5H, F6K, F71, F7H, F7J, F88, F8A, F8K, F9J, FA4, FA8, FBB, FBH, FC4, FDB, FDJ, FE8, FFH, FFJ, FH5, FHB, FHJ, FI4, FI8, FIK, FJ5, FJD, FK4, FK8, G32, G5G, G78, G8J, 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====Additional known quasi-minimal primes (not necessarily the next)==== 40₄₇₃₃₃9G, CF₄₇₉₁₄₇0K ===Base 22=== 11, 17, 19, 1F, 1J, 1L, 23, 29, 2F, 2H, 31, 35, 37, 3D, 3H, 41, 49, 4D, 4F, 4J, 4L, 53, 5H, 5L, 65, 67, 6H, 6J, 73, 79, 7D, 7J, 83, 85, 8F, 8H, 8L, 91, 9D, A3, A7, A9, AD, AJ, AL, B9, BF, BL, C5, C7, CD, CH, CJ, D7, DL, E3, E5, E9, F1, F7, FH, FJ, G1, G7, GF, GL, H5, H9, HF, I1, I5, ID, J1, J3, JD, JF, JL, K3, K9, KH, KL, L1, L5, LH, 103, 12D, 145, 155, 15D, 163, 18D, 1A5, 1BD, 1BH, 1C3, 1D3, 1DH, 1EH, 1G3, 1GH, 1I3, 1K5, 1KD, 221, 227, 22J, 22L, 245, 247, 25D, 25J, 271, 277, 287, 28J, 2A5, 2B7, 2BD, 2BJ, 2D5, 2E1, 2E7, 2ED, 2EL, 2K1, 2KJ, 2LL, 30J, 343, 389, 39J, 3B3, 3GJ, 3IJ, 3J9, 3JJ, 3KF, 3LJ, 427, 443, 445, 457, 4A5, 4C3, 4E7, 4G5, 4I7, 4K5, 4K7, 515, 52D, 551, 559, 55D, 55J, 575, 58D, 59F, 5B1, 5C9, 5CF, 5D1, 5D5, 5DD, 5E1, 5ED, 5G5, 5GJ, 5J5, 5JJ, 5K1, 5KJ, 60D, 61D, 62L, 661, 66D, 689, 6C1, 6D1, 6DD, 6G3, 6KF, 701, 721, 751, 76L, 775, 77F, 77H, 787, 7A5, 7AF, 7B1, 7B7, 7CL, 7E1, 7FF, 7FL, 7H7, 7HH, 7K5, 809, 81D, 821, 827, 82D, 847, 869, 871, 881, 889, 899, 8A1, 8BD, 8BJ, 8D1, 8DJ, 8GJ, 8J7, 907, 90H, 92L, 93J, 943, 947, 95F, 977, 997, 9AF, 9B5, 9EF, 9F5, 9H3, 9HL, 9I7, 9J9, 9JJ, 9K5, A25, A45, A51, A61, A6F, AAH, AB5, ABH, ACF, AG5, AGH, AHH, AK1, B15, B2D, B2J, B33, B45, B47, B57, B71, B75, B81, B87, B8J, BB3, BB7, BC3, BDD, BE7, BEJ, BGD, BGH, BH3, BHD, BHJ, BIH, BJ7, BKJ, CA1, CAF, CB3, CC1, CEF, CG3, CKF, D09, D0J, D13, D21, D33, D39, D3F, D4H, D5J, D63, D81, D8D, DAH, DBD, DBH, DBJ, DCF, DD3, DEJ, DFF, DG9, DGH, DHD, DI3, DIF, DJ9, DK1, DK5, E0F, E0H, E27, E2D, E2L, E47, E7H, E87, E8J, EA1, EAH, EB1, EDH, EEJ, EFF, EFL, EH1, EIF, EIL, EJH, EJJ, EKD, ELF, F25, F43, FB5, FD3, FDD, FDF, FEF, FEL, FFD, FG9, G09, G0D, G25, G3J, G5D, G5J, G63, G8D, G99, GC3, GC9, GD9, GEH, GG5, GJ5, GJ9, GJH, H03, H1D, H21, H2J, H2L, H33, H63, H77, H8J, HCL, HDD, HE1, HE7, HGH, HGJ, HH7, HHL, HI3, HIH, HJH, HK1, HKD, HL3, I07, I0J, I43, I47, I7L, I9J, IBH, IEL, IG3, 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7KC1, 7L27, 7LCF, 7LK7, 802J, 80B1, 80GD, 80JJ, 80KJ, 820J, 86E1, 880D, 882J, 88E7, 88I7, 892J, 89EJ, 8B61, 8BI7, 8CI9, 8CK1, 8D6D, 8DD9, 8DGD, 8E01, 8E07, 8EE1, 8EI7, 8EK1, 8EKJ, 8I77, 8I87, 8IC9, 8IK7, 8J0J, 8K6D, 8KI7, 8KIJ, 8KK7, 9025, 9055, 9089, 9275, 92EJ, 92G5, 92GJ, 93EL, 9455, 9505, 9557, 9599, 96B3, 970L, 976F, 97G5, 982J, 98E7, 98I9, 98K7, 9905, 990J, 9925, 9995, 999H, 99BH, 99EL, 99G9, 99GJ, 99LJ, 9A55, 9B03, 9B27, 9BGJ, 9BH7, 9BK7, 9CG9, 9E6L, 9EHJ, 9EKJ, 9ELL, 9G39, 9G45, 9G4H, 9GA5, 9GAH, 9GBJ, 9GEJ, 9GHH, 9GHJ, 9GI9, 9GIJ, 9H7H, 9H87, 9HAH, 9HB7, 9I89, 9I9H, 9IB3, 9IEH, 9IKF, 9J7H, 9J87, 9JB7, 9JGH, 9K0F, 9K27, 9KGJ, 9KKF, 9L89, 9L9J, 9LG9, 9LGJ, 9LIJ, 9LKF, A081, A14H, A1IH, A201, A2C1, AA15, AA81, AAIF, ABC1, AC01, AHC1, AIIF, AKEF, B005, B01D, B01H, B051, B05D, B0A5, B0B1, B0BJ, B0DH, B0E1, B0GJ, B0H1, B0JH, B143, B16D, B255, B2B5, B2C1, B2G5, B2K7, B4EH, B4G3, B501, B5A5, B5BJ, B5C1, B5IJ, B5K5, B621, B663, B6I3, B6K1, B777, B7I7, B80D, B88D, B8ED, B8KD, BB01, BB0J, BB21, BB25, BB4H, BB6D, BBD5, BBE1, BBEH, BBH1, BBIJ, BBJH, BCK1, BD61, BDB5, BDGJ, BEE1, BG55, BGB5, BGGJ, BGIJ, BH27, BH7H, BHC1, BHH1, BHK7, BI77, BIGJ, BJ0H, BJBH, BJIJ, BJJJ, BK25, BK27, BK55, BKA5, BKK1, C043, C143, C2B1, C32L, C3G9, C601, C6EL, C6G9, C8B1, CBK1, CC2L, CC89, CE21, CECL, CF2L, CF89, CG69, CIG9, D003, D015, D045, D05D, D06D, D06F, D0DH, D0H1, D1D5, D1GD, D205, D26D, D2DJ, D32J, D38J, D403, D525, D561, D56D, D5AF, D5F5, D5GD, D6C9, D6D9, D6DF, D6E1, D6ED, D6F9, D6FD, D8IJ, D8JJ, D945, D993, D99F, D9C9, D9F3, D9G5, D9KJ, DA15, DAA5, DAE1, DAKF, DB25, DB61, DBC1, DBG3, DC43, DC99, DCE1, DD0F, DD1D, DD2D, DD2J, DD5D, DD9H, DDA5, DDD5, DDDJ, DDED, DDH1, DDHJ, DDI9, DDJ5, DE0D, DED1, DEDF, DEFD, DF03, DF45, DF55, DF5D, DF6D, DG05, DGGJ, DH0H, DH43, DHC1, DHEH, DHH3, DHJJ, DI8J, DIC9, DII9, DIJH, DJG5, DJHJ, DJKJ, DK6D, DKAF, DKDD, DKGD, E081, E0BJ, E0DD, E0DJ, E0E1, E0ED, E0J7, E0K7, E0KJ, E1GD, E1IH, E201, E281, E66F, E6BD, E6ED, E6K1, E6LL, E7EF, E861, E86D, E88D, EB0D, EB4H, EBHH, EBI7, EC6F, ECEL, ED0D, ED1D, ED6D, EDAF, EDDD, EDFD, EE01, EE0D, EE1H, EE21, EECF, EEE1, EEGH, EEH7, EF8D, EGGD, EGHH, EGIH, EGIJ, EH07, EH0L, EH8D, EHBH, EHBJ, EHK7, EHL7, EI4H, EIK7, EIKJ, EJ77, EK07, EK0J, EKC1, EKIJ, EKK1, EKK7, EL6L, ELBD, ELCL, ELDJ, ELK7, F059, F20L, F26L, F28D, F2GD, F2KD, F32L, F3AF, F3G3, F455, F56F, F595, F5KD, F6AF, F6GD, F88D, F8I9, F955, F995, F9B3, F9G3, F9KF, FB03, FB8D, FBI3, FC89, FD99, FDA5, FDI9, FEGD, FF59, FG2D, FGI3, FGKD, FI89, FIB3, FIKF, FK2D, FK45, FKD5, FL6D, FLG3, G003, G04H, G055, G0BH, G0HH, G0HJ, G0I3, G0K5, G0KJ, G26D, G2DJ, G2GJ, G303, G333, G393, G3G9, G3I3, G403, G40H, G433, G4AH, G4GH, G4H3, G4IH, G589, G5G9, G80J, G89J, G94H, G9G3, GAA5, GAIH, GB0H, GB43, GB6D, GBB5, GBG3, GBGJ, GBJJ, GD0H, GD45, GDD5, GDKD, GG2D, GG39, GG8J, GG9H, GGAH, GGDJ, GGEJ, GGGH, GGH3, GGKJ, GH0H, GHG3, GHH3, GHHH, GHJJ, GI03, GI2J, GI93, GIAH, GIEJ, GIG9, GII3, GJJJ, GJKJ, GK05, GKDD, GKGD, GKGJ, GKIJ, H081, H087, H0AH, H0BJ, 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5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000BB5, J000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000BIJ, C4IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII3, F0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000066B3, G0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000A5, D5KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKF, HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHBH, L0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000IKF, 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LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLKE7, 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80BN, 80FH, 80LN, 80MN, 840N, 848N, 866B, 86FB, 880B, 880N, 884N, 88CB, 88FB, 88LN, 88MN, 8BBB, 8BLB, 8C6B, 8CCH, 8CFH, 8F0B, 8FHH, 8FLB, 8H0H, 8HCH, 8IGN, 8ILN, 8KKH, 8L8B, 8LBB, 8LFB, 8LIN, 8M8N, 8MLN, 8N0N, 8NGN, 8NLN, 9061, 9091, 90EJ, 90F1, 90GJ, 90K1, 940J, 9501, 95F1, 9CC1, 9E0J, 9E95, 9F61, 9FI5, 9G3J, 9II5, 9K01, 9KK1, 9M01, A007, A05D, A0AD, A33D, A3AD, A3F5, A44J, A727, A9EJ, AA0D, AAAD, AAAJ, ACM7, AD8D, ADKD, AE27, AE9J, AEAJ, AEE7, AIAD, AIDD, AIID, AJ9J, AK5D, AM07, AM27, AM35, AMK5, B08B, B0CB, B0GB, B18B, B1CB, B80B, B8CB, BB21, BB4N, BBCB, BBF1, BBFB, BBK1, BC8B, BCF1, BCLB, BF1B, BF8B, BFB1, BFM1, BGC1, BGF1, BK21, BL8B, BLFB, BM1B, BM3N, BMB1, BMMN, BNF1, C00D, C06B, C077, C0D7, C0H7, C0L7, C0LB, C0M1, C60H, C6LB, C76H, C7E7, CAID, CC01, CCFH, CCKH, CDLB, CGE7, CH07, CHE7, CI8D, CIAD, CK0D, CL8B, CLDB, CLE7, CM01, CM07, CME7, CMM1, D007, D08D, D0C7, D0HH, D0LN, D0M7, D0NN, D207, D2KH, D2M7, D777, D7E7, D80H, D8LD, DA27, DAC7, DAM7, DBFB, DBMB, DC77, DCLB, DDL7, DE77, DF0H, DF2H, DFFH, DFMB, DH27, DH8H, DHC7, DHHH, DILN, DK0H, DK2H, DK8H, DKHH, DLIN, DLL7, DLM7, DLMB, DM07, DMH7, DMMB, DNGN, E07J, E09J, E335, E355, E555, E5A5, E5K5, E79J, E93J, E995, EA35, EE95, EKE5, F00B, F00H, F06H, F08B, F0I5, F11B, F18B, F1L1, F20H, F26H, F2FH, F355, F661, F6K1, F80B, F86B, F8BB, FBGB, FBK1, FBLB, FC0B, FC6H, FCLB, FEK5, FGB1, FH05, FH0H, FH35, FH6H, FHCH, FHF5, FHHH, FI05, FK91, FKK1, FL1B, FLB1, FLBB, FM61, FMBB, FMK1, G00J, G021, G027, G0EJ, G0JJ, G0M1, G0M7, G1CB, G2E7, G40J, G4AJ, G4IJ, G4JJ, G6C1, G701, G94J, G9IJ, GAEJ, GAJJ, GB21, GBM1, GC01, GCF1, GCLB, GE0J, GEAJ, GEE7, GEG7, GEIJ, GEL7, GFM1, GGE7, GGMB, GI0J, GIIJ, GIIN, GJ9J, GM27, GMB1, GNM7, H005, H0K5, H0M5, H207, H2E7, H335, H3I5, H595, H5K5, H60H, H68H, H76H, H80H, H8HH, HAAJ, HE7J, HEC7, HGE7, HGM7, HH35, HI55, HIM5, I00J, I035, I08D, I0CD, I4JJ, IC0D, ICID, II0D, II0J, II35, IIAD, IILD, IIM5, IIMN, IJ9J, ILCD, IM05, IM35, IMNN, INLD, J03J, J0HJ, J0JH, J2CH, J39J, J3ID, J60H, J62H, J8CH, J9IJ, JGAJ, JGJJ, JH9J, JI0J, JIDD, JJ0H, JJCD, JJJD, JJLD, JL3D, JLCD, K0E5, K0I5, K0K1, K0KH, K191, K211, K2F1, K2G1, K591, K5AD, K6F1, K6G1, K9I5, KA0D, KAAD, KAM5, KCCH, KCHH, KD8D, KDDD, KFI5, KG01, KG61, KH0H, KHHH, KI55, KIDD, KK21, KK8H, KKF1, KKK1, KKKD, KM8H, KMHH, KMK5, L027, L0M7, L1C1, L1MB, L211, L727, L8BB, L8BN, L8FB, L8LN, L9C1, L9M1, LB8B, LBC1, LBM1, LCAD, LD77, LDIN, LDL7, LDM7, LF8B, LG21, LIIN, LLLN, LLN7, LM07, LM1B, LM77, LMG1, LN77, LNM1, M00N, M01B, M03N, M055, M077, M08B, M0B1, M0C1, M0GB, M0K1, M0M7, M0N7, M18B, M1BB, M1MB, M26H, M335, M3GN, M3M5, M3MN, M3NN, M501, M53N, M5M1, M5NN, M6BB, M6C1, M6G1, M6KH, M88B, M88N, M8BB, M8NN, MBB1, MC01, MCC1, MCKH, MCM1, ME07, ME35, MEK5, MGGB, MGMB, MH35, MH8H, MHE7, MHM5, MK8H, MKC1, MKG1, MKHH, MKK5, ML8N, MM01, MM8B, MMC1, MMLN, MMM5, MMMN, MMN1, MN0N, MN27, MNGN, MNLN, N007, N027, N077, N0C7, N0DN, N0IN, N1M1, N227, N2M7, N661, N707, N727, N8LD, NA27, NA3D, NC07, ND0D, ND0N, NDLD, NF11, NF61, NGG7, NILN, 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5M0M1, 5MNNN, 5N03D, 5N3LD, 5NA8D, 5NADD, 5NDGN, 5NNGN, 600KH, 61661, 616L1, 61MM1, 66161, 66611, 666B1, 666L1, 666LB, 66BB1, 66BG1, 66BLB, 66G61, 66KF1, 66LBB, 66LG1, 6BBBB, 6BFCB, 6CC11, 6F1M1, 6F66B, 6F6B1, 6F6L1, 6FBCB, 6FLMB, 6FMCB, 6FMM1, 6FMMB, 6GCM1, 6GM61, 6GMC1, 6K1C1, 6K1K1, 6KK11, 6KKL1, 6KL11, 6L1G1, 6LBFB, 6LCC1, 6LFMB, 6MM61, 6MM6B, 70291, 702C1, 702G1, 72CF1, 72EE7, 7433J, 7443J, 77A07, 79901, 799F1, 7AAEJ, 7EE27, 7H9EJ, 7K2KH, 7KK2H, 7KKKH, 7KKMH, 7L2C1, 800NN, 806BB, 808BB, 808LB, 80F8B, 80IIN, 833ID, 860KH, 8886B, 888NN, 8BG4N, 8CH6H, 8CKHH, 8FC0H, 8FFCH, 8HHHH, 8IIIN, 8K0HH, 8LL4N, 8M0NN, 8MNNN, 8NNND, 9000J, 900M1, 9034J, 90IIJ, 94IIJ, 96CM1, 96KF1, 96MM1, 990C1, 990M1, 99591, 99961, 999C1, 99F91, 99FM1, 99KF1, 99M61, 99MK1, 9AAA5, 9FEE5, 9FFA5, 9FFF5, 9II4J, 9K6C1, 9K9C1, 9K9F1, 9KF91, 9M6M1, 9MK61, A02M7, A0A35, A0AM5, A0C77, A0D0D, A0DDD, A0EC7, A0M55, A0MM7, A2ME7, A3335, A33M5, A3555, A3MM5, A550D, A58ID, A5D0D, A5DDD, A74AJ, A7E07, AA0M5, AA3ID, AA3M5, AA83D, AA8ID, AAAM5, AACID, AAICD, AAM05, AC08D, AC0ID, AC0KD, AC8ID, ACA8D, AFA35, AIC8D, AJAJJ, AK0KD, AKI0D, AKKM5, AKM05, AM505, B00FB, B00LB, B0LBB, B1MBB, B1MMB, B2GM1, B3MGN, B88BB, BB3MN, BBB3N, BBB8B, BBBBN, BBBMN, BBCC1, BBGB1, BBGLB, BBMC1, BBMGB, BBNM1, BFB0B, BFBMB, BFGLB, BFGMB, BGGLB, BGMM1, BLMMB, BMC0B, BMGM1, BMMK1, BMNM1, C006H, C00CH, C00M7, C0C11, C0CC1, C0E07, C0F6H, C0GG7, C0K8D, C0KDH, C0KHH, C1CC1, C1CM1, C1MC1, C70F1, C886B, CC06H, CCCCH, CCCF1, CCCM1, CDHH7, CE707, CE7L7, CEE77, CEEG7, CEL07, CFFHH, CGLL7, CHC6H, CHCCH, CHH7H, CHHH7, CHHM7, CI0LD, CK0HH, CKHCH, CL007, CLD07, CLLL7, CM777, CMMM7, D008H, D07L7, D0DE7, D0EL7, D0L77, D0M8H, D0NA7, D22E7, D70A7, D7227, DBLBB, DCL07, DD7A7, DDAE7, DDD8D, DDE07, DDK0D, DDM77, DEE27, DKK8D, DL227, DL707, DLBBB, DLDFB, DLE27, DM2E7, DMM77, DMME7, DN0A7, DNIIN, DNLLN, E000J, E0227, E02E7, E0AAJ, E0GL7, E0I0J, E2E07, E7AAJ, E7E27, EAA55, EAK55, EC777, ECEE7, ECEL7, ECGL7, ECL77, EEC77, EECL7, EEEC7, EEG27, EEGG7, EG0E7, EG0L7, EG207, EGE07, EGG07, EGG27, EGL07, EI9IJ, F02HH, F06LB, F0C6B, F0CCH, F0CHH, F0E55, F0EA5, F0FH5, F0GGB, F0M2H, F0MGB, F0MMB, F1BMB, F3FF5, F3I35, F3II5, F6BCB, FA035, FB1MB, FBBM1, FBBMB, FBM8B, FC0HH, FC88B, FCFHH, FFC0H, FFCFH, FFCHH, FFF0H, FFF6H, FFFH5, FFHI5, FFI55, FG1MB, FGGCB, FGM1B, FHK55, FI5I5, FKEA5, FKKI5, FKL11, FM16B, FM1CB, FM62H, FM6CB, FMBG1, FMM0B, G0001, G00E7, G039J, G06F1, G07C1, G07F1, G0A9J, G0G07, G0GG7, G0I4J, G0I9J, G0LL7, G22M7, G2M07, G339J, G433J, G62M1, G6M61, G6MM1, G903J, G933J, GAA9J, GBCC1, GE007, GGGGB, GGGL7, GJ0IJ, GL007, GL2M7, GLL07, GLLM7, GMGCB, GMM07, GMM1B, H007H, H05I5, H0CCH, H0CM7, H0GG7, H0H27, H0H8H, H0HC7, H0HH5, H0I35, H0MM7, H3555, H35F5, H3F55, H3FF5, H5055, H50F5, H7HEJ, H9995, H9GEJ, HCC0H, HCC6H, HCGG7, HCHM7, HE027, HE0G7, HEE07, HEEG7, HEG27, HF0F5, HF505, HF555, HFF05, HFKF5, HG0G7, HH06H, HH08H, HH0H5, HH5I5, HH7HJ, HH9EJ, HH9I5, HHCHH, HHE07, HHGG7, HHH05, HHH7H, HHH9J, HHKI5, HHM05, HHM07, HHM27, HI0I5, HJ86H, HJC0H, HK055, HK9F5, HKF05, HKFF5, HKFK5, HKII5, HKK95, HM2M7, HME27, HMKM5, HMM05, HMM27, HMM55, HMMM7, I00DD, I00M5, I044J, I0505, I09IJ, I0AAD, I0D0D, I0DDD, I0I05, I0IDD, I0II5, I0IJJ, I0JIJ, I33M5, I4I4J, I5INN, I888N, I8NND, I8NNN, I904J, I94IJ, IA8ID, IAADD, IAI8D, IDDDD, IDINN, II88N, II8NN, IID8D, IIDIN, III8N, IIIDD, IIIID, IIIIN, IIIND, IIN8D, IINDD, IJJ0J, IJJJJ, ILILN, ILLIN, IMM8N, INA0D, INDNN, INGIN, INNDN, INNND, J000H, J002H, J00AJ, J00GJ, J00KH, J02KH, J068H, J080H, J090J, J0A9J, J0AAJ, J0C0H, J0G0J, J0IIJ, J0JGJ, J0JIJ, J0K8H, J2K0H, J2KKH, J6K8H, J86KH, JC00H, JC0KH, JCCCH, JCK0H, JCKCH, JDDLD, JG93J, JIIJJ, JJ0IJ, JJ2KH, JJ9GJ, JJCCH, JJG9J, JJGIJ, JJJ9J, JJJJH, JJK8H, JK08H, JK0CH, JK8KH, JKC0H, JKKKH, K0001, K0091, K020H, K02C1, K03ID, K0611, K06L1, K083D, K08HH, K0961, K09C1, K0CF1, K0F91, K0KM5, K0LG1, K1G21, K20HH, K29K1, K2KHH, K5001, K500D, K58ID, K5D0D, K5L11, K6621, K6C11, K6LC1, K8CKH, K8KCH, K96C1, K99E5, K9F91, K9FA5, K9FE5, K9K91, KA55D, KC011, KCF11, KD02H, KD0MH, KD20H, KDM2H, KEA55, KEAA5, KEK95, KEKK5, KF1G1, KF1K1, KF611, KF6L1, KFEA5, KH8CH, KI005, KIMM5, KK05D, KK0AD, KK0DH, KK2CH, KK2KH, KK33D, KK961, KK9C1, KKA5D, KKD0D, KKE55, KKI0D, KKIID, KKIM5, KKK0H, KKKM5, KLGC1, KMK2H, L188B, L1991, L2007, L22M7, L2EE7, L2MM7, L333D, L3LIN, L7291, L72G1, L88IN, L8C8B, L9991, LBB1B, LBBBB, LBBBN, LD0E7, LDBBN, LE207, LFMCB, LGCC1, LL227, LL3IN, LL48N, LLM27, LLMM7, LMBCB, LME27, LMMBB, LMMM7, LN33D, LN3AD, LNAAD, LNACD, M0007, M0061, M00K5, M0207, M066B, M0BCB, M0EE5, M0G01, M0GM1, M0M8N, M27KH, M2E27, M2M07, M2M27, M5005, M5555, M66CB, M66K1, M6K61, M6MCB, M7007, M7EE7, M8C0B, M8KCH, M8MGN, MBBGB, MBGM1, MCCCH, MCHCH, MEE55, MGBC1, MGMM1, MH227, MH2M7, MHH7H, MKM55, ML3LN, MM0CB, MM16B, MM227, MM661, MM6K1, MME55, MMEE7, MMKE5, MMM07, MMM6B, MMMB1, MMMGB, MMMM7, MNM61, MNN3N, N00CD, N00KD, N03LN, N0A8D, N0AM7, N0D8D, N0KKD, N0L3N, N0LAD, N0NDD, N16L1, N3GIN, N3LAD, N3LIN, N3NNN, N61L1, N96M1, N9M61, NA0CD, NAK0D, NAKKD, NCA8D, NCM77, NDGIN, NDIIN, NDLLN, NF991, NGM07, NIIIN, NINNN, NKKDD, NLNAD, NN0LN, NN191, NN3NN, NN6L1, NN83D, NNAAD, NNDIN, NNGIN, NNL3N, NNLND, NNM61, NNNIN, 166G21, 16G621, 19MMM1, 1BBBMB, 1BBGM1, 1GCCC1, 1GCCM1, 1MMM1B, 200E27, 2E0027, 2HH0HH, 2HHC0H, 2KK0HH, 2M0E27, 2M22E7, 30NNNN, 3333M5, 333AID, 333I35, 33I555, 3F5FF5, 3I3MM5, 3I88GN, 3II8LN, 3IIII5, 400IJJ, 40J00J, 40JJ3J, 40JJJJ, 44403J, 444I0J, 44IJJJ, 44J0JJ, 44JJIJ, 48I8IN, 4I440J, 4II8IN, 4IJ0IJ, 4JIIIJ, 4JJ0JJ, 4JJJ0J, 50033D, 5003AD, 5008ID, 500D8D, 500G01, 500L11, 500LAD, 500MG1, 503LAD, 508ILD, 50DDLD, 50ILAD, 50M001, 516G61, 519MM1, 538NNN, 53NNNN, 55005D, 5508ID, 550D8D, 558ILD, 55F5I5, 56G661, 58333D, 58NNNN, 5999F5, 59AAF5, 5DNNNN, 5F55I5, 5FMMM1, 5G6661, 5K9AA5, 5KK9F5, 5KKK95, 5M0001, 5NDD8D, 5NDINN, 5NN33D, 5NNLAD, 5NNNAD, 5NNNDN, 608K0H, 61CCM1, 61G621, 661G21, 666621, 6666CB, 6666F1, 66K661, 6BCCC1, 6BKKC1, 6F6BBB, 6G6621, 6GCCC1, 6GMMM1, 6K6K61, 6M666B, 70A077, 70L991, 7722E7, 772E27, 7772E7, 777A27, 777L27, 77A777, 77EL27, 7A7077, 7A7777, 7E7227, 7L2E27, 7LEL27, 7LL2E7, 7LLE27, 7LLL27, 800GIN, 80NINN, 80NNNN, 8BBMGN, 8C888B, 8C88LB, 8MM0GN, 900001, 90043J, 959MM1, 96K661, 9999F1, 9999K1, 999AF5, 999FF5, 99EEE5, 99K991, 99MMM1, 9AAFF5, 9EIIIJ, 9F9991, 9F9MM1, 9FEAA5, 9G444J, 9K9991, 9M6661, A000CD, A000KD, A000M5, A0083D, A00I0D, A00M05, A022E7, A07E77, A0FF35, A0K3ID, A0K83D, A4AJJJ, A77777, AA0035, AA0355, AAA035, ADDD0D, ADDDDD, AF0035, AFFF35, AKK8ID, AM0M05, AM7777, B0F0MB, BBBBM1, BBLBMB, BFBBBB, BFM0MB, BFMMMB, BLBBMB, BLMBBB, C00071, C000E7, C007C1, C00G07, C07KKH, C0CC6H, C0CH6H, C0EEE7, C0HHHH, C777L7, C77L77, C7L777, C7LL07, C8088B, CAAK8D, CAKKAD, CC000H, CC0CHH, CD000H, CD0KKH, CE0007, CEE0E7, CELL77, CG0007, CGGL07, CH0CHH, CHCH0H, CHHH6H, CK0C0H, CKAK8D, CKKA8D, CL7707, D002FH, D0D0KD, D0DA77, D0DKKD, D0IIIN, D0K0DD, D0KDKD, D0KKDD, D0KKKH, DC0EE7, DCEEE7, DD0227, DD0D27, DD0DKD, DD0KKD, DD2E27, DDD0D7, DDD0LD, DDD227, DDDA77, DDDBCB, DDDCE7, DDDDFB, DDDMM7, DDEEE7, DDMBCB, DEEC07, DH000H, DHMEE7, DIIIGN, DK0KDD, DKMKKH, DMBBBB, DMEEE7, DMMM27, E00G27, E07727, E0C707, E0CE77, E0E027, E0EEG7, E0EGE7, E0EL27, E0GE27, E0L207, E0LE27, E0LL27, E2E2E7, E7L2E7, E900IJ, E9EEE5, EAAKK5, EC00E7, EC0G07, EC7007, ECEG07, EE0G07, EE0GE7, EE72E7, EE7L27, EECE07, EECEG7, EEEEE5, EEEK55, EEEKA5, EEEL27, EEGLL7, EELE27, EGLLL7, EKK595, EKKA55, EKKAK5, EKKKK5, F000E5, F0AA35, F0F035, F0FFFH, F0HKK5, F0KKE5, F16BB1, F16MM1, F1BBBB, F1MC6B, F666BB, F66BBB, F6GMM1, FB0BBB, FB1BBB, FBBB0B, FBMMG1, FC0FFH, FCFCCH, FEEE55, FEEEA5, FF03F5, FF0FFH, FF3F35, FFEE35, FFF2CH, FFFCCH, FFFFE5, FFI335, FFKFE5, FGLMMB, FK55I5, FKFE55, FLM8CB, FMC66B, FMMC6B, G0AA4J, G0CCC1, G0LE07, G666F1, GG0007, GG00G7, GG0L07, GGLLL7, GGLMM7, GI444J, GJJ33J, GLLE27, GLMMCB, GM0661, GMMM61, H00G07, H05555, H09FF5, H0C0E7, H0CE07, H0CEE7, H0E227, H0H007, H0H5F5, H0H995, H0HHE7, H0HHH7, H55505, H55II5, H5FII5, H99FF5, HEG007, HFFK55, HH0007, HH02M7, HH0C0H, HH7AEJ, HHC0E7, HHE227, HHH0C7, HHH0M7, HHH995, HHHC0H, HHHE27, HHHEAJ, HHHH07, HHHH8H, HHHHE7, HHHHI5, HHHHJH, HHHJ8H, HHHJCH, HHJ00H, HHK095, HHKKM5, HKK0F5, HKK5F5, HKKK55, HKKKK5, HKM555, HMEEE7, I00555, I05555, I0I94J, I333I5, I33555, I444IJ, I55055, I55505, I55555, IAAC8D, ID000D, IDD0LD, II9I4J, III4IJ, III505, IIIC8D, IIJIJJ, IJIIIJ, IM8LLN, IN00AD, INAACD, INCAAD, ININGN, J00CCH, J0IJJJ, J0J09J, J3333D, JIJIIJ, JJ68KH, JJIJIJ, JJJAJJ, JJJHGJ, JJJJAJ, JJJJGJ, JJJJIJ, K0008H, K00161, K001G1, K001L1, K002CH, K002HH, K00521, K00AKD, K00C0H, K00GF1, K00I0D, K00K95, K00M05, K01621, K05021, K0505D, K051G1, K059F5, K05K95, K0C0C1, K0L291, K0M005, K0M505, K1K661, K2CK0H, K33IAD, K3IIID, K5550D, K56121, K59AA5, K612K1, K61CC1, K66661, K6K611, K900C1, K99661, K9AFF5, K9C001, KAKI8D, KC00C1, KDK00D, KF9991, KI0IID, KK000D, KK01L1, KK0661, KK0I8D, KK0L11, KK0M2H, KK5661, KK59F5, KK61C1, KK9995, KK9EE5, KKA3ID, KKA83D, KKAI8D, KKC001, KKC0C1, KKC1C1, KKCCC1, KKD2HH, KKK595, KKK9A5, KKKK95, KKKKKH, KKKMCH, KKM505, KKMEE5, KKMKCH, KM0005, L222E7, L33AAD, L38I8N, LCCC11, LDFBCB, LEL2E7, LELE27, LELL27, LGMMM1, LLE2E7, LM2ME7, M000M5, M006MB, M00E27, M00MM1, M02227, M06M61, M06MM1, M0E227, M0EE27, M0KME5, M0M5GN, M0MM61, M0MMCB, M0MNNN, M0NNM1, M38LLN, M5K505, M77707, M7E227, M7E727, M8CHHH, MBMMCB, MBMMM1, MEEE77, MHH027, MHH505, MHHC6H, MHHH6H, MHHK05, MKK001, MM2ME7, MM7707, MM7E77, MMBMK1, MMM2E7, MMMC0B, MMMK61, N0003D, N0008D, N0030N, N030NN, N0C0AD, N0CKAD, N0DKDD, N0N3GN, N0NN3N, N333AD, N777A7, N77A77, NAACKD, NAAKDD, NACAKD, NACKAD, NC0AKD, NC0KAD, NCA0KD, NCKAKD, NDNNLN, NNNLAD, NNNNLD, 1BBBBBB, 1BBBBG1, 1M6MMMB, 1MMBBBB, 1MMMMK1, 2000227, 2000EE7, 20EEEE7, 2C0FFFH, 2E2EEE7, 2KKKHCH, 2MEE227, 2MEEE27, 333333D, 3333355, 3335555, 333FFF5, 333IIID, 388NNNN, 38INNNN, 3INNNNN, 4000IMN, 4000JJJ, 400IIIN, 444444J, 44JJJJJ, 488888N, 4IIJIIJ, 4JJJ33J, 50002M1, 5001G21, 5006621, 500LGM1, 555083D, 55555I5, 5616G21, 59MMMM1, 5K999A5, 61CCCC1, 66666K1, 6K0000H, 6K0080H, 70000A7, 70077A7, 70700A7, 7070A77, 77700A7, 77770A7, 7777227, 7777E27, 77L2227, 7LE22E7, 888888B, 888888N, 8888BBN, 8888IIN, 888B88B, 888I8IN, 88IINNN, 88NIINN, 88NNIIN, 8INNNNN, 90444IJ, 904I44J, 9666661, 9666FK1, 9666K61, 9966FK1, A00KK0D, A0K000D, AAAAA35, AAKKI8D, BB8888B, BBB0BLB, BBBB1BB, BBBBBB1, BBBBBGB, BBBBBLB, BBBLMBB, C0007KH, C000F11, C00FFFH, C00HH0H, C00K00H, C0C0HHH, C0CCHHH, C0CHH0H, C0CHHCH, C0FFFFH, C0H0H0H, C0KKC0H, CC0HH0H, CCCCC11, CCCCCC1, CCHHHHH, CDKKKKH, CEL7777, CGGG0G7, CGGGGG7, CH00HHH, CHGGGG7, CHHHH0H, CHHHHCH, CHHHHHH, CK0000H, CKDKKKH, D00DDKD, DD0DDD7, DDBBBLB, DDD2EE7, DDDBBLB, DDDDD27, DDDDDBB, DDDDDC7, DDDDDKD, DDDDDMB, DDDDEE7, DDDDKKD, DDDDLDB, DDDFBBB, DDDLFCB, DDDMEE7, DDM2227, DHHEEE7, DK000KD, DK00D0D, DK0D00D, DNN000N, E000CL7, E000EG7, E000GE7, E00C0G7, E00CE07, E00EE27, E0C00G7, E0C0EG7, E0CE007, E0EC0G7, E0EE207, E0G0007, E20EE27, E22EEE7, E2EE227, E2EEE27, E772227, E77LL27, E7L2227, E9IIIIJ, EAKKKA5, EC000G7, ECG00G7, EE00L27, EE0E0G7, EE20EE7, EEE0EG7, EEE22E7, EEEE727, EEEEE27, EEEEG07, EEEEGE7, EEEKKK5, EELLL27, EI0IIIJ, EKKKAA5, ELLLE27, F00FA35, F0333F5, F0F0FE5, F333335, FAAFF35, FCF0FCH, FEEEE35, FF03335, FF0FA35, FF0FE35, FF0FMCH, FFF0A35, FFF0F35, FFFAF35, FFFF5I5, FFFFM2H, FFFI3I5, FFFIII5, FFH5555, FH55555, FL1MMM1, G0000G7, G0000L7, GGGG007, GLE2227, GLLLLE7, GLLLLL7, H000007, H0000C7, H000HCH, H000HM7, H000M27, H000ME7, H00G227, H00HHM7, H02M227, H0C0HHH, H0CH00H, H0E0007, H0FFF35, H0FFFF5, H0H0ME7, H0HFII5, H0HHHCH, H0M0227, H555555, H5F5FF5, HC000G7, HC00H0H, HCCHHCH, HCHHHCH, HCHHHHH, HEEEE27, HFF5FF5, HFF5FI5, HFKKK05, HG00007, HH00E27, HH0G227, HHH2MM7, HHH55F5, HHH9FF5, HHHFFK5, HHHFK55, HHHH7EJ, HHHHCM7, HHHHHAJ, HHHHHF5, HHHHHHJ, HKK5505, I000055, I00A0ID, I0I4IIJ, I0IIIIJ, I88NIIN, III0055, III0I55, III444J, IINNLIN, J000IJJ, K0000DH, K0000KD, K00033D, K000A5D, K000K5D, K00555D, K009995, K00K00D, K00K8ID, K00KI8D, K00KIAD, K01GCC1, K05033D, K0999F5, K2KKKCH, K53333D, K956661, K999991, KCCC1C1, KFFFE55, KFFKKE5, KFKFKE5, KK009A5, KK00C11, KK01GC1, KK99001, KKIII05, KKK09F5, KKKE9E5, KKKEAK5, KKKKI05, KKKKKE5, KMMEEE5, L1BBBG1, LBMMMCB, LBMMMMB, LDEEE07, LEE22E7, LEE2E27, LEEE2E7, LLLLE27, M0000CB, M000C6B, M02EEE7, M0K0005, M0M0005, M2CHHHH, M2HHHHH, M6MMMM1, MC0000B, MCHHHHH, ME7E777, MEE7777, MEEE2E7, MG06661, MHHHCCH, MHHHH27, MHHHHH7, MHM0027, MM6666B, MM77777, MMC000B, MMM7727, MMNM777, N000NLN, N00333D, N003AAD, N0A00DD, N0NN33D, N0NNLLN, N30000N, N777777, NDNNNNN, NN0N0GN, NN0N30N, NNN300N, NNN333D, NNN3LLN, NNNDDDD, NNNNN3N, NNNNNND, 33333F35, 33FFFF35, 3555FFF5, 3FFFFF55, 3NNNNNLN, 40000I0J, 40I0IIIJ, 444440IJ, 4J0000IJ, 500006G1, 5D00DDDD, 5L1MMMM1, 5MMMMMG1, 5NNDDDDD, 5NNNNDDD, 5NNNNN8D, 6000080H, 777777A7, 77777A77, 7944444J, 800000IN, 996666K1, 999999I5, 9999FEA5, A00003ID, AAAAFF35, BBBGMMMB, C0000011, C000007H, C0CC0H0H, C666666B, CCCH0HHH, CCHH0HCH, CE777777, CEEEEE07, CHH0H00H, D00000GN, D000D0LD, D000IIGN, D0DDDDD7, DDD0E2E7, DDDDDDDB, DDDDDME7, DEEEELE7, DEEELEE7, DEELEEE7, DELEE0E7, E00000C7, E00000G7, E0000CG7, E000C0E7, E000G007, E00CG007, E00E0CG7, E0C00007, E0CGGGG7, E0GGGGG7, E20000E7, EAAKAAA5, EAKKAAA5, EE00E727, EE020007, EEEE2027, ELEE2227, F00003F5, F0000A35, F0003335, F0FFFA35, F1999991, F1999MM1, FAAAAF35, FBBBBBG1, FEAAAAA5, FF000A35, FF00FF35, FF0KEEE5, FFAAAF35, FFF555I5, FFFF33I5, FFFFF035, FFFFF3F5, FFFFFKI5, FFFFFMHH, FKFKEEE5, FKKFEEE5, FMMMMMCB, FMMMMMM1, G2000007, GGGGGMM7, GJJJJJ0J, GJJJJJ3J, H0000E27, H0000G27, H000C0G7, H000CEG7, H000CHH7, H000E0E7, H000EE27, H00CHHG7, H00EEE27, H00M0EE7, H05FF5F5, H0E00EE7, H55FF5F5, HCHH0H0H, HE000EE7, HFFIIII5, HGGG2227, HH00CEG7, HH00H0CH, HH0EEEE7, HH0FFFI5, HHEEEEE7, HHH000CH, HHH00EG7, HHHC00G7, HHHFFFF5, HHHHHKK5, HHHK5F55, HK5555F5, I4IIIIIJ, IA0000ID, II0005I5, III000I5, III055I5, III5NNNN, IIIII9IJ, IIIIIII5, IIINNNGN, JAJJJJJJ, JJAJJJJJ, K000005D, K00009A5, K0000M55, K000M555, K008IIID, K00D0K0D, K00III8D, K00K550D, K00LCC11, K0999951, K0D0000H, K0K00595, K0K9AAF5, K0KK0095, K0KK9FF5, K3333IID, KFKFEEE5, KFKKEEE5, KK00000H, KK0000M5, KK099991, KK55583D, KKKEEEA5, KKKKKKI5, LEEEE227, LLLEEE27, LLLL2E07, M000006B, M000M6CB, M0MMMMM1, M222EEE7, M777E777, M7E77777, ME222EE7, ME2EEEE7, MEE222E7, MM0NNNNN, MME77727, MMM6MMM1, N00003GN, N0000ADD, N000N0GN, N000NNND, N033333D, N0NN0NGN, NDDDDKDD, NN000N3N, NN00N03N, NN03000N, NNN003GN, NNNNDNLN, NNNNNADD, 199999MM1, 200FFFFFH, 222MEEEE7, 2FFFFFFCH, 30000000N, 30N00000N, 400000J3J, 500000M01, 5000166G1, 5000666G1, 50DDDDDDD, 8NN33333D, 999999991, C000000FH, C00000K0H, C000H00HH, C77777707, CH00H000H, CHH0000HH, D00000DKD, D00000DLD, D0000200H, D0000KK0D, D000KK00D, D00D0DDLD, D0D00DDLD, D0LEEEEE7, DDBBBBBBB, DDD000KDD, DDDDDDDE7, DK00000DD, DNNNNNNNN, E00000E27, E00007L27, E0000E727, E0E000C07, E20000027, EAAAAKAA5, EAKAAAAK5, EE0000C07, EEE000E27, EEEEEEGL7, F00FFFF35, F0FFFFF35, FF0000035, FF0FFFF35, FF5555FI5, FFFFFFA35, FFFFFFF35, FFFFFFFI5, FKKKKEEE5, FMMMMMMMB, GGGGG2227, GGGGGG207, GJJJJJJJJ, GLMMMMMMB, H000022M7, H000222M7, H000EEEE7, H0EEEEEE7, H0H0000CH, H0IIIIII5, HCH00000H, HE0EEEEE7, HFFFFFI35, HFFFFKKK5, HHHHHHG27, HHHHHHH55, HHHHHHHH7, HHHHHHM55, HHHKK5555, HHIIIII05, HIIIIII05, HKK5555I5, I000000AD, I000000ID, I000A000D, I00A0000D, IIIII0555, IIIIIII9J, K000000AD, K00000595, K000009F5, K0000550D, K099999A5, K0C00000H, K0I00000D, KK0000595, KK0000HCH, KKK000095, KKKFKFFE5, KKKIIIII5, M77777777, MEEEE2227, MMMMMMMM1, N0000000D, N0000003N, N000003NN, N00000N3N, N00000NGN, N00N000GN, N00NNNN8D, N0NNN00GN, N0NNNN3AD, N0NNNNNGN, N999999M1, NN0NNNNGN, NNN000NGN, NNNNNDD8D, NNNNNN0GN, 16MMMMMMMB, 1MMMMMMBCB, 3333333335, 33333333I5, 400000000N, 40IIIIIIJJ, 4IIIIIIIJJ, 4IIIIIIJIJ, 50000000M1, 70F9999991, 777E777727, 9999995MM1, ADD000000D, C00000088B, C000000CF1, C00000F0HH, CH00000H0H, D00KD0000D, D0D0DDDDLD, D0E2EEEEE7, D2EEEEEEE7, DBBBBBBBBB, DD000000KD, DD0000DDLD, DLE0EEEEE7, EEE0000727, EEEAAAAAA5, EEEEEE00G7, EEEEEEE0G7, F000000F35, F00FFKEEE5, F00KFFEEE5, F0M666666B, FCFFFFFFFH, FFFFFFF2HH, FFFKKKEEE5, GGGGGGG227, H00000C06H, H0000HHH6H, H555FFFFF5, H55FFFFF55, H5FFFFFF55, HF5FFFFFF5, HHHH0H0HCH, HHHHH0HHCH, HHHHHH0HCH, HHHHHHHHM5, HHHIIIIII5, IIDNNNNNLN, IIIIIJJIIJ, IIINNNNNLN, IINNNNNNGN, INNNNNNNLN, J0000000IJ, K0000II8ID, K099999995, K0I0000AID, K0K0009FF5, K9999999F5, KK00000095, KKFFFKEEE5, LLLLLLLME7, LLLMEEEEE7, LMEEEEEEE7, M000000005, MHHHHHHHH5, MK00000005, MMMMMMMBCB, NN000000GN, NN0000NNGN, NN99999991, 2HHHHHHHHHH, 38NNNNNNNNN, 3MNNNNNNNNN, 40IIIIIIIIJ, 4AJJJJJJJJJ, 4J000000J0J, 4JJJJJJJJJJ, 506666666G1, 5DDDDDDDDLD, 999999999F5, 99999999EA5, 99999999FE5, A0000000035, C0000000007, C00000000G7, C00000000KH, CEEEEEEEEL7, D0000000FMH, D000DDDDDLD, D0KD000000D, DDDD00000KD, DEEE0EEEEE7, DEL0EEEEEE7, DELEEEEEE07, E0000E20007, E7777777727, EE000000207, EEE20000007, FFFFFFFFMCH, FM66666666B, GGGGGGGG2M7, HFFFFFFFF55, HHHHHHHHH6H, HHHHHHHHHCH, HHHHHK55555, I9IIIIIIIIJ, IIIIIIII44J, IIIIIIIJJIJ, IINNNNNNNNN, JDDDDDDDDDD, JJIIIIIIIIJ, K00000I8IID, LLLLLLLLL27, 9999999EEAA5, AI000000000D, C77700000007, CH0HH000000H, D00D000000LD, DEEEEEEE0EE7, DN000000000N, EAKAAAAAAAA5, EKAAAAAAAAK5, F6666666666B, H000HHHHHH6H, H55FFFFFFFF5, HFFFFFFFFKK5, K00000000I8D, K999999999A5, 3555555555FF5, 5000000000001, 6G66666666661, 99999999999A5, C00000000000H, CFFFFFFFFFFCH, CHHH00000000H, D00000000K0KD, D0000000K00KD, D0D00000000LD, DEEEEEEEEEL07, E000E20000007, E00E200000007, EEE0000000027, GGGGGGGGGGGM7, GGGGGGGGGGM07, H00000000CHHH, H00HC0000000H, HFFFFFFFFFFK5, I0A000000000D, J000000000J9J, K000000000095, K000000000M2H, M0000000000M1, M0EEEEEEEEEE7, MHHHHHHHHHHHH, MMNNNNNNNNNNN, MNNNNNNNNNNNN, N000000DDDDDD, N000DDDDDDDDD, NNDDDDDDDDDDD, 22EEEEEEEEEEE7, 35FFFFFFFFFFF5, 400000000000JJ, 800000000000GN, DDDDDDDDDDD077, DDDDDDDDDDDDD7, E0000000000L27, EAAAAAAAAAAKA5, EEG00000000007, H0000000000C6H, I5500000000005, II0000000000I5, M0666666666661, M6MMMMMMMMMMMB, 4JJ00000000000J, 506666666666661, BGMMMMMMMMMMMCB, CFFFFFFFFFFFFFH, D0000000000KD0D, D0HEEEEEEEEEEE7, F0BBBBBBBBBBBBB, HGGGGGGGGGGGGG7, K0000000000000D, K00000000000MCH, M0M6MMMMMMMMMMB, 5DDDDDDDDDDDDDDD, C00000000000008B, D00000000000000H, DEEEEEEEEEEEE0L7, DEEEEEEEEEEEEEL7, EEE2EEEEEEEEEEE7, GM66666666666661, H5FFFFFFFFFFFFF5, IIIIIIIIIIIIIJJJ, BGMMMMMMMMMMMMMMB, DLEEEEEEEEEEEEEE7, H0000000000000CHH, H000000000C0000HH, I000000000000000D, IIIIIIIIIIIIIIIJJ, INNNNNNNNNNNNNNNN, J000000000000009J, M666666666666666B, N0000000000000LLN, N00DDDDDDDDDDDDDD, 355555555555555555, 60000000000000008H, 6M6666666666666661, C000000000000000F1, N0DDDDDDDDDDDDDDDD, 666666666666666666B, 800000000000000000N, AD000000000000000DD, DEEEEEEEEEEEEEEEEE7, I500000000000000005, 20000000000000000027, 4000000000000000003J, 400000000000000000IJ, 99999999999999999995, DD00DDDDDDDDDDDDDDLD, E2EEEEEEEEEEEEEEEEE7, N00000000000000000LN, 500000000066666666661, EE0000000000000000727, GGGGGGGGGGGGGGGGGGG07, H0000000000000000006H, 40000000000000IIIIIIIJ, AD0000000000000000000D, K0000000000000000000M5, CL777777777777777777777, D000000000000000000000N, D0000000000000000000IIN, HHHHHHHHHHHHHHHHHHHHHK5, NDDDDDDDDDDDDDDDDDDDDDD, 1MMMMMMMMMMMMMMMMMMMMMBB, D00DDDDDDDDDDDDDDDDDDDLD, FFFFFFFFFFFFFFFFFFFFFFFH, 4J0000000000000000000000J, 566666666666666666666666G1, EKKAAAAAAAAAAAAAAAAAAAAAA5, 6666666666666666666666666G1, AJJJJJJJJJJJJJJJJJJJJJJJJJJJ, H00000000000000000000000008H, N0000000000000000000000000GN, DD0000000000000000000000000LD, IIIIIIIIIIIIIIIIIIIIIIIIIIIIJ, G0666666666666666666666666666661, GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG7, K000000000000000000000000000000000H, EAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA5, LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLM7, M2EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE7, C000000000000000000000000000000000000000001, MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMCB, E00000000000000000000000000000000000000000000727, 777777777777777777777777777777777777777777777777727, EG000000000000000000000000000000000000000000000000000007, D000000000000000000000000000000000000000000000000000000000LD, 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===Base 36=== 11, 15, 17, 1B, 1H, 1N, 1P, 1V, 1Z, 21, 27, 2B, 2H, 2P, 2T, 2V, 2Z, 31, 35, 3J, 3N, 3T, 3V, 45, 47, 4D, 4J, 4N, 4T, 4Z, 51, 5B, 5D, 5H, 5J, 5V, 67, 6B, 6D, 6H, 6N, 6P, 6Z, 75, 7B, 7H, 7J, 7P, 7T, 7V, 85, 8J, 8N, 8P, 8T, 97, 9D, 9N, 9P, 9T, 9Z, A7, AD, AJ, AN, AT, B1, B5, BD, BN, BP, BZ, C1, C7, CB, CH, CP, CT, CV, CZ, DB, DJ, DN, DV, DZ, E5, EH, EJ, F1, F7, FH, FN, FT, FV, G1, GB, GH, GN, GP, GV, H1, H5, H7, HJ, HT, HV, HZ, I5, IB, ID, IP, IT, IZ, J7, JH, JP, JZ, K7, KD, KJ, KN, KV, L1, L5, LD, LH, LV, M5, MH, MJ, MT, MV, MZ, N1, NB, NP, NT, NV, NZ, OD, OH, OJ, ON, P7, PB, PJ, PT, Q1, Q5, QB, QH, QV, QZ, R5, RB, RJ, RP, S1, S5, SB, SD, SN, SP, SV, T5, T7, TH, TJ, TP, U7, UB, UD, UH, UN, UT, V1, V7, VD, VZ, W1, WB, WJ, WT, WZ, X5, XD, XP, XT, XZ, Y5, Y7, YD, YP, YZ, ZH, ZJ, ZN, ZT, ZV, 12D, 16J, 18D, 1CD, 1CJ, 1DD, 1GT, 1JD, 1JJ, 1LT, 1QJ, 1RD, 1RT, 1ST, 1XJ, 1YJ, 1YT, 22D, 22J, 22N, 23D, 255, 2A5, 2CD, 2ED, 2EN, 2F5, 2GD, 2GJ, 2IJ, 2JN, 2LN, 2MN, 2ND, 2O5, 2QD, 2QJ, 2U5, 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MYMU1, MYRK1, MYUU1, MYXR1, N000D, N0055, N006J, N007N, N00CN, N00IH, N00O7, N00S7, N029J, N02DD, N0307, N044H, N049H, N0505, N05M7, N05Q7, N06LJ, N070N, N0A55, N0CEN, N0CNN, N0CYN, N0DMD, N0DRD, N0F05, N0FF5, N0FMD, N0GED, N0HNN, N0I4H, N0IS7, N0IXJ, N0JLN, N0JNN, N0K4H, N0KIH, N0L6J, N0LI7, N0LLN, N0M0N, N0MQ7, N0NEN, N0O07, N0O77, N0Q0N, N0QEN, N0RRH, N0S07, N0SS7, N0U0J, N0ULJ, N0W77, N0WC5, N0WL7, N0XO7, N26JJ, N29XJ, N2CNN, N2CYN, N2MMD, N2N6J, N2N9J, N2NLJ, N2YYN, N30ED, N32RD, N33GD, N33MD, N3GGD, N3IW7, N3MR7, N3MX7, N3RGD, N3RI7, N3W2D, N3W77, N3X07, N3X77, N400H, N409H, N44YH, N494H, N49YH, N4AYH, N50K5, N5307, N5537, N5577, N57Q7, N5FK5, N5KK5, N5Q77, N5SQ7, N69LJ, N6L9J, N6U0J, N700D, N7077, N70EN, N70FD, N73RD, N7777, N777N, N7DMD, N7E2N, N7FED, N7M3D, N7MWD, N7SR7, N7WMD, N92LJ, N9XXJ, NA505, NA5F5, NAFK5, NAK05, NAKF5, NARYH, NAWW5, NC00N, NC0EN, NC0NN, NCE0N, NCN0N, NCNQN, NCW05, ND3GD, ND7DD, NDAW5, NDDGD, NDDRD, NDE3D, NDWM7, NDWW7, NE0GD, NED3D, NEDDD, NEL2N, NEMMD, NEMRD, NF0F5, NFEMD, NFKF5, NFWC5, NFWW5, NGDED, NGW2D, NH00H, NH2NN, NHH0H, NHMCN, NHMMD, NHNNN, NI00H, NI0EN, NI0MN, NI0NH, NI0NJ, NI0XJ, NI44H, NI7R7, NI7S7, NII77, NIIM7, NIIMN, NIIYN, NIM0N, NIN0H, NIN0J, NINJJ, NIW37, NIWM7, NIX77, NIXW7, NJ0EN, NJ0NN, NJ30D, NJ33D, NJFMD, NJIEN, NJJ2N, NJJIN, NJJJJ, NJJJN, NJL0J, NJLNN, NJN0N, NJSJJ, NK005, NK04H, NK3KH, NK5F5, NKA05, NKFK5, NKK55, NKKF5, NL09J, NL2IN, NLCNN, NLII7, NLIIN, NLJLN, NLL2J, NLLNJ, NLLNN, NLNCN, NLNIN, NLNLJ, NLNLN, NM00N, NM73D, NM7DD, NM7RD, NME0N, NMELN, NMLL7, NMLQ7, NMMRD, NMQEN, NMRD7, NMRR7, NMWWD, NN02J, NN0AH, NN0EN, NN30H, NN525, NN6UJ, NN92J, NNA55, NNASH, NNCLN, NNCMN, NNELN, NNF25, NNHHN, NNJ2J, NNJJJ, NNLNN, NNN55, NNN9J, NNNMN, NNNNJ, NNNSH, NNNXJ, NNQYN, NNS3H, NNU9J, NNW55, NNXJJ, NO077, NO0W7, NO777, NOI77, NOIM7, NOWL7, NQ00N, NQ0YN, NQ77N, NQ7EN, NQLLN, NQLNN, NQQQN, NQQYN, NRARH, NRAYH, NRDI7, NRHYH, NRQL7, NRRHH, NRW2D, NS0L7, NSA3H, NSHHH, NSIIJ, NSIJJ, NSS07, NSSJJ, NSSL7, NSSS7, NSULJ, NU00J, NUL6J, NUSIJ, NW0C5, NW3W7, NW5W5, NWI77, NWIM7, NWIO7, NWW55, NWWM7, NX0I7, NX0O7, NX3R7, NX9XJ, NXIM7, NXRL7, NXSSJ, NXWI7, NXWW7, NXXSJ, NY44H, NY94H, NYYIN, O0057, O005T, O0077, O0091, O009B, O00BT, O00EV, O00OV, O00TT, O00WP, O00WV, O040V, O0507, O056T, O065T, O08AV, O08E7, O0901, O09AB, O09I1, O09K1, O09WV, O0A4V, O0AI1, O0E9V, O0EAB, O0EAV, O0EFP, O0EKB, O0EOB, O0EU1, O0FMP, O0K6T, O0K91, O0MM1, O0O9B, O0OAB, O0OI1, O0OOB, O0OT1, O0OUV, O0OW7, O0OYT, O0T8V, O0TOT, O0TOV, O0TTV, O0TUV, O0TX1, O0U91, O0UE1, O0W87, O0WOV, O0YOT, O100T, O1EET, O4PAV, O4U0V, O5005, O50EP, O50I7, O50K5, O555P, O55FP, O55UP, O5EFP, O5I07, O5K05, O5KK5, O5OYT, O6LGT, O77E7, O7Q77, O80E7, O8AAZ, O8AFZ, O8AOV, O8FFZ, O8FKB, O8FZB, O8IM7, O8ZRZ, O8ZZB, O900V, O90WV, O96OV, O99LB, O9K01, O9OU1, O9R6V, O9U01, O9UI1, OA091, OA0O1, OA4AV, OA4IV, OA68V, OA8AZ, OA9I1, OAA4V, OAAFZ, OAAO1, OAAOV, OAAZZ, OAFAZ, OAFYB, OAI0V, OAI91, OAOAV, OAOE1, OAOU1, OAUE1, OAUI1, OAY01, OAY0B, OAYI1, OAZZZ, OB66T, OBE0T, OBEET, OE0BT, OE0FB, OE4AV, OE6ET, OE8AV, OE9EB, OEA8V, OEAA1, OEAFB, OEBET, OEBI7, OEEO7, OEFFP, OEFLP, OEKA1, OEKAB, OEKU1, OELMP, OEML7, OEO07, OEO0B, OEO4V, OEO6V, OEOAV, OEOO7, OEOOB, OEOVB, OEPU1, OERET, OERRV, OETY1, OEUK1, OEUU1, OEV9B, OEVFP, OEW8V, OEWW7, OF0FP, OF0OB, OFFFP, OFFMP, OFFZP, OFFZZ, OFMMP, OFMWP, OFOQP, OFPFZ, OFPUZ, OFZ0P, OFZFZ, OFZOB, OFZZZ, OG065, OG0YT, OI0EV, OI7Q7, OI9WV, OIIE7, OIQ77, OIQW7, OIR6V, OIYO1, OK8KB, OKAE1, OKAY1, OKE6T, OKEU1, OKFYB, OKIY1, OKYA1, OKYI1, OL08B, OL4EP, OL777, OL8E7, OLBI7, OLEL7, OLFOP, OLGYT, OLIW7, OLLSZ, OLLZZ, OLOUP, OLR6T, OLUMP, OMAU1, OMOU1, OMXM1, OO0AB, OO0I7, OO0T1, OO1ET, OO4AV, OO4MP, OO4QP, OO6KT, OO6LT, OO6OV, OO7O7, OOA0B, OOAIV, OOAOV, OOBGT, OOEMP, OOERT, OOET1, OOEU1, OOEY1, OOGTT, OOI4V, OOIRV, OOKET, OOLBT, OOMMP, OOMQ7, OOMU1, OOMWP, OOO0B, OOO6T, OOO77, OOOE7, OOOKT, OOOOV, OOORT, OOOW7, OOPY1, OOQ77, OOT01, OOT91, OOTAV, OOTOV, OOTUV, OOU91, OOUUV, OOWIV, OOWMP, OOWVP, OOY01, OOY0B, OOYKB, OOYU1, OOYYB, OP0EV, OP44V, OP8FZ, OPA91, OPAAZ, OPAOV, OPEAV, OPI4V, OPO4V, OPOIV, OPOUV, OPOY1, OPUAZ, OPUEV, OPWUV, OPYU1, OQ7W7, OQ8E7, OQLE7, OQQL7, OR8AZ, ORA8Z, ORKLT, ORS8Z, OS8RZ, OSR8Z, OSS8Z, OT09V, OT0K1, OT66T, OTT8V, OTUOV, OU091, OU0E1, OU0MP, OU4LP, OUAAZ, OUASZ, OUL4P, OUP8Z, OUP91, OUPAZ, OUPY1, OUU0P, OUUPZ, OUYM1, OUZ91, OV0FB, OV0LB, OV54P, OV5WP, OV9K5, OVALB, OVB6T, OVKFB, OVLEB, OVLFP, OVQWP, OW0EV, OW7O7, OW7Q7, OW7W7, OW90V, OWEEP, OWIWV, OWLW7, OWOM7, OWOVP, OWQ87, OWU0V, OWW9V, OWWL7, OWWOV, OXAA1, OXU01, OXUI1, OXXI1, OXXX1, OY00T, OY0E1, OY0RT, OY0U1, OY0YB, OY98B, OYE0T, OYFKB, OYKFB, OYLYB, OYYYB, OZ0OB, OZ0WP, OZ0YB, OZ9EB, OZ9K1, OZ9O1, OZALB, OZAYB, OZEAB, OZEOB, OZFEB, OZFFP, OZFFZ, OZFRZ, OZFZP, OZO0B, OZO91, OZOYB, OZPRZ, OZR8Z, OZUUP, OZZYB, P00W5, P02G5, P049V, P04YV, P0A0V, P0AW5, P0CC5, P0CU5, P0E9V, P0EWV, P0F25, P0FC5, P0G25, P0K3Z, P0KOZ, P0KRH, P0O55, P0OEV, P0PG5, P0PO5, P0PW5, P0R0H, P0ROZ, P0U25, P0UIV, P0UVP, P0V0P, P0VKP, P0W9V, P0YIV, P13WD, P22K5, P2D95, P2NC5, P33ZZ, P38DD, P3GGD, P3SAH, P409V, P444V, P44O1, P44Y1, P4AIV, P4AYV, P4E0V, P4OA1, P4OK1, P4OO1, P4U81, P4UEV, P4UR1, P55EP, P5GZ5, P6A41, P803H, P80AZ, P838D, P8AAZ, P8D8D, P8FKZ, P8K0Z, P8KKZ, P8KXH, P8OE1, P8UE1, P8X0H, P8X3H, P8XKH, P909V, P9941, P99EV, P99U1, P9E9V, P9K91, P9OE1, P9OK1, P9W9V, P9X9H, PA00H, PA441, PA5G5, PA8FZ, PA9O1, PAA8Z, PAI4V, PAI9V, PAMKP, PAOEV, PAR8H, PAUM1, PAVKP, PAZEP, PC0W5, PCAG5, PCAU5, PCCA5, PCWN5, PD0QP, PD0SH, PD33D, PD3AH, PD3MD, PDGC5, PDK3H, PDK8H, PDSAH, PDUAP, PE99V, PEA91, PEAEP, PEEA1, PEEE1, PEER1, PEI9V, PEK61, PEQQP, PERE1, PERK1, PEUY1, PEY0V, PF2K5, PF3CD, PF83D, PFC2D, PFCWD, PFDAP, PFEKP, PFMCD, PFMMD, PFO55, PFR2D, PFZEP, PG295, PG2WD, PG8CD, PGCD5, PGDC5, PGF5Z, PGG8D, PGKF5, PGKK5, PGO95, PGW8D, PH2MD, PHD8D, PK0O5, PK441, PK53Z, PK5GZ, PK83H, PK8KZ, PKAA1, PKAU1, PKKO5, PKP3Z, PKRXH, PKSIH, PMAA1, PMAAP, PMAU1, PMF3D, PMFCD, PMMAP, PMMMD, PMMMP, PMMPD, PMRR1, PMUO1, PN2D5, PN2W5, PNA3H, PNAF5, PNFK5, PNHFD, PNK55, PNKF5, PNSKH, PO09V, PO0EV, PO4AV, PO90V, POAY1, POI4V, POOE1, POUEV, POUY1, POWUV, POWWV, POYA1, POZAZ, POZFZ, PP0QP, PP2CN, PP2MD, PP33D, PP595, PP5W5, PP8CD, PPCNN, PPCRD, PPCU5, PPCW5, PPCWD, PPD05, PPDUP, PPECN, PPF8D, PPFC5, PPFW5, PPGC5, PPGF5, PPGFZ, PPKGZ, PPMCD, PPMCN, PPMEN, PPMND, PPNF5, PPNMN, PPNWD, PPP3Z, PPP95, PPPC5, PPPRZ, PPPZD, PPQKP, PPS0Z, PPW2N, PPWND, PPWWN, PPZC5, PPZSZ, PQQQP, PR1GD, PR8AH, PRA0H, PREK1, PRKO1, PRMM1, PRNFD, PRRM1, PRRRH, PRW2N, PS0ZZ, PS80H, PS80Z, PS8AH, PS8ZZ, PSIKH, PSR3Z, PU025, PU0IV, PU49V, PU4YV, PU8AZ, PU9EV, PUE91, PUE9V, PUI9V, PURK1, PUUM1, PUUR1, PUVAP, PUYIV, PUYO1, PUZMP, PV00P, PV2CN, PV2RN, PVAKP, PVFAP, PVFFP, PVFKP, PVK0P, PVKAP, PVNCN, PVNEN, PW005, PW0C5, PWCWD, PWF8D, PWNC5, PWO9V, PWOWV, PWWOV, PWWWN, PWWWV, PX0IH, PXAIH, PXIAH, PXIKH, PYKE1, PYKO1, PYRK1, PYRM1, PZ0G5, PZ1WD, PZ295, PZ2C5, PZ2G5, PZ481, PZ641, PZE61, PZEAP, PZG25, PZK61, PZKOZ, PZOFZ, PZOO1, PZR41, PZRZZ, PZS0Z, PZSUZ, PZUMP, Q00DT, Q00JD, Q00QT, Q00YN, Q020J, Q03RD, Q0CQN, Q0DRD, Q0FRD, Q0JTT, Q0Q3D, Q0QRN, Q0QXN, Q0XEN, Q0XIJ, Q0XLN, Q0XQN, Q0YYN, Q20RD, Q2D0D, Q32WD, Q3D3D, Q4EKP, Q4PQP, Q7777, Q77Q7, Q7ER7, Q7EW7, Q7LR7, Q7LS7, Q7LW7, Q7QQN, Q7QR7, Q7QYN, Q7RE7, Q7SS7, QAAPP, QAOOP, QAOWP, QAUAP, QAUWP, QAWEP, QAWLP, QCEQN, QCNYN, QCQEN, QD0GD, QD0RD, QD20D, QD33D, QD3DD, QDAWP, QDRET, QDWKP, QE7QN, QECLN, QEEL7, QEES7, QELCN, QEQCN, QEQTT, QERE7, QESR7, QF2WD, QFGUJ, QFR2D, QG00J, QG0IJ, QG7Q7, QG7R7, QGDDD, QGGGD, QGGQD, QGJ2J, QGMQ7, QGOO7, QGQQ7, QGRR7, QJ02J, QJ03D, QJ0SJ, QJ33D, QJ3WD, QJD0D, QJI0J, QK44P, QKPKP, QL7W7, QLES7, QLLL7, QLNNN, QLQ77, QLQL7, QLQM7, QLQPN, QLR87, QLSRT, QMLR7, QMQQ7, QN0YN, QN70N, QNCYN, QNLW7, QNNQN, QNNYN, QNQNN, QO777, QO7E7, QO8M7, QOUWP, QP3RD, QPDAP, QPEEP, QPFRD, QPGGD, QPPQP, QPR2D, QPRGD, QQ0RN, QQ0YN, QQ4LP, QQ4QP, QQAEP, QQCYN, QQELT, QQEPN, QQEQP, QQGDD, QQGGD, QQGO7, QQGQD, QQKKP, QQLAP, QQLPN, QQLRT, QQMR7, QQN77, QQNNN, QQNQN, QQPDD, QQPEN, QQPGD, QQPQP, QQPWD, QQQ0N, QQQ3D, QQQ87, QQQKP, QQQL7, QQQM7, QQQPD, QQQQN, QQQWD, QQRL7, QQRN7, QQRYN, QQSST, QQTDT, QQTQT, QQU4P, QQUAP, QQUUP, QQWPD, QQXEN, QQXQN, QQYXN, QR00N, QR0XN, QR2FD, QR32D, QREKT, QRN0N, QRNL7, QRQQD, QRRE7, QRXXN, QSES7, QSS2J, QSSE7, QSSS7, QSSSJ, QTDET, QTQ2D, QTQLT, QUAAP, QUAWP, QUPPP, QUUAP, QW7G7, QWG77, QWGM7, QWLEP, QWOEP, QWOLP, QX77N, QX7EN, QXELN, QXEQN, QXLLN, QXLQN, QXNQN, QXOE7, QXQXN, QXXNN, R0061, R008D, R00IH, R00NN, R00XN, R013D, R02YN, R030D, R04R1, R06E1, R06ET, R07M1, R08AH, R0A8H, R0AYH, R0D07, R0DDT, R0EK1, R0EYT, R0F3D, R0G8D, R0GDD, R0GGD, R0GQ7, R0H0N, R0KE1, R0LQ7, R0N0N, R0RYN, R0T2N, R0TLT, R0TNN, R0TYN, R0X0N, R0YST, R100T, R130D, R13WD, R166T, R1E0T, R1F3D, R1GFD, R1TGD, R200N, R28WD, R2W8D, R2WFD, R32DD, R330D, R332D, R3W8D, R44XV, R4AAV, R4AYV, R4MO1, R4OI1, R4RO1, R4U4V, R4X9V, R6001, R60K1, R66LT, R66YV, R6E01, R6EE1, R6MK1, R6SST, R6X01, R6X9V, R6XE1, R6XYV, R6Y6V, R7OO1, R7XE1, R80G7, R88FD, R8F8D, R8IE7, R8X8H, R9OAV, R9UVV, R9VOV, R9X6V, RA08H, RAA9V, RAS8Z, RAX0H, RD00D, RD8I7, RD8IH, RDA0H, RDDQT, RDQDT, RE061, RE6KT, RE6LT, REEK1, REEKT, RER01, RERK1, RERR1, RF0DD, RFD0D, RG28D, RGGFD, RGGWD, RGRM7, RGWQD, RH00H, RH0EN, RH8HH, RH9HH, RH9XH, RHH9H, RHHIN, RHHNN, RHIWN, RHNEN, RHWIN, RHWWN, RHX8H, RHXEN, RHY9H, RI00H, RI2IN, RIHEN, RIIWN, RIMRN, RK00T, RKEE1, RKELT, RKL0T, RKQLT, RLEI7, RLQM7, RLR07, RLRE7, RLSSZ, RLSYT, RLZE7, RLZI7, RLZLZ, RM0G7, RM0Q7, RMIWN, RMKO1, RMLQ7, RMOX1, RMR07, RMRR1, RN2YN, RN30D, RND3D, RNI2N, RNIMN, RNMEN, RNW2D, RO0TT, RO66T, RO6KT, ROAAV, ROOKT, ROOOT, ROU9V, ROXM1, ROZK1, RQK0T, RQLKT, RQLST, RQMR7, RQQLT, RQQQT, RQQWD, RQRE7, RQTQD, RR44V, RR4YV, RR601, RR66V, RR6WV, RR9HH, RR9UV, RRA9V, RRAYV, RRE01, RREE1, RRGM7, RRGR7, RRI2N, RRIIN, RRIN7, RRIXN, RRKE1, RRL07, RRLM7, RRM07, RRMG7, RRML7, RRMM1, RRMO1, RRMWN, RRNR7, RRO01, RROI1, RROK1, RRR0N, RRRE1, RRRG7, RRRIN, RRRL7, RRRM1, RRRO1, RRROV, RRRWV, RRU6V, RRV9H, RRVUV, RRVYH, RRWWV, RRXRN, RRY4V, RRY9H, RRYHH, RRYIN, RRYRN, RS8FZ, RSSSZ, RSSYT, RSYST, RT3ZZ, 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====Additional known quasi-minimal primes (not necessarily the next)==== P₈₁₉₉₃SZ ==Unsolved families== Families for which not even a probable prime is known nor can be ruled out as only contain composites (only count the numbers > base (''b'')) by covering congruence, algebraic factorization, or combine of them. {|class=wikitable |base (''b'')||unsolved family (base-''b'' form)||unsolved family (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||current search limit of length||factorization of numbers in this family |- |13||9{5}||(113×13^''n''−5)/12||116000||[http://factordb.com/index.php?query=%28113*13%5En-5%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |13||A{3}A||(41×13^''n''+1+27)/4||111000||[http://factordb.com/index.php?query=%2841*13%5E%28n%2B1%29%2B27%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |16||{3}AF||(16^''n''+2+619)/5||98000||[http://factordb.com/index.php?query=%2816%5E%28n%2B2%29%2B619%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||1{7}||(23×17^''n''−7)/16||32074||[http://factordb.com/index.php?query=%2823*17%5En-7%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||1F{0}7||32×17^''n''+1+7||32074||[http://factordb.com/index.php?query=32*17%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||4{7}A||(71×17^''n''+1+41)/16||32074||[http://factordb.com/index.php?query=%2871*17%5E%28n%2B1%29%2B41%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||51{0}D||86×17^''n''+1+13||32074||[http://factordb.com/index.php?query=86*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||70F{0}D||2038×17^''n''+1+13||32074||[http://factordb.com/index.php?query=2038*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||8{B}9||(139×17^''n''+1−43)/16||32074||[http://factordb.com/index.php?query=%28139*17%5E%28n%2B1%29-43%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||9{5}9||(149×17^''n''+1+59)/16||32074||[http://factordb.com/index.php?query=%28149*17%5E%28n%2B1%29%2B59%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||95{F}||(2543×17^''n''−15)/16||32074||[http://factordb.com/index.php?query=%282543*17%5En-15%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||A{D}F||(173×17^''n''+1+19)/16||32074||[http://factordb.com/index.php?query=%28173*17%5E%28n%2B1%29%2B19%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||B{0}B3||11×17^''n''+2+190||32074||[http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B190&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||B{0}DB||11×17^''n''+2+232||32074||[http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B232&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}2BE||(11×17^''n''+3−41579)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B3%29-41579%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}2E||(11×17^''n''+2−2411)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29-2411%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}E9||(11×17^''n''+2+773)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B773%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}EE||(11×17^''n''+2+853)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B853%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||D0G{D}||(60381×17^''n''−13)/16||32074||[http://factordb.com/index.php?query=%2860381*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||E9{B}||(3963×17^''n''−11)/16||32074||[http://factordb.com/index.php?query=%283963*17%5En-11%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||F1{9}||(4105×17^''n''−9)/16||1000000||[http://factordb.com/index.php?query=%284105*17%5En-9%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||FD0{D}||(72909×17^''n''−13)/16||32074||[http://factordb.com/index.php?query=%2872909*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||2{7}9D||(47×21^''n''+2+953)/20||20000||[http://factordb.com/index.php?query=%2847*21%5E%28n%2B2%29%2B953%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||2F{C}A||(288×21^''n''+1−13)/5||20000||[http://factordb.com/index.php?query=%28288*21%5E%28n%2B1%29-13%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||4{3}B||(83×21^''n''+1+157)/20||20000||[http://factordb.com/index.php?query=%2883*21%5E%28n%2B1%29%2B157%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||5{0}DJ||5×21^''n''+2+292||20000||[http://factordb.com/index.php?query=5*21%5E%28n%2B2%29%2B292&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{5}FEK||(21^''n''+3+18455)/4||20000||[http://factordb.com/index.php?query=%2821%5E%28n%2B3%29%2B18455%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{7}ID||(7×21^''n''+2+4733)/20||20000||[http://factordb.com/index.php?query=%287*21%5E%28n%2B2%29%2B4733%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||99{0}99H||198×21^''n''+3+4175||20000||[http://factordb.com/index.php?query=198*21%5E%28n%2B3%29%2B4175&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{9}0D||(9×21^''n''+2−3709)/20||20000||[http://factordb.com/index.php?query=%289*21%5E%28n%2B2%29-3709%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{9}D||(9×21^''n''+1+71)/20||20000||[http://factordb.com/index.php?query=%289*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B3{0}EB||234×21^''n''+2+305||20000||[http://factordb.com/index.php?query=234*21%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B9{0}E5||240×21^''n''+2+299||20000||[http://factordb.com/index.php?query=240*21%5E%28n%2B2%29%2B299&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B{D}B||(233×21^''n''+1−53)/20||20000||[http://factordb.com/index.php?query=%28233*21%5E%28n%2B1%29-53%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B{H}6H||(237×21^''n''+2−4637)/20||20000||[http://factordb.com/index.php?query=%28237*21%5E%28n%2B2%29-4637%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||DH{D}||(5813×21^''n''−13)/20||20000||[http://factordb.com/index.php?query=%285813*21%5En-13%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||F{9}D||(309×21^''n''+1+71)/20||20000||[http://factordb.com/index.php?query=%28309*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{F}35||(3×21^''n''+2−1051)/4||20000||[http://factordb.com/index.php?query=%283*21%5E%28n%2B2%29-1051%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||G{0}FK||16×21^''n''+2+335||506000||[http://factordb.com/index.php?query=16*21%5E%28n%2B2%29%2B335&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||H{0}7771||17×21^''n''+4+68062||20000||[http://factordb.com/index.php?query=17*21%5E%28n%2B4%29%2B68062&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||H{D}||(353×21^''n''−13)/20||20000||[http://factordb.com/index.php?query=%28353*21%5En-13%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{J}6J||(19×21^''n''+2−5479)/20||20000||[http://factordb.com/index.php?query=%2819*21%5E%28n%2B2%29-5479%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||7{K}Z||(53×36^''n''+1+101)/7||20000||[http://factordb.com/index.php?query=%2853*36%5E%28n%2B1%29%2B101%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||B{0}EUV||11×36^''n''+3+19255||20000||[http://factordb.com/index.php?query=11*36%5E%28n%2B3%29%2B19255&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||HM{0}N||634×36^''n''+1+23||20000||[http://factordb.com/index.php?query=634*36%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||N{0}YYN||23×36^''n''+3+45311||20000||[http://factordb.com/index.php?query=23*36%5E%28n%2B3%29%2B45311&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||O{L}Z||(123×36^''n''+1+67)/5||100000||[http://factordb.com/index.php?query=%28123*36%5E%28n%2B1%29%2B67%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||S{0}8H||28×36^''n''+2+305||20000||[http://factordb.com/index.php?query=28*36%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |} For base 17, the smallest prime in family {B}2BE may or may not be quasi-minimal prime, since another unsolved family is {B}2E For base 21, the smallest prime in families {9}0D and F{9}D may or may not be quasi-minimal primes, since another unsolved family is {9}D, and the smallest prime in family DH{D} may or may not be quasi-minimal prime, since another unsolved family is H{D} ==Primality certificates for the proven primes > 10²⁹⁹== See also: [[w:Primality certificate|Primality certificate]] and [[w:Elliptic curve primality|Elliptic curve primality]] {|class=wikitable |base (''b'')||index of this quasi-minimal prime in base ''b''||quasi-minimal prime (base-''b'' form)||quasi-minimal prime (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||factordb entry of this prime||primality certificate of this prime |- |9||149||76₃₂₉2||(31×9³³⁰−19)/4||[http://factordb.com/index.php?id=1100000002359003642]||[http://factordb.com/cert.php?id=1100000002359003642] |- |9||150||27₆₈₆07||(23×9⁶⁸⁸−511)/8||[http://factordb.com/index.php?id=1100000002495467486]||[http://factordb.com/cert.php?id=1100000002495467486] |- |9||151||30₁₁₅₈11||3×9¹¹⁶⁰+10||[http://factordb.com/index.php?id=1100000002376318423]||[http://factordb.com/cert.php?id=1100000002376318423] |- |11||1065||A₇₁₃58||11⁷¹⁵−58||[http://factordb.com/index.php?id=1100000003576826487]||[http://factordb.com/cert.php?id=1100000003576826487] |- |11||1066||7₇₅₉44||(7×11⁷⁶¹−367)/10||[http://factordb.com/index.php?id=1100000002505568840]||[http://factordb.com/cert.php?id=1100000002505568840] |- |11||1067||557₁₀₁₁||(607×11¹⁰¹¹−7)/10||[http://factordb.com/index.php?id=1100000002361376522]||[http://factordb.com/cert.php?id=1100000002361376522] |- |13||3165||50₂₇₀44||5×13²⁷²+56||[http://factordb.com/index.php?id=1100000002632397005]||[http://factordb.com/cert.php?id=1100000002632397005] |- |13||3166||9₂₇₁095||(3×13²⁷⁴−6103)/4||[http://factordb.com/index.php?id=1100000003590431654]||[http://factordb.com/cert.php?id=1100000003590431654] |- |13||3167||10₂₈₆7771||13²⁹⁰+16654||[http://factordb.com/index.php?id=1100000003590431633]||[http://factordb.com/cert.php?id=1100000003590431633] |- |13||3168||9₃₀₈1||(3×13³⁰⁹−35)/4||[http://factordb.com/index.php?id=1100000000840126705]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=308&c0=-&EN= 13³⁰⁸−1] |- |13||3169||B₃₄₁C4||(11×13³⁴³+61)/12||[http://factordb.com/index.php?id=1100000003590431618]||[http://factordb.com/cert.php?id=1100000003590431618] |- |13||3170||8B₃₄₃||(107×13³⁴³−11)/12||[http://factordb.com/index.php?id=1100000002321018736]||[http://factordb.com/cert.php?id=1100000002321018736] |- |13||3171||710₃₇₁111||92×13³⁷⁴+183||[http://factordb.com/index.php?id=1100000003590431609]||[http://factordb.com/cert.php?id=1100000003590431609] |- |13||3172||75₃₇₅7||(89×13³⁷⁶+19)/12||[http://factordb.com/index.php?id=1100000003590431596]||[http://factordb.com/cert.php?id=1100000003590431596] |- |13||3173||9B0₃₉₁9||128×13³⁹²+9||[http://factordb.com/index.php?id=1100000002632396790]||[http://factordb.com/cert.php?id=1100000002632396790] |- |13||3174||7B0B₃₉₇||(15923×13³⁹⁷−11)/12||[http://factordb.com/index.php?id=1100000003590431574]||[http://factordb.com/cert.php?id=1100000003590431574] |- |13||3175||10₄₁₄93||13⁴¹⁶+120||[http://factordb.com/index.php?id=1100000002523249240]||[http://factordb.com/cert.php?id=1100000002523249240] |- |13||3176||81010₄₁₅1||17746×13⁴¹⁶+1||[http://factordb.com/index.php?id=1100000003590431555]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3177||8110₄₃₅1||1366×13⁴³⁶+1||[http://factordb.com/index.php?id=1100000002373259109]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3178||B7₄₈₆||(139×13⁴⁸⁶−7)/12||[http://factordb.com/index.php?id=1100000002321015892]||[http://factordb.com/cert.php?id=1100000002321015892] |- |13||3179||B₅₆₃C||(11×13⁵⁶⁴+1)/12||[http://factordb.com/index.php?id=1100000000000217927]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=564&c0=-&EN= 13⁵⁶⁴−1] |- |13||3180||1B₅₇₆||(23×13⁵⁷⁶−11)/12||[http://factordb.com/index.php?id=1100000002321021456]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=576&c0=-&EN= 13⁵⁷⁶−1] |- |13||3181||80₆₉₃87||8×13⁶⁹⁵+111||[http://factordb.com/index.php?id=1100000002615636527]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 has a large prime factor, factordb entry of this prime factor is [http://factordb.com/index.php?id=1100000002615636532], and primality certificate of this prime factor is [http://factordb.com/cert.php?id=1100000002615636532] |- |13||3182||CC5₇₁₃||(2021×13⁷¹³−5)/12||[http://factordb.com/index.php?id=1100000002615627353]||[http://factordb.com/cert.php?id=1100000002615627353] |- |13||3183||B₈₃₄74||(11×13⁸³⁶−719)/12||[http://factordb.com/index.php?id=1100000003590430871]||[http://factordb.com/cert.php?id=1100000003590430871] |- |13||3184||9₉₆₈B||(3×13⁹⁶⁹+5)/4||[http://factordb.com/index.php?id=1100000000258566244]||[http://factordb.com/cert.php?id=1100000000258566244] |- |13||3185||10₁₂₉₅181||13¹²⁹⁸+274||[http://factordb.com/index.php?id=1100000002615445013]||[http://factordb.com/cert.php?id=1100000002615445013] |- |13||3186||9₁₃₆₂5||(3×13¹³⁶³−19)/4||[http://factordb.com/index.php?id=1100000002321017776]||[http://factordb.com/cert.php?id=1100000002321017776] |- |13||3187||7₁₅₀₄1||(7×13¹⁵⁰⁵−79)/12||[http://factordb.com/index.php?id=1100000002320890755]||[http://factordb.com/cert.php?id=1100000002320890755] |- |13||3188||930₁₅₅₁1||120×13¹⁵⁵²+1||[http://factordb.com/index.php?id=1100000000765961452]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3189||720₂₂₉₇2||93×13²²⁹⁸+2||[http://factordb.com/index.php?id=1100000002632396910]||[http://factordb.com/cert.php?id=1100000002632396910] |- |13||3190||1770₂₇₀₃17||267×13²⁷⁰⁵+20||[http://factordb.com/index.php?id=1100000003590430825]||[http://factordb.com/cert.php?id=1100000003590430825] |- |13||3191||390₆₂₆₆1||48×13⁶²⁶⁷+1||[http://factordb.com/index.php?id=1100000000765961441]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3192||B0₆₅₄₀BBA||11×13⁶⁵⁴³+2012||[http://factordb.com/index.php?id=1100000002616382906]||[http://factordb.com/cert.php?id=1100000002616382906] |- |13||3193||C₁₀₆₃₁92||13¹⁰⁶³³−50||[http://factordb.com/index.php?id=1100000003590493750]||[http://factordb.com/cert.php?id=1100000003590493750] |- |14||649||34D₇₀₈||47×14⁷⁰⁸−1||[http://factordb.com/index.php?id=1100000001540144903]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |14||650||4D₁₉₆₉₈||5×14¹⁹⁶⁹⁸−1||[http://factordb.com/index.php?id=1100000000884560233]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |16||2328||880₂₄₆7||136×16²⁴⁷+7||[http://factordb.com/index.php?id=1100000002468140199]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has a large prime factor, and this prime factor is < 10²⁹⁹ |- |16||2329||D4₂₆₃D||(199×16²⁶⁴+131)/15||[http://factordb.com/index.php?id=1100000002468170238]||[http://factordb.com/cert.php?id=1100000002468170238] |- |16||2330||E0₂₆₁4DD||14×16²⁶⁴+1245||[http://factordb.com/index.php?id=1100000003588388352]||[http://factordb.com/cert.php?id=1100000003588388352] |- |16||2331||8C0₂₉₀ED||140×16²⁹²+237||[http://factordb.com/index.php?id=1100000003588388307]||[http://factordb.com/cert.php?id=1100000003588388307] |- |16||2332||DA₃₀₅5||(41×16³⁰⁶−17)/3||[http://factordb.com/index.php?id=1100000003588388284]||[http://factordb.com/cert.php?id=1100000003588388284] |- |16||2333||CE80₄₂₂D||3304×16⁴²³+13||[http://factordb.com/index.php?id=1100000003588388257]||[http://factordb.com/cert.php?id=1100000003588388257] |- |16||2334||5F₅₄₄6F||6×16⁵⁴⁶−145||[http://factordb.com/index.php?id=1100000002604723967]||[http://factordb.com/cert.php?id=1100000002604723967] |- |16||2335||88F₅₄₅||137×16⁵⁴⁵−1||[http://factordb.com/index.php?id=1100000000413679658]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |16||2336||BE0₇₉₂BB||190×16⁷⁹⁴+187||[http://factordb.com/index.php?id=1100000003588387938]||[http://factordb.com/cert.php?id=1100000003588387938] |- |16||2337||D9₁₀₅₂||(68×16¹⁰⁵²−3)/5||[http://factordb.com/index.php?id=1100000002321036020]||[http://factordb.com/cert.php?id=1100000002321036020] |- |16||2338||FAF₁₀₆₂45||251×16¹⁰⁶⁴−187||[http://factordb.com/index.php?id=1100000003588387610]||[http://factordb.com/cert.php?id=1100000003588387610] |- |16||2339||F8₁₅₁₇F||(233×16¹⁵¹⁸+97)/15||[http://factordb.com/index.php?id=1100000000633744824]||[http://factordb.com/cert.php?id=1100000000633744824] |- |16||2340||20₁₇₁₃321||2×16¹⁷¹⁶+801||[http://factordb.com/index.php?id=1100000003588386735]||[http://factordb.com/cert.php?id=1100000003588386735] |- |16||2341||300F₁₉₆₀AF||769×16¹⁹⁶²−81||[http://factordb.com/index.php?id=1100000003588368750]||[http://factordb.com/cert.php?id=1100000003588368750] |- |16||2342||90₃₅₄₂91||9×16³⁵⁴⁴+145||[http://factordb.com/index.php?id=1100000000633424191]||[http://factordb.com/cert.php?id=1100000000633424191] |- |16||2343||5BC₃₇₀₀D||(459×16³⁷⁰¹+1)/5||[http://factordb.com/index.php?id=1100000000993764322]||[http://factordb.com/cert.php?id=1100000000993764322] |- |16||2344||D0B₁₇₈₀₄||(3131×16¹⁷⁸⁰⁴−11)/15||[http://factordb.com/index.php?id=1100000003589278511]||[http://factordb.com/cert.php?id=1100000003589278511] |- |18||547||80₂₉₈B||8×18²⁹⁹+11||[http://factordb.com/index.php?id=1100000002355574745]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has sum-of-two-cubes algebraic factorization, 6×18⁹⁹+1 is an algebraic factor of ''N''+1, factordb entry of 6×18⁹⁹+1 is [http://factordb.com/index.php?id=1100000000900149167] |- |18||548||H₇₆₆FH||18⁷⁶⁸−37||[http://factordb.com/index.php?id=1100000003590430490]||[http://factordb.com/cert.php?id=1100000003590430490] |- |18||549||C0₆₂₆₈C5||12×18⁶²⁷⁰+221||[http://factordb.com/index.php?id=1100000003590442437]||[http://factordb.com/cert.php?id=1100000003590442437] |- |20||3301||H₂₄₇A0H||(17×20²⁵⁰−59677)/19||[http://factordb.com/index.php?id=1100000003590502619]||[http://factordb.com/cert.php?id=1100000003590502619] |- |20||3302||7₂₄₉A7||(7×20²⁵¹+1133)/19||[http://factordb.com/index.php?id=1100000003590502602]||[http://factordb.com/cert.php?id=1100000003590502602] |- |20||3303||J7₂₇₀||(368×20²⁷⁰−7)/19||[http://factordb.com/index.php?id=1100000002325395462]||[http://factordb.com/cert.php?id=1100000002325395462] |- |20||3304||J₃₃₀CCC7||20³³⁴−58953||[http://factordb.com/index.php?id=1100000003590502572]||[http://factordb.com/cert.php?id=1100000003590502572] |- |20||3305||40₃₈₇404B||4×20³⁹¹+32091||[http://factordb.com/index.php?id=1100000003590502563]||[http://factordb.com/cert.php?id=1100000003590502563] |- |20||3306||EC0₄₂₉7||292×20⁴³⁰+7||[http://factordb.com/index.php?id=1100000002633348702]||[http://factordb.com/cert.php?id=1100000002633348702] |- |20||3307||G₄₄₇99||(16×20⁴⁴⁹−2809)/19||[http://factordb.com/index.php?id=1100000000840126753]||[http://factordb.com/cert.php?id=1100000000840126753] |- |20||3308||3A₅₂₇3||(67×20⁵²⁸−143)/19||[http://factordb.com/index.php?id=1100000003590502531]||[http://factordb.com/cert.php?id=1100000003590502531] |- |20||3309||E₅₆₆C7||(14×20⁵⁶⁸−907)/19||[http://factordb.com/index.php?id=1100000003590502516]||[http://factordb.com/cert.php?id=1100000003590502516] |- |20||3310||JCJ₆₂₉||393×20⁶²⁹−1||[http://factordb.com/index.php?id=1100000001559454258]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |20||3311||J₆₅₅05J||20⁶⁵⁸−7881||[http://factordb.com/index.php?id=1100000003590502490]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has a large prime factor, factordb entry of this prime factor is [http://factordb.com/index.php?id=1100000003591067052], and primality certificate of this prime factor is [http://factordb.com/cert.php?id=1100000003591067052] |- |20||3312||50₁₁₆₃AJ||5×20¹¹⁶⁵+219||[http://factordb.com/index.php?id=1100000003590502412]||[http://factordb.com/cert.php?id=1100000003590502412] |- |20||3313||CD₂₄₄₉||(241×20²⁴⁴⁹−13)/19||[http://factordb.com/index.php?id=1100000002325393915]||[http://factordb.com/cert.php?id=1100000002325393915] |- |20||3314||G0₆₂₆₉D||16×20⁶²⁷⁰+13||[http://factordb.com/index.php?id=1100000003590539457]||[http://factordb.com/cert.php?id=1100000003590539457] |- |22||7984||I7G0₂₅₄H||8882×22²⁵⁵+17||[http://factordb.com/index.php?id=1100000003591372788]||[http://factordb.com/cert.php?id=1100000003591372788] |- |22||7985||D0₂₅₅5EEF||13×22²⁵⁹+60339||[http://factordb.com/index.php?id=1100000003591371932]||[http://factordb.com/cert.php?id=1100000003591371932] |- |22||7986||IK₃₂₂F||(398×22³²³−125)/21||[http://factordb.com/index.php?id=1100000000840384145]||[http://factordb.com/cert.php?id=1100000000840384145] |- |22||7987||C0₃₄₀G9||12×22³⁴²+361||[http://factordb.com/index.php?id=1100000000840384159]||[http://factordb.com/cert.php?id=1100000000840384159] |- |22||7988||77E₃₄₈K7||(485×22³⁵⁰+373)/3||[http://factordb.com/index.php?id=1100000003591369779]||[http://factordb.com/cert.php?id=1100000003591369779] |- |22||7989||J₃₇₉KJ||(19×22³⁸¹+443)/21||[http://factordb.com/index.php?id=1100000003591369027]||[http://factordb.com/cert.php?id=1100000003591369027] |- |22||7990||J₃₈₈EJ||(19×22³⁹⁰−2329)/21||[http://factordb.com/index.php?id=1100000003591367729]||[http://factordb.com/cert.php?id=1100000003591367729] |- |22||7991||DJ₄₀₀||(292×22⁴⁰⁰−19)/21||[http://factordb.com/index.php?id=1100000002325880110]||[http://factordb.com/cert.php?id=1100000002325880110] |- |22||7992||E₄₀₄K7||(2×22⁴⁰⁶+373)/3||[http://factordb.com/index.php?id=1100000003591366298]||[http://factordb.com/cert.php?id=1100000003591366298] |- |22||7993||66F₄₅₃B3||(971×22⁴⁵⁵−705)/7||[http://factordb.com/index.php?id=1100000003591365809]||[http://factordb.com/cert.php?id=1100000003591365809] |- |22||7994||L0₄₅₄B63||21×22⁴⁵⁷+5459||[http://factordb.com/index.php?id=1100000003591365331]||[http://factordb.com/cert.php?id=1100000003591365331] |- |22||7995||L₄₈₃G3||22⁴⁸⁵−129||[http://factordb.com/index.php?id=1100000003591364730]||[http://factordb.com/cert.php?id=1100000003591364730] |- |22||7996||E60₄₉₆L||314×22⁴⁹⁷+21||[http://factordb.com/index.php?id=1100000000632703239]||[http://factordb.com/cert.php?id=1100000000632703239] |- |22||7997||I₆₂₆AF||(6×22⁶²⁸−1259)/7||[http://factordb.com/index.php?id=1100000000632724334]||[http://factordb.com/cert.php?id=1100000000632724334] |- |22||7998||K0₇₆₀EC1||20×22⁷⁶³+7041||[http://factordb.com/index.php?id=1100000000632724415]||[http://factordb.com/cert.php?id=1100000000632724415] |- |22||7999||J0₇₆₇IGGJ||19×22⁷⁷¹+199779||[http://factordb.com/index.php?id=1100000003591362567]||[http://factordb.com/cert.php?id=1100000003591362567] |- |22||8000||7₉₅₉K7||(22⁹⁶¹+857)/3||[http://factordb.com/index.php?id=1100000003591361817]||[http://factordb.com/cert.php?id=1100000003591361817] |- |22||8001||L₂₃₈₅KE7||22²³⁸⁸−653||[http://factordb.com/index.php?id=1100000003591360774]||[http://factordb.com/cert.php?id=1100000003591360774] |- |22||8002||7₃₈₁₅2L||(22³⁸¹⁷−289)/3||[http://factordb.com/index.php?id=1100000003591359839]||[http://factordb.com/cert.php?id=1100000003591359839] |- |24||3400||I0₂₄₁I5||18×24²⁴³+437||[http://factordb.com/index.php?id=1100000002633360037]||[http://factordb.com/cert.php?id=1100000002633360037] |- |24||3401||D0₂₅₉KKD||13×24²⁶²+12013||[http://factordb.com/index.php?id=1100000003593270725]||[http://factordb.com/cert.php?id=1100000003593270725] |- |24||3402||C7₂₉₈||(283×24²⁹⁸−7)/23||[http://factordb.com/index.php?id=1100000002326181235]||[http://factordb.com/cert.php?id=1100000002326181235] |- |24||3403||20₃₁₃7||2×24³¹⁴+7||[http://factordb.com/index.php?id=1100000002355610241]||[http://factordb.com/cert.php?id=1100000002355610241] |- |24||3404||BC0₃₃₁B||276×24³³²+11||[http://factordb.com/index.php?id=1100000002633359842]||[http://factordb.com/cert.php?id=1100000002633359842] |- |24||3405||N₂₆₄₄LLN||24²⁶⁴⁷−1201||[http://factordb.com/index.php?id=1100000003593270089]||[http://factordb.com/cert.php?id=1100000003593270089] |- |24||3406||D₂₆₉₈LD||(13×24²⁷⁰⁰+4403)/23||[http://factordb.com/index.php?id=1100000003593269876]||[http://factordb.com/cert.php?id=1100000003593269876] |- |24||3407||A0₂₉₅₁8ID||10×24²⁹⁵⁴+5053||[http://factordb.com/index.php?id=1100000003593269654]||[http://factordb.com/cert.php?id=1100000003593269654] |- |24||3408||88N₅₉₅₁||201×24⁵⁹⁵¹−1||[http://factordb.com/index.php?id=1100000003593275880]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |24||3409||N00N₈₁₂₉LN||13249×24⁸¹³¹−49||[http://factordb.com/index.php?id=1100000003593391606]||[http://factordb.com/cert.php?id=1100000003593391606] |- |30||2613||AN₂₀₆||(313×30²⁰⁶−23)/29||[http://factordb.com/index.php?id=1100000002327651073]||[http://factordb.com/cert.php?id=1100000002327651073] |- |30||2614||M₂₄₁QB||(22×30²⁴³+3139)/29||[http://factordb.com/index.php?id=1100000003593408295]||[http://factordb.com/cert.php?id=1100000003593408295] |- |30||2615||M0₅₄₇SS7||22×30⁵⁵⁰+26047||[http://factordb.com/index.php?id=1100000003593407988]||[http://factordb.com/cert.php?id=1100000003593407988] |- |30||2616||C0₁₀₂₂1||12×30¹⁰²³+1||[http://factordb.com/index.php?id=1100000000785448736]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |30||2617||5₄₈₈₂J||(5×30⁴⁸⁸³+401)/29||[http://factordb.com/index.php?id=1100000002327649423]||[http://factordb.com/cert.php?id=1100000002327649423] |- |30||2619||OT₃₄₂₀₅||25×30³⁴²⁰⁵−1||[http://factordb.com/index.php?id=1100000000800812865]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |} ==Unproven PRPs== {|class=wikitable |base (''b'')||index of this quasi-minimal prime in base ''b'' (assuming the primality of all PRP in base ''b'')||unproven PRP (base-''b'' form)||unproven PRP (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||factordb entry of this PRP |- |11||1068||57₆₂₆₆₈||(57×11⁶²⁶⁶⁸−7)/10||[http://factordb.com/index.php?id=1100000003573679860] |- |13||3194||C5₂₃₇₅₅C||(149×13²³⁷⁵⁶+79)/12||[http://factordb.com/index.php?id=1100000003590647776] |- |13||3195||80₃₂₀₁₇111||8×13³²⁰²⁰+183||[http://factordb.com/index.php?id=1100000000490878060] |- |16||2345||DB₃₂₂₃₄||(206×16³²²³⁴−11)/15||[http://factordb.com/index.php?id=1100000002383583629] |- |16||2346||4₇₂₇₈₅DD||(4×16⁷²⁷⁸⁷+2291)/15||[http://factordb.com/index.php?id=1100000003615909841] |- |22||8003||BK₂₂₀₀₁5||(251×22²²⁰⁰²−335)/21||[http://factordb.com/index.php?id=1100000003594696838] |- |30||2618||I0₂₄₆₀₈D||18×30²⁴⁶⁰⁹+13||[http://factordb.com/index.php?id=1100000003593967511] |} All these PRPs pass the [[w:Miller–Rabin primality test|Miller–Rabin primality test]] to bases 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and 61, and pass the [[w:Lucas pseudoprime#Strong Lucas pseudoprimes|strong Lucas primality test]] with parameters (''P'', ''Q'') defined by Selfridge's Method ''A'', and [[w:Trial division|trial factored]] to 10¹⁶. (Thus, they pass the [[w:Baillie–PSW primality test|Baillie–PSW primality test]]) ==Proof== ===Base 2=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. ===Base 3=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (2,1), (2,2) * Case (1,1): ** Since 12, 21, 111 are primes, we only need to consider the family 1{0}1 (since any digits 1, 2 between them will produce smaller primes) *** All numbers of the form 1{0}1 are divisible by 2, thus cannot be prime. * Case (1,2): ** 12 is prime, and thus the only minimal prime in this family. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,2): ** Since 21, 12 are primes, we only need to consider the family 2{0,2}2 (since any digits 1 between them will produce smaller primes) *** All numbers of the form 2{0,2}2 are divisible by 2, thus cannot be prime. ===Base 4=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (2,1), (2,3), (3,1), (3,3) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 11, 31, 221 are primes, we only need to consider the family 2{0}1 (since any digits 1, 2, 3 between them will produce smaller primes) *** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 31, 13, 23 are primes, we only need to consider the family 3{0,3}3 (since any digits 1, 2 between them will produce smaller primes) *** All numbers of the form 3{0,3}3 are divisible by 3, thus cannot be prime. ===Base 5=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4) * Case (1,1): ** Since 12, 21, 111, 131 are primes, we only need to consider the family 1{0,4}1 (since any digits 1, 2, 3 between them will produce smaller primes) *** All numbers of the form 1{0,4}1 are divisible by 2, thus cannot be prime. * Case (1,2): ** 12 is prime, and thus the only minimal prime in this family. * Case (1,3): ** Since 12, 23, 43, 133 are primes, we only need to consider the family 1{0,1}3 (since any digits 2, 3, 4 between them will produce smaller primes) *** Since 111 is prime, we only need to consider the families 1{0}3 and 1{0}1{0}3 (since any digit combo 11 between (1,3) will produce smaller primes) **** All numbers of the form 1{0}3 are divisible by 2, thus cannot be prime. **** For the 1{0}1{0}3 family, since 10103 is prime, we only need to consider the families 1{0}13 and 11{0}3 (since any digit combo 010 between (1,3) will produce smaller primes) ***** The smallest prime of the form 1{0}13 is 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013, which can be written as 1(0^93)13 and equal the prime 5^95+8 ([http://factordb.com/index.php?id=1100000000034686071 factordb]) ***** All numbers of the form 11{0}3 are divisible by 3, thus cannot be prime. * Case (1,4): ** Since 12, 34, 104 are primes, we only need to consider the family 1{1,4}4 (since any digits 0, 2, 3 between them will produce smaller primes) *** Since 111, 414 are primes, we only need to consider the families 1{4}4 and 11{4}4 (since any digit combo 11 or 41 between them will produce smaller primes) **** The smallest prime of the form 1{4}4 is 14444. **** All numbers of the form 11{4}4 are divisible by 2, thus cannot be prime. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,2): ** Since 21, 23, 12, 32 are primes, we only need to consider the family 2{0,2,4}2 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 2{0,2,4}2 are divisible by 2, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,4): ** Since 21, 23, 34 are primes, we only need to consider the family 2{0,2,4}4 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 2{0,2,4}4 are divisible by 2, thus cannot be prime. * Case (3,1): ** Since 32, 34, 21 are primes, we only need to consider the family 3{0,1,3}1 (since any digits 2, 4 between them will produce smaller primes) *** Since 313, 111, 131, 3101 are primes, we only need to consider the families 3{0,3}1 and 3{0,3}11 (since any digit combo 10, 11, 13 between (3,1) will produce smaller primes) **** For the 3{0,3}1 family, we can separate this family to four families: ***** For the 30{0,3}01 family, we have the prime 30301, and the remain case is the family 30{0}01. ****** All numbers of the form 30{0}01 are divisible by 2, thus cannot be prime. ***** For the 30{0,3}31 family, note that there must be an even number of 3's between (30,31), or the result number will be divisible by 2 and cannot be prime. ****** Since 33331 is prime, any digit combo 33 between (30,31) will produce smaller primes. ******* Thus, the only possible prime is the smallest prime in the family 30{0}31, and this prime is 300031. ***** For the 33{0,3}01 family, note that there must be an even number of 3's between (33,01), or the result number will be divisible by 2 and cannot be prime. ****** Since 33331 is prime, any digit combo 33 between (33,01) will produce smaller primes. ******* Thus, the only possible prime is the smallest prime in the family 33{0}01, and this prime is 33001. ***** For the 33{0,3}31 family, we have the prime 33331, and the remain case is the family 33{0}31. ****** All numbers of the form 33{0}31 are divisible by 2, thus cannot be prime. **** All numbers of the form 3{0,3}11 are divisible by 3, thus cannot be prime. * Case (3,2): ** 32 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 32, 34, 23, 43, 313 are primes, we only need to consider the family 3{0,3}3 (since any digits 1, 2, 4 between them will produce smaller primes) *** All numbers of the form 3{0,3}3 are divisible by 3, thus cannot be prime. * Case (3,4): ** 34 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 43, 21, 401 are primes, we only need to consider the family 4{1,4}1 (since any digits 0, 2, 3 between them will produce smaller primes) *** Since 414, 111 are primes, we only need to consider the families 4{4}1 and 4{4}11 (since any digit combo 14 or 11 between them will produce smaller primes) **** The smallest prime of the form 4{4}1 is 44441. **** All numbers of the form 4{4}11 are divisible by 2, thus cannot be prime. * Case (4,2): ** Since 43, 12, 32 are primes, we only need to consider the family 4{0,2,4}2 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 4{0,2,4}2 are divisible by 2, thus cannot be prime. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,4): ** Since 43, 34, 414 are primes, we only need to consider the family 4{0,2,4}4 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 4{0,2,4}4 are divisible by 2, thus cannot be prime. ===Base 6=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,5), (2,1), (2,5), (3,1), (3,5), (4,1), (4,5), (5,1), (5,5) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 11, 21, 31, 51 are primes, we only need to consider the family 4{0,4}1 (since any digits 1, 2, 3, 5 between them will produce smaller primes) *** Since 4401 and 4441 are primes, we only need to consider the families 4{0}1 and 4{0}41 (since any digits combo 40 and 44 between them will produce smaller primes) **** All numbers of the form 4{0}1 are divisible by 5, thus cannot be prime. **** The smallest prime of the form 4{0}41 is 40041 * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 15, 25, 35, 45 are primes, we only need to consider the family 5{0,5}5 (since any digits 1, 2, 3, 4 between them will produce smaller primes) *** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. ===Base 7=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) * Case (1,1): ** Since 14, 16, 41, 61, 131 are primes, we only need to consider the family 1{0,1,2,5}1 (since any digits 3, 4, 6 between them will produce smaller primes) *** Since the digit sum of primes must be odd (otherwise the number will be divisible by 2, thus cannot be prime), there is an odd total number of 1 and 5 in the {} **** If there are >=3 number of 1 and 5 in the {}: ***** If there is 111 in the {}, then we have the prime 11111 ***** If there is 115 in the {}, then the prime 115 is a subsequence ***** If there is 151 in the {}, then the prime 115 is a subsequence ***** If there is 155 in the {}, then the prime 155 is a subsequence ***** If there is 511 in the {}, then the current number is 15111, which has digit sum = 12, but digit sum divisible by 3 will cause the number divisible by 3 and cannot be prime, and we cannot add more 1 or 5 to this number (to avoid 11111, 155, 515, 551 as subsequence), thus we must add at least one 2 to this number, but then the number has both 2 and 5, and will have either 25 or 52 as subsequence, thus cannot be minimal prime ***** If there is 515 in the {}, then the prime 515 is a subsequence ***** If there is 551 in the {}, then the prime 551 is a subsequence ***** If there is 555 in the {}, then the prime 551 is a subsequence **** Thus there is only one 1 (and no 5) or only one 5 (and no 1) in the {}, i.e. we only need to consider the families 1{0,2}1{0,2}1 and 1{0,2}5{0,2}1 ***** For the 1{0,2}1{0,2}1 family, since 1211 is prime, we only need to consider the family 1{0}1{0,2}1 ****** Since all numbers of the form 1{0}1{0}1 are divisible by 3 and cannot be prime, we only need to consider the family 1{0}1{0}2{0}1 ******* Since 11201 is prime, we only need to consider the family 1{0}1{0}21 ******** The smallest prime of the form 11{0}21 is 1100021 ******** All numbers of the form 101{0}21 are divisible by 5, thus cannot be prime ******** The smallest prime of the form 1001{0}21 is 100121 ********* Since this prime has no 0 between 1{0}1 and 21, we do not need to consider more families ***** For the 1{0,2}5{0,2}1 family, since 25 and 52 are primes, we only need to consider the family 1{0}5{0}1 ****** Since 1051 is prime, we only need to consider the family 15{0}1 ******* The smallest prime of the form 15{0}1 is 150001 * Case (1,2): ** Since 14, 16, 32, 52 are primes, we only need to consider the family 1{0,1,2}2 (since any digits 3, 4, 5, 6 between them will produce smaller primes) *** Since 1112 and 1222 are primes, there is at most one 1 and at most one 2 in {} **** If there are one 1 and one 2 in {}, then the digit sum is 6, and the number will be divisible by 6 and cannot be prime. **** If there is one 1 but no 2 in {}, then the digit sum is 4, and the number will be divisible by 2 and cannot be prime. **** If there is no 1 but one 2 in {}, then the form is 1{0}2{0}2 ***** Since 1022 and 1202 are primes, we only need to consider the number 122 ****** 122 is not prime. **** If there is no 1 and no 2 in {}, then the digit sum is 3, and the number will be divisible by 3 and cannot be prime. * Case (1,3): ** Since 14, 16, 23, 43, 113, 133 are primes, we only need to consider the family 1{0,5}3 (since any digits 1, 2, 3, 4, 6 between them will produce smaller primes) *** Since 155 is prime, we only need to consider the family 1{0}3 and 1{0}5{0}3 **** All numbers of the form 1{0}3 are divisible by 2, thus cannot be prime. **** All numbers of the form 1{0}5{0}3 are divisible by 3, thus cannot be prime. * Case (1,4): ** 14 is prime, and thus the only minimal prime in this family. * Case (1,5): ** Since 14, 16, 25, 65, 115, 155 are primes, we only need to consider the family 1{0,3}5 (since any digits 1, 2, 4, 5, 6 between them will produce smaller primes) *** All numbers of the form 1{0,3}5 are divisible by 3, thus cannot be prime. * Case (1,6): ** 16 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 25, 41, 61, 221 are primes, we only need to consider the family 2{0,1}1 (since any digits 2, 3, 4, 5, 6 between them will produce smaller primes) *** Since 2111 is prime, we only need to consider the families 2{0}1 and 2{0}1{0}1 **** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. **** All numbers of the form 2{0}1{0}1 are divisible by 2, thus cannot be prime. * Case (2,2): ** Since 23, 25, 32, 52, 212 are primes, we only need to consider the family 2{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,4): ** Since 23, 25, 14 are primes, we only need to consider the family 2{0,2,4,6}4 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}4 are divisible by 2, thus cannot be prime. * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (2,6): ** Since 23, 25, 16, 56 are primes, we only need to consider the family 2{0,2,4,6}6 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}6 are divisible by 2, thus cannot be prime. * Case (3,1): ** Since 32, 41, 61 are primes, we only need to consider the family 3{0,1,3,5}1 (since any digits 2, 4, 6 between them will produce smaller primes) *** Since 551 is prime, we only need to consider the family 3{0,1,3}1 and 3{0,1,3}5{0,1,3}1 (since any digits combo 55 between (3,1) will produce smaller primes) **** For the 3{0,1,3}1 family, since 3031 and 131 are primes, we only need to consider the families 3{0,1}1 and 3{3}3{0,1}1 (since any digits combo 03, 13 between (3,1) will produce smaller primes, thus for the digits between (3,1), all 3's must be before all 0's and 1's, and thus we can let the red 3 in 3{3}3{0,1}1 be the rightmost 3 between (3,1), all digits before this 3 must be 3's, and all digits after this 3 must be either 0's or 1's) ***** For the 3{0,1}1 family: ****** If there are >=2 0's and >=1 1's between (3,1), then at least one of 30011, 30101, 31001 will be a subsequence. ****** If there are no 1's between (3,1), then the form will be 3{0}1 ******* All numbers of the form 3{0}1 are divisible by 2, thus cannot be prime. ****** If there are no 0's between (3,1), then the form will be 3{1}1 ******* The smallest prime of the form 3{1}1 is 31111 ****** If there are exactly 1 0's between (3,1), then there must be <3 1's between (3,1), or 31111 will be a subsequence. ******* If there are 2 1's between (3,1), then the digit sum is 6, thus the number is divisible by 6 and cannot be prime. ******* If there are 1 1's between (3,1), then the number can only be either 3101 or 3011 ******** Neither 3101 nor 3011 is prime. ******* If there are no 1's between (3,1), then the number must be 301 ******** 301 is not prime. ***** For the 3{3}3{0,1}1 family: ****** If there are at least one 3 between (3,3{0,1}1) and at least one 1 between (3{3}3,1), then 33311 will be a subsequence. ****** If there are no 3 between (3,3{0,1}1), then the form will be 33{0,1}1 ******* If there are at least 3 1's between (33,1), then 31111 will be a subsequence. ******* If there are exactly 2 1's between (33,1), then the digit sum is 12, thus the number is divisible by 3 and cannot be prime. ******* If there are exactly 1 1's between (33,1), then the digit sum is 11, thus the number is divisible by 2 and cannot be prime. ******* If there are no 1's between (33,1), then the form will be 33{0}1 ******** The smallest prime of the form 33{0}1 is 33001 ****** If there are no 1 between (3{3}3,1), then the form will be 3{3}3{0}1 ******* If there are at least 2 0's between (3{3}3,1), then 33001 will be a subsequence. ******* If there are exactly 1 0's between (3{3}3,1), then the form is 3{3}301 ******** The smallest prime of the form 3{3}301 is 33333301 ******* If there are no 0's between (3{3}3,1), then the form is 3{3}31 ******** The smallest prime of the form 3{3}31 is 33333333333333331 **** For the 3{0,1,3}5{0,1,3}1 family, since 335 is prime, we only need to consider the family 3{0,1}5{0,1,3}1 ***** Numbers containing 3 between (3{0,1}5,1): ****** The form is 3{0,1}5{0,1,3}3{0,1,3}1 ******* Since 3031 and 131 are primes, we only need to consider the family 35{3}3{0,1,3}1 (since any digits combo 03, 13 between (3,1) will produce smaller primes) ******** Since 533 is prime, we only need to consider the family 353{0,1}1 (since any digits combo 33 between (35,1) will produce smaller primes) ********* Since 5011 is prime, we only need to consider the family 353{1}{0}1 (since any digits combo 01 between (353,1) will produce smaller primes) ********** If there are at least 3 1's between (353,{0}1), then 31111 will be a subsequence. ********** If there are exactly 2 1's between (353,{0}1), then the digit sum is 20, thus the number is divisible by 2 and cannot be prime. ********** If there are exactly 1 1's between (353,{0}1), then the form is 3531{0}1 *********** The smallest prime of the form 3531{0}1 is 3531001, but it is not minimal prime since 31001 is prime. ********** If there are no 1's between (353,{0}1), then the digit sum is 15, thus the number is divisible by 6 and cannot be prime. ***** Numbers not containing 3 between (3{0,1}5,1): ****** The form is 3{0,1}5{0,1}1 ******* If there are >=2 0's and >=1 1's between (3,1), then at least one of 30011, 30101, 31001 will be a subsequence. ******* If there are no 1's between (3,1), then the form will be 3{0}5{0}1 ******** All numbers of the form 3{0}5{0}1 are divisible by 3, thus cannot be prime. ******* If there are no 0's between (3,1), then the form will be 3{1}5{1}1 ******** If there are >=3 1's between (3,1), then 31111 will be a subsequence. ******** If there are exactly 2 1's between (3,1), then the number can only be 31151, 31511, 35111 ********* None of 31151, 31511, 35111 are primes. ******** If there are exactly 1 1's between (3,1), then the digit sum is 13, thus the number is divisible by 2 and cannot be prime. ******** If there are no 1's between (3,1), then the number is 351 ********* 351 is not prime. ******* If there are exactly 1 0's between (3,1), then the form will be 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1 ******** No matter 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1, if there are >=3 1's between (3,1), then 31111 will be a subsequence. ******** If there are exactly 2 1's between (3,1), then the number can only be 311051, 310151, 310511, 301151, 301511, 305111, 311501, 315101, 315011, 351101, 351011, 350111 ********* Of these numbers, 311051, 301151, 311501, 351101, 350111 are primes. ********** However, 311051, 301151, 311501 have 115 as subsequence, and 350111 has 5011 as subsequence, thus only 351101 is minimal prime. ******** No matter 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1, if there are exactly 1 1's between (3,1), then the digit sum is 13, thus the number is divisible by 2 and cannot be prime. ******** If there are no 1's between (3,1), then the number is 3051 for 3{1}0{1}5{1}1 or 3501 for 3{1}5{1}0{1}1 ********* Neither 3051 nor 3501 is prime. * Case (3,2): ** 32 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 32, 23, 43, 313 are primes, we only need to consider the family 3{0,3,5,6}3 (since any digits 1, 2, 4 between them will produce smaller primes) *** If there are >=2 5's in {}, then 553 will be a subsequence. *** If there are no 5's in {}, then the family will be 3{0,3,6}3 **** All numbers of the form 3{0,3,6}3 are divisible by 3, thus cannot be prime. *** If there are exactly 1 5's in {}, then the family will be 3{0,3,6}5{0,3,6}3 **** Since 335, 65, 3503, 533, 56 are primes, we only need to consider the family 3{0}53 (since any digit 3, 6 between (3,5{0,3,6}3) and any digit 0, 3, 6 between (3{0,3,6}5,3) will produce smaller primes) ***** The smallest prime of the form 3{0}53 is 300053 * Case (3,4): ** Since 32, 14, 304, 344, 364 are primes, we only need to consider the family 3{3,5}4 (since any digits 0, 1, 2, 4, 6 between them will produce smaller primes) *** Since 3334 and 335 are primes, we only need to consider the family 3{5}4 and 3{5}34 (since any digits combo 33, 35 between them will produce smaller primes) **** The smallest prime of the form 3{5}4 is 35555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555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with 9234 5's, which can be written as 3(5^9234)4 and equal the prime (23*7^9235-11)/6 ([http://factordb.com/index.php?id=1100000002766595757 factordb]) ([http://factordb.com/cert.php?id=1100000002766595757 primality certificate]) (not minimal prime, since 35555 and 5554 are primes) **** The smallest prime of the form 3{5}34 is 355555555555555555555555555555555555555555555555555555555555555534 (not minimal prime, since 35555, 553, and 5554 are primes) * Case (3,5): ** Since 32, 25, 65, 335 are primes, we only need to consider the family 3{0,1,4,5}5 (since any digits 2, 3, 6 between them will produce smaller primes) *** If there are at least one 1's and at least one 5's in {}, then either 155 or 515 will be a subsequence. *** If there are at least one 1's and at least one 4's in {}, then either 14 or 41 will be a subsequence. *** If there are at least two 1's in {}, then 115 will be a subsequence. *** If there are exactly one 1's and no 4's or 5's in {}, then the family will be 3{0}1{0}5 **** All numbers of the form 3{0}1{0}5 are divisible by 3, thus cannot be prime. *** If there is no 1's in {}, then the family will be 3{0,4,5}5 **** If there are at least to 4's in {}, then 344 and 445 will be subsequences. **** If there is no 4's in {}, then the family will be 3{0,5}5 ***** Since 3055 and 3505 are primes, we only need to consider the families 3{0}5 and 3{5}5 ****** All numbers of the form 3{0}5 are divisible by 2, thus cannot be prime. ****** The smallest prime of the form 3{5}5 is 35555 **** If there is exactly one 4's in {}, then the family will be 3{0,5}4{0,5}5 ***** Since 304, 3545 are primes, we only need to consider the families 34{0,5}5 (since any digits 0 or 5 between (3,4{0,5}5) will produce small primes) ****** All numbers of the form 34{0,5}5 are divisible by 5, thus cannot be prime. * Case (3,6): ** Since 32, 16, 56, 346 are primes, we only need to consider the family 3{0,3,6}6 (since any digits 1, 2, 4, 5 between them will produce smaller primes) *** All numbers of the form 3{0,3,6}6 are divisible by 3, thus cannot be prime. * Case (4,1): ** 41 is prime, and thus the only minimal prime in this family. * Case (4,2): ** Since 41, 43, 32, 52 are primes, we only need to consider the family 4{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 4{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,4): ** Since 41, 43, 14 are primes, we only need to consider the family 4{0,2,4,5,6}4 (since any digits 1, 3 between them will produce smaller primes) *** If there is no 5's in {}, then the family will be 4{0,2,4,6}4 **** All numbers of the form 4{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there is at least one 5's in {}, then there cannot be 2 in {} (since if so, then either 25 or 52 will be a subsequence) and there cannot be 6 in {} (since if so, then either 65 or 56 will be a subsequence), thus the family is 4{0,4,5}5{0,4,5}4 **** Since 445, 4504, 544 are primes, we only need to consider the family 4{0,5}5{5}4 (since any digit 4 between (4,5{0,4,5}4) and any digit 0, 4 between (4{0,4,5}5,4) will produce smaller primes) ***** If there are at least two 0's between (4,5{0,4,5}4), then 40054 will be a subsequence. ***** If there is no 0's between (4,5{0,4,5}4), then the family will be 4{5}5{5}4, which is equivalent to 4{5}4 ****** The smallest prime of the form 4{5}4 is 45555555555555554 (not minimal prime, since 4555 and 5554 are primes) ***** If there is exactly one 0's between (4,5{0,4,5}4), then the family will be 4{5}0{5}5{5}4 ****** Since 4504 is prime, we only need to consider the family 40{5}5{5}4 (since any digit 5 between (4,0{5}5{5}4) will produce small primes), which is equivalent to 40{5}4 ******* The smallest prime of the form 40{5}4 is 405555555555555554 (not minimal prime, since 4555 and 5554 are primes) * Case (4,5): ** Since 41, 43, 25, 65, 445 are primes, we only need to consider the family 4{0,5}5 (since any digits 1, 2, 3, 4, 6 between them will produce smaller primes) *** If there are at least two 5's in {}, then 4555 will be a subsequence. *** If there is exactly one 5's in {}, then the digit sum is 20, and the number will be divisible by 2 and cannot be prime. *** If there is no 5's in {}, then the family will be 4{0}5 **** All numbers of the form 4{0}5 are divisible by 3, thus cannot be prime. * Case (4,6): ** Since 41, 43, 16, 56 are primes, we only need to consider the family 4{0,2,4,6}6 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 4{0,2,4,6}6 are divisible by 2, thus cannot be prime. * Case (5,1): ** Since 52, 56, 41, 61, 551 are primes, we only need to consider the family 5{0,1,3}1 (since any digits 2, 4, 5, 6 between them will produce smaller primes) *** If there are at least two 3's in {}, then 533 will be a subsequence. *** If there is no 3's in {}, then the family will be 5{0,1}1 **** Since 5011 is prime, we only need to consider the family 5{1}{0}1 ***** Since 11111 is prime, we only need to consider the families 5{0}1, 51{0}1, 511{0}1, 5111{0}1 (since any digits combo 1111 between (5,1) will produce small primes) ****** All numbers of the form 5{0}1 are divisible by 6, thus cannot be prime. ****** The smallest prime of the form 51{0}1 is 5100000001 ****** All numbers of the form 511{0}1 are divisible by 2, thus cannot be prime. ****** All numbers of the form 5111{0}1 are divisible by 3, thus cannot be prime. *** If there is exactly one 3's in {}, then the family will be 5{0,1}3{0,1}1 **** If there is at least one 1's between (5,3{0,1}1), then 131 will be a subsequence. ***** Thus we only need to consider the family 5{0}3{0,1}1 ****** If there are no 1's between (5{0}3,1), then the digit sum is 12, and the number will be divisible by 3 and cannot be prime. ****** If there are exactly one 1's between (5{0}3,1), then the digit sum is 13, and the number will be divisible by 2 and cannot be prime. ****** If there are exactly three 1's between (5{0}3,1), then the digit sum is 15, and the number will be divisible by 6 and cannot be prime. ****** If there are at least four 1's between (5{0}3,1), then 11111 will be a subsequence. ****** If there are exactly two 1's between (5{0}3,1), then the family will be 5{0}3{0}1{0}1{0}1 ******* Since 5011 is prime, we only need to consider the family 5311{0}1 (since any digit 0 between (5,1{0}1) will produce small primes, this includes the leftmost three {} in 5{0}3{0}1{0}1{0}1, and thus only the rightmost {} can contain 0) ******** The smallest prime of the form 5311{0}1 is 531101 * Case (5,2): ** 52 is prime, and thus the only minimal prime in this family. * Case (5,3): ** Since 52, 56, 23, 43, 533, 553 are primes, we only need to consider the family 5{0,1}3 (since any digits 2, 3, 4, 5, 6 between them will produce smaller primes) *** If there are at least two 1's in {}, then 113 will be a subsequence. *** If there is exactly one 1's in {}, then the digit sum is 12, and the number will be divisible by 3 and cannot be prime. *** If there is no 1's in {}, then the digit sum is 11, and the number will be divisible by 2 and cannot be prime. * Case (5,4): ** Since 52, 56, 14, 544 are primes, we only need to consider the family 5{0,3,5}4 (since any digits 1, 2, 4, 6 between them will produce smaller primes) *** If there are no 5's in {}, then the family will be 5{0,3}4 **** All numbers of the form 5{0,3}4 are divisible by 3, thus cannot be prime. *** If there are at least one 5's and at least one 3's in {}, then either 535 or 553 will be a subsequence. *** If there are exactly one 5's and no 3's in {}, then the digit sum is 20, and the number will be divisible by 2 and cannot be prime. *** If there are at least two 5's in {}, then 5554 will be a subsequence. * Case (5,5): ** Since 52, 56, 25, 65, 515, 535 are primes, we only need to consider the family 5{0,4,5}5 (since any digits 1, 2, 3, 6 between them will produce smaller primes) *** If there are no 4's in {}, then the family will be 5{0,5}5 **** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. *** If there are no 5's in {}, then the family will be 5{0,4}5 **** All numbers of the form 5{0,4}5 are divisible by 2, thus cannot be prime. *** If there are at least one 4's and at least one 5's in {}, then either 5455 or 5545 will be a subsequence. * Case (5,6): ** 56 is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,2): ** Since 61, 65, 32, 52 are primes, we only need to consider the family 6{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 6{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (6,3): ** Since 61, 65, 23, 43 are primes, we only need to consider the family 6{0,3,6}3 (since any digits 1, 2, 4, 5 between them will produce smaller primes) *** All numbers of the form 6{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (6,4): ** Since 61, 65, 14 are primes, we only need to consider the family 6{0,2,3,4,6}4 (since any digits 1, 5 between them will produce smaller primes) *** If there is no 3's in {}, then the family will be 6{0,2,4,6}4 **** All numbers of the form 6{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there are exactly two 3's in {}, then the family will be 6{0,2,4,6}3{0,2,4,6}3{0,2,4,6}4 **** All numbers of the form 6{0,2,4,6}3{0,2,4,6}3{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there are at least three 3's in {}, then 3334 will be a subsequence. *** If there is exactly one 3's in {}, then the family will be 6{0,2,4,6}3{0,2,4,6}4 **** If there is 0 between (6,3{0,2,4,6}4), then 6034 will be a subsequence. **** If there is 2 between (6,3{0,2,4,6}4), then 23 will be a subsequence. **** If there is 4 between (6,3{0,2,4,6}4), then 43 will be a subsequence. **** If there is 6 between (6,3{0,2,4,6}4), then 6634 will be a subsequence. **** If there is 0 between (6{0,2,4,6}3,4), then 304 will be a subsequence. **** If there is 2 between (6{0,2,4,6}3,4), then 32 will be a subsequence. **** If there is 4 between (6{0,2,4,6}3,4), then 344 will be a subsequence. **** If there is 6 between (6{0,2,4,6}3,4), then 364 will be a subsequence. **** Thus the number can only be 634 ***** 634 is not prime. * Case (6,5): ** 65 is prime, and thus the only minimal prime in this family. * Case (6,6): ** Since 61, 65, 16, 56 are primes, we only need to consider the family 6{0,2,3,4,6}6 (since any digits 1, 5 between them will produce smaller primes) *** If there is no 3's in {}, then the family will be 6{0,2,4,6}6 **** All numbers of the form 6{0,2,4,6}6 are divisible by 2, thus cannot be prime. *** If there is no 2's and no 4's in {}, then the family will be 6{0,3,6}6 **** All numbers of the form 6{0,3,6}6 are divisible by 3, thus cannot be prime. *** If there is at least one 3's and at least one 2's in {}, then either 32 or 23 will be a subsequence. *** If there is at least one 3's and at least one 4's in {}, then either 346 or 43 will be a subsequence. ===Base 8=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (1,5), (1,7), (2,1), (2,3), (2,5), (2,7), (3,1), (3,3), (3,5), (3,7), (4,1), (4,3), (4,5), (4,7), (5,1), (5,3), (5,5), (5,7), (6,1), (6,3), (6,5), (6,7), (7,1), (7,3), (7,5), (7,7) * Case (1,1): ** Since 13, 15, 21, 51, 111, 141, 161 are primes, we only need to consider the family 1{0,7}1 (since any digits 1, 2, 3, 4, 5, 6 between them will produce smaller primes) *** Since 107, 177, 701 are primes, we only need to consider the number 171 and the family 1{0}1 (since any digits combo 07, 70, 77 between them will produce smaller primes) **** 171 is not prime. **** All numbers of the form 1{0}1 factored as 10^n+1 = (2^n+1) * (4^n-2^n+1) (n≥1) (and since if n≥1, 2^n+1 ≥ 2^1+1 = 3 > 1, 4^n-2^n+1 ≥ 4^1-2^1+1 = 3 > 1, this factorization is nontrivial), thus cannot be prime. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (1,7): ** Since 13, 15, 27, 37, 57, 107, 117, 147, 177 are primes, we only need to consider the family 1{6}7 (since any digits 0, 1, 2, 3, 4, 5, 7 between them will produce smaller primes) *** The smallest prime of the form 1{6}7 is 16667 (not minimal prime, since 667 is prime) * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,5): ** Since 21, 23, 27, 15, 35, 45, 65, 75, 225, 255 are primes, we only need to consider the family 2{0}5 (since any digits 1, 2, 3, 4, 5, 6, 7 between them will produce smaller primes) *** All numbers of the form 2{0}5 are divisible by 7, thus cannot be prime. * Case (2,7): ** 27 is prime, and thus the only minimal prime in this family. * Case (3,1): ** Since 35, 37, 21, 51, 301, 361 are primes, we only need to consider the family 3{1,3,4}1 (since any digits 0, 2, 5, 6, 7 between them will produce smaller primes) *** Since 13, 343, 111, 131, 141, 431, 3331, 3411 are primes, we only need to consider the families 3{3}11, 33{1,4}1, 3{3,4}4{4}1 (since any digits combo 11, 13, 14, 33, 41, 43 between them will produce smaller primes) **** All numbers of the form 3{3}11 are divisible by 3, thus cannot be prime. **** For the 33{1,4}1 family, since 111 and 141 are primes, we only need to consider the families 33{4}1 and 33{4}11 (since any digits combo 11, 14 between them will produce smaller primes) ***** The smallest prime of the form 33{4}1 is 3344441 ***** All numbers of the form 33{4}11 are divisible by 301, thus cannot be prime. **** For the 3{3,4}4{4}1 family, since 3331 and 3344441 are primes, we only need to consider the families 3{4}1, 3{4}31, 3{4}341, 3{4}3441, 3{4}34441 (since any digits combo 33 or 34444 between (3,1) will produce smaller primes) ***** All numbers of the form 3{4}1 are divisible by 31, thus cannot be prime. ***** Since 4443 is prime, we only need to consider the numbers 3431, 34431, 34341, 344341, 343441, 3443441, 3434441, 34434441 (since any digit combo 444 between (3,3{4}1) will produce smaller primes) ****** None of 3431, 34431, 34341, 344341, 343441, 3443441, 3434441, 34434441 are primes. * Case (3,3): ** Since 35, 37, 13, 23, 53, 73, 343 are primes, we only need to consider the family 3{0,3,6}3 (since any digits 1, 2, 4, 5, 7 between them will produce smaller primes) *** All numbers of the form 3{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 21, 51, 401, 431, 471 are primes, we only need to consider the family 4{1,4,6}1 (since any digits 0, 2, 3, 5, 7 between them will produce smaller primes) *** Since 111, 141, 161, 661, 4611 are primes, we only need to consider the families 4{4}11, 4{4,6}4{1,4,6}1, 4{4}6{4}1 (since any digits combo 11, 14, 16, 61, 66 between them will produce smaller primes) **** The smallest prime of the form 4{4}11 is 44444444444444411 (not minimal prime, since 444444441 is prime) **** For the 4{4,6}4{1,4,6}1 family, we can separate this family to 4{4,6}41, 4{4,6}411, 4{4,6}461 ***** For the 4{4,6}41 family, since 661 and 6441 are primes, we only need to consider the families 4{4}41 and 4{4}641 (since any digits combo 64 or 66 between (4,41) will produce smaller primes) ****** The smallest prime of the form 4{4}41 is 444444441 ****** The smallest prime of the form 4{4}641 is 444641 ***** For the 4{4,6}411 family, since 661 and 6441 are primes, we only need to consider the families 4{4}411 and 4{4}6411 (since any digits combo 64 or 66 between (4,411) will produce smaller primes) ****** The smallest prime of the form 4{4}411 is 444444441 ****** The smallest prime of the form 4{4}6411 is 4444444444444446411 (not minimal prime, since 444444441 and 444641 are primes) ***** For the 4{4,6}461 family, since 661 is prime, we only need to consider the family 4{4}461 ****** The smallest prime of the form 4{4}461 is 4444444461 (not minimal prime, since 444444441 is prime) **** For the 4{4}6{4}1 family, since 6441 is prime, we only need to consider the families 4{4}61 and 4{4}641 (since any digits combo 44 between (4{4}6,1) will produce smaller primes) ***** The smallest prime of the form 4{4}61 is 4444444461 (not minimal prime, since 444444441 is prime) ***** The smallest prime of the form 4{4}641 is 444641 * Case (4,3): ** Since 45, 13, 23, 53, 73, 433, 463 are primes, we only need to consider the family 4{0,4}3 (since any digits 1, 2, 3, 5, 6, 7 between them will produce smaller primes) *** Since 4043 and 4443 are primes, we only need to consider the families 4{0}3 and 44{0}3 (since any digits combo 04, 44 between them will produce smaller primes) **** All numbers of the form 4{0}3 are divisible by 7, thus cannot be prime. **** All numbers of the form 44{0}3 are divisible by 3, thus cannot be prime. * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (4,7): ** Since 45, 27, 37, 57, 407, 417, 467 are primes, we only need to consider the family 4{4,7}7 (since any digits 0, 1, 2, 3, 5, 6 between them will produce smaller primes) *** Since 747 is prime, we only need to consider the families 4{4}7, 4{4}77, 4{7}7, 44{7}7 (since any digits combo 74 between (4,7) will produce smaller primes) **** The smallest prime of the form 4{4}7 is 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447, with 220 4's, which can be written as (4^220)7 and equal the prime (4*8^221+17)/7 ([http://factordb.com/index.php?id=1100000000416605822 factordb]) **** The smallest prime of the form 4{4}77 is 4444477 **** The smallest prime of the form 4{7}7 is 47777 **** The smallest prime of the form 44{7}7 is 4477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777, with 851 7's, which can be written as 44(7^851) and equal the prime 37*8^851-1 ([http://factordb.com/index.php?id=1100000000413677646 factordb]) (not minimal prime, since 47777 is prime) * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,3): ** 53 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 53, 57, 15, 35, 45, 65, 75 are primes, we only need to consider the family 5{0,2,5}5 (since any digits 1, 3, 4, 6, 7 between them will produce smaller primes) *** Since 225, 255, 5205 are primes, we only need to consider the families 5{0,5}5 and 5{0,5}25 (since any digits combo 20, 22, 25 between them will produce smaller primes) **** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. **** For the 5{0,5}25 family, since 500025 and 505525 are primes, we only need to consider the number 500525 the families 5{5}25, 5{5}025, 5{5}0025, 5{5}0525, 5{5}00525, 5{5}05025 (since any digits combo 000, 055 between (5,25) will produce smaller primes) ***** 500525 is not prime. ***** The smallest prime of the form 5{5}25 is 555555555555525 ***** The smallest prime of the form 5{5}025 is 55555025 ***** The smallest prime of the form 5{5}0025 is 5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555550025, with 184 5's, which can be written as (5^183)0025 and equal the prime (5*8^187-20333)/7 ([http://factordb.com/index.php?id=1100000002350205912 factordb]) (not minimal prime, since 55555025 and 555555555555525 are primes) ***** The smallest prime of the form 5{5}0525 is 5550525 ***** The smallest prime of the form 5{5}00525 is 5500525 ***** The smallest prime of the form 5{5}05025 is 5555555555555555555555505025 (not minimal prime, since 5550525, 55555025, and 555555555555525 are primes) * Case (5,7): ** 57 is prime, and thus the only minimal prime in this family. * Case (6,1): ** Since 65, 21, 51, 631, 661 are primes, we only need to consider the family 6{0,1,4,7}1 (since any digits 2, 3, 5, 6 between them will produce smaller primes) *** Numbers containing 4: (note that the number cannot contain two or more 4's, or 6441 will be a subsequence) **** The form is 6{0,1,7}4{0,1,7}1 ***** Since 141, 401, 471 are primes, we only need to consider the family 6{0,7}4{1}1 ****** Since 111 is prime, we only need to consider the families 6{0,7}41 and 6{0,7}411 ******* For the 6{0,7}41 family, since 60741 is prime, we only need to consider the family 6{7}{0}41 ******** Since 6777 is prime, we only need to consider the families 6{0}41, 67{0}41, 677{0}41 ********* All numbers of the form 6{0}41 are divisible by 3, thus cannot be prime. ********* All numbers of the form 67{0}41 are divisible by 13, thus cannot be prime. ********* All numbers of the form 677{0}41 are divisible by 3, thus cannot be prime. ******* For the 6{0,7}411 family, since 60411 is prime, we only need to consider the family 6{7}411 ******** The smallest prime of the form 6{7}411 is 67777411 (not minimal prime, since 6777 is prime) *** Numbers not containing 4: **** The form is 6{0,1,7}1 ***** Since 111 is prime, we only need to consider the families 6{0,7}1 and 6{0,7}1{0,7}1 ****** All numbers of the form 6{0,7}1 are divisible by 7, thus cannot be prime. ****** For the 6{0,7}1{0,7}1 family, since 711 and 6101 are primes, we only need to consider the family 6{0}1{7}1 ******* Since 60171 is prime, we only need to consider the families 6{0}11 and 61{7}1 ******** All numbers of the form 6{0}11 are divisible by 3, thus cannot be prime. ******** The smallest prime of the form 61{7}1 is 617771 (not minimal prime, since 6777 is prime) * Case (6,3): ** Since 65, 13, 23, 53, 73, 643 are primes, we only need to consider the family 6{0,3,6}3 (since any digits 1, 2, 4, 5, 7 between them will produce smaller primes) *** All numbers of the form 6{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (6,5): ** 65 is prime, and thus the only minimal prime in this family. * Case (6,7): ** Since 65, 27, 37, 57, 667 are primes, we only need to consider the family 6{0,1,4,7}7 (since any digits 2, 3, 5, 6 between them will produce smaller primes) *** Since 107, 117, 147, 177, 407, 417, 717, 747, 6007, 6477, 6707, 6777 are primes, there cannot be digits combo 00, 10, 11, 14, 17, 40, 41, 47, 70, 71, 74, 77 between them **** If there is 1 between them, then there cannot be 1, 4, 7 before it and cannot be 0, 1, 4, 7 after it, thus the form will be 6{0}17 ***** All numbers of the form 6{0}17 are divisible by 3, thus cannot be prime. **** If there is 7 between them, then there cannot be 1, 4, 7 before it and cannot be 0, 1, 4, 7 after it, thus the form will be 6{0}77 ***** All numbers of the form 6{0}77 are divisible by 3, thus cannot be prime. **** If there is neither 1 nor 7 between them, then the form is 6{0,4}7 ***** Since 6007, 407 at primes, we only need to consider the families 6{4}7 and 60{4}7 (since any digits combo 00, 40 between them will produce smaller primes) ****** All numbers of the form 6{4}7 are divisible by 3, 5, or 15, thus cannot be prime. ****** All numbers of the form 60{4}7 are divisible by 21, thus cannot be prime. * Case (7,1): ** Since 73, 75, 21, 51, 701, 711 are primes, we only need to consider the family 7{4,6,7}1 (since any digits 0, 1, 2, 3, 5 between them will produce smaller primes) *** Since 747, 767, 471, 661, 7461, 7641 are primes, we only need to consider the families 7{4,7}4{4}1, 7{7}61, 7{7}7{4,6,7}1 (since any digits combo 46, 47, 64, 66, 67 between them will produce smaller primes) **** For the 7{4,7}4{4}1 family, since 747, 471 are primes, we only need to consider the family 7{7}{4}1 (since any digits combo 47 between (7,4{4}1) will produce smaller primes) ***** The smallest prime of the form 7{7}1 is 7777777777771 ***** The smallest prime of the form 7{7}41 is 777777777777777777777777777777777777777777777777777777777777777777777777777777741, with 79 7's, which can be written as (7^79)41 and equal the prime 8^81-31 ([http://factordb.com/index.php?id=1100000000294462449 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}441 is 777777777777777777777777777777777777777777777777777777777777777777777777777777777777441, with 84 7's, which can be written as (7^84)441 and equal the prime 8^87-223 ([http://factordb.com/index.php?id=1100000000294462776 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}4441 is 777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777774441, with 233 7's, which can be written as (7^233)4441 and equal the prime 8^237-1759 ([http://factordb.com/index.php?id=1100000002352073382 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}44441 is 7777777777777777777777777777777777777777777777777777777744441, with 56 7's, which can be written as (7^56)44441 and equal the prime 8^61-14047 ([http://factordb.com/index.php?id=1100000002350250002 factordb]) (not minimal prime, since 7777777777771 is prime) ***** All numbers of the form 7{7}444441 are divisible by 7, thus cannot be prime. ***** The smallest prime of the form 7{7}4444441 is 77774444441 ****** Since this prime has just 4 7's, we only need to consider the families with <=3 7's ******* The smallest prime of the form 7{4}1 is 744444441 ******* All numbers of the form 77{4}1 are divisible by 5, thus cannot be prime. ******* The smallest prime of the form 777{4}1 is 777444444444441 (not minimal prime, since 444444441 and 744444441 are primes) * Case (7,3): ** 73 is prime, and thus the only minimal prime in this family. * Case (7,5): ** 75 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 73, 75, 27, 37, 57, 717, 747, 767 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6 between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. ===Base 10=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (1,7), (1,9), (2,1), (2,3), (2,7), (2,9), (3,1), (3,3), (3,7), (3,9), (4,1), (4,3), (4,7), (4,9), (5,1), (5,3), (5,7), (5,9), (6,1), (6,3), (6,7), (6,9), (7,1), (7,3), (7,7), (7,9), (8,1), (8,3), (8,7), (8,9), (9,1), (9,3), (9,7), (9,9) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (1,7): ** 17 is prime, and thus the only minimal prime in this family. * Case (1,9): ** 19 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 29, 11, 31, 41, 61, 71, 251, 281 are primes, we only need to consider the family 2{0,2}1 (since any digits 1, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 2221 and 20201 are primes, we only need to consider the families 2{0}1, 2{0}21, 22{0}1 (since any digits combo 22 or 020 between them will produce smaller primes) **** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. **** The smallest prime of the form 2{0}21 is 20021 **** The smallest prime of the form 22{0}1 is 22000001 * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,7): ** Since 23, 29, 17, 37, 47, 67, 97, 227, 257, 277 are primes, we only need to consider the family 2{0,8}7 (since any digits 1, 2, 3, 4, 5, 6, 7, 9 between them will produce smaller primes) *** Since 887 and 2087 are primes, we only need to consider the families 2{0}7 and 28{0}7 (since any digit combo 08 or 88 between them will produce smaller primes) **** All numbers of the form 2{0}7 are divisible by 3, thus cannot be prime. **** All numbers of the form 28{0}7 are divisible by 7, thus cannot be prime. * Case (2,9): ** 29 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 31, 37, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 3{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 3{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (3,9): ** Since 31, 37, 19, 29, 59, 79, 89, 349 are primes, we only need to consider the family 3{0,3,6,9}9 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 3{0,3,6,9}9 are divisible by 3, thus cannot be prime. * Case (4,1): ** 41 is prime, and thus the only minimal prime in this family. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,7): ** 47 is prime, and thus the only minimal prime in this family. * Case (4,9): ** Since 41, 43, 47, 19, 29, 59, 79, 89, 409, 449, 499 are primes, we only need to consider the family 4{6}9 (since any digits 0, 1, 2, 3, 4, 5, 7, 8, 9 between them will produce smaller primes) *** All numbers of the form 4{6}9 are divisible by 7, thus cannot be prime. * Case (5,1): ** Since 53, 59, 11, 31, 41, 61, 71, 521 are primes, we only need to consider the family 5{0,5,8}1 (since any digits 1, 2, 3, 4, 6, 7, 9 between them will produce smaller primes) *** Since 881 is prime, we only need to consider the families 5{0,5}1 and 5{0,5}8{0,5}1 (since any digit combo 88 between them will produce smaller primes) **** For the 5{0,5}1 family, since 5051 and 5501 are primes, we only need to consider the families 5{0}1 and 5{5}1 (since any digit combo 05 or 50 between them will produce smaller primes) ***** All numbers of the form 5{0}1 are divisible by 3, thus cannot be prime. ***** The smallest prime of the form 5{5}1 is 555555555551 **** For the 5{0,5}8{0,5}1 family, since 5081, 5581, 5801, 5851 are primes, we only need to consider the number 581 ***** 581 is not prime. * Case (5,3): ** 53 is prime, and thus the only minimal prime in this family. * Case (5,7): ** Since 53, 59, 17, 37, 47, 67, 97, 557, 577, 587 are primes, we only need to consider the family 5{0,2}7 (since any digits 1, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 227 and 50207 are primes, we only need to consider the families 5{0}7, 5{0}27, 52{0}7 (since any digits combo 22 or 020 between them will produce smaller primes) **** All numbers of the form 5{0}7 are divisible by 3, thus cannot be prime. **** The smallest prime of the form 5{0}27 is 5000000000000000000000000000027 **** The smallest prime of the form 52{0}7 is 5200007 * Case (5,9): ** 59 is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,3): ** Since 61, 67, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 6{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 6{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (6,7): ** 67 is prime, and thus the only minimal prime in this family. * Case (6,9): ** Since 61, 67, 19, 29, 59, 79, 89 are primes, we only need to consider the family 6{0,3,4,6,9}9 (since any digits 1, 2, 5, 7, 8 between them will produce smaller primes) *** Since 449 is prime, we only need to consider the families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9 (since any digit combo 44 between them will produce smaller primes) **** All numbers of the form 6{0,3,6,9}9 are divisible by 3, thus cannot be prime. **** For the 6{0,3,6,9}4{0,3,6,9}9 family, since 409, 43, 6469, 499 are primes, we only need to consider the family 6{0,3,6,9}49 ***** Since 349, 6949 are primes, we only need to consider the family 6{0,6}49 ****** Since 60649 is prime, we only need to consider the family 6{6}{0}49 (since any digits combo 06 between {6,49} will produce smaller primes) ******* The smallest prime of the form 6{6}49 is 666649 ******** Since this prime has just 4 6's, we only need to consider the families with <=3 6's ********* The smallest prime of the form 6{0}49 is 60000049 ********* The smallest prime of the form 66{0}49 is 66000049 ********* The smallest prime of the form 666{0}49 is 66600049 * Case (7,1): ** 71 is prime, and thus the only minimal prime in this family. * Case (7,3): ** 73 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 71, 73, 79, 17, 37, 47, 67, 97, 727, 757, 787 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6, 8, 9 between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. * Case (7,9): ** 79 is prime, and thus the only minimal prime in this family. * Case (8,1): ** Since 83, 89, 11, 31, 41, 61, 71, 821, 881 are primes, we only need to consider the family 8{0,5}1 (since any digits 1, 2, 3, 4, 6, 7, 8, 9 between them will produce smaller primes) *** Since 8501 is prime, we only need to consider the family 8{0}{5}1 (since any digits combo 50 between them will produce smaller primes) **** Since 80051 is prime, we only need to consider the families 8{0}1, 8{5}1, 80{5}1 (since any digits combo 005 between them will produce smaller primes) ***** All numbers of the form 8{0}1 are divisible by 3, thus cannot be prime. ***** The smallest prime of the form 8{5}1 is 8555555555555555555551 (not minimal prime, since 555555555551 is prime) ***** The smallest prime of the form 80{5}1 is 80555551 * Case (8,3): ** 83 is prime, and thus the only minimal prime in this family. * Case (8,7): ** Since 83, 89, 17, 37, 47, 67, 97, 827, 857, 877, 887 are primes, we only need to consider the family 8{0}7 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** All numbers of the form 8{0}7 are divisible by 3, thus cannot be prime. * Case (8,9): ** 89 is prime, and thus the only minimal prime in this family. * Case (9,1): ** Since 97, 11, 31, 41, 61, 71, 991 are primes, we only need to consider the family 9{0,2,5,8}1 (since any digits 1, 3, 4, 6, 7, 9 between them will produce smaller primes) *** Since 251, 281, 521, 821, 881, 9001, 9221, 9551, 9851 are primes, we only need to consider the families 9{2,5,8}0{2,5,8}1, 9{0}2{0}1, 9{0}5{0,8}1, 9{0,5}8{0}1 (since any digits combo 00, 22, 25, 28, 52, 55, 82, 85, 88 between them will produce smaller primes) **** For the 9{2,5,8}0{2,5,8}1 family, since any digits combo 22, 25, 28, 52, 55, 82, 85, 88 between (9,1) will produce smaller primes, we only need to consider the numbers 901, 9021, 9051, 9081, 9201, 9501, 9801, 90581, 95081, 95801 ***** 95801 is the only prime among 901, 9021, 9051, 9081, 9201, 9501, 9801, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. **** For the 9{0}2{0}1 family, since 9001 is prime, we only need to consider the numbers 921, 9201, 9021 ***** None of 921, 9201, 9021 are primes. **** For the 9{0}5{0,8}1 family, since 9001 and 881 are primes, we only need to consider the numbers 951, 9051, 9501, 9581, 90581, 95081, 95801 ***** 95801 is the only prime among 951, 9051, 9501, 9581, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. **** For the 9{0,5}8{0}1 family, since 9001 and 5581 are primes, we only need to consider the numbers 981, 9081, 9581, 9801, 90581, 95081, 95801 ***** 95801 is the only prime among 981, 9081, 9581, 9801, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. * Case (9,3): ** Since 97, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 9{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 9{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (9,7): ** 97 is prime, and thus the only minimal prime in this family. * Case (9,9): ** Since 97, 19, 29, 59, 79, 89 are primes, we only need to consider the family 9{0,3,4,6,9}9 (since any digits 1, 2, 5, 7, 8 between them will produce smaller primes) *** Since 449 is prime, we only need to consider the families 9{0,3,6,9}9 and 9{0,3,6,9}4{0,3,6,9}9 (since any digit combo 44 between them will produce smaller primes) **** All numbers of the form 9{0,3,6,9}9 are divisible by 3, thus cannot be prime. **** For the 9{0,3,6,9}4{0,3,6,9}9 family, since 9049, 349, 9649, 9949 are primes, we only need to consider the family 94{0,3,6,9}9 ***** Since 409, 43, 499 are primes, we only need to consider the family 94{6}9 (since any digits 0, 3, 9 between (94,9) will produce smaller primes) ****** The smallest prime of the form 94{6}9 is 946669 ===Base 12=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,5), (1,7), (1,B), (2,1), (2,5), (2,7), (2,B), (3,1), (3,5), (3,7), (3,B), (4,1), (4,5), (4,7), (4,B), (5,1), (5,5), (5,7), (5,B), (6,1), (6,5), (6,7), (6,B), (7,1), (7,5), (7,7), (7,B), (8,1), (8,5), (8,7), (8,B), (9,1), (9,5), (9,7), (9,B), (A,1), (A,5), (A,7), (A,B), (B,1), (B,5), (B,7), (B,B) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (1,7): ** 17 is prime, and thus the only minimal prime in this family. * Case (1,B): ** 1B is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 25, 27, 11, 31, 51, 61, 81, 91, 221, 241, 2A1, 2B1 are primes, we only need to consider the family 2{0}1 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B between them will produce smaller primes) *** The smallest prime of the form 2{0}1 is 2001 * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (2,7): ** 27 is prime, and thus the only minimal prime in this family. * Case (2,B): ** Since 25, 27, 1B, 3B, 4B, 5B, 6B, 8B, AB, 2BB are primes, we only need to consider the family 2{0,2,9}B (since any digits 1, 3, 4, 5, 6, 7, 8, A, B between them will produce smaller primes) *** Since 90B, 200B, 202B, 222B, 229B, 292B, 299B are primes, we only need to consider the numbers 20B, 22B, 29B, 209B, 220B (since any digits combo 00, 02, 22, 29, 90, 92, 99 between them will produce smaller primes) **** None of 20B, 22B, 29B, 209B, 220B are primes. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (3,B): ** 3B is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 4B, 11, 31, 51, 61, 81, 91, 401, 421, 471 are primes, we only need to consider the family 4{4,A}1 (since any digit 0, 1, 2, 3, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since A41 and 4441 are primes, we only need to consider the families 4{A}1 and 44{A}1 (since any digit combo 44, A4 between them will produce smaller primes) **** All numbers of the form 4{A}1 are divisible by 5, thus cannot be prime. **** The smallest prime of the form 44{A}1 is 44AAA1 * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (4,7): ** Since 45, 4B, 17, 27, 37, 57, 67, 87, A7, B7, 447, 497 are primes, we only need to consider the family 4{0,7}7 (since any digit 1, 2, 3, 4, 5, 6, 8, 9, A, B between them will produce smaller primes) *** Since 4707 and 4777 are primes, we only need to consider the families 4{0}7 and 4{0}77 (since any digit combo 70, 77 between them will produce smaller primes) **** All numbers of the form 4{0}7 are divisible by B, thus cannot be prime. **** The smallest prime of the form 4{0}77 is 400000000000000000000000000000000000000077 * Case (4,B): ** 4B is prime, and thus the only minimal prime in this family. * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 57, 5B, 15, 25, 35, 45, 75, 85, 95, B5, 565 are primes, we only need to consider the family 5{0,5,A}5 (since any digits 1, 2, 3, 4, 6, 7, 8, 9, B between them will produce smaller primes) *** All numbers of the form 5{0,5,A}5 are divisible by 5, thus cannot be prime. * Case (5,7): ** 57 is prime, and thus the only minimal prime in this family. * Case (5,B): ** 5B is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,5): ** Since 61, 67, 6B, 15, 25, 35, 45, 75, 85, 95, B5, 655, 665 are primes, we only need to consider the family 6{0,A}5 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since 6A05 and 6AA5 are primes, we only need to consider the families 6{0}5 and 6{0}A5 (since any digit combo A0, AA between them will produce smaller primes) **** All numbers of the form 6{0}5 are divisible by B, thus cannot be prime. **** The smallest prime of the form 6{0}A5 is 600A5 * Case (6,7): ** 67 is prime, and thus the only minimal prime in this family. * Case (6,B): ** 6B is prime, and thus the only minimal prime in this family. * Case (7,1): ** Since 75, 11, 31, 51, 61, 81, 91, 701, 721, 771, 7A1 are primes, we only need to consider the family 7{4,B}1 (since any digits 0, 1, 2, 3, 5, 6, 7, 8, 9, A between them will produce smaller primes) *** Since 7BB, 7441 and 7B41 are primes, we only need to consider the numbers 741, 7B1, 74B1 **** None of 741, 7B1, 74B1 are primes. * Case (7,5): ** 75 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 75, 17, 27, 37, 57, 67, 87, A7, B7, 747, 797 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6, 8, 9, A, B between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. * Case (7,B): ** Since 75, 1B, 3B, 4B, 5B, 6B, 8B, AB, 70B, 77B, 7BB are primes, we only need to consider the family 7{2,9}B (since any digits 0, 1, 3, 4, 5, 6, 7, 8, A, B between them will produce smaller primes) *** Since 222B, 729B is prime, we only need to consider the families 7{9}B, 7{9}2B, 7{9}22B (since any digits combo 222, 29 between them will produce smaller primes) **** The smallest prime of the form 7{9}B is 7999B **** The smallest prime of the form 7{9}2B is 79992B (not minimal prime, since 992B and 7999B are primes) **** The smallest prime of the form 7{9}22B is 79922B (not minimal prime, since 992B is prime) * Case (8,1): ** 81 is prime, and thus the only minimal prime in this family. * Case (8,5): ** 85 is prime, and thus the only minimal prime in this family. * Case (8,7): ** 87 is prime, and thus the only minimal prime in this family. * Case (8,B): ** 8B is prime, and thus the only minimal prime in this family. * Case (9,1): ** 91 is prime, and thus the only minimal prime in this family. * Case (9,5): ** 95 is prime, and thus the only minimal prime in this family. * Case (9,7): ** Since 91, 95, 17, 27, 37, 57, 67, 87, A7, B7, 907 are primes, we only need to consider the family 9{4,7,9}7 (since any digit 0, 1, 2, 3, 5, 6, 8, A, B between them will produce smaller primes) *** Since 447, 497, 747, 797, 9777, 9947, 9997 are primes, we only need to consider the numbers 947, 977, 997, 9477, 9977 (since any digits combo 44, 49, 74, 77, 79, 94, 99 between them will produce smaller primes) **** None of 947, 977, 997, 9477, 9977 are primes. * Case (9,B): ** Since 91, 95, 1B, 3B, 4B, 5B, 6B, 8B, AB, 90B, 9BB are primes, we only need to consider the family 9{2,7,9}B (since any digit 0, 1, 3, 4, 5, 6, 8, A, B between them will produce smaller primes) *** Since 27, 77B, 929B, 992B, 997B are primes, we only need to consider the families 9{2,7}2{2}B, 97{2,9}B, 9{7,9}9{9}B (since any digits combo 27, 29, 77, 92, 97 between them will produce smaller primes) **** For the 9{2,7}2{2}B family, since 27 and 77B are primes, we only need to consider the families 9{2}2{2}B and 97{2}2{2}B (since any digits combo 27, 77 between (9,2{2}B) will produce smaller primes) ***** The smallest prime of the form 9{2}2{2}B is 9222B (not minimal prime, since 222B is prime) ***** The smallest prime of the form 97{2}2{2}B is 9722222222222B (not minimal prime, since 222B is prime) **** For the 97{2,9}B family, since 729B and 929B are primes, we only need to consider the family 97{9}{2}B (since any digits combo 29 between (97,B) will produce smaller primes) ***** Since 222B is prime, we only need to consider the families 97{9}B, 97{9}2B, 97{9}22B (since any digit combo 222 between (97,B) will produce smaller primes) ****** All numbers of the form 97{9}B are divisible by 11, thus cannot be prime. ****** The smallest prime of the form 97{9}2B is 979999992B (not minimal prime, since 9999B is prime) ****** All numbers of the form 97{9}22B are divisible by 11, thus cannot be prime. **** For the 9{7,9}9{9}B family, since 77B and 9999B are primes, we only need to consider the numbers 99B, 999B, 979B, 9799B, 9979B ***** None of 99B, 999B, 979B, 9799B, 9979B are primes. * Case (A,1): ** Since A7, AB, 11, 31, 51, 61, 81, 91, A41 are primes, we only need to consider the family A{0,2,A}1 (since any digits 1, 3, 4, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since 221, 2A1, A0A1, A201 are primes, we only need to consider the families A{A}{0}1 and A{A}{0}21 (since any digits combo 0A, 20, 22, 2A between them will produce smaller primes) **** For the A{A}{0}1 family: ***** All numbers of the form A{0}1 are divisible by B, thus cannot be prime. ***** The smallest prime of the form AA{0}1 is AA000001 ***** The smallest prime of the form AAA{0}1 is AAA0001 ***** The smallest prime of the form AAAA{0}1 is AAAA1 ****** Since this prime has no 0's, we do not need to consider the families {A}1, {A}01, {A}001, etc. **** All numbers of the form A{A}{0}21 are divisible by 5, thus cannot be prime. * Case (A,5): ** Since A7, AB, 15, 25, 35, 45, 75, 85, 95, B5 are primes, we only need to consider the family A{0,5,6,A}5 (since any digits 1, 2, 3, 4, 7, 8, 9, B between them will produce smaller primes) *** Since 565, 655, 665, A605, A6A5, AA65 are primes, we only need to consider the families A{0,5,A}5 and A{0}65 (since any digits combo 56, 60, 65, 66, 6A, A6 between them will produce smaller primes) **** All numbers of the form A{0,5,A}5 are divisible by 5, thus cannot be prime. **** The smallest prime of the form A{0}65 is A00065 * Case (A,7): ** A7 is prime, and thus the only minimal prime in this family. * Case (A,B): ** AB is prime, and thus the only minimal prime in this family. * Case (B,1): ** Since B5, B7, 11, 31, 51, 61, 81, 91, B21 are primes, we only need to consider the family B{0,4,A,B}1 (since any digits 1, 2, 3, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 4B, AB, 401, A41, B001, B0B1, BB01, BB41 are primes, we only need to consider the families B{A}0{4,A}1, B{0,4}4{4,A}1, B{0,4,A,B}A{0,A}1, B{B}B{A,B}1 (since any digits combo 00, 0B, 40, 4B, A4, AB, B0, B4 between them will produce smaller primes) **** For the B{A}0{4,A}1 family, since A41 is prime, we only need consider the families B0{4}{A}1 and B{A}0{A}1 ***** For the B0{4}{A}1 family, since B04A1 is prime, we only need to consider the families B0{4}1 and B0{A}1 ****** The smallest prime of the form B0{4}1 is B04441 (not minimal prime, since 4441 is prime) ****** The smallest prime of the form B0{A}1 is B0AAAAA1 (not minimal prime, since AAAA1 is prime) ***** For the B{A}0{A}1 family, since A0A1 is prime, we only need to consider the families B{A}01 and B0{A}1 ****** The smallest prime of the form B{A}01 is BAA01 ****** The smallest prime of the form B0{A}1 is B0AAAAA1 (not minimal prime, since AAAA1 is prime) **** For the B{0,4}4{4,A}1 family, since 4441 is prime, we only need to consider the families B{0}4{4,A}1 and B{0,4}4{A}1 ***** For the B{0}4{4,A}1 family, since B001 is prime, we only need to consider the families B4{4,A}1 and B04{4,A}1 ****** For the B4{4,A}1 family, since A41 is prime, we only need to consider the family B4{4}{A}1 ******* Since 4441 and BAAA1 are primes, we only need to consider the numbers B41, B441, B4A1, B44A1, B4AA1, B44AA1 ******** None of B41, B441, B4A1, B44A1, B4AA1, B44AA1 are primes. ****** For the B04{4,A}1 family, since B04A1 is prime, we only need to consider the family B04{4}1 ******* The smallest prime of the form B04{4}1 is B04441 (not minimal prime, since 4441 is prime) ***** For the B{0,4}4{A}1 family, since 401, 4441, B001 are primes, we only need to consider the families B4{A}1, B04{A}1, B44{A}1, B044{A}1 (since any digits combo 00, 40, 44 between (B,4{A}1) will produce smaller primes) ****** The smallest prime of the form B4{A}1 is B4AAA1 (not minimal prime, since BAAA1 is prime) ****** The smallest prime of the form B04{A}1 is B04A1 ****** The smallest prime of the form B44{A}1 is B44AAAAAAA1 (not minimal prime, since BAAA1 is prime) ****** The smallest prime of the form B044{A}1 is B044A1 (not minimal prime, since B04A1 is prime) **** For the B{0,4,A,B}A{0,A}1 family, since all numbers in this family with 0 between (B,1) are in the B{A}0{4,A}1 family, and all numbers in this family with 4 between (B,1) are in the B{0,4}4{4,A}1 family, we only need to consider the family B{A,B}A{A}1 ***** Since BAAA1 is prime, we only need to consider the families B{A,B}A1 and B{A,B}AA1 ****** For the B{A,B}A1 family, since AB and BAAA1 are primes, we only need to consider the families B{B}A1 and B{B}AA1 ******* All numbers of the form B{B}A1 are divisible by B, thus cannot be prime. ******* The smallest prime of the form B{B}AA1 is BBBAA1 ****** For the B{A,B}AA1 family, since BAAA1 is prime, we only need to consider the families B{B}AA1 ******* The smallest prime of the form B{B}AA1 is BBBAA1 **** For the B{B}B{A,B}1 family, since AB and BAAA1 are primes, we only need to consider the families B{B}B1, B{B}BA1, B{B}BAA1 (since any digits combo AB or AAA between (B{B}B,1) will produce smaller primes) ***** The smallest prime of the form B{B}B1 is BBBB1 ***** All numbers of the form B{B}BA1 are divisible by B, thus cannot be prime. ***** The smallest prime of the form B{B}BAA1 is BBBAA1 * Case (B,5): ** B5 is prime, and thus the only minimal prime in this family. * Case (B,7): ** B7 is prime, and thus the only minimal prime in this family. * Case (B,B): ** Since B5, B7, 1B, 3B, 4B, 5B, 6B, 8B, AB, B2B are primes, we only need to consider the family B{0,9,B}B (since any digits 1, 2, 3, 4, 5, 6, 7, 8, A between them will produce smaller primes) *** Since 90B and 9BB are primes, we only need to consider the families B{0,B}{9}B **** Since 9999B is prime, we only need to consider the families B{0,B}B, B{0,B}9B, B{0,B}99B, B{0,B}999B ***** All numbers of the form B{0,B}B are divisible by B, thus cannot be prime. ***** For the B{0,B}9B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}9B and B{B}9B (since any digits combo 0B, B0 between (B,9B) will produce smaller primes) ******* The smallest prime of the form B{0}9B is B0000000000000000000000000009B ******* All numbers of the from B{B}9B is either divisible by 11 (if totally number of B's is even) or factored as 10^(2*n)-21 = (10^n-5) * (10^n+5) (if totally number of B's is odd number 2*n-1 (n≥1)) (and since if n≥1, 10^n-5 ≥ 10^1-5 = 7 > 1, 10^n+5 ≥ 10^1+5 = 15 > 1, this factorization is nontrivial), thus cannot be prime. ***** For the B{0,B}99B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}99B and B{B}99B (since any digits combo 0B, B0 between (B,99B) will produce smaller primes) ******* The smallest prime of the form B{0}99B is B00099B ******* The smallest prime of the form B{B}99B is BBBBBB99B ***** For the B{0,B}999B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}999B and B{B}999B (since any digits combo 0B, B0 between (B,999B) will produce smaller primes) ******* The smallest prime of the form B{0}999B is B0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000999B, with 1765 0's, which can be written as B(0^1765)999B and equal the prime 11*12^1769+16967 ([http://factordb.com/index.php?id=1100000002378273165 factordb]) ([http://factordb.com/cert.php?id=1100000002378273165 primality certificate]) (not minimal prime, since B00099B and B0000000000000000000000000009B are primes) ******* The smallest prime of the form B{B}999B is BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB999B, with 245 B's, which can be written as (B^244)999B and equal the prime 12^248-3769 ([http://factordb.com/index.php?id=1100000002378270237 factordb]) (not minimal prime, since BBBBBB99B is prime) == Examples of families which can be ruled out as contain no primes > ''b'' == It is not known if this problem is solvable: Problem: Given strings ''x'', ''y'', ''z'', and a base ''b'', does there exist a prime number whose base-''b'' expansion is of the form ''x''{''y''}''z''? It will be necessary for our algorithm to determine if families of the form ''x''{''y''}''z'' contain a prime > ''b'' or not. We use two different heuristic strategies to show that such families contain no primes > ''b''. In the first strategy, we mimic the well-known technique of “covering congruences”, by finding some finite set ''S'' of primes ''p'' such that every number in a given family is divisible by some element of ''S''. In the second strategy, we attempt to find an algebraic factorization, such as difference-of-squares factorization, difference-of-cubes factorization, and Aurifeuillian factorization for numbers of the form ''x''⁴+4''y''⁴. Examples of first strategy: (we can show that the corresponding numbers are > all elements in ''S'', if ''n'' makes corresponding numbers > ''b'' (i.e. ''n''≥1 for 5{1} in base 9 and 2{5} in base 11 and {4}D in base 16 and {8}F in base 16, ''n''≥0 for other examples), thus these factorizations are nontrivial) * In base 10, all numbers of the form 4{6}9 are divisible by 7 * In base 6, all numbers of the form 4{0}1 are divisible by 5 * In base 15, all numbers of the form 9{6}8 are divisible by 11 * In base 9, all numbers of the form 5{1} are divisible by some element of {2, 5} * In base 11, all numbers of the form 2{5} are divisible by some element of {2, 3} * In base 14, all numbers of the form B{0}1 are divisible by some element of {3, 5} * In base 8, all numbers of the form 6{4}7 are divisible by some element of {3, 5, 13} * In base 13, all numbers of the form 3{0}95 are divisible by some element of {5, 7, 17} * In base 16, all numbers of the form {4}D are divisible by some element of {3, 7, 13} * In base 16, all numbers of the form {8}F are divisible by some element of {3, 7, 13} Examples of second strategy: (we can show that both factors are > 1, if ''n'' makes corresponding numbers > ''b'' (i.e. ''n''≥2 for {1} in base 9, ''n''≥0 for 1{0}1 in base 8 and B{4}1 in base 16, ''n''≥1 for other examples), thus these factorizations are nontrivial) * In base 9, all numbers of the form {1} factored as difference of squares * In base 8, all numbers of the form 1{0}1 factored as sum of cubes * In base 9, all numbers of the form 3{8} factored as difference of squares * In base 16, all numbers of the form 8{F} factored as difference of squares * In base 16, all numbers of the form {F}7 factored as difference of squares * In base 9, all numbers of the form 3{1} factored as difference of squares * In base 16, all numbers of the form {4}1 factored as difference of squares * In base 16, all numbers of the form 1{5} factored as difference of squares * In base 16, all numbers of the from {C}D factored as ''x''⁴+4''y''⁴ * In base 16, all numbers of the form B{4}1 factored as difference of squares Examples of combine of the two strategies: (we can show that for the part of the first strategy, the corresponding numbers are > all elements in S, and for the part of the second strategy, both factors are > 1, if n makes corresponding numbers > b, thus these factorizations are nontrivial) * In base 14, numbers of the form 8{D} are divisible by 5 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 12, numbers of the form {B}9B are divisible by 13 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 14, numbers of the form {D}5 are divisible by 5 if ''n'' is even and factored as difference of squares if ''n'' is odd * In base 17, numbers of the form 1{9} are divisible by 2 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 19, numbers of the form 1{6} are divisible by 5 if ''n'' is odd and factored as difference of squares if ''n'' is even == Bases 2≤''b''≤1024 such that these families can be ruled out as contain no primes > ''b'' == (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) === 1{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-powers factorization === 1{0}2 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 1{0}3 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} === 1{0}4 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ === 1{0}5 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 0 mod 5: Finite covering set {5} === 1{0}6 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 7: Finite covering set {7} === 1{0}7 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 7: Finite covering set {7} === 1{0}z === (none) === 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === * ''b'' == 1 mod 3: Finite covering set {3} === 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) === (none) === 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === * ''b'' == 1 mod 3: Finite covering set {3} === {1}0z (not quasi-minimal prime if there is smaller prime of the form {1} or {1}z) === * ''b'' such that ''b'' and 2''b''−1 are both squares: Difference-of-squares factorization (such bases are 25, 841) === {1} === * ''b'' = ''m''^''r'' with ''r''>1: Difference-of-''r''th-powers factorization (some bases still have primes, since for the corresponding length this factorization is trivial, but they only have this prime, they are 4 (length 2), 8 (length 3), 16 (length 2), 27 (length 3), 36 (length 2), 100 (length 2), 128 (length 7), 196 (length 2), 256 (length 2), 400 (length 2), 512 (length 3), 576 (length 2), 676 (length 2)) === {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}) === * ''b'' == 0 mod 2: Finite covering set {2} === 1{2} === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' such that ''b'' and 2(''b''+1) are both squares: Difference-of-squares factorization (such bases are 49) === 1{3} === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' such that ''b'' and 3(''b''+2) are both squares: Difference-of-squares factorization (such bases are 25, 361) * ''b'' == 1 mod 2 such that 3(''b''+2) is square: Combine of finite covering set {2} (when length is even) and difference-of-squares factorization (when length is odd) (such bases are 25, 73, 145, 241, 361, 505, 673, 865) === 1{4} === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' such that ''b'' and 4(''b''+3) are both squares: Difference-of-squares factorization === 1{z} === (none) === 2{0}1 === * ''b'' == 1 mod 3: Finite covering set {3} === 2{0}3 === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 5: Finite covering set {5} === 2{1} (not quasi-minimal prime if there is smaller prime of the form {1}) === * ''b'' such that ''b'' and 2''b''−1 are both squares: Difference-of-squares factorization (such bases are 25, 841) === {2}1 === * ''b'' such that ''b'' and 2(''b''+1) are both squares: Difference-of-squares factorization (such bases are 49) === 2{z} === * ''b'' == 1 mod 2: Finite covering set {2} === 3{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} === 3{0}2 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} === 3{0}4 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 7: Finite covering set {7} === {3}1 === * ''b'' such that ''b'' and 3(2''b''+1) are both squares: Difference-of-squares factorization (such bases are 121) === 3{z} === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === 4{0}1 === * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ === 4{0}3 === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 7: Finite covering set {7} === {4}1 === * ''b'' such that ''b'' and 4(3''b''+1) are both squares: Difference-of-squares factorization (such bases are 16, 225) === 4{z} === * ''b'' == 1 mod 2: Finite covering set {2} === 5{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 5{z} === * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 34 mod 35: Finite covering set {5, 7} * ''b'' = 6''m''² with ''m'' == 2 or 3 mod 5: Combine of finite covering set {5} (when length is odd) and difference-of-squares factorization (when length is even) (such bases are 24, 54, 294, 384, 864, 1014) === 6{0}1 === * ''b'' == 1 mod 7: Finite covering set {7} * ''b'' == 34 mod 35: Finite covering set {5, 7} === 6{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 7{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} === 7{z} === * ''b'' == 1 mod 7: Finite covering set {7} * ''b'' == 20 mod 21: Finite covering set {3, 7} * ''b'' == 83, 307 mod 455: Finite covering set {5, 7, 13} (such bases are 83, 307, 538, 762, 993) * ''b'' = ''m''³: Difference-of-cubes factorization === 8{0}1 === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 20 mod 21: Finite covering set {3, 7} * ''b'' == 47, 83 mod 195: Finite covering set {3, 5, 13} (such bases are 47, 83, 242, 278, 437, 473, 632, 668, 827, 863, 1022) * ''b'' = 467: Finite covering set {3, 5, 7, 19, 37} * ''b'' = 722: Finite covering set {3, 5, 13, 73, 109} * ''b'' = ''m''³: Sum-of-cubes factorization * ''b'' = 128: Cannot have primes since 7''n''+3 cannot be power of 2 === 8{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === 9{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} === 9{z} === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 32 mod 33: Finite covering set {3, 11} === A{0}1 === * ''b'' == 1 mod 11: Finite covering set {11} * ''b'' == 32 mod 33: Finite covering set {3, 11} === A{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} === B{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} === B{z} === * ''b'' == 1 mod 11: Finite covering set {11} * ''b'' == 142 mod 143: Finite covering set {11, 13} * ''b'' = 307: Finite covering set {5, 11, 29} * ''b'' = 901: Finite covering set {7, 11, 13, 19} === C{0}1 === * ''b'' == 1 mod 13: Finite covering set {13} * ''b'' == 142 mod 143: Finite covering set {11, 13} * ''b'' = 296, 901: Finite covering set {7, 11, 13, 19} * ''b'' = 562, 828, 900: Finite covering set {7, 13, 19} * ''b'' = 563: Finite covering set {5, 7, 13, 19, 29} * ''b'' = 597: Finite covering set {5, 13, 29} === {#}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3) === (none) === {#}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) === * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-power factorization === #{z} (for even bases b, # = b/2−1) === (none) === y{z} === (none) === {y}z === (none) === z{0}1 === (none) === {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family) === * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-power factorization (some bases still have primes, since for the corresponding length this factorization is trivial, but they only have this prime, they are 128 (length 7), 216 (length 3), 343 (length 3), 729 (length 3)) * ''b'' = 4''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ (base 4 still have primes, since for the corresponding length this factorization is trivial, but it only have this prime, at length 2) === {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y) === (none) === {z}1 === (none) === {z}t === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 0 mod 7: Finite covering set {7} === {z}u === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 34 mod 35: Finite covering set {5, 7} === {z}v === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 5: Finite covering set {5} === {z}w === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === {z}x === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} === {z}y === * ''b'' == 0 mod 2: Finite covering set {2} == Large known (probable) primes (length ≥10000) in these families (for bases 2≤''b''≤1024) == Format: base (length) (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) === 1{0}1 === (none) === 1{0}2 === (none) === 1{0}3 === (none) === 1{0}4 === 53 (13403) 113 (10647) === 1{0}z === 113 (20089) 123 (64371) === 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === (none) === 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) === 208 (26682) 607 (11032) 828 (19659) === 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === 201 (31276) 222 (52727) 227 (36323) 327 (135983) 425 (11231) 710 (24112) 717 (37508) 719 (13420) === {1} === 152 (270217) 184 (16703) 200 (17807) 311 (36497) 326 (26713) 331 (25033) 371 (15527) 485 (99523) 629 (32233) 649 (43987) 670 (18617) 684 (22573) 691 (62903) 693 (41189) 731 (15427) 752 (32833) 872 (10093) 932 (20431) === {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}) === (none) === 1{z} === 107 (21911) 170 (166429) 278 (43909) 303 (40175) 383 (20957) 515 (58467) 522 (62289) 578 (129469) 590 (15527) 647 (21577) 662 (16591) 698 (127559) 704 (62035) 845 (39407) 938 (40423) 969 (24097) 989 (26869) === 2{0}1 === 101 (192276) 206 (46206) 218 (333926) 236 (161230) 257 (12184) 305 (16808) 467 (126776) 578 (44166) 626 (174204) 695 (94626) 752 (26164) 788 (72918) 869 (49150) 887 (27772) 899 (15732) 932 (13644) === 2{z} === 432 (16003) === 3{0}1 === 912 (132174) === 3{z} === 72 (1119850) 212 (34414) 218 (23050) 270 (89662) 303 (198358) 312 (51566) 422 (21738) 480 (93610) 513 (38032) 527 (46074) 566 (23874) 650 (498102) 686 (16584) 758 (15574) 783 (12508) 800 (33838) 921 (98668) 947 (10056) === 4{0}1 === 107 (32587) 227 (13347) 257 (160423) 355 (10990) 410 (144079) 440 (56087) 452 (14155) 482 (30691) 542 (15983) 579 (67776) 608 (20707) 635 (11723) 650 (96223) 679 (69450) 737 (269303) 740 (58043) 789 (149140) 797 (468703) 920 (103687) 934 (101404) 962 (84235) === 4{z} === 14 (19699) 68 (13575) 254 (15451) 800 (20509) === 5{0}1 === 326 (400786) 350 (20392) 554 (10630) 662 (13390) 926 (40036) === 5{z} === 258 (212135) 272 (148427) 299 (64898) 307 (26263) 354 (25566) 433 (283919) 635 (36163) 678 (40859) 692 (45447) 719 (20552) 768 (70214) 857 (23083) 867 (61411) 972 (36703) === 6{0}1 === 108 (16318) 129 (16797) 409 (369833) 522 (52604) 587 (24120) 643 (164916) 762 (11152) 789 (27297) 986 (21634) === 6{z} === 68 (25396) 332 (15222) 338 (42868) 362 (146342) 488 (33164) 566 (164828) 980 (50878) 986 (12506) 1016 (23336) === 7{0}1 === 398 (17473) 1004 (54849) === 7{z} === 97 (192336) 170 (15423) 194 (38361) 202 (155772) 282 (21413) 283 (164769) 332 (13205) 412 (29792) 560 (19905) 639 (10668) 655 (53009) 811 (31784) 814 (17366) 866 (108591) 908 (61797) 962 (31841) 992 (10605) 997 (15815) === 8{0}1 === 23 (119216) 53 (227184) 158 (123476) 254 (67716) 320 (52004) 410 (279992) 425 (94662) 513 (19076) 518 (11768) 596 (148446) 641 (87702) 684 (23387) 695 (39626) 785 (900326) 788 (11408) 893 (86772) 908 (243440) 920 (107822) 962 (47222) 998 (81240) 1013 (43872) === 8{z} === 138 (35686) 412 (12154) 788 (11326) 990 (23032) === 9{0}1 === 248 (39511) 592 (96870) === 9{z} === 431 (43574) 446 (152028) 458 (126262) 599 (11776) 846 (12781) === A{0}1 === 173 (264235) 198 (47665) 311 (314807) 341 (106009) 449 (18507) 492 (42843) 605 (12395) 708 (17563) 710 (31039) 743 (285479) 744 (137056) 786 (68169) 800 (15105) 802 (149320) 879 (25004) 929 (13065) 977 (125873) 986 (48279) 1004 (10645) === A{z} === 368 (10867) 488 (10231) 534 (80328) 662 (13307) 978 (14066) === B{0}1 === 710 (15272) 740 (33520) 878 (227482) === B{z} === 153 (21660) 186 (112718) 439 (18752) 593 (16064) 602 (36518) 707 (10573) 717 (67707) === C{0}1 === 68 (656922) 219 (29231) 230 (94751) 312 (21163) 334 (83334) 353 (20262) 359 (61295) 457 (10024) 481 (45941) 501 (20140) 593 (42779) 600 (11242) 604 (17371) 641 (26422) 700 (91953) 887 (13961) 919 (45359) 923 (64365) 992 (10300) === {#}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3) === (none) === {#}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) === (none) === #{z} (for even bases b, # = b/2−1) === (none) === y{z} === 38 (136212) 83 (21496) 113 (286644) 188 (13508) 401 (103670) 417 (21003) 458 (46900) 494 (21580) 518 (129372) 527 (65822) 602 (17644) 608 (36228) 638 (74528) 663 (47557) 723 (24536) 758 (50564) 833 (12220) 904 (13430) 938 (50008) 950 (16248) === z{0}1 === 202 (46774) 251 (102979) 272 (16681) 297 (14314) 298 (60671) 326 (64757) 347 (69661) 363 (142877) 452 (71941) 543 (10042) 564 (38065) 634 (84823) 788 (13541) 869 (12289) 890 (37377) 953 (60995) 1004 (29685) === {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family) === 53 (21942) 124 (16426) 175 (31626) 188 (22036) 316 (48538) 365 (25578) 373 (24006) 434 (10090) 530 (11086) 545 (12346) 560 (15072) 596 (12762) 701 (12576) 706 (10656) 821 (13536) 833 (17116) 966 (14820) 983 (11272) === {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y) === (none) === {z}1 === (none) === {z}y === 317 (13896) == Bases 2≤''b''≤1024 which have these families as unsolved families == Unsolved families are families which are neither primes (>''b'') found nor can be ruled out as contain no primes > ''b'' (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) 1{0}1: 38, 50, 62, 68, 86, 92, 98, 104, 122, 144, 168, 182, 186, 200, 202, 212, 214, 218, 244, 246, 252, 258, 286, 294, 298, 302, 304, 308, 322, 324, 338, 344, 354, 356, 362, 368, 380, 390, 394, 398, 402, 404, 410, 416, 422, 424, 446, 450, 454, 458, 468, 480, 482, 484, 500, 514, 518, 524, 528, 530, 534, 538, 552, 558, 564, 572, 574, 578, 580, 590, 602, 604, 608, 620, 622, 626, 632, 638, 648, 650, 662, 666, 668, 670, 678, 684, 692, 694, 698, 706, 712, 720, 722, 724, 734, 744, 746, 752, 754, 762, 766, 770, 792, 794, 802, 806, 812, 814, 818, 836, 840, 842, 844, 848, 854, 868, 870, 872, 878, 888, 896, 902, 904, 908, 922, 924, 926, 932, 938, 942, 944, 948, 954, 958, 964, 968, 974, 978, 980, 988, 994, 998, 1002, 1006, 1014, 1016 (length limit: ≥8388608) 1{0}2: 167, 257, 323, 353, 383, 527, 557, 563, 623, 635, 647, 677, 713, 719, 803, 815, 947, 971, 1013 (length limit: 2000) 1{0}3: 646, 718, 998 (length limit: 2000) 1{0}4: 139, 227, 263, 315, 335, 365, 485, 515, 647, 653, 683, 773, 789, 797, 815, 857, 875, 893, 939, 995, 1007 (length limit: 2000) 1{0}5 1{0}6 1{0}7 1{0}8 1{0}9 1{0}A 1{0}B 1{0}C 1{0}D 1{0}E 1{0}F 1{0}G 1{0}z: 173, 179, 257, 277, 302, 333, 362, 392, 422, 452, 467, 488, 512, 527, 545, 570, 575, 614, 622, 650, 677, 680, 704, 707, 734, 740, 827, 830, 851, 872, 886, 887, 902, 904, 908, 929, 932, 942, 947, 949, 962, 973, 1022 (length limit: 2000) 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1): 198, 213, 318, 327, 353, 375, 513, 591, 647, 732, 734, 738, 759, 948, 951, 957, 1013, 1014 (length limit: 2000) 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}): 575 (length limit: 247000) 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1): 813, 863, 962, 1017 (length limit: ≥100000) {1}0z (not quasi-minimal prime if there is smaller prime of the form {1} or {1}z): 137, 161, 167, 217, 229, 232, 253, 261, 317, 325, 337, 347, 355, 375, 403, 411, 421, 427, 457, 479, 483, 505, 507, 537, 547, 577, 597, 599, 601, 613, 627, 631, 632, 641, 643, 649, 657, 679, 688, 697, 707, 711, 729, 733, 737, 742, 762, 773, 787, 793, 797, 817, 819, 841, 843, 853, 859, 861, 874, 877, 895, 899, 907, 913, 916, 917, 927, 957, 959, 997, 1003, 1009, 1015, 1017 (length limit: 2000) {1}: 185, 269, 281, 380, 384, 385, 394, 452, 465, 511, 574, 601, 631, 632, 636, 711, 713, 759, 771, 795, 861, 866, 881, 938, 948, 951, 956, 963, 1005, 1015 (length limit: ≥100000) 11{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}): 31, 61, 91, 93, 143, 247, 253, 293, 313, 329, 371, 383, 391, 393, 403, 415, 435, 443, 451, 491, 493, 513, 523, 527, 537, 541, 553, 565, 581, 587, 601, 613, 615, 623, 627, 635, 663, 729, 735, 757, 763, 775, 783, 823, 843, 865, 873, 877, 883, 897, 931, 941, 943, 955, 983, 1013, 1015, 1021, 1023 (length limit: 2000) {1}z 1{2}: 265, 355, 379, 391, 481, 649, 661, 709, 745, 811, 877, 977 (length limit: 2000) 1{3}: 107, 133, 179, 281, 305, 365, 473, 485, 487, 491, 535, 541, 601, 617, 665, 737, 775, 787, 802, 827, 905, 911, 928, 953, 955, 995 1{4}: 83, 143, 185, 239, 269, 293, 299, 305, 319, 325, 373, 383, 395, 431, 471, 503, 551, 577, 581, 593, 605, 617, 631, 659, 743, 761, 773, 781, 803, 821, 857, 869, 897, 911, 917, 923, 935, 983, 1019 (length limit: 2000) 1{z}: 581, 992, 1019 (length limit: ≥100000) 2{0}1: 365, 383, 461, 512, 542, 647, 773, 801, 836, 878, 908, 914, 917, 947, 1004 (length limit: ≥100000) 2{0}3: 79, 149, 179, 254, 359, 394, 424, 434, 449, 488, 499, 532, 554, 578, 664, 683, 694, 749, 794, 839, 908, 944, 982 (length limit: 2000) 2{1} (not quasi-minimal prime if there is smaller prime of the form {1}): 109, 117, 137, 147, 157, 175, 177, 201, 227, 235, 256, 269, 271, 297, 310, 331, 335, 397, 417, 427, 430, 437, 442, 451, 465, 467, 481, 502, 517, 547, 557, 567, 572, 577, 591, 597, 607, 627, 649, 654, 655, 667, 679, 687, 691, 697, 715, 727, 739, 759, 766, 782, 787, 796, 797, 808, 817, 821, 829, 841, 852, 877, 881, 899, 903, 907, 937, 947, 955, 1007, 1011, 1021 (length limit: 2000) {2}1: 106, 238, 262, 295, 364, 382, 391, 397, 421, 458, 463, 478, 517, 523, 556, 601, 647, 687, 754, 790, 793, 832, 872, 898, 962, 1002, 1021 (length limit: 2000) 2{z}: 588, 972 (length limit: ≥100000) 3{0}1: 718 (length limit: ≥100000) 3{0}2: 223, 283, 359, 489, 515, 529, 579, 619, 669, 879, 915, 997 (length limit: 2000) 3{0}4: 167, 391, 447, 487, 529, 653, 657, 797, 853, 913, 937 (length limit: 2000) {3}1: 79, 101, 189, 215, 217, 235, 243, 253, 255, 265, 313, 338, 341, 378, 379, 401, 402, 413, 489, 498, 499, 508, 525, 535, 589, 591, 599, 611, 621, 635, 667, 668, 681, 691, 711, 717, 719, 721, 737, 785, 804, 805, 813, 831, 835, 837, 849, 873, 911, 915, 929, 933, 941, 948, 959, 999, 1013, 1019 (length limit: 2000) 3{z}: 275, 438, 647, 653, 812, 927, 968 (length limit: ≥100000) 4{0}1: 32, 53, 155, 174, 204, 212, 230, 332, 334, 335, 395, 467, 512, 593, 767, 803, 848, 875, 1024 (length limit: ≥100000) 4{0}3: 83, 88, 97, 167, 188, 268, 289, 293, 412, 419, 425, 433, 503, 517, 529, 548, 613, 620, 622, 650, 668, 692, 706, 727, 763, 818, 902, 913, 937, 947, 958 (length limit: 2000) {4}1: 46, 77, 103, 107, 119, 152, 198, 203, 211, 217, 229, 257, 263, 291, 296, 305, 332, 371, 374, 407, 413, 416, 440, 445, 446, 464, 467, 500, 542, 545, 548, 557, 566, 586, 587, 605, 611, 614, 632, 638, 641, 653, 659, 698, 701, 731, 733, 736, 755, 786, 812, 820, 821, 827, 830, 887, 896, 899, 901, 922, 923, 935, 941, 953, 977, 983, 991, 1004 (length limit: 2000) 4{z}: 338, 998 (length limit: ≥100000) 5{0}1: 308, 512, 824 (length limit: ≥100000) 5{z}: 234, 412, 549, 553, 573, 619, 750, 878, 894, 954 (length limit: ≥100000) 6{0}1: 212, 509, 579, 625, 774, 794, 993, 999 (length limit: ≥100000) 6{z}: 308, 392, 398, 518, 548, 638, 662, 878 (length limit: ≥100000) 7{0}1: (none) 7{z}: 321, 328, 374, 432, 665, 697, 710, 721, 727, 728, 752, 800, 815, 836, 867, 957, 958, 972 (length limit: ≥100000) 8{0}1: 86, 140, 182, 263, 353, 368, 389, 395, 422, 426, 428, 434, 443, 488, 497, 558, 572, 575, 593, 606, 698, 710, 746, 758, 770, 773, 824, 828, 866, 911, 930, 953, 957, 983, 993, 1014 (length limit: ≥100000) 8{z}: 378, 438, 536, 566, 570, 592, 636, 688, 718, 830, 852, 926, 1010 (length limit: ≥100000) 9{0}1: 724, 884 (length limit: ≥100000) 9{z}: 80, 233, 530, 551, 611, 899, 912, 980 (length limit: ≥100000) A{0}1: 185, 338, 417, 432, 614, 668, 773, 863, 935, 1000 (length limit: ≥100000) A{z}: 214, 422, 444, 452, 458, 542, 638, 668, 804, 872, 950, 962 (length limit: ≥100000) B{0}1: 560, 770, 968 (length limit: ≥100000) B{z}: 263, 615, 912, 978 (length limit: ≥100000) C{0}1: 163, 207, 354, 362, 368, 480, 620, 692, 697, 736, 753, 792, 978, 998, 1019, 1022 (length limit: ≥100000) C{z} D{0}1 D{z} E{0}1 E{z} F{0}1 F{z} G{0}1 {&#35;}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3): 808, 829, 859, 1006 (length limit: 2000) {&#35;}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2): 31, 37, 55, 63, 67, 77, 83, 89, 91, 93, 97, 99, 107, 109, 117, 123, 127, 133, 135, 137, 143, 147, 149, 151, 155, 161, 177, 179, 183, 189, 193, 197, 207, 211, 213, 215, 217, 223, 225, 227, 233, 235, 241, 247, 249, 255, 257, 263, 265, 269, 273, 277, 281, 283, 285, 287, 291, 293, 297, 303, 307, 311, 319, 327, 347, 351, 355, 357, 359, 361, 367, 369, 377, 381, 383, 385, 387, 389, 393, 397, 401, 407, 411, 413, 417, 421, 423, 437, 439, 443, 447, 457, 465, 467, 469, 473, 475, 481, 483, 489, 493, 495, 497, 509, 511, 515, 533, 541, 547, 549, 555, 563, 591, 593, 597, 601, 603, 611, 615, 619, 621, 625, 627, 629, 633, 635, 637, 645, 647, 651, 653, 655, 659, 663, 667, 671, 673, 675, 679, 683, 687, 691, 693, 697, 707, 709, 717, 731, 733, 735, 737, 741, 743, 749, 753, 755, 757, 759, 765, 767, 771, 773, 775, 777, 783, 785, 787, 793, 797, 801, 807, 809, 813, 817, 823, 825, 849, 851, 853, 865, 867, 873, 877, 887, 889, 893, 897, 899, 903, 907, 911, 915, 923, 927, 933, 937, 939, 941, 943, 945, 947, 953, 957, 961, 967, 975, 977, 983, 987, 993, 999, 1003, 1005, 1009, 1017 (length limit: ≥262143) &#35;{z} (for even bases ''b'', # = ''b''/2−1): 108, 278, 296, 338, 386, 494, 626, 920 (length limit: 2000) ${&#35;} (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) x{z} y{z}: 128, 233, 268, 383, 478, 488, 533, 554, 665, 698, 779, 863, 878, 932, 941, 1010 (length limit: ≥200000) z{0}1: 123, 342, 362, 422, 438, 479, 487, 512, 542, 602, 757, 767, 817, 830, 872, 893, 932, 992, 997, 1005, 1007 (length limit: ≥100000) {y}z: 143, 173, 176, 213, 235, 248, 253, 279, 327, 343, 353, 358, 373, 383, 401, 413, 416, 427, 439, 448, 453, 463, 481, 513, 522, 527, 535, 547, 559, 565, 583, 591, 598, 603, 621, 623, 653, 659, 663, 679, 691, 698, 711, 743, 745, 757, 768, 785, 793, 796, 801, 808, 811, 821, 835, 845, 847, 853, 856, 883, 898, 903, 927, 955, 961, 971, 973, 993, 1005, 1013, 1019, 1021 (length limit: 2000) {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family): 97, 103, 113, 186, 187, 220, 304, 306, 309, 335, 414, 416, 428, 433, 445, 459, 486, 498, 539, 550, 557, 587, 592, 597, 598, 617, 624, 637, 659, 665, 671, 677, 696, 717, 726, 730, 740, 754, 766, 790, 851, 873, 890, 914, 923, 929, 943, 944, 965, 984, 985, 996, 1004, 1005 (length limit: ≥17326) zy{z} (not quasi-minimal prime if there is smaller prime of the form y{z}) {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y): 215, 353, 517, 743, 852, 899, 913 (length limit: 2000) {z}01 (not quasi-minimal prime if there is smaller prime of the form {z}1) {z}1: 93, 113, 152, 158, 188, 217, 218, 226, 227, 228, 233, 240, 275, 278, 293, 312, 338, 350, 353, 383, 404, 438, 464, 471, 500, 533, 576, 614, 641, 653, 704, 723, 728, 730, 758, 779, 788, 791, 830, 878, 881, 899, 908, 918, 929, 944, 953, 965, 968, 978, 983, 986, 1013 (length limit: 2000) {z}k {z}l {z}m {z}n {z}o {z}p {z}q {z}r {z}s {z}t {z}u {z}v {z}w: 207, 221, 293, 375, 387, 533, 633, 647, 653, 687, 701, 747, 761, 785, 863, 897, 905, 965, 1017 (length limit: 2000) {z}x: (none) {z}y: 305, 353, 397, 485, 487, 535, 539, 597, 641, 679, 731, 739, 755 (length limit: 2000) == List of lengths for quasi-minimal primes in some simple families == [https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml list of lengths for quasi-minimal primes in some simple families for bases 2≤''b''≤1024] NB: this family is not interpretable in this base (e.g. family 7{0}1 and 7{z} in bases <=7, family {z}x in bases <=3) (including the case which this family has either leading zeros (leading zeros do not count) or ending zeros (numbers ending in zero cannot be prime > base) in this base) RC: this family can be proven to only contain composite numbers (only count numbers > base) unknown: this family has no primes or PRPs found, nor can this family be proven to only contain composite numbers (only count numbers > base) Background color: red for title (bases or families), green for length > 10000, orange for 2500 < length ≤ 10000, white for length ≤ 2500, cyan for "RC", pink for "NB", yellow for "unknown". Search limit for lengths: ≥8388608 for 1{0}1, ≥200000 for y{z}, ≥100000 for ''d''{0}1 (''d'' = one of digits in {2, 3, 4, 5, 6, 7, 8, 9, A, B, C}) and ''d''{z} (''d'' = one of digits in {1, 2, 3, 4, 5, 6, 7, 8, 9, A, B}) and z{0}1 and {1}, ≥5000 for 1{0}2, {z}y, 1{0}z, {z}1, {y}z, ≥2500 for other families. == References == * [https://mersenneforum.org/showthread.php?t=24972 mersenneforum thread of this problem] * [https://docs.google.com/document/d/e/2PACX-1vQct6Hx-IkJd5-iIuDuOKkKdw2teGmmHW-P75MPaxqBXB37u0odFBml5rx0PoLa0odTyuW67N_vn96J/pub Minimal elements for the base ''b'' representations of the primes which are > ''b'' for bases ''b''≤16] * [https://primes.utm.edu/glossary/xpage/MinimalPrime.html article “minimal prime” in The Prime Glossary] * [https://en.wikipedia.org/wiki/Minimal_prime_(recreational_mathematics article “minimal prime” in Wikipedia] * [https://www.primepuzzles.net/puzzles/puzz_178.htm the puzzle of minimal primes (when the restriction of prime>base is not required) in The Prime Puzzles & Problems Connection] * [https://www.primepuzzles.net/problems/prob_083.htm the problem of minimal primes in The Prime Puzzles & Problems Connection] * [https://github.com/xayahrainie4793/non-single-digit-primes my data for these M(Lb) sets for 2 ≤ b ≤ 16] * [http://www.cs.uwaterloo.ca/~shallit/Papers/minimal5.pdf Shallit’s proof of base 10 minimal primes, when the restriction of prime>base is not required] * [https://scholar.colorado.edu/downloads/hh63sw661 proofs of minimal primes in bases b≤10, when the restriction of prime>base is not required] * [https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://cs.uwaterloo.ca/~cbright/talks/minimal-slides.pdf the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://doi.org/10.1080/10586458.2015.1064048 the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://github.com/curtisbright/mepn-data data for these M(Lb) sets and unsolved families for 2 ≤ b ≤ 30, when the restriction of prime>base is not required, search limits of lengths: 1000000 for b=17, 707000 for b=19, 506000 for b=21, 292000 for b=25, 486000 for b=26, 543000 for b=28, 233000 for b=29] * [https://github.com/RaymondDevillers/primes data for these M(Lb) sets and unsolved families for 2 ≤ b ≤ 50, when the restriction of prime>base is not required, search limits of lengths: 10000 for all b] * [http://www.bitman.name/math/article/730 article for minimal primes, when the restriction of prime>base is not required] * [http://www.bitman.name/math/table/497 data for minimal primes in bases 2 ≤ b ≤ 16, when the restriction of prime>base is not required] * [http://www.prothsearch.com/sierp.html the Sierpinski problem] * [http://www.prothsearch.com/rieselprob.html the Riesel problem] * [https://oeis.org/A076336/a076336c.html the dual Sierpinski problem] * [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm generalized Sierpinski conjectures in bases b≤1030, some primes found in these conjectures are minimal primes in base b, especially, all primes for k&lt;b (if exist for a (k,b) combo) are always minimal primes in the base b) (also some examples for simple families contain no primes &gt; b] * [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm generalized Riesel conjectures in bases b≤1030, some primes found in these conjectures are minimal primes in base b, especially, all primes for k&lt;b (if exist for a (k,b) combo) are always minimal primes in the base b) (also some examples for simple families contain no primes &gt; b] * [http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm list for the status of the generalized Sierpinski conjectures and the generalized Riesel conjectures in bases b≤1030] * [https://www.utm.edu/staff/caldwell/preprints/2to100.pdf article for generalized Sierpinski conjectures in bases b≤100] * [http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf article for the mixed (original+dual) Sierpinski problem] * [http://www.fermatquotient.com/PrimSerien/GenRepu.txt generalized repunit primes (primes of the form (bn−1)/(b−1)) in bases b≤160, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html generalized repunit primes (primes of the form (bn−1)/(b−1)) in bases b≤1000, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://jeppesn.dk/generalized-fermat.html generalized Fermat primes (primes of the form b2^n+1) in even bases b≤1000, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://www.noprimeleftbehind.net/crus/GFN-primes.htm generalized Fermat primes (primes of the form b2^n+1) in even bases b≤1030, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt list of generalized half Fermat primes (primes of the form (b2^n+1)/2) sorted by n, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://harvey563.tripod.com/wills.txt primes of the form (b−1)*bn−1 for bases b≤2049, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Williams_prime_MM_least the smallest primes of the form (b−1)*bn−1 for bases b≤2049, these primes (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Williams_prime_MP_least the smallest primes of the form (b−1)*bn+1 for bases b≤1024, these primes (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n the smallest primes of the form k*bn−1 for k≤12 and bases b≤1024, these primes (if exists) is always minimal prime in base b if b>k] * [https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n the smallest primes of the form k*bn+1 for k≤12 and bases b≤1024, these primes (if exists) is always minimal prime in base b if b>k] * [https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml list for the smallest primes in given simple family in bases b≤1024] * [https://www.rose-hulman.edu/~rickert/Compositeseq/ a problem related to this project] * [http://www.worldofnumbers.com/Appending%201s%20to%20n.txt a problem related to this project] * [https://stdkmd.net/nrr/prime/primecount.txt near- and quasi- repdigit (probable) primes sorted by count] * [https://stdkmd.net/nrr/prime/primedifficulty.txt near- and quasi- repdigit (probable) primes sorted by difficulty] * [http://www.prothsearch.com/fermat.html factoring status of Fermat numbers] * [http://www.rieselprime.de/dl/CRUS_pack.zip srsieve, sr1sieve, sr2sieve, pfgw, and llr softwares] * [https://www.bc-team.org/app.php/dlext/?cat=3 srsieve, sr1sieve, sr2sieve, sr5sieve software] * [https://sourceforge.net/projects/openpfgw/ pfgw software] * [http://jpenne.free.fr/index2.html llr software] * [http://www.ellipsa.eu/public/primo/primo.html PRIMO software] * [https://primes.utm.edu/prove/index.html website for primality proving] * [https://primes.utm.edu/curios/page.php?number_id=22380 the largest base 10 minimal prime in Prime Curios!] * [https://oeis.org/A071062 OEIS sequence for base 10 minimal primes, when the restriction of prime>base is not required] * [https://oeis.org/A326609 OEIS sequence for the largest base b minimal prime, when the restriction of prime>base is not required] * [https://primes.utm.edu/primes/lists/all.txt top proven primes] * [http://www.primenumbers.net/prptop/prptop.php top PRPs] * [http://factordb.com online factor database, including many primes which are minimal primes in a small base] 5w51nejs0uriv13av34dnx73317w0hj 2412472 2412470 2022-08-07T03:19:12Z 2402:7500:942:36DD:9962:A44F:536A:30BC /* Primality certificates for the proven primes > 10299 */ wikitext text/x-wiki A '''quasi-minimal prime''' is a [[w:Prime number|prime number]] for which there is no shorter [[w:Subsequence|subsequence]] of its [[w:Numerical digit|digit]]s in a given [[w:Radix|base]] ''b'' that form a prime > ''b''. For example, 857 is a quasi-minimal prime in [[w:Decimal|decimal]] because there is no prime > 10 among the shorter subsequences of the digits: 8, 5, 7, 85, 87, 57. The subsequence does not have to consist of consecutive digits, so 149 is not a quasi-minimal prime in decimal (because 19 is prime and 19 > 10). But it does have to be in the same order; so, for example, 991 is still a quasi-minimal prime in decimal even though a subset of the digits can form the shorter prime 19 > 10 by changing the order. (using A−Z to represent digit values 10 to 35) For the quasi-minimal primes in bases up to 36, I have only solved (found all quasi-minimal primes and proved that these are all such primes) bases 2~12, 14~15, 18, 20, 22, 24, 30 (bases 11, 22, 30 need primality proving of the probable primes). For the remain bases 13, 16~17, 19, 21, 23, 25~29, 31~36, there are some ''x''{''d''}''y'' (with ''x'', ''y'' strings (may be [[w:Empty string|empty]]) with digits in base ''b'', ''d'' digit in base ''b'') families which are not solved (not even a probable prime is known nor can be ruled out as only contain composites (only count the numbers > base (''b'')). I left as a challenge to readers the task of solving (finding all quasi-minimal primes and proving that these are all such primes) bases 13, 16~17, 19, 21, 23, 25~29, 31~36 (this will be a hard problem, e.g. base 23 has a quasi-minimal prime 9E₈₀₀₈₇₃, and base 36 has quasi-minimal prime P₈₁₉₉₃SZ). Proving the set of the quasi-minimal primes in base ''b'' is ''S'', is equivalent to: * Prove that all elements in ''S'', when read as base ''b'' representation, are primes > ''b''. * Prove that all [[w:Proper subset|proper]] subsequence of all elements in ''S'', when read as base ''b'' representation, which are > ''b'', are composite. * Prove that all primes > ''b'', when written in base ''b'', contain at least one element in ''S'' as subsequence (equivalently, prove that all strings not containing any element in ''S'' as subsequence, when read as base ''b'' representation, which are > ''b'', are composite). e.g. proving the set of the quasi-minimal primes in base ''b'' = 10 is {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}, is equivalent to: * Prove that all of 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 are primes > 10. * Prove that all proper subsequence of all elements in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} which are > 10 are composite. * Prove that all primes > 10 contain at least one element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence (equivalently, prove that all numbers > 10 not containing any element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence are composite). ==Condensed table== {|class=wikitable |''b''||number of quasi-minimal primes base ''b''||base-''b'' form of largest known quasi-minimal prime base ''b''||length of largest known quasi-minimal prime base ''b''||algebraic ((''a''×''b''^''n''+''c'')/''d'') form of largest known quasi-minimal prime base ''b'' |- |2||1||11||2||3 |- |3||3||111||3||13 |- |4||5||221||3||41 |- |5||22||10₉₃13||96||5⁹⁵+8 |- |6||11||40041||5||5209 |- |7||71||3₁₆1||17||(7¹⁷−5)/2 |- |8||75||4₂₂₀7||221||(4×8²²¹+17)/7 |- |9||151||30₁₁₅₈11||1161||3×9¹¹⁶⁰+10 |- |10||77||50₂₈27||31||5×10³⁰+27 |- |11^*||1068||57₆₂₆₆₈||62669||(57×11⁶²⁶⁶⁸−7)/10 |- |12||106||40₃₉77||42||4×12⁴¹+91 |- |13^*||3195~3197||80₃₂₀₁₇111||32021||8×13³²⁰²⁰+183 |- |14||650||4D₁₉₆₉₈||19699||5×14¹⁹⁶⁹⁸−1 |- |15||1284||7₁₅₅97||157||(15¹⁵⁷+59)/2 |- |16^*||2346~2347||4₇₂₇₈₅DD||72787||(4×16⁷²⁷⁸⁷+2291)/15 |- |17^*||10409~10428||F70₁₈₆₇₆₇1||186770||262×17¹⁸⁶⁷⁶⁸+1 |- |18||549||C0₆₂₆₈C5||6271||12×18⁶²⁷⁰+221 |- |20||3314||G0₆₂₆₉D||6271||16×20⁶²⁷⁰+13 |- |21^*||13375~13395||CF₄₇₉₁₄₇0K||479150||(51×21⁴⁷⁹¹⁴⁹−1243)/4 |- |22^*||8003||BK₂₂₀₀₁5||22003||(251×22²²⁰⁰²−335)/21 |- |24||3409||N00N₈₁₂₉LN||8134||13249×24⁸¹³¹−49 |- |30^*||2619||OT₃₄₂₀₅||34206||25×30³⁴²⁰⁵−1 |- |36^*||35257~35263||P₈₁₉₉₃SZ||81995||(5×36⁸¹⁹⁹⁵+821)/7 |} ^* Data assumes the primality of the [[w:probable prime|probable prime]]s. Except bases ''b'' = 13, 16, 17, 21, all bases in this table are completely solved (if we allow strong probable primes > 10²⁵⁰⁰⁰), also, except bases ''b'' = 11, 13, 16, 17, 21, 22, 30, 36, all bases in this table are completely solved even if we only allow definitely primes (thus, we can complete the classification of the quasi-minimal primes in these bases, i.e. the “quasi-minimal problems” in these bases are now theorems), for the quasi-minimal primes see the data below. Base ''b'' = 13 has 3195 known quasi-minimal primes (or PRPs), see the data below, and if there are more quasi-minimal primes in base 13, then they must be of the form 9{5} or A{3}A (we are unable to determine if these two families contain a prime or not, i.e. these two families have no known prime members, nor can these two families be ruled out as only containing composites), and must have at least 111000 digits in base 13, besides, since these two families can contain at most one quasi-minimal prime, there are at most 3197 quasi-minimal primes in base 13. (i.e. the quasi-minimal primes in base 13 are the 3195 known quasi-minimal primes in base 13 (they are given in the data section) plus the smallest prime in the family 9{5} in base 13 (if exists) plus the smallest prime in the family A{3}A in base 13 (if exists)) Base ''b'' = 16 has 2346 known quasi-minimal primes (or PRPs), see the data below, and if there are more quasi-minimal primes in base 16, then they must be of the form {3}AF (we are unable to determine if this family contains a prime or not, i.e. this family have no known prime members, nor can this family be ruled out as only containing composites), and must have at least 98000 digits in base 16, besides, since this family can contain at most one quasi-minimal prime, there are at most 2347 quasi-minimal primes in base 16. (i.e. the quasi-minimal primes in base 16 are the 2346 known quasi-minimal primes in base 16 (they are given in the data section) plus the smallest prime in the family {3}AF in base 16 (if exists)) ==Data for quasi-minimal primes== ===Base 2=== 11 ===Base 3=== 12, 21, 111 ===Base 4=== 11, 13, 23, 31, 221 ===Base 5=== 12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013 ===Base 6=== 11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041 ===Base 7=== 14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331 ===Base 8=== 13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 ===Base 9=== 12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011 ===Base 10=== 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 ===Base 11=== 12, 16, 18, 21, 27, 29, 34, 38, 3A, 43, 49, 54, 56, 61, 65, 67, 72, 76, 81, 89, 92, 94, 98, 9A, A3, 10A, 115, 117, 133, 139, 153, 155, 171, 193, 197, 199, 1AA, 225, 232, 236, 25A, 263, 315, 319, 331, 335, 351, 353, 362, 373, 379, 391, 395, 407, 414, 452, 458, 478, 47A, 485, 4A5, 4A7, 502, 508, 511, 513, 533, 535, 539, 551, 571, 579, 588, 595, 623, 632, 70A, 711, 715, 731, 733, 737, 755, 759, 775, 791, 797, 7AA, 803, 847, 858, 85A, 874, 885, 887, 913, 919, 931, 937, 957, 959, 975, 995, A07, A1A, A25, A45, A74, A7A, A85, AA1, AA7, 1101, 11A9, 1305, 1451, 1457, 15A7, 175A, 17A5, 17A9, 2023, 2045, 2052, 2083, 20A5, 2333, 2A05, 2A52, 3013, 3026, 3059, 3097, 3206, 3222, 3233, 3307, 3332, 3505, 4025, 4151, 4157, 4175, 4405, 4445, 4487, 450A, 4575, 5017, 5031, 5059, 5075, 5097, 5099, 5105, 515A, 517A, 520A, 5301, 5583, 5705, 577A, 5853, 5873, 5909, 5A17, 5A57, 5A77, 5A8A, 6683, 66A9, 7019, 7073, 7079, 7088, 7093, 7095, 7309, 7451, 7501, 7507, 7578, 757A, 75A7, 7787, 7804, 7844, 7848, 7853, 7877, 78A4, 7A04, 7A57, 7A79, 7A95, 8078, 8245, 8333, 8355, 8366, 8375, 8425, 8553, 8663, 8708, 8777, 878A, 8A05, 9053, 9101, 9107, 9305, 9505, 9703, A052, A119, A151, A175, A515, A517, A575, A577, A5A8, A719, A779, A911, AAA9, 10011, 10075, 10091, 10109, 10411, 10444, 10705, 10709, 10774, 10901, 11104, 11131, 11144, 11191, 1141A, 114A1, 13757, 1411A, 14477, 144A4, 14A04, 14A11, 17045, 17704, 1774A, 17777, 177A4, 17A47, 1A091, 1A109, 1A114, 1A404, 1A411, 1A709, 20005, 20555, 22203, 25228, 25282, 25552, 25822, 28522, 30037, 30701, 30707, 31113, 33777, 35009, 35757, 39997, 40045, 4041A, 40441, 4045A, 404A1, 4111A, 411A1, 42005, 44401, 44474, 444A1, 44555, 44577, 445AA, 44744, 44A01, 47471, 47477, 47701, 5057A, 50903, 5228A, 52A22, 52A55, 52A82, 55007, 550A9, 55205, 55522, 55557, 55593, 55805, 57007, 57573, 57773, 57807, 5822A, 58307, 58505, 58A22, 59773, 59917, 59973, 59977, 59999, 5A015, 5A2A2, 5AA99, 60836, 60863, 68636, 6A609, 6A669, 6A696, 6A906, 6A966, 70048, 70103, 70471, 70583, 70714, 71474, 717A4, 71A09, 74084, 74444, 74448, 74477, 744A8, 74747, 74774, 7488A, 74A48, 75773, 77144, 77401, 77447, 77799, 77A09, 78008, 78783, 7884A, 78888, 788A8, 79939, 79993, 79999, 7A051, 7A444, 7A471, 80005, 80252, 80405, 80522, 80757, 80AA5, 83002, 84045, 85307, 86883, 88863, 8A788, 90073, 90707, 90901, 95003, 97779, 97939, 99111, 99177, 99973, A0111, A0669, A0966, A0999, A0A09, A1404, A4177, A4401, A4717, A5228, A52AA, A5558, A580A, A5822, A58AA, A5A59, A5AA2, A6096, A6966, A6999, A7051, A7778, A7808, A9055, A9091, A9699, A9969, AA52A, AA58A, 100019, 100079, 101113, 101119, 101911, 107003, 140004, 144011, 144404, 1A0019, 1A0141, 1A5001, 1A7005, 1A9001, 222223, 222823, 300107, 300202, 300323, 303203, 307577, 310007, 332003, 370777, 400555, 401A11, 404001, 404111, 405AAA, 41A011, 440A41, 441011, 451777, 455555, 470051, 470444, 474404, 4A0401, 4A4041, 500015, 500053, 500077, 500507, 505577, 522A2A, 525223, 528A2A, 531707, 550777, 553707, 5555A9, 555A99, 557707, 55A559, 5807A7, 580A0A, 580A55, 58A0AA, 590007, 599907, 5A2228, 5A2822, 5A2AAA, 5A552A, 5AA22A, 5AAA22, 60A069, 683006, 6A0096, 6A0A96, 6A9099, 6A9909, 700778, 701074, 701777, 704408, 704417, 704457, 704484, 707041, 707441, 707708, 707744, 707784, 710777, 717044, 717077, 740008, 74484A, 770441, 770744, 770748, 770771, 777017, 777071, 777448, 777484, 777701, 7778A8, 777A19, 777A48, 778883, 78A808, 790003, 7A1009, 7A4408, 7A7708, 80A555, 828283, 828883, 840555, 850505, 868306, 873005, 883202, 900701, 909739, 909979, 909991, 970771, 977701, 979909, 990739, 990777, 990793, 997099, 999709, 999901, A00009, A00599, A01901, A05509, A0A058, A0A955, A10114, A555A2, A55999, A59991, A5A222, A5A22A, A60609, A66069, A66906, A69006, A79005, A87888, A90099, A90996, A96006, A96666, A97177, A97771, AA0A58, AA5A22, AAA522, 1000501, 1011141, 1030007, 1070047, 111114A, 1111A14, 1111A41, 1144441, 14A4444, 1700005, 1700474, 1A44444, 2555505, 2845055, 3030023, 3100003, 3333397, 4000111, 4011111, 41A1111, 4411111, 444441A, 4444771, 4470004, 4505005, 4744417, 4774441, 4777404, 4777417, 4777747, 4A11111, 4A40001, 5000093, 50005A7, 5005777, 5050553, 5055503, 5070777, 5222222, 5222AAA, 52AAAA2, 52AAAAA, 5505053, 5552AAA, 5555599, 5555A58, 5558A0A, 5558A55, 5558AAA, 55A0009, 55AAA52, 580000A, 5822222, 58AAAAA, 5A2222A, 5AA2222, 6000A69, 6000A96, 6A00069, 7000417, 7000741, 7000835, 7000857, 7007177, 7008305, 7014447, 7017444, 7074177, 7077477, 7077741, 7077747, 7100447, 7174404, 717444A, 7400404, 7700717, 7701077, 7701707, 7707778, 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DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD ===Base 15=== 12, 14, 18, 1E, 21, 27, 2B, 2D, 32, 38, 3E, 41, 47, 4B, 4D, 54, 58, 5E, 67, 6B, 6D, 72, 74, 78, 87, 8B, 92, 94, 9E, A1, A7, AD, B2, B8, BE, C1, CB, CD, D2, D4, E1, ED, 111, 11B, 131, 137, 13B, 13D, 157, 15B, 15D, 171, 177, 197, 19D, 1B7, 1BB, 1D1, 1DB, 1DD, 234, 298, 311, 31B, 337, 33D, 344, 351, 357, 35B, 364, 377, 391, 39B, 39D, 3A4, 3BD, 3C4, 3D7, 3DB, 3DD, 452, 51B, 51D, 531, 53B, 551, 55D, 562, 571, 577, 5A2, 5B1, 5B7, 5BB, 5BD, 5C2, 5D1, 5D7, 634, 652, 681, 698, 717, 71B, 731, 737, 757, 75D, 77D, 79B, 79D, 7B1, 7B7, 7BD, 7D7, 7DD, 801, 852, 88D, 8D8, 91D, 93B, 93D, 95B, 95D, 971, 977, 97B, 97D, 988, 991, 9BD, 9C8, 9D1, A98, AAB, B1D, B31, B3B, B44, B51, B57, B7B, B7D, B97, B9B, BB7, BC4, BD1, BD7, BDD, C07, C34, C52, C7E, C98, CC7, CE7, D0E, D1D, D31, D51, D5B, D68, D77, D7B, D91, D97, DA8, DAE, DCE, DD1, EB4, EEB, 107B, 1091, 10B1, 1107, 110D, 1561, 1651, 1691, 1B01, 2052, 2502, 2522, 303B, 307D, 3097, 30BB, 30D1, 3107, 3361, 3701, 3907, 3B01, 3B0B, 3C97, 4434, 4498, 4834, 4898, 49A8, 4E34, 5037, 507D, 5091, 509B, 5107, 5161, 5202, 53C7, 5552, 570B, 590B, 590D, 59C7, 5A5B, 5C97, 5D0D, 5DAB, 6061, 6151, 6191, 6511, 6601, 6911, 707B, 7091, 7097, 70AE, 70BB, 70CE, 70DB, 7561, 760E, 7691, 76CE, 7907, 7961, 7A0E, 7A3B, 7AEE, 7B0B, 7BAB, 7C0E, 7C77, 7CAE, 7D0B, 7D61, 7DAB, 7E5B, 7E6E, 7E7B, 7EBB, 8098, 811D, 8191, 835D, 853D, 8881, 8908, 8951, 8968, 899D, 8D3D, 8D5D, 8D6E, 8DDD, 8E98, 9011, 9037, 9097, 90D7, 9301, 93C7, 95C7, 9611, 9631, 96A8, 9811, 9851, 989D, 990B, 990D, 998D, 99AB, 99C7, 99D8, 9A08, 9A9B, 9AA8, 9ABB, 9B61, 9BC7, 9D0B, 9DAB, 9DC7, 9DD8, A052, A304, A502, A55B, A9BB, AB04, AB64, B09D, B107, B10B, B161, B1AB, B1C7, B30D, B3C7, B50B, B664, B691, B6A4, B707, B761, B90D, B961, BA5B, BABB, BBAB, BBB4, BC37, BC77, C777, C937, C997, D011, D03D, D05D, D09B, D0B1, D0BD, D101, D10B, D30D, D3AB, D507, D50D, D66E, D761, D7DE, D811, D85D, D86E, D89D, D8C8, D8E8, D9AB, D9D8, DA3B, DA9B, DABB, DB01, DB61, DBAB, DC88, DD07, DD0B, DD7E, DD8D, DDE7, DE6E, E252, E33B, E522, E57B, E7AE, E7CE, E898, E997, E9A8, E9BB, EA34, EB5B, EE98, EEC7, 10017, 10B0D, 170AB, 17A0B, 19001, 19601, 1A09B, 1D0C7, 22E52, 2EA52, 30017, 3001D, 300B1, 301C7, 30334, 30631, 307AB, 3300B, 3333B, 36031, 36301, 37A0B, 37BBB, 39997, 3A30B, 3B0C7, 3D001, 3D601, 40034, 40968, 43334, 49668, 49998, 50022, 5009D, 501C7, 50222, 50507, 505C7, 50611, 50C57, 53007, 53997, 55537, 5555B, 5557B, 5599B, 56101, 56691, 56961, 5700D, 5755B, 59001, 59557, 59997, 5999D, 599DB, 59DDD, 5D99B, 5DD3D, 5DD9D, 60931, 63031, 65691, 66951, 69031, 69361, 69561, 70011, 70051, 7005B, 7006E, 7030D, 703AB, 70501, 70701, 707C7, 71601, 71951, 7300D, 7333B, 75001, 7555B, 75911, 76011, 76051, 766EE, 76EEE, 7700B, 77191, 77661, 7776E, 77771, 777BB, 77911, 77BBB, 79001, 7A05B, 7A66E, 7AA6E, 7AAAE, 7ACCE, 7C6EE, 7CCEE, 7CECE, 7CEEE, 7D3BB, 7E7C7, 7EECE, 80034, 80304, 80434, 809DD, 80A34, 84A34, 850DD, 85961, 86661, 88151, 88331, 88511, 88591, 88898, 890DD, 89998, 89D0D, 8D90D, 8E434, 90017, 90051, 900A8, 900DB, 901C7, 90C57, 90D8D, 91007, 91061, 9199B, 95997, 96068, 96561, 99397, 99537, 9999B, 999B7, 999D7, 999DB, 999DD, 99BBB, 99DBB, 99DD7, 99DDD, 9B007, 9B00B, 9B0AB, 9BB11, 9BBBB, 9D007, 9D08D, 9D537, 9D9BB, 9D9DB, 9DD57, 9DDB7, 9DDDB, 9DDDD, A0A34, A0B5B, A0BBB, A0E34, A2E52, A330B, A8434, A8834, A8E34, A909B, AAA34, AAE52, AB0BB, AB334, ABB34, AE034, AE834, AE99B, AEA52, AEE52, B0011, B0071, B0077, B00B1, B0611, B0A64, B500D, B599D, B6101, B7771, B7911, BA064, BAAA4, BAB34, BB061, BB304, BB53D, BB601, BBB91, BBB9D, BBBBD, BDA0B, BDBBB, D0088, D00D7, D0307, D05C7, D070D, D0888, D0B07, D0BC7, D0C08, D0DC7, D0DD8, D1661, D59DD, D5D3D, D5DDD, D6611, D700D, D8D0D, D900B, D9908, D999D, D9BBB, D9D9D, D9DDB, DB007, DB00D, DB1B1, DB53D, DB59D, DB99D, DBBB1, DD0D8, DD33B, DD3B7, DD3BB, DD57D, DD898, DD9DD, DDB37, DDBDB, DDD08, DDD3D, DDD5D, DDD7D, DDD88, DDD9D, DDDB7, DDDC8, DDDD7, DDE98, DE037, DE998, DEB07, E0098, E00C7, E0537, E0557, E077B, E0834, E0968, E3334, E37AB, E39C7, E4034, E5307, E55AB, E705B, E750B, E766E, E76EE, E8304, E8434, E9608, E9C37, EAE52, EBB0B, EC557, EC597, EC957, 1000BD, 1009AB, 10A90B, 1900AB, 190661, 19099B, 190A0B, 1A900B, 222A52, 2AAA52, 31000D, 330331, 333334, 3733AB, 373ABB, 3BBB61, 430004, 490068, 490608, 5000DB, 500D0B, 505557, 505A0B, 50D00B, 50DDDB, 50DDDD, 522222, 5500AB, 5500C7, 550957, 550A0B, 555A9B, 559057, 560011, 590661, 633331, 666331, 666591, 666661, 7050AB, 705A0B, 706101, 70A50B, 7300AB, 761661, 76666E, 777011, 777101, 77750B, 777A5B, 777CEE, 779051, 791501, 7E7797, 7ECCCE, 7EEE97, 800D9D, 808834, 836631, 83D661, 843004, 856611, 884034, 884304, 888E34, 88A434, 88AE34, 8A4034, 8AEE34, 8E8034, 8E8E34, 8EEE34, 9000BB, 9001AB, 900B07, 900D98, 903661, 905661, 906651, 9080DD, 9099A8, 909D9B, 90A668, 90DD9B, 90DDBB, 910001, 9100AB, 91A00B, 930007, 950001, 956661, 9909A8, 995907, 999068, 999507, 999907, 9B0B1B, 9B0BB1, 9BB01B, 9C5597, 9C5957, 9D09DD, 9D0D9D, 9D800D, 9DB307, 9DD09D, A00034, A0033B, A033B4, A2A252, AAAA52, ABBBBB, B00004, B0001B, B0003D, B00A04, B0555B, B07191, B07711, B07777, B0B911, B0BDBB, B77011, B777C7, BB0001, BB0034, BB035D, BB055B, BB0BDB, BB9101, BBB0DB, BBB50D, BBBB01, BBD0BB, C55397, C55557, C55597, D0003B, D00057, D0007D, D000B7, D000C8, D008DD, D00DAB, D0333B, D05537, D099DD, D09DDD, D0DDBB, D555C7, D5C537, D88008, D88088, D888EE, D909DD, D9D0DD, D9DD0D, DB0BBB, DBBB0B, DBBB0D, DC0008, DC5537, DDDDD8, DDDEBB, DDE99B, DE0808, DE0C57, DE300B, DE5537, DE8888, DEE088, DEE307, DEE888, DEEE37, DEEE57, DEEEC8, E0000B, E007BB, E00A52, E03BC7, E07ABB, E09B07, E0A99B, E0C397, E0E76E, E50057, E55007, E55597, E55937, E730AB, E73A0B, E80E34, E88834, E8E034, E90008, E95557, EA099B, EE4304, EE5057, EE5507, EE8E34, EE9307, EEE434, 100001D, 1000A9B, 1000DC7, 22AA252, 3000BC7, 3033301, 3076661, 333B304, 33B3034, 3B33304, 3D66661, 50007AB, 5005957, 5500597, 5550057, 5559007, 5559597, 5595007, 5966661, 5DDDDDB, 6366631, 7010001, 7066651, 7100061, 733BBBB, 766A6AE, 77505AB, 7776501, 777775B, 777AACE, 777ECCE, 777EEAE, 7CCCCCE, 7E30A0B, 7EEEEAE, 8300004, 8363331, 8693331, 880E834, 8833304, 8888034, 8888434, 888A034, 88A3334, 88E8834, 88EE034, 88EE304, 8AA3334, 8D0009D, 8EE8834, 9000361, 9000668, 9003331, 9005557, 9006008, 9008D0D, 9083331, 9090968, 90BBB01, 90D0908, 9500661, 9555597, 9555957, 9660008, 9900968, 9995597, 9996008, 9999557, 9999597, 9999908, 9A66668, A003B34, A003BB4, AA22252, B00B034, B00B35D, B033334, B0B6661, B0BB01B, B100001, B333304, B777777, B99999D, BA60004, BAA0334, BBB001B, BBB6611, BBBBB11, BBBD00B, BD000AB, D0000DB, D009098, D00CCC8, D00D908, D00D99D, D03000B, D0BB0BB, D0D9008, D0D9998, D1000C7, D800008, D8DDEEE, D90080D, DBBBBBB, DD09998, DDD5557, DDDDBBB, DDDDDBD, DDDE8EE, DECC008, DECCCC8, DEE0CC8, DEEC0C8, E000397, E0003BB, E000434, E00076E, E000937, E007A5B, E00909B, E0090B7, E009307, E00B077, E00E434, E00E797, E00E937, E05999B, E09009B, E0900B7, E0E0937, E0E7E97, E0EAA52, E0EEA52, E555057, E5555C7, E7777C7, E77E797, E88EE34, E999998, EA5999B, EB000BB, EB0BBBB, EE00434, EE0E797, EEE076E, EEE706E, EEE8834, EEEE557, EEEE797, 30333331, 30B66661, 33000034, 33030004, 33B33004, 500575AB, 55000007, 5500075B, 55500907, 55555057, 55555907, 55559507, 60003301, 60033001, 60330001, 7000003D, 70106661, 70666611, 77000001, 7777770B, 777777C7, 77777ACE, 77777EAE, 777E30AB, 777E3A0B, 7CCCC66E, 800005DD, 88AA0834, 90000008, 900008DD, 90099668, 90500557, 90555007, 90666668, 90909998, 90990998, 90996668, 9099999D, 90D00098, 90D90998, 95500057, 99099098, 99555057, 99900998, 99966608, 99966668, 99999668, 99999998, 9D009008, 9D090998, A0803334, A2222252, AAA52222, B00005AB, B000B55B, B0BBBB5B, B3330034, BB0BBB1B, BBAA3334, BBB0BB1B, BBB0BB5B, BBDB000B, D000BBBB, D00100C7, D8888888, D900008D, D9000098, DBB000BB, DC0CCCC8, DCC0CCC8, DCCCC008, DD000908, DD09009D, DDDDDDAB, DDDDDEEE, DDDEEE8E, DDDEEEE8, DEE80008, E0777E97, E0E0E397, E0E77797, E0EE0397, E7777797, E9066668, EE00E397, EE077797, EE0E0397, EEE00797, EEE07E97, EEE0AA52, EEE55397, EEE55557, EEEAAA52, EEEEE834, EEEEEA52, 300003331, 300007661, 300330031, 333000004, 333300001, 333B00034, 3700000AB, 3B3300034, 500000057, 555555007, 555555557, 5DDDDDDDD, 600000331, 7500000AB, 75000A00B, 75A00000B, 761000001, 77000E0C7, 777700EC7, 7777730AB, 7777777AE, 77777EE97, 7777E7E97, 777999997, 7A500000B, 7BBBBBB5B, 88888A834, 900000031, 900666608, 909990098, 90D009998, 950000557, 966666008, 990000007, 990555507, 999999997, A000000B4, A0005999B, AAEEEEE34, B000AA334, BBBBB005B, BBBBBBB5B, D09999998, D0D90009D, D800000DD, D90009998, DCCCC0CC8, DE88EEEEE, DEEEEEE88, E000B7777, E000BBBBB, E003ABBBB, EE0000797, EE0EEE397, EE5555557, EE777EE97, EEEEEE537, EEEEEE937, 2222222252, 3000000071, 3330030001, 3333303001, 3333330001, 500000007B, 5555555097, 7000000071, 77000000C7, 8333333331, 8888883334, 8888888834, 888888AA34, 900000009B, 900000009D, 900000DD9D, 9000099998, 9955555507, 9D0000099D, 9D05555557, AB0000005B, B000000DAB, B00000BBDB, BB00BB0B5B, BB0BB00B5B, D000099998, D00090008D, D0D000909D, D0DDDDDDDB, D300000007, D88EEEEEEE, D900999998, DD00900008, DDD6EEEEEE, DDDDDDD6EE, DDDDDDDDDE, DDDEEEEEEE, DEEEEE8008, E000000797, 7777777CCCE, 88888830004, 90000009D9D, 99955555557, 9999999999D, B00000D00AB, BB000BBB05B, BBBB0000B5B, D000009080D, D000090800D, D090800000D, DDDDDDD999B, DDDDDDDDD9B, EEEEEE00397, EEEEEEE0397, 333000000301, 5000000000DD, 73A00000000B, 9000000000B7, 903333333331, ABB00000000B, D000000001C7, DCCCCCCCCCC8, E0EEEEEEE397, 19A000000000B, 3333333333331, 3BBBBBBBBBBBB, 9333333333331, A00000000099B, B00000000050D, EEEEEEEEEE76E, 1000000000999B, 71000000000001, 908D000000000D, BBBBBBBBBB6661, 77777777777777B, BB00000000BBB5B, DEEEEEEEEEEEEEE, 7777777777777E97, B0BBBBBBBBBBBB1B, BB0000000000DB0B, D000000000000998, D908000000000000D, DDDDDDDDDDDDDDDDB, E9666666666666668, 3330000000000000031, D00000000000000908D, E0BBBBBBBBBBBBBBBBB, 2EEEEEEEEEEEEEEEEE52, 77777777777777777ECE, 5000000000000000005AB, 777777777777777777997, 7BBBBBBBBBBBBBBBBBBBB, BB0000000000000000DBB, DD000000000000000909D, D900000000000000000DDD, DD0000000000000000099D, BBBBBBBBBBBBBBBBBBBBBB1, B00000000000000000000005B, B0700000000000000000000001, B70000000000000000000000001, 705000000000000000000000000B, 633000000000000000000000000001, EBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB, 500000000000000000000000000000000017, 77777777777777777777777777777777777777777777777777777777777CCE, 7777777777777777777777777777777777777777777777777777777777777777777777777CE, 96666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666608, EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE397, 7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777797 ===Base 16=== 11, 13, 17, 1D, 1F, 25, 29, 2B, 2F, 35, 3B, 3D, 43, 47, 49, 4F, 53, 59, 61, 65, 67, 6B, 6D, 71, 7F, 83, 89, 8B, 95, 97, 9D, A3, A7, AD, B3, B5, BF, C1, C5, C7, D3, DF, E3, E5, E9, EF, F1, FB, 14B, 15B, 185, 199, 1A5, 1BB, 1C9, 1EB, 223, 22D, 233, 241, 277, 281, 287, 28D, 2A1, 2D7, 2DD, 2E7, 301, 337, 373, 377, 38F, 3A1, 3A9, 41B, 42D, 445, 455, 45D, 481, 4B1, 4BD, 4CD, 4D5, 4E1, 4EB, 50B, 515, 51B, 527, 551, 557, 55D, 577, 581, 58F, 5AB, 5CB, 5CF, 5D1, 5D5, 5DB, 5E7, 623, 709, 727, 737, 745, 74B, 755, 757, 773, 779, 78D, 7BB, 7C3, 7C9, 7CD, 7DB, 7EB, 7ED, 805, 80F, 815, 821, 827, 841, 851, 85D, 85F, 8A5, 8DD, 8E1, 8F5, 923, 98F, 99B, 9A9, 9EB, A21, A6F, A81, A85, A99, A9F, AA9, AAB, ACF, B1B, B2D, B7B, B8D, B99, B9B, BB7, BB9, BCB, BDD, BE1, C0B, CB9, CBB, CEB, D01, D21, D2D, D55, D69, D79, D81, D85, D87, D8D, DAB, DB7, DBD, DC9, DCD, DD5, DDB, DE7, E21, E27, E4B, E7D, E87, EB1, EB7, ED1, EDB, EED, F07, F0D, F4D, FD9, FFD, 1069, 1505, 1609, 1669, 16A9, 19AB, 1A69, 1AB9, 2027, 204D, 2063, 207D, 20C3, 20ED, 2221, 22E1, 2327, 244D, 26C3, 274D, 2E01, 2E0D, 2ECD, 3023, 3079, 3109, 3263, 3341, 36AF, 3941, 3991, 39AF, 3E41, 3E81, 3EE1, 3EE7, 3F79, 4021, 40DB, 440B, 444B, 44A1, 44AB, 44DB, 4541, 45BB, 4A41, 4B0B, 4BBB, 4C4B, 4D41, 4DED, 5045, 50A1, 50ED, 540D, 5441, 555B, 556F, 5585, 560F, 56FF, 5705, 574D, 580D, 582D, 5855, 588D, 5A01, 5AA1, 5B01, 5B4B, 5B87, 5BB1, 5BEB, 5C4D, 5CDD, 5CED, 5DD7, 5DDD, 5E0D, 5E2D, 5EBB, 68FF, 6A69, 6AC9, 6C8F, 6CA9, 6CAF, 6F8F, 6FAF, 7033, 7063, 7075, 7087, 70A5, 70AB, 7303, 7393, 74DD, 754D, 7603, 7633, 7663, 7669, 7705, 772D, 775D, 77D5, 7807, 7877, 7885, 7939, 7969, 7993, 79AB, 7A05, 7A69, 7A9B, 7AA5, 7B77, 7BA9, 7D4D, 7D75, 7D77, 8077, 808D, 80D7, 80E7, 8587, 86CF, 8777, 8785, 8885, 88CF, 88ED, 88FD, 8C6F, 8C8F, 8E8D, 8EE7, 8F2D, 8F8D, 9031, 9041, 90AF, 90B9, 9221, 9319, 9401, 944B, 9881, 9931, 9941, 9991, 99AF, 9A0F, 9A1B, 9A4B, 9AFF, 9BA1, 9BB1, 9CAF, 9E81, 9EA1, 9FAF, A001, A05B, A0C9, A105, A10B, A4CB, A55B, A6C9, A88F, A91B, A9B1, A9BB, AA15, AB01, AB0B, AB19, ABBB, AC09, AF09, B041, B04B, B069, B07D, B087, B0B1, B0ED, B1A9, B201, B40B, B40D, B609, B70D, B7A9, B807, B9A1, BA41, BAA1, BB4B, BBB1, BBDB, BBED, BD19, BD41, BDBB, BDEB, BE07, BEE7, C0D9, C203, C24D, C6A9, C88D, C88F, C8CF, C8ED, C9AF, C9CB, CA09, CA4B, CA69, CAC9, CC0D, CC23, CC4D, CC9B, CD09, CDD9, CE4D, CEDD, CFA9, CFCD, D04B, D099, D405, D415, D44B, D4A5, D4DD, D50D, D70B, D74D, D77B, D7CB, D91B, D991, DA05, DA09, DA15, DA51, DB91, DBEB, DD7D, DDA1, DDED, DE0B, DE41, DE4D, DEA1, E02D, E07B, E0D7, E1CB, E2CD, E401, E801, EABB, EACB, EAEB, EBAB, EC4D, ECDD, ED07, EDD7, EE7B, EE81, EEAB, EEE1, F08F, F0A9, F227, F2ED, F3AF, F485, F58D, F72D, F763, F769, F787, F7A5, F7E7, F82D, F86F, F877, F88D, F8D7, F8E7, F8FF, FCCD, FED7, FF85, FF8F, FFA9, 100AB, 10BA9, 1A0CB, 1BA09, 200E1, 2C603, 2CC03, 30227, 303AF, 30AAF, 32003, 32207, 32CC3, 330AF, 33169, 33221, 33391, 33881, 33AFF, 38807, 38887, 3AFFF, 3F203, 3F887, 3FAFF, 400BB, 4084D, 40A4B, 42001, 44221, 44401, 444D1, 4480D, 4488D, 44CCB, 44D4D, 44E8D, 4804D, 4840D, 4A0CB, 4A54B, 4CACB, 4D0DD, 4D40D, 4D44D, 5004D, 50075, 502CD, 5044D, 50887, 50EE1, 5448D, 548ED, 55A45, 55F45, 5844D, 5A4A5, 5AE41, 5B0CD, 5B44D, 5BBCD, 5D4ED, 5E0E1, 5EB4D, 5EC8D, 5ECCD, 5EE41, 5F06F, 5F7DD, 5F885, 5F8CD, 5FC8D, 5FF75, 6088F, 60AFF, 630AF, 633AF, 660A9, 668CF, 669AF, 66A09, 66A0F, 66FA9, 6886F, 6A00F, 6A0FF, 6A8AF, 6AFFF, 7002D, 7024D, 70B0D, 70B7D, 7200D, 73363, 73999, 7444D, 770B7, 777D7, 77B07, 77D7D, 77DD7, 79003, 79999, 7B00D, 7D05D, 7D7DD, 8007D, 800D1, 8074D, 82CCD, 82E4D, 8448D, 8484D, 8704D, 8724D, 87887, 88001, 8800D, 880CD, 88507, 88555, 8866F, 8872D, 8877D, 888D1, 888D7, 88AA1, 88C2D, 88D57, 88D75, 88D77, 8AFAF, 8C2CD, 8C40D, 8C8CD, 8CCED, 8CE2D, 8CFED, 8E007, 8E20D, 8E24D, 8F6FF, 8FAAF, 900CB, 901AB, 90901, 909A1, 90AB1, 90AE1, 90EE1, 910AB, 93331, 940AB, 963AF, 966AF, 99019, 99109, 99A01, 9AAE1, 9B00B, 9B0AB, 9B441, 9BABB, 9BBBB, 9E441, A00BB, A0405, A044B, A08AF, A0A51, A0B91, A0C4B, A1B09, A54A5, A5B41, A6609, A904B, A94A1, A9C4B, A9E01, A9E41, AA0A1, AA441, AA501, AA8AF, AAEE1, AAF45, AAF8F, ABBA1, ACC69, AE0BB, AE0EB, AEAE1, AEE0B, AEEA1, AEECB, AF045, AF4A5, AFA8F, B00A1, B00D7, B044D, B0777, B0A0B, B0A91, B0BBD, B0BCD, B0C09, B0DA9, B0EAB, B2207, B4001, B6669, B7707, B7D07, B8081, B9021, BA091, BA109, BA4BB, BB001, BB0EB, BB8A1, BBBEB, BBE0B, BBEBB, BC009, BCECD, BD0A9, BE44D, BEB0D, BEBBB, BEEBB, C0263, C02C3, C02ED, C040D, C0CA9, C0CCD, C2663, C2CED, C32C3, C3323, C400D, C40ED, C44CB, C44ED, C480D, C484D, C4CAB, C60AF, C686F, C6A0F, C86FF, C8C2D, CAA0F, CAFAF, CBCED, CC0AF, CC44B, CC82D, CC8FF, CCAF9, CCAFF, CCCFD, CCFAF, CD00D, CD4CB, CD4ED, CDDDD, CF2C3, CFC8F, CFE8D, D0045, D07DD, D09BB, D0D4D, D0DD7, D0EBB, D0EEB, D1009, D1045, D10B9, D1BA9, D54BB, D54ED, D5AE1, D5D07, D5EE1, D70DD, D7707, D7777, D77DD, D7DD7, D9441, D9AE1, D9B0B, DA9A1, DA9E1, DAA41, DAAA1, DBB0B, DBBA1, DC4CB, DD227, DD44D, DDDD7, E0081, E00E1, E010B, E088D, E08CD, E0B0D, E0BBD, E100B, E4D0D, E777B, E77AB, E7CCB, E844D, E848D, E884D, E88A1, EB0BB, EBB4D, EBBEB, EBEEB, EC8CD, ECBCD, ECC8D, ED04D, EE001, EE0EB, EE4A1, EEEBB, F0085, F09AF, F0C23, F0CAF, F2663, F2C03, F3799, F3887, F4A05, F4AA5, F506F, F5845, F5885, F5C2D, F5ECD, F5F45, F66A9, F688F, F6AFF, F7399, F777D, F8545, F8555, F8AAF, F8F87, F9AAF, FA0F9, FA405, FA669, FAFF9, FC263, FCA0F, FCAFF, FCE8D, FCF23, FD777, FDDDD, FDEDD, FEC2D, FEC8D, FF545, FF6AF, FF739, FF775, FF9AF, FFC23, 100055, 100555, 10A9CB, 1A090B, 1A900B, 1CACCB, 1CCACB, 20DEE1, 266003, 3000AF, 300A0F, 300AFF, 308087, 308E07, 3323E1, 333A0F, 339331, 33CA0F, 33CF23, 33CFAF, 33F323, 380087, 3A00AF, 3A0F0F, 3AA0FF, 3AAF0F, 3C33AF, 3C3A0F, 3C3FAF, 3CCAAF, 3F0FAF, 3F32C3, 3FF0AF, 3FFAAF, 4004CB, 400A05, 4048ED, 404DDD, 40AA05, 40D04D, 40DD4D, 40E0DD, 40E48D, 440041, 44008D, 44044D, 4404DD, 44440D, 4448ED, 4484ED, 448E4D, 44E44D, 48888D, 4AA005, 4DD00D, 4DD04D, 4DDD0D, 4E048D, 4E448D, 4E880D, 5000DD, 500201, 50066F, 5008CD, 500C2D, 500D7D, 50C20D, 520C0D, 544EDD, 54AA05, 54AAA5, 54ED4D, 566AAF, 57D00D, 580087, 5A5545, 5C20CD, 5C8CCD, 5CC2CD, 5D000D, 5D070D, 5F666F, 5FAA45, 5FFF45, 60008F, 600A0F, 603AAF, 6060AF, 6066AF, 60A0AF, 63AA0F, 6663AF, 66668F, 666AAF, 668A8F, 66AFF9, 68888F, 693AAF, 7007B7, 70404D, 70770B, 70770D, 707BE7, 70DD0D, 733339, 733699, 74004D, 74040D, 77007B, 770CCB, 777B4D, 777BE7, 777CCB, 77ACCB, 77B74D, 77D0DD, 7A0CCB, 7B744D, 7CACCB, 7DDD99, 80044D, 800807, 80200D, 8044ED, 80C04D, 80CC2D, 80E44D, 8404ED, 84888D, 84E04D, 84E40D, 86686F, 8668AF, 8686AF, 86F66F, 86FFFF, 87000D, 87744D, 880807, 886AFF, 88824D, 88870D, 888787, 88884D, 88886F, 88887D, 88888D, 888C4D, 888FAF, 88AA8F, 88CC8D, 88F6AF, 88F8AF, 88FA8F, 88FF6F, 88FF87, 88FFAF, 8A8FFF, 8C0C2D, 8C802D, 8CCFFF, 8CE00D, 8CE0CD, 8CFCCF, 8E00CD, 8E044D, 8E0CCD, 8EC0CD, 8F68AF, 8F88F7, 8FCFCF, 8FF887, 8FFCCF, 8FFF6F, 9002E1, 9004AB, 9008A1, 900919, 900ABB, 900B21, 90B801, 90CCCB, 9332E1, 944441, 94ACCB, 990001, 9900A1, 9A4441, 9A4AA1, 9AA4A1, 9AAA41, 9AAAAF, 9B66C9, 9BBA0B, 9BC0C9, 9BC669, 9BC6C9, 9C4ACB, A0094B, A00ECB, A09441, A0A08F, A0E0CB, A0ECCB, A0F669, A40A05, A4AAA5, A50E41, A5AA45, A60069, A8FAFF, A9AA41, AA5E41, AAA4A5, AAA545, AC6669, ACCC4B, ACCCC9, AEAA41, AFF405, AFF669, AFFA45, AFFFF9, B00921, B00BEB, B00CC9, B00D91, B08801, B0D077, B70077, B70E77, B77E77, B88877, B88881, B94421, BAE00B, BB00AB, BB0DA1, BB444D, BB44D1, BB8881, BBBBBD, BBBC4D, BBCCCD, BC0CC9, BC66C9, BCC669, BCC6C9, BCCC09, BE000D, BE00BD, BE0B4D, BE0CCD, BEA00B, BECCCD, C0084D, C00A0F, C0608F, C0668F, C0844D, C0A0FF, C0AFF9, C0C3AF, C0C68F, C0CAAF, C0CDED, C0D0ED, C0E80D, C0EC2D, C0EC8D, C0FA0F, C0FAAF, C2CC63, C30CAF, C333AF, C3CAAF, C3CCAF, C4048D, C40D4D, C4404D, C4408D, C4440D, C44DDD, C4ACCB, C4DCCB, C4DD4D, C6068F, C66AAF, C68AAF, C6AA8F, C8044D, C8440D, C8666F, CA00FF, CA0FFF, CAAAAF, CAAFFF, CAFF0F, CBE0CD, CC008F, CC0C8F, CC3CAF, CC4ACB, CC608F, CC66AF, CCBECD, CCC4AB, CCCA0F, CCCC8F, CCCE8D, CE0C8D, CF0F23, CF0FAF, CFAFFF, CFCAAF, CFFAFF, D0005D, D00BA9, D05EDD, D077D7, D10CCB, D22207, D4000B, D4040D, D4044D, D40CCB, D70077, D7D00D, D90009, D900BB, DB00BB, DB4441, DD400D, DDD109, DDD1A9, DDD919, DDD941, DED00D, E00D4D, E00EEB, E0AAE1, E0AE41, E0AEA1, E0B44D, E0BCCD, E0BEBB, E0D0DD, E0E441, E4048D, E4448D, E800CD, E8200D, EA0E41, EAA0E1, EBB00B, ECCCAB, EDDDDD, EEBE0B, F00263, F0056F, F00A45, F02C63, F03F23, F05405, F060AF, F08585, F0A4A5, F0F2C3, F0F323, F2CCC3, F33203, F33C23, F5F66F, F5FF6F, F68CCF, F6AA8F, F888AF, FA0F45, FAA045, FAA545, FAFC69, FC0AAF, FC66AF, FCCCAF, FCFFAF, FF0323, FF056F, FF3203, FF7903, FFA045, FFA4A5, FFAA45, FFC0AF, FFF4A5, FFF575, FFFA45, FFFCAF, 10A009B, 20000D1, 2CCC663, 30A00FF, 30CCCAF, 30FA00F, 30FCCAF, 3333C23, 333C2C3, 33C3AAF, 33FCAAF, 33FFFAF, 3A0A00F, 3AAAA0F, 3AF000F, 3AFAAAF, 3C0CA0F, 3CCC3AF, 3CFF323, 3F33F23, 3FAA00F, 3FF3323, 4004441, 400DDD1, 400E00D, 400ED0D, 404404D, 404448D, 404E4DD, 440EDDD, 4440EDD, 44444ED, 4444E4D, 44DDDDD, 4A000A5, 4CCCCAB, 4D0CCCB, 4E4404D, 4E4444D, 4E4DDDD, 5000021, 5004221, 5006AAF, 500FF6F, 5042201, 508CCCD, 5400005, 5400AA5, 5555405, 5808007, 5AA4005, 5C0008D, 5CCC8CD, 5D4444D, 5EEEEEB, 5F40005, 5F554A5, 5F6AAAF, 60000AF, 60006A9, 600866F, 6008AAF, 600AA8F, 600F6A9, 606608F, 606686F, 608666F, 60AA08F, 60AAA8F, 66000AF, 66666A9, 6666AF9, 6866A8F, 6AAAAAF, 70070D7, 70077DD, 700DDDD, 707077D, 707D007, 70D00DD, 770077D, 770400D, 770740D, 7777775, 77777B7, 77777DD, 7777ACB, 77B88E7, 77DD00D, 77DDDDD, 7D0D00D, 7DD0D07, 7DDD00D, 800002D, 8000CED, 80C0E0D, 80CECCD, 840400D, 844000D, 844E00D, 868688F, 880444D, 884404D, 887D007, 8888801, 8888881, 8888E07, 8888F77, 8888FE7, 88A8AFF, 88AAAFF, 88FAFFF, 8A8AAAF, 8A8AAFF, 8AAA8FF, 8C00ECD, 8C8444D, 8E4400D, 8FCCCCF, 900BBAB, 90CC4AB, 9908AA1, 99E0E01, 9B00801, 9B6CCC9, A000FF9, A006069, A00A8FF, A01CCCB, A05F545, A0BEEEB, A0E4AA1, AA0008F, AA08FFF, AA40AA5, AA8FFFF, AAAA405, AE04AA1, AE44441, AE4AAA1, AECCCCB, AF40005, AFA5A45, AFFFC69, B000BAB, B000EBB, B0D0007, B222227, B6CCCC9, B8880A1, BA000EB, BA0BEEB, BAEEEEB, BB000CD, BB00C0D, BB0B00D, BC6CC69, BC6CCC9, BCCCC69, BCCCCED, C0000A9, 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4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444DD ===Base 17=== 12, 16, 1C, 1E, 23, 27, 29, 2D, 32, 38, 3A, 3G, 43, 45, 4B, 4F, 54, 5C, 5G, 61, 65, 67, 6B, 78, 7C, 81, 83, 8D, 8F, 94, 9A, 9E, A3, A9, AB, B4, B6, BA, BC, C7, D2, D6, D8, DC, E1, E3, ED, F2, F8, FE, FG, G5, G9, GB, 104, 111, 115, 117, 11B, 137, 139, 13D, 14A, 14G, 155, 159, 15F, 171, 17B, 17D, 188, 191, 197, 19F, 1A4, 1A8, 1B3, 1BB, 1BF, 1DB, 1DD, 1F3, 1FD, 1G8, 1GA, 1GG, 20F, 214, 221, 225, 241, 25A, 25E, 285, 2B8, 2C5, 2CF, 2E5, 2EB, 2F6, 30E, 313, 331, 33B, 346, 34C, 351, 35F, 36E, 375, 37B, 391, 39B, 39D, 3B7, 3B9, 3BF, 3D3, 3D5, 3D9, 3DF, 3E4, 3EC, 3F1, 3F7, 407, 418, 447, 44D, 472, 474, 47E, 47G, 489, 49C, 4A1, 4C1, 4CD, 4D4, 4G1, 502, 506, 508, 50E, 519, 522, 528, 52A, 52E, 533, 53F, 551, 55D, 562, 566, 573, 577, 57F, 582, 593, 599, 59B, 59F, 5A6, 5B5, 5D1, 5D3, 5EA, 5EE, 5F9, 60D, 62F, 634, 649, 689, 692, 6CD, 6EF, 6F4, 6FA, 704, 706, 70G, 71D, 726, 737, 739, 73D, 73F, 753, 755, 764, 766, 76G, 771, 77B, 793, 7AA, 7AE, 7B3, 7BB, 7D7, 7E6, 7F3, 7F9, 7FF, 7G2, 7GE, 7GG, 825, 82B, 849, 852, 85E, 869, 876, 87A, 87G, 88B, 892, 898, 89C, 8C5, 8E7, 8G7, 908, 90G, 913, 91F, 92C, 935, 937, 93B, 951, 953, 957, 95D, 968, 96G, 979, 97B, 98C, 98G, 99D, 9B1, 9B3, 9B9, 9BD, 9BF, 9DB, 9DF, 9F1, 9F5, 9G6, A07, A0D, A1A, A2F, A4D, A72, A7A, A7E, AA1, AA7, ACF, ADA, AG1, AG7, B02, B08, B17, B1D, B28, B2G, B57, B71, B73, B79, B7F, B88, B8E, B8G, B9B, B9F, BB5, BB7, BD7, BDD, BEG, BFF, BGG, C01, C2F, C3E, C56, C6D, C89, C92, C9G, CA5, CBG, CC1, CC5, CF4, CFA, D04, D0A, D15, D3D, D3F, D55, D59, D5B, D71, D75, D7D, D91, D97, D99, D9D, DA4, DAG, DB3, DDB, DF1, DF7, DF9, DFF, E05, E0B, E2B, E52, E58, E69, E92, E9C, EAF, EB8, EC9, ECB, EE5, F04, F15, F1B, F35, F3B, F46, F51, F53, F64, F6A, F73, F79, F95, FAC, FB1, FCA, FD5, FDB, FF1, FF7, FFD, G0D, G0F, G18, G1A, G1G, G2F, G34, G63, G7G, GA7, GC3, GDG, GEF, GFA, GG7, GGD, 1013, 101D, 1033, 1035, 1051, 105B, 105D, 1077, 108A, 109B, 10AG, 10B1, 10B7, 10BD, 10FB, 1149, 1189, 11AF, 11G3, 1303, 130B, 1314, 1341, 1479, 14D9, 1501, 1503, 15A1, 15B8, 1734, 1749, 17AF, 17G3, 1844, 185B, 1875, 1877, 18AG, 18B5, 1903, 1909, 1958, 19BG, 19G3, 1A5D, 1A75, 1A7F, 1ADF, 1AF1, 1B01, 1B09, 1B18, 1B85, 1B89, 1BDG, 1BGD, 1D07, 1D49, 1D9G, 1DF4, 1F09, 1F47, 1F5A, 1F74, 1F7A, 1FA1, 1FAF, 2018, 201G, 202B, 208B, 20G1, 215B, 218G, 21AG, 21B1, 222F, 22AF, 22BG, 22EF, 22F4, 22GF, 251B, 2526, 25F1, 266F, 26FC, 280B, 2A05, 2A58, 2AFC, 2AGF, 2B1B, 2B1F, 2BGE, 2C1G, 2C2B, 2C8B, 2CG1, 2E2F, 2EGF, 2F0C, 2F55, 2FAA, 2FC4, 2FFF, 2GA1, 2GFC, 2GG1, 2GGF, 301B, 301F, 3037, 3053, 3057, 3079, 3095, 30B3, 30BD, 30C4, 31F4, 330D, 3334, 333E, 3349, 3376, 337E, 33CD, 33EF, 3411, 3417, 3499, 3503, 3505, 3509, 353E, 35E5, 35EB, 3604, 36FD, 3701, 3741, 374D, 376F, 3796, 37D4, 37F4, 3956, 3B03, 3B05, 3B0B, 3BBE, 3C04, 3C15, 3C19, 3C4E, 3C59, 3C64, 3CB3, 3CDB, 3CE6, 3D07, 3D14, 3DDE, 3E77, 3E79, 3E7F, 3E99, 3EEE, 3EFB, 3F05, 3F0D, 3FCB, 3FF4, 4009, 4021, 4069, 4098, 40DG, 40GD, 419D, 4201, 4401, 4492, 46AD, 46C9, 46DA, 4719, 476A, 4779, 479D, 47A6, 4906, 4911, 4917, 4919, 491D, 492G, 4982, 4988, 49D7, 49D9, 49GG, 4ADE, 4AE7, 4C49, 4C96, 4CC9, 4D79, 4DAE, 4DEG, 4E7A, 4E96, 4EG7, 4G6D, 4G87, 501B, 5037, 5059, 507D, 50BB, 50BF, 50D7, 50DD, 50F1, 5105, 51A7, 51AD, 521B, 525F, 52FB, 5307, 5356, 53BE, 53DE, 53E9, 5507, 550B, 5587, 5598, 55EF, 560A, 568E, 56AA, 56F3, 5709, 5725, 572B, 575A, 575E, 5769, 57A1, 57B2, 5868, 586E, 58AE, 58B9, 590D, 5918, 5952, 5958, 596D, 5A17, 5A1F, 5ADD, 5ADF, 5AE8, 5B07, 5B21, 5B2F, 5B3E, 5BEF, 5DA7, 5DEB, 5E57, 5E5F, 5E86, 5E97, 5EB9, 5EBF, 5EF5, 5F01, 5F1A, 5F6F, 5FA7, 5FDA, 60AF, 60G3, 64AD, 64DE, 64DG, 663E, 666D, 66AF, 693D, 69CG, 69D3, 69D9, 69G8, 69GC, 6ADE, 6AGD, 6C98, 6D33, 6D4E, 6D93, 6D9F, 6DDD, 6DEE, 6DF3, 6DFD, 6DGE, 6E09, 6G36, 6G4D, 6G6D, 6GD4, 6GDE, 6GFC, 702E, 7057, 705B, 7073, 7079, 7095, 70B5, 70BD, 70D1, 70E2, 70F5, 7107, 7149, 719G, 71BG, 71F4, 724E, 724G, 725F, 72A2, 72BF, 72EE, 72GA, 7314, 733E, 7341, 7363, 73EB, 7419, 742A, 742G, 7442, 74EG, 7501, 750F, 751A, 756D, 757E, 75A1, 75A7, 75BE, 75DA, 75E9, 75F6, 7622, 769F, 76EA, 7734, 773E, 776D, 779G, 77AF, 7905, 790B, 7976, 79B2, 79F6, 79GD, 7A1F, 7A5D, 7AD5, 7ADF, 7AF1, 7AFD, 7B01, 7B09, 7B2F, 7B52, 7B72, 7BE5, 7D01, 7D05, 7D9G, 7DAF, 7DBG, 7E0A, 7E75, 7EA2, 7EA4, 7EB5, 7EBF, 7EE2, 7EF7, 7EG4, 7F0B, 7F14, 7F5A, 7F76, 7FA7, 7G1F, 7G46, 7GA6, 7GD3, 7GDF, 8009, 8058, 80B8, 80E9, 84A7, 850A, 8557, 857B, 85A8, 870E, 8744, 8777, 879B, 87B5, 87B7, 87EE, 8805, 8872, 8887, 8889, 88E9, 8906, 8959, 8966, 89GG, 8A87, 8AE5, 8B0G, 8B59, 8B95, 8B97, 8CB2, 8CB8, 8CE9, 8E56, 8EE9, 9026, 9031, 903D, 907F, 9091, 909B, 90FB, 9101, 910D, 9118, 917G, 9185, 9189, 91B8, 9202, 9288, 92B5, 92FB, 92GG, 93C1, 9505, 950B, 950F, 952B, 956F, 9592, 9596, 9598, 9602, 96D9, 96FD, 971G, 9725, 9752, 97DG, 9855, 9862, 9895, 9899, 98B7, 98BB, 9901, 990B, 9921, 992F, 99G3, 9B0B, 9B2B, 9B8B, 9BB8, 9BBG, 9C19, 9C1B, 9C31, 9C59, 9C95, 9CD5, 9CFB, 9CGC, 9D03, 9D07, 9D7G, 9DG1, 9DGD, 9F0B, 9F76, 9FCB, 9G11, 9G1D, 9G28, 9G3F, 9G7D, 9GCC, 9GD7, 9GF7, 9GFD, 9GG8, A025, A041, A058, A0C5, A0F6, A0GF, A11F, A184, A1F7, A21G, A258, A401, A421, A476, A511, A517, A57D, A5A8, A5E8, A6AD, A6FC, A6GF, A751, A77F, A7F5, A7FD, A7G6, A847, AACD, AC1G, AC41, AC58, AC5E, ACGD, AD0E, AD0G, AD1F, AD51, ADD5, ADE4, ADF5, ADGE, AE56, AE74, AEF6, AEFA, AF77, AF7D, AFA4, AFCC, AFD7, AFDD, AGAF, AGF4, B00G, B037, B055, B05B, B075, B0D5, B0FD, B10F, B198, B25F, B2F1, B2F5, B307, B309, B35E, B3EF, B50D, B589, B7BE, B7BG, B7E7, B875, B952, B958, B97G, B99G, B9G7, B9GD, BB01, BB2F, BB3E, BB89, BB98, BBDE, BD03, BD09, BD5E, BDE5, BDEB, BDG1, BE5F, BF01, BF0D, BG13, BG1F, BG3F, BGD1, BGE2, BGE8, C00B, C034, C05A, C0AF, C0EF, C0GF, C153, C15B, C199, C1B9, C1D1, C1D5, C1F9, C205, C21A, C21G, C252, C258, C2B2, C335, C33D, C35D, C364, C395, C3B3, C3F5, C3FB, C3FD, C414, C41A, C469, C496, C4DA, C4GD, C535, C55B, C5B1, C5BD, C5D9, C5DF, C5E8, C5F3, C5F5, C6E9, C85A, C885, C8B8, C8BE, C8CB, C8E5, C919, C931, C959, C95F, C9D3, CA0F, CA18, CA1G, CAD4, CADE, CAEF, CAGD, CB22, CB33, CB35, CB3F, CB5D, CB82, CB99, CBB1, CBFB, CC49, CCCB, CCDE, CD11, CD1D, CD39, CD4A, CD53, CD93, CDAE, CDD5, CDF3, CDFD, CDG4, CE49, CE5A, CE8B, CF13, CF19, CF5D, CF5F, CFB9, CFBF, CFD9, CFDF, CG14, CG41, CG6F, CGCF, CGF6, CGG1, D01F, D039, D079, D09B, D09F, D0B7, D0BB, D0D1, D0EG, D0GG, D10D, D19G, D1G3, D30B, D347, D3BE, D4E4, D50D, D57E, D5AD, D5FA, D707, D73E, D7E7, D7GF, DA1F, DA57, DAAE, DB01, DB09, DB0D, DB7E, DB9G, DD05, DD7E, DDA5, DDFA, DDG3, DE0G, DE44, DE4A, DE77, DEAE, DEB9, DEBB, DF03, DF05, DG0E, DGDF, E009, E06F, E072, E07G, E089, E0CF, E0E9, E0G7, E47A, E498, E4E7, E50A, E559, E55F, E575, E5B9, E5BF, E5F5, E5F7, E6FC, E722, E724, E72A, E72E, E744, E746, E75B, E76E, E79B, E7A4, E7A6, E7AG, E7B5, E7B7, E7EG, E7G4, E887, E89G, E8E9, E906, E955, E95B, E95F, E988, E99F, E9F9, E9G8, E9GG, EA25, EA7G, EAC5, EAE7, EB7B, EBF5, EBF7, EBFB, EC6F, ECCF, ECEF, EE72, EE76, EE89, EE9G, EF0A, EF44, EF77, EF97, EFA4, EFB5, EFC6, EFFF, EG6F, EG74, EGE7, EGFC, EGGF, F019, F01F, F075, F091, F09B, F0BF, F0FB, F10F, F1A7, F1AD, F1D4, F376, F3CD, F3F4, F40A, F411, F444, F44A, F497, F499, F49D, F4D7, F509, F57A, F5AD, F5F6, F6D3, F6D9, F70D, F741, F747, F76D, F7F6, F7FA, F907, F976, F9CB, FA11, FA7D, FADD, FB09, FC4C, FC5D, FC5F, FC91, FCB9, FD1A, FD41, FD47, FDF4, FF0B, FF56, G021, G07A, G0A1, G0E7, G11F, G17F, G1DF, G1F1, G1F7, G201, G2A1, G306, G311, G36C, G377, G37F, G3CC, G3CE, G3D1, G476, G487, G4DE, G6AF, G6D4, G6F6, G6GF, G713, G724, G731, G742, G74E, G76E, G7A2, G872, G874, GA21, GAC1, GC6F, GCAF, GCD4, GCDA, GCG1, GD73, GD7F, GDAE, GDDF, GDEA, GDFD, GE47, GE7E, GF13, GF33, GF3F, GF4C, GF71, GF7F, GFDD, GG01, GG21, GGAF, GGC1, 1000G, 10053, 100AA, 100B9, 100F1, 100FF, 10301, 10587, 10705, 1075A, 107GF, 10895, 108B9, 10985, 1099G, 10B98, 10B9G, 10D03, 10D0F, 10D7A, 10DG3, 10DG7, 10G1F, 10G3F, 110GF, 1140D, 11D93, 11DG4, 11F0A, 11G4D, 11GD4, 13333, 133FF, 13F44, 14109, 14499, 150A7, 153B1, 1570A, 17005, 17799, 177AG, 17995, 17A7G, 17G47, 18079, 18507, 185A7, 18B07, 18B9G, 19333, 199B5, 1A00A, 1A00G, 1A0F5, 1AAAA, 1AAAG, 1AF05, 1AFFA, 1B07G, 1B10G, 1B807, 1D001, 1D1AA, 1D7G4, 1DG03, 1DG41, 1F001, 1F00F, 1F01A, 1F0A7, 1F199, 1F1F9, 1F414, 1F449, 1F7F5, 1F999, 1FF0A, 1FFAA, 1FFB5, 1G073, 1G14D, 1G1F4, 1G301, 1G477, 1GD01, 1GD47, 1GF07, 1GFF4, 20005, 200A1, 2010A, 20586, 20588, 20A01, 20B11, 20B15, 20BEE, 20C1A, 20CBE, 210B5, 21A1F, 21A51, 21F1A, 21G1F, 21GFF, 222BE, 228B2, 228BE, 22BE2, 22C0B, 22F0A, 252BB, 25505, 25552, 26GAF, 2A001, 2A1FF, 2A55F, 2AEEF, 2AF44, 2B051, 2B20E, 2BB2B, 2BBBG, 2BE22, 2BEE2, 2BEEE, 2BF0B, 2C0BE, 2C18A, 2F101, 2F1FA, 2F44C, 2FCBB, 2G1FF, 2GA6F, 2GF44, 30035, 300B1, 300FB, 30101, 303C5, 30444, 30497, 304D1, 304D7, 30703, 30714, 30734, 30763, 30774, 30CF5, 30CFD, 30D41, 30FC5, 3100B, 31779, 31F5B, 31FB5, 31FFF, 330C5, 330F4, 33357, 33373, 33379, 33555, 33557, 33777, 3379F, 337FD, 33997, 33D44, 33D4E, 33F3D, 33FF5, 34019, 34044, 340D1, 353DD, 35535, 355B3, 355E6, 35BB3, 35DDD, 3636D, 364DD, 3663D, 36DD4, 37003, 3700F, 3717F, 373EE, 37609, 3774E, 37773, 37797, 37977, 3797F, 37EEF, 39007, 390C5, 39777, 39973, 3B355, 3B553, 3BBDB, 3BDB1, 3C03D, 3C0F5, 3C10F, 3C141, 3C444, 3CBE5, 3CD0D, 3CE5B, 3CEBB, 3CEF9, 3D401, 3DEBE, 3E006, 3E066, 3E57E, 3E5E9, 3E666, 3E90F, 3EF6F, 3F33D, 3F3C4, 3F5BB, 3FB33, 3FDDD, 3FF59, 4006D, 400DE, 4011D, 401D9, 40414, 4041G, 404C9, 40966, 40D11, 40D19, 40D1D, 40E49, 41019, 411DA, 41AAG, 4210A, 44049, 4410G, 44144, 441G4, 44441, 444E9, 446E9, 44986, 44E49, 4609G, 460E9, 466DE, 469DD, 46E9G, 4711A, 476D9, 4770D, 47A77, 47D09, 49099, 490D1, 49226, 49622, 49699, 496DD, 49996, 4999G, 499G7, 49G22, 49G77, 4A7DD, 4AA6D, 4ADD7, 4C0E9, 4C999, 4D1DA, 4DADD, 4DD01, 4DD1G, 4DD7A, 4DDA7, 4DDE9, 4DG0G, 4DGAA, 4DGGA, 4DGGE, 4E049, 4E449, 4E49G, 4E4E9, 4E797, 4G7DD, 4GDAA, 4GDD7, 50011, 50079, 50095, 500B1, 500F3, 501A5, 501AF, 50503, 507A5, 50AF7, 50F03, 50F7A, 510A1, 510DA, 511AA, 511DF, 5135B, 515B7, 5180B, 51A0F, 51F0A, 520B1, 53005, 531BD, 53559, 53609, 53B11, 55205, 55357, 553E6, 5555B, 5556E, 55588, 5558A, 555F3, 555FB, 556AF, 556E9, 55759, 5575B, 55805, 55885, 55896, 558B8, 55926, 55BE2, 55E8B, 55F57, 560FF, 5700D, 570A5, 570DA, 575B9, 576AD, 576DA, 579D5, 57A05, 57A52, 57B9D, 57DBD, 58057, 58509, 5855A, 585A7, 587EB, 58857, 588E8, 58A75, 58B0B, 58B87, 58BBE, 58BEB, 58E5B, 591D5, 59201, 59256, 59715, 59807, 5A88A, 5AA88, 5AFAD, 5B001, 5B00B, 5B1F1, 5B31B, 5B7E2, 5B80B, 5BB13, 5BBE8, 5BBFB, 5BE87, 5BE8B, 5BF37, 5BFBD, 5D00F, 5DA05, 5DA5A, 5DAE5, 5DBBD, 5DD95, 5DDAA, 5DFDD, 5E879, 5E8B7, 5E8BB, 5F07A, 5F0AD, 5F37D, 5F70A, 5F7BD, 5FB7B, 5FBBB, 5FBF3, 5FFF3, 6003E, 60098, 603E6, 606GF, 60986, 609C8, 60G6F, 60GCF, 6336D, 633E9, 63CCE, 63E06, 63E66, 6609G, 660E9, 66AD4, 66D4A, 66DG4, 66DGG, 66E98, 66FD9, 66GF6, 69806, 69866, 69C86, 69CC8, 6A66F, 6AAGF, 6AF06, 6AF66, 6AGGF, 6C6G3, 6C6GF, 6CCGF, 6CG03, 6DA0E, 6DAEA, 6DD9G, 6DDE9, 6DEGA, 6DGD3, 6E986, 6EEE9, 6F69D, 6F6DF, 6F96D, 6FD03, 6FD09, 6G003, 6G3F3, 6G3FF, 6G6CF, 6GAAF, 6GCCF, 70031, 70099, 700BF, 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777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777F ====Additional known quasi-minimal primes (not necessarily the next)==== 570₅₁₃₁₀1, 49₁₁₁₃₃₃, 970₁₆₆₀₄₇1, F70₁₈₆₇₆₇1 ===Base 18=== 11, 15, 1B, 1D, 21, 25, 27, 2B, 2H, 35, 37, 3D, 3H, 41, 47, 4B, 4H, 57, 5B, 5D, 5H, 61, 65, 71, 75, 7B, 7D, 85, 87, 8D, 91, 95, 9B, 9H, A1, AB, AD, AH, B1, BD, C7, CB, CD, CH, D5, D7, DH, E5, EB, EH, F1, F7, FB, FD, G5, H1, H5, H7, HB, 107, 167, 16H, 177, 17H, 1G7, 1HH, 20D, 24D, 26D, 29D, 30B, 36B, 381, 3BB, 405, 445, 44D, 49D, 4A5, 4DD, 4F5, 4GD, 501, 545, 5E1, 607, 62D, 64D, 66B, 66H, 67H, 68B, 697, 6A7, 6BB, 6E7, 6G7, 6GB, 6HH, 767, 76H, 77H, 797, 7HH, 801, 80H, 831, 83B, 86B, 88H, 8BB, 8FH, 8GH, 94D, 96D, 977, 9DD, 9ED, 9GD, A77, AC5, AE7, B07, B0H, B55, B77, B8B, B97, BB5, BB7, BBH, BE7, BFH, BGB, C01, C31, CA5, CG1, D2D, D4D, D81, DBB, DD1, DDB, DGD, E0D, E17, E31, E4D, E67, E6D, EA7, EDD, EE1, EED, EG7, F0H, F45, F8H, FC5, FFH, G0D, G17, G2D, G6B, G6H, GBB, GBH, GD1, GDD, GE1, GE7, GED, GFH, GG7, GGB, GHD, GHH, H0D, H2D, H8H, H9D, HGH, HHD, 100H, 19E7, 1A97, 1EE7, 1G8H, 1GGH, 22ED, 22GD, 2DED, 2E2D, 3001, 3031, 30C1, 30E1, 3331, 33G1, 3CC1, 40ED, 45C5, 46ED, 4CC5, 5331, 5551, 55G1, 5C05, 608H, 60ED, 60FH, 60HD, 666D, 66ED, 699D, 6B67, 6BGH, 6D0D, 6DDD, 6E9D, 6EGD, 6G0H, 6G9D, 6HGD, 700H, 70A7, 7A07, 7FGH, 7G77, 808B, 8881, 88G1, 88GB, 8BHH, 8EG1, 8GC1, 8H6H, 900D, 90E7, 90G7, 9667, 9907, 999D, 99E7, 9A67, 9A97, 9E97, 9EE7, 9G07, 9G67, 9GA7, AA45, AA97, AGA7, B005, B03B, B06B, B0C5, B60B, B63B, BAA5, BAA7, BCC5, BFA5, BG8H, C045, C055, C555, C5C1, C5F5, CC05, CC81, CCC5, D06D, D09D, D0ED, D38B, D3E1, D60D, D6DD, D8GB, DD6D, DE9D, DG01, E001, E097, E0G1, E8C1, EDC1, EE97, EGC1, EGG1, EGGD, FH6H, G007, G00B, G00H, G03B, G067, G097, G0C1, G0G1, G1GH, G33B, G38B, G3G1, G70H, G777, G88B, GA67, GAA7, GG81, GGC1, GGGH, H0FH, H66D, HEGD, HFHH, 1AAA7, 222DD, 30GG1, 3388B, 33E01, 38G8B, 3G3C1, 3GGG1, 4002D, 500C5, 50C55, 50CF5, 53GG1, 558C1, 55CC5, 55CF5, 58GG1, 5C8C1, 5CFF5, 5G881, 5GG31, 6000H, 6003B, 6006D, 600DB, 6033B, 606GD, 60D0B, 66GGD, 6D03B, 6D33B, 6H6DD, 6HD6D, 6HDED, 70G07, 70GGH, 777A7, 7AAG7, 7G0GH, 80G0B, 8888B, 8CCE1, 90067, 90097, 9022D, 99967, 99997, 9A007, 9A0A7, 9AA07, 9AAA7, 9E007, A0045, A0455, A0667, A09G7, A0A07, A0G07, A0G97, A9997, AA0A7, AAG67, B0AF5, B6GGH, B7GGH, B8HHH, BA045, BAF05, BG667, C0F05, C5005, C5581, C88C1, C8CC1, C8CE1, CCF55, D03C1, D060B, D080B, D0CC1, D0G0B, D0G8B, D3G3B, D600B, DDDED, DG331, DG80B, E8G81, E9007, F6GGH, G018H, G0301, G0331, G466D, G6667, G66GD, GD08B, GG18H, GG6GD, GGG4D, H060H, HGGGD, HHH6H, 199AA7, 40006D, 40600D, 46600D, 5055C5, 5505C5, 55CCC1, 588CC1, 58CCC1, 60000D, 60009D, 7077G7, 7707G7, 777G07, 88000B, 9099A7, A000A7, A009A7, A09067, A099A7, A0AAA7, A90AA7, A99AA7, AA0007, AA6667, AAAG07, BFFF05, BFFFF5, C0FFF5, CCECC1, CECCC1, CF0FF5, CFF005, D0008B, D0033B, D0088B, D0333B, D033GB, D03G31, D0633B, DD990D, DGGG31, FHHHHH, G00081, G6GGGD, G8GGG1, GGG001, GGG331, GGGGG1, GGGGGD, H0006H, H00H6H, HH600H, 222222D, 22DDDDD, 333333B, 5CCCCC1, 70007G7, 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CDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD, 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71D, 73D, 73H, 73J, 75B, 75H, 768, 77H, 77J, 7B1, 7B5, 7BB, 7BD, 7C8, 7D1, 7DB, 7DD, 7E8, 7F5, 7FB, 7H5, 7HD, 7HH, 7HJ, 7J5, 7JD, 801, 80J, 832, 841, 86H, 86J, 881, 89G, 8E1, 8F4, 8F8, 8FA, 8FK, 8H4, 8IH, 8J4, 8JG, 90K, 91B, 91D, 91H, 93H, 93J, 955, 95H, 95J, 96G, 97B, 97D, 97H, 991, 99J, 9B1, 9BB, 9BH, 9BJ, 9CK, 9D1, 9DB, 9DH, 9DJ, 9EK, 9F5, 9FD, 9H1, 9HB, 9HD, 9IG, 9J5, 9KK, A0B, ABG, AF4, AF8, AG5, B15, B1H, B35, B3H, B3J, B4G, B51, B5B, B5D, B5H, B6G, B71, B75, B7B, B7D, B9B, B9J, BB5, BBH, BBJ, BC4, BCG, BF1, BF5, BFD, BH1, BHJ, BI4, BJB, C2D, C9K, CCD, CDG, CID, D0G, D2G, D35, D3B, D3H, D51, D55, D5B, D5D, D5J, D62, D71, D7H, D91, D95, D9H, DBH, DC2, DD1, DD5, DE2, DEG, DF5, DFJ, DH1, DHB, DI2, DJ1, DJB, DJJ, E14, E4B, E5K, E78, E81, E9G, EA5, EBG, EC1, EE1, EE5, EK5, F04, F11, F1H, F31, F3B, F3D, F44, F4A, F4K, F5D, F5H, F6K, F71, F7H, F7J, F88, F8A, F8K, F9J, FA4, FA8, FBB, FBH, FC4, FDB, FDJ, FE8, FFH, FFJ, FH5, FHB, FHJ, FI4, FI8, FIK, FJ5, FJD, FK4, FK8, G32, G5G, G78, G8J, 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====Additional known quasi-minimal primes (not necessarily the next)==== 40₄₇₃₃₃9G, CF₄₇₉₁₄₇0K ===Base 22=== 11, 17, 19, 1F, 1J, 1L, 23, 29, 2F, 2H, 31, 35, 37, 3D, 3H, 41, 49, 4D, 4F, 4J, 4L, 53, 5H, 5L, 65, 67, 6H, 6J, 73, 79, 7D, 7J, 83, 85, 8F, 8H, 8L, 91, 9D, A3, A7, A9, AD, AJ, AL, B9, BF, BL, C5, C7, CD, CH, CJ, D7, DL, E3, E5, E9, F1, F7, FH, FJ, G1, G7, GF, GL, H5, H9, HF, I1, I5, ID, J1, J3, JD, JF, JL, K3, K9, KH, KL, L1, L5, LH, 103, 12D, 145, 155, 15D, 163, 18D, 1A5, 1BD, 1BH, 1C3, 1D3, 1DH, 1EH, 1G3, 1GH, 1I3, 1K5, 1KD, 221, 227, 22J, 22L, 245, 247, 25D, 25J, 271, 277, 287, 28J, 2A5, 2B7, 2BD, 2BJ, 2D5, 2E1, 2E7, 2ED, 2EL, 2K1, 2KJ, 2LL, 30J, 343, 389, 39J, 3B3, 3GJ, 3IJ, 3J9, 3JJ, 3KF, 3LJ, 427, 443, 445, 457, 4A5, 4C3, 4E7, 4G5, 4I7, 4K5, 4K7, 515, 52D, 551, 559, 55D, 55J, 575, 58D, 59F, 5B1, 5C9, 5CF, 5D1, 5D5, 5DD, 5E1, 5ED, 5G5, 5GJ, 5J5, 5JJ, 5K1, 5KJ, 60D, 61D, 62L, 661, 66D, 689, 6C1, 6D1, 6DD, 6G3, 6KF, 701, 721, 751, 76L, 775, 77F, 77H, 787, 7A5, 7AF, 7B1, 7B7, 7CL, 7E1, 7FF, 7FL, 7H7, 7HH, 7K5, 809, 81D, 821, 827, 82D, 847, 869, 871, 881, 889, 899, 8A1, 8BD, 8BJ, 8D1, 8DJ, 8GJ, 8J7, 907, 90H, 92L, 93J, 943, 947, 95F, 977, 997, 9AF, 9B5, 9EF, 9F5, 9H3, 9HL, 9I7, 9J9, 9JJ, 9K5, A25, A45, A51, A61, A6F, AAH, AB5, ABH, ACF, AG5, AGH, AHH, AK1, B15, B2D, B2J, B33, B45, B47, B57, B71, B75, B81, B87, B8J, BB3, BB7, BC3, BDD, BE7, BEJ, BGD, BGH, BH3, BHD, BHJ, BIH, BJ7, BKJ, CA1, CAF, CB3, CC1, CEF, CG3, CKF, D09, D0J, D13, D21, D33, D39, D3F, D4H, D5J, D63, D81, D8D, DAH, DBD, DBH, DBJ, DCF, DD3, DEJ, DFF, DG9, DGH, DHD, DI3, DIF, DJ9, DK1, DK5, E0F, E0H, E27, E2D, E2L, E47, E7H, E87, E8J, EA1, EAH, EB1, EDH, EEJ, EFF, EFL, EH1, EIF, EIL, EJH, EJJ, EKD, ELF, F25, F43, FB5, FD3, FDD, FDF, FEF, FEL, FFD, FG9, G09, G0D, G25, G3J, G5D, G5J, G63, G8D, G99, GC3, GC9, GD9, GEH, GG5, GJ5, GJ9, GJH, H03, H1D, H21, H2J, H2L, H33, H63, H77, H8J, HCL, HDD, HE1, HE7, HGH, HGJ, HH7, HHL, HI3, HIH, HJH, HK1, HKD, HL3, I07, I0J, I43, I47, I7L, I9J, IBH, IEL, IG3, 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7KC1, 7L27, 7LCF, 7LK7, 802J, 80B1, 80GD, 80JJ, 80KJ, 820J, 86E1, 880D, 882J, 88E7, 88I7, 892J, 89EJ, 8B61, 8BI7, 8CI9, 8CK1, 8D6D, 8DD9, 8DGD, 8E01, 8E07, 8EE1, 8EI7, 8EK1, 8EKJ, 8I77, 8I87, 8IC9, 8IK7, 8J0J, 8K6D, 8KI7, 8KIJ, 8KK7, 9025, 9055, 9089, 9275, 92EJ, 92G5, 92GJ, 93EL, 9455, 9505, 9557, 9599, 96B3, 970L, 976F, 97G5, 982J, 98E7, 98I9, 98K7, 9905, 990J, 9925, 9995, 999H, 99BH, 99EL, 99G9, 99GJ, 99LJ, 9A55, 9B03, 9B27, 9BGJ, 9BH7, 9BK7, 9CG9, 9E6L, 9EHJ, 9EKJ, 9ELL, 9G39, 9G45, 9G4H, 9GA5, 9GAH, 9GBJ, 9GEJ, 9GHH, 9GHJ, 9GI9, 9GIJ, 9H7H, 9H87, 9HAH, 9HB7, 9I89, 9I9H, 9IB3, 9IEH, 9IKF, 9J7H, 9J87, 9JB7, 9JGH, 9K0F, 9K27, 9KGJ, 9KKF, 9L89, 9L9J, 9LG9, 9LGJ, 9LIJ, 9LKF, A081, A14H, A1IH, A201, A2C1, AA15, AA81, AAIF, ABC1, AC01, AHC1, AIIF, AKEF, B005, B01D, B01H, B051, B05D, B0A5, B0B1, B0BJ, B0DH, B0E1, B0GJ, B0H1, B0JH, B143, B16D, B255, B2B5, B2C1, B2G5, B2K7, B4EH, B4G3, B501, B5A5, B5BJ, B5C1, B5IJ, B5K5, B621, B663, B6I3, B6K1, B777, B7I7, B80D, B88D, B8ED, B8KD, BB01, BB0J, BB21, BB25, BB4H, BB6D, BBD5, BBE1, BBEH, BBH1, BBIJ, BBJH, BCK1, BD61, BDB5, BDGJ, BEE1, BG55, BGB5, BGGJ, BGIJ, BH27, BH7H, BHC1, BHH1, BHK7, BI77, BIGJ, BJ0H, BJBH, BJIJ, BJJJ, BK25, BK27, BK55, BKA5, BKK1, C043, C143, C2B1, C32L, C3G9, C601, C6EL, C6G9, C8B1, CBK1, CC2L, CC89, CE21, CECL, CF2L, CF89, CG69, CIG9, D003, D015, D045, D05D, D06D, D06F, D0DH, D0H1, D1D5, D1GD, D205, D26D, D2DJ, D32J, D38J, D403, D525, D561, D56D, D5AF, D5F5, D5GD, D6C9, D6D9, D6DF, D6E1, D6ED, D6F9, D6FD, D8IJ, D8JJ, D945, D993, D99F, D9C9, D9F3, D9G5, D9KJ, DA15, DAA5, DAE1, DAKF, DB25, DB61, DBC1, DBG3, DC43, DC99, DCE1, DD0F, DD1D, DD2D, DD2J, DD5D, DD9H, DDA5, DDD5, DDDJ, DDED, DDH1, DDHJ, DDI9, DDJ5, DE0D, DED1, DEDF, DEFD, DF03, DF45, DF55, DF5D, DF6D, DG05, DGGJ, DH0H, DH43, DHC1, DHEH, DHH3, DHJJ, DI8J, DIC9, DII9, DIJH, DJG5, DJHJ, DJKJ, DK6D, DKAF, DKDD, DKGD, E081, E0BJ, E0DD, E0DJ, E0E1, E0ED, E0J7, E0K7, E0KJ, E1GD, E1IH, E201, E281, E66F, E6BD, E6ED, E6K1, E6LL, E7EF, E861, E86D, E88D, EB0D, EB4H, EBHH, EBI7, EC6F, ECEL, ED0D, ED1D, ED6D, EDAF, EDDD, EDFD, EE01, EE0D, EE1H, EE21, EECF, EEE1, EEGH, EEH7, EF8D, EGGD, EGHH, EGIH, EGIJ, EH07, EH0L, EH8D, EHBH, EHBJ, EHK7, EHL7, EI4H, EIK7, EIKJ, EJ77, EK07, EK0J, EKC1, EKIJ, EKK1, EKK7, EL6L, ELBD, ELCL, ELDJ, ELK7, F059, F20L, F26L, F28D, F2GD, F2KD, F32L, F3AF, F3G3, F455, F56F, F595, F5KD, F6AF, F6GD, F88D, F8I9, F955, F995, F9B3, F9G3, F9KF, FB03, FB8D, FBI3, FC89, FD99, FDA5, FDI9, FEGD, FF59, FG2D, FGI3, FGKD, FI89, FIB3, FIKF, FK2D, FK45, FKD5, FL6D, FLG3, G003, G04H, G055, G0BH, G0HH, G0HJ, G0I3, G0K5, G0KJ, G26D, G2DJ, G2GJ, G303, G333, G393, G3G9, G3I3, G403, G40H, G433, G4AH, G4GH, G4H3, G4IH, G589, G5G9, G80J, G89J, G94H, G9G3, GAA5, GAIH, GB0H, GB43, GB6D, GBB5, GBG3, GBGJ, GBJJ, GD0H, GD45, GDD5, GDKD, GG2D, GG39, GG8J, GG9H, GGAH, GGDJ, GGEJ, GGGH, GGH3, GGKJ, GH0H, GHG3, GHH3, GHHH, GHJJ, GI03, GI2J, GI93, GIAH, GIEJ, GIG9, GII3, GJJJ, GJKJ, GK05, GKDD, GKGD, GKGJ, GKIJ, H081, H087, H0AH, H0BJ, 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5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000BB5, J000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000BIJ, C4IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII3, F0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000066B3, G0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000A5, D5KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKF, HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHBH, L0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000IKF, 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LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLKE7, 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80BN, 80FH, 80LN, 80MN, 840N, 848N, 866B, 86FB, 880B, 880N, 884N, 88CB, 88FB, 88LN, 88MN, 8BBB, 8BLB, 8C6B, 8CCH, 8CFH, 8F0B, 8FHH, 8FLB, 8H0H, 8HCH, 8IGN, 8ILN, 8KKH, 8L8B, 8LBB, 8LFB, 8LIN, 8M8N, 8MLN, 8N0N, 8NGN, 8NLN, 9061, 9091, 90EJ, 90F1, 90GJ, 90K1, 940J, 9501, 95F1, 9CC1, 9E0J, 9E95, 9F61, 9FI5, 9G3J, 9II5, 9K01, 9KK1, 9M01, A007, A05D, A0AD, A33D, A3AD, A3F5, A44J, A727, A9EJ, AA0D, AAAD, AAAJ, ACM7, AD8D, ADKD, AE27, AE9J, AEAJ, AEE7, AIAD, AIDD, AIID, AJ9J, AK5D, AM07, AM27, AM35, AMK5, B08B, B0CB, B0GB, B18B, B1CB, B80B, B8CB, BB21, BB4N, BBCB, BBF1, BBFB, BBK1, BC8B, BCF1, BCLB, BF1B, BF8B, BFB1, BFM1, BGC1, BGF1, BK21, BL8B, BLFB, BM1B, BM3N, BMB1, BMMN, BNF1, C00D, C06B, C077, C0D7, C0H7, C0L7, C0LB, C0M1, C60H, C6LB, C76H, C7E7, CAID, CC01, CCFH, CCKH, CDLB, CGE7, CH07, CHE7, CI8D, CIAD, CK0D, CL8B, CLDB, CLE7, CM01, CM07, CME7, CMM1, D007, D08D, D0C7, D0HH, D0LN, D0M7, D0NN, D207, D2KH, D2M7, D777, D7E7, D80H, D8LD, DA27, DAC7, DAM7, DBFB, DBMB, DC77, DCLB, DDL7, DE77, DF0H, DF2H, DFFH, DFMB, DH27, DH8H, DHC7, DHHH, DILN, DK0H, DK2H, DK8H, DKHH, DLIN, DLL7, DLM7, DLMB, DM07, DMH7, DMMB, DNGN, E07J, E09J, E335, E355, E555, E5A5, E5K5, E79J, E93J, E995, EA35, EE95, EKE5, F00B, F00H, F06H, F08B, F0I5, F11B, F18B, F1L1, F20H, F26H, F2FH, F355, F661, F6K1, F80B, F86B, F8BB, FBGB, FBK1, FBLB, FC0B, FC6H, FCLB, FEK5, FGB1, FH05, FH0H, FH35, FH6H, FHCH, FHF5, FHHH, FI05, FK91, FKK1, FL1B, FLB1, FLBB, FM61, FMBB, FMK1, G00J, G021, G027, G0EJ, G0JJ, G0M1, G0M7, G1CB, G2E7, G40J, G4AJ, G4IJ, G4JJ, G6C1, G701, G94J, G9IJ, GAEJ, GAJJ, GB21, GBM1, GC01, GCF1, GCLB, GE0J, GEAJ, GEE7, GEG7, GEIJ, GEL7, GFM1, GGE7, GGMB, GI0J, GIIJ, GIIN, GJ9J, GM27, GMB1, GNM7, H005, H0K5, H0M5, H207, H2E7, H335, H3I5, H595, H5K5, H60H, H68H, H76H, H80H, H8HH, HAAJ, HE7J, HEC7, HGE7, HGM7, HH35, HI55, HIM5, I00J, I035, I08D, I0CD, I4JJ, IC0D, ICID, II0D, II0J, II35, IIAD, IILD, IIM5, IIMN, IJ9J, ILCD, IM05, IM35, IMNN, INLD, J03J, J0HJ, J0JH, J2CH, J39J, J3ID, J60H, J62H, J8CH, J9IJ, JGAJ, JGJJ, JH9J, JI0J, JIDD, JJ0H, JJCD, JJJD, JJLD, JL3D, JLCD, K0E5, K0I5, K0K1, K0KH, K191, K211, K2F1, K2G1, K591, K5AD, K6F1, K6G1, K9I5, KA0D, KAAD, KAM5, KCCH, KCHH, KD8D, KDDD, KFI5, KG01, KG61, KH0H, KHHH, KI55, KIDD, KK21, KK8H, KKF1, KKK1, KKKD, KM8H, KMHH, KMK5, L027, L0M7, L1C1, L1MB, L211, L727, L8BB, L8BN, L8FB, L8LN, L9C1, L9M1, LB8B, LBC1, LBM1, LCAD, LD77, LDIN, LDL7, LDM7, LF8B, LG21, LIIN, LLLN, LLN7, LM07, LM1B, LM77, LMG1, LN77, LNM1, M00N, M01B, M03N, M055, M077, M08B, M0B1, M0C1, M0GB, M0K1, M0M7, M0N7, M18B, M1BB, M1MB, M26H, M335, M3GN, M3M5, M3MN, M3NN, M501, M53N, M5M1, M5NN, M6BB, M6C1, M6G1, M6KH, M88B, M88N, M8BB, M8NN, MBB1, MC01, MCC1, MCKH, MCM1, ME07, ME35, MEK5, MGGB, MGMB, MH35, MH8H, MHE7, MHM5, MK8H, MKC1, MKG1, MKHH, MKK5, ML8N, MM01, MM8B, MMC1, MMLN, MMM5, MMMN, MMN1, MN0N, MN27, MNGN, MNLN, N007, N027, N077, N0C7, N0DN, N0IN, N1M1, N227, N2M7, N661, N707, N727, N8LD, NA27, NA3D, NC07, ND0D, ND0N, NDLD, NF11, NF61, NGG7, NILN, 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5M0M1, 5MNNN, 5N03D, 5N3LD, 5NA8D, 5NADD, 5NDGN, 5NNGN, 600KH, 61661, 616L1, 61MM1, 66161, 66611, 666B1, 666L1, 666LB, 66BB1, 66BG1, 66BLB, 66G61, 66KF1, 66LBB, 66LG1, 6BBBB, 6BFCB, 6CC11, 6F1M1, 6F66B, 6F6B1, 6F6L1, 6FBCB, 6FLMB, 6FMCB, 6FMM1, 6FMMB, 6GCM1, 6GM61, 6GMC1, 6K1C1, 6K1K1, 6KK11, 6KKL1, 6KL11, 6L1G1, 6LBFB, 6LCC1, 6LFMB, 6MM61, 6MM6B, 70291, 702C1, 702G1, 72CF1, 72EE7, 7433J, 7443J, 77A07, 79901, 799F1, 7AAEJ, 7EE27, 7H9EJ, 7K2KH, 7KK2H, 7KKKH, 7KKMH, 7L2C1, 800NN, 806BB, 808BB, 808LB, 80F8B, 80IIN, 833ID, 860KH, 8886B, 888NN, 8BG4N, 8CH6H, 8CKHH, 8FC0H, 8FFCH, 8HHHH, 8IIIN, 8K0HH, 8LL4N, 8M0NN, 8MNNN, 8NNND, 9000J, 900M1, 9034J, 90IIJ, 94IIJ, 96CM1, 96KF1, 96MM1, 990C1, 990M1, 99591, 99961, 999C1, 99F91, 99FM1, 99KF1, 99M61, 99MK1, 9AAA5, 9FEE5, 9FFA5, 9FFF5, 9II4J, 9K6C1, 9K9C1, 9K9F1, 9KF91, 9M6M1, 9MK61, A02M7, A0A35, A0AM5, A0C77, A0D0D, A0DDD, A0EC7, A0M55, A0MM7, A2ME7, A3335, A33M5, A3555, A3MM5, A550D, A58ID, A5D0D, A5DDD, A74AJ, A7E07, AA0M5, AA3ID, AA3M5, AA83D, AA8ID, AAAM5, AACID, AAICD, AAM05, AC08D, AC0ID, AC0KD, AC8ID, ACA8D, AFA35, AIC8D, AJAJJ, AK0KD, AKI0D, AKKM5, AKM05, AM505, B00FB, B00LB, B0LBB, B1MBB, B1MMB, B2GM1, B3MGN, B88BB, BB3MN, BBB3N, BBB8B, BBBBN, BBBMN, BBCC1, BBGB1, BBGLB, BBMC1, BBMGB, BBNM1, BFB0B, BFBMB, BFGLB, BFGMB, BGGLB, BGMM1, BLMMB, BMC0B, BMGM1, BMMK1, BMNM1, C006H, C00CH, C00M7, C0C11, C0CC1, C0E07, C0F6H, C0GG7, C0K8D, C0KDH, C0KHH, C1CC1, C1CM1, C1MC1, C70F1, C886B, CC06H, CCCCH, CCCF1, CCCM1, CDHH7, CE707, CE7L7, CEE77, CEEG7, CEL07, CFFHH, CGLL7, CHC6H, CHCCH, CHH7H, CHHH7, CHHM7, CI0LD, CK0HH, CKHCH, CL007, CLD07, CLLL7, CM777, CMMM7, D008H, D07L7, D0DE7, D0EL7, D0L77, D0M8H, D0NA7, D22E7, D70A7, D7227, DBLBB, DCL07, DD7A7, DDAE7, DDD8D, DDE07, DDK0D, DDM77, DEE27, DKK8D, DL227, DL707, DLBBB, DLDFB, DLE27, DM2E7, DMM77, DMME7, DN0A7, DNIIN, DNLLN, E000J, E0227, E02E7, E0AAJ, E0GL7, E0I0J, E2E07, E7AAJ, E7E27, EAA55, EAK55, EC777, ECEE7, ECEL7, ECGL7, ECL77, EEC77, EECL7, EEEC7, EEG27, EEGG7, EG0E7, EG0L7, EG207, EGE07, EGG07, EGG27, EGL07, EI9IJ, F02HH, F06LB, F0C6B, F0CCH, F0CHH, F0E55, F0EA5, F0FH5, F0GGB, F0M2H, F0MGB, F0MMB, F1BMB, F3FF5, F3I35, F3II5, F6BCB, FA035, FB1MB, FBBM1, FBBMB, FBM8B, FC0HH, FC88B, FCFHH, FFC0H, FFCFH, FFCHH, FFF0H, FFF6H, FFFH5, FFHI5, FFI55, FG1MB, FGGCB, FGM1B, FHK55, FI5I5, FKEA5, FKKI5, FKL11, FM16B, FM1CB, FM62H, FM6CB, FMBG1, FMM0B, G0001, G00E7, G039J, G06F1, G07C1, G07F1, G0A9J, G0G07, G0GG7, G0I4J, G0I9J, G0LL7, G22M7, G2M07, G339J, G433J, G62M1, G6M61, G6MM1, G903J, G933J, GAA9J, GBCC1, GE007, GGGGB, GGGL7, GJ0IJ, GL007, GL2M7, GLL07, GLLM7, GMGCB, GMM07, GMM1B, H007H, H05I5, H0CCH, H0CM7, H0GG7, H0H27, H0H8H, H0HC7, H0HH5, H0I35, H0MM7, H3555, H35F5, H3F55, H3FF5, H5055, H50F5, H7HEJ, H9995, H9GEJ, HCC0H, HCC6H, HCGG7, HCHM7, HE027, HE0G7, HEE07, HEEG7, HEG27, HF0F5, HF505, HF555, HFF05, HFKF5, HG0G7, HH06H, HH08H, HH0H5, HH5I5, HH7HJ, HH9EJ, HH9I5, HHCHH, HHE07, HHGG7, HHH05, HHH7H, HHH9J, HHKI5, HHM05, HHM07, HHM27, HI0I5, HJ86H, HJC0H, HK055, HK9F5, HKF05, HKFF5, HKFK5, HKII5, HKK95, HM2M7, HME27, HMKM5, HMM05, HMM27, HMM55, HMMM7, I00DD, I00M5, I044J, I0505, I09IJ, I0AAD, I0D0D, I0DDD, I0I05, I0IDD, I0II5, I0IJJ, I0JIJ, I33M5, I4I4J, I5INN, I888N, I8NND, I8NNN, I904J, I94IJ, IA8ID, IAADD, IAI8D, IDDDD, IDINN, II88N, II8NN, IID8D, IIDIN, III8N, IIIDD, IIIID, IIIIN, IIIND, IIN8D, IINDD, IJJ0J, IJJJJ, ILILN, ILLIN, IMM8N, INA0D, INDNN, INGIN, INNDN, INNND, J000H, J002H, J00AJ, J00GJ, J00KH, J02KH, J068H, J080H, J090J, J0A9J, J0AAJ, J0C0H, J0G0J, J0IIJ, J0JGJ, J0JIJ, J0K8H, J2K0H, J2KKH, J6K8H, J86KH, JC00H, JC0KH, JCCCH, JCK0H, JCKCH, JDDLD, JG93J, JIIJJ, JJ0IJ, JJ2KH, JJ9GJ, JJCCH, JJG9J, JJGIJ, JJJ9J, JJJJH, JJK8H, JK08H, JK0CH, JK8KH, JKC0H, JKKKH, K0001, K0091, K020H, K02C1, K03ID, K0611, K06L1, K083D, K08HH, K0961, K09C1, K0CF1, K0F91, K0KM5, K0LG1, K1G21, K20HH, K29K1, K2KHH, K5001, K500D, K58ID, K5D0D, K5L11, K6621, K6C11, K6LC1, K8CKH, K8KCH, K96C1, K99E5, K9F91, K9FA5, K9FE5, K9K91, KA55D, KC011, KCF11, KD02H, KD0MH, KD20H, KDM2H, KEA55, KEAA5, KEK95, KEKK5, KF1G1, KF1K1, KF611, KF6L1, KFEA5, KH8CH, KI005, KIMM5, KK05D, KK0AD, KK0DH, KK2CH, KK2KH, KK33D, KK961, KK9C1, KKA5D, KKD0D, KKE55, KKI0D, KKIID, KKIM5, KKK0H, KKKM5, KLGC1, KMK2H, L188B, L1991, L2007, L22M7, L2EE7, L2MM7, L333D, L3LIN, L7291, L72G1, L88IN, L8C8B, L9991, LBB1B, LBBBB, LBBBN, LD0E7, LDBBN, LE207, LFMCB, LGCC1, LL227, LL3IN, LL48N, LLM27, LLMM7, LMBCB, LME27, LMMBB, LMMM7, LN33D, LN3AD, LNAAD, LNACD, M0007, M0061, M00K5, M0207, M066B, M0BCB, M0EE5, M0G01, M0GM1, M0M8N, M27KH, M2E27, M2M07, M2M27, M5005, M5555, M66CB, M66K1, M6K61, M6MCB, M7007, M7EE7, M8C0B, M8KCH, M8MGN, MBBGB, MBGM1, MCCCH, MCHCH, MEE55, MGBC1, MGMM1, MH227, MH2M7, MHH7H, MKM55, ML3LN, MM0CB, MM16B, MM227, MM661, MM6K1, MME55, MMEE7, MMKE5, MMM07, MMM6B, MMMB1, MMMGB, MMMM7, MNM61, MNN3N, N00CD, N00KD, N03LN, N0A8D, N0AM7, N0D8D, N0KKD, N0L3N, N0LAD, N0NDD, N16L1, N3GIN, N3LAD, N3LIN, N3NNN, N61L1, N96M1, N9M61, NA0CD, NAK0D, NAKKD, NCA8D, NCM77, NDGIN, NDIIN, NDLLN, NF991, NGM07, NIIIN, NINNN, NKKDD, NLNAD, NN0LN, NN191, NN3NN, NN6L1, NN83D, NNAAD, NNDIN, NNGIN, NNL3N, NNLND, NNM61, NNNIN, 166G21, 16G621, 19MMM1, 1BBBMB, 1BBGM1, 1GCCC1, 1GCCM1, 1MMM1B, 200E27, 2E0027, 2HH0HH, 2HHC0H, 2KK0HH, 2M0E27, 2M22E7, 30NNNN, 3333M5, 333AID, 333I35, 33I555, 3F5FF5, 3I3MM5, 3I88GN, 3II8LN, 3IIII5, 400IJJ, 40J00J, 40JJ3J, 40JJJJ, 44403J, 444I0J, 44IJJJ, 44J0JJ, 44JJIJ, 48I8IN, 4I440J, 4II8IN, 4IJ0IJ, 4JIIIJ, 4JJ0JJ, 4JJJ0J, 50033D, 5003AD, 5008ID, 500D8D, 500G01, 500L11, 500LAD, 500MG1, 503LAD, 508ILD, 50DDLD, 50ILAD, 50M001, 516G61, 519MM1, 538NNN, 53NNNN, 55005D, 5508ID, 550D8D, 558ILD, 55F5I5, 56G661, 58333D, 58NNNN, 5999F5, 59AAF5, 5DNNNN, 5F55I5, 5FMMM1, 5G6661, 5K9AA5, 5KK9F5, 5KKK95, 5M0001, 5NDD8D, 5NDINN, 5NN33D, 5NNLAD, 5NNNAD, 5NNNDN, 608K0H, 61CCM1, 61G621, 661G21, 666621, 6666CB, 6666F1, 66K661, 6BCCC1, 6BKKC1, 6F6BBB, 6G6621, 6GCCC1, 6GMMM1, 6K6K61, 6M666B, 70A077, 70L991, 7722E7, 772E27, 7772E7, 777A27, 777L27, 77A777, 77EL27, 7A7077, 7A7777, 7E7227, 7L2E27, 7LEL27, 7LL2E7, 7LLE27, 7LLL27, 800GIN, 80NINN, 80NNNN, 8BBMGN, 8C888B, 8C88LB, 8MM0GN, 900001, 90043J, 959MM1, 96K661, 9999F1, 9999K1, 999AF5, 999FF5, 99EEE5, 99K991, 99MMM1, 9AAFF5, 9EIIIJ, 9F9991, 9F9MM1, 9FEAA5, 9G444J, 9K9991, 9M6661, A000CD, A000KD, A000M5, A0083D, A00I0D, A00M05, A022E7, A07E77, A0FF35, A0K3ID, A0K83D, A4AJJJ, A77777, AA0035, AA0355, AAA035, ADDD0D, ADDDDD, AF0035, AFFF35, AKK8ID, AM0M05, AM7777, B0F0MB, BBBBM1, BBLBMB, BFBBBB, BFM0MB, BFMMMB, BLBBMB, BLMBBB, C00071, C000E7, C007C1, C00G07, C07KKH, C0CC6H, C0CH6H, C0EEE7, C0HHHH, C777L7, C77L77, C7L777, C7LL07, C8088B, CAAK8D, CAKKAD, CC000H, CC0CHH, CD000H, CD0KKH, CE0007, CEE0E7, CELL77, CG0007, CGGL07, CH0CHH, CHCH0H, CHHH6H, CK0C0H, CKAK8D, CKKA8D, CL7707, D002FH, D0D0KD, D0DA77, D0DKKD, D0IIIN, D0K0DD, D0KDKD, D0KKDD, D0KKKH, DC0EE7, DCEEE7, DD0227, DD0D27, DD0DKD, DD0KKD, DD2E27, DDD0D7, DDD0LD, DDD227, DDDA77, DDDBCB, DDDCE7, DDDDFB, DDDMM7, DDEEE7, DDMBCB, DEEC07, DH000H, DHMEE7, DIIIGN, DK0KDD, DKMKKH, DMBBBB, DMEEE7, DMMM27, E00G27, E07727, E0C707, E0CE77, E0E027, E0EEG7, E0EGE7, E0EL27, E0GE27, E0L207, E0LE27, E0LL27, E2E2E7, E7L2E7, E900IJ, E9EEE5, EAAKK5, EC00E7, EC0G07, EC7007, ECEG07, EE0G07, EE0GE7, EE72E7, EE7L27, EECE07, EECEG7, EEEEE5, EEEK55, EEEKA5, EEEL27, EEGLL7, EELE27, EGLLL7, EKK595, EKKA55, EKKAK5, EKKKK5, F000E5, F0AA35, F0F035, F0FFFH, F0HKK5, F0KKE5, F16BB1, F16MM1, F1BBBB, F1MC6B, F666BB, F66BBB, F6GMM1, FB0BBB, FB1BBB, FBBB0B, FBMMG1, FC0FFH, FCFCCH, FEEE55, FEEEA5, FF03F5, FF0FFH, FF3F35, FFEE35, FFF2CH, FFFCCH, FFFFE5, FFI335, FFKFE5, FGLMMB, FK55I5, FKFE55, FLM8CB, FMC66B, FMMC6B, G0AA4J, G0CCC1, G0LE07, G666F1, GG0007, GG00G7, GG0L07, GGLLL7, GGLMM7, GI444J, GJJ33J, GLLE27, GLMMCB, GM0661, GMMM61, H00G07, H05555, H09FF5, H0C0E7, H0CE07, H0CEE7, H0E227, H0H007, H0H5F5, H0H995, H0HHE7, H0HHH7, H55505, H55II5, H5FII5, H99FF5, HEG007, HFFK55, HH0007, HH02M7, HH0C0H, HH7AEJ, HHC0E7, HHE227, HHH0C7, HHH0M7, HHH995, HHHC0H, HHHE27, HHHEAJ, HHHH07, HHHH8H, HHHHE7, HHHHI5, HHHHJH, HHHJ8H, HHHJCH, HHJ00H, HHK095, HHKKM5, HKK0F5, HKK5F5, HKKK55, HKKKK5, HKM555, HMEEE7, I00555, I05555, I0I94J, I333I5, I33555, I444IJ, I55055, I55505, I55555, IAAC8D, ID000D, IDD0LD, II9I4J, III4IJ, III505, IIIC8D, IIJIJJ, IJIIIJ, IM8LLN, IN00AD, INAACD, INCAAD, ININGN, J00CCH, J0IJJJ, J0J09J, J3333D, JIJIIJ, JJ68KH, JJIJIJ, JJJAJJ, JJJHGJ, JJJJAJ, JJJJGJ, JJJJIJ, K0008H, K00161, K001G1, K001L1, K002CH, K002HH, K00521, K00AKD, K00C0H, K00GF1, K00I0D, K00K95, K00M05, K01621, K05021, K0505D, K051G1, K059F5, K05K95, K0C0C1, K0L291, K0M005, K0M505, K1K661, K2CK0H, K33IAD, K3IIID, K5550D, K56121, K59AA5, K612K1, K61CC1, K66661, K6K611, K900C1, K99661, K9AFF5, K9C001, KAKI8D, KC00C1, KDK00D, KF9991, KI0IID, KK000D, KK01L1, KK0661, KK0I8D, KK0L11, KK0M2H, KK5661, KK59F5, KK61C1, KK9995, KK9EE5, KKA3ID, KKA83D, KKAI8D, KKC001, KKC0C1, KKC1C1, KKCCC1, KKD2HH, KKK595, KKK9A5, KKKK95, KKKKKH, KKKMCH, KKM505, KKMEE5, KKMKCH, KM0005, L222E7, L33AAD, L38I8N, LCCC11, LDFBCB, LEL2E7, LELE27, LELL27, LGMMM1, LLE2E7, LM2ME7, M000M5, M006MB, M00E27, M00MM1, M02227, M06M61, M06MM1, M0E227, M0EE27, M0KME5, M0M5GN, M0MM61, M0MMCB, M0MNNN, M0NNM1, M38LLN, M5K505, M77707, M7E227, M7E727, M8CHHH, MBMMCB, MBMMM1, MEEE77, MHH027, MHH505, MHHC6H, MHHH6H, MHHK05, MKK001, MM2ME7, MM7707, MM7E77, MMBMK1, MMM2E7, MMMC0B, MMMK61, N0003D, N0008D, N0030N, N030NN, N0C0AD, N0CKAD, N0DKDD, N0N3GN, N0NN3N, N333AD, N777A7, N77A77, NAACKD, NAAKDD, NACAKD, NACKAD, NC0AKD, NC0KAD, NCA0KD, NCKAKD, NDNNLN, NNNLAD, NNNNLD, 1BBBBBB, 1BBBBG1, 1M6MMMB, 1MMBBBB, 1MMMMK1, 2000227, 2000EE7, 20EEEE7, 2C0FFFH, 2E2EEE7, 2KKKHCH, 2MEE227, 2MEEE27, 333333D, 3333355, 3335555, 333FFF5, 333IIID, 388NNNN, 38INNNN, 3INNNNN, 4000IMN, 4000JJJ, 400IIIN, 444444J, 44JJJJJ, 488888N, 4IIJIIJ, 4JJJ33J, 50002M1, 5001G21, 5006621, 500LGM1, 555083D, 55555I5, 5616G21, 59MMMM1, 5K999A5, 61CCCC1, 66666K1, 6K0000H, 6K0080H, 70000A7, 70077A7, 70700A7, 7070A77, 77700A7, 77770A7, 7777227, 7777E27, 77L2227, 7LE22E7, 888888B, 888888N, 8888BBN, 8888IIN, 888B88B, 888I8IN, 88IINNN, 88NIINN, 88NNIIN, 8INNNNN, 90444IJ, 904I44J, 9666661, 9666FK1, 9666K61, 9966FK1, A00KK0D, A0K000D, AAAAA35, AAKKI8D, BB8888B, BBB0BLB, BBBB1BB, BBBBBB1, BBBBBGB, BBBBBLB, BBBLMBB, C0007KH, C000F11, C00FFFH, C00HH0H, C00K00H, C0C0HHH, C0CCHHH, C0CHH0H, C0CHHCH, C0FFFFH, C0H0H0H, C0KKC0H, CC0HH0H, CCCCC11, CCCCCC1, CCHHHHH, CDKKKKH, CEL7777, CGGG0G7, CGGGGG7, CH00HHH, CHGGGG7, CHHHH0H, CHHHHCH, CHHHHHH, CK0000H, CKDKKKH, D00DDKD, DD0DDD7, DDBBBLB, DDD2EE7, DDDBBLB, DDDDD27, DDDDDBB, DDDDDC7, DDDDDKD, DDDDDMB, DDDDEE7, DDDDKKD, DDDDLDB, DDDFBBB, DDDLFCB, DDDMEE7, DDM2227, DHHEEE7, DK000KD, DK00D0D, DK0D00D, DNN000N, E000CL7, E000EG7, E000GE7, E00C0G7, E00CE07, E00EE27, E0C00G7, E0C0EG7, E0CE007, E0EC0G7, E0EE207, E0G0007, E20EE27, E22EEE7, E2EE227, E2EEE27, E772227, E77LL27, E7L2227, E9IIIIJ, EAKKKA5, EC000G7, ECG00G7, EE00L27, EE0E0G7, EE20EE7, EEE0EG7, EEE22E7, EEEE727, EEEEE27, EEEEG07, EEEEGE7, EEEKKK5, EELLL27, EI0IIIJ, EKKKAA5, ELLLE27, F00FA35, F0333F5, F0F0FE5, F333335, FAAFF35, FCF0FCH, FEEEE35, FF03335, FF0FA35, FF0FE35, FF0FMCH, FFF0A35, FFF0F35, FFFAF35, FFFF5I5, FFFFM2H, FFFI3I5, FFFIII5, FFH5555, FH55555, FL1MMM1, G0000G7, G0000L7, GGGG007, GLE2227, GLLLLE7, GLLLLL7, H000007, H0000C7, H000HCH, H000HM7, H000M27, H000ME7, H00G227, H00HHM7, H02M227, H0C0HHH, H0CH00H, H0E0007, H0FFF35, H0FFFF5, H0H0ME7, H0HFII5, H0HHHCH, H0M0227, H555555, H5F5FF5, HC000G7, HC00H0H, HCCHHCH, HCHHHCH, HCHHHHH, HEEEE27, HFF5FF5, HFF5FI5, HFKKK05, HG00007, HH00E27, HH0G227, HHH2MM7, HHH55F5, HHH9FF5, HHHFFK5, HHHFK55, HHHH7EJ, HHHHCM7, HHHHHAJ, HHHHHF5, HHHHHHJ, HKK5505, I000055, I00A0ID, I0I4IIJ, I0IIIIJ, I88NIIN, III0055, III0I55, III444J, IINNLIN, J000IJJ, K0000DH, K0000KD, K00033D, K000A5D, K000K5D, K00555D, K009995, K00K00D, K00K8ID, K00KI8D, K00KIAD, K01GCC1, K05033D, K0999F5, K2KKKCH, K53333D, K956661, K999991, KCCC1C1, KFFFE55, KFFKKE5, KFKFKE5, KK009A5, KK00C11, KK01GC1, KK99001, KKIII05, KKK09F5, KKKE9E5, KKKEAK5, KKKKI05, KKKKKE5, KMMEEE5, L1BBBG1, LBMMMCB, LBMMMMB, LDEEE07, LEE22E7, LEE2E27, LEEE2E7, LLLLE27, M0000CB, M000C6B, M02EEE7, M0K0005, M0M0005, M2CHHHH, M2HHHHH, M6MMMM1, MC0000B, MCHHHHH, ME7E777, MEE7777, MEEE2E7, MG06661, MHHHCCH, MHHHH27, MHHHHH7, MHM0027, MM6666B, MM77777, MMC000B, MMM7727, MMNM777, N000NLN, N00333D, N003AAD, N0A00DD, N0NN33D, N0NNLLN, N30000N, N777777, NDNNNNN, NN0N0GN, NN0N30N, NNN300N, NNN333D, NNN3LLN, NNNDDDD, NNNNN3N, NNNNNND, 33333F35, 33FFFF35, 3555FFF5, 3FFFFF55, 3NNNNNLN, 40000I0J, 40I0IIIJ, 444440IJ, 4J0000IJ, 500006G1, 5D00DDDD, 5L1MMMM1, 5MMMMMG1, 5NNDDDDD, 5NNNNDDD, 5NNNNN8D, 6000080H, 777777A7, 77777A77, 7944444J, 800000IN, 996666K1, 999999I5, 9999FEA5, A00003ID, AAAAFF35, BBBGMMMB, C0000011, C000007H, C0CC0H0H, C666666B, CCCH0HHH, CCHH0HCH, CE777777, CEEEEE07, CHH0H00H, D00000GN, D000D0LD, D000IIGN, D0DDDDD7, DDD0E2E7, DDDDDDDB, DDDDDME7, DEEEELE7, DEEELEE7, DEELEEE7, DELEE0E7, E00000C7, E00000G7, E0000CG7, E000C0E7, E000G007, E00CG007, E00E0CG7, E0C00007, E0CGGGG7, E0GGGGG7, E20000E7, EAAKAAA5, EAKKAAA5, EE00E727, EE020007, EEEE2027, ELEE2227, F00003F5, F0000A35, F0003335, F0FFFA35, F1999991, F1999MM1, FAAAAF35, FBBBBBG1, FEAAAAA5, FF000A35, FF00FF35, FF0KEEE5, FFAAAF35, FFF555I5, FFFF33I5, FFFFF035, FFFFF3F5, FFFFFKI5, FFFFFMHH, FKFKEEE5, FKKFEEE5, FMMMMMCB, FMMMMMM1, G2000007, GGGGGMM7, GJJJJJ0J, GJJJJJ3J, H0000E27, H0000G27, H000C0G7, H000CEG7, H000CHH7, H000E0E7, H000EE27, H00CHHG7, H00EEE27, H00M0EE7, H05FF5F5, H0E00EE7, H55FF5F5, HCHH0H0H, HE000EE7, HFFIIII5, HGGG2227, HH00CEG7, HH00H0CH, HH0EEEE7, HH0FFFI5, HHEEEEE7, HHH000CH, HHH00EG7, HHHC00G7, HHHFFFF5, HHHHHKK5, HHHK5F55, HK5555F5, I4IIIIIJ, IA0000ID, II0005I5, III000I5, III055I5, III5NNNN, IIIII9IJ, IIIIIII5, IIINNNGN, JAJJJJJJ, JJAJJJJJ, K000005D, K00009A5, K0000M55, K000M555, K008IIID, K00D0K0D, K00III8D, K00K550D, K00LCC11, K0999951, K0D0000H, K0K00595, K0K9AAF5, K0KK0095, K0KK9FF5, K3333IID, KFKFEEE5, KFKKEEE5, KK00000H, KK0000M5, KK099991, KK55583D, KKKEEEA5, KKKKKKI5, LEEEE227, LLLEEE27, LLLL2E07, M000006B, M000M6CB, M0MMMMM1, M222EEE7, M777E777, M7E77777, ME222EE7, ME2EEEE7, MEE222E7, MM0NNNNN, MME77727, MMM6MMM1, N00003GN, N0000ADD, N000N0GN, N000NNND, N033333D, N0NN0NGN, NDDDDKDD, NN000N3N, NN00N03N, NN03000N, NNN003GN, NNNNDNLN, NNNNNADD, 199999MM1, 200FFFFFH, 222MEEEE7, 2FFFFFFCH, 30000000N, 30N00000N, 400000J3J, 500000M01, 5000166G1, 5000666G1, 50DDDDDDD, 8NN33333D, 999999991, C000000FH, C00000K0H, C000H00HH, C77777707, CH00H000H, CHH0000HH, D00000DKD, D00000DLD, D0000200H, D0000KK0D, D000KK00D, D00D0DDLD, D0D00DDLD, D0LEEEEE7, DDBBBBBBB, DDD000KDD, DDDDDDDE7, DK00000DD, DNNNNNNNN, E00000E27, E00007L27, E0000E727, E0E000C07, E20000027, EAAAAKAA5, EAKAAAAK5, EE0000C07, EEE000E27, EEEEEEGL7, F00FFFF35, F0FFFFF35, FF0000035, FF0FFFF35, FF5555FI5, FFFFFFA35, FFFFFFF35, FFFFFFFI5, FKKKKEEE5, FMMMMMMMB, GGGGG2227, GGGGGG207, GJJJJJJJJ, GLMMMMMMB, H000022M7, H000222M7, H000EEEE7, H0EEEEEE7, H0H0000CH, H0IIIIII5, HCH00000H, HE0EEEEE7, HFFFFFI35, HFFFFKKK5, HHHHHHG27, HHHHHHH55, HHHHHHHH7, HHHHHHM55, HHHKK5555, HHIIIII05, HIIIIII05, HKK5555I5, I000000AD, I000000ID, I000A000D, I00A0000D, IIIII0555, IIIIIII9J, K000000AD, K00000595, K000009F5, K0000550D, K099999A5, K0C00000H, K0I00000D, KK0000595, KK0000HCH, KKK000095, KKKFKFFE5, KKKIIIII5, M77777777, MEEEE2227, MMMMMMMM1, N0000000D, N0000003N, N000003NN, N00000N3N, N00000NGN, N00N000GN, N00NNNN8D, N0NNN00GN, N0NNNN3AD, N0NNNNNGN, N999999M1, NN0NNNNGN, NNN000NGN, NNNNNDD8D, NNNNNN0GN, 16MMMMMMMB, 1MMMMMMBCB, 3333333335, 33333333I5, 400000000N, 40IIIIIIJJ, 4IIIIIIIJJ, 4IIIIIIJIJ, 50000000M1, 70F9999991, 777E777727, 9999995MM1, ADD000000D, C00000088B, C000000CF1, C00000F0HH, CH00000H0H, D00KD0000D, D0D0DDDDLD, D0E2EEEEE7, D2EEEEEEE7, DBBBBBBBBB, DD000000KD, DD0000DDLD, DLE0EEEEE7, EEE0000727, EEEAAAAAA5, EEEEEE00G7, EEEEEEE0G7, F000000F35, F00FFKEEE5, F00KFFEEE5, F0M666666B, FCFFFFFFFH, FFFFFFF2HH, FFFKKKEEE5, GGGGGGG227, H00000C06H, H0000HHH6H, H555FFFFF5, H55FFFFF55, H5FFFFFF55, HF5FFFFFF5, HHHH0H0HCH, HHHHH0HHCH, HHHHHH0HCH, HHHHHHHHM5, HHHIIIIII5, IIDNNNNNLN, IIIIIJJIIJ, IIINNNNNLN, IINNNNNNGN, INNNNNNNLN, J0000000IJ, K0000II8ID, K099999995, K0I0000AID, K0K0009FF5, K9999999F5, KK00000095, KKFFFKEEE5, LLLLLLLME7, LLLMEEEEE7, LMEEEEEEE7, M000000005, MHHHHHHHH5, MK00000005, MMMMMMMBCB, NN000000GN, NN0000NNGN, NN99999991, 2HHHHHHHHHH, 38NNNNNNNNN, 3MNNNNNNNNN, 40IIIIIIIIJ, 4AJJJJJJJJJ, 4J000000J0J, 4JJJJJJJJJJ, 506666666G1, 5DDDDDDDDLD, 999999999F5, 99999999EA5, 99999999FE5, A0000000035, C0000000007, C00000000G7, C00000000KH, CEEEEEEEEL7, D0000000FMH, D000DDDDDLD, D0KD000000D, DDDD00000KD, DEEE0EEEEE7, DEL0EEEEEE7, DELEEEEEE07, E0000E20007, E7777777727, EE000000207, EEE20000007, FFFFFFFFMCH, FM66666666B, GGGGGGGG2M7, HFFFFFFFF55, HHHHHHHHH6H, HHHHHHHHHCH, HHHHHK55555, I9IIIIIIIIJ, IIIIIIII44J, IIIIIIIJJIJ, IINNNNNNNNN, JDDDDDDDDDD, JJIIIIIIIIJ, K00000I8IID, LLLLLLLLL27, 9999999EEAA5, AI000000000D, C77700000007, CH0HH000000H, D00D000000LD, DEEEEEEE0EE7, DN000000000N, EAKAAAAAAAA5, EKAAAAAAAAK5, F6666666666B, H000HHHHHH6H, H55FFFFFFFF5, HFFFFFFFFKK5, K00000000I8D, K999999999A5, 3555555555FF5, 5000000000001, 6G66666666661, 99999999999A5, C00000000000H, CFFFFFFFFFFCH, CHHH00000000H, D00000000K0KD, D0000000K00KD, D0D00000000LD, DEEEEEEEEEL07, E000E20000007, E00E200000007, EEE0000000027, GGGGGGGGGGGM7, GGGGGGGGGGM07, H00000000CHHH, H00HC0000000H, HFFFFFFFFFFK5, I0A000000000D, J000000000J9J, K000000000095, K000000000M2H, M0000000000M1, M0EEEEEEEEEE7, MHHHHHHHHHHHH, MMNNNNNNNNNNN, MNNNNNNNNNNNN, N000000DDDDDD, N000DDDDDDDDD, NNDDDDDDDDDDD, 22EEEEEEEEEEE7, 35FFFFFFFFFFF5, 400000000000JJ, 800000000000GN, DDDDDDDDDDD077, DDDDDDDDDDDDD7, E0000000000L27, EAAAAAAAAAAKA5, EEG00000000007, H0000000000C6H, I5500000000005, II0000000000I5, M0666666666661, M6MMMMMMMMMMMB, 4JJ00000000000J, 506666666666661, BGMMMMMMMMMMMCB, CFFFFFFFFFFFFFH, D0000000000KD0D, D0HEEEEEEEEEEE7, F0BBBBBBBBBBBBB, HGGGGGGGGGGGGG7, K0000000000000D, K00000000000MCH, M0M6MMMMMMMMMMB, 5DDDDDDDDDDDDDDD, C00000000000008B, D00000000000000H, DEEEEEEEEEEEE0L7, DEEEEEEEEEEEEEL7, EEE2EEEEEEEEEEE7, GM66666666666661, H5FFFFFFFFFFFFF5, IIIIIIIIIIIIIJJJ, BGMMMMMMMMMMMMMMB, DLEEEEEEEEEEEEEE7, H0000000000000CHH, H000000000C0000HH, I000000000000000D, IIIIIIIIIIIIIIIJJ, INNNNNNNNNNNNNNNN, J000000000000009J, M666666666666666B, N0000000000000LLN, N00DDDDDDDDDDDDDD, 355555555555555555, 60000000000000008H, 6M6666666666666661, C000000000000000F1, N0DDDDDDDDDDDDDDDD, 666666666666666666B, 800000000000000000N, AD000000000000000DD, DEEEEEEEEEEEEEEEEE7, I500000000000000005, 20000000000000000027, 4000000000000000003J, 400000000000000000IJ, 99999999999999999995, DD00DDDDDDDDDDDDDDLD, E2EEEEEEEEEEEEEEEEE7, N00000000000000000LN, 500000000066666666661, EE0000000000000000727, GGGGGGGGGGGGGGGGGGG07, H0000000000000000006H, 40000000000000IIIIIIIJ, AD0000000000000000000D, K0000000000000000000M5, CL777777777777777777777, D000000000000000000000N, D0000000000000000000IIN, HHHHHHHHHHHHHHHHHHHHHK5, NDDDDDDDDDDDDDDDDDDDDDD, 1MMMMMMMMMMMMMMMMMMMMMBB, D00DDDDDDDDDDDDDDDDDDDLD, FFFFFFFFFFFFFFFFFFFFFFFH, 4J0000000000000000000000J, 566666666666666666666666G1, EKKAAAAAAAAAAAAAAAAAAAAAA5, 6666666666666666666666666G1, AJJJJJJJJJJJJJJJJJJJJJJJJJJJ, H00000000000000000000000008H, N0000000000000000000000000GN, DD0000000000000000000000000LD, IIIIIIIIIIIIIIIIIIIIIIIIIIIIJ, G0666666666666666666666666666661, GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG7, K000000000000000000000000000000000H, EAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA5, LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLM7, M2EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE7, C000000000000000000000000000000000000000001, MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMCB, E00000000000000000000000000000000000000000000727, 777777777777777777777777777777777777777777777777727, EG000000000000000000000000000000000000000000000000000007, D000000000000000000000000000000000000000000000000000000000LD, 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===Base 36=== 11, 15, 17, 1B, 1H, 1N, 1P, 1V, 1Z, 21, 27, 2B, 2H, 2P, 2T, 2V, 2Z, 31, 35, 3J, 3N, 3T, 3V, 45, 47, 4D, 4J, 4N, 4T, 4Z, 51, 5B, 5D, 5H, 5J, 5V, 67, 6B, 6D, 6H, 6N, 6P, 6Z, 75, 7B, 7H, 7J, 7P, 7T, 7V, 85, 8J, 8N, 8P, 8T, 97, 9D, 9N, 9P, 9T, 9Z, A7, AD, AJ, AN, AT, B1, B5, BD, BN, BP, BZ, C1, C7, CB, CH, CP, CT, CV, CZ, DB, DJ, DN, DV, DZ, E5, EH, EJ, F1, F7, FH, FN, FT, FV, G1, GB, GH, GN, GP, GV, H1, H5, H7, HJ, HT, HV, HZ, I5, IB, ID, IP, IT, IZ, J7, JH, JP, JZ, K7, KD, KJ, KN, KV, L1, L5, LD, LH, LV, M5, MH, MJ, MT, MV, MZ, N1, NB, NP, NT, NV, NZ, OD, OH, OJ, ON, P7, PB, PJ, PT, Q1, Q5, QB, QH, QV, QZ, R5, RB, RJ, RP, S1, S5, SB, SD, SN, SP, SV, T5, T7, TH, TJ, TP, U7, UB, UD, UH, UN, UT, V1, V7, VD, VZ, W1, WB, WJ, WT, WZ, X5, XD, XP, XT, XZ, Y5, Y7, YD, YP, YZ, ZH, ZJ, ZN, ZT, ZV, 12D, 16J, 18D, 1CD, 1CJ, 1DD, 1GT, 1JD, 1JJ, 1LT, 1QJ, 1RD, 1RT, 1ST, 1XJ, 1YJ, 1YT, 22D, 22J, 22N, 23D, 255, 2A5, 2CD, 2ED, 2EN, 2F5, 2GD, 2GJ, 2IJ, 2JN, 2LN, 2MN, 2ND, 2O5, 2QD, 2QJ, 2U5, 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MYMU1, MYRK1, MYUU1, MYXR1, N000D, N0055, N006J, N007N, N00CN, N00IH, N00O7, N00S7, N029J, N02DD, N0307, N044H, N049H, N0505, N05M7, N05Q7, N06LJ, N070N, N0A55, N0CEN, N0CNN, N0CYN, N0DMD, N0DRD, N0F05, N0FF5, N0FMD, N0GED, N0HNN, N0I4H, N0IS7, N0IXJ, N0JLN, N0JNN, N0K4H, N0KIH, N0L6J, N0LI7, N0LLN, N0M0N, N0MQ7, N0NEN, N0O07, N0O77, N0Q0N, N0QEN, N0RRH, N0S07, N0SS7, N0U0J, N0ULJ, N0W77, N0WC5, N0WL7, N0XO7, N26JJ, N29XJ, N2CNN, N2CYN, N2MMD, N2N6J, N2N9J, N2NLJ, N2YYN, N30ED, N32RD, N33GD, N33MD, N3GGD, N3IW7, N3MR7, N3MX7, N3RGD, N3RI7, N3W2D, N3W77, N3X07, N3X77, N400H, N409H, N44YH, N494H, N49YH, N4AYH, N50K5, N5307, N5537, N5577, N57Q7, N5FK5, N5KK5, N5Q77, N5SQ7, N69LJ, N6L9J, N6U0J, N700D, N7077, N70EN, N70FD, N73RD, N7777, N777N, N7DMD, N7E2N, N7FED, N7M3D, N7MWD, N7SR7, N7WMD, N92LJ, N9XXJ, NA505, NA5F5, NAFK5, NAK05, NAKF5, NARYH, NAWW5, NC00N, NC0EN, NC0NN, NCE0N, NCN0N, NCNQN, NCW05, ND3GD, ND7DD, NDAW5, NDDGD, NDDRD, NDE3D, NDWM7, NDWW7, NE0GD, NED3D, NEDDD, NEL2N, NEMMD, NEMRD, NF0F5, NFEMD, NFKF5, NFWC5, NFWW5, NGDED, NGW2D, NH00H, NH2NN, NHH0H, NHMCN, NHMMD, NHNNN, NI00H, NI0EN, NI0MN, NI0NH, NI0NJ, NI0XJ, NI44H, NI7R7, NI7S7, NII77, NIIM7, NIIMN, NIIYN, NIM0N, NIN0H, NIN0J, NINJJ, NIW37, NIWM7, NIX77, NIXW7, NJ0EN, NJ0NN, NJ30D, NJ33D, NJFMD, NJIEN, NJJ2N, NJJIN, NJJJJ, NJJJN, NJL0J, NJLNN, NJN0N, NJSJJ, NK005, NK04H, NK3KH, NK5F5, NKA05, NKFK5, NKK55, NKKF5, NL09J, NL2IN, NLCNN, NLII7, NLIIN, NLJLN, NLL2J, NLLNJ, NLLNN, NLNCN, NLNIN, NLNLJ, NLNLN, NM00N, NM73D, NM7DD, NM7RD, NME0N, NMELN, NMLL7, NMLQ7, NMMRD, NMQEN, NMRD7, NMRR7, NMWWD, NN02J, NN0AH, NN0EN, NN30H, NN525, NN6UJ, NN92J, NNA55, NNASH, NNCLN, NNCMN, NNELN, NNF25, NNHHN, NNJ2J, NNJJJ, NNLNN, NNN55, NNN9J, NNNMN, NNNNJ, NNNSH, NNNXJ, NNQYN, NNS3H, NNU9J, NNW55, NNXJJ, NO077, NO0W7, NO777, NOI77, NOIM7, NOWL7, NQ00N, NQ0YN, NQ77N, NQ7EN, NQLLN, NQLNN, NQQQN, NQQYN, NRARH, NRAYH, NRDI7, NRHYH, NRQL7, NRRHH, NRW2D, NS0L7, NSA3H, NSHHH, NSIIJ, NSIJJ, NSS07, NSSJJ, NSSL7, NSSS7, NSULJ, NU00J, NUL6J, NUSIJ, NW0C5, NW3W7, NW5W5, NWI77, NWIM7, NWIO7, NWW55, NWWM7, NX0I7, NX0O7, NX3R7, NX9XJ, NXIM7, NXRL7, NXSSJ, NXWI7, NXWW7, NXXSJ, NY44H, NY94H, NYYIN, O0057, O005T, O0077, O0091, O009B, O00BT, O00EV, O00OV, O00TT, O00WP, O00WV, O040V, O0507, O056T, O065T, O08AV, O08E7, O0901, O09AB, O09I1, O09K1, O09WV, O0A4V, O0AI1, O0E9V, O0EAB, O0EAV, O0EFP, O0EKB, O0EOB, O0EU1, O0FMP, O0K6T, O0K91, O0MM1, O0O9B, O0OAB, O0OI1, O0OOB, O0OT1, O0OUV, O0OW7, O0OYT, O0T8V, O0TOT, O0TOV, O0TTV, O0TUV, O0TX1, O0U91, O0UE1, O0W87, O0WOV, O0YOT, O100T, O1EET, O4PAV, O4U0V, O5005, O50EP, O50I7, O50K5, O555P, O55FP, O55UP, O5EFP, O5I07, O5K05, O5KK5, O5OYT, O6LGT, O77E7, O7Q77, O80E7, O8AAZ, O8AFZ, O8AOV, O8FFZ, O8FKB, O8FZB, O8IM7, O8ZRZ, O8ZZB, O900V, O90WV, O96OV, O99LB, O9K01, O9OU1, O9R6V, O9U01, O9UI1, OA091, OA0O1, OA4AV, OA4IV, OA68V, OA8AZ, OA9I1, OAA4V, OAAFZ, OAAO1, OAAOV, OAAZZ, OAFAZ, OAFYB, OAI0V, OAI91, OAOAV, OAOE1, OAOU1, OAUE1, OAUI1, OAY01, OAY0B, OAYI1, OAZZZ, OB66T, OBE0T, OBEET, OE0BT, OE0FB, OE4AV, OE6ET, OE8AV, OE9EB, OEA8V, OEAA1, OEAFB, OEBET, OEBI7, OEEO7, OEFFP, OEFLP, OEKA1, OEKAB, OEKU1, OELMP, OEML7, OEO07, OEO0B, OEO4V, OEO6V, OEOAV, OEOO7, OEOOB, OEOVB, OEPU1, OERET, OERRV, OETY1, OEUK1, OEUU1, OEV9B, OEVFP, OEW8V, OEWW7, OF0FP, OF0OB, OFFFP, OFFMP, OFFZP, OFFZZ, OFMMP, OFMWP, OFOQP, OFPFZ, OFPUZ, OFZ0P, OFZFZ, OFZOB, OFZZZ, OG065, OG0YT, OI0EV, OI7Q7, OI9WV, OIIE7, OIQ77, OIQW7, OIR6V, OIYO1, OK8KB, OKAE1, OKAY1, OKE6T, OKEU1, OKFYB, OKIY1, OKYA1, OKYI1, OL08B, OL4EP, OL777, OL8E7, OLBI7, OLEL7, OLFOP, OLGYT, OLIW7, OLLSZ, OLLZZ, OLOUP, OLR6T, OLUMP, OMAU1, OMOU1, OMXM1, OO0AB, OO0I7, OO0T1, OO1ET, OO4AV, OO4MP, OO4QP, OO6KT, OO6LT, OO6OV, OO7O7, OOA0B, OOAIV, OOAOV, OOBGT, OOEMP, OOERT, OOET1, OOEU1, OOEY1, OOGTT, OOI4V, OOIRV, OOKET, OOLBT, OOMMP, OOMQ7, OOMU1, OOMWP, OOO0B, OOO6T, OOO77, OOOE7, OOOKT, OOOOV, OOORT, OOOW7, OOPY1, OOQ77, OOT01, OOT91, OOTAV, OOTOV, OOTUV, OOU91, OOUUV, OOWIV, OOWMP, OOWVP, OOY01, OOY0B, OOYKB, OOYU1, OOYYB, OP0EV, OP44V, OP8FZ, OPA91, OPAAZ, OPAOV, OPEAV, OPI4V, OPO4V, OPOIV, OPOUV, OPOY1, OPUAZ, OPUEV, OPWUV, OPYU1, OQ7W7, OQ8E7, OQLE7, OQQL7, OR8AZ, ORA8Z, ORKLT, ORS8Z, OS8RZ, OSR8Z, OSS8Z, OT09V, OT0K1, OT66T, OTT8V, OTUOV, OU091, OU0E1, OU0MP, OU4LP, OUAAZ, OUASZ, OUL4P, OUP8Z, OUP91, OUPAZ, OUPY1, OUU0P, OUUPZ, OUYM1, OUZ91, OV0FB, OV0LB, OV54P, OV5WP, OV9K5, OVALB, OVB6T, OVKFB, OVLEB, OVLFP, OVQWP, OW0EV, OW7O7, OW7Q7, OW7W7, OW90V, OWEEP, OWIWV, OWLW7, OWOM7, OWOVP, OWQ87, OWU0V, OWW9V, OWWL7, OWWOV, OXAA1, OXU01, OXUI1, OXXI1, OXXX1, OY00T, OY0E1, OY0RT, OY0U1, OY0YB, OY98B, OYE0T, OYFKB, OYKFB, OYLYB, OYYYB, OZ0OB, OZ0WP, OZ0YB, OZ9EB, OZ9K1, OZ9O1, OZALB, OZAYB, OZEAB, OZEOB, OZFEB, OZFFP, OZFFZ, OZFRZ, OZFZP, OZO0B, OZO91, OZOYB, OZPRZ, OZR8Z, OZUUP, OZZYB, P00W5, P02G5, P049V, P04YV, P0A0V, P0AW5, P0CC5, P0CU5, P0E9V, P0EWV, P0F25, P0FC5, P0G25, P0K3Z, P0KOZ, P0KRH, P0O55, P0OEV, P0PG5, P0PO5, P0PW5, P0R0H, P0ROZ, P0U25, P0UIV, P0UVP, P0V0P, P0VKP, P0W9V, P0YIV, P13WD, P22K5, P2D95, P2NC5, P33ZZ, P38DD, P3GGD, P3SAH, P409V, P444V, P44O1, P44Y1, P4AIV, P4AYV, P4E0V, P4OA1, P4OK1, P4OO1, P4U81, P4UEV, P4UR1, P55EP, P5GZ5, P6A41, P803H, P80AZ, P838D, P8AAZ, P8D8D, P8FKZ, P8K0Z, P8KKZ, P8KXH, P8OE1, P8UE1, P8X0H, P8X3H, P8XKH, P909V, P9941, P99EV, P99U1, P9E9V, P9K91, P9OE1, P9OK1, P9W9V, P9X9H, PA00H, PA441, PA5G5, PA8FZ, PA9O1, PAA8Z, PAI4V, PAI9V, PAMKP, PAOEV, PAR8H, PAUM1, PAVKP, PAZEP, PC0W5, PCAG5, PCAU5, PCCA5, PCWN5, PD0QP, PD0SH, PD33D, PD3AH, PD3MD, PDGC5, PDK3H, PDK8H, PDSAH, PDUAP, PE99V, PEA91, PEAEP, PEEA1, PEEE1, PEER1, PEI9V, PEK61, PEQQP, PERE1, PERK1, PEUY1, PEY0V, PF2K5, PF3CD, PF83D, PFC2D, PFCWD, PFDAP, PFEKP, PFMCD, PFMMD, PFO55, PFR2D, PFZEP, PG295, PG2WD, PG8CD, PGCD5, PGDC5, PGF5Z, PGG8D, PGKF5, PGKK5, PGO95, PGW8D, PH2MD, PHD8D, PK0O5, PK441, PK53Z, PK5GZ, PK83H, PK8KZ, PKAA1, PKAU1, PKKO5, PKP3Z, PKRXH, PKSIH, PMAA1, PMAAP, PMAU1, PMF3D, PMFCD, PMMAP, PMMMD, PMMMP, PMMPD, PMRR1, PMUO1, PN2D5, PN2W5, PNA3H, PNAF5, PNFK5, PNHFD, PNK55, PNKF5, PNSKH, PO09V, PO0EV, PO4AV, PO90V, POAY1, POI4V, POOE1, POUEV, POUY1, POWUV, POWWV, POYA1, POZAZ, POZFZ, PP0QP, PP2CN, PP2MD, PP33D, PP595, PP5W5, PP8CD, PPCNN, PPCRD, PPCU5, PPCW5, PPCWD, PPD05, PPDUP, PPECN, PPF8D, PPFC5, PPFW5, PPGC5, PPGF5, PPGFZ, PPKGZ, PPMCD, PPMCN, PPMEN, PPMND, PPNF5, PPNMN, PPNWD, PPP3Z, PPP95, PPPC5, PPPRZ, PPPZD, PPQKP, PPS0Z, PPW2N, PPWND, PPWWN, PPZC5, PPZSZ, PQQQP, PR1GD, PR8AH, PRA0H, PREK1, PRKO1, PRMM1, PRNFD, PRRM1, PRRRH, PRW2N, PS0ZZ, PS80H, PS80Z, PS8AH, PS8ZZ, PSIKH, PSR3Z, PU025, PU0IV, PU49V, PU4YV, PU8AZ, PU9EV, PUE91, PUE9V, PUI9V, PURK1, PUUM1, PUUR1, PUVAP, PUYIV, PUYO1, PUZMP, PV00P, PV2CN, PV2RN, PVAKP, PVFAP, PVFFP, PVFKP, PVK0P, PVKAP, PVNCN, PVNEN, PW005, PW0C5, PWCWD, PWF8D, PWNC5, PWO9V, PWOWV, PWWOV, PWWWN, PWWWV, PX0IH, PXAIH, PXIAH, PXIKH, PYKE1, PYKO1, PYRK1, PYRM1, PZ0G5, PZ1WD, PZ295, PZ2C5, PZ2G5, PZ481, PZ641, PZE61, PZEAP, PZG25, PZK61, PZKOZ, PZOFZ, PZOO1, PZR41, PZRZZ, PZS0Z, PZSUZ, PZUMP, Q00DT, Q00JD, Q00QT, Q00YN, Q020J, Q03RD, Q0CQN, Q0DRD, Q0FRD, Q0JTT, Q0Q3D, Q0QRN, Q0QXN, Q0XEN, Q0XIJ, Q0XLN, Q0XQN, Q0YYN, Q20RD, Q2D0D, Q32WD, Q3D3D, Q4EKP, Q4PQP, Q7777, Q77Q7, Q7ER7, Q7EW7, Q7LR7, Q7LS7, Q7LW7, Q7QQN, Q7QR7, Q7QYN, Q7RE7, Q7SS7, QAAPP, QAOOP, QAOWP, QAUAP, QAUWP, QAWEP, QAWLP, QCEQN, QCNYN, QCQEN, QD0GD, QD0RD, QD20D, QD33D, QD3DD, QDAWP, QDRET, QDWKP, QE7QN, QECLN, QEEL7, QEES7, QELCN, QEQCN, QEQTT, QERE7, QESR7, QF2WD, QFGUJ, QFR2D, QG00J, QG0IJ, QG7Q7, QG7R7, QGDDD, QGGGD, QGGQD, QGJ2J, QGMQ7, QGOO7, QGQQ7, QGRR7, QJ02J, QJ03D, QJ0SJ, QJ33D, QJ3WD, QJD0D, QJI0J, QK44P, QKPKP, QL7W7, QLES7, QLLL7, QLNNN, QLQ77, QLQL7, QLQM7, QLQPN, QLR87, QLSRT, QMLR7, QMQQ7, QN0YN, QN70N, QNCYN, QNLW7, QNNQN, QNNYN, QNQNN, QO777, QO7E7, QO8M7, QOUWP, QP3RD, QPDAP, QPEEP, QPFRD, QPGGD, QPPQP, QPR2D, QPRGD, QQ0RN, QQ0YN, QQ4LP, QQ4QP, QQAEP, QQCYN, QQELT, QQEPN, QQEQP, QQGDD, QQGGD, QQGO7, QQGQD, QQKKP, QQLAP, QQLPN, QQLRT, QQMR7, QQN77, QQNNN, QQNQN, QQPDD, QQPEN, QQPGD, QQPQP, QQPWD, QQQ0N, QQQ3D, QQQ87, QQQKP, QQQL7, QQQM7, QQQPD, QQQQN, QQQWD, QQRL7, QQRN7, QQRYN, QQSST, QQTDT, QQTQT, QQU4P, QQUAP, QQUUP, QQWPD, QQXEN, QQXQN, QQYXN, QR00N, QR0XN, QR2FD, QR32D, QREKT, QRN0N, QRNL7, QRQQD, QRRE7, QRXXN, QSES7, QSS2J, QSSE7, QSSS7, QSSSJ, QTDET, QTQ2D, QTQLT, QUAAP, QUAWP, QUPPP, QUUAP, QW7G7, QWG77, QWGM7, QWLEP, QWOEP, QWOLP, QX77N, QX7EN, QXELN, QXEQN, QXLLN, QXLQN, QXNQN, QXOE7, QXQXN, QXXNN, R0061, R008D, R00IH, R00NN, R00XN, R013D, R02YN, R030D, R04R1, R06E1, R06ET, R07M1, R08AH, R0A8H, R0AYH, R0D07, R0DDT, R0EK1, R0EYT, R0F3D, R0G8D, R0GDD, R0GGD, R0GQ7, R0H0N, R0KE1, R0LQ7, R0N0N, R0RYN, R0T2N, R0TLT, R0TNN, R0TYN, R0X0N, R0YST, R100T, R130D, R13WD, R166T, R1E0T, R1F3D, R1GFD, R1TGD, R200N, R28WD, R2W8D, R2WFD, R32DD, R330D, R332D, R3W8D, R44XV, R4AAV, R4AYV, R4MO1, R4OI1, R4RO1, R4U4V, R4X9V, R6001, R60K1, R66LT, R66YV, R6E01, R6EE1, R6MK1, R6SST, R6X01, R6X9V, R6XE1, R6XYV, R6Y6V, R7OO1, R7XE1, R80G7, R88FD, R8F8D, R8IE7, R8X8H, R9OAV, R9UVV, R9VOV, R9X6V, RA08H, RAA9V, RAS8Z, RAX0H, RD00D, RD8I7, RD8IH, RDA0H, RDDQT, RDQDT, RE061, RE6KT, RE6LT, REEK1, REEKT, RER01, RERK1, RERR1, RF0DD, RFD0D, RG28D, RGGFD, RGGWD, RGRM7, RGWQD, RH00H, RH0EN, RH8HH, RH9HH, RH9XH, RHH9H, RHHIN, RHHNN, RHIWN, RHNEN, RHWIN, RHWWN, RHX8H, RHXEN, RHY9H, RI00H, RI2IN, RIHEN, RIIWN, RIMRN, RK00T, RKEE1, RKELT, RKL0T, RKQLT, RLEI7, RLQM7, RLR07, RLRE7, RLSSZ, RLSYT, RLZE7, RLZI7, RLZLZ, RM0G7, RM0Q7, RMIWN, RMKO1, RMLQ7, RMOX1, RMR07, RMRR1, RN2YN, RN30D, RND3D, RNI2N, RNIMN, RNMEN, RNW2D, RO0TT, RO66T, RO6KT, ROAAV, ROOKT, ROOOT, ROU9V, ROXM1, ROZK1, RQK0T, RQLKT, RQLST, RQMR7, RQQLT, RQQQT, RQQWD, RQRE7, RQTQD, RR44V, RR4YV, RR601, RR66V, RR6WV, RR9HH, RR9UV, RRA9V, RRAYV, RRE01, RREE1, RRGM7, RRGR7, RRI2N, RRIIN, RRIN7, RRIXN, RRKE1, RRL07, RRLM7, RRM07, RRMG7, RRML7, RRMM1, RRMO1, RRMWN, RRNR7, RRO01, RROI1, RROK1, RRR0N, RRRE1, RRRG7, RRRIN, RRRL7, RRRM1, RRRO1, RRROV, RRRWV, RRU6V, RRV9H, RRVUV, RRVYH, RRWWV, RRXRN, RRY4V, RRY9H, RRYHH, RRYIN, RRYRN, RS8FZ, RSSSZ, RSSYT, RSYST, RT3ZZ, 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====Additional known quasi-minimal primes (not necessarily the next)==== P₈₁₉₉₃SZ ==Unsolved families== Families for which not even a probable prime is known nor can be ruled out as only contain composites (only count the numbers > base (''b'')) by covering congruence, algebraic factorization, or combine of them. {|class=wikitable |base (''b'')||unsolved family (base-''b'' form)||unsolved family (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||current search limit of length||factorization of numbers in this family |- |13||9{5}||(113×13^''n''−5)/12||116000||[http://factordb.com/index.php?query=%28113*13%5En-5%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |13||A{3}A||(41×13^''n''+1+27)/4||111000||[http://factordb.com/index.php?query=%2841*13%5E%28n%2B1%29%2B27%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |16||{3}AF||(16^''n''+2+619)/5||98000||[http://factordb.com/index.php?query=%2816%5E%28n%2B2%29%2B619%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||1{7}||(23×17^''n''−7)/16||32074||[http://factordb.com/index.php?query=%2823*17%5En-7%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||1F{0}7||32×17^''n''+1+7||32074||[http://factordb.com/index.php?query=32*17%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||4{7}A||(71×17^''n''+1+41)/16||32074||[http://factordb.com/index.php?query=%2871*17%5E%28n%2B1%29%2B41%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||51{0}D||86×17^''n''+1+13||32074||[http://factordb.com/index.php?query=86*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||70F{0}D||2038×17^''n''+1+13||32074||[http://factordb.com/index.php?query=2038*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||8{B}9||(139×17^''n''+1−43)/16||32074||[http://factordb.com/index.php?query=%28139*17%5E%28n%2B1%29-43%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||9{5}9||(149×17^''n''+1+59)/16||32074||[http://factordb.com/index.php?query=%28149*17%5E%28n%2B1%29%2B59%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||95{F}||(2543×17^''n''−15)/16||32074||[http://factordb.com/index.php?query=%282543*17%5En-15%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||A{D}F||(173×17^''n''+1+19)/16||32074||[http://factordb.com/index.php?query=%28173*17%5E%28n%2B1%29%2B19%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||B{0}B3||11×17^''n''+2+190||32074||[http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B190&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||B{0}DB||11×17^''n''+2+232||32074||[http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B232&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}2BE||(11×17^''n''+3−41579)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B3%29-41579%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}2E||(11×17^''n''+2−2411)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29-2411%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}E9||(11×17^''n''+2+773)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B773%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}EE||(11×17^''n''+2+853)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B853%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||D0G{D}||(60381×17^''n''−13)/16||32074||[http://factordb.com/index.php?query=%2860381*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||E9{B}||(3963×17^''n''−11)/16||32074||[http://factordb.com/index.php?query=%283963*17%5En-11%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||F1{9}||(4105×17^''n''−9)/16||1000000||[http://factordb.com/index.php?query=%284105*17%5En-9%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||FD0{D}||(72909×17^''n''−13)/16||32074||[http://factordb.com/index.php?query=%2872909*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||2{7}9D||(47×21^''n''+2+953)/20||20000||[http://factordb.com/index.php?query=%2847*21%5E%28n%2B2%29%2B953%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||2F{C}A||(288×21^''n''+1−13)/5||20000||[http://factordb.com/index.php?query=%28288*21%5E%28n%2B1%29-13%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||4{3}B||(83×21^''n''+1+157)/20||20000||[http://factordb.com/index.php?query=%2883*21%5E%28n%2B1%29%2B157%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||5{0}DJ||5×21^''n''+2+292||20000||[http://factordb.com/index.php?query=5*21%5E%28n%2B2%29%2B292&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{5}FEK||(21^''n''+3+18455)/4||20000||[http://factordb.com/index.php?query=%2821%5E%28n%2B3%29%2B18455%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{7}ID||(7×21^''n''+2+4733)/20||20000||[http://factordb.com/index.php?query=%287*21%5E%28n%2B2%29%2B4733%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||99{0}99H||198×21^''n''+3+4175||20000||[http://factordb.com/index.php?query=198*21%5E%28n%2B3%29%2B4175&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{9}0D||(9×21^''n''+2−3709)/20||20000||[http://factordb.com/index.php?query=%289*21%5E%28n%2B2%29-3709%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{9}D||(9×21^''n''+1+71)/20||20000||[http://factordb.com/index.php?query=%289*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B3{0}EB||234×21^''n''+2+305||20000||[http://factordb.com/index.php?query=234*21%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B9{0}E5||240×21^''n''+2+299||20000||[http://factordb.com/index.php?query=240*21%5E%28n%2B2%29%2B299&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B{D}B||(233×21^''n''+1−53)/20||20000||[http://factordb.com/index.php?query=%28233*21%5E%28n%2B1%29-53%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B{H}6H||(237×21^''n''+2−4637)/20||20000||[http://factordb.com/index.php?query=%28237*21%5E%28n%2B2%29-4637%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||DH{D}||(5813×21^''n''−13)/20||20000||[http://factordb.com/index.php?query=%285813*21%5En-13%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||F{9}D||(309×21^''n''+1+71)/20||20000||[http://factordb.com/index.php?query=%28309*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{F}35||(3×21^''n''+2−1051)/4||20000||[http://factordb.com/index.php?query=%283*21%5E%28n%2B2%29-1051%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||G{0}FK||16×21^''n''+2+335||506000||[http://factordb.com/index.php?query=16*21%5E%28n%2B2%29%2B335&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||H{0}7771||17×21^''n''+4+68062||20000||[http://factordb.com/index.php?query=17*21%5E%28n%2B4%29%2B68062&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||H{D}||(353×21^''n''−13)/20||20000||[http://factordb.com/index.php?query=%28353*21%5En-13%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{J}6J||(19×21^''n''+2−5479)/20||20000||[http://factordb.com/index.php?query=%2819*21%5E%28n%2B2%29-5479%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||7{K}Z||(53×36^''n''+1+101)/7||20000||[http://factordb.com/index.php?query=%2853*36%5E%28n%2B1%29%2B101%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||B{0}EUV||11×36^''n''+3+19255||20000||[http://factordb.com/index.php?query=11*36%5E%28n%2B3%29%2B19255&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||HM{0}N||634×36^''n''+1+23||20000||[http://factordb.com/index.php?query=634*36%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||N{0}YYN||23×36^''n''+3+45311||20000||[http://factordb.com/index.php?query=23*36%5E%28n%2B3%29%2B45311&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||O{L}Z||(123×36^''n''+1+67)/5||100000||[http://factordb.com/index.php?query=%28123*36%5E%28n%2B1%29%2B67%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||S{0}8H||28×36^''n''+2+305||20000||[http://factordb.com/index.php?query=28*36%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |} For base 17, the smallest prime in family {B}2BE may or may not be quasi-minimal prime, since another unsolved family is {B}2E For base 21, the smallest prime in families {9}0D and F{9}D may or may not be quasi-minimal primes, since another unsolved family is {9}D, and the smallest prime in family DH{D} may or may not be quasi-minimal prime, since another unsolved family is H{D} ==Primality certificates for the proven primes > 10²⁹⁹== Only list bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 30 See also: [[w:Primality certificate|Primality certificate]] and [[w:Elliptic curve primality|Elliptic curve primality]] {|class=wikitable |base (''b'')||index of this quasi-minimal prime in base ''b''||quasi-minimal prime (base-''b'' form)||quasi-minimal prime (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||factordb entry of this prime||primality certificate of this prime |- |9||149||76₃₂₉2||(31×9³³⁰−19)/4||[http://factordb.com/index.php?id=1100000002359003642]||[http://factordb.com/cert.php?id=1100000002359003642] |- |9||150||27₆₈₆07||(23×9⁶⁸⁸−511)/8||[http://factordb.com/index.php?id=1100000002495467486]||[http://factordb.com/cert.php?id=1100000002495467486] |- |9||151||30₁₁₅₈11||3×9¹¹⁶⁰+10||[http://factordb.com/index.php?id=1100000002376318423]||[http://factordb.com/cert.php?id=1100000002376318423] |- |11||1065||A₇₁₃58||11⁷¹⁵−58||[http://factordb.com/index.php?id=1100000003576826487]||[http://factordb.com/cert.php?id=1100000003576826487] |- |11||1066||7₇₅₉44||(7×11⁷⁶¹−367)/10||[http://factordb.com/index.php?id=1100000002505568840]||[http://factordb.com/cert.php?id=1100000002505568840] |- |11||1067||557₁₀₁₁||(607×11¹⁰¹¹−7)/10||[http://factordb.com/index.php?id=1100000002361376522]||[http://factordb.com/cert.php?id=1100000002361376522] |- |13||3165||50₂₇₀44||5×13²⁷²+56||[http://factordb.com/index.php?id=1100000002632397005]||[http://factordb.com/cert.php?id=1100000002632397005] |- |13||3166||9₂₇₁095||(3×13²⁷⁴−6103)/4||[http://factordb.com/index.php?id=1100000003590431654]||[http://factordb.com/cert.php?id=1100000003590431654] |- |13||3167||10₂₈₆7771||13²⁹⁰+16654||[http://factordb.com/index.php?id=1100000003590431633]||[http://factordb.com/cert.php?id=1100000003590431633] |- |13||3168||9₃₀₈1||(3×13³⁰⁹−35)/4||[http://factordb.com/index.php?id=1100000000840126705]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=308&c0=-&EN= 13³⁰⁸−1] |- |13||3169||B₃₄₁C4||(11×13³⁴³+61)/12||[http://factordb.com/index.php?id=1100000003590431618]||[http://factordb.com/cert.php?id=1100000003590431618] |- |13||3170||8B₃₄₃||(107×13³⁴³−11)/12||[http://factordb.com/index.php?id=1100000002321018736]||[http://factordb.com/cert.php?id=1100000002321018736] |- |13||3171||710₃₇₁111||92×13³⁷⁴+183||[http://factordb.com/index.php?id=1100000003590431609]||[http://factordb.com/cert.php?id=1100000003590431609] |- |13||3172||75₃₇₅7||(89×13³⁷⁶+19)/12||[http://factordb.com/index.php?id=1100000003590431596]||[http://factordb.com/cert.php?id=1100000003590431596] |- |13||3173||9B0₃₉₁9||128×13³⁹²+9||[http://factordb.com/index.php?id=1100000002632396790]||[http://factordb.com/cert.php?id=1100000002632396790] |- |13||3174||7B0B₃₉₇||(15923×13³⁹⁷−11)/12||[http://factordb.com/index.php?id=1100000003590431574]||[http://factordb.com/cert.php?id=1100000003590431574] |- |13||3175||10₄₁₄93||13⁴¹⁶+120||[http://factordb.com/index.php?id=1100000002523249240]||[http://factordb.com/cert.php?id=1100000002523249240] |- |13||3176||81010₄₁₅1||17746×13⁴¹⁶+1||[http://factordb.com/index.php?id=1100000003590431555]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3177||8110₄₃₅1||1366×13⁴³⁶+1||[http://factordb.com/index.php?id=1100000002373259109]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3178||B7₄₈₆||(139×13⁴⁸⁶−7)/12||[http://factordb.com/index.php?id=1100000002321015892]||[http://factordb.com/cert.php?id=1100000002321015892] |- |13||3179||B₅₆₃C||(11×13⁵⁶⁴+1)/12||[http://factordb.com/index.php?id=1100000000000217927]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=564&c0=-&EN= 13⁵⁶⁴−1] |- |13||3180||1B₅₇₆||(23×13⁵⁷⁶−11)/12||[http://factordb.com/index.php?id=1100000002321021456]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=576&c0=-&EN= 13⁵⁷⁶−1] |- |13||3181||80₆₉₃87||8×13⁶⁹⁵+111||[http://factordb.com/index.php?id=1100000002615636527]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 has a large prime factor, factordb entry of this prime factor is [http://factordb.com/index.php?id=1100000002615636532], and primality certificate of this prime factor is [http://factordb.com/cert.php?id=1100000002615636532] |- |13||3182||CC5₇₁₃||(2021×13⁷¹³−5)/12||[http://factordb.com/index.php?id=1100000002615627353]||[http://factordb.com/cert.php?id=1100000002615627353] |- |13||3183||B₈₃₄74||(11×13⁸³⁶−719)/12||[http://factordb.com/index.php?id=1100000003590430871]||[http://factordb.com/cert.php?id=1100000003590430871] |- |13||3184||9₉₆₈B||(3×13⁹⁶⁹+5)/4||[http://factordb.com/index.php?id=1100000000258566244]||[http://factordb.com/cert.php?id=1100000000258566244] |- |13||3185||10₁₂₉₅181||13¹²⁹⁸+274||[http://factordb.com/index.php?id=1100000002615445013]||[http://factordb.com/cert.php?id=1100000002615445013] |- |13||3186||9₁₃₆₂5||(3×13¹³⁶³−19)/4||[http://factordb.com/index.php?id=1100000002321017776]||[http://factordb.com/cert.php?id=1100000002321017776] |- |13||3187||7₁₅₀₄1||(7×13¹⁵⁰⁵−79)/12||[http://factordb.com/index.php?id=1100000002320890755]||[http://factordb.com/cert.php?id=1100000002320890755] |- |13||3188||930₁₅₅₁1||120×13¹⁵⁵²+1||[http://factordb.com/index.php?id=1100000000765961452]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3189||720₂₂₉₇2||93×13²²⁹⁸+2||[http://factordb.com/index.php?id=1100000002632396910]||[http://factordb.com/cert.php?id=1100000002632396910] |- |13||3190||1770₂₇₀₃17||267×13²⁷⁰⁵+20||[http://factordb.com/index.php?id=1100000003590430825]||[http://factordb.com/cert.php?id=1100000003590430825] |- |13||3191||390₆₂₆₆1||48×13⁶²⁶⁷+1||[http://factordb.com/index.php?id=1100000000765961441]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3192||B0₆₅₄₀BBA||11×13⁶⁵⁴³+2012||[http://factordb.com/index.php?id=1100000002616382906]||[http://factordb.com/cert.php?id=1100000002616382906] |- |13||3193||C₁₀₆₃₁92||13¹⁰⁶³³−50||[http://factordb.com/index.php?id=1100000003590493750]||[http://factordb.com/cert.php?id=1100000003590493750] |- |14||649||34D₇₀₈||47×14⁷⁰⁸−1||[http://factordb.com/index.php?id=1100000001540144903]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |14||650||4D₁₉₆₉₈||5×14¹⁹⁶⁹⁸−1||[http://factordb.com/index.php?id=1100000000884560233]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |16||2328||880₂₄₆7||136×16²⁴⁷+7||[http://factordb.com/index.php?id=1100000002468140199]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has a large prime factor, and this prime factor is < 10²⁹⁹ |- |16||2329||D4₂₆₃D||(199×16²⁶⁴+131)/15||[http://factordb.com/index.php?id=1100000002468170238]||[http://factordb.com/cert.php?id=1100000002468170238] |- |16||2330||E0₂₆₁4DD||14×16²⁶⁴+1245||[http://factordb.com/index.php?id=1100000003588388352]||[http://factordb.com/cert.php?id=1100000003588388352] |- |16||2331||8C0₂₉₀ED||140×16²⁹²+237||[http://factordb.com/index.php?id=1100000003588388307]||[http://factordb.com/cert.php?id=1100000003588388307] |- |16||2332||DA₃₀₅5||(41×16³⁰⁶−17)/3||[http://factordb.com/index.php?id=1100000003588388284]||[http://factordb.com/cert.php?id=1100000003588388284] |- |16||2333||CE80₄₂₂D||3304×16⁴²³+13||[http://factordb.com/index.php?id=1100000003588388257]||[http://factordb.com/cert.php?id=1100000003588388257] |- |16||2334||5F₅₄₄6F||6×16⁵⁴⁶−145||[http://factordb.com/index.php?id=1100000002604723967]||[http://factordb.com/cert.php?id=1100000002604723967] |- |16||2335||88F₅₄₅||137×16⁵⁴⁵−1||[http://factordb.com/index.php?id=1100000000413679658]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |16||2336||BE0₇₉₂BB||190×16⁷⁹⁴+187||[http://factordb.com/index.php?id=1100000003588387938]||[http://factordb.com/cert.php?id=1100000003588387938] |- |16||2337||D9₁₀₅₂||(68×16¹⁰⁵²−3)/5||[http://factordb.com/index.php?id=1100000002321036020]||[http://factordb.com/cert.php?id=1100000002321036020] |- |16||2338||FAF₁₀₆₂45||251×16¹⁰⁶⁴−187||[http://factordb.com/index.php?id=1100000003588387610]||[http://factordb.com/cert.php?id=1100000003588387610] |- |16||2339||F8₁₅₁₇F||(233×16¹⁵¹⁸+97)/15||[http://factordb.com/index.php?id=1100000000633744824]||[http://factordb.com/cert.php?id=1100000000633744824] |- |16||2340||20₁₇₁₃321||2×16¹⁷¹⁶+801||[http://factordb.com/index.php?id=1100000003588386735]||[http://factordb.com/cert.php?id=1100000003588386735] |- |16||2341||300F₁₉₆₀AF||769×16¹⁹⁶²−81||[http://factordb.com/index.php?id=1100000003588368750]||[http://factordb.com/cert.php?id=1100000003588368750] |- |16||2342||90₃₅₄₂91||9×16³⁵⁴⁴+145||[http://factordb.com/index.php?id=1100000000633424191]||[http://factordb.com/cert.php?id=1100000000633424191] |- |16||2343||5BC₃₇₀₀D||(459×16³⁷⁰¹+1)/5||[http://factordb.com/index.php?id=1100000000993764322]||[http://factordb.com/cert.php?id=1100000000993764322] |- |16||2344||D0B₁₇₈₀₄||(3131×16¹⁷⁸⁰⁴−11)/15||[http://factordb.com/index.php?id=1100000003589278511]||[http://factordb.com/cert.php?id=1100000003589278511] |- |18||547||80₂₉₈B||8×18²⁹⁹+11||[http://factordb.com/index.php?id=1100000002355574745]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has sum-of-two-cubes algebraic factorization, 6×18⁹⁹+1 is an algebraic factor of ''N''+1, factordb entry of 6×18⁹⁹+1 is [http://factordb.com/index.php?id=1100000000900149167] |- |18||548||H₇₆₆FH||18⁷⁶⁸−37||[http://factordb.com/index.php?id=1100000003590430490]||[http://factordb.com/cert.php?id=1100000003590430490] |- |18||549||C0₆₂₆₈C5||12×18⁶²⁷⁰+221||[http://factordb.com/index.php?id=1100000003590442437]||[http://factordb.com/cert.php?id=1100000003590442437] |- |20||3301||H₂₄₇A0H||(17×20²⁵⁰−59677)/19||[http://factordb.com/index.php?id=1100000003590502619]||[http://factordb.com/cert.php?id=1100000003590502619] |- |20||3302||7₂₄₉A7||(7×20²⁵¹+1133)/19||[http://factordb.com/index.php?id=1100000003590502602]||[http://factordb.com/cert.php?id=1100000003590502602] |- |20||3303||J7₂₇₀||(368×20²⁷⁰−7)/19||[http://factordb.com/index.php?id=1100000002325395462]||[http://factordb.com/cert.php?id=1100000002325395462] |- |20||3304||J₃₃₀CCC7||20³³⁴−58953||[http://factordb.com/index.php?id=1100000003590502572]||[http://factordb.com/cert.php?id=1100000003590502572] |- |20||3305||40₃₈₇404B||4×20³⁹¹+32091||[http://factordb.com/index.php?id=1100000003590502563]||[http://factordb.com/cert.php?id=1100000003590502563] |- |20||3306||EC0₄₂₉7||292×20⁴³⁰+7||[http://factordb.com/index.php?id=1100000002633348702]||[http://factordb.com/cert.php?id=1100000002633348702] |- |20||3307||G₄₄₇99||(16×20⁴⁴⁹−2809)/19||[http://factordb.com/index.php?id=1100000000840126753]||[http://factordb.com/cert.php?id=1100000000840126753] |- |20||3308||3A₅₂₇3||(67×20⁵²⁸−143)/19||[http://factordb.com/index.php?id=1100000003590502531]||[http://factordb.com/cert.php?id=1100000003590502531] |- |20||3309||E₅₆₆C7||(14×20⁵⁶⁸−907)/19||[http://factordb.com/index.php?id=1100000003590502516]||[http://factordb.com/cert.php?id=1100000003590502516] |- |20||3310||JCJ₆₂₉||393×20⁶²⁹−1||[http://factordb.com/index.php?id=1100000001559454258]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |20||3311||J₆₅₅05J||20⁶⁵⁸−7881||[http://factordb.com/index.php?id=1100000003590502490]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has a large prime factor, factordb entry of this prime factor is [http://factordb.com/index.php?id=1100000003591067052], and primality certificate of this prime factor is [http://factordb.com/cert.php?id=1100000003591067052] |- |20||3312||50₁₁₆₃AJ||5×20¹¹⁶⁵+219||[http://factordb.com/index.php?id=1100000003590502412]||[http://factordb.com/cert.php?id=1100000003590502412] |- |20||3313||CD₂₄₄₉||(241×20²⁴⁴⁹−13)/19||[http://factordb.com/index.php?id=1100000002325393915]||[http://factordb.com/cert.php?id=1100000002325393915] |- |20||3314||G0₆₂₆₉D||16×20⁶²⁷⁰+13||[http://factordb.com/index.php?id=1100000003590539457]||[http://factordb.com/cert.php?id=1100000003590539457] |- |22||7984||I7G0₂₅₄H||8882×22²⁵⁵+17||[http://factordb.com/index.php?id=1100000003591372788]||[http://factordb.com/cert.php?id=1100000003591372788] |- |22||7985||D0₂₅₅5EEF||13×22²⁵⁹+60339||[http://factordb.com/index.php?id=1100000003591371932]||[http://factordb.com/cert.php?id=1100000003591371932] |- |22||7986||IK₃₂₂F||(398×22³²³−125)/21||[http://factordb.com/index.php?id=1100000000840384145]||[http://factordb.com/cert.php?id=1100000000840384145] |- |22||7987||C0₃₄₀G9||12×22³⁴²+361||[http://factordb.com/index.php?id=1100000000840384159]||[http://factordb.com/cert.php?id=1100000000840384159] |- |22||7988||77E₃₄₈K7||(485×22³⁵⁰+373)/3||[http://factordb.com/index.php?id=1100000003591369779]||[http://factordb.com/cert.php?id=1100000003591369779] |- |22||7989||J₃₇₉KJ||(19×22³⁸¹+443)/21||[http://factordb.com/index.php?id=1100000003591369027]||[http://factordb.com/cert.php?id=1100000003591369027] |- |22||7990||J₃₈₈EJ||(19×22³⁹⁰−2329)/21||[http://factordb.com/index.php?id=1100000003591367729]||[http://factordb.com/cert.php?id=1100000003591367729] |- |22||7991||DJ₄₀₀||(292×22⁴⁰⁰−19)/21||[http://factordb.com/index.php?id=1100000002325880110]||[http://factordb.com/cert.php?id=1100000002325880110] |- |22||7992||E₄₀₄K7||(2×22⁴⁰⁶+373)/3||[http://factordb.com/index.php?id=1100000003591366298]||[http://factordb.com/cert.php?id=1100000003591366298] |- |22||7993||66F₄₅₃B3||(971×22⁴⁵⁵−705)/7||[http://factordb.com/index.php?id=1100000003591365809]||[http://factordb.com/cert.php?id=1100000003591365809] |- |22||7994||L0₄₅₄B63||21×22⁴⁵⁷+5459||[http://factordb.com/index.php?id=1100000003591365331]||[http://factordb.com/cert.php?id=1100000003591365331] |- |22||7995||L₄₈₃G3||22⁴⁸⁵−129||[http://factordb.com/index.php?id=1100000003591364730]||[http://factordb.com/cert.php?id=1100000003591364730] |- |22||7996||E60₄₉₆L||314×22⁴⁹⁷+21||[http://factordb.com/index.php?id=1100000000632703239]||[http://factordb.com/cert.php?id=1100000000632703239] |- |22||7997||I₆₂₆AF||(6×22⁶²⁸−1259)/7||[http://factordb.com/index.php?id=1100000000632724334]||[http://factordb.com/cert.php?id=1100000000632724334] |- |22||7998||K0₇₆₀EC1||20×22⁷⁶³+7041||[http://factordb.com/index.php?id=1100000000632724415]||[http://factordb.com/cert.php?id=1100000000632724415] |- |22||7999||J0₇₆₇IGGJ||19×22⁷⁷¹+199779||[http://factordb.com/index.php?id=1100000003591362567]||[http://factordb.com/cert.php?id=1100000003591362567] |- |22||8000||7₉₅₉K7||(22⁹⁶¹+857)/3||[http://factordb.com/index.php?id=1100000003591361817]||[http://factordb.com/cert.php?id=1100000003591361817] |- |22||8001||L₂₃₈₅KE7||22²³⁸⁸−653||[http://factordb.com/index.php?id=1100000003591360774]||[http://factordb.com/cert.php?id=1100000003591360774] |- |22||8002||7₃₈₁₅2L||(22³⁸¹⁷−289)/3||[http://factordb.com/index.php?id=1100000003591359839]||[http://factordb.com/cert.php?id=1100000003591359839] |- |24||3400||I0₂₄₁I5||18×24²⁴³+437||[http://factordb.com/index.php?id=1100000002633360037]||[http://factordb.com/cert.php?id=1100000002633360037] |- |24||3401||D0₂₅₉KKD||13×24²⁶²+12013||[http://factordb.com/index.php?id=1100000003593270725]||[http://factordb.com/cert.php?id=1100000003593270725] |- |24||3402||C7₂₉₈||(283×24²⁹⁸−7)/23||[http://factordb.com/index.php?id=1100000002326181235]||[http://factordb.com/cert.php?id=1100000002326181235] |- |24||3403||20₃₁₃7||2×24³¹⁴+7||[http://factordb.com/index.php?id=1100000002355610241]||[http://factordb.com/cert.php?id=1100000002355610241] |- |24||3404||BC0₃₃₁B||276×24³³²+11||[http://factordb.com/index.php?id=1100000002633359842]||[http://factordb.com/cert.php?id=1100000002633359842] |- |24||3405||N₂₆₄₄LLN||24²⁶⁴⁷−1201||[http://factordb.com/index.php?id=1100000003593270089]||[http://factordb.com/cert.php?id=1100000003593270089] |- |24||3406||D₂₆₉₈LD||(13×24²⁷⁰⁰+4403)/23||[http://factordb.com/index.php?id=1100000003593269876]||[http://factordb.com/cert.php?id=1100000003593269876] |- |24||3407||A0₂₉₅₁8ID||10×24²⁹⁵⁴+5053||[http://factordb.com/index.php?id=1100000003593269654]||[http://factordb.com/cert.php?id=1100000003593269654] |- |24||3408||88N₅₉₅₁||201×24⁵⁹⁵¹−1||[http://factordb.com/index.php?id=1100000003593275880]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |24||3409||N00N₈₁₂₉LN||13249×24⁸¹³¹−49||[http://factordb.com/index.php?id=1100000003593391606]||[http://factordb.com/cert.php?id=1100000003593391606] |- |30||2613||AN₂₀₆||(313×30²⁰⁶−23)/29||[http://factordb.com/index.php?id=1100000002327651073]||[http://factordb.com/cert.php?id=1100000002327651073] |- |30||2614||M₂₄₁QB||(22×30²⁴³+3139)/29||[http://factordb.com/index.php?id=1100000003593408295]||[http://factordb.com/cert.php?id=1100000003593408295] |- |30||2615||M0₅₄₇SS7||22×30⁵⁵⁰+26047||[http://factordb.com/index.php?id=1100000003593407988]||[http://factordb.com/cert.php?id=1100000003593407988] |- |30||2616||C0₁₀₂₂1||12×30¹⁰²³+1||[http://factordb.com/index.php?id=1100000000785448736]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |30||2617||5₄₈₈₂J||(5×30⁴⁸⁸³+401)/29||[http://factordb.com/index.php?id=1100000002327649423]||[http://factordb.com/cert.php?id=1100000002327649423] |- |30||2619||OT₃₄₂₀₅||25×30³⁴²⁰⁵−1||[http://factordb.com/index.php?id=1100000000800812865]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |} ==Unproven PRPs== {|class=wikitable |base (''b'')||index of this quasi-minimal prime in base ''b'' (assuming the primality of all PRP in base ''b'')||unproven PRP (base-''b'' form)||unproven PRP (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||factordb entry of this PRP |- |11||1068||57₆₂₆₆₈||(57×11⁶²⁶⁶⁸−7)/10||[http://factordb.com/index.php?id=1100000003573679860] |- |13||3194||C5₂₃₇₅₅C||(149×13²³⁷⁵⁶+79)/12||[http://factordb.com/index.php?id=1100000003590647776] |- |13||3195||80₃₂₀₁₇111||8×13³²⁰²⁰+183||[http://factordb.com/index.php?id=1100000000490878060] |- |16||2345||DB₃₂₂₃₄||(206×16³²²³⁴−11)/15||[http://factordb.com/index.php?id=1100000002383583629] |- |16||2346||4₇₂₇₈₅DD||(4×16⁷²⁷⁸⁷+2291)/15||[http://factordb.com/index.php?id=1100000003615909841] |- |22||8003||BK₂₂₀₀₁5||(251×22²²⁰⁰²−335)/21||[http://factordb.com/index.php?id=1100000003594696838] |- |30||2618||I0₂₄₆₀₈D||18×30²⁴⁶⁰⁹+13||[http://factordb.com/index.php?id=1100000003593967511] |} All these PRPs pass the [[w:Miller–Rabin primality test|Miller–Rabin primality test]] to bases 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and 61, and pass the [[w:Lucas pseudoprime#Strong Lucas pseudoprimes|strong Lucas primality test]] with parameters (''P'', ''Q'') defined by Selfridge's Method ''A'', and [[w:Trial division|trial factored]] to 10¹⁶. (Thus, they pass the [[w:Baillie–PSW primality test|Baillie–PSW primality test]]) ==Proof== ===Base 2=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. ===Base 3=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (2,1), (2,2) * Case (1,1): ** Since 12, 21, 111 are primes, we only need to consider the family 1{0}1 (since any digits 1, 2 between them will produce smaller primes) *** All numbers of the form 1{0}1 are divisible by 2, thus cannot be prime. * Case (1,2): ** 12 is prime, and thus the only minimal prime in this family. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,2): ** Since 21, 12 are primes, we only need to consider the family 2{0,2}2 (since any digits 1 between them will produce smaller primes) *** All numbers of the form 2{0,2}2 are divisible by 2, thus cannot be prime. ===Base 4=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (2,1), (2,3), (3,1), (3,3) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 11, 31, 221 are primes, we only need to consider the family 2{0}1 (since any digits 1, 2, 3 between them will produce smaller primes) *** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 31, 13, 23 are primes, we only need to consider the family 3{0,3}3 (since any digits 1, 2 between them will produce smaller primes) *** All numbers of the form 3{0,3}3 are divisible by 3, thus cannot be prime. ===Base 5=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4) * Case (1,1): ** Since 12, 21, 111, 131 are primes, we only need to consider the family 1{0,4}1 (since any digits 1, 2, 3 between them will produce smaller primes) *** All numbers of the form 1{0,4}1 are divisible by 2, thus cannot be prime. * Case (1,2): ** 12 is prime, and thus the only minimal prime in this family. * Case (1,3): ** Since 12, 23, 43, 133 are primes, we only need to consider the family 1{0,1}3 (since any digits 2, 3, 4 between them will produce smaller primes) *** Since 111 is prime, we only need to consider the families 1{0}3 and 1{0}1{0}3 (since any digit combo 11 between (1,3) will produce smaller primes) **** All numbers of the form 1{0}3 are divisible by 2, thus cannot be prime. **** For the 1{0}1{0}3 family, since 10103 is prime, we only need to consider the families 1{0}13 and 11{0}3 (since any digit combo 010 between (1,3) will produce smaller primes) ***** The smallest prime of the form 1{0}13 is 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013, which can be written as 1(0^93)13 and equal the prime 5^95+8 ([http://factordb.com/index.php?id=1100000000034686071 factordb]) ***** All numbers of the form 11{0}3 are divisible by 3, thus cannot be prime. * Case (1,4): ** Since 12, 34, 104 are primes, we only need to consider the family 1{1,4}4 (since any digits 0, 2, 3 between them will produce smaller primes) *** Since 111, 414 are primes, we only need to consider the families 1{4}4 and 11{4}4 (since any digit combo 11 or 41 between them will produce smaller primes) **** The smallest prime of the form 1{4}4 is 14444. **** All numbers of the form 11{4}4 are divisible by 2, thus cannot be prime. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,2): ** Since 21, 23, 12, 32 are primes, we only need to consider the family 2{0,2,4}2 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 2{0,2,4}2 are divisible by 2, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,4): ** Since 21, 23, 34 are primes, we only need to consider the family 2{0,2,4}4 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 2{0,2,4}4 are divisible by 2, thus cannot be prime. * Case (3,1): ** Since 32, 34, 21 are primes, we only need to consider the family 3{0,1,3}1 (since any digits 2, 4 between them will produce smaller primes) *** Since 313, 111, 131, 3101 are primes, we only need to consider the families 3{0,3}1 and 3{0,3}11 (since any digit combo 10, 11, 13 between (3,1) will produce smaller primes) **** For the 3{0,3}1 family, we can separate this family to four families: ***** For the 30{0,3}01 family, we have the prime 30301, and the remain case is the family 30{0}01. ****** All numbers of the form 30{0}01 are divisible by 2, thus cannot be prime. ***** For the 30{0,3}31 family, note that there must be an even number of 3's between (30,31), or the result number will be divisible by 2 and cannot be prime. ****** Since 33331 is prime, any digit combo 33 between (30,31) will produce smaller primes. ******* Thus, the only possible prime is the smallest prime in the family 30{0}31, and this prime is 300031. ***** For the 33{0,3}01 family, note that there must be an even number of 3's between (33,01), or the result number will be divisible by 2 and cannot be prime. ****** Since 33331 is prime, any digit combo 33 between (33,01) will produce smaller primes. ******* Thus, the only possible prime is the smallest prime in the family 33{0}01, and this prime is 33001. ***** For the 33{0,3}31 family, we have the prime 33331, and the remain case is the family 33{0}31. ****** All numbers of the form 33{0}31 are divisible by 2, thus cannot be prime. **** All numbers of the form 3{0,3}11 are divisible by 3, thus cannot be prime. * Case (3,2): ** 32 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 32, 34, 23, 43, 313 are primes, we only need to consider the family 3{0,3}3 (since any digits 1, 2, 4 between them will produce smaller primes) *** All numbers of the form 3{0,3}3 are divisible by 3, thus cannot be prime. * Case (3,4): ** 34 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 43, 21, 401 are primes, we only need to consider the family 4{1,4}1 (since any digits 0, 2, 3 between them will produce smaller primes) *** Since 414, 111 are primes, we only need to consider the families 4{4}1 and 4{4}11 (since any digit combo 14 or 11 between them will produce smaller primes) **** The smallest prime of the form 4{4}1 is 44441. **** All numbers of the form 4{4}11 are divisible by 2, thus cannot be prime. * Case (4,2): ** Since 43, 12, 32 are primes, we only need to consider the family 4{0,2,4}2 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 4{0,2,4}2 are divisible by 2, thus cannot be prime. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,4): ** Since 43, 34, 414 are primes, we only need to consider the family 4{0,2,4}4 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 4{0,2,4}4 are divisible by 2, thus cannot be prime. ===Base 6=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,5), (2,1), (2,5), (3,1), (3,5), (4,1), (4,5), (5,1), (5,5) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 11, 21, 31, 51 are primes, we only need to consider the family 4{0,4}1 (since any digits 1, 2, 3, 5 between them will produce smaller primes) *** Since 4401 and 4441 are primes, we only need to consider the families 4{0}1 and 4{0}41 (since any digits combo 40 and 44 between them will produce smaller primes) **** All numbers of the form 4{0}1 are divisible by 5, thus cannot be prime. **** The smallest prime of the form 4{0}41 is 40041 * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 15, 25, 35, 45 are primes, we only need to consider the family 5{0,5}5 (since any digits 1, 2, 3, 4 between them will produce smaller primes) *** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. ===Base 7=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) * Case (1,1): ** Since 14, 16, 41, 61, 131 are primes, we only need to consider the family 1{0,1,2,5}1 (since any digits 3, 4, 6 between them will produce smaller primes) *** Since the digit sum of primes must be odd (otherwise the number will be divisible by 2, thus cannot be prime), there is an odd total number of 1 and 5 in the {} **** If there are >=3 number of 1 and 5 in the {}: ***** If there is 111 in the {}, then we have the prime 11111 ***** If there is 115 in the {}, then the prime 115 is a subsequence ***** If there is 151 in the {}, then the prime 115 is a subsequence ***** If there is 155 in the {}, then the prime 155 is a subsequence ***** If there is 511 in the {}, then the current number is 15111, which has digit sum = 12, but digit sum divisible by 3 will cause the number divisible by 3 and cannot be prime, and we cannot add more 1 or 5 to this number (to avoid 11111, 155, 515, 551 as subsequence), thus we must add at least one 2 to this number, but then the number has both 2 and 5, and will have either 25 or 52 as subsequence, thus cannot be minimal prime ***** If there is 515 in the {}, then the prime 515 is a subsequence ***** If there is 551 in the {}, then the prime 551 is a subsequence ***** If there is 555 in the {}, then the prime 551 is a subsequence **** Thus there is only one 1 (and no 5) or only one 5 (and no 1) in the {}, i.e. we only need to consider the families 1{0,2}1{0,2}1 and 1{0,2}5{0,2}1 ***** For the 1{0,2}1{0,2}1 family, since 1211 is prime, we only need to consider the family 1{0}1{0,2}1 ****** Since all numbers of the form 1{0}1{0}1 are divisible by 3 and cannot be prime, we only need to consider the family 1{0}1{0}2{0}1 ******* Since 11201 is prime, we only need to consider the family 1{0}1{0}21 ******** The smallest prime of the form 11{0}21 is 1100021 ******** All numbers of the form 101{0}21 are divisible by 5, thus cannot be prime ******** The smallest prime of the form 1001{0}21 is 100121 ********* Since this prime has no 0 between 1{0}1 and 21, we do not need to consider more families ***** For the 1{0,2}5{0,2}1 family, since 25 and 52 are primes, we only need to consider the family 1{0}5{0}1 ****** Since 1051 is prime, we only need to consider the family 15{0}1 ******* The smallest prime of the form 15{0}1 is 150001 * Case (1,2): ** Since 14, 16, 32, 52 are primes, we only need to consider the family 1{0,1,2}2 (since any digits 3, 4, 5, 6 between them will produce smaller primes) *** Since 1112 and 1222 are primes, there is at most one 1 and at most one 2 in {} **** If there are one 1 and one 2 in {}, then the digit sum is 6, and the number will be divisible by 6 and cannot be prime. **** If there is one 1 but no 2 in {}, then the digit sum is 4, and the number will be divisible by 2 and cannot be prime. **** If there is no 1 but one 2 in {}, then the form is 1{0}2{0}2 ***** Since 1022 and 1202 are primes, we only need to consider the number 122 ****** 122 is not prime. **** If there is no 1 and no 2 in {}, then the digit sum is 3, and the number will be divisible by 3 and cannot be prime. * Case (1,3): ** Since 14, 16, 23, 43, 113, 133 are primes, we only need to consider the family 1{0,5}3 (since any digits 1, 2, 3, 4, 6 between them will produce smaller primes) *** Since 155 is prime, we only need to consider the family 1{0}3 and 1{0}5{0}3 **** All numbers of the form 1{0}3 are divisible by 2, thus cannot be prime. **** All numbers of the form 1{0}5{0}3 are divisible by 3, thus cannot be prime. * Case (1,4): ** 14 is prime, and thus the only minimal prime in this family. * Case (1,5): ** Since 14, 16, 25, 65, 115, 155 are primes, we only need to consider the family 1{0,3}5 (since any digits 1, 2, 4, 5, 6 between them will produce smaller primes) *** All numbers of the form 1{0,3}5 are divisible by 3, thus cannot be prime. * Case (1,6): ** 16 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 25, 41, 61, 221 are primes, we only need to consider the family 2{0,1}1 (since any digits 2, 3, 4, 5, 6 between them will produce smaller primes) *** Since 2111 is prime, we only need to consider the families 2{0}1 and 2{0}1{0}1 **** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. **** All numbers of the form 2{0}1{0}1 are divisible by 2, thus cannot be prime. * Case (2,2): ** Since 23, 25, 32, 52, 212 are primes, we only need to consider the family 2{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,4): ** Since 23, 25, 14 are primes, we only need to consider the family 2{0,2,4,6}4 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}4 are divisible by 2, thus cannot be prime. * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (2,6): ** Since 23, 25, 16, 56 are primes, we only need to consider the family 2{0,2,4,6}6 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}6 are divisible by 2, thus cannot be prime. * Case (3,1): ** Since 32, 41, 61 are primes, we only need to consider the family 3{0,1,3,5}1 (since any digits 2, 4, 6 between them will produce smaller primes) *** Since 551 is prime, we only need to consider the family 3{0,1,3}1 and 3{0,1,3}5{0,1,3}1 (since any digits combo 55 between (3,1) will produce smaller primes) **** For the 3{0,1,3}1 family, since 3031 and 131 are primes, we only need to consider the families 3{0,1}1 and 3{3}3{0,1}1 (since any digits combo 03, 13 between (3,1) will produce smaller primes, thus for the digits between (3,1), all 3's must be before all 0's and 1's, and thus we can let the red 3 in 3{3}3{0,1}1 be the rightmost 3 between (3,1), all digits before this 3 must be 3's, and all digits after this 3 must be either 0's or 1's) ***** For the 3{0,1}1 family: ****** If there are >=2 0's and >=1 1's between (3,1), then at least one of 30011, 30101, 31001 will be a subsequence. ****** If there are no 1's between (3,1), then the form will be 3{0}1 ******* All numbers of the form 3{0}1 are divisible by 2, thus cannot be prime. ****** If there are no 0's between (3,1), then the form will be 3{1}1 ******* The smallest prime of the form 3{1}1 is 31111 ****** If there are exactly 1 0's between (3,1), then there must be <3 1's between (3,1), or 31111 will be a subsequence. ******* If there are 2 1's between (3,1), then the digit sum is 6, thus the number is divisible by 6 and cannot be prime. ******* If there are 1 1's between (3,1), then the number can only be either 3101 or 3011 ******** Neither 3101 nor 3011 is prime. ******* If there are no 1's between (3,1), then the number must be 301 ******** 301 is not prime. ***** For the 3{3}3{0,1}1 family: ****** If there are at least one 3 between (3,3{0,1}1) and at least one 1 between (3{3}3,1), then 33311 will be a subsequence. ****** If there are no 3 between (3,3{0,1}1), then the form will be 33{0,1}1 ******* If there are at least 3 1's between (33,1), then 31111 will be a subsequence. ******* If there are exactly 2 1's between (33,1), then the digit sum is 12, thus the number is divisible by 3 and cannot be prime. ******* If there are exactly 1 1's between (33,1), then the digit sum is 11, thus the number is divisible by 2 and cannot be prime. ******* If there are no 1's between (33,1), then the form will be 33{0}1 ******** The smallest prime of the form 33{0}1 is 33001 ****** If there are no 1 between (3{3}3,1), then the form will be 3{3}3{0}1 ******* If there are at least 2 0's between (3{3}3,1), then 33001 will be a subsequence. ******* If there are exactly 1 0's between (3{3}3,1), then the form is 3{3}301 ******** The smallest prime of the form 3{3}301 is 33333301 ******* If there are no 0's between (3{3}3,1), then the form is 3{3}31 ******** The smallest prime of the form 3{3}31 is 33333333333333331 **** For the 3{0,1,3}5{0,1,3}1 family, since 335 is prime, we only need to consider the family 3{0,1}5{0,1,3}1 ***** Numbers containing 3 between (3{0,1}5,1): ****** The form is 3{0,1}5{0,1,3}3{0,1,3}1 ******* Since 3031 and 131 are primes, we only need to consider the family 35{3}3{0,1,3}1 (since any digits combo 03, 13 between (3,1) will produce smaller primes) ******** Since 533 is prime, we only need to consider the family 353{0,1}1 (since any digits combo 33 between (35,1) will produce smaller primes) ********* Since 5011 is prime, we only need to consider the family 353{1}{0}1 (since any digits combo 01 between (353,1) will produce smaller primes) ********** If there are at least 3 1's between (353,{0}1), then 31111 will be a subsequence. ********** If there are exactly 2 1's between (353,{0}1), then the digit sum is 20, thus the number is divisible by 2 and cannot be prime. ********** If there are exactly 1 1's between (353,{0}1), then the form is 3531{0}1 *********** The smallest prime of the form 3531{0}1 is 3531001, but it is not minimal prime since 31001 is prime. ********** If there are no 1's between (353,{0}1), then the digit sum is 15, thus the number is divisible by 6 and cannot be prime. ***** Numbers not containing 3 between (3{0,1}5,1): ****** The form is 3{0,1}5{0,1}1 ******* If there are >=2 0's and >=1 1's between (3,1), then at least one of 30011, 30101, 31001 will be a subsequence. ******* If there are no 1's between (3,1), then the form will be 3{0}5{0}1 ******** All numbers of the form 3{0}5{0}1 are divisible by 3, thus cannot be prime. ******* If there are no 0's between (3,1), then the form will be 3{1}5{1}1 ******** If there are >=3 1's between (3,1), then 31111 will be a subsequence. ******** If there are exactly 2 1's between (3,1), then the number can only be 31151, 31511, 35111 ********* None of 31151, 31511, 35111 are primes. ******** If there are exactly 1 1's between (3,1), then the digit sum is 13, thus the number is divisible by 2 and cannot be prime. ******** If there are no 1's between (3,1), then the number is 351 ********* 351 is not prime. ******* If there are exactly 1 0's between (3,1), then the form will be 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1 ******** No matter 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1, if there are >=3 1's between (3,1), then 31111 will be a subsequence. ******** If there are exactly 2 1's between (3,1), then the number can only be 311051, 310151, 310511, 301151, 301511, 305111, 311501, 315101, 315011, 351101, 351011, 350111 ********* Of these numbers, 311051, 301151, 311501, 351101, 350111 are primes. ********** However, 311051, 301151, 311501 have 115 as subsequence, and 350111 has 5011 as subsequence, thus only 351101 is minimal prime. ******** No matter 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1, if there are exactly 1 1's between (3,1), then the digit sum is 13, thus the number is divisible by 2 and cannot be prime. ******** If there are no 1's between (3,1), then the number is 3051 for 3{1}0{1}5{1}1 or 3501 for 3{1}5{1}0{1}1 ********* Neither 3051 nor 3501 is prime. * Case (3,2): ** 32 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 32, 23, 43, 313 are primes, we only need to consider the family 3{0,3,5,6}3 (since any digits 1, 2, 4 between them will produce smaller primes) *** If there are >=2 5's in {}, then 553 will be a subsequence. *** If there are no 5's in {}, then the family will be 3{0,3,6}3 **** All numbers of the form 3{0,3,6}3 are divisible by 3, thus cannot be prime. *** If there are exactly 1 5's in {}, then the family will be 3{0,3,6}5{0,3,6}3 **** Since 335, 65, 3503, 533, 56 are primes, we only need to consider the family 3{0}53 (since any digit 3, 6 between (3,5{0,3,6}3) and any digit 0, 3, 6 between (3{0,3,6}5,3) will produce smaller primes) ***** The smallest prime of the form 3{0}53 is 300053 * Case (3,4): ** Since 32, 14, 304, 344, 364 are primes, we only need to consider the family 3{3,5}4 (since any digits 0, 1, 2, 4, 6 between them will produce smaller primes) *** Since 3334 and 335 are primes, we only need to consider the family 3{5}4 and 3{5}34 (since any digits combo 33, 35 between them will produce smaller primes) **** The smallest prime of the form 3{5}4 is 35555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555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with 9234 5's, which can be written as 3(5^9234)4 and equal the prime (23*7^9235-11)/6 ([http://factordb.com/index.php?id=1100000002766595757 factordb]) ([http://factordb.com/cert.php?id=1100000002766595757 primality certificate]) (not minimal prime, since 35555 and 5554 are primes) **** The smallest prime of the form 3{5}34 is 355555555555555555555555555555555555555555555555555555555555555534 (not minimal prime, since 35555, 553, and 5554 are primes) * Case (3,5): ** Since 32, 25, 65, 335 are primes, we only need to consider the family 3{0,1,4,5}5 (since any digits 2, 3, 6 between them will produce smaller primes) *** If there are at least one 1's and at least one 5's in {}, then either 155 or 515 will be a subsequence. *** If there are at least one 1's and at least one 4's in {}, then either 14 or 41 will be a subsequence. *** If there are at least two 1's in {}, then 115 will be a subsequence. *** If there are exactly one 1's and no 4's or 5's in {}, then the family will be 3{0}1{0}5 **** All numbers of the form 3{0}1{0}5 are divisible by 3, thus cannot be prime. *** If there is no 1's in {}, then the family will be 3{0,4,5}5 **** If there are at least to 4's in {}, then 344 and 445 will be subsequences. **** If there is no 4's in {}, then the family will be 3{0,5}5 ***** Since 3055 and 3505 are primes, we only need to consider the families 3{0}5 and 3{5}5 ****** All numbers of the form 3{0}5 are divisible by 2, thus cannot be prime. ****** The smallest prime of the form 3{5}5 is 35555 **** If there is exactly one 4's in {}, then the family will be 3{0,5}4{0,5}5 ***** Since 304, 3545 are primes, we only need to consider the families 34{0,5}5 (since any digits 0 or 5 between (3,4{0,5}5) will produce small primes) ****** All numbers of the form 34{0,5}5 are divisible by 5, thus cannot be prime. * Case (3,6): ** Since 32, 16, 56, 346 are primes, we only need to consider the family 3{0,3,6}6 (since any digits 1, 2, 4, 5 between them will produce smaller primes) *** All numbers of the form 3{0,3,6}6 are divisible by 3, thus cannot be prime. * Case (4,1): ** 41 is prime, and thus the only minimal prime in this family. * Case (4,2): ** Since 41, 43, 32, 52 are primes, we only need to consider the family 4{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 4{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,4): ** Since 41, 43, 14 are primes, we only need to consider the family 4{0,2,4,5,6}4 (since any digits 1, 3 between them will produce smaller primes) *** If there is no 5's in {}, then the family will be 4{0,2,4,6}4 **** All numbers of the form 4{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there is at least one 5's in {}, then there cannot be 2 in {} (since if so, then either 25 or 52 will be a subsequence) and there cannot be 6 in {} (since if so, then either 65 or 56 will be a subsequence), thus the family is 4{0,4,5}5{0,4,5}4 **** Since 445, 4504, 544 are primes, we only need to consider the family 4{0,5}5{5}4 (since any digit 4 between (4,5{0,4,5}4) and any digit 0, 4 between (4{0,4,5}5,4) will produce smaller primes) ***** If there are at least two 0's between (4,5{0,4,5}4), then 40054 will be a subsequence. ***** If there is no 0's between (4,5{0,4,5}4), then the family will be 4{5}5{5}4, which is equivalent to 4{5}4 ****** The smallest prime of the form 4{5}4 is 45555555555555554 (not minimal prime, since 4555 and 5554 are primes) ***** If there is exactly one 0's between (4,5{0,4,5}4), then the family will be 4{5}0{5}5{5}4 ****** Since 4504 is prime, we only need to consider the family 40{5}5{5}4 (since any digit 5 between (4,0{5}5{5}4) will produce small primes), which is equivalent to 40{5}4 ******* The smallest prime of the form 40{5}4 is 405555555555555554 (not minimal prime, since 4555 and 5554 are primes) * Case (4,5): ** Since 41, 43, 25, 65, 445 are primes, we only need to consider the family 4{0,5}5 (since any digits 1, 2, 3, 4, 6 between them will produce smaller primes) *** If there are at least two 5's in {}, then 4555 will be a subsequence. *** If there is exactly one 5's in {}, then the digit sum is 20, and the number will be divisible by 2 and cannot be prime. *** If there is no 5's in {}, then the family will be 4{0}5 **** All numbers of the form 4{0}5 are divisible by 3, thus cannot be prime. * Case (4,6): ** Since 41, 43, 16, 56 are primes, we only need to consider the family 4{0,2,4,6}6 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 4{0,2,4,6}6 are divisible by 2, thus cannot be prime. * Case (5,1): ** Since 52, 56, 41, 61, 551 are primes, we only need to consider the family 5{0,1,3}1 (since any digits 2, 4, 5, 6 between them will produce smaller primes) *** If there are at least two 3's in {}, then 533 will be a subsequence. *** If there is no 3's in {}, then the family will be 5{0,1}1 **** Since 5011 is prime, we only need to consider the family 5{1}{0}1 ***** Since 11111 is prime, we only need to consider the families 5{0}1, 51{0}1, 511{0}1, 5111{0}1 (since any digits combo 1111 between (5,1) will produce small primes) ****** All numbers of the form 5{0}1 are divisible by 6, thus cannot be prime. ****** The smallest prime of the form 51{0}1 is 5100000001 ****** All numbers of the form 511{0}1 are divisible by 2, thus cannot be prime. ****** All numbers of the form 5111{0}1 are divisible by 3, thus cannot be prime. *** If there is exactly one 3's in {}, then the family will be 5{0,1}3{0,1}1 **** If there is at least one 1's between (5,3{0,1}1), then 131 will be a subsequence. ***** Thus we only need to consider the family 5{0}3{0,1}1 ****** If there are no 1's between (5{0}3,1), then the digit sum is 12, and the number will be divisible by 3 and cannot be prime. ****** If there are exactly one 1's between (5{0}3,1), then the digit sum is 13, and the number will be divisible by 2 and cannot be prime. ****** If there are exactly three 1's between (5{0}3,1), then the digit sum is 15, and the number will be divisible by 6 and cannot be prime. ****** If there are at least four 1's between (5{0}3,1), then 11111 will be a subsequence. ****** If there are exactly two 1's between (5{0}3,1), then the family will be 5{0}3{0}1{0}1{0}1 ******* Since 5011 is prime, we only need to consider the family 5311{0}1 (since any digit 0 between (5,1{0}1) will produce small primes, this includes the leftmost three {} in 5{0}3{0}1{0}1{0}1, and thus only the rightmost {} can contain 0) ******** The smallest prime of the form 5311{0}1 is 531101 * Case (5,2): ** 52 is prime, and thus the only minimal prime in this family. * Case (5,3): ** Since 52, 56, 23, 43, 533, 553 are primes, we only need to consider the family 5{0,1}3 (since any digits 2, 3, 4, 5, 6 between them will produce smaller primes) *** If there are at least two 1's in {}, then 113 will be a subsequence. *** If there is exactly one 1's in {}, then the digit sum is 12, and the number will be divisible by 3 and cannot be prime. *** If there is no 1's in {}, then the digit sum is 11, and the number will be divisible by 2 and cannot be prime. * Case (5,4): ** Since 52, 56, 14, 544 are primes, we only need to consider the family 5{0,3,5}4 (since any digits 1, 2, 4, 6 between them will produce smaller primes) *** If there are no 5's in {}, then the family will be 5{0,3}4 **** All numbers of the form 5{0,3}4 are divisible by 3, thus cannot be prime. *** If there are at least one 5's and at least one 3's in {}, then either 535 or 553 will be a subsequence. *** If there are exactly one 5's and no 3's in {}, then the digit sum is 20, and the number will be divisible by 2 and cannot be prime. *** If there are at least two 5's in {}, then 5554 will be a subsequence. * Case (5,5): ** Since 52, 56, 25, 65, 515, 535 are primes, we only need to consider the family 5{0,4,5}5 (since any digits 1, 2, 3, 6 between them will produce smaller primes) *** If there are no 4's in {}, then the family will be 5{0,5}5 **** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. *** If there are no 5's in {}, then the family will be 5{0,4}5 **** All numbers of the form 5{0,4}5 are divisible by 2, thus cannot be prime. *** If there are at least one 4's and at least one 5's in {}, then either 5455 or 5545 will be a subsequence. * Case (5,6): ** 56 is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,2): ** Since 61, 65, 32, 52 are primes, we only need to consider the family 6{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 6{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (6,3): ** Since 61, 65, 23, 43 are primes, we only need to consider the family 6{0,3,6}3 (since any digits 1, 2, 4, 5 between them will produce smaller primes) *** All numbers of the form 6{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (6,4): ** Since 61, 65, 14 are primes, we only need to consider the family 6{0,2,3,4,6}4 (since any digits 1, 5 between them will produce smaller primes) *** If there is no 3's in {}, then the family will be 6{0,2,4,6}4 **** All numbers of the form 6{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there are exactly two 3's in {}, then the family will be 6{0,2,4,6}3{0,2,4,6}3{0,2,4,6}4 **** All numbers of the form 6{0,2,4,6}3{0,2,4,6}3{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there are at least three 3's in {}, then 3334 will be a subsequence. *** If there is exactly one 3's in {}, then the family will be 6{0,2,4,6}3{0,2,4,6}4 **** If there is 0 between (6,3{0,2,4,6}4), then 6034 will be a subsequence. **** If there is 2 between (6,3{0,2,4,6}4), then 23 will be a subsequence. **** If there is 4 between (6,3{0,2,4,6}4), then 43 will be a subsequence. **** If there is 6 between (6,3{0,2,4,6}4), then 6634 will be a subsequence. **** If there is 0 between (6{0,2,4,6}3,4), then 304 will be a subsequence. **** If there is 2 between (6{0,2,4,6}3,4), then 32 will be a subsequence. **** If there is 4 between (6{0,2,4,6}3,4), then 344 will be a subsequence. **** If there is 6 between (6{0,2,4,6}3,4), then 364 will be a subsequence. **** Thus the number can only be 634 ***** 634 is not prime. * Case (6,5): ** 65 is prime, and thus the only minimal prime in this family. * Case (6,6): ** Since 61, 65, 16, 56 are primes, we only need to consider the family 6{0,2,3,4,6}6 (since any digits 1, 5 between them will produce smaller primes) *** If there is no 3's in {}, then the family will be 6{0,2,4,6}6 **** All numbers of the form 6{0,2,4,6}6 are divisible by 2, thus cannot be prime. *** If there is no 2's and no 4's in {}, then the family will be 6{0,3,6}6 **** All numbers of the form 6{0,3,6}6 are divisible by 3, thus cannot be prime. *** If there is at least one 3's and at least one 2's in {}, then either 32 or 23 will be a subsequence. *** If there is at least one 3's and at least one 4's in {}, then either 346 or 43 will be a subsequence. ===Base 8=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (1,5), (1,7), (2,1), (2,3), (2,5), (2,7), (3,1), (3,3), (3,5), (3,7), (4,1), (4,3), (4,5), (4,7), (5,1), (5,3), (5,5), (5,7), (6,1), (6,3), (6,5), (6,7), (7,1), (7,3), (7,5), (7,7) * Case (1,1): ** Since 13, 15, 21, 51, 111, 141, 161 are primes, we only need to consider the family 1{0,7}1 (since any digits 1, 2, 3, 4, 5, 6 between them will produce smaller primes) *** Since 107, 177, 701 are primes, we only need to consider the number 171 and the family 1{0}1 (since any digits combo 07, 70, 77 between them will produce smaller primes) **** 171 is not prime. **** All numbers of the form 1{0}1 factored as 10^n+1 = (2^n+1) * (4^n-2^n+1) (n≥1) (and since if n≥1, 2^n+1 ≥ 2^1+1 = 3 > 1, 4^n-2^n+1 ≥ 4^1-2^1+1 = 3 > 1, this factorization is nontrivial), thus cannot be prime. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (1,7): ** Since 13, 15, 27, 37, 57, 107, 117, 147, 177 are primes, we only need to consider the family 1{6}7 (since any digits 0, 1, 2, 3, 4, 5, 7 between them will produce smaller primes) *** The smallest prime of the form 1{6}7 is 16667 (not minimal prime, since 667 is prime) * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,5): ** Since 21, 23, 27, 15, 35, 45, 65, 75, 225, 255 are primes, we only need to consider the family 2{0}5 (since any digits 1, 2, 3, 4, 5, 6, 7 between them will produce smaller primes) *** All numbers of the form 2{0}5 are divisible by 7, thus cannot be prime. * Case (2,7): ** 27 is prime, and thus the only minimal prime in this family. * Case (3,1): ** Since 35, 37, 21, 51, 301, 361 are primes, we only need to consider the family 3{1,3,4}1 (since any digits 0, 2, 5, 6, 7 between them will produce smaller primes) *** Since 13, 343, 111, 131, 141, 431, 3331, 3411 are primes, we only need to consider the families 3{3}11, 33{1,4}1, 3{3,4}4{4}1 (since any digits combo 11, 13, 14, 33, 41, 43 between them will produce smaller primes) **** All numbers of the form 3{3}11 are divisible by 3, thus cannot be prime. **** For the 33{1,4}1 family, since 111 and 141 are primes, we only need to consider the families 33{4}1 and 33{4}11 (since any digits combo 11, 14 between them will produce smaller primes) ***** The smallest prime of the form 33{4}1 is 3344441 ***** All numbers of the form 33{4}11 are divisible by 301, thus cannot be prime. **** For the 3{3,4}4{4}1 family, since 3331 and 3344441 are primes, we only need to consider the families 3{4}1, 3{4}31, 3{4}341, 3{4}3441, 3{4}34441 (since any digits combo 33 or 34444 between (3,1) will produce smaller primes) ***** All numbers of the form 3{4}1 are divisible by 31, thus cannot be prime. ***** Since 4443 is prime, we only need to consider the numbers 3431, 34431, 34341, 344341, 343441, 3443441, 3434441, 34434441 (since any digit combo 444 between (3,3{4}1) will produce smaller primes) ****** None of 3431, 34431, 34341, 344341, 343441, 3443441, 3434441, 34434441 are primes. * Case (3,3): ** Since 35, 37, 13, 23, 53, 73, 343 are primes, we only need to consider the family 3{0,3,6}3 (since any digits 1, 2, 4, 5, 7 between them will produce smaller primes) *** All numbers of the form 3{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 21, 51, 401, 431, 471 are primes, we only need to consider the family 4{1,4,6}1 (since any digits 0, 2, 3, 5, 7 between them will produce smaller primes) *** Since 111, 141, 161, 661, 4611 are primes, we only need to consider the families 4{4}11, 4{4,6}4{1,4,6}1, 4{4}6{4}1 (since any digits combo 11, 14, 16, 61, 66 between them will produce smaller primes) **** The smallest prime of the form 4{4}11 is 44444444444444411 (not minimal prime, since 444444441 is prime) **** For the 4{4,6}4{1,4,6}1 family, we can separate this family to 4{4,6}41, 4{4,6}411, 4{4,6}461 ***** For the 4{4,6}41 family, since 661 and 6441 are primes, we only need to consider the families 4{4}41 and 4{4}641 (since any digits combo 64 or 66 between (4,41) will produce smaller primes) ****** The smallest prime of the form 4{4}41 is 444444441 ****** The smallest prime of the form 4{4}641 is 444641 ***** For the 4{4,6}411 family, since 661 and 6441 are primes, we only need to consider the families 4{4}411 and 4{4}6411 (since any digits combo 64 or 66 between (4,411) will produce smaller primes) ****** The smallest prime of the form 4{4}411 is 444444441 ****** The smallest prime of the form 4{4}6411 is 4444444444444446411 (not minimal prime, since 444444441 and 444641 are primes) ***** For the 4{4,6}461 family, since 661 is prime, we only need to consider the family 4{4}461 ****** The smallest prime of the form 4{4}461 is 4444444461 (not minimal prime, since 444444441 is prime) **** For the 4{4}6{4}1 family, since 6441 is prime, we only need to consider the families 4{4}61 and 4{4}641 (since any digits combo 44 between (4{4}6,1) will produce smaller primes) ***** The smallest prime of the form 4{4}61 is 4444444461 (not minimal prime, since 444444441 is prime) ***** The smallest prime of the form 4{4}641 is 444641 * Case (4,3): ** Since 45, 13, 23, 53, 73, 433, 463 are primes, we only need to consider the family 4{0,4}3 (since any digits 1, 2, 3, 5, 6, 7 between them will produce smaller primes) *** Since 4043 and 4443 are primes, we only need to consider the families 4{0}3 and 44{0}3 (since any digits combo 04, 44 between them will produce smaller primes) **** All numbers of the form 4{0}3 are divisible by 7, thus cannot be prime. **** All numbers of the form 44{0}3 are divisible by 3, thus cannot be prime. * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (4,7): ** Since 45, 27, 37, 57, 407, 417, 467 are primes, we only need to consider the family 4{4,7}7 (since any digits 0, 1, 2, 3, 5, 6 between them will produce smaller primes) *** Since 747 is prime, we only need to consider the families 4{4}7, 4{4}77, 4{7}7, 44{7}7 (since any digits combo 74 between (4,7) will produce smaller primes) **** The smallest prime of the form 4{4}7 is 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447, with 220 4's, which can be written as (4^220)7 and equal the prime (4*8^221+17)/7 ([http://factordb.com/index.php?id=1100000000416605822 factordb]) **** The smallest prime of the form 4{4}77 is 4444477 **** The smallest prime of the form 4{7}7 is 47777 **** The smallest prime of the form 44{7}7 is 4477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777, with 851 7's, which can be written as 44(7^851) and equal the prime 37*8^851-1 ([http://factordb.com/index.php?id=1100000000413677646 factordb]) (not minimal prime, since 47777 is prime) * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,3): ** 53 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 53, 57, 15, 35, 45, 65, 75 are primes, we only need to consider the family 5{0,2,5}5 (since any digits 1, 3, 4, 6, 7 between them will produce smaller primes) *** Since 225, 255, 5205 are primes, we only need to consider the families 5{0,5}5 and 5{0,5}25 (since any digits combo 20, 22, 25 between them will produce smaller primes) **** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. **** For the 5{0,5}25 family, since 500025 and 505525 are primes, we only need to consider the number 500525 the families 5{5}25, 5{5}025, 5{5}0025, 5{5}0525, 5{5}00525, 5{5}05025 (since any digits combo 000, 055 between (5,25) will produce smaller primes) ***** 500525 is not prime. ***** The smallest prime of the form 5{5}25 is 555555555555525 ***** The smallest prime of the form 5{5}025 is 55555025 ***** The smallest prime of the form 5{5}0025 is 5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555550025, with 184 5's, which can be written as (5^183)0025 and equal the prime (5*8^187-20333)/7 ([http://factordb.com/index.php?id=1100000002350205912 factordb]) (not minimal prime, since 55555025 and 555555555555525 are primes) ***** The smallest prime of the form 5{5}0525 is 5550525 ***** The smallest prime of the form 5{5}00525 is 5500525 ***** The smallest prime of the form 5{5}05025 is 5555555555555555555555505025 (not minimal prime, since 5550525, 55555025, and 555555555555525 are primes) * Case (5,7): ** 57 is prime, and thus the only minimal prime in this family. * Case (6,1): ** Since 65, 21, 51, 631, 661 are primes, we only need to consider the family 6{0,1,4,7}1 (since any digits 2, 3, 5, 6 between them will produce smaller primes) *** Numbers containing 4: (note that the number cannot contain two or more 4's, or 6441 will be a subsequence) **** The form is 6{0,1,7}4{0,1,7}1 ***** Since 141, 401, 471 are primes, we only need to consider the family 6{0,7}4{1}1 ****** Since 111 is prime, we only need to consider the families 6{0,7}41 and 6{0,7}411 ******* For the 6{0,7}41 family, since 60741 is prime, we only need to consider the family 6{7}{0}41 ******** Since 6777 is prime, we only need to consider the families 6{0}41, 67{0}41, 677{0}41 ********* All numbers of the form 6{0}41 are divisible by 3, thus cannot be prime. ********* All numbers of the form 67{0}41 are divisible by 13, thus cannot be prime. ********* All numbers of the form 677{0}41 are divisible by 3, thus cannot be prime. ******* For the 6{0,7}411 family, since 60411 is prime, we only need to consider the family 6{7}411 ******** The smallest prime of the form 6{7}411 is 67777411 (not minimal prime, since 6777 is prime) *** Numbers not containing 4: **** The form is 6{0,1,7}1 ***** Since 111 is prime, we only need to consider the families 6{0,7}1 and 6{0,7}1{0,7}1 ****** All numbers of the form 6{0,7}1 are divisible by 7, thus cannot be prime. ****** For the 6{0,7}1{0,7}1 family, since 711 and 6101 are primes, we only need to consider the family 6{0}1{7}1 ******* Since 60171 is prime, we only need to consider the families 6{0}11 and 61{7}1 ******** All numbers of the form 6{0}11 are divisible by 3, thus cannot be prime. ******** The smallest prime of the form 61{7}1 is 617771 (not minimal prime, since 6777 is prime) * Case (6,3): ** Since 65, 13, 23, 53, 73, 643 are primes, we only need to consider the family 6{0,3,6}3 (since any digits 1, 2, 4, 5, 7 between them will produce smaller primes) *** All numbers of the form 6{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (6,5): ** 65 is prime, and thus the only minimal prime in this family. * Case (6,7): ** Since 65, 27, 37, 57, 667 are primes, we only need to consider the family 6{0,1,4,7}7 (since any digits 2, 3, 5, 6 between them will produce smaller primes) *** Since 107, 117, 147, 177, 407, 417, 717, 747, 6007, 6477, 6707, 6777 are primes, there cannot be digits combo 00, 10, 11, 14, 17, 40, 41, 47, 70, 71, 74, 77 between them **** If there is 1 between them, then there cannot be 1, 4, 7 before it and cannot be 0, 1, 4, 7 after it, thus the form will be 6{0}17 ***** All numbers of the form 6{0}17 are divisible by 3, thus cannot be prime. **** If there is 7 between them, then there cannot be 1, 4, 7 before it and cannot be 0, 1, 4, 7 after it, thus the form will be 6{0}77 ***** All numbers of the form 6{0}77 are divisible by 3, thus cannot be prime. **** If there is neither 1 nor 7 between them, then the form is 6{0,4}7 ***** Since 6007, 407 at primes, we only need to consider the families 6{4}7 and 60{4}7 (since any digits combo 00, 40 between them will produce smaller primes) ****** All numbers of the form 6{4}7 are divisible by 3, 5, or 15, thus cannot be prime. ****** All numbers of the form 60{4}7 are divisible by 21, thus cannot be prime. * Case (7,1): ** Since 73, 75, 21, 51, 701, 711 are primes, we only need to consider the family 7{4,6,7}1 (since any digits 0, 1, 2, 3, 5 between them will produce smaller primes) *** Since 747, 767, 471, 661, 7461, 7641 are primes, we only need to consider the families 7{4,7}4{4}1, 7{7}61, 7{7}7{4,6,7}1 (since any digits combo 46, 47, 64, 66, 67 between them will produce smaller primes) **** For the 7{4,7}4{4}1 family, since 747, 471 are primes, we only need to consider the family 7{7}{4}1 (since any digits combo 47 between (7,4{4}1) will produce smaller primes) ***** The smallest prime of the form 7{7}1 is 7777777777771 ***** The smallest prime of the form 7{7}41 is 777777777777777777777777777777777777777777777777777777777777777777777777777777741, with 79 7's, which can be written as (7^79)41 and equal the prime 8^81-31 ([http://factordb.com/index.php?id=1100000000294462449 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}441 is 777777777777777777777777777777777777777777777777777777777777777777777777777777777777441, with 84 7's, which can be written as (7^84)441 and equal the prime 8^87-223 ([http://factordb.com/index.php?id=1100000000294462776 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}4441 is 777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777774441, with 233 7's, which can be written as (7^233)4441 and equal the prime 8^237-1759 ([http://factordb.com/index.php?id=1100000002352073382 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}44441 is 7777777777777777777777777777777777777777777777777777777744441, with 56 7's, which can be written as (7^56)44441 and equal the prime 8^61-14047 ([http://factordb.com/index.php?id=1100000002350250002 factordb]) (not minimal prime, since 7777777777771 is prime) ***** All numbers of the form 7{7}444441 are divisible by 7, thus cannot be prime. ***** The smallest prime of the form 7{7}4444441 is 77774444441 ****** Since this prime has just 4 7's, we only need to consider the families with <=3 7's ******* The smallest prime of the form 7{4}1 is 744444441 ******* All numbers of the form 77{4}1 are divisible by 5, thus cannot be prime. ******* The smallest prime of the form 777{4}1 is 777444444444441 (not minimal prime, since 444444441 and 744444441 are primes) * Case (7,3): ** 73 is prime, and thus the only minimal prime in this family. * Case (7,5): ** 75 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 73, 75, 27, 37, 57, 717, 747, 767 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6 between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. ===Base 10=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (1,7), (1,9), (2,1), (2,3), (2,7), (2,9), (3,1), (3,3), (3,7), (3,9), (4,1), (4,3), (4,7), (4,9), (5,1), (5,3), (5,7), (5,9), (6,1), (6,3), (6,7), (6,9), (7,1), (7,3), (7,7), (7,9), (8,1), (8,3), (8,7), (8,9), (9,1), (9,3), (9,7), (9,9) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (1,7): ** 17 is prime, and thus the only minimal prime in this family. * Case (1,9): ** 19 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 29, 11, 31, 41, 61, 71, 251, 281 are primes, we only need to consider the family 2{0,2}1 (since any digits 1, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 2221 and 20201 are primes, we only need to consider the families 2{0}1, 2{0}21, 22{0}1 (since any digits combo 22 or 020 between them will produce smaller primes) **** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. **** The smallest prime of the form 2{0}21 is 20021 **** The smallest prime of the form 22{0}1 is 22000001 * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,7): ** Since 23, 29, 17, 37, 47, 67, 97, 227, 257, 277 are primes, we only need to consider the family 2{0,8}7 (since any digits 1, 2, 3, 4, 5, 6, 7, 9 between them will produce smaller primes) *** Since 887 and 2087 are primes, we only need to consider the families 2{0}7 and 28{0}7 (since any digit combo 08 or 88 between them will produce smaller primes) **** All numbers of the form 2{0}7 are divisible by 3, thus cannot be prime. **** All numbers of the form 28{0}7 are divisible by 7, thus cannot be prime. * Case (2,9): ** 29 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 31, 37, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 3{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 3{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (3,9): ** Since 31, 37, 19, 29, 59, 79, 89, 349 are primes, we only need to consider the family 3{0,3,6,9}9 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 3{0,3,6,9}9 are divisible by 3, thus cannot be prime. * Case (4,1): ** 41 is prime, and thus the only minimal prime in this family. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,7): ** 47 is prime, and thus the only minimal prime in this family. * Case (4,9): ** Since 41, 43, 47, 19, 29, 59, 79, 89, 409, 449, 499 are primes, we only need to consider the family 4{6}9 (since any digits 0, 1, 2, 3, 4, 5, 7, 8, 9 between them will produce smaller primes) *** All numbers of the form 4{6}9 are divisible by 7, thus cannot be prime. * Case (5,1): ** Since 53, 59, 11, 31, 41, 61, 71, 521 are primes, we only need to consider the family 5{0,5,8}1 (since any digits 1, 2, 3, 4, 6, 7, 9 between them will produce smaller primes) *** Since 881 is prime, we only need to consider the families 5{0,5}1 and 5{0,5}8{0,5}1 (since any digit combo 88 between them will produce smaller primes) **** For the 5{0,5}1 family, since 5051 and 5501 are primes, we only need to consider the families 5{0}1 and 5{5}1 (since any digit combo 05 or 50 between them will produce smaller primes) ***** All numbers of the form 5{0}1 are divisible by 3, thus cannot be prime. ***** The smallest prime of the form 5{5}1 is 555555555551 **** For the 5{0,5}8{0,5}1 family, since 5081, 5581, 5801, 5851 are primes, we only need to consider the number 581 ***** 581 is not prime. * Case (5,3): ** 53 is prime, and thus the only minimal prime in this family. * Case (5,7): ** Since 53, 59, 17, 37, 47, 67, 97, 557, 577, 587 are primes, we only need to consider the family 5{0,2}7 (since any digits 1, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 227 and 50207 are primes, we only need to consider the families 5{0}7, 5{0}27, 52{0}7 (since any digits combo 22 or 020 between them will produce smaller primes) **** All numbers of the form 5{0}7 are divisible by 3, thus cannot be prime. **** The smallest prime of the form 5{0}27 is 5000000000000000000000000000027 **** The smallest prime of the form 52{0}7 is 5200007 * Case (5,9): ** 59 is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,3): ** Since 61, 67, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 6{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 6{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (6,7): ** 67 is prime, and thus the only minimal prime in this family. * Case (6,9): ** Since 61, 67, 19, 29, 59, 79, 89 are primes, we only need to consider the family 6{0,3,4,6,9}9 (since any digits 1, 2, 5, 7, 8 between them will produce smaller primes) *** Since 449 is prime, we only need to consider the families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9 (since any digit combo 44 between them will produce smaller primes) **** All numbers of the form 6{0,3,6,9}9 are divisible by 3, thus cannot be prime. **** For the 6{0,3,6,9}4{0,3,6,9}9 family, since 409, 43, 6469, 499 are primes, we only need to consider the family 6{0,3,6,9}49 ***** Since 349, 6949 are primes, we only need to consider the family 6{0,6}49 ****** Since 60649 is prime, we only need to consider the family 6{6}{0}49 (since any digits combo 06 between {6,49} will produce smaller primes) ******* The smallest prime of the form 6{6}49 is 666649 ******** Since this prime has just 4 6's, we only need to consider the families with <=3 6's ********* The smallest prime of the form 6{0}49 is 60000049 ********* The smallest prime of the form 66{0}49 is 66000049 ********* The smallest prime of the form 666{0}49 is 66600049 * Case (7,1): ** 71 is prime, and thus the only minimal prime in this family. * Case (7,3): ** 73 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 71, 73, 79, 17, 37, 47, 67, 97, 727, 757, 787 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6, 8, 9 between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. * Case (7,9): ** 79 is prime, and thus the only minimal prime in this family. * Case (8,1): ** Since 83, 89, 11, 31, 41, 61, 71, 821, 881 are primes, we only need to consider the family 8{0,5}1 (since any digits 1, 2, 3, 4, 6, 7, 8, 9 between them will produce smaller primes) *** Since 8501 is prime, we only need to consider the family 8{0}{5}1 (since any digits combo 50 between them will produce smaller primes) **** Since 80051 is prime, we only need to consider the families 8{0}1, 8{5}1, 80{5}1 (since any digits combo 005 between them will produce smaller primes) ***** All numbers of the form 8{0}1 are divisible by 3, thus cannot be prime. ***** The smallest prime of the form 8{5}1 is 8555555555555555555551 (not minimal prime, since 555555555551 is prime) ***** The smallest prime of the form 80{5}1 is 80555551 * Case (8,3): ** 83 is prime, and thus the only minimal prime in this family. * Case (8,7): ** Since 83, 89, 17, 37, 47, 67, 97, 827, 857, 877, 887 are primes, we only need to consider the family 8{0}7 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** All numbers of the form 8{0}7 are divisible by 3, thus cannot be prime. * Case (8,9): ** 89 is prime, and thus the only minimal prime in this family. * Case (9,1): ** Since 97, 11, 31, 41, 61, 71, 991 are primes, we only need to consider the family 9{0,2,5,8}1 (since any digits 1, 3, 4, 6, 7, 9 between them will produce smaller primes) *** Since 251, 281, 521, 821, 881, 9001, 9221, 9551, 9851 are primes, we only need to consider the families 9{2,5,8}0{2,5,8}1, 9{0}2{0}1, 9{0}5{0,8}1, 9{0,5}8{0}1 (since any digits combo 00, 22, 25, 28, 52, 55, 82, 85, 88 between them will produce smaller primes) **** For the 9{2,5,8}0{2,5,8}1 family, since any digits combo 22, 25, 28, 52, 55, 82, 85, 88 between (9,1) will produce smaller primes, we only need to consider the numbers 901, 9021, 9051, 9081, 9201, 9501, 9801, 90581, 95081, 95801 ***** 95801 is the only prime among 901, 9021, 9051, 9081, 9201, 9501, 9801, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. **** For the 9{0}2{0}1 family, since 9001 is prime, we only need to consider the numbers 921, 9201, 9021 ***** None of 921, 9201, 9021 are primes. **** For the 9{0}5{0,8}1 family, since 9001 and 881 are primes, we only need to consider the numbers 951, 9051, 9501, 9581, 90581, 95081, 95801 ***** 95801 is the only prime among 951, 9051, 9501, 9581, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. **** For the 9{0,5}8{0}1 family, since 9001 and 5581 are primes, we only need to consider the numbers 981, 9081, 9581, 9801, 90581, 95081, 95801 ***** 95801 is the only prime among 981, 9081, 9581, 9801, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. * Case (9,3): ** Since 97, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 9{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 9{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (9,7): ** 97 is prime, and thus the only minimal prime in this family. * Case (9,9): ** Since 97, 19, 29, 59, 79, 89 are primes, we only need to consider the family 9{0,3,4,6,9}9 (since any digits 1, 2, 5, 7, 8 between them will produce smaller primes) *** Since 449 is prime, we only need to consider the families 9{0,3,6,9}9 and 9{0,3,6,9}4{0,3,6,9}9 (since any digit combo 44 between them will produce smaller primes) **** All numbers of the form 9{0,3,6,9}9 are divisible by 3, thus cannot be prime. **** For the 9{0,3,6,9}4{0,3,6,9}9 family, since 9049, 349, 9649, 9949 are primes, we only need to consider the family 94{0,3,6,9}9 ***** Since 409, 43, 499 are primes, we only need to consider the family 94{6}9 (since any digits 0, 3, 9 between (94,9) will produce smaller primes) ****** The smallest prime of the form 94{6}9 is 946669 ===Base 12=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,5), (1,7), (1,B), (2,1), (2,5), (2,7), (2,B), (3,1), (3,5), (3,7), (3,B), (4,1), (4,5), (4,7), (4,B), (5,1), (5,5), (5,7), (5,B), (6,1), (6,5), (6,7), (6,B), (7,1), (7,5), (7,7), (7,B), (8,1), (8,5), (8,7), (8,B), (9,1), (9,5), (9,7), (9,B), (A,1), (A,5), (A,7), (A,B), (B,1), (B,5), (B,7), (B,B) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (1,7): ** 17 is prime, and thus the only minimal prime in this family. * Case (1,B): ** 1B is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 25, 27, 11, 31, 51, 61, 81, 91, 221, 241, 2A1, 2B1 are primes, we only need to consider the family 2{0}1 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B between them will produce smaller primes) *** The smallest prime of the form 2{0}1 is 2001 * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (2,7): ** 27 is prime, and thus the only minimal prime in this family. * Case (2,B): ** Since 25, 27, 1B, 3B, 4B, 5B, 6B, 8B, AB, 2BB are primes, we only need to consider the family 2{0,2,9}B (since any digits 1, 3, 4, 5, 6, 7, 8, A, B between them will produce smaller primes) *** Since 90B, 200B, 202B, 222B, 229B, 292B, 299B are primes, we only need to consider the numbers 20B, 22B, 29B, 209B, 220B (since any digits combo 00, 02, 22, 29, 90, 92, 99 between them will produce smaller primes) **** None of 20B, 22B, 29B, 209B, 220B are primes. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (3,B): ** 3B is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 4B, 11, 31, 51, 61, 81, 91, 401, 421, 471 are primes, we only need to consider the family 4{4,A}1 (since any digit 0, 1, 2, 3, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since A41 and 4441 are primes, we only need to consider the families 4{A}1 and 44{A}1 (since any digit combo 44, A4 between them will produce smaller primes) **** All numbers of the form 4{A}1 are divisible by 5, thus cannot be prime. **** The smallest prime of the form 44{A}1 is 44AAA1 * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (4,7): ** Since 45, 4B, 17, 27, 37, 57, 67, 87, A7, B7, 447, 497 are primes, we only need to consider the family 4{0,7}7 (since any digit 1, 2, 3, 4, 5, 6, 8, 9, A, B between them will produce smaller primes) *** Since 4707 and 4777 are primes, we only need to consider the families 4{0}7 and 4{0}77 (since any digit combo 70, 77 between them will produce smaller primes) **** All numbers of the form 4{0}7 are divisible by B, thus cannot be prime. **** The smallest prime of the form 4{0}77 is 400000000000000000000000000000000000000077 * Case (4,B): ** 4B is prime, and thus the only minimal prime in this family. * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 57, 5B, 15, 25, 35, 45, 75, 85, 95, B5, 565 are primes, we only need to consider the family 5{0,5,A}5 (since any digits 1, 2, 3, 4, 6, 7, 8, 9, B between them will produce smaller primes) *** All numbers of the form 5{0,5,A}5 are divisible by 5, thus cannot be prime. * Case (5,7): ** 57 is prime, and thus the only minimal prime in this family. * Case (5,B): ** 5B is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,5): ** Since 61, 67, 6B, 15, 25, 35, 45, 75, 85, 95, B5, 655, 665 are primes, we only need to consider the family 6{0,A}5 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since 6A05 and 6AA5 are primes, we only need to consider the families 6{0}5 and 6{0}A5 (since any digit combo A0, AA between them will produce smaller primes) **** All numbers of the form 6{0}5 are divisible by B, thus cannot be prime. **** The smallest prime of the form 6{0}A5 is 600A5 * Case (6,7): ** 67 is prime, and thus the only minimal prime in this family. * Case (6,B): ** 6B is prime, and thus the only minimal prime in this family. * Case (7,1): ** Since 75, 11, 31, 51, 61, 81, 91, 701, 721, 771, 7A1 are primes, we only need to consider the family 7{4,B}1 (since any digits 0, 1, 2, 3, 5, 6, 7, 8, 9, A between them will produce smaller primes) *** Since 7BB, 7441 and 7B41 are primes, we only need to consider the numbers 741, 7B1, 74B1 **** None of 741, 7B1, 74B1 are primes. * Case (7,5): ** 75 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 75, 17, 27, 37, 57, 67, 87, A7, B7, 747, 797 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6, 8, 9, A, B between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. * Case (7,B): ** Since 75, 1B, 3B, 4B, 5B, 6B, 8B, AB, 70B, 77B, 7BB are primes, we only need to consider the family 7{2,9}B (since any digits 0, 1, 3, 4, 5, 6, 7, 8, A, B between them will produce smaller primes) *** Since 222B, 729B is prime, we only need to consider the families 7{9}B, 7{9}2B, 7{9}22B (since any digits combo 222, 29 between them will produce smaller primes) **** The smallest prime of the form 7{9}B is 7999B **** The smallest prime of the form 7{9}2B is 79992B (not minimal prime, since 992B and 7999B are primes) **** The smallest prime of the form 7{9}22B is 79922B (not minimal prime, since 992B is prime) * Case (8,1): ** 81 is prime, and thus the only minimal prime in this family. * Case (8,5): ** 85 is prime, and thus the only minimal prime in this family. * Case (8,7): ** 87 is prime, and thus the only minimal prime in this family. * Case (8,B): ** 8B is prime, and thus the only minimal prime in this family. * Case (9,1): ** 91 is prime, and thus the only minimal prime in this family. * Case (9,5): ** 95 is prime, and thus the only minimal prime in this family. * Case (9,7): ** Since 91, 95, 17, 27, 37, 57, 67, 87, A7, B7, 907 are primes, we only need to consider the family 9{4,7,9}7 (since any digit 0, 1, 2, 3, 5, 6, 8, A, B between them will produce smaller primes) *** Since 447, 497, 747, 797, 9777, 9947, 9997 are primes, we only need to consider the numbers 947, 977, 997, 9477, 9977 (since any digits combo 44, 49, 74, 77, 79, 94, 99 between them will produce smaller primes) **** None of 947, 977, 997, 9477, 9977 are primes. * Case (9,B): ** Since 91, 95, 1B, 3B, 4B, 5B, 6B, 8B, AB, 90B, 9BB are primes, we only need to consider the family 9{2,7,9}B (since any digit 0, 1, 3, 4, 5, 6, 8, A, B between them will produce smaller primes) *** Since 27, 77B, 929B, 992B, 997B are primes, we only need to consider the families 9{2,7}2{2}B, 97{2,9}B, 9{7,9}9{9}B (since any digits combo 27, 29, 77, 92, 97 between them will produce smaller primes) **** For the 9{2,7}2{2}B family, since 27 and 77B are primes, we only need to consider the families 9{2}2{2}B and 97{2}2{2}B (since any digits combo 27, 77 between (9,2{2}B) will produce smaller primes) ***** The smallest prime of the form 9{2}2{2}B is 9222B (not minimal prime, since 222B is prime) ***** The smallest prime of the form 97{2}2{2}B is 9722222222222B (not minimal prime, since 222B is prime) **** For the 97{2,9}B family, since 729B and 929B are primes, we only need to consider the family 97{9}{2}B (since any digits combo 29 between (97,B) will produce smaller primes) ***** Since 222B is prime, we only need to consider the families 97{9}B, 97{9}2B, 97{9}22B (since any digit combo 222 between (97,B) will produce smaller primes) ****** All numbers of the form 97{9}B are divisible by 11, thus cannot be prime. ****** The smallest prime of the form 97{9}2B is 979999992B (not minimal prime, since 9999B is prime) ****** All numbers of the form 97{9}22B are divisible by 11, thus cannot be prime. **** For the 9{7,9}9{9}B family, since 77B and 9999B are primes, we only need to consider the numbers 99B, 999B, 979B, 9799B, 9979B ***** None of 99B, 999B, 979B, 9799B, 9979B are primes. * Case (A,1): ** Since A7, AB, 11, 31, 51, 61, 81, 91, A41 are primes, we only need to consider the family A{0,2,A}1 (since any digits 1, 3, 4, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since 221, 2A1, A0A1, A201 are primes, we only need to consider the families A{A}{0}1 and A{A}{0}21 (since any digits combo 0A, 20, 22, 2A between them will produce smaller primes) **** For the A{A}{0}1 family: ***** All numbers of the form A{0}1 are divisible by B, thus cannot be prime. ***** The smallest prime of the form AA{0}1 is AA000001 ***** The smallest prime of the form AAA{0}1 is AAA0001 ***** The smallest prime of the form AAAA{0}1 is AAAA1 ****** Since this prime has no 0's, we do not need to consider the families {A}1, {A}01, {A}001, etc. **** All numbers of the form A{A}{0}21 are divisible by 5, thus cannot be prime. * Case (A,5): ** Since A7, AB, 15, 25, 35, 45, 75, 85, 95, B5 are primes, we only need to consider the family A{0,5,6,A}5 (since any digits 1, 2, 3, 4, 7, 8, 9, B between them will produce smaller primes) *** Since 565, 655, 665, A605, A6A5, AA65 are primes, we only need to consider the families A{0,5,A}5 and A{0}65 (since any digits combo 56, 60, 65, 66, 6A, A6 between them will produce smaller primes) **** All numbers of the form A{0,5,A}5 are divisible by 5, thus cannot be prime. **** The smallest prime of the form A{0}65 is A00065 * Case (A,7): ** A7 is prime, and thus the only minimal prime in this family. * Case (A,B): ** AB is prime, and thus the only minimal prime in this family. * Case (B,1): ** Since B5, B7, 11, 31, 51, 61, 81, 91, B21 are primes, we only need to consider the family B{0,4,A,B}1 (since any digits 1, 2, 3, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 4B, AB, 401, A41, B001, B0B1, BB01, BB41 are primes, we only need to consider the families B{A}0{4,A}1, B{0,4}4{4,A}1, B{0,4,A,B}A{0,A}1, B{B}B{A,B}1 (since any digits combo 00, 0B, 40, 4B, A4, AB, B0, B4 between them will produce smaller primes) **** For the B{A}0{4,A}1 family, since A41 is prime, we only need consider the families B0{4}{A}1 and B{A}0{A}1 ***** For the B0{4}{A}1 family, since B04A1 is prime, we only need to consider the families B0{4}1 and B0{A}1 ****** The smallest prime of the form B0{4}1 is B04441 (not minimal prime, since 4441 is prime) ****** The smallest prime of the form B0{A}1 is B0AAAAA1 (not minimal prime, since AAAA1 is prime) ***** For the B{A}0{A}1 family, since A0A1 is prime, we only need to consider the families B{A}01 and B0{A}1 ****** The smallest prime of the form B{A}01 is BAA01 ****** The smallest prime of the form B0{A}1 is B0AAAAA1 (not minimal prime, since AAAA1 is prime) **** For the B{0,4}4{4,A}1 family, since 4441 is prime, we only need to consider the families B{0}4{4,A}1 and B{0,4}4{A}1 ***** For the B{0}4{4,A}1 family, since B001 is prime, we only need to consider the families B4{4,A}1 and B04{4,A}1 ****** For the B4{4,A}1 family, since A41 is prime, we only need to consider the family B4{4}{A}1 ******* Since 4441 and BAAA1 are primes, we only need to consider the numbers B41, B441, B4A1, B44A1, B4AA1, B44AA1 ******** None of B41, B441, B4A1, B44A1, B4AA1, B44AA1 are primes. ****** For the B04{4,A}1 family, since B04A1 is prime, we only need to consider the family B04{4}1 ******* The smallest prime of the form B04{4}1 is B04441 (not minimal prime, since 4441 is prime) ***** For the B{0,4}4{A}1 family, since 401, 4441, B001 are primes, we only need to consider the families B4{A}1, B04{A}1, B44{A}1, B044{A}1 (since any digits combo 00, 40, 44 between (B,4{A}1) will produce smaller primes) ****** The smallest prime of the form B4{A}1 is B4AAA1 (not minimal prime, since BAAA1 is prime) ****** The smallest prime of the form B04{A}1 is B04A1 ****** The smallest prime of the form B44{A}1 is B44AAAAAAA1 (not minimal prime, since BAAA1 is prime) ****** The smallest prime of the form B044{A}1 is B044A1 (not minimal prime, since B04A1 is prime) **** For the B{0,4,A,B}A{0,A}1 family, since all numbers in this family with 0 between (B,1) are in the B{A}0{4,A}1 family, and all numbers in this family with 4 between (B,1) are in the B{0,4}4{4,A}1 family, we only need to consider the family B{A,B}A{A}1 ***** Since BAAA1 is prime, we only need to consider the families B{A,B}A1 and B{A,B}AA1 ****** For the B{A,B}A1 family, since AB and BAAA1 are primes, we only need to consider the families B{B}A1 and B{B}AA1 ******* All numbers of the form B{B}A1 are divisible by B, thus cannot be prime. ******* The smallest prime of the form B{B}AA1 is BBBAA1 ****** For the B{A,B}AA1 family, since BAAA1 is prime, we only need to consider the families B{B}AA1 ******* The smallest prime of the form B{B}AA1 is BBBAA1 **** For the B{B}B{A,B}1 family, since AB and BAAA1 are primes, we only need to consider the families B{B}B1, B{B}BA1, B{B}BAA1 (since any digits combo AB or AAA between (B{B}B,1) will produce smaller primes) ***** The smallest prime of the form B{B}B1 is BBBB1 ***** All numbers of the form B{B}BA1 are divisible by B, thus cannot be prime. ***** The smallest prime of the form B{B}BAA1 is BBBAA1 * Case (B,5): ** B5 is prime, and thus the only minimal prime in this family. * Case (B,7): ** B7 is prime, and thus the only minimal prime in this family. * Case (B,B): ** Since B5, B7, 1B, 3B, 4B, 5B, 6B, 8B, AB, B2B are primes, we only need to consider the family B{0,9,B}B (since any digits 1, 2, 3, 4, 5, 6, 7, 8, A between them will produce smaller primes) *** Since 90B and 9BB are primes, we only need to consider the families B{0,B}{9}B **** Since 9999B is prime, we only need to consider the families B{0,B}B, B{0,B}9B, B{0,B}99B, B{0,B}999B ***** All numbers of the form B{0,B}B are divisible by B, thus cannot be prime. ***** For the B{0,B}9B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}9B and B{B}9B (since any digits combo 0B, B0 between (B,9B) will produce smaller primes) ******* The smallest prime of the form B{0}9B is B0000000000000000000000000009B ******* All numbers of the from B{B}9B is either divisible by 11 (if totally number of B's is even) or factored as 10^(2*n)-21 = (10^n-5) * (10^n+5) (if totally number of B's is odd number 2*n-1 (n≥1)) (and since if n≥1, 10^n-5 ≥ 10^1-5 = 7 > 1, 10^n+5 ≥ 10^1+5 = 15 > 1, this factorization is nontrivial), thus cannot be prime. ***** For the B{0,B}99B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}99B and B{B}99B (since any digits combo 0B, B0 between (B,99B) will produce smaller primes) ******* The smallest prime of the form B{0}99B is B00099B ******* The smallest prime of the form B{B}99B is BBBBBB99B ***** For the B{0,B}999B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}999B and B{B}999B (since any digits combo 0B, B0 between (B,999B) will produce smaller primes) ******* The smallest prime of the form B{0}999B is B0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000999B, with 1765 0's, which can be written as B(0^1765)999B and equal the prime 11*12^1769+16967 ([http://factordb.com/index.php?id=1100000002378273165 factordb]) ([http://factordb.com/cert.php?id=1100000002378273165 primality certificate]) (not minimal prime, since B00099B and B0000000000000000000000000009B are primes) ******* The smallest prime of the form B{B}999B is BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB999B, with 245 B's, which can be written as (B^244)999B and equal the prime 12^248-3769 ([http://factordb.com/index.php?id=1100000002378270237 factordb]) (not minimal prime, since BBBBBB99B is prime) == Examples of families which can be ruled out as contain no primes > ''b'' == It is not known if this problem is solvable: Problem: Given strings ''x'', ''y'', ''z'', and a base ''b'', does there exist a prime number whose base-''b'' expansion is of the form ''x''{''y''}''z''? It will be necessary for our algorithm to determine if families of the form ''x''{''y''}''z'' contain a prime > ''b'' or not. We use two different heuristic strategies to show that such families contain no primes > ''b''. In the first strategy, we mimic the well-known technique of “covering congruences”, by finding some finite set ''S'' of primes ''p'' such that every number in a given family is divisible by some element of ''S''. In the second strategy, we attempt to find an algebraic factorization, such as difference-of-squares factorization, difference-of-cubes factorization, and Aurifeuillian factorization for numbers of the form ''x''⁴+4''y''⁴. Examples of first strategy: (we can show that the corresponding numbers are > all elements in ''S'', if ''n'' makes corresponding numbers > ''b'' (i.e. ''n''≥1 for 5{1} in base 9 and 2{5} in base 11 and {4}D in base 16 and {8}F in base 16, ''n''≥0 for other examples), thus these factorizations are nontrivial) * In base 10, all numbers of the form 4{6}9 are divisible by 7 * In base 6, all numbers of the form 4{0}1 are divisible by 5 * In base 15, all numbers of the form 9{6}8 are divisible by 11 * In base 9, all numbers of the form 5{1} are divisible by some element of {2, 5} * In base 11, all numbers of the form 2{5} are divisible by some element of {2, 3} * In base 14, all numbers of the form B{0}1 are divisible by some element of {3, 5} * In base 8, all numbers of the form 6{4}7 are divisible by some element of {3, 5, 13} * In base 13, all numbers of the form 3{0}95 are divisible by some element of {5, 7, 17} * In base 16, all numbers of the form {4}D are divisible by some element of {3, 7, 13} * In base 16, all numbers of the form {8}F are divisible by some element of {3, 7, 13} Examples of second strategy: (we can show that both factors are > 1, if ''n'' makes corresponding numbers > ''b'' (i.e. ''n''≥2 for {1} in base 9, ''n''≥0 for 1{0}1 in base 8 and B{4}1 in base 16, ''n''≥1 for other examples), thus these factorizations are nontrivial) * In base 9, all numbers of the form {1} factored as difference of squares * In base 8, all numbers of the form 1{0}1 factored as sum of cubes * In base 9, all numbers of the form 3{8} factored as difference of squares * In base 16, all numbers of the form 8{F} factored as difference of squares * In base 16, all numbers of the form {F}7 factored as difference of squares * In base 9, all numbers of the form 3{1} factored as difference of squares * In base 16, all numbers of the form {4}1 factored as difference of squares * In base 16, all numbers of the form 1{5} factored as difference of squares * In base 16, all numbers of the from {C}D factored as ''x''⁴+4''y''⁴ * In base 16, all numbers of the form B{4}1 factored as difference of squares Examples of combine of the two strategies: (we can show that for the part of the first strategy, the corresponding numbers are > all elements in S, and for the part of the second strategy, both factors are > 1, if n makes corresponding numbers > b, thus these factorizations are nontrivial) * In base 14, numbers of the form 8{D} are divisible by 5 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 12, numbers of the form {B}9B are divisible by 13 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 14, numbers of the form {D}5 are divisible by 5 if ''n'' is even and factored as difference of squares if ''n'' is odd * In base 17, numbers of the form 1{9} are divisible by 2 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 19, numbers of the form 1{6} are divisible by 5 if ''n'' is odd and factored as difference of squares if ''n'' is even == Bases 2≤''b''≤1024 such that these families can be ruled out as contain no primes > ''b'' == (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) === 1{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-powers factorization === 1{0}2 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 1{0}3 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} === 1{0}4 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ === 1{0}5 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 0 mod 5: Finite covering set {5} === 1{0}6 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 7: Finite covering set {7} === 1{0}7 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 7: Finite covering set {7} === 1{0}z === (none) === 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === * ''b'' == 1 mod 3: Finite covering set {3} === 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) === (none) === 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === * ''b'' == 1 mod 3: Finite covering set {3} === {1}0z (not quasi-minimal prime if there is smaller prime of the form {1} or {1}z) === * ''b'' such that ''b'' and 2''b''−1 are both squares: Difference-of-squares factorization (such bases are 25, 841) === {1} === * ''b'' = ''m''^''r'' with ''r''>1: Difference-of-''r''th-powers factorization (some bases still have primes, since for the corresponding length this factorization is trivial, but they only have this prime, they are 4 (length 2), 8 (length 3), 16 (length 2), 27 (length 3), 36 (length 2), 100 (length 2), 128 (length 7), 196 (length 2), 256 (length 2), 400 (length 2), 512 (length 3), 576 (length 2), 676 (length 2)) === {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}) === * ''b'' == 0 mod 2: Finite covering set {2} === 1{2} === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' such that ''b'' and 2(''b''+1) are both squares: Difference-of-squares factorization (such bases are 49) === 1{3} === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' such that ''b'' and 3(''b''+2) are both squares: Difference-of-squares factorization (such bases are 25, 361) * ''b'' == 1 mod 2 such that 3(''b''+2) is square: Combine of finite covering set {2} (when length is even) and difference-of-squares factorization (when length is odd) (such bases are 25, 73, 145, 241, 361, 505, 673, 865) === 1{4} === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' such that ''b'' and 4(''b''+3) are both squares: Difference-of-squares factorization === 1{z} === (none) === 2{0}1 === * ''b'' == 1 mod 3: Finite covering set {3} === 2{0}3 === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 5: Finite covering set {5} === 2{1} (not quasi-minimal prime if there is smaller prime of the form {1}) === * ''b'' such that ''b'' and 2''b''−1 are both squares: Difference-of-squares factorization (such bases are 25, 841) === {2}1 === * ''b'' such that ''b'' and 2(''b''+1) are both squares: Difference-of-squares factorization (such bases are 49) === 2{z} === * ''b'' == 1 mod 2: Finite covering set {2} === 3{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} === 3{0}2 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} === 3{0}4 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 7: Finite covering set {7} === {3}1 === * ''b'' such that ''b'' and 3(2''b''+1) are both squares: Difference-of-squares factorization (such bases are 121) === 3{z} === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === 4{0}1 === * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ === 4{0}3 === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 7: Finite covering set {7} === {4}1 === * ''b'' such that ''b'' and 4(3''b''+1) are both squares: Difference-of-squares factorization (such bases are 16, 225) === 4{z} === * ''b'' == 1 mod 2: Finite covering set {2} === 5{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 5{z} === * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 34 mod 35: Finite covering set {5, 7} * ''b'' = 6''m''² with ''m'' == 2 or 3 mod 5: Combine of finite covering set {5} (when length is odd) and difference-of-squares factorization (when length is even) (such bases are 24, 54, 294, 384, 864, 1014) === 6{0}1 === * ''b'' == 1 mod 7: Finite covering set {7} * ''b'' == 34 mod 35: Finite covering set {5, 7} === 6{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 7{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} === 7{z} === * ''b'' == 1 mod 7: Finite covering set {7} * ''b'' == 20 mod 21: Finite covering set {3, 7} * ''b'' == 83, 307 mod 455: Finite covering set {5, 7, 13} (such bases are 83, 307, 538, 762, 993) * ''b'' = ''m''³: Difference-of-cubes factorization === 8{0}1 === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 20 mod 21: Finite covering set {3, 7} * ''b'' == 47, 83 mod 195: Finite covering set {3, 5, 13} (such bases are 47, 83, 242, 278, 437, 473, 632, 668, 827, 863, 1022) * ''b'' = 467: Finite covering set {3, 5, 7, 19, 37} * ''b'' = 722: Finite covering set {3, 5, 13, 73, 109} * ''b'' = ''m''³: Sum-of-cubes factorization * ''b'' = 128: Cannot have primes since 7''n''+3 cannot be power of 2 === 8{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === 9{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} === 9{z} === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 32 mod 33: Finite covering set {3, 11} === A{0}1 === * ''b'' == 1 mod 11: Finite covering set {11} * ''b'' == 32 mod 33: Finite covering set {3, 11} === A{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} === B{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} === B{z} === * ''b'' == 1 mod 11: Finite covering set {11} * ''b'' == 142 mod 143: Finite covering set {11, 13} * ''b'' = 307: Finite covering set {5, 11, 29} * ''b'' = 901: Finite covering set {7, 11, 13, 19} === C{0}1 === * ''b'' == 1 mod 13: Finite covering set {13} * ''b'' == 142 mod 143: Finite covering set {11, 13} * ''b'' = 296, 901: Finite covering set {7, 11, 13, 19} * ''b'' = 562, 828, 900: Finite covering set {7, 13, 19} * ''b'' = 563: Finite covering set {5, 7, 13, 19, 29} * ''b'' = 597: Finite covering set {5, 13, 29} === {#}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3) === (none) === {#}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) === * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-power factorization === #{z} (for even bases b, # = b/2−1) === (none) === y{z} === (none) === {y}z === (none) === z{0}1 === (none) === {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family) === * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-power factorization (some bases still have primes, since for the corresponding length this factorization is trivial, but they only have this prime, they are 128 (length 7), 216 (length 3), 343 (length 3), 729 (length 3)) * ''b'' = 4''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ (base 4 still have primes, since for the corresponding length this factorization is trivial, but it only have this prime, at length 2) === {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y) === (none) === {z}1 === (none) === {z}t === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 0 mod 7: Finite covering set {7} === {z}u === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 34 mod 35: Finite covering set {5, 7} === {z}v === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 5: Finite covering set {5} === {z}w === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === {z}x === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} === {z}y === * ''b'' == 0 mod 2: Finite covering set {2} == Large known (probable) primes (length ≥10000) in these families (for bases 2≤''b''≤1024) == Format: base (length) (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) === 1{0}1 === (none) === 1{0}2 === (none) === 1{0}3 === (none) === 1{0}4 === 53 (13403) 113 (10647) === 1{0}z === 113 (20089) 123 (64371) === 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === (none) === 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) === 208 (26682) 607 (11032) 828 (19659) === 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === 201 (31276) 222 (52727) 227 (36323) 327 (135983) 425 (11231) 710 (24112) 717 (37508) 719 (13420) === {1} === 152 (270217) 184 (16703) 200 (17807) 311 (36497) 326 (26713) 331 (25033) 371 (15527) 485 (99523) 629 (32233) 649 (43987) 670 (18617) 684 (22573) 691 (62903) 693 (41189) 731 (15427) 752 (32833) 872 (10093) 932 (20431) === {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}) === (none) === 1{z} === 107 (21911) 170 (166429) 278 (43909) 303 (40175) 383 (20957) 515 (58467) 522 (62289) 578 (129469) 590 (15527) 647 (21577) 662 (16591) 698 (127559) 704 (62035) 845 (39407) 938 (40423) 969 (24097) 989 (26869) === 2{0}1 === 101 (192276) 206 (46206) 218 (333926) 236 (161230) 257 (12184) 305 (16808) 467 (126776) 578 (44166) 626 (174204) 695 (94626) 752 (26164) 788 (72918) 869 (49150) 887 (27772) 899 (15732) 932 (13644) === 2{z} === 432 (16003) === 3{0}1 === 912 (132174) === 3{z} === 72 (1119850) 212 (34414) 218 (23050) 270 (89662) 303 (198358) 312 (51566) 422 (21738) 480 (93610) 513 (38032) 527 (46074) 566 (23874) 650 (498102) 686 (16584) 758 (15574) 783 (12508) 800 (33838) 921 (98668) 947 (10056) === 4{0}1 === 107 (32587) 227 (13347) 257 (160423) 355 (10990) 410 (144079) 440 (56087) 452 (14155) 482 (30691) 542 (15983) 579 (67776) 608 (20707) 635 (11723) 650 (96223) 679 (69450) 737 (269303) 740 (58043) 789 (149140) 797 (468703) 920 (103687) 934 (101404) 962 (84235) === 4{z} === 14 (19699) 68 (13575) 254 (15451) 800 (20509) === 5{0}1 === 326 (400786) 350 (20392) 554 (10630) 662 (13390) 926 (40036) === 5{z} === 258 (212135) 272 (148427) 299 (64898) 307 (26263) 354 (25566) 433 (283919) 635 (36163) 678 (40859) 692 (45447) 719 (20552) 768 (70214) 857 (23083) 867 (61411) 972 (36703) === 6{0}1 === 108 (16318) 129 (16797) 409 (369833) 522 (52604) 587 (24120) 643 (164916) 762 (11152) 789 (27297) 986 (21634) === 6{z} === 68 (25396) 332 (15222) 338 (42868) 362 (146342) 488 (33164) 566 (164828) 980 (50878) 986 (12506) 1016 (23336) === 7{0}1 === 398 (17473) 1004 (54849) === 7{z} === 97 (192336) 170 (15423) 194 (38361) 202 (155772) 282 (21413) 283 (164769) 332 (13205) 412 (29792) 560 (19905) 639 (10668) 655 (53009) 811 (31784) 814 (17366) 866 (108591) 908 (61797) 962 (31841) 992 (10605) 997 (15815) === 8{0}1 === 23 (119216) 53 (227184) 158 (123476) 254 (67716) 320 (52004) 410 (279992) 425 (94662) 513 (19076) 518 (11768) 596 (148446) 641 (87702) 684 (23387) 695 (39626) 785 (900326) 788 (11408) 893 (86772) 908 (243440) 920 (107822) 962 (47222) 998 (81240) 1013 (43872) === 8{z} === 138 (35686) 412 (12154) 788 (11326) 990 (23032) === 9{0}1 === 248 (39511) 592 (96870) === 9{z} === 431 (43574) 446 (152028) 458 (126262) 599 (11776) 846 (12781) === A{0}1 === 173 (264235) 198 (47665) 311 (314807) 341 (106009) 449 (18507) 492 (42843) 605 (12395) 708 (17563) 710 (31039) 743 (285479) 744 (137056) 786 (68169) 800 (15105) 802 (149320) 879 (25004) 929 (13065) 977 (125873) 986 (48279) 1004 (10645) === A{z} === 368 (10867) 488 (10231) 534 (80328) 662 (13307) 978 (14066) === B{0}1 === 710 (15272) 740 (33520) 878 (227482) === B{z} === 153 (21660) 186 (112718) 439 (18752) 593 (16064) 602 (36518) 707 (10573) 717 (67707) === C{0}1 === 68 (656922) 219 (29231) 230 (94751) 312 (21163) 334 (83334) 353 (20262) 359 (61295) 457 (10024) 481 (45941) 501 (20140) 593 (42779) 600 (11242) 604 (17371) 641 (26422) 700 (91953) 887 (13961) 919 (45359) 923 (64365) 992 (10300) === {#}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3) === (none) === {#}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) === (none) === #{z} (for even bases b, # = b/2−1) === (none) === y{z} === 38 (136212) 83 (21496) 113 (286644) 188 (13508) 401 (103670) 417 (21003) 458 (46900) 494 (21580) 518 (129372) 527 (65822) 602 (17644) 608 (36228) 638 (74528) 663 (47557) 723 (24536) 758 (50564) 833 (12220) 904 (13430) 938 (50008) 950 (16248) === z{0}1 === 202 (46774) 251 (102979) 272 (16681) 297 (14314) 298 (60671) 326 (64757) 347 (69661) 363 (142877) 452 (71941) 543 (10042) 564 (38065) 634 (84823) 788 (13541) 869 (12289) 890 (37377) 953 (60995) 1004 (29685) === {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family) === 53 (21942) 124 (16426) 175 (31626) 188 (22036) 316 (48538) 365 (25578) 373 (24006) 434 (10090) 530 (11086) 545 (12346) 560 (15072) 596 (12762) 701 (12576) 706 (10656) 821 (13536) 833 (17116) 966 (14820) 983 (11272) === {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y) === (none) === {z}1 === (none) === {z}y === 317 (13896) == Bases 2≤''b''≤1024 which have these families as unsolved families == Unsolved families are families which are neither primes (>''b'') found nor can be ruled out as contain no primes > ''b'' (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) 1{0}1: 38, 50, 62, 68, 86, 92, 98, 104, 122, 144, 168, 182, 186, 200, 202, 212, 214, 218, 244, 246, 252, 258, 286, 294, 298, 302, 304, 308, 322, 324, 338, 344, 354, 356, 362, 368, 380, 390, 394, 398, 402, 404, 410, 416, 422, 424, 446, 450, 454, 458, 468, 480, 482, 484, 500, 514, 518, 524, 528, 530, 534, 538, 552, 558, 564, 572, 574, 578, 580, 590, 602, 604, 608, 620, 622, 626, 632, 638, 648, 650, 662, 666, 668, 670, 678, 684, 692, 694, 698, 706, 712, 720, 722, 724, 734, 744, 746, 752, 754, 762, 766, 770, 792, 794, 802, 806, 812, 814, 818, 836, 840, 842, 844, 848, 854, 868, 870, 872, 878, 888, 896, 902, 904, 908, 922, 924, 926, 932, 938, 942, 944, 948, 954, 958, 964, 968, 974, 978, 980, 988, 994, 998, 1002, 1006, 1014, 1016 (length limit: ≥8388608) 1{0}2: 167, 257, 323, 353, 383, 527, 557, 563, 623, 635, 647, 677, 713, 719, 803, 815, 947, 971, 1013 (length limit: 2000) 1{0}3: 646, 718, 998 (length limit: 2000) 1{0}4: 139, 227, 263, 315, 335, 365, 485, 515, 647, 653, 683, 773, 789, 797, 815, 857, 875, 893, 939, 995, 1007 (length limit: 2000) 1{0}5 1{0}6 1{0}7 1{0}8 1{0}9 1{0}A 1{0}B 1{0}C 1{0}D 1{0}E 1{0}F 1{0}G 1{0}z: 173, 179, 257, 277, 302, 333, 362, 392, 422, 452, 467, 488, 512, 527, 545, 570, 575, 614, 622, 650, 677, 680, 704, 707, 734, 740, 827, 830, 851, 872, 886, 887, 902, 904, 908, 929, 932, 942, 947, 949, 962, 973, 1022 (length limit: 2000) 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1): 198, 213, 318, 327, 353, 375, 513, 591, 647, 732, 734, 738, 759, 948, 951, 957, 1013, 1014 (length limit: 2000) 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}): 575 (length limit: 247000) 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1): 813, 863, 962, 1017 (length limit: ≥100000) {1}0z (not quasi-minimal prime if there is smaller prime of the form {1} or {1}z): 137, 161, 167, 217, 229, 232, 253, 261, 317, 325, 337, 347, 355, 375, 403, 411, 421, 427, 457, 479, 483, 505, 507, 537, 547, 577, 597, 599, 601, 613, 627, 631, 632, 641, 643, 649, 657, 679, 688, 697, 707, 711, 729, 733, 737, 742, 762, 773, 787, 793, 797, 817, 819, 841, 843, 853, 859, 861, 874, 877, 895, 899, 907, 913, 916, 917, 927, 957, 959, 997, 1003, 1009, 1015, 1017 (length limit: 2000) {1}: 185, 269, 281, 380, 384, 385, 394, 452, 465, 511, 574, 601, 631, 632, 636, 711, 713, 759, 771, 795, 861, 866, 881, 938, 948, 951, 956, 963, 1005, 1015 (length limit: ≥100000) 11{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}): 31, 61, 91, 93, 143, 247, 253, 293, 313, 329, 371, 383, 391, 393, 403, 415, 435, 443, 451, 491, 493, 513, 523, 527, 537, 541, 553, 565, 581, 587, 601, 613, 615, 623, 627, 635, 663, 729, 735, 757, 763, 775, 783, 823, 843, 865, 873, 877, 883, 897, 931, 941, 943, 955, 983, 1013, 1015, 1021, 1023 (length limit: 2000) {1}z 1{2}: 265, 355, 379, 391, 481, 649, 661, 709, 745, 811, 877, 977 (length limit: 2000) 1{3}: 107, 133, 179, 281, 305, 365, 473, 485, 487, 491, 535, 541, 601, 617, 665, 737, 775, 787, 802, 827, 905, 911, 928, 953, 955, 995 1{4}: 83, 143, 185, 239, 269, 293, 299, 305, 319, 325, 373, 383, 395, 431, 471, 503, 551, 577, 581, 593, 605, 617, 631, 659, 743, 761, 773, 781, 803, 821, 857, 869, 897, 911, 917, 923, 935, 983, 1019 (length limit: 2000) 1{z}: 581, 992, 1019 (length limit: ≥100000) 2{0}1: 365, 383, 461, 512, 542, 647, 773, 801, 836, 878, 908, 914, 917, 947, 1004 (length limit: ≥100000) 2{0}3: 79, 149, 179, 254, 359, 394, 424, 434, 449, 488, 499, 532, 554, 578, 664, 683, 694, 749, 794, 839, 908, 944, 982 (length limit: 2000) 2{1} (not quasi-minimal prime if there is smaller prime of the form {1}): 109, 117, 137, 147, 157, 175, 177, 201, 227, 235, 256, 269, 271, 297, 310, 331, 335, 397, 417, 427, 430, 437, 442, 451, 465, 467, 481, 502, 517, 547, 557, 567, 572, 577, 591, 597, 607, 627, 649, 654, 655, 667, 679, 687, 691, 697, 715, 727, 739, 759, 766, 782, 787, 796, 797, 808, 817, 821, 829, 841, 852, 877, 881, 899, 903, 907, 937, 947, 955, 1007, 1011, 1021 (length limit: 2000) {2}1: 106, 238, 262, 295, 364, 382, 391, 397, 421, 458, 463, 478, 517, 523, 556, 601, 647, 687, 754, 790, 793, 832, 872, 898, 962, 1002, 1021 (length limit: 2000) 2{z}: 588, 972 (length limit: ≥100000) 3{0}1: 718 (length limit: ≥100000) 3{0}2: 223, 283, 359, 489, 515, 529, 579, 619, 669, 879, 915, 997 (length limit: 2000) 3{0}4: 167, 391, 447, 487, 529, 653, 657, 797, 853, 913, 937 (length limit: 2000) {3}1: 79, 101, 189, 215, 217, 235, 243, 253, 255, 265, 313, 338, 341, 378, 379, 401, 402, 413, 489, 498, 499, 508, 525, 535, 589, 591, 599, 611, 621, 635, 667, 668, 681, 691, 711, 717, 719, 721, 737, 785, 804, 805, 813, 831, 835, 837, 849, 873, 911, 915, 929, 933, 941, 948, 959, 999, 1013, 1019 (length limit: 2000) 3{z}: 275, 438, 647, 653, 812, 927, 968 (length limit: ≥100000) 4{0}1: 32, 53, 155, 174, 204, 212, 230, 332, 334, 335, 395, 467, 512, 593, 767, 803, 848, 875, 1024 (length limit: ≥100000) 4{0}3: 83, 88, 97, 167, 188, 268, 289, 293, 412, 419, 425, 433, 503, 517, 529, 548, 613, 620, 622, 650, 668, 692, 706, 727, 763, 818, 902, 913, 937, 947, 958 (length limit: 2000) {4}1: 46, 77, 103, 107, 119, 152, 198, 203, 211, 217, 229, 257, 263, 291, 296, 305, 332, 371, 374, 407, 413, 416, 440, 445, 446, 464, 467, 500, 542, 545, 548, 557, 566, 586, 587, 605, 611, 614, 632, 638, 641, 653, 659, 698, 701, 731, 733, 736, 755, 786, 812, 820, 821, 827, 830, 887, 896, 899, 901, 922, 923, 935, 941, 953, 977, 983, 991, 1004 (length limit: 2000) 4{z}: 338, 998 (length limit: ≥100000) 5{0}1: 308, 512, 824 (length limit: ≥100000) 5{z}: 234, 412, 549, 553, 573, 619, 750, 878, 894, 954 (length limit: ≥100000) 6{0}1: 212, 509, 579, 625, 774, 794, 993, 999 (length limit: ≥100000) 6{z}: 308, 392, 398, 518, 548, 638, 662, 878 (length limit: ≥100000) 7{0}1: (none) 7{z}: 321, 328, 374, 432, 665, 697, 710, 721, 727, 728, 752, 800, 815, 836, 867, 957, 958, 972 (length limit: ≥100000) 8{0}1: 86, 140, 182, 263, 353, 368, 389, 395, 422, 426, 428, 434, 443, 488, 497, 558, 572, 575, 593, 606, 698, 710, 746, 758, 770, 773, 824, 828, 866, 911, 930, 953, 957, 983, 993, 1014 (length limit: ≥100000) 8{z}: 378, 438, 536, 566, 570, 592, 636, 688, 718, 830, 852, 926, 1010 (length limit: ≥100000) 9{0}1: 724, 884 (length limit: ≥100000) 9{z}: 80, 233, 530, 551, 611, 899, 912, 980 (length limit: ≥100000) A{0}1: 185, 338, 417, 432, 614, 668, 773, 863, 935, 1000 (length limit: ≥100000) A{z}: 214, 422, 444, 452, 458, 542, 638, 668, 804, 872, 950, 962 (length limit: ≥100000) B{0}1: 560, 770, 968 (length limit: ≥100000) B{z}: 263, 615, 912, 978 (length limit: ≥100000) C{0}1: 163, 207, 354, 362, 368, 480, 620, 692, 697, 736, 753, 792, 978, 998, 1019, 1022 (length limit: ≥100000) C{z} D{0}1 D{z} E{0}1 E{z} F{0}1 F{z} G{0}1 {&#35;}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3): 808, 829, 859, 1006 (length limit: 2000) {&#35;}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2): 31, 37, 55, 63, 67, 77, 83, 89, 91, 93, 97, 99, 107, 109, 117, 123, 127, 133, 135, 137, 143, 147, 149, 151, 155, 161, 177, 179, 183, 189, 193, 197, 207, 211, 213, 215, 217, 223, 225, 227, 233, 235, 241, 247, 249, 255, 257, 263, 265, 269, 273, 277, 281, 283, 285, 287, 291, 293, 297, 303, 307, 311, 319, 327, 347, 351, 355, 357, 359, 361, 367, 369, 377, 381, 383, 385, 387, 389, 393, 397, 401, 407, 411, 413, 417, 421, 423, 437, 439, 443, 447, 457, 465, 467, 469, 473, 475, 481, 483, 489, 493, 495, 497, 509, 511, 515, 533, 541, 547, 549, 555, 563, 591, 593, 597, 601, 603, 611, 615, 619, 621, 625, 627, 629, 633, 635, 637, 645, 647, 651, 653, 655, 659, 663, 667, 671, 673, 675, 679, 683, 687, 691, 693, 697, 707, 709, 717, 731, 733, 735, 737, 741, 743, 749, 753, 755, 757, 759, 765, 767, 771, 773, 775, 777, 783, 785, 787, 793, 797, 801, 807, 809, 813, 817, 823, 825, 849, 851, 853, 865, 867, 873, 877, 887, 889, 893, 897, 899, 903, 907, 911, 915, 923, 927, 933, 937, 939, 941, 943, 945, 947, 953, 957, 961, 967, 975, 977, 983, 987, 993, 999, 1003, 1005, 1009, 1017 (length limit: ≥262143) &#35;{z} (for even bases ''b'', # = ''b''/2−1): 108, 278, 296, 338, 386, 494, 626, 920 (length limit: 2000) ${&#35;} (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) x{z} y{z}: 128, 233, 268, 383, 478, 488, 533, 554, 665, 698, 779, 863, 878, 932, 941, 1010 (length limit: ≥200000) z{0}1: 123, 342, 362, 422, 438, 479, 487, 512, 542, 602, 757, 767, 817, 830, 872, 893, 932, 992, 997, 1005, 1007 (length limit: ≥100000) {y}z: 143, 173, 176, 213, 235, 248, 253, 279, 327, 343, 353, 358, 373, 383, 401, 413, 416, 427, 439, 448, 453, 463, 481, 513, 522, 527, 535, 547, 559, 565, 583, 591, 598, 603, 621, 623, 653, 659, 663, 679, 691, 698, 711, 743, 745, 757, 768, 785, 793, 796, 801, 808, 811, 821, 835, 845, 847, 853, 856, 883, 898, 903, 927, 955, 961, 971, 973, 993, 1005, 1013, 1019, 1021 (length limit: 2000) {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family): 97, 103, 113, 186, 187, 220, 304, 306, 309, 335, 414, 416, 428, 433, 445, 459, 486, 498, 539, 550, 557, 587, 592, 597, 598, 617, 624, 637, 659, 665, 671, 677, 696, 717, 726, 730, 740, 754, 766, 790, 851, 873, 890, 914, 923, 929, 943, 944, 965, 984, 985, 996, 1004, 1005 (length limit: ≥17326) zy{z} (not quasi-minimal prime if there is smaller prime of the form y{z}) {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y): 215, 353, 517, 743, 852, 899, 913 (length limit: 2000) {z}01 (not quasi-minimal prime if there is smaller prime of the form {z}1) {z}1: 93, 113, 152, 158, 188, 217, 218, 226, 227, 228, 233, 240, 275, 278, 293, 312, 338, 350, 353, 383, 404, 438, 464, 471, 500, 533, 576, 614, 641, 653, 704, 723, 728, 730, 758, 779, 788, 791, 830, 878, 881, 899, 908, 918, 929, 944, 953, 965, 968, 978, 983, 986, 1013 (length limit: 2000) {z}k {z}l {z}m {z}n {z}o {z}p {z}q {z}r {z}s {z}t {z}u {z}v {z}w: 207, 221, 293, 375, 387, 533, 633, 647, 653, 687, 701, 747, 761, 785, 863, 897, 905, 965, 1017 (length limit: 2000) {z}x: (none) {z}y: 305, 353, 397, 485, 487, 535, 539, 597, 641, 679, 731, 739, 755 (length limit: 2000) == List of lengths for quasi-minimal primes in some simple families == [https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml list of lengths for quasi-minimal primes in some simple families for bases 2≤''b''≤1024] NB: this family is not interpretable in this base (e.g. family 7{0}1 and 7{z} in bases <=7, family {z}x in bases <=3) (including the case which this family has either leading zeros (leading zeros do not count) or ending zeros (numbers ending in zero cannot be prime > base) in this base) RC: this family can be proven to only contain composite numbers (only count numbers > base) unknown: this family has no primes or PRPs found, nor can this family be proven to only contain composite numbers (only count numbers > base) Background color: red for title (bases or families), green for length > 10000, orange for 2500 < length ≤ 10000, white for length ≤ 2500, cyan for "RC", pink for "NB", yellow for "unknown". Search limit for lengths: ≥8388608 for 1{0}1, ≥200000 for y{z}, ≥100000 for ''d''{0}1 (''d'' = one of digits in {2, 3, 4, 5, 6, 7, 8, 9, A, B, C}) and ''d''{z} (''d'' = one of digits in {1, 2, 3, 4, 5, 6, 7, 8, 9, A, B}) and z{0}1 and {1}, ≥5000 for 1{0}2, {z}y, 1{0}z, {z}1, {y}z, ≥2500 for other families. == References == * [https://mersenneforum.org/showthread.php?t=24972 mersenneforum thread of this problem] * [https://docs.google.com/document/d/e/2PACX-1vQct6Hx-IkJd5-iIuDuOKkKdw2teGmmHW-P75MPaxqBXB37u0odFBml5rx0PoLa0odTyuW67N_vn96J/pub Minimal elements for the base ''b'' representations of the primes which are > ''b'' for bases ''b''≤16] * [https://primes.utm.edu/glossary/xpage/MinimalPrime.html article “minimal prime” in The Prime Glossary] * [https://en.wikipedia.org/wiki/Minimal_prime_(recreational_mathematics article “minimal prime” in Wikipedia] * [https://www.primepuzzles.net/puzzles/puzz_178.htm the puzzle of minimal primes (when the restriction of prime>base is not required) in The Prime Puzzles & Problems Connection] * [https://www.primepuzzles.net/problems/prob_083.htm the problem of minimal primes in The Prime Puzzles & Problems Connection] * [https://github.com/xayahrainie4793/non-single-digit-primes my data for these M(Lb) sets for 2 ≤ b ≤ 16] * [http://www.cs.uwaterloo.ca/~shallit/Papers/minimal5.pdf Shallit’s proof of base 10 minimal primes, when the restriction of prime>base is not required] * [https://scholar.colorado.edu/downloads/hh63sw661 proofs of minimal primes in bases b≤10, when the restriction of prime>base is not required] * [https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://cs.uwaterloo.ca/~cbright/talks/minimal-slides.pdf the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://doi.org/10.1080/10586458.2015.1064048 the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://github.com/curtisbright/mepn-data data for these M(Lb) sets and unsolved families for 2 ≤ b ≤ 30, when the restriction of prime>base is not required, search limits of lengths: 1000000 for b=17, 707000 for b=19, 506000 for b=21, 292000 for b=25, 486000 for b=26, 543000 for b=28, 233000 for b=29] * [https://github.com/RaymondDevillers/primes data for these M(Lb) sets and unsolved families for 2 ≤ b ≤ 50, when the restriction of prime>base is not required, search limits of lengths: 10000 for all b] * [http://www.bitman.name/math/article/730 article for minimal primes, when the restriction of prime>base is not required] * [http://www.bitman.name/math/table/497 data for minimal primes in bases 2 ≤ b ≤ 16, when the restriction of prime>base is not required] * [http://www.prothsearch.com/sierp.html the Sierpinski problem] * [http://www.prothsearch.com/rieselprob.html the Riesel problem] * [https://oeis.org/A076336/a076336c.html the dual Sierpinski problem] * [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm generalized Sierpinski conjectures in bases b≤1030, some primes found in these conjectures are minimal primes in base b, especially, all primes for k&lt;b (if exist for a (k,b) combo) are always minimal primes in the base b) (also some examples for simple families contain no primes &gt; b] * [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm generalized Riesel conjectures in bases b≤1030, some primes found in these conjectures are minimal primes in base b, especially, all primes for k&lt;b (if exist for a (k,b) combo) are always minimal primes in the base b) (also some examples for simple families contain no primes &gt; b] * [http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm list for the status of the generalized Sierpinski conjectures and the generalized Riesel conjectures in bases b≤1030] * [https://www.utm.edu/staff/caldwell/preprints/2to100.pdf article for generalized Sierpinski conjectures in bases b≤100] * [http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf article for the mixed (original+dual) Sierpinski problem] * [http://www.fermatquotient.com/PrimSerien/GenRepu.txt generalized repunit primes (primes of the form (bn−1)/(b−1)) in bases b≤160, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html generalized repunit primes (primes of the form (bn−1)/(b−1)) in bases b≤1000, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://jeppesn.dk/generalized-fermat.html generalized Fermat primes (primes of the form b2^n+1) in even bases b≤1000, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://www.noprimeleftbehind.net/crus/GFN-primes.htm generalized Fermat primes (primes of the form b2^n+1) in even bases b≤1030, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt list of generalized half Fermat primes (primes of the form (b2^n+1)/2) sorted by n, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://harvey563.tripod.com/wills.txt primes of the form (b−1)*bn−1 for bases b≤2049, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Williams_prime_MM_least the smallest primes of the form (b−1)*bn−1 for bases b≤2049, these primes (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Williams_prime_MP_least the smallest primes of the form (b−1)*bn+1 for bases b≤1024, these primes (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n the smallest primes of the form k*bn−1 for k≤12 and bases b≤1024, these primes (if exists) is always minimal prime in base b if b>k] * [https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n the smallest primes of the form k*bn+1 for k≤12 and bases b≤1024, these primes (if exists) is always minimal prime in base b if b>k] * [https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml list for the smallest primes in given simple family in bases b≤1024] * [https://www.rose-hulman.edu/~rickert/Compositeseq/ a problem related to this project] * [http://www.worldofnumbers.com/Appending%201s%20to%20n.txt a problem related to this project] * [https://stdkmd.net/nrr/prime/primecount.txt near- and quasi- repdigit (probable) primes sorted by count] * [https://stdkmd.net/nrr/prime/primedifficulty.txt near- and quasi- repdigit (probable) primes sorted by difficulty] * [http://www.prothsearch.com/fermat.html factoring status of Fermat numbers] * [http://www.rieselprime.de/dl/CRUS_pack.zip srsieve, sr1sieve, sr2sieve, pfgw, and llr softwares] * [https://www.bc-team.org/app.php/dlext/?cat=3 srsieve, sr1sieve, sr2sieve, sr5sieve software] * [https://sourceforge.net/projects/openpfgw/ pfgw software] * [http://jpenne.free.fr/index2.html llr software] * [http://www.ellipsa.eu/public/primo/primo.html PRIMO software] * [https://primes.utm.edu/prove/index.html website for primality proving] * [https://primes.utm.edu/curios/page.php?number_id=22380 the largest base 10 minimal prime in Prime Curios!] * [https://oeis.org/A071062 OEIS sequence for base 10 minimal primes, when the restriction of prime>base is not required] * [https://oeis.org/A326609 OEIS sequence for the largest base b minimal prime, when the restriction of prime>base is not required] * [https://primes.utm.edu/primes/lists/all.txt top proven primes] * [http://www.primenumbers.net/prptop/prptop.php top PRPs] * [http://factordb.com online factor database, including many primes which are minimal primes in a small base] 4wnpn8ac2sd061disfbcj6ibfh2ggci 2412473 2412472 2022-08-07T03:19:28Z 2402:7500:942:36DD:9962:A44F:536A:30BC /* Unproven PRPs */ wikitext text/x-wiki A '''quasi-minimal prime''' is a [[w:Prime number|prime number]] for which there is no shorter [[w:Subsequence|subsequence]] of its [[w:Numerical digit|digit]]s in a given [[w:Radix|base]] ''b'' that form a prime > ''b''. For example, 857 is a quasi-minimal prime in [[w:Decimal|decimal]] because there is no prime > 10 among the shorter subsequences of the digits: 8, 5, 7, 85, 87, 57. The subsequence does not have to consist of consecutive digits, so 149 is not a quasi-minimal prime in decimal (because 19 is prime and 19 > 10). But it does have to be in the same order; so, for example, 991 is still a quasi-minimal prime in decimal even though a subset of the digits can form the shorter prime 19 > 10 by changing the order. (using A−Z to represent digit values 10 to 35) For the quasi-minimal primes in bases up to 36, I have only solved (found all quasi-minimal primes and proved that these are all such primes) bases 2~12, 14~15, 18, 20, 22, 24, 30 (bases 11, 22, 30 need primality proving of the probable primes). For the remain bases 13, 16~17, 19, 21, 23, 25~29, 31~36, there are some ''x''{''d''}''y'' (with ''x'', ''y'' strings (may be [[w:Empty string|empty]]) with digits in base ''b'', ''d'' digit in base ''b'') families which are not solved (not even a probable prime is known nor can be ruled out as only contain composites (only count the numbers > base (''b'')). I left as a challenge to readers the task of solving (finding all quasi-minimal primes and proving that these are all such primes) bases 13, 16~17, 19, 21, 23, 25~29, 31~36 (this will be a hard problem, e.g. base 23 has a quasi-minimal prime 9E₈₀₀₈₇₃, and base 36 has quasi-minimal prime P₈₁₉₉₃SZ). Proving the set of the quasi-minimal primes in base ''b'' is ''S'', is equivalent to: * Prove that all elements in ''S'', when read as base ''b'' representation, are primes > ''b''. * Prove that all [[w:Proper subset|proper]] subsequence of all elements in ''S'', when read as base ''b'' representation, which are > ''b'', are composite. * Prove that all primes > ''b'', when written in base ''b'', contain at least one element in ''S'' as subsequence (equivalently, prove that all strings not containing any element in ''S'' as subsequence, when read as base ''b'' representation, which are > ''b'', are composite). e.g. proving the set of the quasi-minimal primes in base ''b'' = 10 is {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}, is equivalent to: * Prove that all of 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 are primes > 10. * Prove that all proper subsequence of all elements in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} which are > 10 are composite. * Prove that all primes > 10 contain at least one element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence (equivalently, prove that all numbers > 10 not containing any element in {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} as subsequence are composite). ==Condensed table== {|class=wikitable |''b''||number of quasi-minimal primes base ''b''||base-''b'' form of largest known quasi-minimal prime base ''b''||length of largest known quasi-minimal prime base ''b''||algebraic ((''a''×''b''^''n''+''c'')/''d'') form of largest known quasi-minimal prime base ''b'' |- |2||1||11||2||3 |- |3||3||111||3||13 |- |4||5||221||3||41 |- |5||22||10₉₃13||96||5⁹⁵+8 |- |6||11||40041||5||5209 |- |7||71||3₁₆1||17||(7¹⁷−5)/2 |- |8||75||4₂₂₀7||221||(4×8²²¹+17)/7 |- |9||151||30₁₁₅₈11||1161||3×9¹¹⁶⁰+10 |- |10||77||50₂₈27||31||5×10³⁰+27 |- |11^*||1068||57₆₂₆₆₈||62669||(57×11⁶²⁶⁶⁸−7)/10 |- |12||106||40₃₉77||42||4×12⁴¹+91 |- |13^*||3195~3197||80₃₂₀₁₇111||32021||8×13³²⁰²⁰+183 |- |14||650||4D₁₉₆₉₈||19699||5×14¹⁹⁶⁹⁸−1 |- |15||1284||7₁₅₅97||157||(15¹⁵⁷+59)/2 |- |16^*||2346~2347||4₇₂₇₈₅DD||72787||(4×16⁷²⁷⁸⁷+2291)/15 |- |17^*||10409~10428||F70₁₈₆₇₆₇1||186770||262×17¹⁸⁶⁷⁶⁸+1 |- |18||549||C0₆₂₆₈C5||6271||12×18⁶²⁷⁰+221 |- |20||3314||G0₆₂₆₉D||6271||16×20⁶²⁷⁰+13 |- |21^*||13375~13395||CF₄₇₉₁₄₇0K||479150||(51×21⁴⁷⁹¹⁴⁹−1243)/4 |- |22^*||8003||BK₂₂₀₀₁5||22003||(251×22²²⁰⁰²−335)/21 |- |24||3409||N00N₈₁₂₉LN||8134||13249×24⁸¹³¹−49 |- |30^*||2619||OT₃₄₂₀₅||34206||25×30³⁴²⁰⁵−1 |- |36^*||35257~35263||P₈₁₉₉₃SZ||81995||(5×36⁸¹⁹⁹⁵+821)/7 |} ^* Data assumes the primality of the [[w:probable prime|probable prime]]s. Except bases ''b'' = 13, 16, 17, 21, all bases in this table are completely solved (if we allow strong probable primes > 10²⁵⁰⁰⁰), also, except bases ''b'' = 11, 13, 16, 17, 21, 22, 30, 36, all bases in this table are completely solved even if we only allow definitely primes (thus, we can complete the classification of the quasi-minimal primes in these bases, i.e. the “quasi-minimal problems” in these bases are now theorems), for the quasi-minimal primes see the data below. Base ''b'' = 13 has 3195 known quasi-minimal primes (or PRPs), see the data below, and if there are more quasi-minimal primes in base 13, then they must be of the form 9{5} or A{3}A (we are unable to determine if these two families contain a prime or not, i.e. these two families have no known prime members, nor can these two families be ruled out as only containing composites), and must have at least 111000 digits in base 13, besides, since these two families can contain at most one quasi-minimal prime, there are at most 3197 quasi-minimal primes in base 13. (i.e. the quasi-minimal primes in base 13 are the 3195 known quasi-minimal primes in base 13 (they are given in the data section) plus the smallest prime in the family 9{5} in base 13 (if exists) plus the smallest prime in the family A{3}A in base 13 (if exists)) Base ''b'' = 16 has 2346 known quasi-minimal primes (or PRPs), see the data below, and if there are more quasi-minimal primes in base 16, then they must be of the form {3}AF (we are unable to determine if this family contains a prime or not, i.e. this family have no known prime members, nor can this family be ruled out as only containing composites), and must have at least 98000 digits in base 16, besides, since this family can contain at most one quasi-minimal prime, there are at most 2347 quasi-minimal primes in base 16. (i.e. the quasi-minimal primes in base 16 are the 2346 known quasi-minimal primes in base 16 (they are given in the data section) plus the smallest prime in the family {3}AF in base 16 (if exists)) ==Data for quasi-minimal primes== ===Base 2=== 11 ===Base 3=== 12, 21, 111 ===Base 4=== 11, 13, 23, 31, 221 ===Base 5=== 12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013 ===Base 6=== 11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041 ===Base 7=== 14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331 ===Base 8=== 13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447 ===Base 9=== 12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011 ===Base 10=== 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027 ===Base 11=== 12, 16, 18, 21, 27, 29, 34, 38, 3A, 43, 49, 54, 56, 61, 65, 67, 72, 76, 81, 89, 92, 94, 98, 9A, A3, 10A, 115, 117, 133, 139, 153, 155, 171, 193, 197, 199, 1AA, 225, 232, 236, 25A, 263, 315, 319, 331, 335, 351, 353, 362, 373, 379, 391, 395, 407, 414, 452, 458, 478, 47A, 485, 4A5, 4A7, 502, 508, 511, 513, 533, 535, 539, 551, 571, 579, 588, 595, 623, 632, 70A, 711, 715, 731, 733, 737, 755, 759, 775, 791, 797, 7AA, 803, 847, 858, 85A, 874, 885, 887, 913, 919, 931, 937, 957, 959, 975, 995, A07, A1A, A25, A45, A74, A7A, A85, AA1, AA7, 1101, 11A9, 1305, 1451, 1457, 15A7, 175A, 17A5, 17A9, 2023, 2045, 2052, 2083, 20A5, 2333, 2A05, 2A52, 3013, 3026, 3059, 3097, 3206, 3222, 3233, 3307, 3332, 3505, 4025, 4151, 4157, 4175, 4405, 4445, 4487, 450A, 4575, 5017, 5031, 5059, 5075, 5097, 5099, 5105, 515A, 517A, 520A, 5301, 5583, 5705, 577A, 5853, 5873, 5909, 5A17, 5A57, 5A77, 5A8A, 6683, 66A9, 7019, 7073, 7079, 7088, 7093, 7095, 7309, 7451, 7501, 7507, 7578, 757A, 75A7, 7787, 7804, 7844, 7848, 7853, 7877, 78A4, 7A04, 7A57, 7A79, 7A95, 8078, 8245, 8333, 8355, 8366, 8375, 8425, 8553, 8663, 8708, 8777, 878A, 8A05, 9053, 9101, 9107, 9305, 9505, 9703, A052, A119, A151, A175, A515, A517, A575, A577, A5A8, A719, A779, A911, AAA9, 10011, 10075, 10091, 10109, 10411, 10444, 10705, 10709, 10774, 10901, 11104, 11131, 11144, 11191, 1141A, 114A1, 13757, 1411A, 14477, 144A4, 14A04, 14A11, 17045, 17704, 1774A, 17777, 177A4, 17A47, 1A091, 1A109, 1A114, 1A404, 1A411, 1A709, 20005, 20555, 22203, 25228, 25282, 25552, 25822, 28522, 30037, 30701, 30707, 31113, 33777, 35009, 35757, 39997, 40045, 4041A, 40441, 4045A, 404A1, 4111A, 411A1, 42005, 44401, 44474, 444A1, 44555, 44577, 445AA, 44744, 44A01, 47471, 47477, 47701, 5057A, 50903, 5228A, 52A22, 52A55, 52A82, 55007, 550A9, 55205, 55522, 55557, 55593, 55805, 57007, 57573, 57773, 57807, 5822A, 58307, 58505, 58A22, 59773, 59917, 59973, 59977, 59999, 5A015, 5A2A2, 5AA99, 60836, 60863, 68636, 6A609, 6A669, 6A696, 6A906, 6A966, 70048, 70103, 70471, 70583, 70714, 71474, 717A4, 71A09, 74084, 74444, 74448, 74477, 744A8, 74747, 74774, 7488A, 74A48, 75773, 77144, 77401, 77447, 77799, 77A09, 78008, 78783, 7884A, 78888, 788A8, 79939, 79993, 79999, 7A051, 7A444, 7A471, 80005, 80252, 80405, 80522, 80757, 80AA5, 83002, 84045, 85307, 86883, 88863, 8A788, 90073, 90707, 90901, 95003, 97779, 97939, 99111, 99177, 99973, A0111, A0669, A0966, A0999, A0A09, A1404, A4177, A4401, A4717, A5228, A52AA, A5558, A580A, A5822, A58AA, A5A59, A5AA2, A6096, A6966, A6999, A7051, A7778, A7808, A9055, A9091, A9699, A9969, AA52A, AA58A, 100019, 100079, 101113, 101119, 101911, 107003, 140004, 144011, 144404, 1A0019, 1A0141, 1A5001, 1A7005, 1A9001, 222223, 222823, 300107, 300202, 300323, 303203, 307577, 310007, 332003, 370777, 400555, 401A11, 404001, 404111, 405AAA, 41A011, 440A41, 441011, 451777, 455555, 470051, 470444, 474404, 4A0401, 4A4041, 500015, 500053, 500077, 500507, 505577, 522A2A, 525223, 528A2A, 531707, 550777, 553707, 5555A9, 555A99, 557707, 55A559, 5807A7, 580A0A, 580A55, 58A0AA, 590007, 599907, 5A2228, 5A2822, 5A2AAA, 5A552A, 5AA22A, 5AAA22, 60A069, 683006, 6A0096, 6A0A96, 6A9099, 6A9909, 700778, 701074, 701777, 704408, 704417, 704457, 704484, 707041, 707441, 707708, 707744, 707784, 710777, 717044, 717077, 740008, 74484A, 770441, 770744, 770748, 770771, 777017, 777071, 777448, 777484, 777701, 7778A8, 777A19, 777A48, 778883, 78A808, 790003, 7A1009, 7A4408, 7A7708, 80A555, 828283, 828883, 840555, 850505, 868306, 873005, 883202, 900701, 909739, 909979, 909991, 970771, 977701, 979909, 990739, 990777, 990793, 997099, 999709, 999901, A00009, A00599, A01901, A05509, A0A058, A0A955, A10114, A555A2, A55999, A59991, A5A222, A5A22A, A60609, A66069, A66906, A69006, A79005, A87888, A90099, A90996, A96006, A96666, A97177, A97771, AA0A58, AA5A22, AAA522, 1000501, 1011141, 1030007, 1070047, 111114A, 1111A14, 1111A41, 1144441, 14A4444, 1700005, 1700474, 1A44444, 2555505, 2845055, 3030023, 3100003, 3333397, 4000111, 4011111, 41A1111, 4411111, 444441A, 4444771, 4470004, 4505005, 4744417, 4774441, 4777404, 4777417, 4777747, 4A11111, 4A40001, 5000093, 50005A7, 5005777, 5050553, 5055503, 5070777, 5222222, 5222AAA, 52AAAA2, 52AAAAA, 5505053, 5552AAA, 5555599, 5555A58, 5558A0A, 5558A55, 5558AAA, 55A0009, 55AAA52, 580000A, 5822222, 58AAAAA, 5A2222A, 5AA2222, 6000A69, 6000A96, 6A00069, 7000417, 7000741, 7000835, 7000857, 7007177, 7008305, 7014447, 7017444, 7074177, 7077477, 7077741, 7077747, 7100447, 7174404, 717444A, 7400404, 7700717, 7701077, 7701707, 7707778, 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DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD ===Base 15=== 12, 14, 18, 1E, 21, 27, 2B, 2D, 32, 38, 3E, 41, 47, 4B, 4D, 54, 58, 5E, 67, 6B, 6D, 72, 74, 78, 87, 8B, 92, 94, 9E, A1, A7, AD, B2, B8, BE, C1, CB, CD, D2, D4, E1, ED, 111, 11B, 131, 137, 13B, 13D, 157, 15B, 15D, 171, 177, 197, 19D, 1B7, 1BB, 1D1, 1DB, 1DD, 234, 298, 311, 31B, 337, 33D, 344, 351, 357, 35B, 364, 377, 391, 39B, 39D, 3A4, 3BD, 3C4, 3D7, 3DB, 3DD, 452, 51B, 51D, 531, 53B, 551, 55D, 562, 571, 577, 5A2, 5B1, 5B7, 5BB, 5BD, 5C2, 5D1, 5D7, 634, 652, 681, 698, 717, 71B, 731, 737, 757, 75D, 77D, 79B, 79D, 7B1, 7B7, 7BD, 7D7, 7DD, 801, 852, 88D, 8D8, 91D, 93B, 93D, 95B, 95D, 971, 977, 97B, 97D, 988, 991, 9BD, 9C8, 9D1, A98, AAB, B1D, B31, B3B, B44, B51, B57, B7B, B7D, B97, B9B, BB7, BC4, BD1, BD7, BDD, C07, C34, C52, C7E, C98, CC7, CE7, D0E, D1D, D31, D51, D5B, D68, D77, D7B, D91, D97, DA8, DAE, DCE, DD1, EB4, EEB, 107B, 1091, 10B1, 1107, 110D, 1561, 1651, 1691, 1B01, 2052, 2502, 2522, 303B, 307D, 3097, 30BB, 30D1, 3107, 3361, 3701, 3907, 3B01, 3B0B, 3C97, 4434, 4498, 4834, 4898, 49A8, 4E34, 5037, 507D, 5091, 509B, 5107, 5161, 5202, 53C7, 5552, 570B, 590B, 590D, 59C7, 5A5B, 5C97, 5D0D, 5DAB, 6061, 6151, 6191, 6511, 6601, 6911, 707B, 7091, 7097, 70AE, 70BB, 70CE, 70DB, 7561, 760E, 7691, 76CE, 7907, 7961, 7A0E, 7A3B, 7AEE, 7B0B, 7BAB, 7C0E, 7C77, 7CAE, 7D0B, 7D61, 7DAB, 7E5B, 7E6E, 7E7B, 7EBB, 8098, 811D, 8191, 835D, 853D, 8881, 8908, 8951, 8968, 899D, 8D3D, 8D5D, 8D6E, 8DDD, 8E98, 9011, 9037, 9097, 90D7, 9301, 93C7, 95C7, 9611, 9631, 96A8, 9811, 9851, 989D, 990B, 990D, 998D, 99AB, 99C7, 99D8, 9A08, 9A9B, 9AA8, 9ABB, 9B61, 9BC7, 9D0B, 9DAB, 9DC7, 9DD8, A052, A304, A502, A55B, A9BB, AB04, AB64, B09D, B107, B10B, B161, B1AB, B1C7, B30D, B3C7, B50B, B664, B691, B6A4, B707, B761, B90D, B961, BA5B, BABB, BBAB, BBB4, BC37, BC77, C777, C937, C997, D011, D03D, D05D, D09B, D0B1, D0BD, D101, D10B, D30D, D3AB, D507, D50D, D66E, D761, D7DE, D811, D85D, D86E, D89D, D8C8, D8E8, D9AB, D9D8, DA3B, DA9B, DABB, DB01, DB61, DBAB, DC88, DD07, DD0B, DD7E, DD8D, DDE7, DE6E, E252, E33B, E522, E57B, E7AE, E7CE, E898, E997, E9A8, E9BB, EA34, EB5B, EE98, EEC7, 10017, 10B0D, 170AB, 17A0B, 19001, 19601, 1A09B, 1D0C7, 22E52, 2EA52, 30017, 3001D, 300B1, 301C7, 30334, 30631, 307AB, 3300B, 3333B, 36031, 36301, 37A0B, 37BBB, 39997, 3A30B, 3B0C7, 3D001, 3D601, 40034, 40968, 43334, 49668, 49998, 50022, 5009D, 501C7, 50222, 50507, 505C7, 50611, 50C57, 53007, 53997, 55537, 5555B, 5557B, 5599B, 56101, 56691, 56961, 5700D, 5755B, 59001, 59557, 59997, 5999D, 599DB, 59DDD, 5D99B, 5DD3D, 5DD9D, 60931, 63031, 65691, 66951, 69031, 69361, 69561, 70011, 70051, 7005B, 7006E, 7030D, 703AB, 70501, 70701, 707C7, 71601, 71951, 7300D, 7333B, 75001, 7555B, 75911, 76011, 76051, 766EE, 76EEE, 7700B, 77191, 77661, 7776E, 77771, 777BB, 77911, 77BBB, 79001, 7A05B, 7A66E, 7AA6E, 7AAAE, 7ACCE, 7C6EE, 7CCEE, 7CECE, 7CEEE, 7D3BB, 7E7C7, 7EECE, 80034, 80304, 80434, 809DD, 80A34, 84A34, 850DD, 85961, 86661, 88151, 88331, 88511, 88591, 88898, 890DD, 89998, 89D0D, 8D90D, 8E434, 90017, 90051, 900A8, 900DB, 901C7, 90C57, 90D8D, 91007, 91061, 9199B, 95997, 96068, 96561, 99397, 99537, 9999B, 999B7, 999D7, 999DB, 999DD, 99BBB, 99DBB, 99DD7, 99DDD, 9B007, 9B00B, 9B0AB, 9BB11, 9BBBB, 9D007, 9D08D, 9D537, 9D9BB, 9D9DB, 9DD57, 9DDB7, 9DDDB, 9DDDD, A0A34, A0B5B, A0BBB, A0E34, A2E52, A330B, A8434, A8834, A8E34, A909B, AAA34, AAE52, AB0BB, AB334, ABB34, AE034, AE834, AE99B, AEA52, AEE52, B0011, B0071, B0077, B00B1, B0611, B0A64, B500D, B599D, B6101, B7771, B7911, BA064, BAAA4, BAB34, BB061, BB304, BB53D, BB601, BBB91, BBB9D, BBBBD, BDA0B, BDBBB, D0088, D00D7, D0307, D05C7, D070D, D0888, D0B07, D0BC7, D0C08, D0DC7, D0DD8, D1661, D59DD, D5D3D, D5DDD, D6611, D700D, D8D0D, D900B, D9908, D999D, D9BBB, D9D9D, D9DDB, DB007, DB00D, DB1B1, DB53D, DB59D, DB99D, DBBB1, DD0D8, DD33B, DD3B7, DD3BB, DD57D, DD898, DD9DD, DDB37, DDBDB, DDD08, DDD3D, DDD5D, DDD7D, DDD88, DDD9D, DDDB7, DDDC8, DDDD7, DDE98, DE037, DE998, DEB07, E0098, E00C7, E0537, E0557, E077B, E0834, E0968, E3334, E37AB, E39C7, E4034, E5307, E55AB, E705B, E750B, E766E, E76EE, E8304, E8434, E9608, E9C37, EAE52, EBB0B, EC557, EC597, EC957, 1000BD, 1009AB, 10A90B, 1900AB, 190661, 19099B, 190A0B, 1A900B, 222A52, 2AAA52, 31000D, 330331, 333334, 3733AB, 373ABB, 3BBB61, 430004, 490068, 490608, 5000DB, 500D0B, 505557, 505A0B, 50D00B, 50DDDB, 50DDDD, 522222, 5500AB, 5500C7, 550957, 550A0B, 555A9B, 559057, 560011, 590661, 633331, 666331, 666591, 666661, 7050AB, 705A0B, 706101, 70A50B, 7300AB, 761661, 76666E, 777011, 777101, 77750B, 777A5B, 777CEE, 779051, 791501, 7E7797, 7ECCCE, 7EEE97, 800D9D, 808834, 836631, 83D661, 843004, 856611, 884034, 884304, 888E34, 88A434, 88AE34, 8A4034, 8AEE34, 8E8034, 8E8E34, 8EEE34, 9000BB, 9001AB, 900B07, 900D98, 903661, 905661, 906651, 9080DD, 9099A8, 909D9B, 90A668, 90DD9B, 90DDBB, 910001, 9100AB, 91A00B, 930007, 950001, 956661, 9909A8, 995907, 999068, 999507, 999907, 9B0B1B, 9B0BB1, 9BB01B, 9C5597, 9C5957, 9D09DD, 9D0D9D, 9D800D, 9DB307, 9DD09D, A00034, A0033B, A033B4, A2A252, AAAA52, ABBBBB, B00004, B0001B, B0003D, B00A04, B0555B, B07191, B07711, B07777, B0B911, B0BDBB, B77011, B777C7, BB0001, BB0034, BB035D, BB055B, BB0BDB, BB9101, BBB0DB, BBB50D, BBBB01, BBD0BB, C55397, C55557, C55597, D0003B, D00057, D0007D, D000B7, D000C8, D008DD, D00DAB, D0333B, D05537, D099DD, D09DDD, D0DDBB, D555C7, D5C537, D88008, D88088, D888EE, D909DD, D9D0DD, D9DD0D, DB0BBB, DBBB0B, DBBB0D, DC0008, DC5537, DDDDD8, DDDEBB, DDE99B, DE0808, DE0C57, DE300B, DE5537, DE8888, DEE088, DEE307, DEE888, DEEE37, DEEE57, DEEEC8, E0000B, E007BB, E00A52, E03BC7, E07ABB, E09B07, E0A99B, E0C397, E0E76E, E50057, E55007, E55597, E55937, E730AB, E73A0B, E80E34, E88834, E8E034, E90008, E95557, EA099B, EE4304, EE5057, EE5507, EE8E34, EE9307, EEE434, 100001D, 1000A9B, 1000DC7, 22AA252, 3000BC7, 3033301, 3076661, 333B304, 33B3034, 3B33304, 3D66661, 50007AB, 5005957, 5500597, 5550057, 5559007, 5559597, 5595007, 5966661, 5DDDDDB, 6366631, 7010001, 7066651, 7100061, 733BBBB, 766A6AE, 77505AB, 7776501, 777775B, 777AACE, 777ECCE, 777EEAE, 7CCCCCE, 7E30A0B, 7EEEEAE, 8300004, 8363331, 8693331, 880E834, 8833304, 8888034, 8888434, 888A034, 88A3334, 88E8834, 88EE034, 88EE304, 8AA3334, 8D0009D, 8EE8834, 9000361, 9000668, 9003331, 9005557, 9006008, 9008D0D, 9083331, 9090968, 90BBB01, 90D0908, 9500661, 9555597, 9555957, 9660008, 9900968, 9995597, 9996008, 9999557, 9999597, 9999908, 9A66668, A003B34, A003BB4, AA22252, B00B034, B00B35D, B033334, B0B6661, B0BB01B, B100001, B333304, B777777, B99999D, BA60004, BAA0334, BBB001B, BBB6611, BBBBB11, BBBD00B, BD000AB, D0000DB, D009098, D00CCC8, D00D908, D00D99D, D03000B, D0BB0BB, D0D9008, D0D9998, D1000C7, D800008, D8DDEEE, D90080D, DBBBBBB, DD09998, DDD5557, DDDDBBB, DDDDDBD, DDDE8EE, DECC008, DECCCC8, DEE0CC8, DEEC0C8, E000397, E0003BB, E000434, E00076E, E000937, E007A5B, E00909B, E0090B7, E009307, E00B077, E00E434, E00E797, E00E937, E05999B, E09009B, E0900B7, E0E0937, E0E7E97, E0EAA52, E0EEA52, E555057, E5555C7, E7777C7, E77E797, E88EE34, E999998, EA5999B, EB000BB, EB0BBBB, EE00434, EE0E797, EEE076E, EEE706E, EEE8834, EEEE557, EEEE797, 30333331, 30B66661, 33000034, 33030004, 33B33004, 500575AB, 55000007, 5500075B, 55500907, 55555057, 55555907, 55559507, 60003301, 60033001, 60330001, 7000003D, 70106661, 70666611, 77000001, 7777770B, 777777C7, 77777ACE, 77777EAE, 777E30AB, 777E3A0B, 7CCCC66E, 800005DD, 88AA0834, 90000008, 900008DD, 90099668, 90500557, 90555007, 90666668, 90909998, 90990998, 90996668, 9099999D, 90D00098, 90D90998, 95500057, 99099098, 99555057, 99900998, 99966608, 99966668, 99999668, 99999998, 9D009008, 9D090998, A0803334, A2222252, AAA52222, B00005AB, B000B55B, B0BBBB5B, B3330034, BB0BBB1B, BBAA3334, BBB0BB1B, BBB0BB5B, BBDB000B, D000BBBB, D00100C7, D8888888, D900008D, D9000098, DBB000BB, DC0CCCC8, DCC0CCC8, DCCCC008, DD000908, DD09009D, DDDDDDAB, DDDDDEEE, DDDEEE8E, DDDEEEE8, DEE80008, E0777E97, E0E0E397, E0E77797, E0EE0397, E7777797, E9066668, EE00E397, EE077797, EE0E0397, EEE00797, EEE07E97, EEE0AA52, EEE55397, EEE55557, EEEAAA52, EEEEE834, EEEEEA52, 300003331, 300007661, 300330031, 333000004, 333300001, 333B00034, 3700000AB, 3B3300034, 500000057, 555555007, 555555557, 5DDDDDDDD, 600000331, 7500000AB, 75000A00B, 75A00000B, 761000001, 77000E0C7, 777700EC7, 7777730AB, 7777777AE, 77777EE97, 7777E7E97, 777999997, 7A500000B, 7BBBBBB5B, 88888A834, 900000031, 900666608, 909990098, 90D009998, 950000557, 966666008, 990000007, 990555507, 999999997, A000000B4, A0005999B, AAEEEEE34, B000AA334, BBBBB005B, BBBBBBB5B, D09999998, D0D90009D, D800000DD, D90009998, DCCCC0CC8, DE88EEEEE, DEEEEEE88, E000B7777, E000BBBBB, E003ABBBB, EE0000797, EE0EEE397, EE5555557, EE777EE97, EEEEEE537, EEEEEE937, 2222222252, 3000000071, 3330030001, 3333303001, 3333330001, 500000007B, 5555555097, 7000000071, 77000000C7, 8333333331, 8888883334, 8888888834, 888888AA34, 900000009B, 900000009D, 900000DD9D, 9000099998, 9955555507, 9D0000099D, 9D05555557, AB0000005B, B000000DAB, B00000BBDB, BB00BB0B5B, BB0BB00B5B, D000099998, D00090008D, D0D000909D, D0DDDDDDDB, D300000007, D88EEEEEEE, D900999998, DD00900008, DDD6EEEEEE, DDDDDDD6EE, DDDDDDDDDE, DDDEEEEEEE, DEEEEE8008, E000000797, 7777777CCCE, 88888830004, 90000009D9D, 99955555557, 9999999999D, B00000D00AB, BB000BBB05B, BBBB0000B5B, D000009080D, D000090800D, D090800000D, DDDDDDD999B, DDDDDDDDD9B, EEEEEE00397, EEEEEEE0397, 333000000301, 5000000000DD, 73A00000000B, 9000000000B7, 903333333331, ABB00000000B, D000000001C7, DCCCCCCCCCC8, E0EEEEEEE397, 19A000000000B, 3333333333331, 3BBBBBBBBBBBB, 9333333333331, A00000000099B, B00000000050D, EEEEEEEEEE76E, 1000000000999B, 71000000000001, 908D000000000D, BBBBBBBBBB6661, 77777777777777B, BB00000000BBB5B, DEEEEEEEEEEEEEE, 7777777777777E97, B0BBBBBBBBBBBB1B, BB0000000000DB0B, D000000000000998, D908000000000000D, DDDDDDDDDDDDDDDDB, E9666666666666668, 3330000000000000031, D00000000000000908D, E0BBBBBBBBBBBBBBBBB, 2EEEEEEEEEEEEEEEEE52, 77777777777777777ECE, 5000000000000000005AB, 777777777777777777997, 7BBBBBBBBBBBBBBBBBBBB, BB0000000000000000DBB, DD000000000000000909D, D900000000000000000DDD, DD0000000000000000099D, BBBBBBBBBBBBBBBBBBBBBB1, B00000000000000000000005B, B0700000000000000000000001, B70000000000000000000000001, 705000000000000000000000000B, 633000000000000000000000000001, EBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB, 500000000000000000000000000000000017, 77777777777777777777777777777777777777777777777777777777777CCE, 7777777777777777777777777777777777777777777777777777777777777777777777777CE, 96666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666608, EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE397, 7777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777797 ===Base 16=== 11, 13, 17, 1D, 1F, 25, 29, 2B, 2F, 35, 3B, 3D, 43, 47, 49, 4F, 53, 59, 61, 65, 67, 6B, 6D, 71, 7F, 83, 89, 8B, 95, 97, 9D, A3, A7, AD, B3, B5, BF, C1, C5, C7, D3, DF, E3, E5, E9, EF, F1, FB, 14B, 15B, 185, 199, 1A5, 1BB, 1C9, 1EB, 223, 22D, 233, 241, 277, 281, 287, 28D, 2A1, 2D7, 2DD, 2E7, 301, 337, 373, 377, 38F, 3A1, 3A9, 41B, 42D, 445, 455, 45D, 481, 4B1, 4BD, 4CD, 4D5, 4E1, 4EB, 50B, 515, 51B, 527, 551, 557, 55D, 577, 581, 58F, 5AB, 5CB, 5CF, 5D1, 5D5, 5DB, 5E7, 623, 709, 727, 737, 745, 74B, 755, 757, 773, 779, 78D, 7BB, 7C3, 7C9, 7CD, 7DB, 7EB, 7ED, 805, 80F, 815, 821, 827, 841, 851, 85D, 85F, 8A5, 8DD, 8E1, 8F5, 923, 98F, 99B, 9A9, 9EB, A21, A6F, A81, A85, A99, A9F, AA9, AAB, ACF, B1B, B2D, B7B, B8D, B99, B9B, BB7, BB9, BCB, BDD, BE1, C0B, CB9, CBB, CEB, D01, D21, D2D, D55, D69, D79, D81, D85, D87, D8D, DAB, DB7, DBD, DC9, DCD, DD5, DDB, DE7, E21, E27, E4B, E7D, E87, EB1, EB7, ED1, EDB, EED, F07, F0D, F4D, FD9, FFD, 1069, 1505, 1609, 1669, 16A9, 19AB, 1A69, 1AB9, 2027, 204D, 2063, 207D, 20C3, 20ED, 2221, 22E1, 2327, 244D, 26C3, 274D, 2E01, 2E0D, 2ECD, 3023, 3079, 3109, 3263, 3341, 36AF, 3941, 3991, 39AF, 3E41, 3E81, 3EE1, 3EE7, 3F79, 4021, 40DB, 440B, 444B, 44A1, 44AB, 44DB, 4541, 45BB, 4A41, 4B0B, 4BBB, 4C4B, 4D41, 4DED, 5045, 50A1, 50ED, 540D, 5441, 555B, 556F, 5585, 560F, 56FF, 5705, 574D, 580D, 582D, 5855, 588D, 5A01, 5AA1, 5B01, 5B4B, 5B87, 5BB1, 5BEB, 5C4D, 5CDD, 5CED, 5DD7, 5DDD, 5E0D, 5E2D, 5EBB, 68FF, 6A69, 6AC9, 6C8F, 6CA9, 6CAF, 6F8F, 6FAF, 7033, 7063, 7075, 7087, 70A5, 70AB, 7303, 7393, 74DD, 754D, 7603, 7633, 7663, 7669, 7705, 772D, 775D, 77D5, 7807, 7877, 7885, 7939, 7969, 7993, 79AB, 7A05, 7A69, 7A9B, 7AA5, 7B77, 7BA9, 7D4D, 7D75, 7D77, 8077, 808D, 80D7, 80E7, 8587, 86CF, 8777, 8785, 8885, 88CF, 88ED, 88FD, 8C6F, 8C8F, 8E8D, 8EE7, 8F2D, 8F8D, 9031, 9041, 90AF, 90B9, 9221, 9319, 9401, 944B, 9881, 9931, 9941, 9991, 99AF, 9A0F, 9A1B, 9A4B, 9AFF, 9BA1, 9BB1, 9CAF, 9E81, 9EA1, 9FAF, A001, A05B, A0C9, A105, A10B, A4CB, A55B, A6C9, A88F, A91B, A9B1, A9BB, AA15, AB01, AB0B, AB19, ABBB, AC09, AF09, B041, B04B, B069, B07D, B087, B0B1, B0ED, B1A9, B201, B40B, B40D, B609, B70D, B7A9, B807, B9A1, BA41, BAA1, BB4B, BBB1, BBDB, BBED, BD19, BD41, BDBB, BDEB, BE07, BEE7, C0D9, C203, C24D, C6A9, C88D, C88F, C8CF, C8ED, C9AF, C9CB, CA09, CA4B, CA69, CAC9, CC0D, CC23, CC4D, CC9B, CD09, CDD9, CE4D, CEDD, CFA9, CFCD, D04B, D099, D405, D415, D44B, D4A5, D4DD, D50D, D70B, D74D, D77B, D7CB, D91B, D991, DA05, DA09, DA15, DA51, DB91, DBEB, DD7D, DDA1, DDED, DE0B, DE41, DE4D, DEA1, E02D, E07B, E0D7, E1CB, E2CD, E401, E801, EABB, EACB, EAEB, EBAB, EC4D, ECDD, ED07, EDD7, EE7B, EE81, EEAB, EEE1, F08F, F0A9, F227, F2ED, F3AF, F485, F58D, F72D, F763, F769, F787, F7A5, F7E7, F82D, F86F, F877, F88D, F8D7, F8E7, F8FF, FCCD, FED7, FF85, FF8F, FFA9, 100AB, 10BA9, 1A0CB, 1BA09, 200E1, 2C603, 2CC03, 30227, 303AF, 30AAF, 32003, 32207, 32CC3, 330AF, 33169, 33221, 33391, 33881, 33AFF, 38807, 38887, 3AFFF, 3F203, 3F887, 3FAFF, 400BB, 4084D, 40A4B, 42001, 44221, 44401, 444D1, 4480D, 4488D, 44CCB, 44D4D, 44E8D, 4804D, 4840D, 4A0CB, 4A54B, 4CACB, 4D0DD, 4D40D, 4D44D, 5004D, 50075, 502CD, 5044D, 50887, 50EE1, 5448D, 548ED, 55A45, 55F45, 5844D, 5A4A5, 5AE41, 5B0CD, 5B44D, 5BBCD, 5D4ED, 5E0E1, 5EB4D, 5EC8D, 5ECCD, 5EE41, 5F06F, 5F7DD, 5F885, 5F8CD, 5FC8D, 5FF75, 6088F, 60AFF, 630AF, 633AF, 660A9, 668CF, 669AF, 66A09, 66A0F, 66FA9, 6886F, 6A00F, 6A0FF, 6A8AF, 6AFFF, 7002D, 7024D, 70B0D, 70B7D, 7200D, 73363, 73999, 7444D, 770B7, 777D7, 77B07, 77D7D, 77DD7, 79003, 79999, 7B00D, 7D05D, 7D7DD, 8007D, 800D1, 8074D, 82CCD, 82E4D, 8448D, 8484D, 8704D, 8724D, 87887, 88001, 8800D, 880CD, 88507, 88555, 8866F, 8872D, 8877D, 888D1, 888D7, 88AA1, 88C2D, 88D57, 88D75, 88D77, 8AFAF, 8C2CD, 8C40D, 8C8CD, 8CCED, 8CE2D, 8CFED, 8E007, 8E20D, 8E24D, 8F6FF, 8FAAF, 900CB, 901AB, 90901, 909A1, 90AB1, 90AE1, 90EE1, 910AB, 93331, 940AB, 963AF, 966AF, 99019, 99109, 99A01, 9AAE1, 9B00B, 9B0AB, 9B441, 9BABB, 9BBBB, 9E441, A00BB, A0405, A044B, A08AF, A0A51, A0B91, A0C4B, A1B09, A54A5, A5B41, A6609, A904B, A94A1, A9C4B, A9E01, A9E41, AA0A1, AA441, AA501, AA8AF, AAEE1, AAF45, AAF8F, ABBA1, ACC69, AE0BB, AE0EB, AEAE1, AEE0B, AEEA1, AEECB, AF045, AF4A5, AFA8F, B00A1, B00D7, B044D, B0777, B0A0B, B0A91, B0BBD, B0BCD, B0C09, B0DA9, B0EAB, B2207, B4001, B6669, B7707, B7D07, B8081, B9021, BA091, BA109, BA4BB, BB001, BB0EB, BB8A1, BBBEB, BBE0B, BBEBB, BC009, BCECD, BD0A9, BE44D, BEB0D, BEBBB, BEEBB, C0263, C02C3, C02ED, C040D, C0CA9, C0CCD, C2663, C2CED, C32C3, C3323, C400D, C40ED, C44CB, C44ED, C480D, C484D, C4CAB, C60AF, C686F, C6A0F, C86FF, C8C2D, CAA0F, CAFAF, CBCED, CC0AF, CC44B, CC82D, CC8FF, CCAF9, CCAFF, CCCFD, CCFAF, CD00D, CD4CB, CD4ED, CDDDD, CF2C3, CFC8F, CFE8D, D0045, D07DD, D09BB, D0D4D, D0DD7, D0EBB, D0EEB, D1009, D1045, D10B9, D1BA9, D54BB, D54ED, D5AE1, D5D07, D5EE1, D70DD, D7707, D7777, D77DD, D7DD7, D9441, D9AE1, D9B0B, DA9A1, DA9E1, DAA41, DAAA1, DBB0B, DBBA1, DC4CB, DD227, DD44D, DDDD7, E0081, E00E1, E010B, E088D, E08CD, E0B0D, E0BBD, E100B, E4D0D, E777B, E77AB, E7CCB, E844D, E848D, E884D, E88A1, EB0BB, EBB4D, EBBEB, EBEEB, EC8CD, ECBCD, ECC8D, ED04D, EE001, EE0EB, EE4A1, EEEBB, F0085, F09AF, F0C23, F0CAF, F2663, F2C03, F3799, F3887, F4A05, F4AA5, F506F, F5845, F5885, F5C2D, F5ECD, F5F45, F66A9, F688F, F6AFF, F7399, F777D, F8545, F8555, F8AAF, F8F87, F9AAF, FA0F9, FA405, FA669, FAFF9, FC263, FCA0F, FCAFF, FCE8D, FCF23, FD777, FDDDD, FDEDD, FEC2D, FEC8D, FF545, FF6AF, FF739, FF775, FF9AF, FFC23, 100055, 100555, 10A9CB, 1A090B, 1A900B, 1CACCB, 1CCACB, 20DEE1, 266003, 3000AF, 300A0F, 300AFF, 308087, 308E07, 3323E1, 333A0F, 339331, 33CA0F, 33CF23, 33CFAF, 33F323, 380087, 3A00AF, 3A0F0F, 3AA0FF, 3AAF0F, 3C33AF, 3C3A0F, 3C3FAF, 3CCAAF, 3F0FAF, 3F32C3, 3FF0AF, 3FFAAF, 4004CB, 400A05, 4048ED, 404DDD, 40AA05, 40D04D, 40DD4D, 40E0DD, 40E48D, 440041, 44008D, 44044D, 4404DD, 44440D, 4448ED, 4484ED, 448E4D, 44E44D, 48888D, 4AA005, 4DD00D, 4DD04D, 4DDD0D, 4E048D, 4E448D, 4E880D, 5000DD, 500201, 50066F, 5008CD, 500C2D, 500D7D, 50C20D, 520C0D, 544EDD, 54AA05, 54AAA5, 54ED4D, 566AAF, 57D00D, 580087, 5A5545, 5C20CD, 5C8CCD, 5CC2CD, 5D000D, 5D070D, 5F666F, 5FAA45, 5FFF45, 60008F, 600A0F, 603AAF, 6060AF, 6066AF, 60A0AF, 63AA0F, 6663AF, 66668F, 666AAF, 668A8F, 66AFF9, 68888F, 693AAF, 7007B7, 70404D, 70770B, 70770D, 707BE7, 70DD0D, 733339, 733699, 74004D, 74040D, 77007B, 770CCB, 777B4D, 777BE7, 777CCB, 77ACCB, 77B74D, 77D0DD, 7A0CCB, 7B744D, 7CACCB, 7DDD99, 80044D, 800807, 80200D, 8044ED, 80C04D, 80CC2D, 80E44D, 8404ED, 84888D, 84E04D, 84E40D, 86686F, 8668AF, 8686AF, 86F66F, 86FFFF, 87000D, 87744D, 880807, 886AFF, 88824D, 88870D, 888787, 88884D, 88886F, 88887D, 88888D, 888C4D, 888FAF, 88AA8F, 88CC8D, 88F6AF, 88F8AF, 88FA8F, 88FF6F, 88FF87, 88FFAF, 8A8FFF, 8C0C2D, 8C802D, 8CCFFF, 8CE00D, 8CE0CD, 8CFCCF, 8E00CD, 8E044D, 8E0CCD, 8EC0CD, 8F68AF, 8F88F7, 8FCFCF, 8FF887, 8FFCCF, 8FFF6F, 9002E1, 9004AB, 9008A1, 900919, 900ABB, 900B21, 90B801, 90CCCB, 9332E1, 944441, 94ACCB, 990001, 9900A1, 9A4441, 9A4AA1, 9AA4A1, 9AAA41, 9AAAAF, 9B66C9, 9BBA0B, 9BC0C9, 9BC669, 9BC6C9, 9C4ACB, A0094B, A00ECB, A09441, A0A08F, A0E0CB, A0ECCB, A0F669, A40A05, A4AAA5, A50E41, A5AA45, A60069, A8FAFF, A9AA41, AA5E41, AAA4A5, AAA545, AC6669, ACCC4B, ACCCC9, AEAA41, AFF405, AFF669, AFFA45, AFFFF9, B00921, B00BEB, B00CC9, B00D91, B08801, B0D077, B70077, B70E77, B77E77, B88877, B88881, B94421, BAE00B, BB00AB, BB0DA1, BB444D, BB44D1, BB8881, BBBBBD, BBBC4D, BBCCCD, BC0CC9, BC66C9, BCC669, BCC6C9, BCCC09, BE000D, BE00BD, BE0B4D, BE0CCD, BEA00B, BECCCD, C0084D, C00A0F, C0608F, C0668F, C0844D, C0A0FF, C0AFF9, C0C3AF, C0C68F, C0CAAF, C0CDED, C0D0ED, C0E80D, C0EC2D, C0EC8D, C0FA0F, C0FAAF, C2CC63, C30CAF, C333AF, C3CAAF, C3CCAF, C4048D, C40D4D, C4404D, C4408D, C4440D, C44DDD, C4ACCB, C4DCCB, C4DD4D, C6068F, C66AAF, C68AAF, C6AA8F, C8044D, C8440D, C8666F, CA00FF, CA0FFF, CAAAAF, CAAFFF, CAFF0F, CBE0CD, CC008F, CC0C8F, CC3CAF, CC4ACB, CC608F, CC66AF, CCBECD, CCC4AB, CCCA0F, CCCC8F, CCCE8D, CE0C8D, CF0F23, CF0FAF, CFAFFF, CFCAAF, CFFAFF, D0005D, D00BA9, D05EDD, D077D7, D10CCB, D22207, D4000B, D4040D, D4044D, D40CCB, D70077, D7D00D, D90009, D900BB, DB00BB, DB4441, DD400D, DDD109, DDD1A9, DDD919, DDD941, DED00D, E00D4D, E00EEB, E0AAE1, E0AE41, E0AEA1, E0B44D, E0BCCD, E0BEBB, E0D0DD, E0E441, E4048D, E4448D, E800CD, E8200D, EA0E41, EAA0E1, EBB00B, ECCCAB, EDDDDD, EEBE0B, F00263, F0056F, F00A45, F02C63, F03F23, F05405, F060AF, F08585, F0A4A5, F0F2C3, F0F323, F2CCC3, F33203, F33C23, F5F66F, F5FF6F, F68CCF, F6AA8F, F888AF, FA0F45, FAA045, FAA545, FAFC69, FC0AAF, FC66AF, FCCCAF, FCFFAF, FF0323, FF056F, FF3203, FF7903, FFA045, FFA4A5, FFAA45, FFC0AF, FFF4A5, FFF575, FFFA45, FFFCAF, 10A009B, 20000D1, 2CCC663, 30A00FF, 30CCCAF, 30FA00F, 30FCCAF, 3333C23, 333C2C3, 33C3AAF, 33FCAAF, 33FFFAF, 3A0A00F, 3AAAA0F, 3AF000F, 3AFAAAF, 3C0CA0F, 3CCC3AF, 3CFF323, 3F33F23, 3FAA00F, 3FF3323, 4004441, 400DDD1, 400E00D, 400ED0D, 404404D, 404448D, 404E4DD, 440EDDD, 4440EDD, 44444ED, 4444E4D, 44DDDDD, 4A000A5, 4CCCCAB, 4D0CCCB, 4E4404D, 4E4444D, 4E4DDDD, 5000021, 5004221, 5006AAF, 500FF6F, 5042201, 508CCCD, 5400005, 5400AA5, 5555405, 5808007, 5AA4005, 5C0008D, 5CCC8CD, 5D4444D, 5EEEEEB, 5F40005, 5F554A5, 5F6AAAF, 60000AF, 60006A9, 600866F, 6008AAF, 600AA8F, 600F6A9, 606608F, 606686F, 608666F, 60AA08F, 60AAA8F, 66000AF, 66666A9, 6666AF9, 6866A8F, 6AAAAAF, 70070D7, 70077DD, 700DDDD, 707077D, 707D007, 70D00DD, 770077D, 770400D, 770740D, 7777775, 77777B7, 77777DD, 7777ACB, 77B88E7, 77DD00D, 77DDDDD, 7D0D00D, 7DD0D07, 7DDD00D, 800002D, 8000CED, 80C0E0D, 80CECCD, 840400D, 844000D, 844E00D, 868688F, 880444D, 884404D, 887D007, 8888801, 8888881, 8888E07, 8888F77, 8888FE7, 88A8AFF, 88AAAFF, 88FAFFF, 8A8AAAF, 8A8AAFF, 8AAA8FF, 8C00ECD, 8C8444D, 8E4400D, 8FCCCCF, 900BBAB, 90CC4AB, 9908AA1, 99E0E01, 9B00801, 9B6CCC9, A000FF9, A006069, A00A8FF, A01CCCB, A05F545, A0BEEEB, A0E4AA1, AA0008F, AA08FFF, AA40AA5, AA8FFFF, AAAA405, AE04AA1, AE44441, AE4AAA1, AECCCCB, AF40005, AFA5A45, AFFFC69, B000BAB, B000EBB, B0D0007, B222227, B6CCCC9, B8880A1, BA000EB, BA0BEEB, BAEEEEB, BB000CD, BB00C0D, BB0B00D, BC6CC69, BC6CCC9, BCCCC69, BCCCCED, C0000A9, 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4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444DD ===Base 17=== 12, 16, 1C, 1E, 23, 27, 29, 2D, 32, 38, 3A, 3G, 43, 45, 4B, 4F, 54, 5C, 5G, 61, 65, 67, 6B, 78, 7C, 81, 83, 8D, 8F, 94, 9A, 9E, A3, A9, AB, B4, B6, BA, BC, C7, D2, D6, D8, DC, E1, E3, ED, F2, F8, FE, FG, G5, G9, GB, 104, 111, 115, 117, 11B, 137, 139, 13D, 14A, 14G, 155, 159, 15F, 171, 17B, 17D, 188, 191, 197, 19F, 1A4, 1A8, 1B3, 1BB, 1BF, 1DB, 1DD, 1F3, 1FD, 1G8, 1GA, 1GG, 20F, 214, 221, 225, 241, 25A, 25E, 285, 2B8, 2C5, 2CF, 2E5, 2EB, 2F6, 30E, 313, 331, 33B, 346, 34C, 351, 35F, 36E, 375, 37B, 391, 39B, 39D, 3B7, 3B9, 3BF, 3D3, 3D5, 3D9, 3DF, 3E4, 3EC, 3F1, 3F7, 407, 418, 447, 44D, 472, 474, 47E, 47G, 489, 49C, 4A1, 4C1, 4CD, 4D4, 4G1, 502, 506, 508, 50E, 519, 522, 528, 52A, 52E, 533, 53F, 551, 55D, 562, 566, 573, 577, 57F, 582, 593, 599, 59B, 59F, 5A6, 5B5, 5D1, 5D3, 5EA, 5EE, 5F9, 60D, 62F, 634, 649, 689, 692, 6CD, 6EF, 6F4, 6FA, 704, 706, 70G, 71D, 726, 737, 739, 73D, 73F, 753, 755, 764, 766, 76G, 771, 77B, 793, 7AA, 7AE, 7B3, 7BB, 7D7, 7E6, 7F3, 7F9, 7FF, 7G2, 7GE, 7GG, 825, 82B, 849, 852, 85E, 869, 876, 87A, 87G, 88B, 892, 898, 89C, 8C5, 8E7, 8G7, 908, 90G, 913, 91F, 92C, 935, 937, 93B, 951, 953, 957, 95D, 968, 96G, 979, 97B, 98C, 98G, 99D, 9B1, 9B3, 9B9, 9BD, 9BF, 9DB, 9DF, 9F1, 9F5, 9G6, A07, A0D, A1A, A2F, A4D, A72, A7A, A7E, AA1, AA7, ACF, ADA, AG1, AG7, B02, B08, B17, B1D, B28, B2G, B57, B71, B73, B79, B7F, B88, B8E, B8G, B9B, B9F, BB5, BB7, BD7, BDD, BEG, BFF, BGG, C01, C2F, C3E, C56, C6D, C89, C92, C9G, CA5, CBG, CC1, CC5, CF4, CFA, D04, D0A, D15, D3D, D3F, D55, D59, D5B, D71, D75, D7D, D91, D97, D99, D9D, DA4, DAG, DB3, DDB, DF1, DF7, DF9, DFF, E05, E0B, E2B, E52, E58, E69, E92, E9C, EAF, EB8, EC9, ECB, EE5, F04, F15, F1B, F35, F3B, F46, F51, F53, F64, F6A, F73, F79, F95, FAC, FB1, FCA, FD5, FDB, FF1, FF7, FFD, G0D, G0F, G18, G1A, G1G, G2F, G34, G63, G7G, GA7, GC3, GDG, GEF, GFA, GG7, GGD, 1013, 101D, 1033, 1035, 1051, 105B, 105D, 1077, 108A, 109B, 10AG, 10B1, 10B7, 10BD, 10FB, 1149, 1189, 11AF, 11G3, 1303, 130B, 1314, 1341, 1479, 14D9, 1501, 1503, 15A1, 15B8, 1734, 1749, 17AF, 17G3, 1844, 185B, 1875, 1877, 18AG, 18B5, 1903, 1909, 1958, 19BG, 19G3, 1A5D, 1A75, 1A7F, 1ADF, 1AF1, 1B01, 1B09, 1B18, 1B85, 1B89, 1BDG, 1BGD, 1D07, 1D49, 1D9G, 1DF4, 1F09, 1F47, 1F5A, 1F74, 1F7A, 1FA1, 1FAF, 2018, 201G, 202B, 208B, 20G1, 215B, 218G, 21AG, 21B1, 222F, 22AF, 22BG, 22EF, 22F4, 22GF, 251B, 2526, 25F1, 266F, 26FC, 280B, 2A05, 2A58, 2AFC, 2AGF, 2B1B, 2B1F, 2BGE, 2C1G, 2C2B, 2C8B, 2CG1, 2E2F, 2EGF, 2F0C, 2F55, 2FAA, 2FC4, 2FFF, 2GA1, 2GFC, 2GG1, 2GGF, 301B, 301F, 3037, 3053, 3057, 3079, 3095, 30B3, 30BD, 30C4, 31F4, 330D, 3334, 333E, 3349, 3376, 337E, 33CD, 33EF, 3411, 3417, 3499, 3503, 3505, 3509, 353E, 35E5, 35EB, 3604, 36FD, 3701, 3741, 374D, 376F, 3796, 37D4, 37F4, 3956, 3B03, 3B05, 3B0B, 3BBE, 3C04, 3C15, 3C19, 3C4E, 3C59, 3C64, 3CB3, 3CDB, 3CE6, 3D07, 3D14, 3DDE, 3E77, 3E79, 3E7F, 3E99, 3EEE, 3EFB, 3F05, 3F0D, 3FCB, 3FF4, 4009, 4021, 4069, 4098, 40DG, 40GD, 419D, 4201, 4401, 4492, 46AD, 46C9, 46DA, 4719, 476A, 4779, 479D, 47A6, 4906, 4911, 4917, 4919, 491D, 492G, 4982, 4988, 49D7, 49D9, 49GG, 4ADE, 4AE7, 4C49, 4C96, 4CC9, 4D79, 4DAE, 4DEG, 4E7A, 4E96, 4EG7, 4G6D, 4G87, 501B, 5037, 5059, 507D, 50BB, 50BF, 50D7, 50DD, 50F1, 5105, 51A7, 51AD, 521B, 525F, 52FB, 5307, 5356, 53BE, 53DE, 53E9, 5507, 550B, 5587, 5598, 55EF, 560A, 568E, 56AA, 56F3, 5709, 5725, 572B, 575A, 575E, 5769, 57A1, 57B2, 5868, 586E, 58AE, 58B9, 590D, 5918, 5952, 5958, 596D, 5A17, 5A1F, 5ADD, 5ADF, 5AE8, 5B07, 5B21, 5B2F, 5B3E, 5BEF, 5DA7, 5DEB, 5E57, 5E5F, 5E86, 5E97, 5EB9, 5EBF, 5EF5, 5F01, 5F1A, 5F6F, 5FA7, 5FDA, 60AF, 60G3, 64AD, 64DE, 64DG, 663E, 666D, 66AF, 693D, 69CG, 69D3, 69D9, 69G8, 69GC, 6ADE, 6AGD, 6C98, 6D33, 6D4E, 6D93, 6D9F, 6DDD, 6DEE, 6DF3, 6DFD, 6DGE, 6E09, 6G36, 6G4D, 6G6D, 6GD4, 6GDE, 6GFC, 702E, 7057, 705B, 7073, 7079, 7095, 70B5, 70BD, 70D1, 70E2, 70F5, 7107, 7149, 719G, 71BG, 71F4, 724E, 724G, 725F, 72A2, 72BF, 72EE, 72GA, 7314, 733E, 7341, 7363, 73EB, 7419, 742A, 742G, 7442, 74EG, 7501, 750F, 751A, 756D, 757E, 75A1, 75A7, 75BE, 75DA, 75E9, 75F6, 7622, 769F, 76EA, 7734, 773E, 776D, 779G, 77AF, 7905, 790B, 7976, 79B2, 79F6, 79GD, 7A1F, 7A5D, 7AD5, 7ADF, 7AF1, 7AFD, 7B01, 7B09, 7B2F, 7B52, 7B72, 7BE5, 7D01, 7D05, 7D9G, 7DAF, 7DBG, 7E0A, 7E75, 7EA2, 7EA4, 7EB5, 7EBF, 7EE2, 7EF7, 7EG4, 7F0B, 7F14, 7F5A, 7F76, 7FA7, 7G1F, 7G46, 7GA6, 7GD3, 7GDF, 8009, 8058, 80B8, 80E9, 84A7, 850A, 8557, 857B, 85A8, 870E, 8744, 8777, 879B, 87B5, 87B7, 87EE, 8805, 8872, 8887, 8889, 88E9, 8906, 8959, 8966, 89GG, 8A87, 8AE5, 8B0G, 8B59, 8B95, 8B97, 8CB2, 8CB8, 8CE9, 8E56, 8EE9, 9026, 9031, 903D, 907F, 9091, 909B, 90FB, 9101, 910D, 9118, 917G, 9185, 9189, 91B8, 9202, 9288, 92B5, 92FB, 92GG, 93C1, 9505, 950B, 950F, 952B, 956F, 9592, 9596, 9598, 9602, 96D9, 96FD, 971G, 9725, 9752, 97DG, 9855, 9862, 9895, 9899, 98B7, 98BB, 9901, 990B, 9921, 992F, 99G3, 9B0B, 9B2B, 9B8B, 9BB8, 9BBG, 9C19, 9C1B, 9C31, 9C59, 9C95, 9CD5, 9CFB, 9CGC, 9D03, 9D07, 9D7G, 9DG1, 9DGD, 9F0B, 9F76, 9FCB, 9G11, 9G1D, 9G28, 9G3F, 9G7D, 9GCC, 9GD7, 9GF7, 9GFD, 9GG8, A025, A041, A058, A0C5, A0F6, A0GF, A11F, A184, A1F7, A21G, A258, A401, A421, A476, A511, A517, A57D, A5A8, A5E8, A6AD, A6FC, A6GF, A751, A77F, A7F5, A7FD, A7G6, A847, AACD, AC1G, AC41, AC58, AC5E, ACGD, AD0E, AD0G, AD1F, AD51, ADD5, ADE4, ADF5, ADGE, AE56, AE74, AEF6, AEFA, AF77, AF7D, AFA4, AFCC, AFD7, AFDD, AGAF, AGF4, B00G, B037, B055, B05B, B075, B0D5, B0FD, B10F, B198, B25F, B2F1, B2F5, B307, B309, B35E, B3EF, B50D, B589, B7BE, B7BG, B7E7, B875, B952, B958, B97G, B99G, B9G7, B9GD, BB01, BB2F, BB3E, BB89, BB98, BBDE, BD03, BD09, BD5E, BDE5, BDEB, BDG1, BE5F, BF01, BF0D, BG13, BG1F, BG3F, BGD1, BGE2, BGE8, C00B, C034, C05A, C0AF, C0EF, C0GF, C153, C15B, C199, C1B9, C1D1, C1D5, C1F9, C205, C21A, C21G, C252, C258, C2B2, C335, C33D, C35D, C364, C395, C3B3, C3F5, C3FB, C3FD, C414, C41A, C469, C496, C4DA, C4GD, C535, C55B, C5B1, C5BD, C5D9, C5DF, C5E8, C5F3, C5F5, C6E9, C85A, C885, C8B8, C8BE, C8CB, C8E5, C919, C931, C959, C95F, C9D3, CA0F, CA18, CA1G, CAD4, CADE, CAEF, CAGD, CB22, CB33, CB35, CB3F, CB5D, CB82, CB99, CBB1, CBFB, CC49, CCCB, CCDE, CD11, CD1D, CD39, CD4A, CD53, CD93, CDAE, CDD5, CDF3, CDFD, CDG4, CE49, CE5A, CE8B, CF13, CF19, CF5D, CF5F, CFB9, CFBF, CFD9, CFDF, CG14, CG41, CG6F, CGCF, CGF6, CGG1, D01F, D039, D079, D09B, D09F, D0B7, D0BB, D0D1, D0EG, D0GG, D10D, D19G, D1G3, D30B, D347, D3BE, D4E4, D50D, D57E, D5AD, D5FA, D707, D73E, D7E7, D7GF, DA1F, DA57, DAAE, DB01, DB09, DB0D, DB7E, DB9G, DD05, DD7E, DDA5, DDFA, DDG3, DE0G, DE44, DE4A, DE77, DEAE, DEB9, DEBB, DF03, DF05, DG0E, DGDF, E009, E06F, E072, E07G, E089, E0CF, E0E9, E0G7, E47A, E498, E4E7, E50A, E559, E55F, E575, E5B9, E5BF, E5F5, E5F7, E6FC, E722, E724, E72A, E72E, E744, E746, E75B, E76E, E79B, E7A4, E7A6, E7AG, E7B5, E7B7, E7EG, E7G4, E887, E89G, E8E9, E906, E955, E95B, E95F, E988, E99F, E9F9, E9G8, E9GG, EA25, EA7G, EAC5, EAE7, EB7B, EBF5, EBF7, EBFB, EC6F, ECCF, ECEF, EE72, EE76, EE89, EE9G, EF0A, EF44, EF77, EF97, EFA4, EFB5, EFC6, EFFF, EG6F, EG74, EGE7, EGFC, EGGF, F019, F01F, F075, F091, F09B, F0BF, F0FB, F10F, F1A7, F1AD, F1D4, F376, F3CD, F3F4, F40A, F411, F444, F44A, F497, F499, F49D, F4D7, F509, F57A, F5AD, F5F6, F6D3, F6D9, F70D, F741, F747, F76D, F7F6, F7FA, F907, F976, F9CB, FA11, FA7D, FADD, FB09, FC4C, FC5D, FC5F, FC91, FCB9, FD1A, FD41, FD47, FDF4, FF0B, FF56, G021, G07A, G0A1, G0E7, G11F, G17F, G1DF, G1F1, G1F7, G201, G2A1, G306, G311, G36C, G377, G37F, G3CC, G3CE, G3D1, G476, G487, G4DE, G6AF, G6D4, G6F6, G6GF, G713, G724, G731, G742, G74E, G76E, G7A2, G872, G874, GA21, GAC1, GC6F, GCAF, GCD4, GCDA, GCG1, GD73, GD7F, GDAE, GDDF, GDEA, GDFD, GE47, GE7E, GF13, GF33, GF3F, GF4C, GF71, GF7F, GFDD, GG01, GG21, GGAF, GGC1, 1000G, 10053, 100AA, 100B9, 100F1, 100FF, 10301, 10587, 10705, 1075A, 107GF, 10895, 108B9, 10985, 1099G, 10B98, 10B9G, 10D03, 10D0F, 10D7A, 10DG3, 10DG7, 10G1F, 10G3F, 110GF, 1140D, 11D93, 11DG4, 11F0A, 11G4D, 11GD4, 13333, 133FF, 13F44, 14109, 14499, 150A7, 153B1, 1570A, 17005, 17799, 177AG, 17995, 17A7G, 17G47, 18079, 18507, 185A7, 18B07, 18B9G, 19333, 199B5, 1A00A, 1A00G, 1A0F5, 1AAAA, 1AAAG, 1AF05, 1AFFA, 1B07G, 1B10G, 1B807, 1D001, 1D1AA, 1D7G4, 1DG03, 1DG41, 1F001, 1F00F, 1F01A, 1F0A7, 1F199, 1F1F9, 1F414, 1F449, 1F7F5, 1F999, 1FF0A, 1FFAA, 1FFB5, 1G073, 1G14D, 1G1F4, 1G301, 1G477, 1GD01, 1GD47, 1GF07, 1GFF4, 20005, 200A1, 2010A, 20586, 20588, 20A01, 20B11, 20B15, 20BEE, 20C1A, 20CBE, 210B5, 21A1F, 21A51, 21F1A, 21G1F, 21GFF, 222BE, 228B2, 228BE, 22BE2, 22C0B, 22F0A, 252BB, 25505, 25552, 26GAF, 2A001, 2A1FF, 2A55F, 2AEEF, 2AF44, 2B051, 2B20E, 2BB2B, 2BBBG, 2BE22, 2BEE2, 2BEEE, 2BF0B, 2C0BE, 2C18A, 2F101, 2F1FA, 2F44C, 2FCBB, 2G1FF, 2GA6F, 2GF44, 30035, 300B1, 300FB, 30101, 303C5, 30444, 30497, 304D1, 304D7, 30703, 30714, 30734, 30763, 30774, 30CF5, 30CFD, 30D41, 30FC5, 3100B, 31779, 31F5B, 31FB5, 31FFF, 330C5, 330F4, 33357, 33373, 33379, 33555, 33557, 33777, 3379F, 337FD, 33997, 33D44, 33D4E, 33F3D, 33FF5, 34019, 34044, 340D1, 353DD, 35535, 355B3, 355E6, 35BB3, 35DDD, 3636D, 364DD, 3663D, 36DD4, 37003, 3700F, 3717F, 373EE, 37609, 3774E, 37773, 37797, 37977, 3797F, 37EEF, 39007, 390C5, 39777, 39973, 3B355, 3B553, 3BBDB, 3BDB1, 3C03D, 3C0F5, 3C10F, 3C141, 3C444, 3CBE5, 3CD0D, 3CE5B, 3CEBB, 3CEF9, 3D401, 3DEBE, 3E006, 3E066, 3E57E, 3E5E9, 3E666, 3E90F, 3EF6F, 3F33D, 3F3C4, 3F5BB, 3FB33, 3FDDD, 3FF59, 4006D, 400DE, 4011D, 401D9, 40414, 4041G, 404C9, 40966, 40D11, 40D19, 40D1D, 40E49, 41019, 411DA, 41AAG, 4210A, 44049, 4410G, 44144, 441G4, 44441, 444E9, 446E9, 44986, 44E49, 4609G, 460E9, 466DE, 469DD, 46E9G, 4711A, 476D9, 4770D, 47A77, 47D09, 49099, 490D1, 49226, 49622, 49699, 496DD, 49996, 4999G, 499G7, 49G22, 49G77, 4A7DD, 4AA6D, 4ADD7, 4C0E9, 4C999, 4D1DA, 4DADD, 4DD01, 4DD1G, 4DD7A, 4DDA7, 4DDE9, 4DG0G, 4DGAA, 4DGGA, 4DGGE, 4E049, 4E449, 4E49G, 4E4E9, 4E797, 4G7DD, 4GDAA, 4GDD7, 50011, 50079, 50095, 500B1, 500F3, 501A5, 501AF, 50503, 507A5, 50AF7, 50F03, 50F7A, 510A1, 510DA, 511AA, 511DF, 5135B, 515B7, 5180B, 51A0F, 51F0A, 520B1, 53005, 531BD, 53559, 53609, 53B11, 55205, 55357, 553E6, 5555B, 5556E, 55588, 5558A, 555F3, 555FB, 556AF, 556E9, 55759, 5575B, 55805, 55885, 55896, 558B8, 55926, 55BE2, 55E8B, 55F57, 560FF, 5700D, 570A5, 570DA, 575B9, 576AD, 576DA, 579D5, 57A05, 57A52, 57B9D, 57DBD, 58057, 58509, 5855A, 585A7, 587EB, 58857, 588E8, 58A75, 58B0B, 58B87, 58BBE, 58BEB, 58E5B, 591D5, 59201, 59256, 59715, 59807, 5A88A, 5AA88, 5AFAD, 5B001, 5B00B, 5B1F1, 5B31B, 5B7E2, 5B80B, 5BB13, 5BBE8, 5BBFB, 5BE87, 5BE8B, 5BF37, 5BFBD, 5D00F, 5DA05, 5DA5A, 5DAE5, 5DBBD, 5DD95, 5DDAA, 5DFDD, 5E879, 5E8B7, 5E8BB, 5F07A, 5F0AD, 5F37D, 5F70A, 5F7BD, 5FB7B, 5FBBB, 5FBF3, 5FFF3, 6003E, 60098, 603E6, 606GF, 60986, 609C8, 60G6F, 60GCF, 6336D, 633E9, 63CCE, 63E06, 63E66, 6609G, 660E9, 66AD4, 66D4A, 66DG4, 66DGG, 66E98, 66FD9, 66GF6, 69806, 69866, 69C86, 69CC8, 6A66F, 6AAGF, 6AF06, 6AF66, 6AGGF, 6C6G3, 6C6GF, 6CCGF, 6CG03, 6DA0E, 6DAEA, 6DD9G, 6DDE9, 6DEGA, 6DGD3, 6E986, 6EEE9, 6F69D, 6F6DF, 6F96D, 6FD03, 6FD09, 6G003, 6G3F3, 6G3FF, 6G6CF, 6GAAF, 6GCCF, 70031, 70099, 700BF, 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777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777F ====Additional known quasi-minimal primes (not necessarily the next)==== 570₅₁₃₁₀1, 49₁₁₁₃₃₃, 970₁₆₆₀₄₇1, F70₁₈₆₇₆₇1 ===Base 18=== 11, 15, 1B, 1D, 21, 25, 27, 2B, 2H, 35, 37, 3D, 3H, 41, 47, 4B, 4H, 57, 5B, 5D, 5H, 61, 65, 71, 75, 7B, 7D, 85, 87, 8D, 91, 95, 9B, 9H, A1, AB, AD, AH, B1, BD, C7, CB, CD, CH, D5, D7, DH, E5, EB, EH, F1, F7, FB, FD, G5, H1, H5, H7, HB, 107, 167, 16H, 177, 17H, 1G7, 1HH, 20D, 24D, 26D, 29D, 30B, 36B, 381, 3BB, 405, 445, 44D, 49D, 4A5, 4DD, 4F5, 4GD, 501, 545, 5E1, 607, 62D, 64D, 66B, 66H, 67H, 68B, 697, 6A7, 6BB, 6E7, 6G7, 6GB, 6HH, 767, 76H, 77H, 797, 7HH, 801, 80H, 831, 83B, 86B, 88H, 8BB, 8FH, 8GH, 94D, 96D, 977, 9DD, 9ED, 9GD, A77, AC5, AE7, B07, B0H, B55, B77, B8B, B97, BB5, BB7, BBH, BE7, BFH, BGB, C01, C31, CA5, CG1, D2D, D4D, D81, DBB, DD1, DDB, DGD, E0D, E17, E31, E4D, E67, E6D, EA7, EDD, EE1, EED, EG7, F0H, F45, F8H, FC5, FFH, G0D, G17, G2D, G6B, G6H, GBB, GBH, GD1, GDD, GE1, GE7, GED, GFH, GG7, GGB, GHD, GHH, H0D, H2D, H8H, H9D, HGH, HHD, 100H, 19E7, 1A97, 1EE7, 1G8H, 1GGH, 22ED, 22GD, 2DED, 2E2D, 3001, 3031, 30C1, 30E1, 3331, 33G1, 3CC1, 40ED, 45C5, 46ED, 4CC5, 5331, 5551, 55G1, 5C05, 608H, 60ED, 60FH, 60HD, 666D, 66ED, 699D, 6B67, 6BGH, 6D0D, 6DDD, 6E9D, 6EGD, 6G0H, 6G9D, 6HGD, 700H, 70A7, 7A07, 7FGH, 7G77, 808B, 8881, 88G1, 88GB, 8BHH, 8EG1, 8GC1, 8H6H, 900D, 90E7, 90G7, 9667, 9907, 999D, 99E7, 9A67, 9A97, 9E97, 9EE7, 9G07, 9G67, 9GA7, AA45, AA97, AGA7, B005, B03B, B06B, B0C5, B60B, B63B, BAA5, BAA7, BCC5, BFA5, BG8H, C045, C055, C555, C5C1, C5F5, CC05, CC81, CCC5, D06D, D09D, D0ED, D38B, D3E1, D60D, D6DD, D8GB, DD6D, DE9D, DG01, E001, E097, E0G1, E8C1, EDC1, EE97, EGC1, EGG1, EGGD, FH6H, G007, G00B, G00H, G03B, G067, G097, G0C1, G0G1, G1GH, G33B, G38B, G3G1, G70H, G777, G88B, GA67, GAA7, GG81, GGC1, GGGH, H0FH, H66D, HEGD, HFHH, 1AAA7, 222DD, 30GG1, 3388B, 33E01, 38G8B, 3G3C1, 3GGG1, 4002D, 500C5, 50C55, 50CF5, 53GG1, 558C1, 55CC5, 55CF5, 58GG1, 5C8C1, 5CFF5, 5G881, 5GG31, 6000H, 6003B, 6006D, 600DB, 6033B, 606GD, 60D0B, 66GGD, 6D03B, 6D33B, 6H6DD, 6HD6D, 6HDED, 70G07, 70GGH, 777A7, 7AAG7, 7G0GH, 80G0B, 8888B, 8CCE1, 90067, 90097, 9022D, 99967, 99997, 9A007, 9A0A7, 9AA07, 9AAA7, 9E007, A0045, A0455, A0667, A09G7, A0A07, A0G07, A0G97, A9997, AA0A7, AAG67, B0AF5, B6GGH, B7GGH, B8HHH, BA045, BAF05, BG667, C0F05, C5005, C5581, C88C1, C8CC1, C8CE1, CCF55, D03C1, D060B, D080B, D0CC1, D0G0B, D0G8B, D3G3B, D600B, DDDED, DG331, DG80B, E8G81, E9007, F6GGH, G018H, G0301, G0331, G466D, G6667, G66GD, GD08B, GG18H, GG6GD, GGG4D, H060H, HGGGD, HHH6H, 199AA7, 40006D, 40600D, 46600D, 5055C5, 5505C5, 55CCC1, 588CC1, 58CCC1, 60000D, 60009D, 7077G7, 7707G7, 777G07, 88000B, 9099A7, A000A7, A009A7, A09067, A099A7, A0AAA7, A90AA7, A99AA7, AA0007, AA6667, AAAG07, BFFF05, BFFFF5, C0FFF5, CCECC1, CECCC1, CF0FF5, CFF005, D0008B, D0033B, D0088B, D0333B, D033GB, D03G31, D0633B, DD990D, DGGG31, FHHHHH, G00081, G6GGGD, G8GGG1, GGG001, GGG331, GGGGG1, GGGGGD, H0006H, H00H6H, HH600H, 222222D, 22DDDDD, 333333B, 5CCCCC1, 70007G7, 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CDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD, 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71D, 73D, 73H, 73J, 75B, 75H, 768, 77H, 77J, 7B1, 7B5, 7BB, 7BD, 7C8, 7D1, 7DB, 7DD, 7E8, 7F5, 7FB, 7H5, 7HD, 7HH, 7HJ, 7J5, 7JD, 801, 80J, 832, 841, 86H, 86J, 881, 89G, 8E1, 8F4, 8F8, 8FA, 8FK, 8H4, 8IH, 8J4, 8JG, 90K, 91B, 91D, 91H, 93H, 93J, 955, 95H, 95J, 96G, 97B, 97D, 97H, 991, 99J, 9B1, 9BB, 9BH, 9BJ, 9CK, 9D1, 9DB, 9DH, 9DJ, 9EK, 9F5, 9FD, 9H1, 9HB, 9HD, 9IG, 9J5, 9KK, A0B, ABG, AF4, AF8, AG5, B15, B1H, B35, B3H, B3J, B4G, B51, B5B, B5D, B5H, B6G, B71, B75, B7B, B7D, B9B, B9J, BB5, BBH, BBJ, BC4, BCG, BF1, BF5, BFD, BH1, BHJ, BI4, BJB, C2D, C9K, CCD, CDG, CID, D0G, D2G, D35, D3B, D3H, D51, D55, D5B, D5D, D5J, D62, D71, D7H, D91, D95, D9H, DBH, DC2, DD1, DD5, DE2, DEG, DF5, DFJ, DH1, DHB, DI2, DJ1, DJB, DJJ, E14, E4B, E5K, E78, E81, E9G, EA5, EBG, EC1, EE1, EE5, EK5, F04, F11, F1H, F31, F3B, F3D, F44, F4A, F4K, F5D, F5H, F6K, F71, F7H, F7J, F88, F8A, F8K, F9J, FA4, FA8, FBB, FBH, FC4, FDB, FDJ, FE8, FFH, FFJ, FH5, FHB, FHJ, FI4, FI8, FIK, FJ5, FJD, FK4, FK8, G32, G5G, G78, G8J, 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====Additional known quasi-minimal primes (not necessarily the next)==== 40₄₇₃₃₃9G, CF₄₇₉₁₄₇0K ===Base 22=== 11, 17, 19, 1F, 1J, 1L, 23, 29, 2F, 2H, 31, 35, 37, 3D, 3H, 41, 49, 4D, 4F, 4J, 4L, 53, 5H, 5L, 65, 67, 6H, 6J, 73, 79, 7D, 7J, 83, 85, 8F, 8H, 8L, 91, 9D, A3, A7, A9, AD, AJ, AL, B9, BF, BL, C5, C7, CD, CH, CJ, D7, DL, E3, E5, E9, F1, F7, FH, FJ, G1, G7, GF, GL, H5, H9, HF, I1, I5, ID, J1, J3, JD, JF, JL, K3, K9, KH, KL, L1, L5, LH, 103, 12D, 145, 155, 15D, 163, 18D, 1A5, 1BD, 1BH, 1C3, 1D3, 1DH, 1EH, 1G3, 1GH, 1I3, 1K5, 1KD, 221, 227, 22J, 22L, 245, 247, 25D, 25J, 271, 277, 287, 28J, 2A5, 2B7, 2BD, 2BJ, 2D5, 2E1, 2E7, 2ED, 2EL, 2K1, 2KJ, 2LL, 30J, 343, 389, 39J, 3B3, 3GJ, 3IJ, 3J9, 3JJ, 3KF, 3LJ, 427, 443, 445, 457, 4A5, 4C3, 4E7, 4G5, 4I7, 4K5, 4K7, 515, 52D, 551, 559, 55D, 55J, 575, 58D, 59F, 5B1, 5C9, 5CF, 5D1, 5D5, 5DD, 5E1, 5ED, 5G5, 5GJ, 5J5, 5JJ, 5K1, 5KJ, 60D, 61D, 62L, 661, 66D, 689, 6C1, 6D1, 6DD, 6G3, 6KF, 701, 721, 751, 76L, 775, 77F, 77H, 787, 7A5, 7AF, 7B1, 7B7, 7CL, 7E1, 7FF, 7FL, 7H7, 7HH, 7K5, 809, 81D, 821, 827, 82D, 847, 869, 871, 881, 889, 899, 8A1, 8BD, 8BJ, 8D1, 8DJ, 8GJ, 8J7, 907, 90H, 92L, 93J, 943, 947, 95F, 977, 997, 9AF, 9B5, 9EF, 9F5, 9H3, 9HL, 9I7, 9J9, 9JJ, 9K5, A25, A45, A51, A61, A6F, AAH, AB5, ABH, ACF, AG5, AGH, AHH, AK1, B15, B2D, B2J, B33, B45, B47, B57, B71, B75, B81, B87, B8J, BB3, BB7, BC3, BDD, BE7, BEJ, BGD, BGH, BH3, BHD, BHJ, BIH, BJ7, BKJ, CA1, CAF, CB3, CC1, CEF, CG3, CKF, D09, D0J, D13, D21, D33, D39, D3F, D4H, D5J, D63, D81, D8D, DAH, DBD, DBH, DBJ, DCF, DD3, DEJ, DFF, DG9, DGH, DHD, DI3, DIF, DJ9, DK1, DK5, E0F, E0H, E27, E2D, E2L, E47, E7H, E87, E8J, EA1, EAH, EB1, EDH, EEJ, EFF, EFL, EH1, EIF, EIL, EJH, EJJ, EKD, ELF, F25, F43, FB5, FD3, FDD, FDF, FEF, FEL, FFD, FG9, G09, G0D, G25, G3J, G5D, G5J, G63, G8D, G99, GC3, GC9, GD9, GEH, GG5, GJ5, GJ9, GJH, H03, H1D, H21, H2J, H2L, H33, H63, H77, H8J, HCL, HDD, HE1, HE7, HGH, HGJ, HH7, HHL, HI3, HIH, HJH, HK1, HKD, HL3, I07, I0J, I43, I47, I7L, I9J, IBH, IEL, IG3, 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7KC1, 7L27, 7LCF, 7LK7, 802J, 80B1, 80GD, 80JJ, 80KJ, 820J, 86E1, 880D, 882J, 88E7, 88I7, 892J, 89EJ, 8B61, 8BI7, 8CI9, 8CK1, 8D6D, 8DD9, 8DGD, 8E01, 8E07, 8EE1, 8EI7, 8EK1, 8EKJ, 8I77, 8I87, 8IC9, 8IK7, 8J0J, 8K6D, 8KI7, 8KIJ, 8KK7, 9025, 9055, 9089, 9275, 92EJ, 92G5, 92GJ, 93EL, 9455, 9505, 9557, 9599, 96B3, 970L, 976F, 97G5, 982J, 98E7, 98I9, 98K7, 9905, 990J, 9925, 9995, 999H, 99BH, 99EL, 99G9, 99GJ, 99LJ, 9A55, 9B03, 9B27, 9BGJ, 9BH7, 9BK7, 9CG9, 9E6L, 9EHJ, 9EKJ, 9ELL, 9G39, 9G45, 9G4H, 9GA5, 9GAH, 9GBJ, 9GEJ, 9GHH, 9GHJ, 9GI9, 9GIJ, 9H7H, 9H87, 9HAH, 9HB7, 9I89, 9I9H, 9IB3, 9IEH, 9IKF, 9J7H, 9J87, 9JB7, 9JGH, 9K0F, 9K27, 9KGJ, 9KKF, 9L89, 9L9J, 9LG9, 9LGJ, 9LIJ, 9LKF, A081, A14H, A1IH, A201, A2C1, AA15, AA81, AAIF, ABC1, AC01, AHC1, AIIF, AKEF, B005, B01D, B01H, B051, B05D, B0A5, B0B1, B0BJ, B0DH, B0E1, B0GJ, B0H1, B0JH, B143, B16D, B255, B2B5, B2C1, B2G5, B2K7, B4EH, B4G3, B501, B5A5, B5BJ, B5C1, B5IJ, B5K5, B621, B663, B6I3, B6K1, B777, B7I7, B80D, B88D, B8ED, B8KD, BB01, BB0J, BB21, BB25, BB4H, BB6D, BBD5, BBE1, BBEH, BBH1, BBIJ, BBJH, BCK1, BD61, BDB5, BDGJ, BEE1, BG55, BGB5, BGGJ, BGIJ, BH27, BH7H, BHC1, BHH1, BHK7, BI77, BIGJ, BJ0H, BJBH, BJIJ, BJJJ, BK25, BK27, BK55, BKA5, BKK1, C043, C143, C2B1, C32L, C3G9, C601, C6EL, C6G9, C8B1, CBK1, CC2L, CC89, CE21, CECL, CF2L, CF89, CG69, CIG9, D003, D015, D045, D05D, D06D, D06F, D0DH, D0H1, D1D5, D1GD, D205, D26D, D2DJ, D32J, D38J, D403, D525, D561, D56D, D5AF, D5F5, D5GD, D6C9, D6D9, D6DF, D6E1, D6ED, D6F9, D6FD, D8IJ, D8JJ, D945, D993, D99F, D9C9, D9F3, D9G5, D9KJ, DA15, DAA5, DAE1, DAKF, DB25, DB61, DBC1, DBG3, DC43, DC99, DCE1, DD0F, DD1D, DD2D, DD2J, DD5D, DD9H, DDA5, DDD5, DDDJ, DDED, DDH1, DDHJ, DDI9, DDJ5, DE0D, DED1, DEDF, DEFD, DF03, DF45, DF55, DF5D, DF6D, DG05, DGGJ, DH0H, DH43, DHC1, DHEH, DHH3, DHJJ, DI8J, DIC9, DII9, DIJH, DJG5, DJHJ, DJKJ, DK6D, DKAF, DKDD, DKGD, E081, E0BJ, E0DD, E0DJ, E0E1, E0ED, E0J7, E0K7, E0KJ, E1GD, E1IH, E201, E281, E66F, E6BD, E6ED, E6K1, E6LL, E7EF, E861, E86D, E88D, EB0D, EB4H, EBHH, EBI7, EC6F, ECEL, ED0D, ED1D, ED6D, EDAF, EDDD, EDFD, EE01, EE0D, EE1H, EE21, EECF, EEE1, EEGH, EEH7, EF8D, EGGD, EGHH, EGIH, EGIJ, EH07, EH0L, EH8D, EHBH, EHBJ, EHK7, EHL7, EI4H, EIK7, EIKJ, EJ77, EK07, EK0J, EKC1, EKIJ, EKK1, EKK7, EL6L, ELBD, ELCL, ELDJ, ELK7, F059, F20L, F26L, F28D, F2GD, F2KD, F32L, F3AF, F3G3, F455, F56F, F595, F5KD, F6AF, F6GD, F88D, F8I9, F955, F995, F9B3, F9G3, F9KF, FB03, FB8D, FBI3, FC89, FD99, FDA5, FDI9, FEGD, FF59, FG2D, FGI3, FGKD, FI89, FIB3, FIKF, FK2D, FK45, FKD5, FL6D, FLG3, G003, G04H, G055, G0BH, G0HH, G0HJ, G0I3, G0K5, G0KJ, G26D, G2DJ, G2GJ, G303, G333, G393, G3G9, G3I3, G403, G40H, G433, G4AH, G4GH, G4H3, G4IH, G589, G5G9, G80J, G89J, G94H, G9G3, GAA5, GAIH, GB0H, GB43, GB6D, GBB5, GBG3, GBGJ, GBJJ, GD0H, GD45, GDD5, GDKD, GG2D, GG39, GG8J, GG9H, GGAH, GGDJ, GGEJ, GGGH, GGH3, GGKJ, GH0H, GHG3, GHH3, GHHH, GHJJ, GI03, GI2J, GI93, GIAH, GIEJ, GIG9, GII3, GJJJ, GJKJ, GK05, GKDD, GKGD, GKGJ, GKIJ, H081, H087, H0AH, H0BJ, 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5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000BB5, J000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000BIJ, C4IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII3, F0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000066B3, G0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000A5, D5KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKF, HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHBH, L0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000IKF, 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LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLKE7, 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80BN, 80FH, 80LN, 80MN, 840N, 848N, 866B, 86FB, 880B, 880N, 884N, 88CB, 88FB, 88LN, 88MN, 8BBB, 8BLB, 8C6B, 8CCH, 8CFH, 8F0B, 8FHH, 8FLB, 8H0H, 8HCH, 8IGN, 8ILN, 8KKH, 8L8B, 8LBB, 8LFB, 8LIN, 8M8N, 8MLN, 8N0N, 8NGN, 8NLN, 9061, 9091, 90EJ, 90F1, 90GJ, 90K1, 940J, 9501, 95F1, 9CC1, 9E0J, 9E95, 9F61, 9FI5, 9G3J, 9II5, 9K01, 9KK1, 9M01, A007, A05D, A0AD, A33D, A3AD, A3F5, A44J, A727, A9EJ, AA0D, AAAD, AAAJ, ACM7, AD8D, ADKD, AE27, AE9J, AEAJ, AEE7, AIAD, AIDD, AIID, AJ9J, AK5D, AM07, AM27, AM35, AMK5, B08B, B0CB, B0GB, B18B, B1CB, B80B, B8CB, BB21, BB4N, BBCB, BBF1, BBFB, BBK1, BC8B, BCF1, BCLB, BF1B, BF8B, BFB1, BFM1, BGC1, BGF1, BK21, BL8B, BLFB, BM1B, BM3N, BMB1, BMMN, BNF1, C00D, C06B, C077, C0D7, C0H7, C0L7, C0LB, C0M1, C60H, C6LB, C76H, C7E7, CAID, CC01, CCFH, CCKH, CDLB, CGE7, CH07, CHE7, CI8D, CIAD, CK0D, CL8B, CLDB, CLE7, CM01, CM07, CME7, CMM1, D007, D08D, D0C7, D0HH, D0LN, D0M7, D0NN, D207, D2KH, D2M7, D777, D7E7, D80H, D8LD, DA27, DAC7, DAM7, DBFB, DBMB, DC77, DCLB, DDL7, DE77, DF0H, DF2H, DFFH, DFMB, DH27, DH8H, DHC7, DHHH, DILN, DK0H, DK2H, DK8H, DKHH, DLIN, DLL7, DLM7, DLMB, DM07, DMH7, DMMB, DNGN, E07J, E09J, E335, E355, E555, E5A5, E5K5, E79J, E93J, E995, EA35, EE95, EKE5, F00B, F00H, F06H, F08B, F0I5, F11B, F18B, F1L1, F20H, F26H, F2FH, F355, F661, F6K1, F80B, F86B, F8BB, FBGB, FBK1, FBLB, FC0B, FC6H, FCLB, FEK5, FGB1, FH05, FH0H, FH35, FH6H, FHCH, FHF5, FHHH, FI05, FK91, FKK1, FL1B, FLB1, FLBB, FM61, FMBB, FMK1, G00J, G021, G027, G0EJ, G0JJ, G0M1, G0M7, G1CB, G2E7, G40J, G4AJ, G4IJ, G4JJ, G6C1, G701, G94J, G9IJ, GAEJ, GAJJ, GB21, GBM1, GC01, GCF1, GCLB, GE0J, GEAJ, GEE7, GEG7, GEIJ, GEL7, GFM1, GGE7, GGMB, GI0J, GIIJ, GIIN, GJ9J, GM27, GMB1, GNM7, H005, H0K5, H0M5, H207, H2E7, H335, H3I5, H595, H5K5, H60H, H68H, H76H, H80H, H8HH, HAAJ, HE7J, HEC7, HGE7, HGM7, HH35, HI55, HIM5, I00J, I035, I08D, I0CD, I4JJ, IC0D, ICID, II0D, II0J, II35, IIAD, IILD, IIM5, IIMN, IJ9J, ILCD, IM05, IM35, IMNN, INLD, J03J, J0HJ, J0JH, J2CH, J39J, J3ID, J60H, J62H, J8CH, J9IJ, JGAJ, JGJJ, JH9J, JI0J, JIDD, JJ0H, JJCD, JJJD, JJLD, JL3D, JLCD, K0E5, K0I5, K0K1, K0KH, K191, K211, K2F1, K2G1, K591, K5AD, K6F1, K6G1, K9I5, KA0D, KAAD, KAM5, KCCH, KCHH, KD8D, KDDD, KFI5, KG01, KG61, KH0H, KHHH, KI55, KIDD, KK21, KK8H, KKF1, KKK1, KKKD, KM8H, KMHH, KMK5, L027, L0M7, L1C1, L1MB, L211, L727, L8BB, L8BN, L8FB, L8LN, L9C1, L9M1, LB8B, LBC1, LBM1, LCAD, LD77, LDIN, LDL7, LDM7, LF8B, LG21, LIIN, LLLN, LLN7, LM07, LM1B, LM77, LMG1, LN77, LNM1, M00N, M01B, M03N, M055, M077, M08B, M0B1, M0C1, M0GB, M0K1, M0M7, M0N7, M18B, M1BB, M1MB, M26H, M335, M3GN, M3M5, M3MN, M3NN, M501, M53N, M5M1, M5NN, M6BB, M6C1, M6G1, M6KH, M88B, M88N, M8BB, M8NN, MBB1, MC01, MCC1, MCKH, MCM1, ME07, ME35, MEK5, MGGB, MGMB, MH35, MH8H, MHE7, MHM5, MK8H, MKC1, MKG1, MKHH, MKK5, ML8N, MM01, MM8B, MMC1, MMLN, MMM5, MMMN, MMN1, MN0N, MN27, MNGN, MNLN, N007, N027, N077, N0C7, N0DN, N0IN, N1M1, N227, N2M7, N661, N707, N727, N8LD, NA27, NA3D, NC07, ND0D, ND0N, NDLD, NF11, NF61, NGG7, NILN, 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5M0M1, 5MNNN, 5N03D, 5N3LD, 5NA8D, 5NADD, 5NDGN, 5NNGN, 600KH, 61661, 616L1, 61MM1, 66161, 66611, 666B1, 666L1, 666LB, 66BB1, 66BG1, 66BLB, 66G61, 66KF1, 66LBB, 66LG1, 6BBBB, 6BFCB, 6CC11, 6F1M1, 6F66B, 6F6B1, 6F6L1, 6FBCB, 6FLMB, 6FMCB, 6FMM1, 6FMMB, 6GCM1, 6GM61, 6GMC1, 6K1C1, 6K1K1, 6KK11, 6KKL1, 6KL11, 6L1G1, 6LBFB, 6LCC1, 6LFMB, 6MM61, 6MM6B, 70291, 702C1, 702G1, 72CF1, 72EE7, 7433J, 7443J, 77A07, 79901, 799F1, 7AAEJ, 7EE27, 7H9EJ, 7K2KH, 7KK2H, 7KKKH, 7KKMH, 7L2C1, 800NN, 806BB, 808BB, 808LB, 80F8B, 80IIN, 833ID, 860KH, 8886B, 888NN, 8BG4N, 8CH6H, 8CKHH, 8FC0H, 8FFCH, 8HHHH, 8IIIN, 8K0HH, 8LL4N, 8M0NN, 8MNNN, 8NNND, 9000J, 900M1, 9034J, 90IIJ, 94IIJ, 96CM1, 96KF1, 96MM1, 990C1, 990M1, 99591, 99961, 999C1, 99F91, 99FM1, 99KF1, 99M61, 99MK1, 9AAA5, 9FEE5, 9FFA5, 9FFF5, 9II4J, 9K6C1, 9K9C1, 9K9F1, 9KF91, 9M6M1, 9MK61, A02M7, A0A35, A0AM5, A0C77, A0D0D, A0DDD, A0EC7, A0M55, A0MM7, A2ME7, A3335, A33M5, A3555, A3MM5, A550D, A58ID, A5D0D, A5DDD, A74AJ, A7E07, AA0M5, AA3ID, AA3M5, AA83D, AA8ID, AAAM5, AACID, AAICD, AAM05, AC08D, AC0ID, AC0KD, AC8ID, ACA8D, AFA35, AIC8D, AJAJJ, AK0KD, AKI0D, AKKM5, AKM05, AM505, B00FB, B00LB, B0LBB, B1MBB, B1MMB, B2GM1, B3MGN, B88BB, BB3MN, BBB3N, BBB8B, BBBBN, BBBMN, BBCC1, BBGB1, BBGLB, BBMC1, BBMGB, BBNM1, BFB0B, BFBMB, BFGLB, BFGMB, BGGLB, BGMM1, BLMMB, BMC0B, BMGM1, BMMK1, BMNM1, C006H, C00CH, C00M7, C0C11, C0CC1, C0E07, C0F6H, C0GG7, C0K8D, C0KDH, C0KHH, C1CC1, C1CM1, C1MC1, C70F1, C886B, CC06H, CCCCH, CCCF1, CCCM1, CDHH7, CE707, CE7L7, CEE77, CEEG7, CEL07, CFFHH, CGLL7, CHC6H, CHCCH, CHH7H, CHHH7, CHHM7, CI0LD, CK0HH, CKHCH, CL007, CLD07, CLLL7, CM777, CMMM7, D008H, D07L7, D0DE7, D0EL7, D0L77, D0M8H, D0NA7, D22E7, D70A7, D7227, DBLBB, DCL07, DD7A7, DDAE7, DDD8D, DDE07, DDK0D, DDM77, DEE27, DKK8D, DL227, DL707, DLBBB, DLDFB, DLE27, DM2E7, DMM77, DMME7, DN0A7, DNIIN, DNLLN, E000J, E0227, E02E7, E0AAJ, E0GL7, E0I0J, E2E07, E7AAJ, E7E27, EAA55, EAK55, EC777, ECEE7, ECEL7, ECGL7, ECL77, EEC77, EECL7, EEEC7, EEG27, EEGG7, EG0E7, EG0L7, EG207, EGE07, EGG07, EGG27, EGL07, EI9IJ, F02HH, F06LB, F0C6B, F0CCH, F0CHH, F0E55, F0EA5, F0FH5, F0GGB, F0M2H, F0MGB, F0MMB, F1BMB, F3FF5, F3I35, F3II5, F6BCB, FA035, FB1MB, FBBM1, FBBMB, FBM8B, FC0HH, FC88B, FCFHH, FFC0H, FFCFH, FFCHH, FFF0H, FFF6H, FFFH5, FFHI5, FFI55, FG1MB, FGGCB, FGM1B, FHK55, FI5I5, FKEA5, FKKI5, FKL11, FM16B, FM1CB, FM62H, FM6CB, FMBG1, FMM0B, G0001, G00E7, G039J, G06F1, G07C1, G07F1, G0A9J, G0G07, G0GG7, G0I4J, G0I9J, G0LL7, G22M7, G2M07, G339J, G433J, G62M1, G6M61, G6MM1, G903J, G933J, GAA9J, GBCC1, GE007, GGGGB, GGGL7, GJ0IJ, GL007, GL2M7, GLL07, GLLM7, GMGCB, GMM07, GMM1B, H007H, H05I5, H0CCH, H0CM7, H0GG7, H0H27, H0H8H, H0HC7, H0HH5, H0I35, H0MM7, H3555, H35F5, H3F55, H3FF5, H5055, H50F5, H7HEJ, H9995, H9GEJ, HCC0H, HCC6H, HCGG7, HCHM7, HE027, HE0G7, HEE07, HEEG7, HEG27, HF0F5, HF505, HF555, HFF05, HFKF5, HG0G7, HH06H, HH08H, HH0H5, HH5I5, HH7HJ, HH9EJ, HH9I5, HHCHH, HHE07, HHGG7, HHH05, HHH7H, HHH9J, HHKI5, HHM05, HHM07, HHM27, HI0I5, HJ86H, HJC0H, HK055, HK9F5, HKF05, HKFF5, HKFK5, HKII5, HKK95, HM2M7, HME27, HMKM5, HMM05, HMM27, HMM55, HMMM7, I00DD, I00M5, I044J, I0505, I09IJ, I0AAD, I0D0D, I0DDD, I0I05, I0IDD, I0II5, I0IJJ, I0JIJ, I33M5, I4I4J, I5INN, I888N, I8NND, I8NNN, I904J, I94IJ, IA8ID, IAADD, IAI8D, IDDDD, IDINN, II88N, II8NN, IID8D, IIDIN, III8N, IIIDD, IIIID, IIIIN, IIIND, IIN8D, IINDD, IJJ0J, IJJJJ, ILILN, ILLIN, IMM8N, INA0D, INDNN, INGIN, INNDN, INNND, J000H, J002H, J00AJ, J00GJ, J00KH, J02KH, J068H, J080H, J090J, J0A9J, J0AAJ, J0C0H, J0G0J, J0IIJ, J0JGJ, J0JIJ, J0K8H, J2K0H, J2KKH, J6K8H, J86KH, JC00H, JC0KH, JCCCH, JCK0H, JCKCH, JDDLD, JG93J, JIIJJ, JJ0IJ, JJ2KH, JJ9GJ, JJCCH, JJG9J, JJGIJ, JJJ9J, JJJJH, JJK8H, JK08H, JK0CH, JK8KH, JKC0H, JKKKH, K0001, K0091, K020H, K02C1, K03ID, K0611, K06L1, K083D, K08HH, K0961, K09C1, K0CF1, K0F91, K0KM5, K0LG1, K1G21, K20HH, K29K1, K2KHH, K5001, K500D, K58ID, K5D0D, K5L11, K6621, K6C11, K6LC1, K8CKH, K8KCH, K96C1, K99E5, K9F91, K9FA5, K9FE5, K9K91, KA55D, KC011, KCF11, KD02H, KD0MH, KD20H, KDM2H, KEA55, KEAA5, KEK95, KEKK5, KF1G1, KF1K1, KF611, KF6L1, KFEA5, KH8CH, KI005, KIMM5, KK05D, KK0AD, KK0DH, KK2CH, KK2KH, KK33D, KK961, KK9C1, KKA5D, KKD0D, KKE55, KKI0D, KKIID, KKIM5, KKK0H, KKKM5, KLGC1, KMK2H, L188B, L1991, L2007, L22M7, L2EE7, L2MM7, L333D, L3LIN, L7291, L72G1, L88IN, L8C8B, L9991, LBB1B, LBBBB, LBBBN, LD0E7, LDBBN, LE207, LFMCB, LGCC1, LL227, LL3IN, LL48N, LLM27, LLMM7, LMBCB, LME27, LMMBB, LMMM7, LN33D, LN3AD, LNAAD, LNACD, M0007, M0061, M00K5, M0207, M066B, M0BCB, M0EE5, M0G01, M0GM1, M0M8N, M27KH, M2E27, M2M07, M2M27, M5005, M5555, M66CB, M66K1, M6K61, M6MCB, M7007, M7EE7, M8C0B, M8KCH, M8MGN, MBBGB, MBGM1, MCCCH, MCHCH, MEE55, MGBC1, MGMM1, MH227, MH2M7, MHH7H, MKM55, ML3LN, MM0CB, MM16B, MM227, MM661, MM6K1, MME55, MMEE7, MMKE5, MMM07, MMM6B, MMMB1, MMMGB, MMMM7, MNM61, MNN3N, N00CD, N00KD, N03LN, N0A8D, N0AM7, N0D8D, N0KKD, N0L3N, N0LAD, N0NDD, N16L1, N3GIN, N3LAD, N3LIN, N3NNN, N61L1, N96M1, N9M61, NA0CD, NAK0D, NAKKD, NCA8D, NCM77, NDGIN, NDIIN, NDLLN, NF991, NGM07, NIIIN, NINNN, NKKDD, NLNAD, NN0LN, NN191, NN3NN, NN6L1, NN83D, NNAAD, NNDIN, NNGIN, NNL3N, NNLND, NNM61, NNNIN, 166G21, 16G621, 19MMM1, 1BBBMB, 1BBGM1, 1GCCC1, 1GCCM1, 1MMM1B, 200E27, 2E0027, 2HH0HH, 2HHC0H, 2KK0HH, 2M0E27, 2M22E7, 30NNNN, 3333M5, 333AID, 333I35, 33I555, 3F5FF5, 3I3MM5, 3I88GN, 3II8LN, 3IIII5, 400IJJ, 40J00J, 40JJ3J, 40JJJJ, 44403J, 444I0J, 44IJJJ, 44J0JJ, 44JJIJ, 48I8IN, 4I440J, 4II8IN, 4IJ0IJ, 4JIIIJ, 4JJ0JJ, 4JJJ0J, 50033D, 5003AD, 5008ID, 500D8D, 500G01, 500L11, 500LAD, 500MG1, 503LAD, 508ILD, 50DDLD, 50ILAD, 50M001, 516G61, 519MM1, 538NNN, 53NNNN, 55005D, 5508ID, 550D8D, 558ILD, 55F5I5, 56G661, 58333D, 58NNNN, 5999F5, 59AAF5, 5DNNNN, 5F55I5, 5FMMM1, 5G6661, 5K9AA5, 5KK9F5, 5KKK95, 5M0001, 5NDD8D, 5NDINN, 5NN33D, 5NNLAD, 5NNNAD, 5NNNDN, 608K0H, 61CCM1, 61G621, 661G21, 666621, 6666CB, 6666F1, 66K661, 6BCCC1, 6BKKC1, 6F6BBB, 6G6621, 6GCCC1, 6GMMM1, 6K6K61, 6M666B, 70A077, 70L991, 7722E7, 772E27, 7772E7, 777A27, 777L27, 77A777, 77EL27, 7A7077, 7A7777, 7E7227, 7L2E27, 7LEL27, 7LL2E7, 7LLE27, 7LLL27, 800GIN, 80NINN, 80NNNN, 8BBMGN, 8C888B, 8C88LB, 8MM0GN, 900001, 90043J, 959MM1, 96K661, 9999F1, 9999K1, 999AF5, 999FF5, 99EEE5, 99K991, 99MMM1, 9AAFF5, 9EIIIJ, 9F9991, 9F9MM1, 9FEAA5, 9G444J, 9K9991, 9M6661, A000CD, A000KD, A000M5, A0083D, A00I0D, A00M05, A022E7, A07E77, A0FF35, A0K3ID, A0K83D, A4AJJJ, A77777, AA0035, AA0355, AAA035, ADDD0D, ADDDDD, AF0035, AFFF35, AKK8ID, AM0M05, AM7777, B0F0MB, BBBBM1, BBLBMB, BFBBBB, BFM0MB, BFMMMB, BLBBMB, BLMBBB, C00071, C000E7, C007C1, C00G07, C07KKH, C0CC6H, C0CH6H, C0EEE7, C0HHHH, C777L7, C77L77, C7L777, C7LL07, C8088B, CAAK8D, CAKKAD, CC000H, CC0CHH, CD000H, CD0KKH, CE0007, CEE0E7, CELL77, CG0007, CGGL07, CH0CHH, CHCH0H, CHHH6H, CK0C0H, CKAK8D, CKKA8D, CL7707, D002FH, D0D0KD, D0DA77, D0DKKD, D0IIIN, D0K0DD, D0KDKD, D0KKDD, D0KKKH, DC0EE7, DCEEE7, DD0227, DD0D27, DD0DKD, DD0KKD, DD2E27, DDD0D7, DDD0LD, DDD227, DDDA77, DDDBCB, DDDCE7, DDDDFB, DDDMM7, DDEEE7, DDMBCB, DEEC07, DH000H, DHMEE7, DIIIGN, DK0KDD, DKMKKH, DMBBBB, DMEEE7, DMMM27, E00G27, E07727, E0C707, E0CE77, E0E027, E0EEG7, E0EGE7, E0EL27, E0GE27, E0L207, E0LE27, E0LL27, E2E2E7, E7L2E7, E900IJ, E9EEE5, EAAKK5, EC00E7, EC0G07, EC7007, ECEG07, EE0G07, EE0GE7, EE72E7, EE7L27, EECE07, EECEG7, EEEEE5, EEEK55, EEEKA5, EEEL27, EEGLL7, EELE27, EGLLL7, EKK595, EKKA55, EKKAK5, EKKKK5, F000E5, F0AA35, F0F035, F0FFFH, F0HKK5, F0KKE5, F16BB1, F16MM1, F1BBBB, F1MC6B, F666BB, F66BBB, F6GMM1, FB0BBB, FB1BBB, FBBB0B, FBMMG1, FC0FFH, FCFCCH, FEEE55, FEEEA5, FF03F5, FF0FFH, FF3F35, FFEE35, FFF2CH, FFFCCH, FFFFE5, FFI335, FFKFE5, FGLMMB, FK55I5, FKFE55, FLM8CB, FMC66B, FMMC6B, G0AA4J, G0CCC1, G0LE07, G666F1, GG0007, GG00G7, GG0L07, GGLLL7, GGLMM7, GI444J, GJJ33J, GLLE27, GLMMCB, GM0661, GMMM61, H00G07, H05555, H09FF5, H0C0E7, H0CE07, H0CEE7, H0E227, H0H007, H0H5F5, H0H995, H0HHE7, H0HHH7, H55505, H55II5, H5FII5, H99FF5, HEG007, HFFK55, HH0007, HH02M7, HH0C0H, HH7AEJ, HHC0E7, HHE227, HHH0C7, HHH0M7, HHH995, HHHC0H, HHHE27, HHHEAJ, HHHH07, HHHH8H, HHHHE7, HHHHI5, HHHHJH, HHHJ8H, HHHJCH, HHJ00H, HHK095, HHKKM5, HKK0F5, HKK5F5, HKKK55, HKKKK5, HKM555, HMEEE7, I00555, I05555, I0I94J, I333I5, I33555, I444IJ, I55055, I55505, I55555, IAAC8D, ID000D, IDD0LD, II9I4J, III4IJ, III505, IIIC8D, IIJIJJ, IJIIIJ, IM8LLN, IN00AD, INAACD, INCAAD, ININGN, J00CCH, J0IJJJ, J0J09J, J3333D, JIJIIJ, JJ68KH, JJIJIJ, JJJAJJ, JJJHGJ, JJJJAJ, JJJJGJ, JJJJIJ, K0008H, K00161, K001G1, K001L1, K002CH, K002HH, K00521, K00AKD, K00C0H, K00GF1, K00I0D, K00K95, K00M05, K01621, K05021, K0505D, K051G1, K059F5, K05K95, K0C0C1, K0L291, K0M005, K0M505, K1K661, K2CK0H, K33IAD, K3IIID, K5550D, K56121, K59AA5, K612K1, K61CC1, K66661, K6K611, K900C1, K99661, K9AFF5, K9C001, KAKI8D, KC00C1, KDK00D, KF9991, KI0IID, KK000D, KK01L1, KK0661, KK0I8D, KK0L11, KK0M2H, KK5661, KK59F5, KK61C1, KK9995, KK9EE5, KKA3ID, KKA83D, KKAI8D, KKC001, KKC0C1, KKC1C1, KKCCC1, KKD2HH, KKK595, KKK9A5, KKKK95, KKKKKH, KKKMCH, KKM505, KKMEE5, KKMKCH, KM0005, L222E7, L33AAD, L38I8N, LCCC11, LDFBCB, LEL2E7, LELE27, LELL27, LGMMM1, LLE2E7, LM2ME7, M000M5, M006MB, M00E27, M00MM1, M02227, M06M61, M06MM1, M0E227, M0EE27, M0KME5, M0M5GN, M0MM61, M0MMCB, M0MNNN, M0NNM1, M38LLN, M5K505, M77707, M7E227, M7E727, M8CHHH, MBMMCB, MBMMM1, MEEE77, MHH027, MHH505, MHHC6H, MHHH6H, MHHK05, MKK001, MM2ME7, MM7707, MM7E77, MMBMK1, MMM2E7, MMMC0B, MMMK61, N0003D, N0008D, N0030N, N030NN, N0C0AD, N0CKAD, N0DKDD, N0N3GN, N0NN3N, N333AD, N777A7, N77A77, NAACKD, NAAKDD, NACAKD, NACKAD, NC0AKD, NC0KAD, NCA0KD, NCKAKD, NDNNLN, NNNLAD, NNNNLD, 1BBBBBB, 1BBBBG1, 1M6MMMB, 1MMBBBB, 1MMMMK1, 2000227, 2000EE7, 20EEEE7, 2C0FFFH, 2E2EEE7, 2KKKHCH, 2MEE227, 2MEEE27, 333333D, 3333355, 3335555, 333FFF5, 333IIID, 388NNNN, 38INNNN, 3INNNNN, 4000IMN, 4000JJJ, 400IIIN, 444444J, 44JJJJJ, 488888N, 4IIJIIJ, 4JJJ33J, 50002M1, 5001G21, 5006621, 500LGM1, 555083D, 55555I5, 5616G21, 59MMMM1, 5K999A5, 61CCCC1, 66666K1, 6K0000H, 6K0080H, 70000A7, 70077A7, 70700A7, 7070A77, 77700A7, 77770A7, 7777227, 7777E27, 77L2227, 7LE22E7, 888888B, 888888N, 8888BBN, 8888IIN, 888B88B, 888I8IN, 88IINNN, 88NIINN, 88NNIIN, 8INNNNN, 90444IJ, 904I44J, 9666661, 9666FK1, 9666K61, 9966FK1, A00KK0D, A0K000D, AAAAA35, AAKKI8D, BB8888B, BBB0BLB, BBBB1BB, BBBBBB1, BBBBBGB, BBBBBLB, BBBLMBB, C0007KH, C000F11, C00FFFH, C00HH0H, C00K00H, C0C0HHH, C0CCHHH, C0CHH0H, C0CHHCH, C0FFFFH, C0H0H0H, C0KKC0H, CC0HH0H, CCCCC11, CCCCCC1, CCHHHHH, CDKKKKH, CEL7777, CGGG0G7, CGGGGG7, CH00HHH, CHGGGG7, CHHHH0H, CHHHHCH, CHHHHHH, CK0000H, CKDKKKH, D00DDKD, DD0DDD7, DDBBBLB, DDD2EE7, DDDBBLB, DDDDD27, DDDDDBB, DDDDDC7, DDDDDKD, DDDDDMB, DDDDEE7, DDDDKKD, DDDDLDB, DDDFBBB, DDDLFCB, DDDMEE7, DDM2227, DHHEEE7, DK000KD, DK00D0D, DK0D00D, DNN000N, E000CL7, E000EG7, E000GE7, E00C0G7, E00CE07, E00EE27, E0C00G7, E0C0EG7, E0CE007, E0EC0G7, E0EE207, E0G0007, E20EE27, E22EEE7, E2EE227, E2EEE27, E772227, E77LL27, E7L2227, E9IIIIJ, EAKKKA5, EC000G7, ECG00G7, EE00L27, EE0E0G7, EE20EE7, EEE0EG7, EEE22E7, EEEE727, EEEEE27, EEEEG07, EEEEGE7, EEEKKK5, EELLL27, EI0IIIJ, EKKKAA5, ELLLE27, F00FA35, F0333F5, F0F0FE5, F333335, FAAFF35, FCF0FCH, FEEEE35, FF03335, FF0FA35, FF0FE35, FF0FMCH, FFF0A35, FFF0F35, FFFAF35, FFFF5I5, FFFFM2H, FFFI3I5, FFFIII5, FFH5555, FH55555, FL1MMM1, G0000G7, G0000L7, GGGG007, GLE2227, GLLLLE7, GLLLLL7, H000007, H0000C7, H000HCH, H000HM7, H000M27, H000ME7, H00G227, H00HHM7, H02M227, H0C0HHH, H0CH00H, H0E0007, H0FFF35, H0FFFF5, H0H0ME7, H0HFII5, H0HHHCH, H0M0227, H555555, H5F5FF5, HC000G7, HC00H0H, HCCHHCH, HCHHHCH, HCHHHHH, HEEEE27, HFF5FF5, HFF5FI5, HFKKK05, HG00007, HH00E27, HH0G227, HHH2MM7, HHH55F5, HHH9FF5, HHHFFK5, HHHFK55, HHHH7EJ, HHHHCM7, HHHHHAJ, HHHHHF5, HHHHHHJ, HKK5505, I000055, I00A0ID, I0I4IIJ, I0IIIIJ, I88NIIN, III0055, III0I55, III444J, IINNLIN, J000IJJ, K0000DH, K0000KD, K00033D, K000A5D, K000K5D, K00555D, K009995, K00K00D, K00K8ID, K00KI8D, K00KIAD, K01GCC1, K05033D, K0999F5, K2KKKCH, K53333D, K956661, K999991, KCCC1C1, KFFFE55, KFFKKE5, KFKFKE5, KK009A5, KK00C11, KK01GC1, KK99001, KKIII05, KKK09F5, KKKE9E5, KKKEAK5, KKKKI05, KKKKKE5, KMMEEE5, L1BBBG1, LBMMMCB, LBMMMMB, LDEEE07, LEE22E7, LEE2E27, LEEE2E7, LLLLE27, M0000CB, M000C6B, M02EEE7, M0K0005, M0M0005, M2CHHHH, M2HHHHH, M6MMMM1, MC0000B, MCHHHHH, ME7E777, MEE7777, MEEE2E7, MG06661, MHHHCCH, MHHHH27, MHHHHH7, MHM0027, MM6666B, MM77777, MMC000B, MMM7727, MMNM777, N000NLN, N00333D, N003AAD, N0A00DD, N0NN33D, N0NNLLN, N30000N, N777777, NDNNNNN, NN0N0GN, NN0N30N, NNN300N, NNN333D, NNN3LLN, NNNDDDD, NNNNN3N, NNNNNND, 33333F35, 33FFFF35, 3555FFF5, 3FFFFF55, 3NNNNNLN, 40000I0J, 40I0IIIJ, 444440IJ, 4J0000IJ, 500006G1, 5D00DDDD, 5L1MMMM1, 5MMMMMG1, 5NNDDDDD, 5NNNNDDD, 5NNNNN8D, 6000080H, 777777A7, 77777A77, 7944444J, 800000IN, 996666K1, 999999I5, 9999FEA5, A00003ID, AAAAFF35, BBBGMMMB, C0000011, C000007H, C0CC0H0H, C666666B, CCCH0HHH, CCHH0HCH, CE777777, CEEEEE07, CHH0H00H, D00000GN, D000D0LD, D000IIGN, D0DDDDD7, DDD0E2E7, DDDDDDDB, DDDDDME7, DEEEELE7, DEEELEE7, DEELEEE7, DELEE0E7, E00000C7, E00000G7, E0000CG7, E000C0E7, E000G007, E00CG007, E00E0CG7, E0C00007, E0CGGGG7, E0GGGGG7, E20000E7, EAAKAAA5, EAKKAAA5, EE00E727, EE020007, EEEE2027, ELEE2227, F00003F5, F0000A35, F0003335, F0FFFA35, F1999991, F1999MM1, FAAAAF35, FBBBBBG1, FEAAAAA5, FF000A35, FF00FF35, FF0KEEE5, FFAAAF35, FFF555I5, FFFF33I5, FFFFF035, FFFFF3F5, FFFFFKI5, FFFFFMHH, FKFKEEE5, FKKFEEE5, FMMMMMCB, FMMMMMM1, G2000007, GGGGGMM7, GJJJJJ0J, GJJJJJ3J, H0000E27, H0000G27, H000C0G7, H000CEG7, H000CHH7, H000E0E7, H000EE27, H00CHHG7, H00EEE27, H00M0EE7, H05FF5F5, H0E00EE7, H55FF5F5, HCHH0H0H, HE000EE7, HFFIIII5, HGGG2227, HH00CEG7, HH00H0CH, HH0EEEE7, HH0FFFI5, HHEEEEE7, HHH000CH, HHH00EG7, HHHC00G7, HHHFFFF5, HHHHHKK5, HHHK5F55, HK5555F5, I4IIIIIJ, IA0000ID, II0005I5, III000I5, III055I5, III5NNNN, IIIII9IJ, IIIIIII5, IIINNNGN, JAJJJJJJ, JJAJJJJJ, K000005D, K00009A5, K0000M55, K000M555, K008IIID, K00D0K0D, K00III8D, K00K550D, K00LCC11, K0999951, K0D0000H, K0K00595, K0K9AAF5, K0KK0095, K0KK9FF5, K3333IID, KFKFEEE5, KFKKEEE5, KK00000H, KK0000M5, KK099991, KK55583D, KKKEEEA5, KKKKKKI5, LEEEE227, LLLEEE27, LLLL2E07, M000006B, M000M6CB, M0MMMMM1, M222EEE7, M777E777, M7E77777, ME222EE7, ME2EEEE7, MEE222E7, MM0NNNNN, MME77727, MMM6MMM1, N00003GN, N0000ADD, N000N0GN, N000NNND, N033333D, N0NN0NGN, NDDDDKDD, NN000N3N, NN00N03N, NN03000N, NNN003GN, NNNNDNLN, NNNNNADD, 199999MM1, 200FFFFFH, 222MEEEE7, 2FFFFFFCH, 30000000N, 30N00000N, 400000J3J, 500000M01, 5000166G1, 5000666G1, 50DDDDDDD, 8NN33333D, 999999991, C000000FH, C00000K0H, C000H00HH, C77777707, CH00H000H, CHH0000HH, D00000DKD, D00000DLD, D0000200H, D0000KK0D, D000KK00D, D00D0DDLD, D0D00DDLD, D0LEEEEE7, DDBBBBBBB, DDD000KDD, DDDDDDDE7, DK00000DD, DNNNNNNNN, E00000E27, E00007L27, E0000E727, E0E000C07, E20000027, EAAAAKAA5, EAKAAAAK5, EE0000C07, EEE000E27, EEEEEEGL7, F00FFFF35, F0FFFFF35, FF0000035, FF0FFFF35, FF5555FI5, FFFFFFA35, FFFFFFF35, FFFFFFFI5, FKKKKEEE5, FMMMMMMMB, GGGGG2227, GGGGGG207, GJJJJJJJJ, GLMMMMMMB, H000022M7, H000222M7, H000EEEE7, H0EEEEEE7, H0H0000CH, H0IIIIII5, HCH00000H, HE0EEEEE7, HFFFFFI35, HFFFFKKK5, HHHHHHG27, HHHHHHH55, HHHHHHHH7, HHHHHHM55, HHHKK5555, HHIIIII05, HIIIIII05, HKK5555I5, I000000AD, I000000ID, I000A000D, I00A0000D, IIIII0555, IIIIIII9J, K000000AD, K00000595, K000009F5, K0000550D, K099999A5, K0C00000H, K0I00000D, KK0000595, KK0000HCH, KKK000095, KKKFKFFE5, KKKIIIII5, M77777777, MEEEE2227, MMMMMMMM1, N0000000D, N0000003N, N000003NN, N00000N3N, N00000NGN, N00N000GN, N00NNNN8D, N0NNN00GN, N0NNNN3AD, N0NNNNNGN, N999999M1, NN0NNNNGN, NNN000NGN, NNNNNDD8D, NNNNNN0GN, 16MMMMMMMB, 1MMMMMMBCB, 3333333335, 33333333I5, 400000000N, 40IIIIIIJJ, 4IIIIIIIJJ, 4IIIIIIJIJ, 50000000M1, 70F9999991, 777E777727, 9999995MM1, ADD000000D, C00000088B, C000000CF1, C00000F0HH, CH00000H0H, D00KD0000D, D0D0DDDDLD, D0E2EEEEE7, D2EEEEEEE7, DBBBBBBBBB, DD000000KD, DD0000DDLD, DLE0EEEEE7, EEE0000727, EEEAAAAAA5, EEEEEE00G7, EEEEEEE0G7, F000000F35, F00FFKEEE5, F00KFFEEE5, F0M666666B, FCFFFFFFFH, FFFFFFF2HH, FFFKKKEEE5, GGGGGGG227, H00000C06H, H0000HHH6H, H555FFFFF5, H55FFFFF55, H5FFFFFF55, HF5FFFFFF5, HHHH0H0HCH, HHHHH0HHCH, HHHHHH0HCH, HHHHHHHHM5, HHHIIIIII5, IIDNNNNNLN, IIIIIJJIIJ, IIINNNNNLN, IINNNNNNGN, INNNNNNNLN, J0000000IJ, K0000II8ID, K099999995, K0I0000AID, K0K0009FF5, K9999999F5, KK00000095, KKFFFKEEE5, LLLLLLLME7, LLLMEEEEE7, LMEEEEEEE7, M000000005, MHHHHHHHH5, MK00000005, MMMMMMMBCB, NN000000GN, NN0000NNGN, NN99999991, 2HHHHHHHHHH, 38NNNNNNNNN, 3MNNNNNNNNN, 40IIIIIIIIJ, 4AJJJJJJJJJ, 4J000000J0J, 4JJJJJJJJJJ, 506666666G1, 5DDDDDDDDLD, 999999999F5, 99999999EA5, 99999999FE5, A0000000035, C0000000007, C00000000G7, C00000000KH, CEEEEEEEEL7, D0000000FMH, D000DDDDDLD, D0KD000000D, DDDD00000KD, DEEE0EEEEE7, DEL0EEEEEE7, DELEEEEEE07, E0000E20007, E7777777727, EE000000207, EEE20000007, FFFFFFFFMCH, FM66666666B, GGGGGGGG2M7, HFFFFFFFF55, HHHHHHHHH6H, HHHHHHHHHCH, HHHHHK55555, I9IIIIIIIIJ, IIIIIIII44J, IIIIIIIJJIJ, IINNNNNNNNN, JDDDDDDDDDD, JJIIIIIIIIJ, K00000I8IID, LLLLLLLLL27, 9999999EEAA5, AI000000000D, C77700000007, CH0HH000000H, D00D000000LD, DEEEEEEE0EE7, DN000000000N, EAKAAAAAAAA5, EKAAAAAAAAK5, F6666666666B, H000HHHHHH6H, H55FFFFFFFF5, HFFFFFFFFKK5, K00000000I8D, K999999999A5, 3555555555FF5, 5000000000001, 6G66666666661, 99999999999A5, C00000000000H, CFFFFFFFFFFCH, CHHH00000000H, D00000000K0KD, D0000000K00KD, D0D00000000LD, DEEEEEEEEEL07, E000E20000007, E00E200000007, EEE0000000027, GGGGGGGGGGGM7, GGGGGGGGGGM07, H00000000CHHH, H00HC0000000H, HFFFFFFFFFFK5, I0A000000000D, J000000000J9J, K000000000095, K000000000M2H, M0000000000M1, M0EEEEEEEEEE7, MHHHHHHHHHHHH, MMNNNNNNNNNNN, MNNNNNNNNNNNN, N000000DDDDDD, N000DDDDDDDDD, NNDDDDDDDDDDD, 22EEEEEEEEEEE7, 35FFFFFFFFFFF5, 400000000000JJ, 800000000000GN, DDDDDDDDDDD077, DDDDDDDDDDDDD7, E0000000000L27, EAAAAAAAAAAKA5, EEG00000000007, H0000000000C6H, I5500000000005, II0000000000I5, M0666666666661, M6MMMMMMMMMMMB, 4JJ00000000000J, 506666666666661, BGMMMMMMMMMMMCB, CFFFFFFFFFFFFFH, D0000000000KD0D, D0HEEEEEEEEEEE7, F0BBBBBBBBBBBBB, HGGGGGGGGGGGGG7, K0000000000000D, K00000000000MCH, M0M6MMMMMMMMMMB, 5DDDDDDDDDDDDDDD, C00000000000008B, D00000000000000H, DEEEEEEEEEEEE0L7, DEEEEEEEEEEEEEL7, EEE2EEEEEEEEEEE7, GM66666666666661, H5FFFFFFFFFFFFF5, IIIIIIIIIIIIIJJJ, BGMMMMMMMMMMMMMMB, DLEEEEEEEEEEEEEE7, H0000000000000CHH, H000000000C0000HH, I000000000000000D, IIIIIIIIIIIIIIIJJ, INNNNNNNNNNNNNNNN, J000000000000009J, M666666666666666B, N0000000000000LLN, N00DDDDDDDDDDDDDD, 355555555555555555, 60000000000000008H, 6M6666666666666661, C000000000000000F1, N0DDDDDDDDDDDDDDDD, 666666666666666666B, 800000000000000000N, AD000000000000000DD, DEEEEEEEEEEEEEEEEE7, I500000000000000005, 20000000000000000027, 4000000000000000003J, 400000000000000000IJ, 99999999999999999995, DD00DDDDDDDDDDDDDDLD, E2EEEEEEEEEEEEEEEEE7, N00000000000000000LN, 500000000066666666661, EE0000000000000000727, GGGGGGGGGGGGGGGGGGG07, H0000000000000000006H, 40000000000000IIIIIIIJ, AD0000000000000000000D, K0000000000000000000M5, CL777777777777777777777, D000000000000000000000N, D0000000000000000000IIN, HHHHHHHHHHHHHHHHHHHHHK5, NDDDDDDDDDDDDDDDDDDDDDD, 1MMMMMMMMMMMMMMMMMMMMMBB, D00DDDDDDDDDDDDDDDDDDDLD, FFFFFFFFFFFFFFFFFFFFFFFH, 4J0000000000000000000000J, 566666666666666666666666G1, EKKAAAAAAAAAAAAAAAAAAAAAA5, 6666666666666666666666666G1, AJJJJJJJJJJJJJJJJJJJJJJJJJJJ, H00000000000000000000000008H, N0000000000000000000000000GN, DD0000000000000000000000000LD, IIIIIIIIIIIIIIIIIIIIIIIIIIIIJ, G0666666666666666666666666666661, GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG7, K000000000000000000000000000000000H, EAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA5, LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLM7, M2EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE7, C000000000000000000000000000000000000000001, MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMCB, E00000000000000000000000000000000000000000000727, 777777777777777777777777777777777777777777777777727, EG000000000000000000000000000000000000000000000000000007, D000000000000000000000000000000000000000000000000000000000LD, 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===Base 36=== 11, 15, 17, 1B, 1H, 1N, 1P, 1V, 1Z, 21, 27, 2B, 2H, 2P, 2T, 2V, 2Z, 31, 35, 3J, 3N, 3T, 3V, 45, 47, 4D, 4J, 4N, 4T, 4Z, 51, 5B, 5D, 5H, 5J, 5V, 67, 6B, 6D, 6H, 6N, 6P, 6Z, 75, 7B, 7H, 7J, 7P, 7T, 7V, 85, 8J, 8N, 8P, 8T, 97, 9D, 9N, 9P, 9T, 9Z, A7, AD, AJ, AN, AT, B1, B5, BD, BN, BP, BZ, C1, C7, CB, CH, CP, CT, CV, CZ, DB, DJ, DN, DV, DZ, E5, EH, EJ, F1, F7, FH, FN, FT, FV, G1, GB, GH, GN, GP, GV, H1, H5, H7, HJ, HT, HV, HZ, I5, IB, ID, IP, IT, IZ, J7, JH, JP, JZ, K7, KD, KJ, KN, KV, L1, L5, LD, LH, LV, M5, MH, MJ, MT, MV, MZ, N1, NB, NP, NT, NV, NZ, OD, OH, OJ, ON, P7, PB, PJ, PT, Q1, Q5, QB, QH, QV, QZ, R5, RB, RJ, RP, S1, S5, SB, SD, SN, SP, SV, T5, T7, TH, TJ, TP, U7, UB, UD, UH, UN, UT, V1, V7, VD, VZ, W1, WB, WJ, WT, WZ, X5, XD, XP, XT, XZ, Y5, Y7, YD, YP, YZ, ZH, ZJ, ZN, ZT, ZV, 12D, 16J, 18D, 1CD, 1CJ, 1DD, 1GT, 1JD, 1JJ, 1LT, 1QJ, 1RD, 1RT, 1ST, 1XJ, 1YJ, 1YT, 22D, 22J, 22N, 23D, 255, 2A5, 2CD, 2ED, 2EN, 2F5, 2GD, 2GJ, 2IJ, 2JN, 2LN, 2MN, 2ND, 2O5, 2QD, 2QJ, 2U5, 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MYMU1, MYRK1, MYUU1, MYXR1, N000D, N0055, N006J, N007N, N00CN, N00IH, N00O7, N00S7, N029J, N02DD, N0307, N044H, N049H, N0505, N05M7, N05Q7, N06LJ, N070N, N0A55, N0CEN, N0CNN, N0CYN, N0DMD, N0DRD, N0F05, N0FF5, N0FMD, N0GED, N0HNN, N0I4H, N0IS7, N0IXJ, N0JLN, N0JNN, N0K4H, N0KIH, N0L6J, N0LI7, N0LLN, N0M0N, N0MQ7, N0NEN, N0O07, N0O77, N0Q0N, N0QEN, N0RRH, N0S07, N0SS7, N0U0J, N0ULJ, N0W77, N0WC5, N0WL7, N0XO7, N26JJ, N29XJ, N2CNN, N2CYN, N2MMD, N2N6J, N2N9J, N2NLJ, N2YYN, N30ED, N32RD, N33GD, N33MD, N3GGD, N3IW7, N3MR7, N3MX7, N3RGD, N3RI7, N3W2D, N3W77, N3X07, N3X77, N400H, N409H, N44YH, N494H, N49YH, N4AYH, N50K5, N5307, N5537, N5577, N57Q7, N5FK5, N5KK5, N5Q77, N5SQ7, N69LJ, N6L9J, N6U0J, N700D, N7077, N70EN, N70FD, N73RD, N7777, N777N, N7DMD, N7E2N, N7FED, N7M3D, N7MWD, N7SR7, N7WMD, N92LJ, N9XXJ, NA505, NA5F5, NAFK5, NAK05, NAKF5, NARYH, NAWW5, NC00N, NC0EN, NC0NN, NCE0N, NCN0N, NCNQN, NCW05, ND3GD, ND7DD, NDAW5, NDDGD, NDDRD, NDE3D, NDWM7, NDWW7, NE0GD, NED3D, NEDDD, NEL2N, NEMMD, NEMRD, NF0F5, NFEMD, NFKF5, NFWC5, NFWW5, NGDED, NGW2D, NH00H, NH2NN, NHH0H, NHMCN, NHMMD, NHNNN, NI00H, NI0EN, NI0MN, NI0NH, NI0NJ, NI0XJ, NI44H, NI7R7, NI7S7, NII77, NIIM7, NIIMN, NIIYN, NIM0N, NIN0H, NIN0J, NINJJ, NIW37, NIWM7, NIX77, NIXW7, NJ0EN, NJ0NN, NJ30D, NJ33D, NJFMD, NJIEN, NJJ2N, NJJIN, NJJJJ, NJJJN, NJL0J, NJLNN, NJN0N, NJSJJ, NK005, NK04H, NK3KH, NK5F5, NKA05, NKFK5, NKK55, NKKF5, NL09J, NL2IN, NLCNN, NLII7, NLIIN, NLJLN, NLL2J, NLLNJ, NLLNN, NLNCN, NLNIN, NLNLJ, NLNLN, NM00N, NM73D, NM7DD, NM7RD, NME0N, NMELN, NMLL7, NMLQ7, NMMRD, NMQEN, NMRD7, NMRR7, NMWWD, NN02J, NN0AH, NN0EN, NN30H, NN525, NN6UJ, NN92J, NNA55, NNASH, NNCLN, NNCMN, NNELN, NNF25, NNHHN, NNJ2J, NNJJJ, NNLNN, NNN55, NNN9J, NNNMN, NNNNJ, NNNSH, NNNXJ, NNQYN, NNS3H, NNU9J, NNW55, NNXJJ, NO077, NO0W7, NO777, NOI77, NOIM7, NOWL7, NQ00N, NQ0YN, NQ77N, NQ7EN, NQLLN, NQLNN, NQQQN, NQQYN, NRARH, NRAYH, NRDI7, NRHYH, NRQL7, NRRHH, NRW2D, NS0L7, NSA3H, NSHHH, NSIIJ, NSIJJ, NSS07, NSSJJ, NSSL7, NSSS7, NSULJ, NU00J, NUL6J, NUSIJ, NW0C5, NW3W7, NW5W5, NWI77, NWIM7, NWIO7, NWW55, NWWM7, NX0I7, NX0O7, NX3R7, NX9XJ, NXIM7, NXRL7, NXSSJ, NXWI7, NXWW7, NXXSJ, NY44H, NY94H, NYYIN, O0057, O005T, O0077, O0091, O009B, O00BT, O00EV, O00OV, O00TT, O00WP, O00WV, O040V, O0507, O056T, O065T, O08AV, O08E7, O0901, O09AB, O09I1, O09K1, O09WV, O0A4V, O0AI1, O0E9V, O0EAB, O0EAV, O0EFP, O0EKB, O0EOB, O0EU1, O0FMP, O0K6T, O0K91, O0MM1, O0O9B, O0OAB, O0OI1, O0OOB, O0OT1, O0OUV, O0OW7, O0OYT, O0T8V, O0TOT, O0TOV, O0TTV, O0TUV, O0TX1, O0U91, O0UE1, O0W87, O0WOV, O0YOT, O100T, O1EET, O4PAV, O4U0V, O5005, O50EP, O50I7, O50K5, O555P, O55FP, O55UP, O5EFP, O5I07, O5K05, O5KK5, O5OYT, O6LGT, O77E7, O7Q77, O80E7, O8AAZ, O8AFZ, O8AOV, O8FFZ, O8FKB, O8FZB, O8IM7, O8ZRZ, O8ZZB, O900V, O90WV, O96OV, O99LB, O9K01, O9OU1, O9R6V, O9U01, O9UI1, OA091, OA0O1, OA4AV, OA4IV, OA68V, OA8AZ, OA9I1, OAA4V, OAAFZ, OAAO1, OAAOV, OAAZZ, OAFAZ, OAFYB, OAI0V, OAI91, OAOAV, OAOE1, OAOU1, OAUE1, OAUI1, OAY01, OAY0B, OAYI1, OAZZZ, OB66T, OBE0T, OBEET, OE0BT, OE0FB, OE4AV, OE6ET, OE8AV, OE9EB, OEA8V, OEAA1, OEAFB, OEBET, OEBI7, OEEO7, OEFFP, OEFLP, OEKA1, OEKAB, OEKU1, OELMP, OEML7, OEO07, OEO0B, OEO4V, OEO6V, OEOAV, OEOO7, OEOOB, OEOVB, OEPU1, OERET, OERRV, OETY1, OEUK1, OEUU1, OEV9B, OEVFP, OEW8V, OEWW7, OF0FP, OF0OB, OFFFP, OFFMP, OFFZP, OFFZZ, OFMMP, OFMWP, OFOQP, OFPFZ, OFPUZ, OFZ0P, OFZFZ, OFZOB, OFZZZ, OG065, OG0YT, OI0EV, OI7Q7, OI9WV, OIIE7, OIQ77, OIQW7, OIR6V, OIYO1, OK8KB, OKAE1, OKAY1, OKE6T, OKEU1, OKFYB, OKIY1, OKYA1, OKYI1, OL08B, OL4EP, OL777, OL8E7, OLBI7, OLEL7, OLFOP, OLGYT, OLIW7, OLLSZ, OLLZZ, OLOUP, OLR6T, OLUMP, OMAU1, OMOU1, OMXM1, OO0AB, OO0I7, OO0T1, OO1ET, OO4AV, OO4MP, OO4QP, OO6KT, OO6LT, OO6OV, OO7O7, OOA0B, OOAIV, OOAOV, OOBGT, OOEMP, OOERT, OOET1, OOEU1, OOEY1, OOGTT, OOI4V, OOIRV, OOKET, OOLBT, OOMMP, OOMQ7, OOMU1, OOMWP, OOO0B, OOO6T, OOO77, OOOE7, OOOKT, OOOOV, OOORT, OOOW7, OOPY1, OOQ77, OOT01, OOT91, OOTAV, OOTOV, OOTUV, OOU91, OOUUV, OOWIV, OOWMP, OOWVP, OOY01, OOY0B, OOYKB, OOYU1, OOYYB, OP0EV, OP44V, OP8FZ, OPA91, OPAAZ, OPAOV, OPEAV, OPI4V, OPO4V, OPOIV, OPOUV, OPOY1, OPUAZ, OPUEV, OPWUV, OPYU1, OQ7W7, OQ8E7, OQLE7, OQQL7, OR8AZ, ORA8Z, ORKLT, ORS8Z, OS8RZ, OSR8Z, OSS8Z, OT09V, OT0K1, OT66T, OTT8V, OTUOV, OU091, OU0E1, OU0MP, OU4LP, OUAAZ, OUASZ, OUL4P, OUP8Z, OUP91, OUPAZ, OUPY1, OUU0P, OUUPZ, OUYM1, OUZ91, OV0FB, OV0LB, OV54P, OV5WP, OV9K5, OVALB, OVB6T, OVKFB, OVLEB, OVLFP, OVQWP, OW0EV, OW7O7, OW7Q7, OW7W7, OW90V, OWEEP, OWIWV, OWLW7, OWOM7, OWOVP, OWQ87, OWU0V, OWW9V, OWWL7, OWWOV, OXAA1, OXU01, OXUI1, OXXI1, OXXX1, OY00T, OY0E1, OY0RT, OY0U1, OY0YB, OY98B, OYE0T, OYFKB, OYKFB, OYLYB, OYYYB, OZ0OB, OZ0WP, OZ0YB, OZ9EB, OZ9K1, OZ9O1, OZALB, OZAYB, OZEAB, OZEOB, OZFEB, OZFFP, OZFFZ, OZFRZ, OZFZP, OZO0B, OZO91, OZOYB, OZPRZ, OZR8Z, OZUUP, OZZYB, P00W5, P02G5, P049V, P04YV, P0A0V, P0AW5, P0CC5, P0CU5, P0E9V, P0EWV, P0F25, P0FC5, P0G25, P0K3Z, P0KOZ, P0KRH, P0O55, P0OEV, P0PG5, P0PO5, P0PW5, P0R0H, P0ROZ, P0U25, P0UIV, P0UVP, P0V0P, P0VKP, P0W9V, P0YIV, P13WD, P22K5, P2D95, P2NC5, P33ZZ, P38DD, P3GGD, P3SAH, P409V, P444V, P44O1, P44Y1, P4AIV, P4AYV, P4E0V, P4OA1, P4OK1, P4OO1, P4U81, P4UEV, P4UR1, P55EP, P5GZ5, P6A41, P803H, P80AZ, P838D, P8AAZ, P8D8D, P8FKZ, P8K0Z, P8KKZ, P8KXH, P8OE1, P8UE1, P8X0H, P8X3H, P8XKH, P909V, P9941, P99EV, P99U1, P9E9V, P9K91, P9OE1, P9OK1, P9W9V, P9X9H, PA00H, PA441, PA5G5, PA8FZ, PA9O1, PAA8Z, PAI4V, PAI9V, PAMKP, PAOEV, PAR8H, PAUM1, PAVKP, PAZEP, PC0W5, PCAG5, PCAU5, PCCA5, PCWN5, PD0QP, PD0SH, PD33D, PD3AH, PD3MD, PDGC5, PDK3H, PDK8H, PDSAH, PDUAP, PE99V, PEA91, PEAEP, PEEA1, PEEE1, PEER1, PEI9V, PEK61, PEQQP, PERE1, PERK1, PEUY1, PEY0V, PF2K5, PF3CD, PF83D, PFC2D, PFCWD, PFDAP, PFEKP, PFMCD, PFMMD, PFO55, PFR2D, PFZEP, PG295, PG2WD, PG8CD, PGCD5, PGDC5, PGF5Z, PGG8D, PGKF5, PGKK5, PGO95, PGW8D, PH2MD, PHD8D, PK0O5, PK441, PK53Z, PK5GZ, PK83H, PK8KZ, PKAA1, PKAU1, PKKO5, PKP3Z, PKRXH, PKSIH, PMAA1, PMAAP, PMAU1, PMF3D, PMFCD, PMMAP, PMMMD, PMMMP, PMMPD, PMRR1, PMUO1, PN2D5, PN2W5, PNA3H, PNAF5, PNFK5, PNHFD, PNK55, PNKF5, PNSKH, PO09V, PO0EV, PO4AV, PO90V, POAY1, POI4V, POOE1, POUEV, POUY1, POWUV, POWWV, POYA1, POZAZ, POZFZ, PP0QP, PP2CN, PP2MD, PP33D, PP595, PP5W5, PP8CD, PPCNN, PPCRD, PPCU5, PPCW5, PPCWD, PPD05, PPDUP, PPECN, PPF8D, PPFC5, PPFW5, PPGC5, PPGF5, PPGFZ, PPKGZ, PPMCD, PPMCN, PPMEN, PPMND, PPNF5, PPNMN, PPNWD, PPP3Z, PPP95, PPPC5, PPPRZ, PPPZD, PPQKP, PPS0Z, PPW2N, PPWND, PPWWN, PPZC5, PPZSZ, PQQQP, PR1GD, PR8AH, PRA0H, PREK1, PRKO1, PRMM1, PRNFD, PRRM1, PRRRH, PRW2N, PS0ZZ, PS80H, PS80Z, PS8AH, PS8ZZ, PSIKH, PSR3Z, PU025, PU0IV, PU49V, PU4YV, PU8AZ, PU9EV, PUE91, PUE9V, PUI9V, PURK1, PUUM1, PUUR1, PUVAP, PUYIV, PUYO1, PUZMP, PV00P, PV2CN, PV2RN, PVAKP, PVFAP, PVFFP, PVFKP, PVK0P, PVKAP, PVNCN, PVNEN, PW005, PW0C5, PWCWD, PWF8D, PWNC5, PWO9V, PWOWV, PWWOV, PWWWN, PWWWV, PX0IH, PXAIH, PXIAH, PXIKH, PYKE1, PYKO1, PYRK1, PYRM1, PZ0G5, PZ1WD, PZ295, PZ2C5, PZ2G5, PZ481, PZ641, PZE61, PZEAP, PZG25, PZK61, PZKOZ, PZOFZ, PZOO1, PZR41, PZRZZ, PZS0Z, PZSUZ, PZUMP, Q00DT, Q00JD, Q00QT, Q00YN, Q020J, Q03RD, Q0CQN, Q0DRD, Q0FRD, Q0JTT, Q0Q3D, Q0QRN, Q0QXN, Q0XEN, Q0XIJ, Q0XLN, Q0XQN, Q0YYN, Q20RD, Q2D0D, Q32WD, Q3D3D, Q4EKP, Q4PQP, Q7777, Q77Q7, Q7ER7, Q7EW7, Q7LR7, Q7LS7, Q7LW7, Q7QQN, Q7QR7, Q7QYN, Q7RE7, Q7SS7, QAAPP, QAOOP, QAOWP, QAUAP, QAUWP, QAWEP, QAWLP, QCEQN, QCNYN, QCQEN, QD0GD, QD0RD, QD20D, QD33D, QD3DD, QDAWP, QDRET, QDWKP, QE7QN, QECLN, QEEL7, QEES7, QELCN, QEQCN, QEQTT, QERE7, QESR7, QF2WD, QFGUJ, QFR2D, QG00J, QG0IJ, QG7Q7, QG7R7, QGDDD, QGGGD, QGGQD, QGJ2J, QGMQ7, QGOO7, QGQQ7, QGRR7, QJ02J, QJ03D, QJ0SJ, QJ33D, QJ3WD, QJD0D, QJI0J, QK44P, QKPKP, QL7W7, QLES7, QLLL7, QLNNN, QLQ77, QLQL7, QLQM7, QLQPN, QLR87, QLSRT, QMLR7, QMQQ7, QN0YN, QN70N, QNCYN, QNLW7, QNNQN, QNNYN, QNQNN, QO777, QO7E7, QO8M7, QOUWP, QP3RD, QPDAP, QPEEP, QPFRD, QPGGD, QPPQP, QPR2D, QPRGD, QQ0RN, QQ0YN, QQ4LP, QQ4QP, QQAEP, QQCYN, QQELT, QQEPN, QQEQP, QQGDD, QQGGD, QQGO7, QQGQD, QQKKP, QQLAP, QQLPN, QQLRT, QQMR7, QQN77, QQNNN, QQNQN, QQPDD, QQPEN, QQPGD, QQPQP, QQPWD, QQQ0N, QQQ3D, QQQ87, QQQKP, QQQL7, QQQM7, QQQPD, QQQQN, QQQWD, QQRL7, QQRN7, QQRYN, QQSST, QQTDT, QQTQT, QQU4P, QQUAP, QQUUP, QQWPD, QQXEN, QQXQN, QQYXN, QR00N, QR0XN, QR2FD, QR32D, QREKT, QRN0N, QRNL7, QRQQD, QRRE7, QRXXN, QSES7, QSS2J, QSSE7, QSSS7, QSSSJ, QTDET, QTQ2D, QTQLT, QUAAP, QUAWP, QUPPP, QUUAP, QW7G7, QWG77, QWGM7, QWLEP, QWOEP, QWOLP, QX77N, QX7EN, QXELN, QXEQN, QXLLN, QXLQN, QXNQN, QXOE7, QXQXN, QXXNN, R0061, R008D, R00IH, R00NN, R00XN, R013D, R02YN, R030D, R04R1, R06E1, R06ET, R07M1, R08AH, R0A8H, R0AYH, R0D07, R0DDT, R0EK1, R0EYT, R0F3D, R0G8D, R0GDD, R0GGD, R0GQ7, R0H0N, R0KE1, R0LQ7, R0N0N, R0RYN, R0T2N, R0TLT, R0TNN, R0TYN, R0X0N, R0YST, R100T, R130D, R13WD, R166T, R1E0T, R1F3D, R1GFD, R1TGD, R200N, R28WD, R2W8D, R2WFD, R32DD, R330D, R332D, R3W8D, R44XV, R4AAV, R4AYV, R4MO1, R4OI1, R4RO1, R4U4V, R4X9V, R6001, R60K1, R66LT, R66YV, R6E01, R6EE1, R6MK1, R6SST, R6X01, R6X9V, R6XE1, R6XYV, R6Y6V, R7OO1, R7XE1, R80G7, R88FD, R8F8D, R8IE7, R8X8H, R9OAV, R9UVV, R9VOV, R9X6V, RA08H, RAA9V, RAS8Z, RAX0H, RD00D, RD8I7, RD8IH, RDA0H, RDDQT, RDQDT, RE061, RE6KT, RE6LT, REEK1, REEKT, RER01, RERK1, RERR1, RF0DD, RFD0D, RG28D, RGGFD, RGGWD, RGRM7, RGWQD, RH00H, RH0EN, RH8HH, RH9HH, RH9XH, RHH9H, RHHIN, RHHNN, RHIWN, RHNEN, RHWIN, RHWWN, RHX8H, RHXEN, RHY9H, RI00H, RI2IN, RIHEN, RIIWN, RIMRN, RK00T, RKEE1, RKELT, RKL0T, RKQLT, RLEI7, RLQM7, RLR07, RLRE7, RLSSZ, RLSYT, RLZE7, RLZI7, RLZLZ, RM0G7, RM0Q7, RMIWN, RMKO1, RMLQ7, RMOX1, RMR07, RMRR1, RN2YN, RN30D, RND3D, RNI2N, RNIMN, RNMEN, RNW2D, RO0TT, RO66T, RO6KT, ROAAV, ROOKT, ROOOT, ROU9V, ROXM1, ROZK1, RQK0T, RQLKT, RQLST, RQMR7, RQQLT, RQQQT, RQQWD, RQRE7, RQTQD, RR44V, RR4YV, RR601, RR66V, RR6WV, RR9HH, RR9UV, RRA9V, RRAYV, RRE01, RREE1, RRGM7, RRGR7, RRI2N, RRIIN, RRIN7, RRIXN, RRKE1, RRL07, RRLM7, RRM07, RRMG7, RRML7, RRMM1, RRMO1, RRMWN, RRNR7, RRO01, RROI1, RROK1, RRR0N, RRRE1, RRRG7, RRRIN, RRRL7, RRRM1, RRRO1, RRROV, RRRWV, RRU6V, RRV9H, RRVUV, RRVYH, RRWWV, RRXRN, RRY4V, RRY9H, RRYHH, RRYIN, RRYRN, RS8FZ, RSSSZ, RSSYT, RSYST, RT3ZZ, 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====Additional known quasi-minimal primes (not necessarily the next)==== P₈₁₉₉₃SZ ==Unsolved families== Families for which not even a probable prime is known nor can be ruled out as only contain composites (only count the numbers > base (''b'')) by covering congruence, algebraic factorization, or combine of them. {|class=wikitable |base (''b'')||unsolved family (base-''b'' form)||unsolved family (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||current search limit of length||factorization of numbers in this family |- |13||9{5}||(113×13^''n''−5)/12||116000||[http://factordb.com/index.php?query=%28113*13%5En-5%29%2F12&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |13||A{3}A||(41×13^''n''+1+27)/4||111000||[http://factordb.com/index.php?query=%2841*13%5E%28n%2B1%29%2B27%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |16||{3}AF||(16^''n''+2+619)/5||98000||[http://factordb.com/index.php?query=%2816%5E%28n%2B2%29%2B619%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||1{7}||(23×17^''n''−7)/16||32074||[http://factordb.com/index.php?query=%2823*17%5En-7%29%2F16&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||1F{0}7||32×17^''n''+1+7||32074||[http://factordb.com/index.php?query=32*17%5E%28n%2B1%29%2B7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||4{7}A||(71×17^''n''+1+41)/16||32074||[http://factordb.com/index.php?query=%2871*17%5E%28n%2B1%29%2B41%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||51{0}D||86×17^''n''+1+13||32074||[http://factordb.com/index.php?query=86*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||70F{0}D||2038×17^''n''+1+13||32074||[http://factordb.com/index.php?query=2038*17%5E%28n%2B1%29%2B13&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||8{B}9||(139×17^''n''+1−43)/16||32074||[http://factordb.com/index.php?query=%28139*17%5E%28n%2B1%29-43%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||9{5}9||(149×17^''n''+1+59)/16||32074||[http://factordb.com/index.php?query=%28149*17%5E%28n%2B1%29%2B59%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||95{F}||(2543×17^''n''−15)/16||32074||[http://factordb.com/index.php?query=%282543*17%5En-15%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||A{D}F||(173×17^''n''+1+19)/16||32074||[http://factordb.com/index.php?query=%28173*17%5E%28n%2B1%29%2B19%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||B{0}B3||11×17^''n''+2+190||32074||[http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B190&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||B{0}DB||11×17^''n''+2+232||32074||[http://factordb.com/index.php?query=11*17%5E%28n%2B2%29%2B232&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}2BE||(11×17^''n''+3−41579)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B3%29-41579%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}2E||(11×17^''n''+2−2411)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29-2411%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}E9||(11×17^''n''+2+773)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B773%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||{B}EE||(11×17^''n''+2+853)/16||32074||[http://factordb.com/index.php?query=%2811*17%5E%28n%2B2%29%2B853%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||D0G{D}||(60381×17^''n''−13)/16||32074||[http://factordb.com/index.php?query=%2860381*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||E9{B}||(3963×17^''n''−11)/16||32074||[http://factordb.com/index.php?query=%283963*17%5En-11%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||F1{9}||(4105×17^''n''−9)/16||1000000||[http://factordb.com/index.php?query=%284105*17%5En-9%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |17||FD0{D}||(72909×17^''n''−13)/16||32074||[http://factordb.com/index.php?query=%2872909*17%5En-13%29%2F16&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||2{7}9D||(47×21^''n''+2+953)/20||20000||[http://factordb.com/index.php?query=%2847*21%5E%28n%2B2%29%2B953%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||2F{C}A||(288×21^''n''+1−13)/5||20000||[http://factordb.com/index.php?query=%28288*21%5E%28n%2B1%29-13%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||4{3}B||(83×21^''n''+1+157)/20||20000||[http://factordb.com/index.php?query=%2883*21%5E%28n%2B1%29%2B157%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||5{0}DJ||5×21^''n''+2+292||20000||[http://factordb.com/index.php?query=5*21%5E%28n%2B2%29%2B292&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{5}FEK||(21^''n''+3+18455)/4||20000||[http://factordb.com/index.php?query=%2821%5E%28n%2B3%29%2B18455%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{7}ID||(7×21^''n''+2+4733)/20||20000||[http://factordb.com/index.php?query=%287*21%5E%28n%2B2%29%2B4733%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||99{0}99H||198×21^''n''+3+4175||20000||[http://factordb.com/index.php?query=198*21%5E%28n%2B3%29%2B4175&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{9}0D||(9×21^''n''+2−3709)/20||20000||[http://factordb.com/index.php?query=%289*21%5E%28n%2B2%29-3709%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{9}D||(9×21^''n''+1+71)/20||20000||[http://factordb.com/index.php?query=%289*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B3{0}EB||234×21^''n''+2+305||20000||[http://factordb.com/index.php?query=234*21%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B9{0}E5||240×21^''n''+2+299||20000||[http://factordb.com/index.php?query=240*21%5E%28n%2B2%29%2B299&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B{D}B||(233×21^''n''+1−53)/20||20000||[http://factordb.com/index.php?query=%28233*21%5E%28n%2B1%29-53%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||B{H}6H||(237×21^''n''+2−4637)/20||20000||[http://factordb.com/index.php?query=%28237*21%5E%28n%2B2%29-4637%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||DH{D}||(5813×21^''n''−13)/20||20000||[http://factordb.com/index.php?query=%285813*21%5En-13%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||F{9}D||(309×21^''n''+1+71)/20||20000||[http://factordb.com/index.php?query=%28309*21%5E%28n%2B1%29%2B71%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{F}35||(3×21^''n''+2−1051)/4||20000||[http://factordb.com/index.php?query=%283*21%5E%28n%2B2%29-1051%29%2F4&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||G{0}FK||16×21^''n''+2+335||506000||[http://factordb.com/index.php?query=16*21%5E%28n%2B2%29%2B335&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||H{0}7771||17×21^''n''+4+68062||20000||[http://factordb.com/index.php?query=17*21%5E%28n%2B4%29%2B68062&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||H{D}||(353×21^''n''−13)/20||20000||[http://factordb.com/index.php?query=%28353*21%5En-13%29%2F20&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |21||{J}6J||(19×21^''n''+2−5479)/20||20000||[http://factordb.com/index.php?query=%2819*21%5E%28n%2B2%29-5479%29%2F20&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||7{K}Z||(53×36^''n''+1+101)/7||20000||[http://factordb.com/index.php?query=%2853*36%5E%28n%2B1%29%2B101%29%2F7&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||B{0}EUV||11×36^''n''+3+19255||20000||[http://factordb.com/index.php?query=11*36%5E%28n%2B3%29%2B19255&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||HM{0}N||634×36^''n''+1+23||20000||[http://factordb.com/index.php?query=634*36%5E%28n%2B1%29%2B23&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||N{0}YYN||23×36^''n''+3+45311||20000||[http://factordb.com/index.php?query=23*36%5E%28n%2B3%29%2B45311&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||O{L}Z||(123×36^''n''+1+67)/5||100000||[http://factordb.com/index.php?query=%28123*36%5E%28n%2B1%29%2B67%29%2F5&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |- |36||S{0}8H||28×36^''n''+2+305||20000||[http://factordb.com/index.php?query=28*36%5E%28n%2B2%29%2B305&use=n&n=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show] |} For base 17, the smallest prime in family {B}2BE may or may not be quasi-minimal prime, since another unsolved family is {B}2E For base 21, the smallest prime in families {9}0D and F{9}D may or may not be quasi-minimal primes, since another unsolved family is {9}D, and the smallest prime in family DH{D} may or may not be quasi-minimal prime, since another unsolved family is H{D} ==Primality certificates for the proven primes > 10²⁹⁹== Only list bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 30 See also: [[w:Primality certificate|Primality certificate]] and [[w:Elliptic curve primality|Elliptic curve primality]] {|class=wikitable |base (''b'')||index of this quasi-minimal prime in base ''b''||quasi-minimal prime (base-''b'' form)||quasi-minimal prime (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||factordb entry of this prime||primality certificate of this prime |- |9||149||76₃₂₉2||(31×9³³⁰−19)/4||[http://factordb.com/index.php?id=1100000002359003642]||[http://factordb.com/cert.php?id=1100000002359003642] |- |9||150||27₆₈₆07||(23×9⁶⁸⁸−511)/8||[http://factordb.com/index.php?id=1100000002495467486]||[http://factordb.com/cert.php?id=1100000002495467486] |- |9||151||30₁₁₅₈11||3×9¹¹⁶⁰+10||[http://factordb.com/index.php?id=1100000002376318423]||[http://factordb.com/cert.php?id=1100000002376318423] |- |11||1065||A₇₁₃58||11⁷¹⁵−58||[http://factordb.com/index.php?id=1100000003576826487]||[http://factordb.com/cert.php?id=1100000003576826487] |- |11||1066||7₇₅₉44||(7×11⁷⁶¹−367)/10||[http://factordb.com/index.php?id=1100000002505568840]||[http://factordb.com/cert.php?id=1100000002505568840] |- |11||1067||557₁₀₁₁||(607×11¹⁰¹¹−7)/10||[http://factordb.com/index.php?id=1100000002361376522]||[http://factordb.com/cert.php?id=1100000002361376522] |- |13||3165||50₂₇₀44||5×13²⁷²+56||[http://factordb.com/index.php?id=1100000002632397005]||[http://factordb.com/cert.php?id=1100000002632397005] |- |13||3166||9₂₇₁095||(3×13²⁷⁴−6103)/4||[http://factordb.com/index.php?id=1100000003590431654]||[http://factordb.com/cert.php?id=1100000003590431654] |- |13||3167||10₂₈₆7771||13²⁹⁰+16654||[http://factordb.com/index.php?id=1100000003590431633]||[http://factordb.com/cert.php?id=1100000003590431633] |- |13||3168||9₃₀₈1||(3×13³⁰⁹−35)/4||[http://factordb.com/index.php?id=1100000000840126705]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=308&c0=-&EN= 13³⁰⁸−1] |- |13||3169||B₃₄₁C4||(11×13³⁴³+61)/12||[http://factordb.com/index.php?id=1100000003590431618]||[http://factordb.com/cert.php?id=1100000003590431618] |- |13||3170||8B₃₄₃||(107×13³⁴³−11)/12||[http://factordb.com/index.php?id=1100000002321018736]||[http://factordb.com/cert.php?id=1100000002321018736] |- |13||3171||710₃₇₁111||92×13³⁷⁴+183||[http://factordb.com/index.php?id=1100000003590431609]||[http://factordb.com/cert.php?id=1100000003590431609] |- |13||3172||75₃₇₅7||(89×13³⁷⁶+19)/12||[http://factordb.com/index.php?id=1100000003590431596]||[http://factordb.com/cert.php?id=1100000003590431596] |- |13||3173||9B0₃₉₁9||128×13³⁹²+9||[http://factordb.com/index.php?id=1100000002632396790]||[http://factordb.com/cert.php?id=1100000002632396790] |- |13||3174||7B0B₃₉₇||(15923×13³⁹⁷−11)/12||[http://factordb.com/index.php?id=1100000003590431574]||[http://factordb.com/cert.php?id=1100000003590431574] |- |13||3175||10₄₁₄93||13⁴¹⁶+120||[http://factordb.com/index.php?id=1100000002523249240]||[http://factordb.com/cert.php?id=1100000002523249240] |- |13||3176||81010₄₁₅1||17746×13⁴¹⁶+1||[http://factordb.com/index.php?id=1100000003590431555]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3177||8110₄₃₅1||1366×13⁴³⁶+1||[http://factordb.com/index.php?id=1100000002373259109]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3178||B7₄₈₆||(139×13⁴⁸⁶−7)/12||[http://factordb.com/index.php?id=1100000002321015892]||[http://factordb.com/cert.php?id=1100000002321015892] |- |13||3179||B₅₆₃C||(11×13⁵⁶⁴+1)/12||[http://factordb.com/index.php?id=1100000000000217927]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=564&c0=-&EN= 13⁵⁶⁴−1] |- |13||3180||1B₅₇₆||(23×13⁵⁷⁶−11)/12||[http://factordb.com/index.php?id=1100000002321021456]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], factor ''N''−1 is equivalent to factor [http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=576&c0=-&EN= 13⁵⁷⁶−1] |- |13||3181||80₆₉₃87||8×13⁶⁹⁵+111||[http://factordb.com/index.php?id=1100000002615636527]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 has a large prime factor, factordb entry of this prime factor is [http://factordb.com/index.php?id=1100000002615636532], and primality certificate of this prime factor is [http://factordb.com/cert.php?id=1100000002615636532] |- |13||3182||CC5₇₁₃||(2021×13⁷¹³−5)/12||[http://factordb.com/index.php?id=1100000002615627353]||[http://factordb.com/cert.php?id=1100000002615627353] |- |13||3183||B₈₃₄74||(11×13⁸³⁶−719)/12||[http://factordb.com/index.php?id=1100000003590430871]||[http://factordb.com/cert.php?id=1100000003590430871] |- |13||3184||9₉₆₈B||(3×13⁹⁶⁹+5)/4||[http://factordb.com/index.php?id=1100000000258566244]||[http://factordb.com/cert.php?id=1100000000258566244] |- |13||3185||10₁₂₉₅181||13¹²⁹⁸+274||[http://factordb.com/index.php?id=1100000002615445013]||[http://factordb.com/cert.php?id=1100000002615445013] |- |13||3186||9₁₃₆₂5||(3×13¹³⁶³−19)/4||[http://factordb.com/index.php?id=1100000002321017776]||[http://factordb.com/cert.php?id=1100000002321017776] |- |13||3187||7₁₅₀₄1||(7×13¹⁵⁰⁵−79)/12||[http://factordb.com/index.php?id=1100000002320890755]||[http://factordb.com/cert.php?id=1100000002320890755] |- |13||3188||930₁₅₅₁1||120×13¹⁵⁵²+1||[http://factordb.com/index.php?id=1100000000765961452]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3189||720₂₂₉₇2||93×13²²⁹⁸+2||[http://factordb.com/index.php?id=1100000002632396910]||[http://factordb.com/cert.php?id=1100000002632396910] |- |13||3190||1770₂₇₀₃17||267×13²⁷⁰⁵+20||[http://factordb.com/index.php?id=1100000003590430825]||[http://factordb.com/cert.php?id=1100000003590430825] |- |13||3191||390₆₂₆₆1||48×13⁶²⁶⁷+1||[http://factordb.com/index.php?id=1100000000765961441]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |13||3192||B0₆₅₄₀BBA||11×13⁶⁵⁴³+2012||[http://factordb.com/index.php?id=1100000002616382906]||[http://factordb.com/cert.php?id=1100000002616382906] |- |13||3193||C₁₀₆₃₁92||13¹⁰⁶³³−50||[http://factordb.com/index.php?id=1100000003590493750]||[http://factordb.com/cert.php?id=1100000003590493750] |- |14||649||34D₇₀₈||47×14⁷⁰⁸−1||[http://factordb.com/index.php?id=1100000001540144903]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |14||650||4D₁₉₆₉₈||5×14¹⁹⁶⁹⁸−1||[http://factordb.com/index.php?id=1100000000884560233]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |16||2328||880₂₄₆7||136×16²⁴⁷+7||[http://factordb.com/index.php?id=1100000002468140199]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has a large prime factor, and this prime factor is < 10²⁹⁹ |- |16||2329||D4₂₆₃D||(199×16²⁶⁴+131)/15||[http://factordb.com/index.php?id=1100000002468170238]||[http://factordb.com/cert.php?id=1100000002468170238] |- |16||2330||E0₂₆₁4DD||14×16²⁶⁴+1245||[http://factordb.com/index.php?id=1100000003588388352]||[http://factordb.com/cert.php?id=1100000003588388352] |- |16||2331||8C0₂₉₀ED||140×16²⁹²+237||[http://factordb.com/index.php?id=1100000003588388307]||[http://factordb.com/cert.php?id=1100000003588388307] |- |16||2332||DA₃₀₅5||(41×16³⁰⁶−17)/3||[http://factordb.com/index.php?id=1100000003588388284]||[http://factordb.com/cert.php?id=1100000003588388284] |- |16||2333||CE80₄₂₂D||3304×16⁴²³+13||[http://factordb.com/index.php?id=1100000003588388257]||[http://factordb.com/cert.php?id=1100000003588388257] |- |16||2334||5F₅₄₄6F||6×16⁵⁴⁶−145||[http://factordb.com/index.php?id=1100000002604723967]||[http://factordb.com/cert.php?id=1100000002604723967] |- |16||2335||88F₅₄₅||137×16⁵⁴⁵−1||[http://factordb.com/index.php?id=1100000000413679658]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |16||2336||BE0₇₉₂BB||190×16⁷⁹⁴+187||[http://factordb.com/index.php?id=1100000003588387938]||[http://factordb.com/cert.php?id=1100000003588387938] |- |16||2337||D9₁₀₅₂||(68×16¹⁰⁵²−3)/5||[http://factordb.com/index.php?id=1100000002321036020]||[http://factordb.com/cert.php?id=1100000002321036020] |- |16||2338||FAF₁₀₆₂45||251×16¹⁰⁶⁴−187||[http://factordb.com/index.php?id=1100000003588387610]||[http://factordb.com/cert.php?id=1100000003588387610] |- |16||2339||F8₁₅₁₇F||(233×16¹⁵¹⁸+97)/15||[http://factordb.com/index.php?id=1100000000633744824]||[http://factordb.com/cert.php?id=1100000000633744824] |- |16||2340||20₁₇₁₃321||2×16¹⁷¹⁶+801||[http://factordb.com/index.php?id=1100000003588386735]||[http://factordb.com/cert.php?id=1100000003588386735] |- |16||2341||300F₁₉₆₀AF||769×16¹⁹⁶²−81||[http://factordb.com/index.php?id=1100000003588368750]||[http://factordb.com/cert.php?id=1100000003588368750] |- |16||2342||90₃₅₄₂91||9×16³⁵⁴⁴+145||[http://factordb.com/index.php?id=1100000000633424191]||[http://factordb.com/cert.php?id=1100000000633424191] |- |16||2343||5BC₃₇₀₀D||(459×16³⁷⁰¹+1)/5||[http://factordb.com/index.php?id=1100000000993764322]||[http://factordb.com/cert.php?id=1100000000993764322] |- |16||2344||D0B₁₇₈₀₄||(3131×16¹⁷⁸⁰⁴−11)/15||[http://factordb.com/index.php?id=1100000003589278511]||[http://factordb.com/cert.php?id=1100000003589278511] |- |18||547||80₂₉₈B||8×18²⁹⁹+11||[http://factordb.com/index.php?id=1100000002355574745]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has sum-of-two-cubes algebraic factorization, 6×18⁹⁹+1 is an algebraic factor of ''N''+1, factordb entry of 6×18⁹⁹+1 is [http://factordb.com/index.php?id=1100000000900149167] |- |18||548||H₇₆₆FH||18⁷⁶⁸−37||[http://factordb.com/index.php?id=1100000003590430490]||[http://factordb.com/cert.php?id=1100000003590430490] |- |18||549||C0₆₂₆₈C5||12×18⁶²⁷⁰+221||[http://factordb.com/index.php?id=1100000003590442437]||[http://factordb.com/cert.php?id=1100000003590442437] |- |20||3301||H₂₄₇A0H||(17×20²⁵⁰−59677)/19||[http://factordb.com/index.php?id=1100000003590502619]||[http://factordb.com/cert.php?id=1100000003590502619] |- |20||3302||7₂₄₉A7||(7×20²⁵¹+1133)/19||[http://factordb.com/index.php?id=1100000003590502602]||[http://factordb.com/cert.php?id=1100000003590502602] |- |20||3303||J7₂₇₀||(368×20²⁷⁰−7)/19||[http://factordb.com/index.php?id=1100000002325395462]||[http://factordb.com/cert.php?id=1100000002325395462] |- |20||3304||J₃₃₀CCC7||20³³⁴−58953||[http://factordb.com/index.php?id=1100000003590502572]||[http://factordb.com/cert.php?id=1100000003590502572] |- |20||3305||40₃₈₇404B||4×20³⁹¹+32091||[http://factordb.com/index.php?id=1100000003590502563]||[http://factordb.com/cert.php?id=1100000003590502563] |- |20||3306||EC0₄₂₉7||292×20⁴³⁰+7||[http://factordb.com/index.php?id=1100000002633348702]||[http://factordb.com/cert.php?id=1100000002633348702] |- |20||3307||G₄₄₇99||(16×20⁴⁴⁹−2809)/19||[http://factordb.com/index.php?id=1100000000840126753]||[http://factordb.com/cert.php?id=1100000000840126753] |- |20||3308||3A₅₂₇3||(67×20⁵²⁸−143)/19||[http://factordb.com/index.php?id=1100000003590502531]||[http://factordb.com/cert.php?id=1100000003590502531] |- |20||3309||E₅₆₆C7||(14×20⁵⁶⁸−907)/19||[http://factordb.com/index.php?id=1100000003590502516]||[http://factordb.com/cert.php?id=1100000003590502516] |- |20||3310||JCJ₆₂₉||393×20⁶²⁹−1||[http://factordb.com/index.php?id=1100000001559454258]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |20||3311||J₆₅₅05J||20⁶⁵⁸−7881||[http://factordb.com/index.php?id=1100000003590502490]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 has a large prime factor, factordb entry of this prime factor is [http://factordb.com/index.php?id=1100000003591067052], and primality certificate of this prime factor is [http://factordb.com/cert.php?id=1100000003591067052] |- |20||3312||50₁₁₆₃AJ||5×20¹¹⁶⁵+219||[http://factordb.com/index.php?id=1100000003590502412]||[http://factordb.com/cert.php?id=1100000003590502412] |- |20||3313||CD₂₄₄₉||(241×20²⁴⁴⁹−13)/19||[http://factordb.com/index.php?id=1100000002325393915]||[http://factordb.com/cert.php?id=1100000002325393915] |- |20||3314||G0₆₂₆₉D||16×20⁶²⁷⁰+13||[http://factordb.com/index.php?id=1100000003590539457]||[http://factordb.com/cert.php?id=1100000003590539457] |- |22||7984||I7G0₂₅₄H||8882×22²⁵⁵+17||[http://factordb.com/index.php?id=1100000003591372788]||[http://factordb.com/cert.php?id=1100000003591372788] |- |22||7985||D0₂₅₅5EEF||13×22²⁵⁹+60339||[http://factordb.com/index.php?id=1100000003591371932]||[http://factordb.com/cert.php?id=1100000003591371932] |- |22||7986||IK₃₂₂F||(398×22³²³−125)/21||[http://factordb.com/index.php?id=1100000000840384145]||[http://factordb.com/cert.php?id=1100000000840384145] |- |22||7987||C0₃₄₀G9||12×22³⁴²+361||[http://factordb.com/index.php?id=1100000000840384159]||[http://factordb.com/cert.php?id=1100000000840384159] |- |22||7988||77E₃₄₈K7||(485×22³⁵⁰+373)/3||[http://factordb.com/index.php?id=1100000003591369779]||[http://factordb.com/cert.php?id=1100000003591369779] |- |22||7989||J₃₇₉KJ||(19×22³⁸¹+443)/21||[http://factordb.com/index.php?id=1100000003591369027]||[http://factordb.com/cert.php?id=1100000003591369027] |- |22||7990||J₃₈₈EJ||(19×22³⁹⁰−2329)/21||[http://factordb.com/index.php?id=1100000003591367729]||[http://factordb.com/cert.php?id=1100000003591367729] |- |22||7991||DJ₄₀₀||(292×22⁴⁰⁰−19)/21||[http://factordb.com/index.php?id=1100000002325880110]||[http://factordb.com/cert.php?id=1100000002325880110] |- |22||7992||E₄₀₄K7||(2×22⁴⁰⁶+373)/3||[http://factordb.com/index.php?id=1100000003591366298]||[http://factordb.com/cert.php?id=1100000003591366298] |- |22||7993||66F₄₅₃B3||(971×22⁴⁵⁵−705)/7||[http://factordb.com/index.php?id=1100000003591365809]||[http://factordb.com/cert.php?id=1100000003591365809] |- |22||7994||L0₄₅₄B63||21×22⁴⁵⁷+5459||[http://factordb.com/index.php?id=1100000003591365331]||[http://factordb.com/cert.php?id=1100000003591365331] |- |22||7995||L₄₈₃G3||22⁴⁸⁵−129||[http://factordb.com/index.php?id=1100000003591364730]||[http://factordb.com/cert.php?id=1100000003591364730] |- |22||7996||E60₄₉₆L||314×22⁴⁹⁷+21||[http://factordb.com/index.php?id=1100000000632703239]||[http://factordb.com/cert.php?id=1100000000632703239] |- |22||7997||I₆₂₆AF||(6×22⁶²⁸−1259)/7||[http://factordb.com/index.php?id=1100000000632724334]||[http://factordb.com/cert.php?id=1100000000632724334] |- |22||7998||K0₇₆₀EC1||20×22⁷⁶³+7041||[http://factordb.com/index.php?id=1100000000632724415]||[http://factordb.com/cert.php?id=1100000000632724415] |- |22||7999||J0₇₆₇IGGJ||19×22⁷⁷¹+199779||[http://factordb.com/index.php?id=1100000003591362567]||[http://factordb.com/cert.php?id=1100000003591362567] |- |22||8000||7₉₅₉K7||(22⁹⁶¹+857)/3||[http://factordb.com/index.php?id=1100000003591361817]||[http://factordb.com/cert.php?id=1100000003591361817] |- |22||8001||L₂₃₈₅KE7||22²³⁸⁸−653||[http://factordb.com/index.php?id=1100000003591360774]||[http://factordb.com/cert.php?id=1100000003591360774] |- |22||8002||7₃₈₁₅2L||(22³⁸¹⁷−289)/3||[http://factordb.com/index.php?id=1100000003591359839]||[http://factordb.com/cert.php?id=1100000003591359839] |- |24||3400||I0₂₄₁I5||18×24²⁴³+437||[http://factordb.com/index.php?id=1100000002633360037]||[http://factordb.com/cert.php?id=1100000002633360037] |- |24||3401||D0₂₅₉KKD||13×24²⁶²+12013||[http://factordb.com/index.php?id=1100000003593270725]||[http://factordb.com/cert.php?id=1100000003593270725] |- |24||3402||C7₂₉₈||(283×24²⁹⁸−7)/23||[http://factordb.com/index.php?id=1100000002326181235]||[http://factordb.com/cert.php?id=1100000002326181235] |- |24||3403||20₃₁₃7||2×24³¹⁴+7||[http://factordb.com/index.php?id=1100000002355610241]||[http://factordb.com/cert.php?id=1100000002355610241] |- |24||3404||BC0₃₃₁B||276×24³³²+11||[http://factordb.com/index.php?id=1100000002633359842]||[http://factordb.com/cert.php?id=1100000002633359842] |- |24||3405||N₂₆₄₄LLN||24²⁶⁴⁷−1201||[http://factordb.com/index.php?id=1100000003593270089]||[http://factordb.com/cert.php?id=1100000003593270089] |- |24||3406||D₂₆₉₈LD||(13×24²⁷⁰⁰+4403)/23||[http://factordb.com/index.php?id=1100000003593269876]||[http://factordb.com/cert.php?id=1100000003593269876] |- |24||3407||A0₂₉₅₁8ID||10×24²⁹⁵⁴+5053||[http://factordb.com/index.php?id=1100000003593269654]||[http://factordb.com/cert.php?id=1100000003593269654] |- |24||3408||88N₅₉₅₁||201×24⁵⁹⁵¹−1||[http://factordb.com/index.php?id=1100000003593275880]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |- |24||3409||N00N₈₁₂₉LN||13249×24⁸¹³¹−49||[http://factordb.com/index.php?id=1100000003593391606]||[http://factordb.com/cert.php?id=1100000003593391606] |- |30||2613||AN₂₀₆||(313×30²⁰⁶−23)/29||[http://factordb.com/index.php?id=1100000002327651073]||[http://factordb.com/cert.php?id=1100000002327651073] |- |30||2614||M₂₄₁QB||(22×30²⁴³+3139)/29||[http://factordb.com/index.php?id=1100000003593408295]||[http://factordb.com/cert.php?id=1100000003593408295] |- |30||2615||M0₅₄₇SS7||22×30⁵⁵⁰+26047||[http://factordb.com/index.php?id=1100000003593407988]||[http://factordb.com/cert.php?id=1100000003593407988] |- |30||2616||C0₁₀₂₂1||12×30¹⁰²³+1||[http://factordb.com/index.php?id=1100000000785448736]||proven prime by [https://primes.utm.edu/prove/prove3_1.html ''N''−1 primality test], ''N''−1 is trivially 100% factored |- |30||2617||5₄₈₈₂J||(5×30⁴⁸⁸³+401)/29||[http://factordb.com/index.php?id=1100000002327649423]||[http://factordb.com/cert.php?id=1100000002327649423] |- |30||2619||OT₃₄₂₀₅||25×30³⁴²⁰⁵−1||[http://factordb.com/index.php?id=1100000000800812865]||proven prime by [https://primes.utm.edu/prove/prove3_2.html ''N''+1 primality test], ''N''+1 is trivially 100% factored |} ==Unproven PRPs== Only list bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 30 {|class=wikitable |base (''b'')||index of this quasi-minimal prime in base ''b'' (assuming the primality of all PRP in base ''b'')||unproven PRP (base-''b'' form)||unproven PRP (algebraic ((''a''×''b''^''n''+''c'')/''d'') form)||factordb entry of this PRP |- |11||1068||57₆₂₆₆₈||(57×11⁶²⁶⁶⁸−7)/10||[http://factordb.com/index.php?id=1100000003573679860] |- |13||3194||C5₂₃₇₅₅C||(149×13²³⁷⁵⁶+79)/12||[http://factordb.com/index.php?id=1100000003590647776] |- |13||3195||80₃₂₀₁₇111||8×13³²⁰²⁰+183||[http://factordb.com/index.php?id=1100000000490878060] |- |16||2345||DB₃₂₂₃₄||(206×16³²²³⁴−11)/15||[http://factordb.com/index.php?id=1100000002383583629] |- |16||2346||4₇₂₇₈₅DD||(4×16⁷²⁷⁸⁷+2291)/15||[http://factordb.com/index.php?id=1100000003615909841] |- |22||8003||BK₂₂₀₀₁5||(251×22²²⁰⁰²−335)/21||[http://factordb.com/index.php?id=1100000003594696838] |- |30||2618||I0₂₄₆₀₈D||18×30²⁴⁶⁰⁹+13||[http://factordb.com/index.php?id=1100000003593967511] |} All these PRPs pass the [[w:Miller–Rabin primality test|Miller–Rabin primality test]] to bases 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and 61, and pass the [[w:Lucas pseudoprime#Strong Lucas pseudoprimes|strong Lucas primality test]] with parameters (''P'', ''Q'') defined by Selfridge's Method ''A'', and [[w:Trial division|trial factored]] to 10¹⁶. (Thus, they pass the [[w:Baillie–PSW primality test|Baillie–PSW primality test]]) ==Proof== ===Base 2=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. ===Base 3=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (2,1), (2,2) * Case (1,1): ** Since 12, 21, 111 are primes, we only need to consider the family 1{0}1 (since any digits 1, 2 between them will produce smaller primes) *** All numbers of the form 1{0}1 are divisible by 2, thus cannot be prime. * Case (1,2): ** 12 is prime, and thus the only minimal prime in this family. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,2): ** Since 21, 12 are primes, we only need to consider the family 2{0,2}2 (since any digits 1 between them will produce smaller primes) *** All numbers of the form 2{0,2}2 are divisible by 2, thus cannot be prime. ===Base 4=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (2,1), (2,3), (3,1), (3,3) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 11, 31, 221 are primes, we only need to consider the family 2{0}1 (since any digits 1, 2, 3 between them will produce smaller primes) *** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 31, 13, 23 are primes, we only need to consider the family 3{0,3}3 (since any digits 1, 2 between them will produce smaller primes) *** All numbers of the form 3{0,3}3 are divisible by 3, thus cannot be prime. ===Base 5=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4) * Case (1,1): ** Since 12, 21, 111, 131 are primes, we only need to consider the family 1{0,4}1 (since any digits 1, 2, 3 between them will produce smaller primes) *** All numbers of the form 1{0,4}1 are divisible by 2, thus cannot be prime. * Case (1,2): ** 12 is prime, and thus the only minimal prime in this family. * Case (1,3): ** Since 12, 23, 43, 133 are primes, we only need to consider the family 1{0,1}3 (since any digits 2, 3, 4 between them will produce smaller primes) *** Since 111 is prime, we only need to consider the families 1{0}3 and 1{0}1{0}3 (since any digit combo 11 between (1,3) will produce smaller primes) **** All numbers of the form 1{0}3 are divisible by 2, thus cannot be prime. **** For the 1{0}1{0}3 family, since 10103 is prime, we only need to consider the families 1{0}13 and 11{0}3 (since any digit combo 010 between (1,3) will produce smaller primes) ***** The smallest prime of the form 1{0}13 is 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013, which can be written as 1(0^93)13 and equal the prime 5^95+8 ([http://factordb.com/index.php?id=1100000000034686071 factordb]) ***** All numbers of the form 11{0}3 are divisible by 3, thus cannot be prime. * Case (1,4): ** Since 12, 34, 104 are primes, we only need to consider the family 1{1,4}4 (since any digits 0, 2, 3 between them will produce smaller primes) *** Since 111, 414 are primes, we only need to consider the families 1{4}4 and 11{4}4 (since any digit combo 11 or 41 between them will produce smaller primes) **** The smallest prime of the form 1{4}4 is 14444. **** All numbers of the form 11{4}4 are divisible by 2, thus cannot be prime. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,2): ** Since 21, 23, 12, 32 are primes, we only need to consider the family 2{0,2,4}2 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 2{0,2,4}2 are divisible by 2, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,4): ** Since 21, 23, 34 are primes, we only need to consider the family 2{0,2,4}4 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 2{0,2,4}4 are divisible by 2, thus cannot be prime. * Case (3,1): ** Since 32, 34, 21 are primes, we only need to consider the family 3{0,1,3}1 (since any digits 2, 4 between them will produce smaller primes) *** Since 313, 111, 131, 3101 are primes, we only need to consider the families 3{0,3}1 and 3{0,3}11 (since any digit combo 10, 11, 13 between (3,1) will produce smaller primes) **** For the 3{0,3}1 family, we can separate this family to four families: ***** For the 30{0,3}01 family, we have the prime 30301, and the remain case is the family 30{0}01. ****** All numbers of the form 30{0}01 are divisible by 2, thus cannot be prime. ***** For the 30{0,3}31 family, note that there must be an even number of 3's between (30,31), or the result number will be divisible by 2 and cannot be prime. ****** Since 33331 is prime, any digit combo 33 between (30,31) will produce smaller primes. ******* Thus, the only possible prime is the smallest prime in the family 30{0}31, and this prime is 300031. ***** For the 33{0,3}01 family, note that there must be an even number of 3's between (33,01), or the result number will be divisible by 2 and cannot be prime. ****** Since 33331 is prime, any digit combo 33 between (33,01) will produce smaller primes. ******* Thus, the only possible prime is the smallest prime in the family 33{0}01, and this prime is 33001. ***** For the 33{0,3}31 family, we have the prime 33331, and the remain case is the family 33{0}31. ****** All numbers of the form 33{0}31 are divisible by 2, thus cannot be prime. **** All numbers of the form 3{0,3}11 are divisible by 3, thus cannot be prime. * Case (3,2): ** 32 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 32, 34, 23, 43, 313 are primes, we only need to consider the family 3{0,3}3 (since any digits 1, 2, 4 between them will produce smaller primes) *** All numbers of the form 3{0,3}3 are divisible by 3, thus cannot be prime. * Case (3,4): ** 34 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 43, 21, 401 are primes, we only need to consider the family 4{1,4}1 (since any digits 0, 2, 3 between them will produce smaller primes) *** Since 414, 111 are primes, we only need to consider the families 4{4}1 and 4{4}11 (since any digit combo 14 or 11 between them will produce smaller primes) **** The smallest prime of the form 4{4}1 is 44441. **** All numbers of the form 4{4}11 are divisible by 2, thus cannot be prime. * Case (4,2): ** Since 43, 12, 32 are primes, we only need to consider the family 4{0,2,4}2 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 4{0,2,4}2 are divisible by 2, thus cannot be prime. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,4): ** Since 43, 34, 414 are primes, we only need to consider the family 4{0,2,4}4 (since any digits 1, 3 between them will produce smaller primes) *** All numbers of the form 4{0,2,4}4 are divisible by 2, thus cannot be prime. ===Base 6=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,5), (2,1), (2,5), (3,1), (3,5), (4,1), (4,5), (5,1), (5,5) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 11, 21, 31, 51 are primes, we only need to consider the family 4{0,4}1 (since any digits 1, 2, 3, 5 between them will produce smaller primes) *** Since 4401 and 4441 are primes, we only need to consider the families 4{0}1 and 4{0}41 (since any digits combo 40 and 44 between them will produce smaller primes) **** All numbers of the form 4{0}1 are divisible by 5, thus cannot be prime. **** The smallest prime of the form 4{0}41 is 40041 * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 15, 25, 35, 45 are primes, we only need to consider the family 5{0,5}5 (since any digits 1, 2, 3, 4 between them will produce smaller primes) *** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. ===Base 7=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) * Case (1,1): ** Since 14, 16, 41, 61, 131 are primes, we only need to consider the family 1{0,1,2,5}1 (since any digits 3, 4, 6 between them will produce smaller primes) *** Since the digit sum of primes must be odd (otherwise the number will be divisible by 2, thus cannot be prime), there is an odd total number of 1 and 5 in the {} **** If there are >=3 number of 1 and 5 in the {}: ***** If there is 111 in the {}, then we have the prime 11111 ***** If there is 115 in the {}, then the prime 115 is a subsequence ***** If there is 151 in the {}, then the prime 115 is a subsequence ***** If there is 155 in the {}, then the prime 155 is a subsequence ***** If there is 511 in the {}, then the current number is 15111, which has digit sum = 12, but digit sum divisible by 3 will cause the number divisible by 3 and cannot be prime, and we cannot add more 1 or 5 to this number (to avoid 11111, 155, 515, 551 as subsequence), thus we must add at least one 2 to this number, but then the number has both 2 and 5, and will have either 25 or 52 as subsequence, thus cannot be minimal prime ***** If there is 515 in the {}, then the prime 515 is a subsequence ***** If there is 551 in the {}, then the prime 551 is a subsequence ***** If there is 555 in the {}, then the prime 551 is a subsequence **** Thus there is only one 1 (and no 5) or only one 5 (and no 1) in the {}, i.e. we only need to consider the families 1{0,2}1{0,2}1 and 1{0,2}5{0,2}1 ***** For the 1{0,2}1{0,2}1 family, since 1211 is prime, we only need to consider the family 1{0}1{0,2}1 ****** Since all numbers of the form 1{0}1{0}1 are divisible by 3 and cannot be prime, we only need to consider the family 1{0}1{0}2{0}1 ******* Since 11201 is prime, we only need to consider the family 1{0}1{0}21 ******** The smallest prime of the form 11{0}21 is 1100021 ******** All numbers of the form 101{0}21 are divisible by 5, thus cannot be prime ******** The smallest prime of the form 1001{0}21 is 100121 ********* Since this prime has no 0 between 1{0}1 and 21, we do not need to consider more families ***** For the 1{0,2}5{0,2}1 family, since 25 and 52 are primes, we only need to consider the family 1{0}5{0}1 ****** Since 1051 is prime, we only need to consider the family 15{0}1 ******* The smallest prime of the form 15{0}1 is 150001 * Case (1,2): ** Since 14, 16, 32, 52 are primes, we only need to consider the family 1{0,1,2}2 (since any digits 3, 4, 5, 6 between them will produce smaller primes) *** Since 1112 and 1222 are primes, there is at most one 1 and at most one 2 in {} **** If there are one 1 and one 2 in {}, then the digit sum is 6, and the number will be divisible by 6 and cannot be prime. **** If there is one 1 but no 2 in {}, then the digit sum is 4, and the number will be divisible by 2 and cannot be prime. **** If there is no 1 but one 2 in {}, then the form is 1{0}2{0}2 ***** Since 1022 and 1202 are primes, we only need to consider the number 122 ****** 122 is not prime. **** If there is no 1 and no 2 in {}, then the digit sum is 3, and the number will be divisible by 3 and cannot be prime. * Case (1,3): ** Since 14, 16, 23, 43, 113, 133 are primes, we only need to consider the family 1{0,5}3 (since any digits 1, 2, 3, 4, 6 between them will produce smaller primes) *** Since 155 is prime, we only need to consider the family 1{0}3 and 1{0}5{0}3 **** All numbers of the form 1{0}3 are divisible by 2, thus cannot be prime. **** All numbers of the form 1{0}5{0}3 are divisible by 3, thus cannot be prime. * Case (1,4): ** 14 is prime, and thus the only minimal prime in this family. * Case (1,5): ** Since 14, 16, 25, 65, 115, 155 are primes, we only need to consider the family 1{0,3}5 (since any digits 1, 2, 4, 5, 6 between them will produce smaller primes) *** All numbers of the form 1{0,3}5 are divisible by 3, thus cannot be prime. * Case (1,6): ** 16 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 25, 41, 61, 221 are primes, we only need to consider the family 2{0,1}1 (since any digits 2, 3, 4, 5, 6 between them will produce smaller primes) *** Since 2111 is prime, we only need to consider the families 2{0}1 and 2{0}1{0}1 **** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. **** All numbers of the form 2{0}1{0}1 are divisible by 2, thus cannot be prime. * Case (2,2): ** Since 23, 25, 32, 52, 212 are primes, we only need to consider the family 2{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,4): ** Since 23, 25, 14 are primes, we only need to consider the family 2{0,2,4,6}4 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}4 are divisible by 2, thus cannot be prime. * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (2,6): ** Since 23, 25, 16, 56 are primes, we only need to consider the family 2{0,2,4,6}6 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 2{0,2,4,6}6 are divisible by 2, thus cannot be prime. * Case (3,1): ** Since 32, 41, 61 are primes, we only need to consider the family 3{0,1,3,5}1 (since any digits 2, 4, 6 between them will produce smaller primes) *** Since 551 is prime, we only need to consider the family 3{0,1,3}1 and 3{0,1,3}5{0,1,3}1 (since any digits combo 55 between (3,1) will produce smaller primes) **** For the 3{0,1,3}1 family, since 3031 and 131 are primes, we only need to consider the families 3{0,1}1 and 3{3}3{0,1}1 (since any digits combo 03, 13 between (3,1) will produce smaller primes, thus for the digits between (3,1), all 3's must be before all 0's and 1's, and thus we can let the red 3 in 3{3}3{0,1}1 be the rightmost 3 between (3,1), all digits before this 3 must be 3's, and all digits after this 3 must be either 0's or 1's) ***** For the 3{0,1}1 family: ****** If there are >=2 0's and >=1 1's between (3,1), then at least one of 30011, 30101, 31001 will be a subsequence. ****** If there are no 1's between (3,1), then the form will be 3{0}1 ******* All numbers of the form 3{0}1 are divisible by 2, thus cannot be prime. ****** If there are no 0's between (3,1), then the form will be 3{1}1 ******* The smallest prime of the form 3{1}1 is 31111 ****** If there are exactly 1 0's between (3,1), then there must be <3 1's between (3,1), or 31111 will be a subsequence. ******* If there are 2 1's between (3,1), then the digit sum is 6, thus the number is divisible by 6 and cannot be prime. ******* If there are 1 1's between (3,1), then the number can only be either 3101 or 3011 ******** Neither 3101 nor 3011 is prime. ******* If there are no 1's between (3,1), then the number must be 301 ******** 301 is not prime. ***** For the 3{3}3{0,1}1 family: ****** If there are at least one 3 between (3,3{0,1}1) and at least one 1 between (3{3}3,1), then 33311 will be a subsequence. ****** If there are no 3 between (3,3{0,1}1), then the form will be 33{0,1}1 ******* If there are at least 3 1's between (33,1), then 31111 will be a subsequence. ******* If there are exactly 2 1's between (33,1), then the digit sum is 12, thus the number is divisible by 3 and cannot be prime. ******* If there are exactly 1 1's between (33,1), then the digit sum is 11, thus the number is divisible by 2 and cannot be prime. ******* If there are no 1's between (33,1), then the form will be 33{0}1 ******** The smallest prime of the form 33{0}1 is 33001 ****** If there are no 1 between (3{3}3,1), then the form will be 3{3}3{0}1 ******* If there are at least 2 0's between (3{3}3,1), then 33001 will be a subsequence. ******* If there are exactly 1 0's between (3{3}3,1), then the form is 3{3}301 ******** The smallest prime of the form 3{3}301 is 33333301 ******* If there are no 0's between (3{3}3,1), then the form is 3{3}31 ******** The smallest prime of the form 3{3}31 is 33333333333333331 **** For the 3{0,1,3}5{0,1,3}1 family, since 335 is prime, we only need to consider the family 3{0,1}5{0,1,3}1 ***** Numbers containing 3 between (3{0,1}5,1): ****** The form is 3{0,1}5{0,1,3}3{0,1,3}1 ******* Since 3031 and 131 are primes, we only need to consider the family 35{3}3{0,1,3}1 (since any digits combo 03, 13 between (3,1) will produce smaller primes) ******** Since 533 is prime, we only need to consider the family 353{0,1}1 (since any digits combo 33 between (35,1) will produce smaller primes) ********* Since 5011 is prime, we only need to consider the family 353{1}{0}1 (since any digits combo 01 between (353,1) will produce smaller primes) ********** If there are at least 3 1's between (353,{0}1), then 31111 will be a subsequence. ********** If there are exactly 2 1's between (353,{0}1), then the digit sum is 20, thus the number is divisible by 2 and cannot be prime. ********** If there are exactly 1 1's between (353,{0}1), then the form is 3531{0}1 *********** The smallest prime of the form 3531{0}1 is 3531001, but it is not minimal prime since 31001 is prime. ********** If there are no 1's between (353,{0}1), then the digit sum is 15, thus the number is divisible by 6 and cannot be prime. ***** Numbers not containing 3 between (3{0,1}5,1): ****** The form is 3{0,1}5{0,1}1 ******* If there are >=2 0's and >=1 1's between (3,1), then at least one of 30011, 30101, 31001 will be a subsequence. ******* If there are no 1's between (3,1), then the form will be 3{0}5{0}1 ******** All numbers of the form 3{0}5{0}1 are divisible by 3, thus cannot be prime. ******* If there are no 0's between (3,1), then the form will be 3{1}5{1}1 ******** If there are >=3 1's between (3,1), then 31111 will be a subsequence. ******** If there are exactly 2 1's between (3,1), then the number can only be 31151, 31511, 35111 ********* None of 31151, 31511, 35111 are primes. ******** If there are exactly 1 1's between (3,1), then the digit sum is 13, thus the number is divisible by 2 and cannot be prime. ******** If there are no 1's between (3,1), then the number is 351 ********* 351 is not prime. ******* If there are exactly 1 0's between (3,1), then the form will be 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1 ******** No matter 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1, if there are >=3 1's between (3,1), then 31111 will be a subsequence. ******** If there are exactly 2 1's between (3,1), then the number can only be 311051, 310151, 310511, 301151, 301511, 305111, 311501, 315101, 315011, 351101, 351011, 350111 ********* Of these numbers, 311051, 301151, 311501, 351101, 350111 are primes. ********** However, 311051, 301151, 311501 have 115 as subsequence, and 350111 has 5011 as subsequence, thus only 351101 is minimal prime. ******** No matter 3{1}0{1}5{1}1 or 3{1}5{1}0{1}1, if there are exactly 1 1's between (3,1), then the digit sum is 13, thus the number is divisible by 2 and cannot be prime. ******** If there are no 1's between (3,1), then the number is 3051 for 3{1}0{1}5{1}1 or 3501 for 3{1}5{1}0{1}1 ********* Neither 3051 nor 3501 is prime. * Case (3,2): ** 32 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 32, 23, 43, 313 are primes, we only need to consider the family 3{0,3,5,6}3 (since any digits 1, 2, 4 between them will produce smaller primes) *** If there are >=2 5's in {}, then 553 will be a subsequence. *** If there are no 5's in {}, then the family will be 3{0,3,6}3 **** All numbers of the form 3{0,3,6}3 are divisible by 3, thus cannot be prime. *** If there are exactly 1 5's in {}, then the family will be 3{0,3,6}5{0,3,6}3 **** Since 335, 65, 3503, 533, 56 are primes, we only need to consider the family 3{0}53 (since any digit 3, 6 between (3,5{0,3,6}3) and any digit 0, 3, 6 between (3{0,3,6}5,3) will produce smaller primes) ***** The smallest prime of the form 3{0}53 is 300053 * Case (3,4): ** Since 32, 14, 304, 344, 364 are primes, we only need to consider the family 3{3,5}4 (since any digits 0, 1, 2, 4, 6 between them will produce smaller primes) *** Since 3334 and 335 are primes, we only need to consider the family 3{5}4 and 3{5}34 (since any digits combo 33, 35 between them will produce smaller primes) **** The smallest prime of the form 3{5}4 is 35555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555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with 9234 5's, which can be written as 3(5^9234)4 and equal the prime (23*7^9235-11)/6 ([http://factordb.com/index.php?id=1100000002766595757 factordb]) ([http://factordb.com/cert.php?id=1100000002766595757 primality certificate]) (not minimal prime, since 35555 and 5554 are primes) **** The smallest prime of the form 3{5}34 is 355555555555555555555555555555555555555555555555555555555555555534 (not minimal prime, since 35555, 553, and 5554 are primes) * Case (3,5): ** Since 32, 25, 65, 335 are primes, we only need to consider the family 3{0,1,4,5}5 (since any digits 2, 3, 6 between them will produce smaller primes) *** If there are at least one 1's and at least one 5's in {}, then either 155 or 515 will be a subsequence. *** If there are at least one 1's and at least one 4's in {}, then either 14 or 41 will be a subsequence. *** If there are at least two 1's in {}, then 115 will be a subsequence. *** If there are exactly one 1's and no 4's or 5's in {}, then the family will be 3{0}1{0}5 **** All numbers of the form 3{0}1{0}5 are divisible by 3, thus cannot be prime. *** If there is no 1's in {}, then the family will be 3{0,4,5}5 **** If there are at least to 4's in {}, then 344 and 445 will be subsequences. **** If there is no 4's in {}, then the family will be 3{0,5}5 ***** Since 3055 and 3505 are primes, we only need to consider the families 3{0}5 and 3{5}5 ****** All numbers of the form 3{0}5 are divisible by 2, thus cannot be prime. ****** The smallest prime of the form 3{5}5 is 35555 **** If there is exactly one 4's in {}, then the family will be 3{0,5}4{0,5}5 ***** Since 304, 3545 are primes, we only need to consider the families 34{0,5}5 (since any digits 0 or 5 between (3,4{0,5}5) will produce small primes) ****** All numbers of the form 34{0,5}5 are divisible by 5, thus cannot be prime. * Case (3,6): ** Since 32, 16, 56, 346 are primes, we only need to consider the family 3{0,3,6}6 (since any digits 1, 2, 4, 5 between them will produce smaller primes) *** All numbers of the form 3{0,3,6}6 are divisible by 3, thus cannot be prime. * Case (4,1): ** 41 is prime, and thus the only minimal prime in this family. * Case (4,2): ** Since 41, 43, 32, 52 are primes, we only need to consider the family 4{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 4{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,4): ** Since 41, 43, 14 are primes, we only need to consider the family 4{0,2,4,5,6}4 (since any digits 1, 3 between them will produce smaller primes) *** If there is no 5's in {}, then the family will be 4{0,2,4,6}4 **** All numbers of the form 4{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there is at least one 5's in {}, then there cannot be 2 in {} (since if so, then either 25 or 52 will be a subsequence) and there cannot be 6 in {} (since if so, then either 65 or 56 will be a subsequence), thus the family is 4{0,4,5}5{0,4,5}4 **** Since 445, 4504, 544 are primes, we only need to consider the family 4{0,5}5{5}4 (since any digit 4 between (4,5{0,4,5}4) and any digit 0, 4 between (4{0,4,5}5,4) will produce smaller primes) ***** If there are at least two 0's between (4,5{0,4,5}4), then 40054 will be a subsequence. ***** If there is no 0's between (4,5{0,4,5}4), then the family will be 4{5}5{5}4, which is equivalent to 4{5}4 ****** The smallest prime of the form 4{5}4 is 45555555555555554 (not minimal prime, since 4555 and 5554 are primes) ***** If there is exactly one 0's between (4,5{0,4,5}4), then the family will be 4{5}0{5}5{5}4 ****** Since 4504 is prime, we only need to consider the family 40{5}5{5}4 (since any digit 5 between (4,0{5}5{5}4) will produce small primes), which is equivalent to 40{5}4 ******* The smallest prime of the form 40{5}4 is 405555555555555554 (not minimal prime, since 4555 and 5554 are primes) * Case (4,5): ** Since 41, 43, 25, 65, 445 are primes, we only need to consider the family 4{0,5}5 (since any digits 1, 2, 3, 4, 6 between them will produce smaller primes) *** If there are at least two 5's in {}, then 4555 will be a subsequence. *** If there is exactly one 5's in {}, then the digit sum is 20, and the number will be divisible by 2 and cannot be prime. *** If there is no 5's in {}, then the family will be 4{0}5 **** All numbers of the form 4{0}5 are divisible by 3, thus cannot be prime. * Case (4,6): ** Since 41, 43, 16, 56 are primes, we only need to consider the family 4{0,2,4,6}6 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 4{0,2,4,6}6 are divisible by 2, thus cannot be prime. * Case (5,1): ** Since 52, 56, 41, 61, 551 are primes, we only need to consider the family 5{0,1,3}1 (since any digits 2, 4, 5, 6 between them will produce smaller primes) *** If there are at least two 3's in {}, then 533 will be a subsequence. *** If there is no 3's in {}, then the family will be 5{0,1}1 **** Since 5011 is prime, we only need to consider the family 5{1}{0}1 ***** Since 11111 is prime, we only need to consider the families 5{0}1, 51{0}1, 511{0}1, 5111{0}1 (since any digits combo 1111 between (5,1) will produce small primes) ****** All numbers of the form 5{0}1 are divisible by 6, thus cannot be prime. ****** The smallest prime of the form 51{0}1 is 5100000001 ****** All numbers of the form 511{0}1 are divisible by 2, thus cannot be prime. ****** All numbers of the form 5111{0}1 are divisible by 3, thus cannot be prime. *** If there is exactly one 3's in {}, then the family will be 5{0,1}3{0,1}1 **** If there is at least one 1's between (5,3{0,1}1), then 131 will be a subsequence. ***** Thus we only need to consider the family 5{0}3{0,1}1 ****** If there are no 1's between (5{0}3,1), then the digit sum is 12, and the number will be divisible by 3 and cannot be prime. ****** If there are exactly one 1's between (5{0}3,1), then the digit sum is 13, and the number will be divisible by 2 and cannot be prime. ****** If there are exactly three 1's between (5{0}3,1), then the digit sum is 15, and the number will be divisible by 6 and cannot be prime. ****** If there are at least four 1's between (5{0}3,1), then 11111 will be a subsequence. ****** If there are exactly two 1's between (5{0}3,1), then the family will be 5{0}3{0}1{0}1{0}1 ******* Since 5011 is prime, we only need to consider the family 5311{0}1 (since any digit 0 between (5,1{0}1) will produce small primes, this includes the leftmost three {} in 5{0}3{0}1{0}1{0}1, and thus only the rightmost {} can contain 0) ******** The smallest prime of the form 5311{0}1 is 531101 * Case (5,2): ** 52 is prime, and thus the only minimal prime in this family. * Case (5,3): ** Since 52, 56, 23, 43, 533, 553 are primes, we only need to consider the family 5{0,1}3 (since any digits 2, 3, 4, 5, 6 between them will produce smaller primes) *** If there are at least two 1's in {}, then 113 will be a subsequence. *** If there is exactly one 1's in {}, then the digit sum is 12, and the number will be divisible by 3 and cannot be prime. *** If there is no 1's in {}, then the digit sum is 11, and the number will be divisible by 2 and cannot be prime. * Case (5,4): ** Since 52, 56, 14, 544 are primes, we only need to consider the family 5{0,3,5}4 (since any digits 1, 2, 4, 6 between them will produce smaller primes) *** If there are no 5's in {}, then the family will be 5{0,3}4 **** All numbers of the form 5{0,3}4 are divisible by 3, thus cannot be prime. *** If there are at least one 5's and at least one 3's in {}, then either 535 or 553 will be a subsequence. *** If there are exactly one 5's and no 3's in {}, then the digit sum is 20, and the number will be divisible by 2 and cannot be prime. *** If there are at least two 5's in {}, then 5554 will be a subsequence. * Case (5,5): ** Since 52, 56, 25, 65, 515, 535 are primes, we only need to consider the family 5{0,4,5}5 (since any digits 1, 2, 3, 6 between them will produce smaller primes) *** If there are no 4's in {}, then the family will be 5{0,5}5 **** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. *** If there are no 5's in {}, then the family will be 5{0,4}5 **** All numbers of the form 5{0,4}5 are divisible by 2, thus cannot be prime. *** If there are at least one 4's and at least one 5's in {}, then either 5455 or 5545 will be a subsequence. * Case (5,6): ** 56 is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,2): ** Since 61, 65, 32, 52 are primes, we only need to consider the family 6{0,2,4,6}2 (since any digits 1, 3, 5 between them will produce smaller primes) *** All numbers of the form 6{0,2,4,6}2 are divisible by 2, thus cannot be prime. * Case (6,3): ** Since 61, 65, 23, 43 are primes, we only need to consider the family 6{0,3,6}3 (since any digits 1, 2, 4, 5 between them will produce smaller primes) *** All numbers of the form 6{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (6,4): ** Since 61, 65, 14 are primes, we only need to consider the family 6{0,2,3,4,6}4 (since any digits 1, 5 between them will produce smaller primes) *** If there is no 3's in {}, then the family will be 6{0,2,4,6}4 **** All numbers of the form 6{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there are exactly two 3's in {}, then the family will be 6{0,2,4,6}3{0,2,4,6}3{0,2,4,6}4 **** All numbers of the form 6{0,2,4,6}3{0,2,4,6}3{0,2,4,6}4 are divisible by 2, thus cannot be prime. *** If there are at least three 3's in {}, then 3334 will be a subsequence. *** If there is exactly one 3's in {}, then the family will be 6{0,2,4,6}3{0,2,4,6}4 **** If there is 0 between (6,3{0,2,4,6}4), then 6034 will be a subsequence. **** If there is 2 between (6,3{0,2,4,6}4), then 23 will be a subsequence. **** If there is 4 between (6,3{0,2,4,6}4), then 43 will be a subsequence. **** If there is 6 between (6,3{0,2,4,6}4), then 6634 will be a subsequence. **** If there is 0 between (6{0,2,4,6}3,4), then 304 will be a subsequence. **** If there is 2 between (6{0,2,4,6}3,4), then 32 will be a subsequence. **** If there is 4 between (6{0,2,4,6}3,4), then 344 will be a subsequence. **** If there is 6 between (6{0,2,4,6}3,4), then 364 will be a subsequence. **** Thus the number can only be 634 ***** 634 is not prime. * Case (6,5): ** 65 is prime, and thus the only minimal prime in this family. * Case (6,6): ** Since 61, 65, 16, 56 are primes, we only need to consider the family 6{0,2,3,4,6}6 (since any digits 1, 5 between them will produce smaller primes) *** If there is no 3's in {}, then the family will be 6{0,2,4,6}6 **** All numbers of the form 6{0,2,4,6}6 are divisible by 2, thus cannot be prime. *** If there is no 2's and no 4's in {}, then the family will be 6{0,3,6}6 **** All numbers of the form 6{0,3,6}6 are divisible by 3, thus cannot be prime. *** If there is at least one 3's and at least one 2's in {}, then either 32 or 23 will be a subsequence. *** If there is at least one 3's and at least one 4's in {}, then either 346 or 43 will be a subsequence. ===Base 8=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (1,5), (1,7), (2,1), (2,3), (2,5), (2,7), (3,1), (3,3), (3,5), (3,7), (4,1), (4,3), (4,5), (4,7), (5,1), (5,3), (5,5), (5,7), (6,1), (6,3), (6,5), (6,7), (7,1), (7,3), (7,5), (7,7) * Case (1,1): ** Since 13, 15, 21, 51, 111, 141, 161 are primes, we only need to consider the family 1{0,7}1 (since any digits 1, 2, 3, 4, 5, 6 between them will produce smaller primes) *** Since 107, 177, 701 are primes, we only need to consider the number 171 and the family 1{0}1 (since any digits combo 07, 70, 77 between them will produce smaller primes) **** 171 is not prime. **** All numbers of the form 1{0}1 factored as 10^n+1 = (2^n+1) * (4^n-2^n+1) (n≥1) (and since if n≥1, 2^n+1 ≥ 2^1+1 = 3 > 1, 4^n-2^n+1 ≥ 4^1-2^1+1 = 3 > 1, this factorization is nontrivial), thus cannot be prime. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (1,7): ** Since 13, 15, 27, 37, 57, 107, 117, 147, 177 are primes, we only need to consider the family 1{6}7 (since any digits 0, 1, 2, 3, 4, 5, 7 between them will produce smaller primes) *** The smallest prime of the form 1{6}7 is 16667 (not minimal prime, since 667 is prime) * Case (2,1): ** 21 is prime, and thus the only minimal prime in this family. * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,5): ** Since 21, 23, 27, 15, 35, 45, 65, 75, 225, 255 are primes, we only need to consider the family 2{0}5 (since any digits 1, 2, 3, 4, 5, 6, 7 between them will produce smaller primes) *** All numbers of the form 2{0}5 are divisible by 7, thus cannot be prime. * Case (2,7): ** 27 is prime, and thus the only minimal prime in this family. * Case (3,1): ** Since 35, 37, 21, 51, 301, 361 are primes, we only need to consider the family 3{1,3,4}1 (since any digits 0, 2, 5, 6, 7 between them will produce smaller primes) *** Since 13, 343, 111, 131, 141, 431, 3331, 3411 are primes, we only need to consider the families 3{3}11, 33{1,4}1, 3{3,4}4{4}1 (since any digits combo 11, 13, 14, 33, 41, 43 between them will produce smaller primes) **** All numbers of the form 3{3}11 are divisible by 3, thus cannot be prime. **** For the 33{1,4}1 family, since 111 and 141 are primes, we only need to consider the families 33{4}1 and 33{4}11 (since any digits combo 11, 14 between them will produce smaller primes) ***** The smallest prime of the form 33{4}1 is 3344441 ***** All numbers of the form 33{4}11 are divisible by 301, thus cannot be prime. **** For the 3{3,4}4{4}1 family, since 3331 and 3344441 are primes, we only need to consider the families 3{4}1, 3{4}31, 3{4}341, 3{4}3441, 3{4}34441 (since any digits combo 33 or 34444 between (3,1) will produce smaller primes) ***** All numbers of the form 3{4}1 are divisible by 31, thus cannot be prime. ***** Since 4443 is prime, we only need to consider the numbers 3431, 34431, 34341, 344341, 343441, 3443441, 3434441, 34434441 (since any digit combo 444 between (3,3{4}1) will produce smaller primes) ****** None of 3431, 34431, 34341, 344341, 343441, 3443441, 3434441, 34434441 are primes. * Case (3,3): ** Since 35, 37, 13, 23, 53, 73, 343 are primes, we only need to consider the family 3{0,3,6}3 (since any digits 1, 2, 4, 5, 7 between them will produce smaller primes) *** All numbers of the form 3{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 21, 51, 401, 431, 471 are primes, we only need to consider the family 4{1,4,6}1 (since any digits 0, 2, 3, 5, 7 between them will produce smaller primes) *** Since 111, 141, 161, 661, 4611 are primes, we only need to consider the families 4{4}11, 4{4,6}4{1,4,6}1, 4{4}6{4}1 (since any digits combo 11, 14, 16, 61, 66 between them will produce smaller primes) **** The smallest prime of the form 4{4}11 is 44444444444444411 (not minimal prime, since 444444441 is prime) **** For the 4{4,6}4{1,4,6}1 family, we can separate this family to 4{4,6}41, 4{4,6}411, 4{4,6}461 ***** For the 4{4,6}41 family, since 661 and 6441 are primes, we only need to consider the families 4{4}41 and 4{4}641 (since any digits combo 64 or 66 between (4,41) will produce smaller primes) ****** The smallest prime of the form 4{4}41 is 444444441 ****** The smallest prime of the form 4{4}641 is 444641 ***** For the 4{4,6}411 family, since 661 and 6441 are primes, we only need to consider the families 4{4}411 and 4{4}6411 (since any digits combo 64 or 66 between (4,411) will produce smaller primes) ****** The smallest prime of the form 4{4}411 is 444444441 ****** The smallest prime of the form 4{4}6411 is 4444444444444446411 (not minimal prime, since 444444441 and 444641 are primes) ***** For the 4{4,6}461 family, since 661 is prime, we only need to consider the family 4{4}461 ****** The smallest prime of the form 4{4}461 is 4444444461 (not minimal prime, since 444444441 is prime) **** For the 4{4}6{4}1 family, since 6441 is prime, we only need to consider the families 4{4}61 and 4{4}641 (since any digits combo 44 between (4{4}6,1) will produce smaller primes) ***** The smallest prime of the form 4{4}61 is 4444444461 (not minimal prime, since 444444441 is prime) ***** The smallest prime of the form 4{4}641 is 444641 * Case (4,3): ** Since 45, 13, 23, 53, 73, 433, 463 are primes, we only need to consider the family 4{0,4}3 (since any digits 1, 2, 3, 5, 6, 7 between them will produce smaller primes) *** Since 4043 and 4443 are primes, we only need to consider the families 4{0}3 and 44{0}3 (since any digits combo 04, 44 between them will produce smaller primes) **** All numbers of the form 4{0}3 are divisible by 7, thus cannot be prime. **** All numbers of the form 44{0}3 are divisible by 3, thus cannot be prime. * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (4,7): ** Since 45, 27, 37, 57, 407, 417, 467 are primes, we only need to consider the family 4{4,7}7 (since any digits 0, 1, 2, 3, 5, 6 between them will produce smaller primes) *** Since 747 is prime, we only need to consider the families 4{4}7, 4{4}77, 4{7}7, 44{7}7 (since any digits combo 74 between (4,7) will produce smaller primes) **** The smallest prime of the form 4{4}7 is 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447, with 220 4's, which can be written as (4^220)7 and equal the prime (4*8^221+17)/7 ([http://factordb.com/index.php?id=1100000000416605822 factordb]) **** The smallest prime of the form 4{4}77 is 4444477 **** The smallest prime of the form 4{7}7 is 47777 **** The smallest prime of the form 44{7}7 is 4477777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777, with 851 7's, which can be written as 44(7^851) and equal the prime 37*8^851-1 ([http://factordb.com/index.php?id=1100000000413677646 factordb]) (not minimal prime, since 47777 is prime) * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,3): ** 53 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 53, 57, 15, 35, 45, 65, 75 are primes, we only need to consider the family 5{0,2,5}5 (since any digits 1, 3, 4, 6, 7 between them will produce smaller primes) *** Since 225, 255, 5205 are primes, we only need to consider the families 5{0,5}5 and 5{0,5}25 (since any digits combo 20, 22, 25 between them will produce smaller primes) **** All numbers of the form 5{0,5}5 are divisible by 5, thus cannot be prime. **** For the 5{0,5}25 family, since 500025 and 505525 are primes, we only need to consider the number 500525 the families 5{5}25, 5{5}025, 5{5}0025, 5{5}0525, 5{5}00525, 5{5}05025 (since any digits combo 000, 055 between (5,25) will produce smaller primes) ***** 500525 is not prime. ***** The smallest prime of the form 5{5}25 is 555555555555525 ***** The smallest prime of the form 5{5}025 is 55555025 ***** The smallest prime of the form 5{5}0025 is 5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555550025, with 184 5's, which can be written as (5^183)0025 and equal the prime (5*8^187-20333)/7 ([http://factordb.com/index.php?id=1100000002350205912 factordb]) (not minimal prime, since 55555025 and 555555555555525 are primes) ***** The smallest prime of the form 5{5}0525 is 5550525 ***** The smallest prime of the form 5{5}00525 is 5500525 ***** The smallest prime of the form 5{5}05025 is 5555555555555555555555505025 (not minimal prime, since 5550525, 55555025, and 555555555555525 are primes) * Case (5,7): ** 57 is prime, and thus the only minimal prime in this family. * Case (6,1): ** Since 65, 21, 51, 631, 661 are primes, we only need to consider the family 6{0,1,4,7}1 (since any digits 2, 3, 5, 6 between them will produce smaller primes) *** Numbers containing 4: (note that the number cannot contain two or more 4's, or 6441 will be a subsequence) **** The form is 6{0,1,7}4{0,1,7}1 ***** Since 141, 401, 471 are primes, we only need to consider the family 6{0,7}4{1}1 ****** Since 111 is prime, we only need to consider the families 6{0,7}41 and 6{0,7}411 ******* For the 6{0,7}41 family, since 60741 is prime, we only need to consider the family 6{7}{0}41 ******** Since 6777 is prime, we only need to consider the families 6{0}41, 67{0}41, 677{0}41 ********* All numbers of the form 6{0}41 are divisible by 3, thus cannot be prime. ********* All numbers of the form 67{0}41 are divisible by 13, thus cannot be prime. ********* All numbers of the form 677{0}41 are divisible by 3, thus cannot be prime. ******* For the 6{0,7}411 family, since 60411 is prime, we only need to consider the family 6{7}411 ******** The smallest prime of the form 6{7}411 is 67777411 (not minimal prime, since 6777 is prime) *** Numbers not containing 4: **** The form is 6{0,1,7}1 ***** Since 111 is prime, we only need to consider the families 6{0,7}1 and 6{0,7}1{0,7}1 ****** All numbers of the form 6{0,7}1 are divisible by 7, thus cannot be prime. ****** For the 6{0,7}1{0,7}1 family, since 711 and 6101 are primes, we only need to consider the family 6{0}1{7}1 ******* Since 60171 is prime, we only need to consider the families 6{0}11 and 61{7}1 ******** All numbers of the form 6{0}11 are divisible by 3, thus cannot be prime. ******** The smallest prime of the form 61{7}1 is 617771 (not minimal prime, since 6777 is prime) * Case (6,3): ** Since 65, 13, 23, 53, 73, 643 are primes, we only need to consider the family 6{0,3,6}3 (since any digits 1, 2, 4, 5, 7 between them will produce smaller primes) *** All numbers of the form 6{0,3,6}3 are divisible by 3, thus cannot be prime. * Case (6,5): ** 65 is prime, and thus the only minimal prime in this family. * Case (6,7): ** Since 65, 27, 37, 57, 667 are primes, we only need to consider the family 6{0,1,4,7}7 (since any digits 2, 3, 5, 6 between them will produce smaller primes) *** Since 107, 117, 147, 177, 407, 417, 717, 747, 6007, 6477, 6707, 6777 are primes, there cannot be digits combo 00, 10, 11, 14, 17, 40, 41, 47, 70, 71, 74, 77 between them **** If there is 1 between them, then there cannot be 1, 4, 7 before it and cannot be 0, 1, 4, 7 after it, thus the form will be 6{0}17 ***** All numbers of the form 6{0}17 are divisible by 3, thus cannot be prime. **** If there is 7 between them, then there cannot be 1, 4, 7 before it and cannot be 0, 1, 4, 7 after it, thus the form will be 6{0}77 ***** All numbers of the form 6{0}77 are divisible by 3, thus cannot be prime. **** If there is neither 1 nor 7 between them, then the form is 6{0,4}7 ***** Since 6007, 407 at primes, we only need to consider the families 6{4}7 and 60{4}7 (since any digits combo 00, 40 between them will produce smaller primes) ****** All numbers of the form 6{4}7 are divisible by 3, 5, or 15, thus cannot be prime. ****** All numbers of the form 60{4}7 are divisible by 21, thus cannot be prime. * Case (7,1): ** Since 73, 75, 21, 51, 701, 711 are primes, we only need to consider the family 7{4,6,7}1 (since any digits 0, 1, 2, 3, 5 between them will produce smaller primes) *** Since 747, 767, 471, 661, 7461, 7641 are primes, we only need to consider the families 7{4,7}4{4}1, 7{7}61, 7{7}7{4,6,7}1 (since any digits combo 46, 47, 64, 66, 67 between them will produce smaller primes) **** For the 7{4,7}4{4}1 family, since 747, 471 are primes, we only need to consider the family 7{7}{4}1 (since any digits combo 47 between (7,4{4}1) will produce smaller primes) ***** The smallest prime of the form 7{7}1 is 7777777777771 ***** The smallest prime of the form 7{7}41 is 777777777777777777777777777777777777777777777777777777777777777777777777777777741, with 79 7's, which can be written as (7^79)41 and equal the prime 8^81-31 ([http://factordb.com/index.php?id=1100000000294462449 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}441 is 777777777777777777777777777777777777777777777777777777777777777777777777777777777777441, with 84 7's, which can be written as (7^84)441 and equal the prime 8^87-223 ([http://factordb.com/index.php?id=1100000000294462776 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}4441 is 777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777774441, with 233 7's, which can be written as (7^233)4441 and equal the prime 8^237-1759 ([http://factordb.com/index.php?id=1100000002352073382 factordb]) (not minimal prime, since 7777777777771 is prime) ***** The smallest prime of the form 7{7}44441 is 7777777777777777777777777777777777777777777777777777777744441, with 56 7's, which can be written as (7^56)44441 and equal the prime 8^61-14047 ([http://factordb.com/index.php?id=1100000002350250002 factordb]) (not minimal prime, since 7777777777771 is prime) ***** All numbers of the form 7{7}444441 are divisible by 7, thus cannot be prime. ***** The smallest prime of the form 7{7}4444441 is 77774444441 ****** Since this prime has just 4 7's, we only need to consider the families with <=3 7's ******* The smallest prime of the form 7{4}1 is 744444441 ******* All numbers of the form 77{4}1 are divisible by 5, thus cannot be prime. ******* The smallest prime of the form 777{4}1 is 777444444444441 (not minimal prime, since 444444441 and 744444441 are primes) * Case (7,3): ** 73 is prime, and thus the only minimal prime in this family. * Case (7,5): ** 75 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 73, 75, 27, 37, 57, 717, 747, 767 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6 between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. ===Base 10=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,3), (1,7), (1,9), (2,1), (2,3), (2,7), (2,9), (3,1), (3,3), (3,7), (3,9), (4,1), (4,3), (4,7), (4,9), (5,1), (5,3), (5,7), (5,9), (6,1), (6,3), (6,7), (6,9), (7,1), (7,3), (7,7), (7,9), (8,1), (8,3), (8,7), (8,9), (9,1), (9,3), (9,7), (9,9) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,3): ** 13 is prime, and thus the only minimal prime in this family. * Case (1,7): ** 17 is prime, and thus the only minimal prime in this family. * Case (1,9): ** 19 is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 23, 29, 11, 31, 41, 61, 71, 251, 281 are primes, we only need to consider the family 2{0,2}1 (since any digits 1, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 2221 and 20201 are primes, we only need to consider the families 2{0}1, 2{0}21, 22{0}1 (since any digits combo 22 or 020 between them will produce smaller primes) **** All numbers of the form 2{0}1 are divisible by 3, thus cannot be prime. **** The smallest prime of the form 2{0}21 is 20021 **** The smallest prime of the form 22{0}1 is 22000001 * Case (2,3): ** 23 is prime, and thus the only minimal prime in this family. * Case (2,7): ** Since 23, 29, 17, 37, 47, 67, 97, 227, 257, 277 are primes, we only need to consider the family 2{0,8}7 (since any digits 1, 2, 3, 4, 5, 6, 7, 9 between them will produce smaller primes) *** Since 887 and 2087 are primes, we only need to consider the families 2{0}7 and 28{0}7 (since any digit combo 08 or 88 between them will produce smaller primes) **** All numbers of the form 2{0}7 are divisible by 3, thus cannot be prime. **** All numbers of the form 28{0}7 are divisible by 7, thus cannot be prime. * Case (2,9): ** 29 is prime, and thus the only minimal prime in this family. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,3): ** Since 31, 37, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 3{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 3{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (3,9): ** Since 31, 37, 19, 29, 59, 79, 89, 349 are primes, we only need to consider the family 3{0,3,6,9}9 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 3{0,3,6,9}9 are divisible by 3, thus cannot be prime. * Case (4,1): ** 41 is prime, and thus the only minimal prime in this family. * Case (4,3): ** 43 is prime, and thus the only minimal prime in this family. * Case (4,7): ** 47 is prime, and thus the only minimal prime in this family. * Case (4,9): ** Since 41, 43, 47, 19, 29, 59, 79, 89, 409, 449, 499 are primes, we only need to consider the family 4{6}9 (since any digits 0, 1, 2, 3, 4, 5, 7, 8, 9 between them will produce smaller primes) *** All numbers of the form 4{6}9 are divisible by 7, thus cannot be prime. * Case (5,1): ** Since 53, 59, 11, 31, 41, 61, 71, 521 are primes, we only need to consider the family 5{0,5,8}1 (since any digits 1, 2, 3, 4, 6, 7, 9 between them will produce smaller primes) *** Since 881 is prime, we only need to consider the families 5{0,5}1 and 5{0,5}8{0,5}1 (since any digit combo 88 between them will produce smaller primes) **** For the 5{0,5}1 family, since 5051 and 5501 are primes, we only need to consider the families 5{0}1 and 5{5}1 (since any digit combo 05 or 50 between them will produce smaller primes) ***** All numbers of the form 5{0}1 are divisible by 3, thus cannot be prime. ***** The smallest prime of the form 5{5}1 is 555555555551 **** For the 5{0,5}8{0,5}1 family, since 5081, 5581, 5801, 5851 are primes, we only need to consider the number 581 ***** 581 is not prime. * Case (5,3): ** 53 is prime, and thus the only minimal prime in this family. * Case (5,7): ** Since 53, 59, 17, 37, 47, 67, 97, 557, 577, 587 are primes, we only need to consider the family 5{0,2}7 (since any digits 1, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 227 and 50207 are primes, we only need to consider the families 5{0}7, 5{0}27, 52{0}7 (since any digits combo 22 or 020 between them will produce smaller primes) **** All numbers of the form 5{0}7 are divisible by 3, thus cannot be prime. **** The smallest prime of the form 5{0}27 is 5000000000000000000000000000027 **** The smallest prime of the form 52{0}7 is 5200007 * Case (5,9): ** 59 is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,3): ** Since 61, 67, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 6{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 6{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (6,7): ** 67 is prime, and thus the only minimal prime in this family. * Case (6,9): ** Since 61, 67, 19, 29, 59, 79, 89 are primes, we only need to consider the family 6{0,3,4,6,9}9 (since any digits 1, 2, 5, 7, 8 between them will produce smaller primes) *** Since 449 is prime, we only need to consider the families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9 (since any digit combo 44 between them will produce smaller primes) **** All numbers of the form 6{0,3,6,9}9 are divisible by 3, thus cannot be prime. **** For the 6{0,3,6,9}4{0,3,6,9}9 family, since 409, 43, 6469, 499 are primes, we only need to consider the family 6{0,3,6,9}49 ***** Since 349, 6949 are primes, we only need to consider the family 6{0,6}49 ****** Since 60649 is prime, we only need to consider the family 6{6}{0}49 (since any digits combo 06 between {6,49} will produce smaller primes) ******* The smallest prime of the form 6{6}49 is 666649 ******** Since this prime has just 4 6's, we only need to consider the families with <=3 6's ********* The smallest prime of the form 6{0}49 is 60000049 ********* The smallest prime of the form 66{0}49 is 66000049 ********* The smallest prime of the form 666{0}49 is 66600049 * Case (7,1): ** 71 is prime, and thus the only minimal prime in this family. * Case (7,3): ** 73 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 71, 73, 79, 17, 37, 47, 67, 97, 727, 757, 787 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6, 8, 9 between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. * Case (7,9): ** 79 is prime, and thus the only minimal prime in this family. * Case (8,1): ** Since 83, 89, 11, 31, 41, 61, 71, 821, 881 are primes, we only need to consider the family 8{0,5}1 (since any digits 1, 2, 3, 4, 6, 7, 8, 9 between them will produce smaller primes) *** Since 8501 is prime, we only need to consider the family 8{0}{5}1 (since any digits combo 50 between them will produce smaller primes) **** Since 80051 is prime, we only need to consider the families 8{0}1, 8{5}1, 80{5}1 (since any digits combo 005 between them will produce smaller primes) ***** All numbers of the form 8{0}1 are divisible by 3, thus cannot be prime. ***** The smallest prime of the form 8{5}1 is 8555555555555555555551 (not minimal prime, since 555555555551 is prime) ***** The smallest prime of the form 80{5}1 is 80555551 * Case (8,3): ** 83 is prime, and thus the only minimal prime in this family. * Case (8,7): ** Since 83, 89, 17, 37, 47, 67, 97, 827, 857, 877, 887 are primes, we only need to consider the family 8{0}7 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9 between them will produce smaller primes) *** All numbers of the form 8{0}7 are divisible by 3, thus cannot be prime. * Case (8,9): ** 89 is prime, and thus the only minimal prime in this family. * Case (9,1): ** Since 97, 11, 31, 41, 61, 71, 991 are primes, we only need to consider the family 9{0,2,5,8}1 (since any digits 1, 3, 4, 6, 7, 9 between them will produce smaller primes) *** Since 251, 281, 521, 821, 881, 9001, 9221, 9551, 9851 are primes, we only need to consider the families 9{2,5,8}0{2,5,8}1, 9{0}2{0}1, 9{0}5{0,8}1, 9{0,5}8{0}1 (since any digits combo 00, 22, 25, 28, 52, 55, 82, 85, 88 between them will produce smaller primes) **** For the 9{2,5,8}0{2,5,8}1 family, since any digits combo 22, 25, 28, 52, 55, 82, 85, 88 between (9,1) will produce smaller primes, we only need to consider the numbers 901, 9021, 9051, 9081, 9201, 9501, 9801, 90581, 95081, 95801 ***** 95801 is the only prime among 901, 9021, 9051, 9081, 9201, 9501, 9801, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. **** For the 9{0}2{0}1 family, since 9001 is prime, we only need to consider the numbers 921, 9201, 9021 ***** None of 921, 9201, 9021 are primes. **** For the 9{0}5{0,8}1 family, since 9001 and 881 are primes, we only need to consider the numbers 951, 9051, 9501, 9581, 90581, 95081, 95801 ***** 95801 is the only prime among 951, 9051, 9501, 9581, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. **** For the 9{0,5}8{0}1 family, since 9001 and 5581 are primes, we only need to consider the numbers 981, 9081, 9581, 9801, 90581, 95081, 95801 ***** 95801 is the only prime among 981, 9081, 9581, 9801, 90581, 95081, 95801, but it is not minimal prime since 5801 is prime. * Case (9,3): ** Since 97, 13, 23, 43, 53, 73, 83 are primes, we only need to consider the family 9{0,3,6,9}3 (since any digits 1, 2, 4, 5, 7, 8 between them will produce smaller primes) *** All numbers of the form 9{0,3,6,9}3 are divisible by 3, thus cannot be prime. * Case (9,7): ** 97 is prime, and thus the only minimal prime in this family. * Case (9,9): ** Since 97, 19, 29, 59, 79, 89 are primes, we only need to consider the family 9{0,3,4,6,9}9 (since any digits 1, 2, 5, 7, 8 between them will produce smaller primes) *** Since 449 is prime, we only need to consider the families 9{0,3,6,9}9 and 9{0,3,6,9}4{0,3,6,9}9 (since any digit combo 44 between them will produce smaller primes) **** All numbers of the form 9{0,3,6,9}9 are divisible by 3, thus cannot be prime. **** For the 9{0,3,6,9}4{0,3,6,9}9 family, since 9049, 349, 9649, 9949 are primes, we only need to consider the family 94{0,3,6,9}9 ***** Since 409, 43, 499 are primes, we only need to consider the family 94{6}9 (since any digits 0, 3, 9 between (94,9) will produce smaller primes) ****** The smallest prime of the form 94{6}9 is 946669 ===Base 12=== The possible (first digit,last digit) combo for a quasi-minimal prime with ≥3 digits are: (1,1), (1,5), (1,7), (1,B), (2,1), (2,5), (2,7), (2,B), (3,1), (3,5), (3,7), (3,B), (4,1), (4,5), (4,7), (4,B), (5,1), (5,5), (5,7), (5,B), (6,1), (6,5), (6,7), (6,B), (7,1), (7,5), (7,7), (7,B), (8,1), (8,5), (8,7), (8,B), (9,1), (9,5), (9,7), (9,B), (A,1), (A,5), (A,7), (A,B), (B,1), (B,5), (B,7), (B,B) * Case (1,1): ** 11 is prime, and thus the only minimal prime in this family. * Case (1,5): ** 15 is prime, and thus the only minimal prime in this family. * Case (1,7): ** 17 is prime, and thus the only minimal prime in this family. * Case (1,B): ** 1B is prime, and thus the only minimal prime in this family. * Case (2,1): ** Since 25, 27, 11, 31, 51, 61, 81, 91, 221, 241, 2A1, 2B1 are primes, we only need to consider the family 2{0}1 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B between them will produce smaller primes) *** The smallest prime of the form 2{0}1 is 2001 * Case (2,5): ** 25 is prime, and thus the only minimal prime in this family. * Case (2,7): ** 27 is prime, and thus the only minimal prime in this family. * Case (2,B): ** Since 25, 27, 1B, 3B, 4B, 5B, 6B, 8B, AB, 2BB are primes, we only need to consider the family 2{0,2,9}B (since any digits 1, 3, 4, 5, 6, 7, 8, A, B between them will produce smaller primes) *** Since 90B, 200B, 202B, 222B, 229B, 292B, 299B are primes, we only need to consider the numbers 20B, 22B, 29B, 209B, 220B (since any digits combo 00, 02, 22, 29, 90, 92, 99 between them will produce smaller primes) **** None of 20B, 22B, 29B, 209B, 220B are primes. * Case (3,1): ** 31 is prime, and thus the only minimal prime in this family. * Case (3,5): ** 35 is prime, and thus the only minimal prime in this family. * Case (3,7): ** 37 is prime, and thus the only minimal prime in this family. * Case (3,B): ** 3B is prime, and thus the only minimal prime in this family. * Case (4,1): ** Since 45, 4B, 11, 31, 51, 61, 81, 91, 401, 421, 471 are primes, we only need to consider the family 4{4,A}1 (since any digit 0, 1, 2, 3, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since A41 and 4441 are primes, we only need to consider the families 4{A}1 and 44{A}1 (since any digit combo 44, A4 between them will produce smaller primes) **** All numbers of the form 4{A}1 are divisible by 5, thus cannot be prime. **** The smallest prime of the form 44{A}1 is 44AAA1 * Case (4,5): ** 45 is prime, and thus the only minimal prime in this family. * Case (4,7): ** Since 45, 4B, 17, 27, 37, 57, 67, 87, A7, B7, 447, 497 are primes, we only need to consider the family 4{0,7}7 (since any digit 1, 2, 3, 4, 5, 6, 8, 9, A, B between them will produce smaller primes) *** Since 4707 and 4777 are primes, we only need to consider the families 4{0}7 and 4{0}77 (since any digit combo 70, 77 between them will produce smaller primes) **** All numbers of the form 4{0}7 are divisible by B, thus cannot be prime. **** The smallest prime of the form 4{0}77 is 400000000000000000000000000000000000000077 * Case (4,B): ** 4B is prime, and thus the only minimal prime in this family. * Case (5,1): ** 51 is prime, and thus the only minimal prime in this family. * Case (5,5): ** Since 51, 57, 5B, 15, 25, 35, 45, 75, 85, 95, B5, 565 are primes, we only need to consider the family 5{0,5,A}5 (since any digits 1, 2, 3, 4, 6, 7, 8, 9, B between them will produce smaller primes) *** All numbers of the form 5{0,5,A}5 are divisible by 5, thus cannot be prime. * Case (5,7): ** 57 is prime, and thus the only minimal prime in this family. * Case (5,B): ** 5B is prime, and thus the only minimal prime in this family. * Case (6,1): ** 61 is prime, and thus the only minimal prime in this family. * Case (6,5): ** Since 61, 67, 6B, 15, 25, 35, 45, 75, 85, 95, B5, 655, 665 are primes, we only need to consider the family 6{0,A}5 (since any digits 1, 2, 3, 4, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since 6A05 and 6AA5 are primes, we only need to consider the families 6{0}5 and 6{0}A5 (since any digit combo A0, AA between them will produce smaller primes) **** All numbers of the form 6{0}5 are divisible by B, thus cannot be prime. **** The smallest prime of the form 6{0}A5 is 600A5 * Case (6,7): ** 67 is prime, and thus the only minimal prime in this family. * Case (6,B): ** 6B is prime, and thus the only minimal prime in this family. * Case (7,1): ** Since 75, 11, 31, 51, 61, 81, 91, 701, 721, 771, 7A1 are primes, we only need to consider the family 7{4,B}1 (since any digits 0, 1, 2, 3, 5, 6, 7, 8, 9, A between them will produce smaller primes) *** Since 7BB, 7441 and 7B41 are primes, we only need to consider the numbers 741, 7B1, 74B1 **** None of 741, 7B1, 74B1 are primes. * Case (7,5): ** 75 is prime, and thus the only minimal prime in this family. * Case (7,7): ** Since 75, 17, 27, 37, 57, 67, 87, A7, B7, 747, 797 are primes, we only need to consider the family 7{0,7}7 (since any digits 1, 2, 3, 4, 5, 6, 8, 9, A, B between them will produce smaller primes) *** All numbers of the form 7{0,7}7 are divisible by 7, thus cannot be prime. * Case (7,B): ** Since 75, 1B, 3B, 4B, 5B, 6B, 8B, AB, 70B, 77B, 7BB are primes, we only need to consider the family 7{2,9}B (since any digits 0, 1, 3, 4, 5, 6, 7, 8, A, B between them will produce smaller primes) *** Since 222B, 729B is prime, we only need to consider the families 7{9}B, 7{9}2B, 7{9}22B (since any digits combo 222, 29 between them will produce smaller primes) **** The smallest prime of the form 7{9}B is 7999B **** The smallest prime of the form 7{9}2B is 79992B (not minimal prime, since 992B and 7999B are primes) **** The smallest prime of the form 7{9}22B is 79922B (not minimal prime, since 992B is prime) * Case (8,1): ** 81 is prime, and thus the only minimal prime in this family. * Case (8,5): ** 85 is prime, and thus the only minimal prime in this family. * Case (8,7): ** 87 is prime, and thus the only minimal prime in this family. * Case (8,B): ** 8B is prime, and thus the only minimal prime in this family. * Case (9,1): ** 91 is prime, and thus the only minimal prime in this family. * Case (9,5): ** 95 is prime, and thus the only minimal prime in this family. * Case (9,7): ** Since 91, 95, 17, 27, 37, 57, 67, 87, A7, B7, 907 are primes, we only need to consider the family 9{4,7,9}7 (since any digit 0, 1, 2, 3, 5, 6, 8, A, B between them will produce smaller primes) *** Since 447, 497, 747, 797, 9777, 9947, 9997 are primes, we only need to consider the numbers 947, 977, 997, 9477, 9977 (since any digits combo 44, 49, 74, 77, 79, 94, 99 between them will produce smaller primes) **** None of 947, 977, 997, 9477, 9977 are primes. * Case (9,B): ** Since 91, 95, 1B, 3B, 4B, 5B, 6B, 8B, AB, 90B, 9BB are primes, we only need to consider the family 9{2,7,9}B (since any digit 0, 1, 3, 4, 5, 6, 8, A, B between them will produce smaller primes) *** Since 27, 77B, 929B, 992B, 997B are primes, we only need to consider the families 9{2,7}2{2}B, 97{2,9}B, 9{7,9}9{9}B (since any digits combo 27, 29, 77, 92, 97 between them will produce smaller primes) **** For the 9{2,7}2{2}B family, since 27 and 77B are primes, we only need to consider the families 9{2}2{2}B and 97{2}2{2}B (since any digits combo 27, 77 between (9,2{2}B) will produce smaller primes) ***** The smallest prime of the form 9{2}2{2}B is 9222B (not minimal prime, since 222B is prime) ***** The smallest prime of the form 97{2}2{2}B is 9722222222222B (not minimal prime, since 222B is prime) **** For the 97{2,9}B family, since 729B and 929B are primes, we only need to consider the family 97{9}{2}B (since any digits combo 29 between (97,B) will produce smaller primes) ***** Since 222B is prime, we only need to consider the families 97{9}B, 97{9}2B, 97{9}22B (since any digit combo 222 between (97,B) will produce smaller primes) ****** All numbers of the form 97{9}B are divisible by 11, thus cannot be prime. ****** The smallest prime of the form 97{9}2B is 979999992B (not minimal prime, since 9999B is prime) ****** All numbers of the form 97{9}22B are divisible by 11, thus cannot be prime. **** For the 9{7,9}9{9}B family, since 77B and 9999B are primes, we only need to consider the numbers 99B, 999B, 979B, 9799B, 9979B ***** None of 99B, 999B, 979B, 9799B, 9979B are primes. * Case (A,1): ** Since A7, AB, 11, 31, 51, 61, 81, 91, A41 are primes, we only need to consider the family A{0,2,A}1 (since any digits 1, 3, 4, 5, 6, 7, 8, 9, B between them will produce smaller primes) *** Since 221, 2A1, A0A1, A201 are primes, we only need to consider the families A{A}{0}1 and A{A}{0}21 (since any digits combo 0A, 20, 22, 2A between them will produce smaller primes) **** For the A{A}{0}1 family: ***** All numbers of the form A{0}1 are divisible by B, thus cannot be prime. ***** The smallest prime of the form AA{0}1 is AA000001 ***** The smallest prime of the form AAA{0}1 is AAA0001 ***** The smallest prime of the form AAAA{0}1 is AAAA1 ****** Since this prime has no 0's, we do not need to consider the families {A}1, {A}01, {A}001, etc. **** All numbers of the form A{A}{0}21 are divisible by 5, thus cannot be prime. * Case (A,5): ** Since A7, AB, 15, 25, 35, 45, 75, 85, 95, B5 are primes, we only need to consider the family A{0,5,6,A}5 (since any digits 1, 2, 3, 4, 7, 8, 9, B between them will produce smaller primes) *** Since 565, 655, 665, A605, A6A5, AA65 are primes, we only need to consider the families A{0,5,A}5 and A{0}65 (since any digits combo 56, 60, 65, 66, 6A, A6 between them will produce smaller primes) **** All numbers of the form A{0,5,A}5 are divisible by 5, thus cannot be prime. **** The smallest prime of the form A{0}65 is A00065 * Case (A,7): ** A7 is prime, and thus the only minimal prime in this family. * Case (A,B): ** AB is prime, and thus the only minimal prime in this family. * Case (B,1): ** Since B5, B7, 11, 31, 51, 61, 81, 91, B21 are primes, we only need to consider the family B{0,4,A,B}1 (since any digits 1, 2, 3, 5, 6, 7, 8, 9 between them will produce smaller primes) *** Since 4B, AB, 401, A41, B001, B0B1, BB01, BB41 are primes, we only need to consider the families B{A}0{4,A}1, B{0,4}4{4,A}1, B{0,4,A,B}A{0,A}1, B{B}B{A,B}1 (since any digits combo 00, 0B, 40, 4B, A4, AB, B0, B4 between them will produce smaller primes) **** For the B{A}0{4,A}1 family, since A41 is prime, we only need consider the families B0{4}{A}1 and B{A}0{A}1 ***** For the B0{4}{A}1 family, since B04A1 is prime, we only need to consider the families B0{4}1 and B0{A}1 ****** The smallest prime of the form B0{4}1 is B04441 (not minimal prime, since 4441 is prime) ****** The smallest prime of the form B0{A}1 is B0AAAAA1 (not minimal prime, since AAAA1 is prime) ***** For the B{A}0{A}1 family, since A0A1 is prime, we only need to consider the families B{A}01 and B0{A}1 ****** The smallest prime of the form B{A}01 is BAA01 ****** The smallest prime of the form B0{A}1 is B0AAAAA1 (not minimal prime, since AAAA1 is prime) **** For the B{0,4}4{4,A}1 family, since 4441 is prime, we only need to consider the families B{0}4{4,A}1 and B{0,4}4{A}1 ***** For the B{0}4{4,A}1 family, since B001 is prime, we only need to consider the families B4{4,A}1 and B04{4,A}1 ****** For the B4{4,A}1 family, since A41 is prime, we only need to consider the family B4{4}{A}1 ******* Since 4441 and BAAA1 are primes, we only need to consider the numbers B41, B441, B4A1, B44A1, B4AA1, B44AA1 ******** None of B41, B441, B4A1, B44A1, B4AA1, B44AA1 are primes. ****** For the B04{4,A}1 family, since B04A1 is prime, we only need to consider the family B04{4}1 ******* The smallest prime of the form B04{4}1 is B04441 (not minimal prime, since 4441 is prime) ***** For the B{0,4}4{A}1 family, since 401, 4441, B001 are primes, we only need to consider the families B4{A}1, B04{A}1, B44{A}1, B044{A}1 (since any digits combo 00, 40, 44 between (B,4{A}1) will produce smaller primes) ****** The smallest prime of the form B4{A}1 is B4AAA1 (not minimal prime, since BAAA1 is prime) ****** The smallest prime of the form B04{A}1 is B04A1 ****** The smallest prime of the form B44{A}1 is B44AAAAAAA1 (not minimal prime, since BAAA1 is prime) ****** The smallest prime of the form B044{A}1 is B044A1 (not minimal prime, since B04A1 is prime) **** For the B{0,4,A,B}A{0,A}1 family, since all numbers in this family with 0 between (B,1) are in the B{A}0{4,A}1 family, and all numbers in this family with 4 between (B,1) are in the B{0,4}4{4,A}1 family, we only need to consider the family B{A,B}A{A}1 ***** Since BAAA1 is prime, we only need to consider the families B{A,B}A1 and B{A,B}AA1 ****** For the B{A,B}A1 family, since AB and BAAA1 are primes, we only need to consider the families B{B}A1 and B{B}AA1 ******* All numbers of the form B{B}A1 are divisible by B, thus cannot be prime. ******* The smallest prime of the form B{B}AA1 is BBBAA1 ****** For the B{A,B}AA1 family, since BAAA1 is prime, we only need to consider the families B{B}AA1 ******* The smallest prime of the form B{B}AA1 is BBBAA1 **** For the B{B}B{A,B}1 family, since AB and BAAA1 are primes, we only need to consider the families B{B}B1, B{B}BA1, B{B}BAA1 (since any digits combo AB or AAA between (B{B}B,1) will produce smaller primes) ***** The smallest prime of the form B{B}B1 is BBBB1 ***** All numbers of the form B{B}BA1 are divisible by B, thus cannot be prime. ***** The smallest prime of the form B{B}BAA1 is BBBAA1 * Case (B,5): ** B5 is prime, and thus the only minimal prime in this family. * Case (B,7): ** B7 is prime, and thus the only minimal prime in this family. * Case (B,B): ** Since B5, B7, 1B, 3B, 4B, 5B, 6B, 8B, AB, B2B are primes, we only need to consider the family B{0,9,B}B (since any digits 1, 2, 3, 4, 5, 6, 7, 8, A between them will produce smaller primes) *** Since 90B and 9BB are primes, we only need to consider the families B{0,B}{9}B **** Since 9999B is prime, we only need to consider the families B{0,B}B, B{0,B}9B, B{0,B}99B, B{0,B}999B ***** All numbers of the form B{0,B}B are divisible by B, thus cannot be prime. ***** For the B{0,B}9B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}9B and B{B}9B (since any digits combo 0B, B0 between (B,9B) will produce smaller primes) ******* The smallest prime of the form B{0}9B is B0000000000000000000000000009B ******* All numbers of the from B{B}9B is either divisible by 11 (if totally number of B's is even) or factored as 10^(2*n)-21 = (10^n-5) * (10^n+5) (if totally number of B's is odd number 2*n-1 (n≥1)) (and since if n≥1, 10^n-5 ≥ 10^1-5 = 7 > 1, 10^n+5 ≥ 10^1+5 = 15 > 1, this factorization is nontrivial), thus cannot be prime. ***** For the B{0,B}99B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}99B and B{B}99B (since any digits combo 0B, B0 between (B,99B) will produce smaller primes) ******* The smallest prime of the form B{0}99B is B00099B ******* The smallest prime of the form B{B}99B is BBBBBB99B ***** For the B{0,B}999B family: ****** Since B0B9B and BB09B are primes, we only need to consider the families B{0}999B and B{B}999B (since any digits combo 0B, B0 between (B,999B) will produce smaller primes) ******* The smallest prime of the form B{0}999B is B0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000999B, with 1765 0's, which can be written as B(0^1765)999B and equal the prime 11*12^1769+16967 ([http://factordb.com/index.php?id=1100000002378273165 factordb]) ([http://factordb.com/cert.php?id=1100000002378273165 primality certificate]) (not minimal prime, since B00099B and B0000000000000000000000000009B are primes) ******* The smallest prime of the form B{B}999B is BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB999B, with 245 B's, which can be written as (B^244)999B and equal the prime 12^248-3769 ([http://factordb.com/index.php?id=1100000002378270237 factordb]) (not minimal prime, since BBBBBB99B is prime) == Examples of families which can be ruled out as contain no primes > ''b'' == It is not known if this problem is solvable: Problem: Given strings ''x'', ''y'', ''z'', and a base ''b'', does there exist a prime number whose base-''b'' expansion is of the form ''x''{''y''}''z''? It will be necessary for our algorithm to determine if families of the form ''x''{''y''}''z'' contain a prime > ''b'' or not. We use two different heuristic strategies to show that such families contain no primes > ''b''. In the first strategy, we mimic the well-known technique of “covering congruences”, by finding some finite set ''S'' of primes ''p'' such that every number in a given family is divisible by some element of ''S''. In the second strategy, we attempt to find an algebraic factorization, such as difference-of-squares factorization, difference-of-cubes factorization, and Aurifeuillian factorization for numbers of the form ''x''⁴+4''y''⁴. Examples of first strategy: (we can show that the corresponding numbers are > all elements in ''S'', if ''n'' makes corresponding numbers > ''b'' (i.e. ''n''≥1 for 5{1} in base 9 and 2{5} in base 11 and {4}D in base 16 and {8}F in base 16, ''n''≥0 for other examples), thus these factorizations are nontrivial) * In base 10, all numbers of the form 4{6}9 are divisible by 7 * In base 6, all numbers of the form 4{0}1 are divisible by 5 * In base 15, all numbers of the form 9{6}8 are divisible by 11 * In base 9, all numbers of the form 5{1} are divisible by some element of {2, 5} * In base 11, all numbers of the form 2{5} are divisible by some element of {2, 3} * In base 14, all numbers of the form B{0}1 are divisible by some element of {3, 5} * In base 8, all numbers of the form 6{4}7 are divisible by some element of {3, 5, 13} * In base 13, all numbers of the form 3{0}95 are divisible by some element of {5, 7, 17} * In base 16, all numbers of the form {4}D are divisible by some element of {3, 7, 13} * In base 16, all numbers of the form {8}F are divisible by some element of {3, 7, 13} Examples of second strategy: (we can show that both factors are > 1, if ''n'' makes corresponding numbers > ''b'' (i.e. ''n''≥2 for {1} in base 9, ''n''≥0 for 1{0}1 in base 8 and B{4}1 in base 16, ''n''≥1 for other examples), thus these factorizations are nontrivial) * In base 9, all numbers of the form {1} factored as difference of squares * In base 8, all numbers of the form 1{0}1 factored as sum of cubes * In base 9, all numbers of the form 3{8} factored as difference of squares * In base 16, all numbers of the form 8{F} factored as difference of squares * In base 16, all numbers of the form {F}7 factored as difference of squares * In base 9, all numbers of the form 3{1} factored as difference of squares * In base 16, all numbers of the form {4}1 factored as difference of squares * In base 16, all numbers of the form 1{5} factored as difference of squares * In base 16, all numbers of the from {C}D factored as ''x''⁴+4''y''⁴ * In base 16, all numbers of the form B{4}1 factored as difference of squares Examples of combine of the two strategies: (we can show that for the part of the first strategy, the corresponding numbers are > all elements in S, and for the part of the second strategy, both factors are > 1, if n makes corresponding numbers > b, thus these factorizations are nontrivial) * In base 14, numbers of the form 8{D} are divisible by 5 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 12, numbers of the form {B}9B are divisible by 13 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 14, numbers of the form {D}5 are divisible by 5 if ''n'' is even and factored as difference of squares if ''n'' is odd * In base 17, numbers of the form 1{9} are divisible by 2 if ''n'' is odd and factored as difference of squares if ''n'' is even * In base 19, numbers of the form 1{6} are divisible by 5 if ''n'' is odd and factored as difference of squares if ''n'' is even == Bases 2≤''b''≤1024 such that these families can be ruled out as contain no primes > ''b'' == (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) === 1{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-powers factorization === 1{0}2 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 1{0}3 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} === 1{0}4 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ === 1{0}5 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 0 mod 5: Finite covering set {5} === 1{0}6 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 7: Finite covering set {7} === 1{0}7 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 7: Finite covering set {7} === 1{0}z === (none) === 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === * ''b'' == 1 mod 3: Finite covering set {3} === 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) === (none) === 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === * ''b'' == 1 mod 3: Finite covering set {3} === {1}0z (not quasi-minimal prime if there is smaller prime of the form {1} or {1}z) === * ''b'' such that ''b'' and 2''b''−1 are both squares: Difference-of-squares factorization (such bases are 25, 841) === {1} === * ''b'' = ''m''^''r'' with ''r''>1: Difference-of-''r''th-powers factorization (some bases still have primes, since for the corresponding length this factorization is trivial, but they only have this prime, they are 4 (length 2), 8 (length 3), 16 (length 2), 27 (length 3), 36 (length 2), 100 (length 2), 128 (length 7), 196 (length 2), 256 (length 2), 400 (length 2), 512 (length 3), 576 (length 2), 676 (length 2)) === {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}) === * ''b'' == 0 mod 2: Finite covering set {2} === 1{2} === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' such that ''b'' and 2(''b''+1) are both squares: Difference-of-squares factorization (such bases are 49) === 1{3} === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' such that ''b'' and 3(''b''+2) are both squares: Difference-of-squares factorization (such bases are 25, 361) * ''b'' == 1 mod 2 such that 3(''b''+2) is square: Combine of finite covering set {2} (when length is even) and difference-of-squares factorization (when length is odd) (such bases are 25, 73, 145, 241, 361, 505, 673, 865) === 1{4} === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' such that ''b'' and 4(''b''+3) are both squares: Difference-of-squares factorization === 1{z} === (none) === 2{0}1 === * ''b'' == 1 mod 3: Finite covering set {3} === 2{0}3 === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 5: Finite covering set {5} === 2{1} (not quasi-minimal prime if there is smaller prime of the form {1}) === * ''b'' such that ''b'' and 2''b''−1 are both squares: Difference-of-squares factorization (such bases are 25, 841) === {2}1 === * ''b'' such that ''b'' and 2(''b''+1) are both squares: Difference-of-squares factorization (such bases are 49) === 2{z} === * ''b'' == 1 mod 2: Finite covering set {2} === 3{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} === 3{0}2 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} === 3{0}4 === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 7: Finite covering set {7} === {3}1 === * ''b'' such that ''b'' and 3(2''b''+1) are both squares: Difference-of-squares factorization (such bases are 121) === 3{z} === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === 4{0}1 === * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ === 4{0}3 === * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 7: Finite covering set {7} === {4}1 === * ''b'' such that ''b'' and 4(3''b''+1) are both squares: Difference-of-squares factorization (such bases are 16, 225) === 4{z} === * ''b'' == 1 mod 2: Finite covering set {2} === 5{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 5{z} === * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 34 mod 35: Finite covering set {5, 7} * ''b'' = 6''m''² with ''m'' == 2 or 3 mod 5: Combine of finite covering set {5} (when length is odd) and difference-of-squares factorization (when length is even) (such bases are 24, 54, 294, 384, 864, 1014) === 6{0}1 === * ''b'' == 1 mod 7: Finite covering set {7} * ''b'' == 34 mod 35: Finite covering set {5, 7} === 6{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} === 7{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} === 7{z} === * ''b'' == 1 mod 7: Finite covering set {7} * ''b'' == 20 mod 21: Finite covering set {3, 7} * ''b'' == 83, 307 mod 455: Finite covering set {5, 7, 13} (such bases are 83, 307, 538, 762, 993) * ''b'' = ''m''³: Difference-of-cubes factorization === 8{0}1 === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 20 mod 21: Finite covering set {3, 7} * ''b'' == 47, 83 mod 195: Finite covering set {3, 5, 13} (such bases are 47, 83, 242, 278, 437, 473, 632, 668, 827, 863, 1022) * ''b'' = 467: Finite covering set {3, 5, 7, 19, 37} * ''b'' = 722: Finite covering set {3, 5, 13, 73, 109} * ''b'' = ''m''³: Sum-of-cubes factorization * ''b'' = 128: Cannot have primes since 7''n''+3 cannot be power of 2 === 8{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === 9{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} === 9{z} === * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 32 mod 33: Finite covering set {3, 11} === A{0}1 === * ''b'' == 1 mod 11: Finite covering set {11} * ''b'' == 32 mod 33: Finite covering set {3, 11} === A{z} === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 14 mod 15: Finite covering set {3, 5} === B{0}1 === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} === B{z} === * ''b'' == 1 mod 11: Finite covering set {11} * ''b'' == 142 mod 143: Finite covering set {11, 13} * ''b'' = 307: Finite covering set {5, 11, 29} * ''b'' = 901: Finite covering set {7, 11, 13, 19} === C{0}1 === * ''b'' == 1 mod 13: Finite covering set {13} * ''b'' == 142 mod 143: Finite covering set {11, 13} * ''b'' = 296, 901: Finite covering set {7, 11, 13, 19} * ''b'' = 562, 828, 900: Finite covering set {7, 13, 19} * ''b'' = 563: Finite covering set {5, 7, 13, 19, 29} * ''b'' = 597: Finite covering set {5, 13, 29} === {#}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3) === (none) === {#}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) === * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-power factorization === #{z} (for even bases b, # = b/2−1) === (none) === y{z} === (none) === {y}z === (none) === z{0}1 === (none) === {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family) === * ''b'' = ''m''^''r'' with odd ''r''>1: Sum-of-''r''th-power factorization (some bases still have primes, since for the corresponding length this factorization is trivial, but they only have this prime, they are 128 (length 7), 216 (length 3), 343 (length 3), 729 (length 3)) * ''b'' = 4''m''⁴: Aurifeuillian factorization of ''x''⁴+4''y''⁴ (base 4 still have primes, since for the corresponding length this factorization is trivial, but it only have this prime, at length 2) === {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y) === (none) === {z}1 === (none) === {z}t === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 0 mod 7: Finite covering set {7} === {z}u === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} * ''b'' == 1 mod 5: Finite covering set {5} * ''b'' == 34 mod 35: Finite covering set {5, 7} === {z}v === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 5: Finite covering set {5} === {z}w === * ''b'' == 0 mod 2: Finite covering set {2} * ''b'' == 1 mod 3: Finite covering set {3} * ''b'' == 14 mod 15: Finite covering set {3, 5} * ''b'' = ''m''²: Difference-of-squares factorization * ''b'' == 4 mod 5: Combine of finite covering set {5} (when length is even) and difference-of-squares factorization (when length is odd) === {z}x === * ''b'' == 1 mod 2: Finite covering set {2} * ''b'' == 0 mod 3: Finite covering set {3} === {z}y === * ''b'' == 0 mod 2: Finite covering set {2} == Large known (probable) primes (length ≥10000) in these families (for bases 2≤''b''≤1024) == Format: base (length) (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) === 1{0}1 === (none) === 1{0}2 === (none) === 1{0}3 === (none) === 1{0}4 === 53 (13403) 113 (10647) === 1{0}z === 113 (20089) 123 (64371) === 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === (none) === 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) === 208 (26682) 607 (11032) 828 (19659) === 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1) === 201 (31276) 222 (52727) 227 (36323) 327 (135983) 425 (11231) 710 (24112) 717 (37508) 719 (13420) === {1} === 152 (270217) 184 (16703) 200 (17807) 311 (36497) 326 (26713) 331 (25033) 371 (15527) 485 (99523) 629 (32233) 649 (43987) 670 (18617) 684 (22573) 691 (62903) 693 (41189) 731 (15427) 752 (32833) 872 (10093) 932 (20431) === {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}) === (none) === 1{z} === 107 (21911) 170 (166429) 278 (43909) 303 (40175) 383 (20957) 515 (58467) 522 (62289) 578 (129469) 590 (15527) 647 (21577) 662 (16591) 698 (127559) 704 (62035) 845 (39407) 938 (40423) 969 (24097) 989 (26869) === 2{0}1 === 101 (192276) 206 (46206) 218 (333926) 236 (161230) 257 (12184) 305 (16808) 467 (126776) 578 (44166) 626 (174204) 695 (94626) 752 (26164) 788 (72918) 869 (49150) 887 (27772) 899 (15732) 932 (13644) === 2{z} === 432 (16003) === 3{0}1 === 912 (132174) === 3{z} === 72 (1119850) 212 (34414) 218 (23050) 270 (89662) 303 (198358) 312 (51566) 422 (21738) 480 (93610) 513 (38032) 527 (46074) 566 (23874) 650 (498102) 686 (16584) 758 (15574) 783 (12508) 800 (33838) 921 (98668) 947 (10056) === 4{0}1 === 107 (32587) 227 (13347) 257 (160423) 355 (10990) 410 (144079) 440 (56087) 452 (14155) 482 (30691) 542 (15983) 579 (67776) 608 (20707) 635 (11723) 650 (96223) 679 (69450) 737 (269303) 740 (58043) 789 (149140) 797 (468703) 920 (103687) 934 (101404) 962 (84235) === 4{z} === 14 (19699) 68 (13575) 254 (15451) 800 (20509) === 5{0}1 === 326 (400786) 350 (20392) 554 (10630) 662 (13390) 926 (40036) === 5{z} === 258 (212135) 272 (148427) 299 (64898) 307 (26263) 354 (25566) 433 (283919) 635 (36163) 678 (40859) 692 (45447) 719 (20552) 768 (70214) 857 (23083) 867 (61411) 972 (36703) === 6{0}1 === 108 (16318) 129 (16797) 409 (369833) 522 (52604) 587 (24120) 643 (164916) 762 (11152) 789 (27297) 986 (21634) === 6{z} === 68 (25396) 332 (15222) 338 (42868) 362 (146342) 488 (33164) 566 (164828) 980 (50878) 986 (12506) 1016 (23336) === 7{0}1 === 398 (17473) 1004 (54849) === 7{z} === 97 (192336) 170 (15423) 194 (38361) 202 (155772) 282 (21413) 283 (164769) 332 (13205) 412 (29792) 560 (19905) 639 (10668) 655 (53009) 811 (31784) 814 (17366) 866 (108591) 908 (61797) 962 (31841) 992 (10605) 997 (15815) === 8{0}1 === 23 (119216) 53 (227184) 158 (123476) 254 (67716) 320 (52004) 410 (279992) 425 (94662) 513 (19076) 518 (11768) 596 (148446) 641 (87702) 684 (23387) 695 (39626) 785 (900326) 788 (11408) 893 (86772) 908 (243440) 920 (107822) 962 (47222) 998 (81240) 1013 (43872) === 8{z} === 138 (35686) 412 (12154) 788 (11326) 990 (23032) === 9{0}1 === 248 (39511) 592 (96870) === 9{z} === 431 (43574) 446 (152028) 458 (126262) 599 (11776) 846 (12781) === A{0}1 === 173 (264235) 198 (47665) 311 (314807) 341 (106009) 449 (18507) 492 (42843) 605 (12395) 708 (17563) 710 (31039) 743 (285479) 744 (137056) 786 (68169) 800 (15105) 802 (149320) 879 (25004) 929 (13065) 977 (125873) 986 (48279) 1004 (10645) === A{z} === 368 (10867) 488 (10231) 534 (80328) 662 (13307) 978 (14066) === B{0}1 === 710 (15272) 740 (33520) 878 (227482) === B{z} === 153 (21660) 186 (112718) 439 (18752) 593 (16064) 602 (36518) 707 (10573) 717 (67707) === C{0}1 === 68 (656922) 219 (29231) 230 (94751) 312 (21163) 334 (83334) 353 (20262) 359 (61295) 457 (10024) 481 (45941) 501 (20140) 593 (42779) 600 (11242) 604 (17371) 641 (26422) 700 (91953) 887 (13961) 919 (45359) 923 (64365) 992 (10300) === {#}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3) === (none) === {#}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) === (none) === #{z} (for even bases b, # = b/2−1) === (none) === y{z} === 38 (136212) 83 (21496) 113 (286644) 188 (13508) 401 (103670) 417 (21003) 458 (46900) 494 (21580) 518 (129372) 527 (65822) 602 (17644) 608 (36228) 638 (74528) 663 (47557) 723 (24536) 758 (50564) 833 (12220) 904 (13430) 938 (50008) 950 (16248) === z{0}1 === 202 (46774) 251 (102979) 272 (16681) 297 (14314) 298 (60671) 326 (64757) 347 (69661) 363 (142877) 452 (71941) 543 (10042) 564 (38065) 634 (84823) 788 (13541) 869 (12289) 890 (37377) 953 (60995) 1004 (29685) === {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family) === 53 (21942) 124 (16426) 175 (31626) 188 (22036) 316 (48538) 365 (25578) 373 (24006) 434 (10090) 530 (11086) 545 (12346) 560 (15072) 596 (12762) 701 (12576) 706 (10656) 821 (13536) 833 (17116) 966 (14820) 983 (11272) === {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y) === (none) === {z}1 === (none) === {z}y === 317 (13896) == Bases 2≤''b''≤1024 which have these families as unsolved families == Unsolved families are families which are neither primes (>''b'') found nor can be ruled out as contain no primes > ''b'' (using A−Z to represent digit values 10 to 35, z−a to represent digit values ''b''−1 to ''b''−26 (e.g. "z" means 1 in base 2, 2 in base 3, 3 in base 4, ..., 8 in base 9, 9 in base 10, A in base 11, B in base 12, ..., Y in base 35, Z in base 36, ...), only consider bases which these families are interpretable, e.g. digit "7" is only interpretable for bases ≥8, and digit "u" (means ''b''−6) is only interpretable for bases ≥7) 1{0}1: 38, 50, 62, 68, 86, 92, 98, 104, 122, 144, 168, 182, 186, 200, 202, 212, 214, 218, 244, 246, 252, 258, 286, 294, 298, 302, 304, 308, 322, 324, 338, 344, 354, 356, 362, 368, 380, 390, 394, 398, 402, 404, 410, 416, 422, 424, 446, 450, 454, 458, 468, 480, 482, 484, 500, 514, 518, 524, 528, 530, 534, 538, 552, 558, 564, 572, 574, 578, 580, 590, 602, 604, 608, 620, 622, 626, 632, 638, 648, 650, 662, 666, 668, 670, 678, 684, 692, 694, 698, 706, 712, 720, 722, 724, 734, 744, 746, 752, 754, 762, 766, 770, 792, 794, 802, 806, 812, 814, 818, 836, 840, 842, 844, 848, 854, 868, 870, 872, 878, 888, 896, 902, 904, 908, 922, 924, 926, 932, 938, 942, 944, 948, 954, 958, 964, 968, 974, 978, 980, 988, 994, 998, 1002, 1006, 1014, 1016 (length limit: ≥8388608) 1{0}2: 167, 257, 323, 353, 383, 527, 557, 563, 623, 635, 647, 677, 713, 719, 803, 815, 947, 971, 1013 (length limit: 2000) 1{0}3: 646, 718, 998 (length limit: 2000) 1{0}4: 139, 227, 263, 315, 335, 365, 485, 515, 647, 653, 683, 773, 789, 797, 815, 857, 875, 893, 939, 995, 1007 (length limit: 2000) 1{0}5 1{0}6 1{0}7 1{0}8 1{0}9 1{0}A 1{0}B 1{0}C 1{0}D 1{0}E 1{0}F 1{0}G 1{0}z: 173, 179, 257, 277, 302, 333, 362, 392, 422, 452, 467, 488, 512, 527, 545, 570, 575, 614, 622, 650, 677, 680, 704, 707, 734, 740, 827, 830, 851, 872, 886, 887, 902, 904, 908, 929, 932, 942, 947, 949, 962, 973, 1022 (length limit: 2000) 1{0}11 (not quasi-minimal prime if there is smaller prime of the form 1{0}1): 198, 213, 318, 327, 353, 375, 513, 591, 647, 732, 734, 738, 759, 948, 951, 957, 1013, 1014 (length limit: 2000) 10{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}): 575 (length limit: 247000) 11{0}1 (not quasi-minimal prime if there is smaller prime of the form 1{0}1): 813, 863, 962, 1017 (length limit: ≥100000) {1}0z (not quasi-minimal prime if there is smaller prime of the form {1} or {1}z): 137, 161, 167, 217, 229, 232, 253, 261, 317, 325, 337, 347, 355, 375, 403, 411, 421, 427, 457, 479, 483, 505, 507, 537, 547, 577, 597, 599, 601, 613, 627, 631, 632, 641, 643, 649, 657, 679, 688, 697, 707, 711, 729, 733, 737, 742, 762, 773, 787, 793, 797, 817, 819, 841, 843, 853, 859, 861, 874, 877, 895, 899, 907, 913, 916, 917, 927, 957, 959, 997, 1003, 1009, 1015, 1017 (length limit: 2000) {1}: 185, 269, 281, 380, 384, 385, 394, 452, 465, 511, 574, 601, 631, 632, 636, 711, 713, 759, 771, 795, 861, 866, 881, 938, 948, 951, 956, 963, 1005, 1015 (length limit: ≥100000) 11{z} (not quasi-minimal prime if there is smaller prime of the form 1{z}) {1}2 (not quasi-minimal prime if there is smaller prime of the form {1}): 31, 61, 91, 93, 143, 247, 253, 293, 313, 329, 371, 383, 391, 393, 403, 415, 435, 443, 451, 491, 493, 513, 523, 527, 537, 541, 553, 565, 581, 587, 601, 613, 615, 623, 627, 635, 663, 729, 735, 757, 763, 775, 783, 823, 843, 865, 873, 877, 883, 897, 931, 941, 943, 955, 983, 1013, 1015, 1021, 1023 (length limit: 2000) {1}z 1{2}: 265, 355, 379, 391, 481, 649, 661, 709, 745, 811, 877, 977 (length limit: 2000) 1{3}: 107, 133, 179, 281, 305, 365, 473, 485, 487, 491, 535, 541, 601, 617, 665, 737, 775, 787, 802, 827, 905, 911, 928, 953, 955, 995 1{4}: 83, 143, 185, 239, 269, 293, 299, 305, 319, 325, 373, 383, 395, 431, 471, 503, 551, 577, 581, 593, 605, 617, 631, 659, 743, 761, 773, 781, 803, 821, 857, 869, 897, 911, 917, 923, 935, 983, 1019 (length limit: 2000) 1{z}: 581, 992, 1019 (length limit: ≥100000) 2{0}1: 365, 383, 461, 512, 542, 647, 773, 801, 836, 878, 908, 914, 917, 947, 1004 (length limit: ≥100000) 2{0}3: 79, 149, 179, 254, 359, 394, 424, 434, 449, 488, 499, 532, 554, 578, 664, 683, 694, 749, 794, 839, 908, 944, 982 (length limit: 2000) 2{1} (not quasi-minimal prime if there is smaller prime of the form {1}): 109, 117, 137, 147, 157, 175, 177, 201, 227, 235, 256, 269, 271, 297, 310, 331, 335, 397, 417, 427, 430, 437, 442, 451, 465, 467, 481, 502, 517, 547, 557, 567, 572, 577, 591, 597, 607, 627, 649, 654, 655, 667, 679, 687, 691, 697, 715, 727, 739, 759, 766, 782, 787, 796, 797, 808, 817, 821, 829, 841, 852, 877, 881, 899, 903, 907, 937, 947, 955, 1007, 1011, 1021 (length limit: 2000) {2}1: 106, 238, 262, 295, 364, 382, 391, 397, 421, 458, 463, 478, 517, 523, 556, 601, 647, 687, 754, 790, 793, 832, 872, 898, 962, 1002, 1021 (length limit: 2000) 2{z}: 588, 972 (length limit: ≥100000) 3{0}1: 718 (length limit: ≥100000) 3{0}2: 223, 283, 359, 489, 515, 529, 579, 619, 669, 879, 915, 997 (length limit: 2000) 3{0}4: 167, 391, 447, 487, 529, 653, 657, 797, 853, 913, 937 (length limit: 2000) {3}1: 79, 101, 189, 215, 217, 235, 243, 253, 255, 265, 313, 338, 341, 378, 379, 401, 402, 413, 489, 498, 499, 508, 525, 535, 589, 591, 599, 611, 621, 635, 667, 668, 681, 691, 711, 717, 719, 721, 737, 785, 804, 805, 813, 831, 835, 837, 849, 873, 911, 915, 929, 933, 941, 948, 959, 999, 1013, 1019 (length limit: 2000) 3{z}: 275, 438, 647, 653, 812, 927, 968 (length limit: ≥100000) 4{0}1: 32, 53, 155, 174, 204, 212, 230, 332, 334, 335, 395, 467, 512, 593, 767, 803, 848, 875, 1024 (length limit: ≥100000) 4{0}3: 83, 88, 97, 167, 188, 268, 289, 293, 412, 419, 425, 433, 503, 517, 529, 548, 613, 620, 622, 650, 668, 692, 706, 727, 763, 818, 902, 913, 937, 947, 958 (length limit: 2000) {4}1: 46, 77, 103, 107, 119, 152, 198, 203, 211, 217, 229, 257, 263, 291, 296, 305, 332, 371, 374, 407, 413, 416, 440, 445, 446, 464, 467, 500, 542, 545, 548, 557, 566, 586, 587, 605, 611, 614, 632, 638, 641, 653, 659, 698, 701, 731, 733, 736, 755, 786, 812, 820, 821, 827, 830, 887, 896, 899, 901, 922, 923, 935, 941, 953, 977, 983, 991, 1004 (length limit: 2000) 4{z}: 338, 998 (length limit: ≥100000) 5{0}1: 308, 512, 824 (length limit: ≥100000) 5{z}: 234, 412, 549, 553, 573, 619, 750, 878, 894, 954 (length limit: ≥100000) 6{0}1: 212, 509, 579, 625, 774, 794, 993, 999 (length limit: ≥100000) 6{z}: 308, 392, 398, 518, 548, 638, 662, 878 (length limit: ≥100000) 7{0}1: (none) 7{z}: 321, 328, 374, 432, 665, 697, 710, 721, 727, 728, 752, 800, 815, 836, 867, 957, 958, 972 (length limit: ≥100000) 8{0}1: 86, 140, 182, 263, 353, 368, 389, 395, 422, 426, 428, 434, 443, 488, 497, 558, 572, 575, 593, 606, 698, 710, 746, 758, 770, 773, 824, 828, 866, 911, 930, 953, 957, 983, 993, 1014 (length limit: ≥100000) 8{z}: 378, 438, 536, 566, 570, 592, 636, 688, 718, 830, 852, 926, 1010 (length limit: ≥100000) 9{0}1: 724, 884 (length limit: ≥100000) 9{z}: 80, 233, 530, 551, 611, 899, 912, 980 (length limit: ≥100000) A{0}1: 185, 338, 417, 432, 614, 668, 773, 863, 935, 1000 (length limit: ≥100000) A{z}: 214, 422, 444, 452, 458, 542, 638, 668, 804, 872, 950, 962 (length limit: ≥100000) B{0}1: 560, 770, 968 (length limit: ≥100000) B{z}: 263, 615, 912, 978 (length limit: ≥100000) C{0}1: 163, 207, 354, 362, 368, 480, 620, 692, 697, 736, 753, 792, 978, 998, 1019, 1022 (length limit: ≥100000) C{z} D{0}1 D{z} E{0}1 E{z} F{0}1 F{z} G{0}1 {&#35;}$ (for bases ''b'' == 1 mod 3, # = (''b''−1)/3, $ = (''b''+2)/3): 808, 829, 859, 1006 (length limit: 2000) {&#35;}$ (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2): 31, 37, 55, 63, 67, 77, 83, 89, 91, 93, 97, 99, 107, 109, 117, 123, 127, 133, 135, 137, 143, 147, 149, 151, 155, 161, 177, 179, 183, 189, 193, 197, 207, 211, 213, 215, 217, 223, 225, 227, 233, 235, 241, 247, 249, 255, 257, 263, 265, 269, 273, 277, 281, 283, 285, 287, 291, 293, 297, 303, 307, 311, 319, 327, 347, 351, 355, 357, 359, 361, 367, 369, 377, 381, 383, 385, 387, 389, 393, 397, 401, 407, 411, 413, 417, 421, 423, 437, 439, 443, 447, 457, 465, 467, 469, 473, 475, 481, 483, 489, 493, 495, 497, 509, 511, 515, 533, 541, 547, 549, 555, 563, 591, 593, 597, 601, 603, 611, 615, 619, 621, 625, 627, 629, 633, 635, 637, 645, 647, 651, 653, 655, 659, 663, 667, 671, 673, 675, 679, 683, 687, 691, 693, 697, 707, 709, 717, 731, 733, 735, 737, 741, 743, 749, 753, 755, 757, 759, 765, 767, 771, 773, 775, 777, 783, 785, 787, 793, 797, 801, 807, 809, 813, 817, 823, 825, 849, 851, 853, 865, 867, 873, 877, 887, 889, 893, 897, 899, 903, 907, 911, 915, 923, 927, 933, 937, 939, 941, 943, 945, 947, 953, 957, 961, 967, 975, 977, 983, 987, 993, 999, 1003, 1005, 1009, 1017 (length limit: ≥262143) &#35;{z} (for even bases ''b'', # = ''b''/2−1): 108, 278, 296, 338, 386, 494, 626, 920 (length limit: 2000) ${&#35;} (for odd bases ''b'', # = (''b''−1)/2, $ = (''b''+1)/2) x{z} y{z}: 128, 233, 268, 383, 478, 488, 533, 554, 665, 698, 779, 863, 878, 932, 941, 1010 (length limit: ≥200000) z{0}1: 123, 342, 362, 422, 438, 479, 487, 512, 542, 602, 757, 767, 817, 830, 872, 893, 932, 992, 997, 1005, 1007 (length limit: ≥100000) {y}z: 143, 173, 176, 213, 235, 248, 253, 279, 327, 343, 353, 358, 373, 383, 401, 413, 416, 427, 439, 448, 453, 463, 481, 513, 522, 527, 535, 547, 559, 565, 583, 591, 598, 603, 621, 623, 653, 659, 663, 679, 691, 698, 711, 743, 745, 757, 768, 785, 793, 796, 801, 808, 811, 821, 835, 845, 847, 853, 856, 883, 898, 903, 927, 955, 961, 971, 973, 993, 1005, 1013, 1019, 1021 (length limit: 2000) {z0}z1 (almost cannot be quasi-minimal prime, since this is not simple family): 97, 103, 113, 186, 187, 220, 304, 306, 309, 335, 414, 416, 428, 433, 445, 459, 486, 498, 539, 550, 557, 587, 592, 597, 598, 617, 624, 637, 659, 665, 671, 677, 696, 717, 726, 730, 740, 754, 766, 790, 851, 873, 890, 914, 923, 929, 943, 944, 965, 984, 985, 996, 1004, 1005 (length limit: ≥17326) zy{z} (not quasi-minimal prime if there is smaller prime of the form y{z}) {z}yz (not quasi-minimal prime if there is smaller prime of the form {z}y): 215, 353, 517, 743, 852, 899, 913 (length limit: 2000) {z}01 (not quasi-minimal prime if there is smaller prime of the form {z}1) {z}1: 93, 113, 152, 158, 188, 217, 218, 226, 227, 228, 233, 240, 275, 278, 293, 312, 338, 350, 353, 383, 404, 438, 464, 471, 500, 533, 576, 614, 641, 653, 704, 723, 728, 730, 758, 779, 788, 791, 830, 878, 881, 899, 908, 918, 929, 944, 953, 965, 968, 978, 983, 986, 1013 (length limit: 2000) {z}k {z}l {z}m {z}n {z}o {z}p {z}q {z}r {z}s {z}t {z}u {z}v {z}w: 207, 221, 293, 375, 387, 533, 633, 647, 653, 687, 701, 747, 761, 785, 863, 897, 905, 965, 1017 (length limit: 2000) {z}x: (none) {z}y: 305, 353, 397, 485, 487, 535, 539, 597, 641, 679, 731, 739, 755 (length limit: 2000) == List of lengths for quasi-minimal primes in some simple families == [https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml list of lengths for quasi-minimal primes in some simple families for bases 2≤''b''≤1024] NB: this family is not interpretable in this base (e.g. family 7{0}1 and 7{z} in bases <=7, family {z}x in bases <=3) (including the case which this family has either leading zeros (leading zeros do not count) or ending zeros (numbers ending in zero cannot be prime > base) in this base) RC: this family can be proven to only contain composite numbers (only count numbers > base) unknown: this family has no primes or PRPs found, nor can this family be proven to only contain composite numbers (only count numbers > base) Background color: red for title (bases or families), green for length > 10000, orange for 2500 < length ≤ 10000, white for length ≤ 2500, cyan for "RC", pink for "NB", yellow for "unknown". Search limit for lengths: ≥8388608 for 1{0}1, ≥200000 for y{z}, ≥100000 for ''d''{0}1 (''d'' = one of digits in {2, 3, 4, 5, 6, 7, 8, 9, A, B, C}) and ''d''{z} (''d'' = one of digits in {1, 2, 3, 4, 5, 6, 7, 8, 9, A, B}) and z{0}1 and {1}, ≥5000 for 1{0}2, {z}y, 1{0}z, {z}1, {y}z, ≥2500 for other families. == References == * [https://mersenneforum.org/showthread.php?t=24972 mersenneforum thread of this problem] * [https://docs.google.com/document/d/e/2PACX-1vQct6Hx-IkJd5-iIuDuOKkKdw2teGmmHW-P75MPaxqBXB37u0odFBml5rx0PoLa0odTyuW67N_vn96J/pub Minimal elements for the base ''b'' representations of the primes which are > ''b'' for bases ''b''≤16] * [https://primes.utm.edu/glossary/xpage/MinimalPrime.html article “minimal prime” in The Prime Glossary] * [https://en.wikipedia.org/wiki/Minimal_prime_(recreational_mathematics article “minimal prime” in Wikipedia] * [https://www.primepuzzles.net/puzzles/puzz_178.htm the puzzle of minimal primes (when the restriction of prime>base is not required) in The Prime Puzzles & Problems Connection] * [https://www.primepuzzles.net/problems/prob_083.htm the problem of minimal primes in The Prime Puzzles & Problems Connection] * [https://github.com/xayahrainie4793/non-single-digit-primes my data for these M(Lb) sets for 2 ≤ b ≤ 16] * [http://www.cs.uwaterloo.ca/~shallit/Papers/minimal5.pdf Shallit’s proof of base 10 minimal primes, when the restriction of prime>base is not required] * [https://scholar.colorado.edu/downloads/hh63sw661 proofs of minimal primes in bases b≤10, when the restriction of prime>base is not required] * [https://cs.uwaterloo.ca/~cbright/reports/mepn.pdf the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://cs.uwaterloo.ca/~cbright/talks/minimal-slides.pdf the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://doi.org/10.1080/10586458.2015.1064048 the article for this minimal prime problem in bases b≤30, when the restriction of prime>base is not required] * [https://github.com/curtisbright/mepn-data data for these M(Lb) sets and unsolved families for 2 ≤ b ≤ 30, when the restriction of prime>base is not required, search limits of lengths: 1000000 for b=17, 707000 for b=19, 506000 for b=21, 292000 for b=25, 486000 for b=26, 543000 for b=28, 233000 for b=29] * [https://github.com/RaymondDevillers/primes data for these M(Lb) sets and unsolved families for 2 ≤ b ≤ 50, when the restriction of prime>base is not required, search limits of lengths: 10000 for all b] * [http://www.bitman.name/math/article/730 article for minimal primes, when the restriction of prime>base is not required] * [http://www.bitman.name/math/table/497 data for minimal primes in bases 2 ≤ b ≤ 16, when the restriction of prime>base is not required] * [http://www.prothsearch.com/sierp.html the Sierpinski problem] * [http://www.prothsearch.com/rieselprob.html the Riesel problem] * [https://oeis.org/A076336/a076336c.html the dual Sierpinski problem] * [http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm generalized Sierpinski conjectures in bases b≤1030, some primes found in these conjectures are minimal primes in base b, especially, all primes for k&lt;b (if exist for a (k,b) combo) are always minimal primes in the base b) (also some examples for simple families contain no primes &gt; b] * [http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm generalized Riesel conjectures in bases b≤1030, some primes found in these conjectures are minimal primes in base b, especially, all primes for k&lt;b (if exist for a (k,b) combo) are always minimal primes in the base b) (also some examples for simple families contain no primes &gt; b] * [http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm list for the status of the generalized Sierpinski conjectures and the generalized Riesel conjectures in bases b≤1030] * [https://www.utm.edu/staff/caldwell/preprints/2to100.pdf article for generalized Sierpinski conjectures in bases b≤100] * [http://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/i61/i61.pdf article for the mixed (original+dual) Sierpinski problem] * [http://www.fermatquotient.com/PrimSerien/GenRepu.txt generalized repunit primes (primes of the form (bn−1)/(b−1)) in bases b≤160, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html generalized repunit primes (primes of the form (bn−1)/(b−1)) in bases b≤1000, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://jeppesn.dk/generalized-fermat.html generalized Fermat primes (primes of the form b2^n+1) in even bases b≤1000, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://www.noprimeleftbehind.net/crus/GFN-primes.htm generalized Fermat primes (primes of the form b2^n+1) in even bases b≤1030, the smallest such prime for base b (if exists) is always minimal prime in base b] * [http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt list of generalized half Fermat primes (primes of the form (b2^n+1)/2) sorted by n, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://harvey563.tripod.com/wills.txt primes of the form (b−1)*bn−1 for bases b≤2049, the smallest such prime for base b (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Williams_prime_MM_least the smallest primes of the form (b−1)*bn−1 for bases b≤2049, these primes (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Williams_prime_MP_least the smallest primes of the form (b−1)*bn+1 for bases b≤1024, these primes (if exists) is always minimal prime in base b] * [https://www.rieselprime.de/ziki/Riesel_prime_small_bases_least_n the smallest primes of the form k*bn−1 for k≤12 and bases b≤1024, these primes (if exists) is always minimal prime in base b if b>k] * [https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n the smallest primes of the form k*bn+1 for k≤12 and bases b≤1024, these primes (if exists) is always minimal prime in base b if b>k] * [https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml list for the smallest primes in given simple family in bases b≤1024] * [https://www.rose-hulman.edu/~rickert/Compositeseq/ a problem related to this project] * [http://www.worldofnumbers.com/Appending%201s%20to%20n.txt a problem related to this project] * [https://stdkmd.net/nrr/prime/primecount.txt near- and quasi- repdigit (probable) primes sorted by count] * [https://stdkmd.net/nrr/prime/primedifficulty.txt near- and quasi- repdigit (probable) primes sorted by difficulty] * [http://www.prothsearch.com/fermat.html factoring status of Fermat numbers] * [http://www.rieselprime.de/dl/CRUS_pack.zip srsieve, sr1sieve, sr2sieve, pfgw, and llr softwares] * [https://www.bc-team.org/app.php/dlext/?cat=3 srsieve, sr1sieve, sr2sieve, sr5sieve software] * [https://sourceforge.net/projects/openpfgw/ pfgw software] * [http://jpenne.free.fr/index2.html llr software] * [http://www.ellipsa.eu/public/primo/primo.html PRIMO software] * [https://primes.utm.edu/prove/index.html website for primality proving] * [https://primes.utm.edu/curios/page.php?number_id=22380 the largest base 10 minimal prime in Prime Curios!] * [https://oeis.org/A071062 OEIS sequence for base 10 minimal primes, when the restriction of prime>base is not required] * [https://oeis.org/A326609 OEIS sequence for the largest base b minimal prime, when the restriction of prime>base is not required] * [https://primes.utm.edu/primes/lists/all.txt top proven primes] * [http://www.primenumbers.net/prptop/prptop.php top PRPs] * [http://factordb.com online factor database, including many primes which are minimal primes in a small base] o2ot8sxlnigiiemibcwhay8dcui0pb4 2 273648 2412435 2405328 2022-08-06T23:22:33Z SophiaSemper 2916858 /* Recent developments */ wikitext text/x-wiki <big> Ectopolitan • 外局人 • एक्टोपॉलिटन • Ectopolita • ექტოპოლიტი • Ektopolitas • Ektopolīts • Ектополитен • Ectopolite • خارجبوليتان • বাহিরেবিশ্বজনীন • Эктополит • Ektopolitan • ایکٹوپولیٹن • Ektopolit • エクトポリタン • اکتوپولیتن • ਐਕਟੋਪੋਲੀਟਨ • ఎక్టోపాలిటన్ • 엑토폴리탄 • Người ngoài • எக்டோபாலிட்டன் • خارج وطنی • ความเป็นข้างนอก • બહારગરિક • ኤክቶፖሊታን • Waje siyasa • Ektopolityczny • ಎಕ್ಟೋಪಾಲಿಟನ್ • Ектополіт • എക്ടോപൊളിറ്റൻ • ଏକ୍ଟୋପଲିଟାନ୍ • اکتوشهری • ນອກໂລກ • Ectopolitische • এক্টোপলিটান • ඒක්ටොපොලිටන් • Ektopolît • Εκτοπολίτικος • Ektopolita • Ektopolitní • Ectopolit • Ектополитска • Ektopolitiska • ኢክቶፖሊታን • Ìta olóṣèlú • Ngaphandle kwepolitiki • Ngaphandle kwezopolitiko • Ektopolitiese • Эктапаліт • Էկտոպոլիտան • Ektopolitisk • Ектополит • Ektopoliittinen • Ektopolitiske • Ektopolitný • ཕྱིའི་མི་སྣ • אַקְטוֹפּוֹלִיטִי • Ektopoliit • Utanborgari • Ektopolito • A-muigh-poilitigs • Waho-politika • Jawa llaqta • ᐁᒃᑐᐳᓕᑕᓐ • Ectopolites • ɒɈiloqoɈɔɘ '''''Nota Bene'': the article below may not be published in formats permissible for citizens of UN member countries, or even for cosmopolitans, and/or for stateless people, as the human being below is an [http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''ectopolitan''], which means that he does not identify or align with, nor permits traditional politics, and/or business, to influence or undermine his life, his natural affections, his natural affiliations, and/or his natural community. The individual below considers all UN member countries as no more dignified than Aristotelian zoos, which constantly violate human rights, treat ''de jure'' citizens like ''de facto'' slaves, and national and multinational corporations as entities authorised to violate human rights by their respective states or countries (ie, as criminal entities), and with no actual legal accountability in the constitutions of states or countries for their crimes against natural human beings.''' {|width="280" cellspacing="0" cellpadding="4" border="1" align="right" style="margin: 0 0 1em 1em; border: 1px #aaaaaa solid; border-collapse: collapse; font-size: 95%;" |style="background: #f9f9f9; text-align: center;" colspan="2"|<big><br>'''Make natural science,<br>not war on nature.<br>&mdash; ''Kaisiris Tallini''<br><br>'''</big> |- |style="background: #E8E8F8; text-align: center;" colspan="2"|<br><big>'''Meddíss Túvtiks Kaisiris Tallini'''</big><br />''born''<br>'''Hon Most Rev Dr Cesidio Tallini'''</br></br> |-bgcolor="#f9f9f9" |style="text-align: center;" colspan="2"|[[File:Hmrdct.jpg|270px]]<br />Kaisiris in 2009 |- |style="background: #f9f9f9; text-align: center;" colspan="2"|'''Personal info under Cesidian law''' |-bgcolor="#f9f9f9" |'''Ectopolitan name''' |Kaisiris Tallini |-bgcolor="#f9f9f9" |'''Born again''' |Week K2<br>Neptunday 22 Jung 2013<br>460 millidays<br>(K2Ψ22J2013•460) |-bgcolor="#f9f9f9" |'''Pythagorean name''' |Cesidio Tallini |-bgcolor="#f9f9f9" |'''Born''' |Week S1<br>Neptunday 26 Edison 1962<br>229 millidays<br>(S1Ψ26E1962•229) |-bgcolor="#f9f9f9" |'''Spouses or Partners (''stirpes'')''' |None |-bgcolor="#f9f9f9" |'''Clan name or ''gentilicius'' (''gens'')''' |Kaisiris (Kaisiris Clan), INN (Interfaith Nutrition Network) |-bgcolor="#f9f9f9" |'''Demonym or gentilic (''curia'')''' |Cesidian or Holocartesian (Cesidian Network) |-bgcolor="#f9f9f9" |'''Nationalities (''tribus'')''' |Neocartesian (Saint René Descartes University), Cal Alumnus (Cal Alumni Association), Penn State Alumnus (Penn State Alumni Association), Honourary Antarctican (by affiliation) |-bgcolor="#f9f9f9" |'''Citizenships (''cives'')''' |Pythagorean (Centre for Cesidian Law and Paradiplomatic Affairs), Nature Israel conservationist (American Society for the Protection of Nature in Israel) |-bgcolor="#f9f9f9" |'''Delineation (''genus'')''' |[http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''Ectopolitan''] |-bgcolor="#f9f9f9" |'''Ectoprofessions''' |Analytic theologian; multidisciplinary scholar |-bgcolor="#f9f9f9" |'''Website''' |[http://5wcwiki.pbworks.com/w/page/143342355/mtkt >>LINK<<] |} '''MT<ref>Kaisiris Tallini is neither a 'Mister' (Mr), nor a 'Doctor' (Dr). These terms are wholly political or professional terms which states and countries have invented, which in fact treat adult persons as slaves or subjects of states or countries, not as independent and dignity-deserving adults. Kaisiris Tallini is a 'MT', an abbreviation for the Oscan words «''Meddíss Túvtiks''». The ''Meddíss Túvtiks'' — Oscan-Latinish: «''Meddix Tuticus''»; English: Community Manager — was the name of the supreme magistrate among the Oscan people. The MT was the single magistrate on whom would devolve military command, civil and criminal jurisdiction, functions of political and religious representation, and several other responsibilities, for the MT could also have been a great teacher and healer, besides being a man of religion. Think of a real tribal chieftain or the tribune of a natural society, and you can begin to understand what a 'MT' was. Kaisiris Tallini is also a 'SD', an abbreviation for the Ectoenglish words 'Salubriology Doyen'. An SD in the health field — there are also SDs in the organisational, engineering, education, legal, and religious fields — is a genuine physician, or ''iatros'' (ιατρός) in Ectogreek. Kaisiris Tallini considers the appellative 'Mr Tallini' offensive, besides being grossly inaccurate, because it should imply that he is a master of the Tallinis, or of any adult person with a Tallini surname, yet he considers the Tallinis related to him as lower than beasts (reptiles) on the human spiritual scale, or completely vile, vulgar, and plutocratic.</ref> [http://5wcwiki.pbworks.com/w/page/144142176/Kaisiris%20multilingual Kaisiris Tallini]''' (New York, [https://takemeback.to/10-May-1962 10 May 1962] – Ω) — born ''Cesidio Tallini''<ref>The name 'Cesidio Tallini' has existed since Thursday, 10 May 1962 [S1Ψ26E1962•229], or since his birthdate. It should be noted, however, that the name 'Kaisiris Tallini' has existed only since Tuesday, 3 September 2013 [K2Ψ22J2013•460], when it was registered for the first time through the Paradiplomatic Affairs ectogovernmental organisation (EGO).</ref> — is Analytic Theologian and founder of the Cesidian Network; Chancellor of Saint René Descartes University; and Rector of the Centre for Cesidian Law. Kaisiris is the world's first [https://www.britannica.com/topic/micronation micronationalist] recognised in ''de jure'', or acknowledged in ''de facto'' fashion by several government or quasi-government bodies<ref>[http://selfherald.blogspot.com/2017/11/who-is-cesidio-tallini.html Who is Cesidio Tallini?] article.</ref>. He is also the first micronationalist to be recognised for multiple nationalities within the same developing new region of the world, so Kaisiris is both a micronationalist and a multinationalist. Kaisiris has assisted two micronations — ''Principado Independente do Ilhéu da Pontinha'', and Kingdom of Ourania — with their development; claims two Native African — [https://en.wikipedia.org/wiki/Republic_of_Cabinda Republic of Cabinda] and [https://en.wikipedia.org/wiki/Southern_Cameroons Southern Cameroons (Ambazonia)] — nationalities by naturalisation; and claims to be the world's first full Antarctic national by affiliation. Since 2 April 2021, Kaisiris is also the world's first ''de jure'' [http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''ectopolitan''], a word which comes from the Greek, and describes a person outside of politics altogether, a ''delineate'' of the world, rather than a citizen of the world. An ectopolitan can be described as a spiritual, and/or physical expatriate to all countries; a wannabe extraterrestrial; an earthling who is even more odd to locals than a cosmopolitan; or someone who doesn't feel related to the United Nations, and/or any of its member countries. Kaisiris has earned both American and Italian high school diplomas in the past; has earned several different post-secondary education diplomas and certificates, including a National Work Readiness Credential from the National Work Readiness Council, and a Certificate of Qualification to Practice from the Law Society of Cabinda; and has earned a BS degree from the University of Phoenix, another BSc degree, two religious doctorate degrees, and was awarded two honourary doctorates. Kaisiris has also recently earned a degree from Saint René Descartes University, after becoming the world's first self-made Salubriology Doyen (SD), so besides being ''Kohen Gadol'' [כּוֹהֵן גָדוֹל] of Lineage of the Blessed Hermes (LBH), and ''Meddíss Túvtiks'' of the Kaisiris Clan, he is also ''Archiatros'' (Αρχιατρός) of the Salubriology School. Kaisiris is also the ''de facto'' or ''de jure'' author of several books in English and Italian; the father of Cesidian law, Cesidian analytic theology, Cesidian salubriology, Cesidian societal-political science, and Cesidian spiritual science; the developer of several indigenous and novel time, linguistic, educational, and intellectual property systems; and an independent scholar. Finally, Kaisiris is also Regent of Paradiplomatic Affairs (PdA), and ''Wujieren'' (无界人) and founder of Global Earth Oceans (GEO), a new region under development. ==Early life== Kaisiris was born in Jamaica Hospital, New York, on 10 May 1962. He has resided for extensive periods of time both in Italy and in the United States. He moved to Italy at the age of 9, where he continued his education. He eventually earned an Italian ''Diploma di Maturità Scientifica'' from La Scuola D'Italia "Guglielmo Marconi" of New York City, and an American High School Equivalency Diploma from the University at Albany (SUNY). ==Later developments== Kaisiris is an honourary alumnus of the University of California at Berkeley since October 2010; an honourary alumnus of Pennsylvania State University since May 2011; and an international life member of the Chamber of Computer Logistics People (CCLP) Worldwide since August 2011. Most post-1998 developments in Kaisiris' life are at least indirectly related to Cesidian societal-political science, although even more legal, theological, and linguistics developments have taken place through time. Kaisiris co-founded the Cesidian Root in September 2005, but no longer has a relationship with the organisation<ref>[https://www.foxnews.com/tech/the-cesidian-root-a-bizarre-peek-at-the-world-wide-weird The Cesidian Root: A bizarre peek at the world wide weird] article.</ref><ref>[https://second.wiki/wiki/cesidian_root Cesidian Root] wiki article.</ref>. On 30 April 2007, Kaisiris earned a Bachelor of Science in Information Technology from the University of Phoenix (with honours). On 13 December 2007, [https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes René Descartes] is consecrated as the first saint of the Cesidian Church. Kaisiris also founded the United Micronations Multi-Oceanic Archipelago (UMMOA) political party in May 2008, but disbanded the party in June 2017. On 8 August 2009, Kaisiris issued the first Print Monopoly ⓟⓜ. On 20 January 2010, Kaisiris received an honourary Doctor of Philosophy (PhD) in International law from the Academy of Universal Global Peace. On 8 July 2011, Kaisiris was ordained as an Independent Catholic Priest and appointed to the title of Bishop, with apostolic succession and lineage to Christ. He also became a member of the Board of Bishops of the Universal Life Church World Headquarters (later renamed "Universal One Church"). On 22 July 2011, the Cesidian Church was granted a church charter by the Universal Life Church World Headquarters (later renamed "Universal One Church"). Kaisiris has also earned a Doctor of Divinity (DD), and a Doctor of Theology (ThD) from the Universal Life Church World Headquarters School of Theology. On 1 November 2011, upon certification by the Examining Committee of the Law Society of Cabinda, Kaisiris was admitted as an Advocate, and is now authorised to practice before all the Courts and Tribunals of the Republic of Cabinda. On 23 January 2012, Kaisiris was appointed Communications Director for the Organization of Emerging African States (OEAS). During the 7th Meeting of the Committee on NGOs, held on 2 February 2012 at the United Nations Headquarters in New York, the Chamber of Computer Logistics People Worldwide (CCLP Worldwide) was recommended for Special Consultative Status. This development became possible after CCLP Worldwide's Special Representative Cesidio Tallini managed to overcome to the persistent objections of the Distinguished Representative of Pakistan on the night of 1 February 2012. In August 2012, CCLP Worldwide was granted Special Consultative Status with the United Nations' Economic and Social Council (ECOSOC). On 27 December 2012, Kaisiris was made Ambassador at Large of Antarctica and Unrepresented or Underrepresented Polities for The Multipurpose Inter-Parliamentary Union (TMIPU). On 31 December 2012, Kaisiris was appointed Interim Deputy Minister of Information for the Republic of Cabinda. On 8 April 2013, the Saint René Descartes University's 2013 Nobel Peace Prize recommendation is welcomed by the Norwegian Nobel Committee, and Saint René Descartes University's Scholar's Degree (SD) is also accepted. On 7 June 2013, the Paradiplomatic Affairs (PDA) agency was launched. On 3 September 2013, the Hernici (8ED) tribe is formally registered with Paradiplomatic Affairs (PDA). This marks the beginning of the official existence of the Aboriginal European Hernici (8ED) Tribe. On 22 September 2013, the Government of Southern Cameroons recognises the UMMOA's Aphrodite Island claim. On 9 January 2014, Kaisiris provides the first services as Ambassador at Large of Antarctica to a Native Antarctican. On 3 October 2014, it is first noticed that UMMOA English (UGV; en-UGV; ⓤ) had appeared authoritatively in Google searches. What was originally judged as a new English variety, variant, or lect†, since 30 December 2020 is called Ectoenglish (ⓔ), the world's first ectolanguage. Kaisiris has also started to develop other ectolanguages besides Ectoenglishⓔ, ectoitalianoⓘ [Ectoitalian], and ⓞoɔƨooɈɔɘ [Ectooscan]. On 5 November 2015, the Aphrodite Island claim/name is accepted by author and geographer Nick Middleton (in the English language). On 11 November 2015, the [https://time.is/CMT Cyberterra Mean Time] (CMT) standard appeared in ''AcronymFinder.com'' for the first time. On 21 January 2016, the UK's Foreign and Commonwealth Office published a summary of the UMMOA party's views. This is the first indirect acknowledgement of the work of the Paradiplomatic Affairs (PDA) agency. On 5 October 2017, the Indigo race (or ''Homo sapiens ethicus''/''Homo noeticus'') concept is accepted by author and social anthropologist Beth Singler. On 11 August 2019, Lady Anna Tallini, Kaisiris' mother, passed away. This is Kaisiris' greatest loss. ==Recent developments== Since his mother's passing, and the end of the Marian Christianity (11.02.1858 – 11.08.2019) era, Kaisiris has founded the asocial, but not anti-social Kaisiris Clan (11.08.2019 – Ω), and the Cesidian Network (09.10.2019 – Ω) is beyond its conception or birth, beyond its ''bar/bat mitzvah'' age, and may be considered at least a college graduate, following all these actual developments: * Johannine Christianity (11.08.2019 – 09.07.2020) era started [first post-Marian Christian era which failed to materialise] * Cesidian spiritual science (Css) or Cesidianism conception: 29.11.2019 * Cesidian law gentilisation/neoaristocratic union process: 09.01.2020 * Polyphilia and multisocietalism concepts: 23.01.2020 * Cesidian law curialisation/neoecclesiastic union process: 05.02.2020 * Conception of Cesidian psychology: 24.03.2020 * Conception of the Restored Ancient Order of Melchizedek (RAOM): 20.05.2020 * Magdalene Christianity (09.07.2020 – 03.02.2021) era started [second post-Marian Christian era which failed to materialise] * Css/Cesidianism graduates into a post-tribal religion tradition (foreshadowing of the Cesidian era): 28.09.2020 * Cesidian psychology development of the redefined Maslow's pyramid of human needs: 15.11.2020 * Cesidian law "all speech is political speech" development: 17.11.2020 [a sign non-Cesidian law is largely a fiction] * New ectopolitical or multisocietal, rather than political or cosmopolitan paradigm development (''Homo sapiens ethicus''): 29.12.2020 * Birth of Ectoenglishⓔ, Ectoitalianⓘ, ectolanguages, and ectolinguistics: 30.12.2020 * New ectojournalism and ectohistorian development: 15.01.2021 * Birth of Ectofrenchⓕ: 17.01.2021 * Ectolinguistics and Cesidian law connection: 02.02.2021 * Cyberterra ectogeography connection (new ''genus'' not continental, and more ocean- than island-based): 03.02.2021 * Cesidian era started (post-Christianity, or post-religion without spirituality era): 03.02.2021 * Ecology, agriculture, and zoology connections (politics favours zookeepers, and is unfavourable even to wild and domesticated species): 08.02.2021 * Copernican (astronomical) versus the Cesidian (religious, legal, linguistic, holoscientific<ref>The ''holoscientific'' term was coined on 3 April 2022 [N1Χ15D2022•065].</ref>) revolution: 09.02.2021 * Biological or adopted, social or societal, religious or spiritual, economic or scientific, ethical or legal brothers concept: 21.02.2021 * Birth of Ectochineseⓩ: 27.02.2021 * Even cities like London (main-belt asteroid of 8837 London in particular) can be both cosmopolitan and ''ectopolitan'': 18.03.2021 * Birth of Ectohebrewⓗ: 26.03.2021 * Birth of Ectolatinⓛ: 28.03.2021 * Birth of Ectogreekⓖ: 28.03.2021 * New Marian Dogma — Mary is both ''Theotokos'' (Θεοτόκος) and ''Theogonos'' (Θεογόνος): 28.03.2021 * Cesidianism is a form of Ectochristianity: 07.04.2021 * Birth of Ectooscanⓞ: 14.04.2021 * First quality ⓔⓘⓞ triectolingual message posted: 17.04.2021 * Birth of The Ectolanguage Organism ⓔⓛⓞ, the first societal organism: 28.04.2021 * The Fleming 2021 Declaration: 14.05.2021 * Conception of ecto-governmental organisation (ego) concept: 21.06.2021 * Formation of ''Asking Facebook for a 'No Country' or ''Ectopolitan'' country option'' group: 14.07.2021 * Made admin of ''The World Academy of Buddhist Scholars'' Facebook group: 06.08.2021 * The regular English (en-GB/en-US) word 'wife' became archaic or obsolete in Ectoenglish (ⓔ; een): 19.09.2021 * The regular English (en-GB/en-US) word 'citizen' became archaic or obsolete in Ectoenglish (ⓔ; een): 23.09.2021 * The 'ectoinformatics' term is born: 29.09.2021 * The 'ectoagriculture' and 'ectoenvironmental' terms are born: 07.10.2021 * Single's Day holiday is introduced into the Cesidian calendar: 11.11.2021 * Decision made to introduce first ''Ectopolitans''' Day and Ectohomes' Day on 13.05.2022 and 23.08.2022 respectively into the Cesidian calendar: 22.11.2021 * The all-out assault (AOA) on "science" began: 10.12.2021 * All-out assault (AOA) on the world government quadropus: 16.12.2021 * Formation of the Lineage of the Blessed Hermes (LBH): 28.12.2021 * Birth of Ectokoreanⓚ: 06.01.2022 * The difference between a wiki and an 'ectowiki' is first shown: 11.01.2022 * After a new and improved translation of 'ectopolitan' in Ojibwe, 5 new ectolanguages were born: Ectogermanⓓ, Ectojapaneseⓙ, Ectoportugueseⓟ, Ectorussianⓡ, and Ectospanishⓢ: 24.01.2022 * Realisation Kaisiris Tallini is the first ''de facto'' [http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''ectopolitan''], but also the first ''de jure'' or legal [http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''ectopolitan'']: 26.02.2022 * Birth of Ectovietnameseⓥ: 10.03.2022 * With the rigourous proof that ectopolitans are gods, Cesidian spiritual science (Css) graduates into the "Queen of the Sciences": 14.03.2022 * The ''centimilliday'' (cmd) was introduced into the Cyberterra Mean Time format (CMTf): 15.03.2022 * Birth of Ectocurrency Unit (Ɇ; ECU), and possible Cesidian economics revolution concept: 17.03.2022 * Acknowledgement of ectoeducational science component of Cesidian revolution: 24.03.2022 * The 'holoscientific' term is born: 03.04.2022 * Start of Ectopolitan Wiki: 06.04.2022 * Birth of Ectobattery Hens in Hazmat Suits Organisation (EBHHSO): 28.04.2022 * Development of Cesidian analytic theology's "People of the Book" graph: 30.05.2022 * The 'ectoprofessional' term is born: 05.06.2022 * The 'ectoscientist' term is born: 05.06.2022 * First language–ectolanguage translation: 07.06.2022 * The 7th and 8th Cesidian saint is canonised: 08.06.2022 * "Cesidian pyramid" addition to the redefined Maslow's pyramid of human needs: 25.06.2022 * First legal document certifying [http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''ectopolitan''] status devised and signed: 04.07.2022 * Ectoenglish update: the once, twice, and thrice etc list, completed for Ectoenglish up to ten times (''tence''): 14.07.2022 * Discovery of the parallels between ectopolitans or gods, and the Ancient Greek ''daimones'' (δαίμονες) concept [singular: ''daimon'' (δαίμων)]; discovery of the parallels between exopolitans or Gods, and the Ancient Greek ''theoi''/''thees'' (θεοί/θεές) concept [singular: ''theos''/''thea'' (θεός/θεά)]; as well as the discovery that the Cesidian ''Homo noeticus'' ['self-knowing' person], and the Buddhist ''Bodhisattva'' [person both 'awake' (''bodhi''), and 'sentient' (''sattva'')] concepts, are actually synonymous: 17.07.2022 * Published ''The Far High Theory'' (ectoscientific concept) article: 27.07.2022 * Published ''The Cesidian Age started for scientific reasons'' (ectohistorical concept) article: 06.08.2022 It should be noted that while the socially limited Kaisiris Clan (11.08.2019 – Ω), and the Cesidian Network (09.10.2019 – Ω) high spirituality organisation are connected with some real micronationalists, there is no Judaeo-Christian group which is. Yet Kaisiris is treated like ''persona non grata'' by most micronationalists (non-[http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''ectopolitans'']), so he enjoys no understanding among most micronationalists, but also receives no support. All current forms of micronationalism are either purely self-centred simulations and entertainment, or primordial forms of tribalism without genuine societalistic or [http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''ectopolitan''] foundations. It should also be noted that Saint René Descartes University (24.11.2007 – Ω), and its Centre for Cesidian law (08.08.2006 – Ω) and Salubriology School (11.02.2009 – Ω) continue to exist, and are active as genuine educational and research institutions, and the Paradiplomatic Affairs (24.05.2013 – Ω) agency continues to exist as a paradiplomatic and [http://5wcwiki.pbworks.com/w/page/147494235/ectopolitan ''ectopolitan''] organisation, albeit less actively. Cesidian spiritual science (Css) has become, in essence, Cesidian legal, spiritual and theological, salubriological and psychological, linguistic, journalistic and historical, geological, geographic and astronomical, economics, societal and political, ecological and agricultural, informatics, educational and library science, or the world's first holistic, ethical, and scientific paradigm. Cesidian spiritual science (Css) milestones: * 29.11.2019 → Css term is coined. * 21.12.2019 → fishy Christianity "facts". * 05.02.2020 → curialisation/neoecclesiastic union process. * 29.12.2020 → ectolinguistics begins: ectopolitical/ectopolitics terms. * 03.02.2021 → Cyberterra ectogeography connection. * 14.03.2022 → proof ectopolitans are gods; Css "Queen of the Sciences". ==Important ectonyms and exonyms ([http://5wcwiki.pbworks.com/w/page/144142176/Kaisiris%20multilingual multilingual plus sound])== * Ectoenglishⓔ: Kaisiris Tallini [born Cesidio Tallini] * Ectoespañolⓢ: Kaisiris Tallini [nacido Cesidio Tallini] * Català: Kaisiris Tallini [nascut Cesidio Tallini] * 外中文ⓩ： 凯西里斯·塔利尼（出生：塞西迪奥·塔利尼） * Oʻzbekcha: Kaisiris Tallini * Қазақша: Кайсирис Таллини [туылған: Сесидио Таллини] * Türkmençe: Kaisiris Tallini [doglan Cesidio Tallini] * Тоҷикӣ: Кайсирис Таллини [таваллуд: Сесидио Таллини] * Монгол: Кайсирис Таллини [төрсөн: Сесидио Таллини] * བོད་ཡིག༇ཁའི་སིཨའིརིས་ཏལིནའི༺འཁྲུངས་ཆེསིདིཨོ་ཏལིནའི༻ * Ektodeutschⓓ: Kaisiris Tallini [geboren Cesidio Tallini] * Nederlands: Kaisiris Tallini * Svenska: Kaisiris Tallini * Dansk: Kaissiris Tallini * Suomi: Kaisiris Tallini * Norsk bokmål: Kaisiris Tallini * Íslenska: Kaisiris Tallini * Gàidhlig: Kaisiris Tallini * Cymraeg: Kaisiris Tallini * Bahasa Indonesia: Kaisiris Tallini * Jawa: Kaisiris Tallini * Sunda: Kaisiris Tallini * Ectofrançaisⓕ: Kaisiris Tallini [né Césidio Tallini] * Kreyòl ayisyen: Kaisiris Tallini * Corsu: Kaisiris Tallini [natu Cesidio Tallini] * Экторусскийⓡ: Кайсирис Таллини [урожденный Чесидио Таллини] * Беларуская: Кайсірыс Талліні * Кыргызча: Кайсирис Таллини * Українська: Кайсіріс Талліні * Română: Kaisiris Tallini * Српски: Каисирис Таллини * Հայերեն: Կայզիրիս Տալլինի * ქართველი: კაისირის ტალლინი * ｴｸﾄﾆﾎﾝｺﾞⓙ: ｶｲｼﾘｽ･ﾀﾘｰﾆ (ｳﾏﾚ: ﾁｪｼﾃﾞｨｵ･ﾀﾘｰﾆ) * Ectoitalianoⓘ: Kaisiris Tallini [nato Cesidio Tallini] * Hrvatski: Kaisiris Tallini * Slovenščina: Kaisiris Tallini * Magyar: Kaissiris Tallini * Shqip: Kaisiris Tallini * Македонски: Каисирис Таллини * Bosanski: Kaisiris Tallini * አማርኛ፦ ካይሲሪስ ታልሊኒ * ቲግሪንያ፦ ካይሲሪስ ታልሊኒ * Čeština: Kaisiris Tallini * Slovenčina: Kaisiris Tallini * Hausa: Kaisiris Tallini * Yorùbá: Kaisiris Tallini * Igbo: Kaisiris Tallini * Malagasy: Kaisiris Tallini * Kiswahili: Kaisiris Tallini * IsiZulu: Kaisiris Tallini * Ikinyarwanda: Kaisiris Tallini * IsiXhosa: Kaisiris Tallini * Afrikaans: Kaiciris Tallini * Vèneto: Kaisiris Tallini [nato Cesidio Tallini] * Napulitano: Kaisiris Tallini [nato Cesidio Tallini] * Sicilianu: Kaisiris Tallini [nascitu Cesidio Tallini] * Sardu: Kaisiris Tallini [nasciu Cesidio Tallini] * Malti: Kaisiris Tallini [imwieled Cesidio Tallini] * Ōlelo Hawaiʻi: Kaisiris Tallini [hānau ʻia ʻo Cesidio Tallini] * Εκτοελληνικάⓖ: Καϊσίρης Ταλλίνι [αρχικά Τσεσίδιο Ταλλίνι] * Ectoportuguêsⓟ: Kaisiris Tallini [nascido Cesidio Tallini] * Interlingua: Kaisiris Tallini [nascite Cesidio Tallini] * Esperanto: Kaisiris Tallini [origine Cesidio Tallini] * Polski: Kaisiris Tallini * Eesti: Kaisiris Tallini * Lietuvių: Kaisiris Tallini * Latviešu: Kaisiris Tallini * Türkçe: Kaisiris Tallini * Azərbaycanca: Kaisiris Tallini * Kurdî: Kaisiris Tallini * Български: Кайсирис Таллини * 엑토한국어ⓚ: 카이시리스 탈리니 (태어난: 체시디오 탈리니) * Ngoài tiếng việtⓥ: Kaisíris Tallini [sinh ra: Chêsidio Tallini] * Tagalog: Kaisiris Tallini [ipinanganak na Cesidio Tallini] * Cebuano: Kaisiris Tallini [natawo nga Cesidio Tallini] * ไทย: ไคสิริส ทัลลินี [เกิด: เชศรีดิโอ ทัลลินี] * Ectolatinaⓛ: Kaisidis Tallini [natus Caesidius Tallini] * Qhichwa: Kaisiris Tallini * ᐊᓂᔑᓈᐯᒧᐎᓐ: ᑲᐃᓯᕆᔅ ᑕᓪᓕᓂ [ᓃᑭ ᒉᓯᑎᐅ ᑕᓪᓕᓂ] * हिंदी: काईसिरिस तालिनी * বাংলা: কাইসিরিস তালিনি * नेपाली: कैसिरिस तल्लिनी * తెలుగు: కైసిరిస్ తల్లిని * தமிழ்: கைசிரிஸ் தாலினி * मराठी: काईसीरिस तल्लीनी * ગુજરાતી: કૈસીરીસ તલ્લિની * ಕನ್ನಡ: ಕೈಸಿರಿಸ್ ಟಾಲಿನಿ * മലയാളം: കൈസിരിസ് തല്ലിനി * ଓଡିଆ: କେସିରିସ୍ ତାଲିନି * ລາວ: ໄຄຊີຣິສ ທາລິນີ * অসমীয়া: কাইচিৰিছ টালিনি * සිංහල: කෛසිරිස් ටල්ලිනි * ਪੰਜਾਬੀ: ਕੈਸੀਰਿਸ ਟੱਲੀਨੀ <big>پنجابی: قیصریس تلینی </big>▪ <big>دری: قیصریس تالینی </big>▪ <big>فارسی: کایسیریس تالینی </big>▪ <big>[קַאִיסִירִיס טָאללִינִי [נוֹלַד צ'סִידָיו טָאללִינִי :ⓗאַקְטוֹעִבְרִית </big>▪ '''[inillɒɈ oibiƨɘɔ oɈɒn] †inillɒɈ ƨiɿiƨiɒʞ :ⓞoɔƨooɈɔɘ''' ▪ <big>[عربى: كايسيريس تاليني [ولد سيسيديو تاليني </big>▪ <big>اردو: کائیسیرس تاللینی </big>▪ † ''Originally named UMMOA or UGV English, it wasn't judged a new language, but as a new English variety, variant, or lect (assessment provided by Melinda Lyons, ISO 639-3 registration authority for SIL International). Since 30.12.2020, UMMOA or UGV English is now called Ectoenglishⓔ, the world's first ectolanguage. Kaisiris has also started to develop other ectolanguages besides Ectoenglishⓔ, ectoitalianoⓘ [Ectoitalian], and ⓞoɔƨooɈɔɘ [Ectooscan].'' ==Citations== </big> 7eaq68i3sb1tnd2hyxv3xefv34zg8s5 3 274637 2412393 2305260 2022-08-06T18:16:55Z Pathoschild 14426 add talk page header ([[m:Synchbot|requested by MdsShakil]]) wikitext text/x-wiki {{User talk:MdsShakil/header}} {{Robelbox|theme=9|title=Welcome!|width=100%}} <div style="{{Robelbox/pad}}"> '''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] MdsShakil!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. Please remember to [[Wikiversity:Signature|sign and date]] your finished comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. The signature icon [[File:OOUI JS signature icon LTR.svg]] above the edit window makes it simple. All users are expected to abide by our [[Wikiversity:Privacy policy|Privacy]], [[Wikiversity:Civility|Civility]], and the [[Foundation:Terms of Use|Terms of Use]] policies while at Wikiversity. To [[Wikiversity:Introduction|get started]], you may <!-- The Left column --> <div style="width:50.0%; float:left"> * [[Help:guides|Take a guided tour]] and learn [[Help:Editing|to edit]]. * Visit a (kind of) [[Wikiversity:Random|random project]]. * [[Wikiversity:Browse|Browse]] Wikiversity, or visit a portal corresponding to your educational level: [[Portal: Pre-school Education|pre-school]], [[Portal: Primary Education|primary]], [[Portal:Secondary Education|secondary]], [[Portal:Tertiary Education|tertiary]], [[Portal:Non-formal Education|non-formal education]]. * Find out about [[Wikiversity:Research|research]] activities on Wikiversity. * [[Wikiversity:Introduction explore|Explore]] Wikiversity with the links to your left. </div> <!-- The Right column --> <div style="width:50.0%; float:left"> * Enable VisualEditor under [[Special:Preferences#mw-prefsection-betafeatures|Beta]] settings to make article editing easier. * Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] and find out [[Help:How to write an educational resource|how to write an educational resource]] for Wikiversity. * Give [[Wikiversity:Feedback|feedback]] about your initial observations. * Discuss Wikiversity issues or ask questions at the [[Wikiversity:Colloquium|colloquium]]. * [[Wikiversity:Chat|Chat]] with other Wikiversitans on [[:freenode:wikiversity|<kbd>#wikiversity</kbd>]]. </div> <br clear="both"/> You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 02:59, 26 May 2021 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} ==Reversion== [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2021&type=revision&diff=2302057&oldid=2302056 Why this edit?] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 12:55, 3 August 2021 (UTC) :@[[User:Jtneill|Jtneill]] It was inadvertently clicked. I will be more careful about this in future --[[User:MdsShakil|MdsShakil]] ([[User talk:MdsShakil|discuss]] • [[Special:Contributions/MdsShakil|contribs]]) 13:54, 3 August 2021 (UTC) ==[[Motivation and emotion/Book/2021]]== {{At|MdsShakil}}, I have reverted [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2021%2FHolistic_care_needs_of_the_imminently_dying&type=revision&diff=2305243&oldid=2305233 this edit] because these pages are currently being developed by students, so be patient. May I politely request that you refrain from editing these pages for now unless you have useful content to add? Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 09:22, 12 August 2021 (UTC) 4ap3o1u3kweu11hvizf6y817h0isppq 0 277657 2412434 2412344 2022-08-06T23:12:42Z Tamika Afeaki 2947781 wikitext text/x-wiki {{/Banner}} ==Motivation== # [[Academic help-seeking]] - What are the barriers and enablers of AHS and how can AHS be fostered? - [[User:MyUserName|MyUserName]] # [[/Academic self-regulation/]] - What is academic self-regulation, why does it matter, and how can it be fostered? - [[U3216563]] # [[/Actively open-minded thinking/]] - How can AOT be used to improve human performance? - [[User:MyUserName|MyUserName]] # [[/Active transport motivation/]] - What motivates use of active transport and how can people be encouraged to use it? - [[User:MyUserName|MyUserName]] # [[/Antidepressants and motivation/]] - What are the effects of popular antidepressants on motivation? - [[User:U3222363|U3222363]] # [[/Approach motivation/]] - What is approach motivation and how does it lead to behaviour? - [[User:U3189370|U3189370]] # [[/Behavioural economics and motivation/]] - What aspects of motivation theory are useful in behavioural economics? - [[User:U3141987|U3141987]] # [[/Behavioural model of health services/]] - What is the BMHS and how can it be used? - SoSilverLibby # [[/Beneficence as a psychological need/]] - What is beneficence and what are its implications as a psychological need? - [[User:MyUserName|CaitlinEmc]] # [[/Brief motivational interviewing as a health intervention/]] - How can brief motivational interviewing be used as a health intervention? - [[User:MyUserName|MyUserName]] # [[/Choice overload/]] - What is choice overload? What is the optimal amount of choice? - [[UserGeorgiaFairweather|GeorgiaFairweather]] # [[/Chunking and goal pursuit/]] - How does chunking affect goal pursuit? - [[User:MyUserName|MyUserName]] # [[/Cognitive entrenchment/]] - What is cognitive entrenchment and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[/Climate change helplessness/]] - How does learned helpless impact motivation to engage in behaviours to limit climate change? - [[User:MyUserName|MyUserName]] # [[/Closeness communication bias/]] - What is the CCB, why does it occur, and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Commitment bias/]] - What motivates escalation of commitment even it does not lead to desirably outcomes? - [[User:MyUserName|MyUserName]] # [[/Conspiracy theory motivation/]] - What motivates people to believe in conspiracy theories? - [[User:KingMob221|KingMob221]] # [[/Construal level theory/]] - What is construal level theory and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Courage motivation/]] - What is courage, what motivates courage, and how can courage be enhanced? -[[User:Hanarose123|Hanarose123]] # [[/Death drive/]] - What is the death drive and how can it be negotiated? - [[User:U3086459|U3086459]] # [[Motivation and emotion/Book/2022/Drugs-violence nexus and motivation Atu3202070|Drugs-violence nexus and motivation]] - What is the role of motivation in the drugs-violence nexus? - [[Atu3202070|Atu3202070]] # [[/Episodic future thinking and delay discounting/]] - What is the relationship between between EFT and DD? - [[User:MyUserName|MyUserName]] # [[/Episodic memory and planning/]] - What role does episodic memory play in planning? - [[User:MyUserName|U3246310]] # [[/Equity theory/]] - What is equity theory and how can it be applied? - [[EKS2001|EKS2001]] # [[/ERG theory/]] - What is Alderfer's ERG theory? - [[User:MyUserName|MyUserName]] # [[/Frame of reference and motivation/]] - How does frame of reference affect motivation? - [[User:MyUserName|MyUserName]] # [[/Freedom and motivation/]] - What is the effect of freedom on motivation? - [[Cedevlin9|Cedevlin9]] # [[/Fully functioning person/]] - What is a FFP and how can full functioning be developed? - [[User:Sebastian Armstrong|Sebastian Armstrong]] # [[/Functional fixedness/]] - What is functional fixedness and how can it be overcome? - [[User:U3214117|U3214117]] # [[/Functional imagery training/]] - What is FIT and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Gamification and work motivation/]] - How can gamification enhance work motivation? - [[U3211125|U3211125]] # [[/Giving up goals/]] - When should we give up goals and when should we persist? - [[User:MyUserName|U3161584]] # [[/Green prescription motivation/]] - What motivates green prescription compliance? - [[User:Earthxangel|Earthxangel]] # [[/Health belief model/]] - What is the HBM and how can it be used to enhance motivation for health-promoting behaviour? - [[SoSilverLibby]] # [[/Help-seeking among boys/]] - What are the barriers to help-seeking for boys and what motivates them to seek help? - [[User:BradMcGrath|BradMcGrath]] # [[/Hidden costs of reward/]] - What are the hidden costs of motivating by reward? - [[User:MyUserName|MyUserName]] # [[/Hijack hypothesis of drug addiction/]] - What is the hijack hypothesis, what is the evidence, and how does it help to understand drug addiction? - [[U3218292|U3218292]] # [[/Honesty motivation/]] - What motivates honesty? - [[User:U3200859|U3200859]] # [[/Humour, leadership, and work/]] - What role does humour play in effective leadership in the workplace? - [[User:U3210264|U3210264]] # [[/IKEA effect/]] - What is the IKEA effect and how can it be applied? - [[U3216963|U]]3216963 # [[/Intertemporal choice/]] - What are intertemporal choices and how can they be effectively negotiated? - [[User:MyUserName|MyUserName]] # [[/Kindness motivation/]] - What motivates kindness? - u3205429 # [[/Motivational music and exercise/]] - How can music be used to help motivate exercise? - [[User:MyUserName|U3183466]] # [[/Novelty-variety as a psychological need/]] - What is novelty-variety and what are its implications as a psychological need? - [[User:MyUserName|MyUserName]] # [[/Nucleus accumbens and motivation/]] - What role does the nucleus accumbens play in motivation? - [[User:U3213250|U3213250]] # [[/Perfectionism/]] - What motivates perfectionism? Is perfectionism good or bad? How can it be managed? - [[User:AEMOR|AEMOR]] # [[/Physiological needs/]] - How do human's physiological needs affect motivation? - [[U3203655]] # [[/Protection motivation theory and COVID-19/]] - How does PMT apply to managing COVID-19? - [[User:U3200956|U3200956]] # [[/Relative deprivation and motivation/]] - What is the effect of relative deprivation on motivation? - [[User:U3191574 (PHP)|U3191574 (PHP)]] # [[/Retrospective regret/]] - What is the motivational role of retrospective regret? - [[User:Will-U3214082|Will-U3214082]] # [[/Revenge motivation/]] - What motivates revenge and how does it affect us? - [[User:U3216654|U3216654]] # [[/Self-efficacy and academic achievement/]] - What role does self-efficacy play in academic achievement? - [[User:U943292|U943292]]a # [[/Self-efficacy and achievement/]] - What role does self-efficacy play in achievement outcomes? - [[User:U3216513mt|U3216513mt]] # [[/Sexual harassment at work motivation/]] - What motivates sexual harassment at work and what can be done about it? - [[User:U3037979|U3037979]] # [[/Signature strengths/]] - What are signature strengths and how can they be applied? - [[User:MyUserName|MyUserName]] # [[/Social cure/]] - What is the social cure and how can it be applied? - [[User:U3215976|U3215976]] # [[/System justification theory/]] - What is SJT, how does it affect our lives, and what can be done about it? - [[User:MyUserName|MyUserName]] # [[/Stretch goals/]] - What are stretch goals? Do they work? - [[User:MyUserName|MyUserName]] # [[/Sublimation/]] - What is sublimation and how can it be fostered? - [[User:MyUserName|MyUserName]] # [[/Survival needs and motivation/]] - What are survival needs and how do they influence motivation? - [[User:U3148161|U3148161]] # [[/Task initiation/]] - What are the challenges with task initiation and how to get get started? - [[User:MyUserName|MyUserName]] # [[/Theoretical domains framework/]] - What is the TDF and how can be used to guide behaviour change? - [[User:MyUserName|MyUserName]] # [[/Time and motivation/]] - What is the effect of time on motivation? - [[User:Lturner2311|Lturner2311]] # [[/Time management/]] - How can one's time be managed effectively? - [[User:CNK.20|CNK.20]] # [[/To-do lists/]] - Are to-do lists a good idea? What are their pros and cons? How can they be used effectively? - [[User:U3207458|U3207458]] # [[/Uncertainty avoidance/]] - What is uncertainty avoidance, why does it occur, and what are its consequences? - [[User:Franklin Brightt|Franklin Brightt]] # [[/Urgency bias and productivity/]] - What is the impact of urgency bias on productivity and what can be done about it? - U3055143 # [[/Vocational identity/]] - What is vocational identity and how does it develop? - [[User:MyUserName|MyUserName]] # [[/Volunteer tourism motivation/]] - What motivates volunteer tourism? - [[User:U962051|U962051]] # [[/Wanting and liking/]] - What are the similarities and differences between wanting and liking, and what are the implications? - [[User:MyUserName|MyUserName]] # [[/Work breaks, well-being, and productivity/]] - How do work breaks affect well-being and productivity? - [[User:MyUserName|U3215603]] # [[/Work and flow/]] - What characteristics of work can produce flow and how can flow at work be fostered? - [[User:U3213441|U3213441]] ==Emotion== # [[/Animal emotion/]] - What is the emotional experience of animals? - [[U3216502]] # [[/Attributions and emotion/]] - How do attributions affect emotion? - [[User:MyUserName|MyUserName]] # [[/Autonomous sensory meridian response and emotion/]] - What emotions are involved in ASMR experiences and why do they occur? - [[User:U3186959|U3186959]] # [[/Benzodiazepines and emotion/]] - What are the effects of benzodiazepines on emotion? - [[User:FulaAjeo22|FulaAjeo22]] # [[/Bewilderment/]] - What is bewilderment and how can it be dealt with? - [[User:MyUserName|MyUserName]] # [[/Burnout/]] - What is burnout and how can be it be managed and prevented? - [[User:U3211603|U3211603]] # [[/Cognitive dissonance reduction/]] - What strategies do people use to reduce cognitive dissonance and how effective are they? - [[User:Tatjurate|Tatjurate]] # [[/Colonisation and emotion in Australia/]] - What are the emotional responses to colonisation in Australia? - [[User:Micabaker1|Micabaker1]] # [[/Compassion/]] - What is compassion, what are its pros and cons, and how can it be fostered? - u3203545 # [[/Connection to country and well-being/]] - What is the relationship between connection to country and well-being? - [[User:MyUserName|MyUserName]] # [[/Contempt/]] - What is contempt, what causes it, and how can it be managed? - [[User:MyUserName|MyUserName]] # [[/Core emotions/]] - What are the core emotions and what is their function? U3203140 # [[/Creative arts and trauma/]] - How can creative arts help in dealing with trauma? - [[MyUserName|SashaBrooksby]] # [[/Cultural influences on shame, guilt, and pride/]] - How does culture influence shame, guilt, and pride? - [[User:Tamika Afeaki|Tamika Afeaki]] # [[/Default mode network and the self/]] - What is the relationship between the DMN and the self? - [[User:MyUserName|MyUserName]] # [[/Difficult conversations and emotion/]] - What communication and emotional skills are needed to successfully negotiate difficult conversations? - [[User:u3158968|u3158968]] # [[/Disappointment/]] - What is disappointment, what causes disappointment, and how can disappointment be managed? - [[User:U3216256|U3216256]] # [[/DMT and spirituality/]] - How can DMT facilitate spiritual experiences? - [[DenniseSoleymani]] # [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? - [[User:MyUserName|MyUserName]] # [[/Ecological grief/]] - What is ecological grief and what can be done about it? - [[User:Brewerjr|Brewerjr]] # [[/Ecopsychology and stress/]] - How can ecopsychology help to explain and deal with stress? - [[User:MyUserName|MyUserName]] # [[/Embarrassment/]] - What is embarrassment, what causes it, and how can it be managed? - u3190353 # [[/Emotional intelligence training/]] - How can emotional intelligence be trained? - Eimilerous22 # [[/Emotion knowledge/]] - What is emotion knowledge and how can it be developed? - [[User:GabbieUC|GabbieUC]] # [[/Emotion across the lifespan/]] - How does emotion develop across the lifespan? - u3230861 # [[/Endocannabinoid system and emotion/]] - What is the role of the endocannabinoid system in emotion? - [[User:RWilliams12|Rwilliams12]] # [[/Environmental grief/]] - What is eco-grief, its causes and consequences, and what can be done? - [[User:Gabrielle Eagling|Gabrielle Eagling]] # [[/Exercise and endocannabinoids/]] - What is the relationship between exercise and the endocannabinoid system? - [[User:MyUserName|MyUserName]] # [[/Expressive suppression and emotion regulation/]] - What is the role of expressive suppression in emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Fairness and emotion/]] - What is the relation between fairness and emotion? - [[User:MyUserName|MyUserName]] # [[/Fatigue and emotion/]] - What is the effect of fatigue on emotion and what can be done about it? - [[User:Lewis.Kusk|Lewis.Kusk]] # [[/Fear/]] - What is fear, what causes it, and how can it be managed? - [[User:Icantchooseone|Icantchooseone]] # [[/Fear of working out/]] - What is FOWO and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Fundamental attribution error and emotion/]] - What is the relationship between the FAE and emotion? - [[User:MyUserName|MyUserName]] # [[/Gratitude and subjective wellbeing/]] - What is the relationship between gratitude and subjective wellbeing? - [[User:MyUserName|MyUserName]] # [[/Gloatrage/]] - What is gloatrage, what causes it, and what are its consequences? - [[User:MyUserName|MyUserName]] # [[/Heart rate variability and emotion regulation/]] - What is the relationship between HRV and emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Hedonic adaptation prevention model/]] - What is the HAP model and how can it be applied? - [[User:Lyndel Lemon|Lyndel Lemon]] # [[/Humility/]] - What is humility, what causes it, and is it desirable? - [[User:MyUserName|MyUserName]] # [[/Hypomania and emotion/]] - What are the emotional characteristics of hypomania? - [[User:Alec.cortez|Alec.cortez]] # [[/Impact bias/]] - What is impact bias, what causes it, what are its consequences, and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[Indigenous Australian emotionality]] - In what ways is emotionality experienced by Indigenous Australian people? - [[User:MyUserName|MyUserName]] # [[/Indigenous Australian mindfulness/]] - How has Indigenous Australian culture traditionally conceived of, and practiced, mindfulness? - [[User:MyUserName|MyUserName]] # [[/Inspiration/]] - What is inspiration, what causes it, what are its consequences, and how can it be fostered? - [[User:MyUserName|u3227354]] # [[/Insular cortex and emotion/]] - What role does the insular cortex play in emotion? - [[User:U3190094|U3190094]] # [[/Interoception and emotion/]] - What is the relationship between interoception and emotion? - [[User:MyUserName|MyUserName]] # [[/Kama muta/]] - What is kama muta, what are its effects, and how can it be fostered? - [[User:U3183521|U3183521]] # [[/Linguistic relativism and emotion/]] - What is the role of linguistic relativism in emotion? - [[User:U3119310|U3119310]] # [[/Menstrual cycle mood disorders/]] - What causes menstrual cycle mood disorders and how can they be managed? - [[User:MyUserName|U3217109]] # [[/Mindfulness and creativity/]] - How can mindfulness enhance creativity? - [[CaityDcr1603]] # [[/Mindful self-care/]] - What is mindful self-care, why does it matter, and how can it be developed? - [[User:clairelogan|clairelogan]] # [[/Mixed emotions/]] - What are mixed emotions, what causes them, and how can they be managed? - [[User:MyUserName|MyUserName]] # [[/Mudita/]] - What is mudita and how can it be developed? - [[User:MyUserName|MyUserName]] # [[/Natural disasters and emotion/]] - How do people respond emotionally to natural disasters and how can they be supported? -[[User:U3148366_Chris|U3148366_Chris]] # [[/Nature therapy/]] - What is nature therapy and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Narcissism and emotion/]] - What is the relationship between narcissism and emotion? - [[User:A Super Villain|A Super Villain]] # [[/Narrative therapy and emotion/]] - What is the role of emotion in narrative therapy? - [[User:MyUserName|MyUserName]] # [[/Needle fear/]] - How does needle fear develop, what are its consequences, and what can be done about it? - [[User:U3166273|U3166273]] # [[/Positivity ratio/]] - What is the positivity ratio and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Post-traumatic stress disorder and emotion/]] - What is the effect of PTSD on emotion? - [[User:JorjaFive|JorjaFive]] # [[/Psychological distress/]] - What is PD, what are the main types, and how can they be managed? - [[User:U3190773|U3190773]] # [[/Psychological trauma/]] - What causes psychological trauma, what are the consequences, and how can people recover from psychological trauma? - [[User:U3210431|U3210431]] # [[/Psilocybin assisted psychotherapy/]] - How can psilocybin be used to assist psychotherapy? - [[User:U3083720|U3083720]] # [[/Rational compassion/]] - What is rational compassion and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? - [[User:MyUserName|MyUserName]] # [[/Religiosity and coping/]] - What is the relationship between religiosity and coping? - [[User:MyUserName|MyUserName]] # [[/Resentment/]] - What is resentment, what causes it, and what are its consequences? - [[User:U3216389|U3216389]] # [[/Risk-as-feelings/]] - What is the emotional experience of risk and how does it influence decision-making and behaviour? - [[User:MyUserName|MyUserName]] # [[/Self-esteem and culture/]] - What are the cultural influences on self-esteem? - [[User:MyUserName|MyUserName]] # [[/Smiling and emotion/]] - What is the relationship between smiling and emotion? - U3200902 # [[/Social media and suicide prevention/]] - How can social media be used to help prevent suicide? - [[JaimeTegan|JaimeTegan]] # [[/Sorry business/]] - What is sorry business and what role does it play in Indigenous communities in Australia? - Isaacem13 # [[/Stress control mindset/]] - What is a SCM, why does it matter, and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Suffering as emotion/]] - What is the emotional experience of suffering and how can people cope with suffering? - [[User:Brookewin|Brookewin]] # [[/Telemental health/]] - What are the pros and cons of TMH and what are the key ingredients for effective TMH practices? - [[User:MyUserName|MyUserName]] # [[/Topophilia/]] - What is topophilia, how does it develop, and what are the psychological impacts? - [[User:RSPMeredith|RSPMeredith]] # [[/Triumph/]] - What is triumph, what causes it, and how can it be managed? - [[User:Bill.miosge|Bill.miosge]] # [[/Unemployment and mental health/]]: What is the relationship between unemployment and mental health? - [[User:MyUserName|U3216958 - Tiarna.Wilson-Ginn]] # [[/Viewing natural scenes and emotion/]] - What is the effect of viewing natural scenes on emotion and how can this be applied? - [[User:MyUserName|Ana028]] # [[/Wave metaphor for emotion/]] - In what respects is an ocean wave a helpful metaphor for understanding human emotions? - [[jamieepiper]] # [[/Window of tolerance/]] - What is the window of tolerance and how this concept be used? - [[User:U3223109|U3223109]] # [[/Workplace mental health training/]] - What is WMHT, what techniques are used, and what are the impacts? - [[ArtOfHappiness]] # [[/Zoom fatigue/]] - What is Zoom fatigue, what causes it, what are its consequences, and what can be done about it? - [[User:MyUserName|MyUserName]] ==Motivation and emotion== # [[/Financial investing, motivation, and emotion/]] - What role does motivation and emotion play in financial investing? - [[U3217287|U3217287]] # [[/Hostage negotiation, motivation, and emotion/]] - What role does motivation and emotion play in hostage negotiation? - [[User:U3213549|U3213549]] # [[/Money priming, motivation, and emotion/]] - What is the effect of money priming on motivation and emotion? - [[User:MyUserName|MyUserName]] # [[/Motivational dimensional model of affect/]] - What is the motivational dimensional model of affect and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Napping, motivation, and emotion/]] - What are the motivational and emotional effects of napping? - [[User:MyUserName|MyUserName]] # [[/Overchoice, emotion, and motivation/]] - What are the emotional and motivational effects of overchoice? - [[User:MyUserName|MyUserName]] # [[/Patience and impatience/]] - What are the psychological causes and consequences of patience and impatience? - [[User:MyUserName|MyUserName]] # [[/Reward system, motivation, and emotion/]] - What role does the reward system play in motivation and emotion? - [[User:U3162201|U3162201]] [[Category:Motivation and emotion/Book/2022]] kg5242ke532784b4o6y8j6vfyiic3gw 2412490 2412434 2022-08-07T06:34:56Z U3210490 2947795 /* Emotion */ u32101490 wikitext text/x-wiki {{/Banner}} ==Motivation== # [[Academic help-seeking]] - What are the barriers and enablers of AHS and how can AHS be fostered? - [[User:MyUserName|MyUserName]] # [[/Academic self-regulation/]] - What is academic self-regulation, why does it matter, and how can it be fostered? - [[U3216563]] # [[/Actively open-minded thinking/]] - How can AOT be used to improve human performance? - [[User:MyUserName|MyUserName]] # [[/Active transport motivation/]] - What motivates use of active transport and how can people be encouraged to use it? - [[User:MyUserName|MyUserName]] # [[/Antidepressants and motivation/]] - What are the effects of popular antidepressants on motivation? - [[User:U3222363|U3222363]] # [[/Approach motivation/]] - What is approach motivation and how does it lead to behaviour? - [[User:U3189370|U3189370]] # [[/Behavioural economics and motivation/]] - What aspects of motivation theory are useful in behavioural economics? - [[User:U3141987|U3141987]] # [[/Behavioural model of health services/]] - What is the BMHS and how can it be used? - SoSilverLibby # [[/Beneficence as a psychological need/]] - What is beneficence and what are its implications as a psychological need? - [[User:MyUserName|CaitlinEmc]] # [[/Brief motivational interviewing as a health intervention/]] - How can brief motivational interviewing be used as a health intervention? - [[User:MyUserName|MyUserName]] # [[/Choice overload/]] - What is choice overload? What is the optimal amount of choice? - [[UserGeorgiaFairweather|GeorgiaFairweather]] # [[/Chunking and goal pursuit/]] - How does chunking affect goal pursuit? - [[User:MyUserName|MyUserName]] # [[/Cognitive entrenchment/]] - What is cognitive entrenchment and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[/Climate change helplessness/]] - How does learned helpless impact motivation to engage in behaviours to limit climate change? - [[User:MyUserName|MyUserName]] # [[/Closeness communication bias/]] - What is the CCB, why does it occur, and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Commitment bias/]] - What motivates escalation of commitment even it does not lead to desirably outcomes? - [[User:MyUserName|MyUserName]] # [[/Conspiracy theory motivation/]] - What motivates people to believe in conspiracy theories? - [[User:KingMob221|KingMob221]] # [[/Construal level theory/]] - What is construal level theory and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Courage motivation/]] - What is courage, what motivates courage, and how can courage be enhanced? -[[User:Hanarose123|Hanarose123]] # [[/Death drive/]] - What is the death drive and how can it be negotiated? - [[User:U3086459|U3086459]] # [[Motivation and emotion/Book/2022/Drugs-violence nexus and motivation Atu3202070|Drugs-violence nexus and motivation]] - What is the role of motivation in the drugs-violence nexus? - [[Atu3202070|Atu3202070]] # [[/Episodic future thinking and delay discounting/]] - What is the relationship between between EFT and DD? - [[User:MyUserName|MyUserName]] # [[/Episodic memory and planning/]] - What role does episodic memory play in planning? - [[User:MyUserName|U3246310]] # [[/Equity theory/]] - What is equity theory and how can it be applied? - [[EKS2001|EKS2001]] # [[/ERG theory/]] - What is Alderfer's ERG theory? - [[User:MyUserName|MyUserName]] # [[/Frame of reference and motivation/]] - How does frame of reference affect motivation? - [[User:MyUserName|MyUserName]] # [[/Freedom and motivation/]] - What is the effect of freedom on motivation? - [[Cedevlin9|Cedevlin9]] # [[/Fully functioning person/]] - What is a FFP and how can full functioning be developed? - [[User:Sebastian Armstrong|Sebastian Armstrong]] # [[/Functional fixedness/]] - What is functional fixedness and how can it be overcome? - [[User:U3214117|U3214117]] # [[/Functional imagery training/]] - What is FIT and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Gamification and work motivation/]] - How can gamification enhance work motivation? - [[U3211125|U3211125]] # [[/Giving up goals/]] - When should we give up goals and when should we persist? - [[User:MyUserName|U3161584]] # [[/Green prescription motivation/]] - What motivates green prescription compliance? - [[User:Earthxangel|Earthxangel]] # [[/Health belief model/]] - What is the HBM and how can it be used to enhance motivation for health-promoting behaviour? - [[SoSilverLibby]] # [[/Help-seeking among boys/]] - What are the barriers to help-seeking for boys and what motivates them to seek help? - [[User:BradMcGrath|BradMcGrath]] # [[/Hidden costs of reward/]] - What are the hidden costs of motivating by reward? - [[User:MyUserName|MyUserName]] # [[/Hijack hypothesis of drug addiction/]] - What is the hijack hypothesis, what is the evidence, and how does it help to understand drug addiction? - [[U3218292|U3218292]] # [[/Honesty motivation/]] - What motivates honesty? - [[User:U3200859|U3200859]] # [[/Humour, leadership, and work/]] - What role does humour play in effective leadership in the workplace? - [[User:U3210264|U3210264]] # [[/IKEA effect/]] - What is the IKEA effect and how can it be applied? - [[U3216963|U]]3216963 # [[/Intertemporal choice/]] - What are intertemporal choices and how can they be effectively negotiated? - [[User:MyUserName|MyUserName]] # [[/Kindness motivation/]] - What motivates kindness? - u3205429 # [[/Motivational music and exercise/]] - How can music be used to help motivate exercise? - [[User:MyUserName|U3183466]] # [[/Novelty-variety as a psychological need/]] - What is novelty-variety and what are its implications as a psychological need? - [[User:MyUserName|MyUserName]] # [[/Nucleus accumbens and motivation/]] - What role does the nucleus accumbens play in motivation? - [[User:U3213250|U3213250]] # [[/Perfectionism/]] - What motivates perfectionism? Is perfectionism good or bad? How can it be managed? - [[User:AEMOR|AEMOR]] # [[/Physiological needs/]] - How do human's physiological needs affect motivation? - [[U3203655]] # [[/Protection motivation theory and COVID-19/]] - How does PMT apply to managing COVID-19? - [[User:U3200956|U3200956]] # [[/Relative deprivation and motivation/]] - What is the effect of relative deprivation on motivation? - [[User:U3191574 (PHP)|U3191574 (PHP)]] # [[/Retrospective regret/]] - What is the motivational role of retrospective regret? - [[User:Will-U3214082|Will-U3214082]] # [[/Revenge motivation/]] - What motivates revenge and how does it affect us? - [[User:U3216654|U3216654]] # [[/Self-efficacy and academic achievement/]] - What role does self-efficacy play in academic achievement? - [[User:U943292|U943292]]a # [[/Self-efficacy and achievement/]] - What role does self-efficacy play in achievement outcomes? - [[User:U3216513mt|U3216513mt]] # [[/Sexual harassment at work motivation/]] - What motivates sexual harassment at work and what can be done about it? - [[User:U3037979|U3037979]] # [[/Signature strengths/]] - What are signature strengths and how can they be applied? - [[User:MyUserName|MyUserName]] # [[/Social cure/]] - What is the social cure and how can it be applied? - [[User:U3215976|U3215976]] # [[/System justification theory/]] - What is SJT, how does it affect our lives, and what can be done about it? - [[User:MyUserName|MyUserName]] # [[/Stretch goals/]] - What are stretch goals? Do they work? - [[User:MyUserName|MyUserName]] # [[/Sublimation/]] - What is sublimation and how can it be fostered? - [[User:MyUserName|MyUserName]] # [[/Survival needs and motivation/]] - What are survival needs and how do they influence motivation? - [[User:U3148161|U3148161]] # [[/Task initiation/]] - What are the challenges with task initiation and how to get get started? - [[User:MyUserName|MyUserName]] # [[/Theoretical domains framework/]] - What is the TDF and how can be used to guide behaviour change? - [[User:MyUserName|MyUserName]] # [[/Time and motivation/]] - What is the effect of time on motivation? - [[User:Lturner2311|Lturner2311]] # [[/Time management/]] - How can one's time be managed effectively? - [[User:CNK.20|CNK.20]] # [[/To-do lists/]] - Are to-do lists a good idea? What are their pros and cons? How can they be used effectively? - [[User:U3207458|U3207458]] # [[/Uncertainty avoidance/]] - What is uncertainty avoidance, why does it occur, and what are its consequences? - [[User:Franklin Brightt|Franklin Brightt]] # [[/Urgency bias and productivity/]] - What is the impact of urgency bias on productivity and what can be done about it? - U3055143 # [[/Vocational identity/]] - What is vocational identity and how does it develop? - [[User:MyUserName|MyUserName]] # [[/Volunteer tourism motivation/]] - What motivates volunteer tourism? - [[User:U962051|U962051]] # [[/Wanting and liking/]] - What are the similarities and differences between wanting and liking, and what are the implications? - [[User:MyUserName|MyUserName]] # [[/Work breaks, well-being, and productivity/]] - How do work breaks affect well-being and productivity? - [[User:MyUserName|U3215603]] # [[/Work and flow/]] - What characteristics of work can produce flow and how can flow at work be fostered? - [[User:U3213441|U3213441]] ==Emotion== # [[/Animal emotion/]] - What is the emotional experience of animals? - [[U3216502]] # [[/Attributions and emotion/]] - How do attributions affect emotion? - [[User:MyUserName|MyUserName]] # [[/Autonomous sensory meridian response and emotion/]] - What emotions are involved in ASMR experiences and why do they occur? - [[User:U3186959|U3186959]] # [[/Benzodiazepines and emotion/]] - What are the effects of benzodiazepines on emotion? - [[User:FulaAjeo22|FulaAjeo22]] # [[/Bewilderment/]] - What is bewilderment and how can it be dealt with? - [[User:MyUserName|MyUserName]] # [[/Burnout/]] - What is burnout and how can be it be managed and prevented? - [[User:U3211603|U3211603]] # [[/Cognitive dissonance reduction/]] - What strategies do people use to reduce cognitive dissonance and how effective are they? - [[User:Tatjurate|Tatjurate]] # [[/Colonisation and emotion in Australia/]] - What are the emotional responses to colonisation in Australia? - [[User:Micabaker1|Micabaker1]] # [[/Compassion/]] - What is compassion, what are its pros and cons, and how can it be fostered? - u3203545 # [[/Connection to country and well-being/]] - What is the relationship between connection to country and well-being? - [[User:MyUserName|MyUserName]] # [[/Contempt/]] - What is contempt, what causes it, and how can it be managed? - [[User:MyUserName|MyUserName]] # [[/Core emotions/]] - What are the core emotions and what is their function? U3203140 # [[/Creative arts and trauma/]] - How can creative arts help in dealing with trauma? - [[MyUserName|SashaBrooksby]] # [[/Cultural influences on shame, guilt, and pride/]] - How does culture influence shame, guilt, and pride? - [[User:Tamika Afeaki|Tamika Afeaki]] # [[/Default mode network and the self/]] - What is the relationship between the DMN and the self? - [[User:MyUserName|MyUserName]] # [[/Difficult conversations and emotion/]] - What communication and emotional skills are needed to successfully negotiate difficult conversations? - [[User:u3158968|u3158968]] # [[/Disappointment/]] - What is disappointment, what causes disappointment, and how can disappointment be managed? - [[User:U3216256|U3216256]] # [[/DMT and spirituality/]] - How can DMT facilitate spiritual experiences? - [[DenniseSoleymani]] # [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? - [[User:MyUserName|MyUserName]] # [[/Ecological grief/]] - What is ecological grief and what can be done about it? - [[User:Brewerjr|Brewerjr]] # [[/Ecopsychology and stress/]] - How can ecopsychology help to explain and deal with stress? - [[User:MyUserName|MyUserName]] # [[/Embarrassment/]] - What is embarrassment, what causes it, and how can it be managed? - u3190353 # [[/Emotional intelligence training/]] - How can emotional intelligence be trained? - Eimilerous22 # [[/Emotion knowledge/]] - What is emotion knowledge and how can it be developed? - [[User:GabbieUC|GabbieUC]] # [[/Emotion across the lifespan/]] - How does emotion develop across the lifespan? - u3230861 # [[/Endocannabinoid system and emotion/]] - What is the role of the endocannabinoid system in emotion? - [[User:RWilliams12|Rwilliams12]] # [[/Environmental grief/]] - What is eco-grief, its causes and consequences, and what can be done? - [[User:Gabrielle Eagling|Gabrielle Eagling]] # [[/Exercise and endocannabinoids/]] - What is the relationship between exercise and the endocannabinoid system? - [[User:MyUserName|MyUserName]] # [[/Expressive suppression and emotion regulation/]] - What is the role of expressive suppression in emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Fairness and emotion/]] - What is the relation between fairness and emotion? - [[User:MyUserName|MyUserName]] # [[/Fatigue and emotion/]] - What is the effect of fatigue on emotion and what can be done about it? - [[User:Lewis.Kusk|Lewis.Kusk]] # [[/Fear/]] - What is fear, what causes it, and how can it be managed? - [[User:Icantchooseone|Icantchooseone]] # [[/Fear of working out/]] - What is FOWO and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Fundamental attribution error and emotion/]] - What is the relationship between the FAE and emotion? - [[User:MyUserName|MyUserName]] # [[/Gratitude and subjective wellbeing/]] - What is the relationship between gratitude and subjective wellbeing? - [[User:MyUserName|MyUserName]] # [[/Gloatrage/]] - What is gloatrage, what causes it, and what are its consequences? - [[User:MyUserName|MyUserName]] # [[/Heart rate variability and emotion regulation/]] - What is the relationship between HRV and emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Hedonic adaptation prevention model/]] - What is the HAP model and how can it be applied? - [[User:Lyndel Lemon|Lyndel Lemon]] # [[/Humility/]] - What is humility, what causes it, and is it desirable? - [[User:MyUserName|MyUserName]] # [[/Hypomania and emotion/]] - What are the emotional characteristics of hypomania? - [[User:Alec.cortez|Alec.cortez]] # [[/Impact bias/]] - What is impact bias, what causes it, what are its consequences, and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[Indigenous Australian emotionality]] - In what ways is emotionality experienced by Indigenous Australian people? - [[User:MyUserName|MyUserName]] # [[/Indigenous Australian mindfulness/]] - How has Indigenous Australian culture traditionally conceived of, and practiced, mindfulness? - [[User:MyUserName|MyUserName]] # [[/Inspiration/]] - What is inspiration, what causes it, what are its consequences, and how can it be fostered? - [[User:MyUserName|u3227354]] # [[/Insular cortex and emotion/]] - What role does the insular cortex play in emotion? - [[User:U3190094|U3190094]] # [[/Interoception and emotion/]] - What is the relationship between interoception and emotion? - [[User:MyUserName|MyUserName]] # [[/Kama muta/]] - What is kama muta, what are its effects, and how can it be fostered? - [[User:U3183521|U3183521]] # [[/Linguistic relativism and emotion/]] - What is the role of linguistic relativism in emotion? - [[User:U3119310|U3119310]] # [[/Menstrual cycle mood disorders/]] - What causes menstrual cycle mood disorders and how can they be managed? - [[User:MyUserName|U3217109]] # [[/Mindfulness and creativity/]] - How can mindfulness enhance creativity? - [[CaityDcr1603]] # [[/Mindful self-care/]] - What is mindful self-care, why does it matter, and how can it be developed? - [[User:clairelogan|clairelogan]] # [[/Mixed emotions/]] - What are mixed emotions, what causes them, and how can they be managed? - [[User:MyUserName|u3210490]] # [[/Mudita/]] - What is mudita and how can it be developed? - [[User:MyUserName|MyUserName]] # [[/Natural disasters and emotion/]] - How do people respond emotionally to natural disasters and how can they be supported? -[[User:U3148366_Chris|U3148366_Chris]] # [[/Nature therapy/]] - What is nature therapy and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Narcissism and emotion/]] - What is the relationship between narcissism and emotion? - [[User:A Super Villain|A Super Villain]] # [[/Narrative therapy and emotion/]] - What is the role of emotion in narrative therapy? - [[User:MyUserName|MyUserName]] # [[/Needle fear/]] - How does needle fear develop, what are its consequences, and what can be done about it? - [[User:U3166273|U3166273]] # [[/Positivity ratio/]] - What is the positivity ratio and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Post-traumatic stress disorder and emotion/]] - What is the effect of PTSD on emotion? - [[User:JorjaFive|JorjaFive]] # [[/Psychological distress/]] - What is PD, what are the main types, and how can they be managed? - [[User:U3190773|U3190773]] # [[/Psychological trauma/]] - What causes psychological trauma, what are the consequences, and how can people recover from psychological trauma? - [[User:U3210431|U3210431]] # [[/Psilocybin assisted psychotherapy/]] - How can psilocybin be used to assist psychotherapy? - [[User:U3083720|U3083720]] # [[/Rational compassion/]] - What is rational compassion and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? - [[User:MyUserName|MyUserName]] # [[/Religiosity and coping/]] - What is the relationship between religiosity and coping? - [[User:MyUserName|MyUserName]] # [[/Resentment/]] - What is resentment, what causes it, and what are its consequences? - [[User:U3216389|U3216389]] # [[/Risk-as-feelings/]] - What is the emotional experience of risk and how does it influence decision-making and behaviour? - [[User:MyUserName|MyUserName]] # [[/Self-esteem and culture/]] - What are the cultural influences on self-esteem? - [[User:MyUserName|MyUserName]] # [[/Smiling and emotion/]] - What is the relationship between smiling and emotion? - U3200902 # [[/Social media and suicide prevention/]] - How can social media be used to help prevent suicide? - [[JaimeTegan|JaimeTegan]] # [[/Sorry business/]] - What is sorry business and what role does it play in Indigenous communities in Australia? - Isaacem13 # [[/Stress control mindset/]] - What is a SCM, why does it matter, and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Suffering as emotion/]] - What is the emotional experience of suffering and how can people cope with suffering? - [[User:Brookewin|Brookewin]] # [[/Telemental health/]] - What are the pros and cons of TMH and what are the key ingredients for effective TMH practices? - [[User:MyUserName|MyUserName]] # [[/Topophilia/]] - What is topophilia, how does it develop, and what are the psychological impacts? - [[User:RSPMeredith|RSPMeredith]] # [[/Triumph/]] - What is triumph, what causes it, and how can it be managed? - [[User:Bill.miosge|Bill.miosge]] # [[/Unemployment and mental health/]]: What is the relationship between unemployment and mental health? - [[User:MyUserName|U3216958 - Tiarna.Wilson-Ginn]] # [[/Viewing natural scenes and emotion/]] - What is the effect of viewing natural scenes on emotion and how can this be applied? - [[User:MyUserName|Ana028]] # [[/Wave metaphor for emotion/]] - In what respects is an ocean wave a helpful metaphor for understanding human emotions? - [[jamieepiper]] # [[/Window of tolerance/]] - What is the window of tolerance and how this concept be used? - [[User:U3223109|U3223109]] # [[/Workplace mental health training/]] - What is WMHT, what techniques are used, and what are the impacts? - [[ArtOfHappiness]] # [[/Zoom fatigue/]] - What is Zoom fatigue, what causes it, what are its consequences, and what can be done about it? - [[User:MyUserName|MyUserName]] ==Motivation and emotion== # [[/Financial investing, motivation, and emotion/]] - What role does motivation and emotion play in financial investing? - [[U3217287|U3217287]] # [[/Hostage negotiation, motivation, and emotion/]] - What role does motivation and emotion play in hostage negotiation? - [[User:U3213549|U3213549]] # [[/Money priming, motivation, and emotion/]] - What is the effect of money priming on motivation and emotion? - [[User:MyUserName|MyUserName]] # [[/Motivational dimensional model of affect/]] - What is the motivational dimensional model of affect and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Napping, motivation, and emotion/]] - What are the motivational and emotional effects of napping? - [[User:MyUserName|MyUserName]] # [[/Overchoice, emotion, and motivation/]] - What are the emotional and motivational effects of overchoice? - [[User:MyUserName|MyUserName]] # [[/Patience and impatience/]] - What are the psychological causes and consequences of patience and impatience? - [[User:MyUserName|MyUserName]] # [[/Reward system, motivation, and emotion/]] - What role does the reward system play in motivation and emotion? - [[User:U3162201|U3162201]] [[Category:Motivation and emotion/Book/2022]] nbl0pd33gebv2daezh2jqit6uw2hfxa 2412495 2412490 2022-08-07T06:55:21Z U3219905 2947550 Called dibs wikitext text/x-wiki {{/Banner}} ==Motivation== # [[Academic help-seeking]] - What are the barriers and enablers of AHS and how can AHS be fostered? - [[User:MyUserName|MyUserName]] # [[/Academic self-regulation/]] - What is academic self-regulation, why does it matter, and how can it be fostered? - [[U3216563]] # [[/Actively open-minded thinking/]] - How can AOT be used to improve human performance? - [[User:MyUserName|MyUserName]] # [[/Active transport motivation/]] - What motivates use of active transport and how can people be encouraged to use it? - [[User:MyUserName|MyUserName]] # [[/Antidepressants and motivation/]] - What are the effects of popular antidepressants on motivation? - [[User:U3222363|U3222363]] # [[/Approach motivation/]] - What is approach motivation and how does it lead to behaviour? - [[User:U3189370|U3189370]] # [[/Behavioural economics and motivation/]] - What aspects of motivation theory are useful in behavioural economics? - [[User:U3141987|U3141987]] # [[/Behavioural model of health services/]] - What is the BMHS and how can it be used? - SoSilverLibby # [[/Beneficence as a psychological need/]] - What is beneficence and what are its implications as a psychological need? - [[User:MyUserName|CaitlinEmc]] # [[/Brief motivational interviewing as a health intervention/]] - How can brief motivational interviewing be used as a health intervention? - [[User:MyUserName|MyUserName]] # [[/Choice overload/]] - What is choice overload? What is the optimal amount of choice? - [[UserGeorgiaFairweather|GeorgiaFairweather]] # [[/Chunking and goal pursuit/]] - How does chunking affect goal pursuit? - [[User:MyUserName|MyUserName]] # [[/Cognitive entrenchment/]] - What is cognitive entrenchment and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[/Climate change helplessness/]] - How does learned helpless impact motivation to engage in behaviours to limit climate change? - [[User:MyUserName|MyUserName]] # [[/Closeness communication bias/]] - What is the CCB, why does it occur, and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Commitment bias/]] - What motivates escalation of commitment even it does not lead to desirably outcomes? - [[User:MyUserName|MyUserName]] # [[/Conspiracy theory motivation/]] - What motivates people to believe in conspiracy theories? - [[User:KingMob221|KingMob221]] # [[/Construal level theory/]] - What is construal level theory and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Courage motivation/]] - What is courage, what motivates courage, and how can courage be enhanced? -[[User:Hanarose123|Hanarose123]] # [[/Death drive/]] - What is the death drive and how can it be negotiated? - [[User:U3086459|U3086459]] # [[Motivation and emotion/Book/2022/Drugs-violence nexus and motivation Atu3202070|Drugs-violence nexus and motivation]] - What is the role of motivation in the drugs-violence nexus? - [[Atu3202070|Atu3202070]] # [[/Episodic future thinking and delay discounting/]] - What is the relationship between between EFT and DD? - [[User:MyUserName|MyUserName]] # [[/Episodic memory and planning/]] - What role does episodic memory play in planning? - [[User:MyUserName|U3246310]] # [[/Equity theory/]] - What is equity theory and how can it be applied? - [[EKS2001|EKS2001]] # [[/ERG theory/]] - What is Alderfer's ERG theory? - [[User:MyUserName|MyUserName]] # [[/Frame of reference and motivation/]] - How does frame of reference affect motivation? - [[User:MyUserName|MyUserName]] # [[/Freedom and motivation/]] - What is the effect of freedom on motivation? - [[Cedevlin9|Cedevlin9]] # [[/Fully functioning person/]] - What is a FFP and how can full functioning be developed? - [[User:Sebastian Armstrong|Sebastian Armstrong]] # [[/Functional fixedness/]] - What is functional fixedness and how can it be overcome? - [[User:U3214117|U3214117]] # [[/Functional imagery training/]] - What is FIT and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Gamification and work motivation/]] - How can gamification enhance work motivation? - [[U3211125|U3211125]] # [[/Giving up goals/]] - When should we give up goals and when should we persist? - [[User:MyUserName|U3161584]] # [[/Green prescription motivation/]] - What motivates green prescription compliance? - [[User:Earthxangel|Earthxangel]] # [[/Health belief model/]] - What is the HBM and how can it be used to enhance motivation for health-promoting behaviour? - [[SoSilverLibby]] # [[/Help-seeking among boys/]] - What are the barriers to help-seeking for boys and what motivates them to seek help? - [[User:BradMcGrath|BradMcGrath]] # [[/Hidden costs of reward/]] - What are the hidden costs of motivating by reward? - [[User:MyUserName|MyUserName]] # [[/Hijack hypothesis of drug addiction/]] - What is the hijack hypothesis, what is the evidence, and how does it help to understand drug addiction? - [[U3218292|U3218292]] # [[/Honesty motivation/]] - What motivates honesty? - [[User:U3200859|U3200859]] # [[/Humour, leadership, and work/]] - What role does humour play in effective leadership in the workplace? - [[User:U3210264|U3210264]] # [[/IKEA effect/]] - What is the IKEA effect and how can it be applied? - [[U3216963|U]]3216963 # [[/Intertemporal choice/]] - What are intertemporal choices and how can they be effectively negotiated? - [[User:MyUserName|MyUserName]] # [[/Kindness motivation/]] - What motivates kindness? - u3205429 # [[/Motivational music and exercise/]] - How can music be used to help motivate exercise? - [[User:MyUserName|U3183466]] # [[/Novelty-variety as a psychological need/]] - What is novelty-variety and what are its implications as a psychological need? - [[User:MyUserName|MyUserName]] # [[/Nucleus accumbens and motivation/]] - What role does the nucleus accumbens play in motivation? - [[User:U3213250|U3213250]] # [[/Perfectionism/]] - What motivates perfectionism? Is perfectionism good or bad? How can it be managed? - [[User:AEMOR|AEMOR]] # [[/Physiological needs/]] - How do human's physiological needs affect motivation? - [[U3203655]] # [[/Protection motivation theory and COVID-19/]] - How does PMT apply to managing COVID-19? - [[User:U3200956|U3200956]] # [[/Relative deprivation and motivation/]] - What is the effect of relative deprivation on motivation? - [[User:U3191574 (PHP)|U3191574 (PHP)]] # [[/Retrospective regret/]] - What is the motivational role of retrospective regret? - [[User:Will-U3214082|Will-U3214082]] # [[/Revenge motivation/]] - What motivates revenge and how does it affect us? - [[User:U3216654|U3216654]] # [[/Self-efficacy and academic achievement/]] - What role does self-efficacy play in academic achievement? - [[User:U943292|U943292]]a # [[/Self-efficacy and achievement/]] - What role does self-efficacy play in achievement outcomes? - [[User:U3216513mt|U3216513mt]] # [[/Sexual harassment at work motivation/]] - What motivates sexual harassment at work and what can be done about it? - [[User:U3037979|U3037979]] # [[/Signature strengths/]] - What are signature strengths and how can they be applied? - [[User:MyUserName|MyUserName]] # [[/Social cure/]] - What is the social cure and how can it be applied? - [[User:U3215976|U3215976]] # [[/System justification theory/]] - What is SJT, how does it affect our lives, and what can be done about it? - [[User:MyUserName|MyUserName]] # [[/Stretch goals/]] - What are stretch goals? Do they work? - [[User:MyUserName|MyUserName]] # [[/Sublimation/]] - What is sublimation and how can it be fostered? - [[User:MyUserName|MyUserName]] # [[/Survival needs and motivation/]] - What are survival needs and how do they influence motivation? - [[User:U3148161|U3148161]] # [[/Task initiation/]] - What are the challenges with task initiation and how to get get started? - [[User:MyUserName|MyUserName]] # [[/Theoretical domains framework/]] - What is the TDF and how can be used to guide behaviour change? - [[User:MyUserName|MyUserName]] # [[/Time and motivation/]] - What is the effect of time on motivation? - [[User:Lturner2311|Lturner2311]] # [[/Time management/]] - How can one's time be managed effectively? - [[User:CNK.20|CNK.20]] # [[/To-do lists/]] - Are to-do lists a good idea? What are their pros and cons? How can they be used effectively? - [[User:U3207458|U3207458]] # [[/Uncertainty avoidance/]] - What is uncertainty avoidance, why does it occur, and what are its consequences? - [[User:Franklin Brightt|Franklin Brightt]] # [[/Urgency bias and productivity/]] - What is the impact of urgency bias on productivity and what can be done about it? - U3055143 # [[/Vocational identity/]] - What is vocational identity and how does it develop? - [[User:MyUserName|MyUserName]] # [[/Volunteer tourism motivation/]] - What motivates volunteer tourism? - [[User:U962051|U962051]] # [[/Wanting and liking/]] - What are the similarities and differences between wanting and liking, and what are the implications? - [[User:MyUserName|MyUserName]] # [[/Work breaks, well-being, and productivity/]] - How do work breaks affect well-being and productivity? - [[User:MyUserName|U3215603]] # [[/Work and flow/]] - What characteristics of work can produce flow and how can flow at work be fostered? - [[User:U3213441|U3213441]] ==Emotion== # [[/Animal emotion/]] - What is the emotional experience of animals? - [[U3216502]] # [[/Attributions and emotion/]] - How do attributions affect emotion? - [[User:MyUserName|MyUserName]] # [[/Autonomous sensory meridian response and emotion/]] - What emotions are involved in ASMR experiences and why do they occur? - [[User:U3186959|U3186959]] # [[/Benzodiazepines and emotion/]] - What are the effects of benzodiazepines on emotion? - [[User:FulaAjeo22|FulaAjeo22]] # [[/Bewilderment/]] - What is bewilderment and how can it be dealt with? - [[User:MyUserName|MyUserName]] # [[/Burnout/]] - What is burnout and how can be it be managed and prevented? - [[User:U3211603|U3211603]] # [[/Cognitive dissonance reduction/]] - What strategies do people use to reduce cognitive dissonance and how effective are they? - [[User:Tatjurate|Tatjurate]] # [[/Colonisation and emotion in Australia/]] - What are the emotional responses to colonisation in Australia? - [[User:Micabaker1|Micabaker1]] # [[/Compassion/]] - What is compassion, what are its pros and cons, and how can it be fostered? - u3203545 # [[/Connection to country and well-being/]] - What is the relationship between connection to country and well-being? - [[User:MyUserName|MyUserName]] # [[/Contempt/]] - What is contempt, what causes it, and how can it be managed? - [[User:MyUserName|u3219905]] # [[/Core emotions/]] - What are the core emotions and what is their function? U3203140 # [[/Creative arts and trauma/]] - How can creative arts help in dealing with trauma? - [[MyUserName|SashaBrooksby]] # [[/Cultural influences on shame, guilt, and pride/]] - How does culture influence shame, guilt, and pride? - [[User:Tamika Afeaki|Tamika Afeaki]] # [[/Default mode network and the self/]] - What is the relationship between the DMN and the self? - [[User:MyUserName|MyUserName]] # [[/Difficult conversations and emotion/]] - What communication and emotional skills are needed to successfully negotiate difficult conversations? - [[User:u3158968|u3158968]] # [[/Disappointment/]] - What is disappointment, what causes disappointment, and how can disappointment be managed? - [[User:U3216256|U3216256]] # [[/DMT and spirituality/]] - How can DMT facilitate spiritual experiences? - [[DenniseSoleymani]] # [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? - [[User:MyUserName|MyUserName]] # [[/Ecological grief/]] - What is ecological grief and what can be done about it? - [[User:Brewerjr|Brewerjr]] # [[/Ecopsychology and stress/]] - How can ecopsychology help to explain and deal with stress? - [[User:MyUserName|MyUserName]] # [[/Embarrassment/]] - What is embarrassment, what causes it, and how can it be managed? - u3190353 # [[/Emotional intelligence training/]] - How can emotional intelligence be trained? - Eimilerous22 # [[/Emotion knowledge/]] - What is emotion knowledge and how can it be developed? - [[User:GabbieUC|GabbieUC]] # [[/Emotion across the lifespan/]] - How does emotion develop across the lifespan? - u3230861 # [[/Endocannabinoid system and emotion/]] - What is the role of the endocannabinoid system in emotion? - [[User:RWilliams12|Rwilliams12]] # [[/Environmental grief/]] - What is eco-grief, its causes and consequences, and what can be done? - [[User:Gabrielle Eagling|Gabrielle Eagling]] # [[/Exercise and endocannabinoids/]] - What is the relationship between exercise and the endocannabinoid system? - [[User:MyUserName|MyUserName]] # [[/Expressive suppression and emotion regulation/]] - What is the role of expressive suppression in emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Fairness and emotion/]] - What is the relation between fairness and emotion? - [[User:MyUserName|MyUserName]] # [[/Fatigue and emotion/]] - What is the effect of fatigue on emotion and what can be done about it? - [[User:Lewis.Kusk|Lewis.Kusk]] # [[/Fear/]] - What is fear, what causes it, and how can it be managed? - [[User:Icantchooseone|Icantchooseone]] # [[/Fear of working out/]] - What is FOWO and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Fundamental attribution error and emotion/]] - What is the relationship between the FAE and emotion? - [[User:MyUserName|MyUserName]] # [[/Gratitude and subjective wellbeing/]] - What is the relationship between gratitude and subjective wellbeing? - [[User:MyUserName|MyUserName]] # [[/Gloatrage/]] - What is gloatrage, what causes it, and what are its consequences? - [[User:MyUserName|MyUserName]] # [[/Heart rate variability and emotion regulation/]] - What is the relationship between HRV and emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Hedonic adaptation prevention model/]] - What is the HAP model and how can it be applied? - [[User:Lyndel Lemon|Lyndel Lemon]] # [[/Humility/]] - What is humility, what causes it, and is it desirable? - [[User:MyUserName|MyUserName]] # [[/Hypomania and emotion/]] - What are the emotional characteristics of hypomania? - [[User:Alec.cortez|Alec.cortez]] # [[/Impact bias/]] - What is impact bias, what causes it, what are its consequences, and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[Indigenous Australian emotionality]] - In what ways is emotionality experienced by Indigenous Australian people? - [[User:MyUserName|MyUserName]] # [[/Indigenous Australian mindfulness/]] - How has Indigenous Australian culture traditionally conceived of, and practiced, mindfulness? - [[User:MyUserName|MyUserName]] # [[/Inspiration/]] - What is inspiration, what causes it, what are its consequences, and how can it be fostered? - [[User:MyUserName|u3227354]] # [[/Insular cortex and emotion/]] - What role does the insular cortex play in emotion? - [[User:U3190094|U3190094]] # [[/Interoception and emotion/]] - What is the relationship between interoception and emotion? - [[User:MyUserName|MyUserName]] # [[/Kama muta/]] - What is kama muta, what are its effects, and how can it be fostered? - [[User:U3183521|U3183521]] # [[/Linguistic relativism and emotion/]] - What is the role of linguistic relativism in emotion? - [[User:U3119310|U3119310]] # [[/Menstrual cycle mood disorders/]] - What causes menstrual cycle mood disorders and how can they be managed? - [[User:MyUserName|U3217109]] # [[/Mindfulness and creativity/]] - How can mindfulness enhance creativity? - [[CaityDcr1603]] # [[/Mindful self-care/]] - What is mindful self-care, why does it matter, and how can it be developed? - [[User:clairelogan|clairelogan]] # [[/Mixed emotions/]] - What are mixed emotions, what causes them, and how can they be managed? - [[User:MyUserName|u3210490]] # [[/Mudita/]] - What is mudita and how can it be developed? - [[User:MyUserName|MyUserName]] # [[/Natural disasters and emotion/]] - How do people respond emotionally to natural disasters and how can they be supported? -[[User:U3148366_Chris|U3148366_Chris]] # [[/Nature therapy/]] - What is nature therapy and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Narcissism and emotion/]] - What is the relationship between narcissism and emotion? - [[User:A Super Villain|A Super Villain]] # [[/Narrative therapy and emotion/]] - What is the role of emotion in narrative therapy? - [[User:MyUserName|MyUserName]] # [[/Needle fear/]] - How does needle fear develop, what are its consequences, and what can be done about it? - [[User:U3166273|U3166273]] # [[/Positivity ratio/]] - What is the positivity ratio and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Post-traumatic stress disorder and emotion/]] - What is the effect of PTSD on emotion? - [[User:JorjaFive|JorjaFive]] # [[/Psychological distress/]] - What is PD, what are the main types, and how can they be managed? - [[User:U3190773|U3190773]] # [[/Psychological trauma/]] - What causes psychological trauma, what are the consequences, and how can people recover from psychological trauma? - [[User:U3210431|U3210431]] # [[/Psilocybin assisted psychotherapy/]] - How can psilocybin be used to assist psychotherapy? - [[User:U3083720|U3083720]] # [[/Rational compassion/]] - What is rational compassion and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? - [[User:MyUserName|MyUserName]] # [[/Religiosity and coping/]] - What is the relationship between religiosity and coping? - [[User:MyUserName|MyUserName]] # [[/Resentment/]] - What is resentment, what causes it, and what are its consequences? - [[User:U3216389|U3216389]] # [[/Risk-as-feelings/]] - What is the emotional experience of risk and how does it influence decision-making and behaviour? - [[User:MyUserName|MyUserName]] # [[/Self-esteem and culture/]] - What are the cultural influences on self-esteem? - [[User:MyUserName|MyUserName]] # [[/Smiling and emotion/]] - What is the relationship between smiling and emotion? - U3200902 # [[/Social media and suicide prevention/]] - How can social media be used to help prevent suicide? - [[JaimeTegan|JaimeTegan]] # [[/Sorry business/]] - What is sorry business and what role does it play in Indigenous communities in Australia? - Isaacem13 # [[/Stress control mindset/]] - What is a SCM, why does it matter, and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Suffering as emotion/]] - What is the emotional experience of suffering and how can people cope with suffering? - [[User:Brookewin|Brookewin]] # [[/Telemental health/]] - What are the pros and cons of TMH and what are the key ingredients for effective TMH practices? - [[User:MyUserName|MyUserName]] # [[/Topophilia/]] - What is topophilia, how does it develop, and what are the psychological impacts? - [[User:RSPMeredith|RSPMeredith]] # [[/Triumph/]] - What is triumph, what causes it, and how can it be managed? - [[User:Bill.miosge|Bill.miosge]] # [[/Unemployment and mental health/]]: What is the relationship between unemployment and mental health? - [[User:MyUserName|U3216958 - Tiarna.Wilson-Ginn]] # [[/Viewing natural scenes and emotion/]] - What is the effect of viewing natural scenes on emotion and how can this be applied? - [[User:MyUserName|Ana028]] # [[/Wave metaphor for emotion/]] - In what respects is an ocean wave a helpful metaphor for understanding human emotions? - [[jamieepiper]] # [[/Window of tolerance/]] - What is the window of tolerance and how this concept be used? - [[User:U3223109|U3223109]] # [[/Workplace mental health training/]] - What is WMHT, what techniques are used, and what are the impacts? - [[ArtOfHappiness]] # [[/Zoom fatigue/]] - What is Zoom fatigue, what causes it, what are its consequences, and what can be done about it? - [[User:MyUserName|MyUserName]] ==Motivation and emotion== # [[/Financial investing, motivation, and emotion/]] - What role does motivation and emotion play in financial investing? - [[U3217287|U3217287]] # [[/Hostage negotiation, motivation, and emotion/]] - What role does motivation and emotion play in hostage negotiation? - [[User:U3213549|U3213549]] # [[/Money priming, motivation, and emotion/]] - What is the effect of money priming on motivation and emotion? - [[User:MyUserName|MyUserName]] # [[/Motivational dimensional model of affect/]] - What is the motivational dimensional model of affect and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Napping, motivation, and emotion/]] - What are the motivational and emotional effects of napping? - [[User:MyUserName|MyUserName]] # [[/Overchoice, emotion, and motivation/]] - What are the emotional and motivational effects of overchoice? - [[User:MyUserName|MyUserName]] # [[/Patience and impatience/]] - What are the psychological causes and consequences of patience and impatience? - [[User:MyUserName|MyUserName]] # [[/Reward system, motivation, and emotion/]] - What role does the reward system play in motivation and emotion? - [[User:U3162201|U3162201]] [[Category:Motivation and emotion/Book/2022]] bfo6u744chsulu3me8z7jlfccz4xs0v 2412498 2412495 2022-08-07T09:26:59Z Ana028 2947571 Topic change wikitext text/x-wiki {{/Banner}} ==Motivation== # [[Academic help-seeking]] - What are the barriers and enablers of AHS and how can AHS be fostered? - [[User:MyUserName|MyUserName]] # [[/Academic self-regulation/]] - What is academic self-regulation, why does it matter, and how can it be fostered? - [[U3216563]] # [[/Actively open-minded thinking/]] - How can AOT be used to improve human performance? - [[User:MyUserName|MyUserName]] # [[/Active transport motivation/]] - What motivates use of active transport and how can people be encouraged to use it? - [[User:MyUserName|MyUserName]] # [[/Antidepressants and motivation/]] - What are the effects of popular antidepressants on motivation? - [[User:U3222363|U3222363]] # [[/Approach motivation/]] - What is approach motivation and how does it lead to behaviour? - [[User:U3189370|U3189370]] # [[/Behavioural economics and motivation/]] - What aspects of motivation theory are useful in behavioural economics? - [[User:U3141987|U3141987]] # [[/Behavioural model of health services/]] - What is the BMHS and how can it be used? - SoSilverLibby # [[/Beneficence as a psychological need/]] - What is beneficence and what are its implications as a psychological need? - [[User:MyUserName|CaitlinEmc]] # [[/Brief motivational interviewing as a health intervention/]] - How can brief motivational interviewing be used as a health intervention? - [[User:MyUserName|MyUserName]] # [[/Choice overload/]] - What is choice overload? What is the optimal amount of choice? - [[UserGeorgiaFairweather|GeorgiaFairweather]] # [[/Chunking and goal pursuit/]] - How does chunking affect goal pursuit? - [[User:MyUserName|MyUserName]] # [[/Cognitive entrenchment/]] - What is cognitive entrenchment and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[/Climate change helplessness/]] - How does learned helpless impact motivation to engage in behaviours to limit climate change? - [[User:MyUserName|MyUserName]] # [[/Closeness communication bias/]] - What is the CCB, why does it occur, and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Commitment bias/]] - What motivates escalation of commitment even it does not lead to desirably outcomes? - [[User:MyUserName|MyUserName]] # [[/Conspiracy theory motivation/]] - What motivates people to believe in conspiracy theories? - [[User:KingMob221|KingMob221]] # [[/Construal level theory/]] - What is construal level theory and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Courage motivation/]] - What is courage, what motivates courage, and how can courage be enhanced? -[[User:Hanarose123|Hanarose123]] # [[/Death drive/]] - What is the death drive and how can it be negotiated? - [[User:U3086459|U3086459]] # [[Motivation and emotion/Book/2022/Drugs-violence nexus and motivation Atu3202070|Drugs-violence nexus and motivation]] - What is the role of motivation in the drugs-violence nexus? - [[Atu3202070|Atu3202070]] # [[/Episodic future thinking and delay discounting/]] - What is the relationship between between EFT and DD? - [[User:MyUserName|MyUserName]] # [[/Episodic memory and planning/]] - What role does episodic memory play in planning? - [[User:MyUserName|U3246310]] # [[/Equity theory/]] - What is equity theory and how can it be applied? - [[EKS2001|EKS2001]] # [[/ERG theory/]] - What is Alderfer's ERG theory? - [[User:MyUserName|MyUserName]] # [[/Frame of reference and motivation/]] - How does frame of reference affect motivation? - [[User:MyUserName|MyUserName]] # [[/Freedom and motivation/]] - What is the effect of freedom on motivation? - [[Cedevlin9|Cedevlin9]] # [[/Fully functioning person/]] - What is a FFP and how can full functioning be developed? - [[User:Sebastian Armstrong|Sebastian Armstrong]] # [[/Functional fixedness/]] - What is functional fixedness and how can it be overcome? - [[User:U3214117|U3214117]] # [[/Functional imagery training/]] - What is FIT and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Gamification and work motivation/]] - How can gamification enhance work motivation? - [[U3211125|U3211125]] # [[/Giving up goals/]] - When should we give up goals and when should we persist? - [[User:MyUserName|U3161584]] # [[/Green prescription motivation/]] - What motivates green prescription compliance? - [[User:Earthxangel|Earthxangel]] # [[/Health belief model/]] - What is the HBM and how can it be used to enhance motivation for health-promoting behaviour? - [[SoSilverLibby]] # [[/Help-seeking among boys/]] - What are the barriers to help-seeking for boys and what motivates them to seek help? - [[User:BradMcGrath|BradMcGrath]] # [[/Hidden costs of reward/]] - What are the hidden costs of motivating by reward? - [[User:MyUserName|MyUserName]] # [[/Hijack hypothesis of drug addiction/]] - What is the hijack hypothesis, what is the evidence, and how does it help to understand drug addiction? - [[U3218292|U3218292]] # [[/Honesty motivation/]] - What motivates honesty? - [[User:U3200859|U3200859]] # [[/Humour, leadership, and work/]] - What role does humour play in effective leadership in the workplace? - [[User:U3210264|U3210264]] # [[/IKEA effect/]] - What is the IKEA effect and how can it be applied? - [[U3216963|U]]3216963 # [[/Intertemporal choice/]] - What are intertemporal choices and how can they be effectively negotiated? - [[User:MyUserName|MyUserName]] # [[/Kindness motivation/]] - What motivates kindness? - u3205429 # [[/Motivational music and exercise/]] - How can music be used to help motivate exercise? - [[User:MyUserName|U3183466]] # [[/Novelty-variety as a psychological need/]] - What is novelty-variety and what are its implications as a psychological need? - [[User:MyUserName|MyUserName]] # [[/Nucleus accumbens and motivation/]] - What role does the nucleus accumbens play in motivation? - [[User:U3213250|U3213250]] # [[/Perfectionism/]] - What motivates perfectionism? Is perfectionism good or bad? How can it be managed? - [[User:AEMOR|AEMOR]] # [[/Physiological needs/]] - How do human's physiological needs affect motivation? - [[U3203655]] # [[/Protection motivation theory and COVID-19/]] - How does PMT apply to managing COVID-19? - [[User:U3200956|U3200956]] # [[/Relative deprivation and motivation/]] - What is the effect of relative deprivation on motivation? - [[User:U3191574 (PHP)|U3191574 (PHP)]] # [[/Retrospective regret/]] - What is the motivational role of retrospective regret? - [[User:Will-U3214082|Will-U3214082]] # [[/Revenge motivation/]] - What motivates revenge and how does it affect us? - [[User:U3216654|U3216654]] # [[/Self-efficacy and academic achievement/]] - What role does self-efficacy play in academic achievement? - [[User:U943292|U943292]]a # [[/Self-efficacy and achievement/]] - What role does self-efficacy play in achievement outcomes? - [[User:U3216513mt|U3216513mt]] # [[/Sexual harassment at work motivation/]] - What motivates sexual harassment at work and what can be done about it? - [[User:U3037979|U3037979]] # [[/Signature strengths/]] - What are signature strengths and how can they be applied? - [[User:MyUserName|MyUserName]] # [[/Social cure/]] - What is the social cure and how can it be applied? - [[User:U3215976|U3215976]] # [[/System justification theory/]] - What is SJT, how does it affect our lives, and what can be done about it? - [[User:MyUserName|MyUserName]] # [[/Stretch goals/]] - What are stretch goals? Do they work? - [[User:MyUserName|MyUserName]] # [[/Sublimation/]] - What is sublimation and how can it be fostered? - [[User:MyUserName|MyUserName]] # [[/Survival needs and motivation/]] - What are survival needs and how do they influence motivation? - [[User:U3148161|U3148161]] # [[/Task initiation/]] - What are the challenges with task initiation and how to get get started? - [[User:MyUserName|MyUserName]] # [[/Theoretical domains framework/]] - What is the TDF and how can be used to guide behaviour change? - [[User:MyUserName|MyUserName]] # [[/Time and motivation/]] - What is the effect of time on motivation? - [[User:Lturner2311|Lturner2311]] # [[/Time management/]] - How can one's time be managed effectively? - [[User:CNK.20|CNK.20]] # [[/To-do lists/]] - Are to-do lists a good idea? What are their pros and cons? How can they be used effectively? - [[User:U3207458|U3207458]] # [[/Uncertainty avoidance/]] - What is uncertainty avoidance, why does it occur, and what are its consequences? - [[User:Franklin Brightt|Franklin Brightt]] # [[/Urgency bias and productivity/]] - What is the impact of urgency bias on productivity and what can be done about it? - U3055143 # [[/Vocational identity/]] - What is vocational identity and how does it develop? - [[User:MyUserName|MyUserName]] # [[/Volunteer tourism motivation/]] - What motivates volunteer tourism? - [[User:U962051|U962051]] # [[/Wanting and liking/]] - What are the similarities and differences between wanting and liking, and what are the implications? - [[User:MyUserName|MyUserName]] # [[/Work breaks, well-being, and productivity/]] - How do work breaks affect well-being and productivity? - [[User:MyUserName|U3215603]] # [[/Work and flow/]] - What characteristics of work can produce flow and how can flow at work be fostered? - [[User:U3213441|U3213441]] ==Emotion== # [[/Animal emotion/]] - What is the emotional experience of animals? - [[U3216502]] # [[/Attributions and emotion/]] - How do attributions affect emotion? - [[User:MyUserName|MyUserName]] # [[/Autonomous sensory meridian response and emotion/]] - What emotions are involved in ASMR experiences and why do they occur? - [[User:U3186959|U3186959]] # [[/Benzodiazepines and emotion/]] - What are the effects of benzodiazepines on emotion? - [[User:FulaAjeo22|FulaAjeo22]] # [[/Bewilderment/]] - What is bewilderment and how can it be dealt with? - [[User:MyUserName|MyUserName]] # [[/Burnout/]] - What is burnout and how can be it be managed and prevented? - [[User:U3211603|U3211603]] # [[/Cognitive dissonance reduction/]] - What strategies do people use to reduce cognitive dissonance and how effective are they? - [[User:Tatjurate|Tatjurate]] # [[/Colonisation and emotion in Australia/]] - What are the emotional responses to colonisation in Australia? - [[User:Micabaker1|Micabaker1]] # [[/Compassion/]] - What is compassion, what are its pros and cons, and how can it be fostered? - u3203545 # [[/Connection to country and well-being/]] - What is the relationship between connection to country and well-being? - [[User:MyUserName|MyUserName]] # [[/Contempt/]] - What is contempt, what causes it, and how can it be managed? - [[User:MyUserName|u3219905]] # [[/Core emotions/]] - What are the core emotions and what is their function? U3203140 # [[/Creative arts and trauma/]] - How can creative arts help in dealing with trauma? - [[MyUserName|SashaBrooksby]] # [[/Cultural influences on shame, guilt, and pride/]] - How does culture influence shame, guilt, and pride? - [[User:Tamika Afeaki|Tamika Afeaki]] # [[/Default mode network and the self/]] - What is the relationship between the DMN and the self? - [[User:MyUserName|MyUserName]] # [[/Difficult conversations and emotion/]] - What communication and emotional skills are needed to successfully negotiate difficult conversations? - [[User:u3158968|u3158968]] # [[/Disappointment/]] - What is disappointment, what causes disappointment, and how can disappointment be managed? - [[User:U3216256|U3216256]] # [[/DMT and spirituality/]] - How can DMT facilitate spiritual experiences? - [[DenniseSoleymani]] # [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? - [[User:MyUserName|MyUserName]] # [[/Ecological grief/]] - What is ecological grief and what can be done about it? - [[User:Brewerjr|Brewerjr]] # [[/Ecopsychology and stress/]] - How can ecopsychology help to explain and deal with stress? - [[User:MyUserName|MyUserName]] # [[/Embarrassment/]] - What is embarrassment, what causes it, and how can it be managed? - u3190353 # [[/Emotional intelligence training/]] - How can emotional intelligence be trained? - Eimilerous22 # [[/Emotion knowledge/]] - What is emotion knowledge and how can it be developed? - [[User:GabbieUC|GabbieUC]] # [[/Emotion across the lifespan/]] - How does emotion develop across the lifespan? - u3230861 # [[/Endocannabinoid system and emotion/]] - What is the role of the endocannabinoid system in emotion? - [[User:RWilliams12|Rwilliams12]] # [[/Environmental grief/]] - What is eco-grief, its causes and consequences, and what can be done? - [[User:Gabrielle Eagling|Gabrielle Eagling]] # [[/Exercise and endocannabinoids/]] - What is the relationship between exercise and the endocannabinoid system? - [[User:MyUserName|MyUserName]] # [[/Expressive suppression and emotion regulation/]] - What is the role of expressive suppression in emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Fairness and emotion/]] - What is the relation between fairness and emotion? - [[User:MyUserName|MyUserName]] # [[/Fatigue and emotion/]] - What is the effect of fatigue on emotion and what can be done about it? - [[User:Lewis.Kusk|Lewis.Kusk]] # [[/Fear/]] - What is fear, what causes it, and how can it be managed? - [[User:Icantchooseone|Icantchooseone]] # [[/Fear of working out/]] - What is FOWO and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Fundamental attribution error and emotion/]] - What is the relationship between the FAE and emotion? - [[User:MyUserName|MyUserName]] # [[/Gratitude and subjective wellbeing/]] - What is the relationship between gratitude and subjective wellbeing? - [[User:MyUserName|MyUserName]] # [[/Gloatrage/]] - What is gloatrage, what causes it, and what are its consequences? - [[User:MyUserName|MyUserName]] # [[/Heart rate variability and emotion regulation/]] - What is the relationship between HRV and emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Hedonic adaptation prevention model/]] - What is the HAP model and how can it be applied? - [[User:Lyndel Lemon|Lyndel Lemon]] # [[/Humility/]] - What is humility, what causes it, and is it desirable? - [[User:MyUserName|MyUserName]] # [[/Hypomania and emotion/]] - What are the emotional characteristics of hypomania? - [[User:Alec.cortez|Alec.cortez]] # [[/Impact bias/]] - What is impact bias, what causes it, what are its consequences, and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[Indigenous Australian emotionality]] - In what ways is emotionality experienced by Indigenous Australian people? - [[User:MyUserName|MyUserName]] # [[/Indigenous Australian mindfulness/]] - How has Indigenous Australian culture traditionally conceived of, and practiced, mindfulness? - [[User:MyUserName|MyUserName]] # [[/Inspiration/]] - What is inspiration, what causes it, what are its consequences, and how can it be fostered? - [[User:MyUserName|u3227354]] # [[/Insular cortex and emotion/]] - What role does the insular cortex play in emotion? - [[User:U3190094|U3190094]] # [[/Interoception and emotion/]] - What is the relationship between interoception and emotion? - [[User:MyUserName|MyUserName]] # [[/Kama muta/]] - What is kama muta, what are its effects, and how can it be fostered? - [[User:U3183521|U3183521]] # [[/Linguistic relativism and emotion/]] - What is the role of linguistic relativism in emotion? - [[User:U3119310|U3119310]] # [[/Menstrual cycle mood disorders/]] - What causes menstrual cycle mood disorders and how can they be managed? - [[User:MyUserName|U3217109]] # [[/Mindfulness and creativity/]] - How can mindfulness enhance creativity? - [[CaityDcr1603]] # [[/Mindful self-care/]] - What is mindful self-care, why does it matter, and how can it be developed? - [[User:clairelogan|clairelogan]] # [[/Mixed emotions/]] - What are mixed emotions, what causes them, and how can they be managed? - [[User:MyUserName|u3210490]] # [[/Mudita/]] - What is mudita and how can it be developed? - [[User:MyUserName|MyUserName]] # [[/Natural disasters and emotion/]] - How do people respond emotionally to natural disasters and how can they be supported? -[[User:U3148366_Chris|U3148366_Chris]] # [[/Nature therapy/]] - What is nature therapy and how can it be applied? - Ana028 # [[/Narcissism and emotion/]] - What is the relationship between narcissism and emotion? - [[User:A Super Villain|A Super Villain]] # [[/Narrative therapy and emotion/]] - What is the role of emotion in narrative therapy? - [[User:MyUserName|MyUserName]] # [[/Needle fear/]] - How does needle fear develop, what are its consequences, and what can be done about it? - [[User:U3166273|U3166273]] # [[/Positivity ratio/]] - What is the positivity ratio and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Post-traumatic stress disorder and emotion/]] - What is the effect of PTSD on emotion? - [[User:JorjaFive|JorjaFive]] # [[/Psychological distress/]] - What is PD, what are the main types, and how can they be managed? - [[User:U3190773|U3190773]] # [[/Psychological trauma/]] - What causes psychological trauma, what are the consequences, and how can people recover from psychological trauma? - [[User:U3210431|U3210431]] # [[/Psilocybin assisted psychotherapy/]] - How can psilocybin be used to assist psychotherapy? - [[User:U3083720|U3083720]] # [[/Rational compassion/]] - What is rational compassion and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? - [[User:MyUserName|MyUserName]] # [[/Religiosity and coping/]] - What is the relationship between religiosity and coping? - [[User:MyUserName|MyUserName]] # [[/Resentment/]] - What is resentment, what causes it, and what are its consequences? - [[User:U3216389|U3216389]] # [[/Risk-as-feelings/]] - What is the emotional experience of risk and how does it influence decision-making and behaviour? - [[User:MyUserName|MyUserName]] # [[/Self-esteem and culture/]] - What are the cultural influences on self-esteem? - [[User:MyUserName|MyUserName]] # [[/Smiling and emotion/]] - What is the relationship between smiling and emotion? - U3200902 # [[/Social media and suicide prevention/]] - How can social media be used to help prevent suicide? - [[JaimeTegan|JaimeTegan]] # [[/Sorry business/]] - What is sorry business and what role does it play in Indigenous communities in Australia? - Isaacem13 # [[/Stress control mindset/]] - What is a SCM, why does it matter, and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Suffering as emotion/]] - What is the emotional experience of suffering and how can people cope with suffering? - [[User:Brookewin|Brookewin]] # [[/Telemental health/]] - What are the pros and cons of TMH and what are the key ingredients for effective TMH practices? - [[User:MyUserName|MyUserName]] # [[/Topophilia/]] - What is topophilia, how does it develop, and what are the psychological impacts? - [[User:RSPMeredith|RSPMeredith]] # [[/Triumph/]] - What is triumph, what causes it, and how can it be managed? - [[User:Bill.miosge|Bill.miosge]] # [[/Unemployment and mental health/]]: What is the relationship between unemployment and mental health? - [[User:MyUserName|U3216958 - Tiarna.Wilson-Ginn]] # [[/Viewing natural scenes and emotion/]] - What is the effect of viewing natural scenes on emotion and how can this be applied? - [[User:MyUserName|MyUserName]] # [[/Wave metaphor for emotion/]] - In what respects is an ocean wave a helpful metaphor for understanding human emotions? - [[jamieepiper]] # [[/Window of tolerance/]] - What is the window of tolerance and how this concept be used? - [[User:U3223109|U3223109]] # [[/Workplace mental health training/]] - What is WMHT, what techniques are used, and what are the impacts? - [[ArtOfHappiness]] # [[/Zoom fatigue/]] - What is Zoom fatigue, what causes it, what are its consequences, and what can be done about it? - [[User:MyUserName|MyUserName]] ==Motivation and emotion== # [[/Financial investing, motivation, and emotion/]] - What role does motivation and emotion play in financial investing? - [[U3217287|U3217287]] # [[/Hostage negotiation, motivation, and emotion/]] - What role does motivation and emotion play in hostage negotiation? - [[User:U3213549|U3213549]] # [[/Money priming, motivation, and emotion/]] - What is the effect of money priming on motivation and emotion? - [[User:MyUserName|MyUserName]] # [[/Motivational dimensional model of affect/]] - What is the motivational dimensional model of affect and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Napping, motivation, and emotion/]] - What are the motivational and emotional effects of napping? - [[User:MyUserName|MyUserName]] # [[/Overchoice, emotion, and motivation/]] - What are the emotional and motivational effects of overchoice? - [[User:MyUserName|MyUserName]] # [[/Patience and impatience/]] - What are the psychological causes and consequences of patience and impatience? - [[User:MyUserName|MyUserName]] # [[/Reward system, motivation, and emotion/]] - What role does the reward system play in motivation and emotion? - [[User:U3162201|U3162201]] [[Category:Motivation and emotion/Book/2022]] funogx8eg060divdq1ajxj71xcvkhr4 2412501 2412498 2022-08-07T10:54:26Z U3211603 2947419 Changed the Selected Topic from Burnout to Zoom Fatigue wikitext text/x-wiki {{/Banner}} ==Motivation== # [[Academic help-seeking]] - What are the barriers and enablers of AHS and how can AHS be fostered? - [[User:MyUserName|MyUserName]] # [[/Academic self-regulation/]] - What is academic self-regulation, why does it matter, and how can it be fostered? - [[U3216563]] # [[/Actively open-minded thinking/]] - How can AOT be used to improve human performance? - [[User:MyUserName|MyUserName]] # [[/Active transport motivation/]] - What motivates use of active transport and how can people be encouraged to use it? - [[User:MyUserName|MyUserName]] # [[/Antidepressants and motivation/]] - What are the effects of popular antidepressants on motivation? - [[User:U3222363|U3222363]] # [[/Approach motivation/]] - What is approach motivation and how does it lead to behaviour? - [[User:U3189370|U3189370]] # [[/Behavioural economics and motivation/]] - What aspects of motivation theory are useful in behavioural economics? - [[User:U3141987|U3141987]] # [[/Behavioural model of health services/]] - What is the BMHS and how can it be used? - SoSilverLibby # [[/Beneficence as a psychological need/]] - What is beneficence and what are its implications as a psychological need? - [[User:MyUserName|CaitlinEmc]] # [[/Brief motivational interviewing as a health intervention/]] - How can brief motivational interviewing be used as a health intervention? - [[User:MyUserName|MyUserName]] # [[/Choice overload/]] - What is choice overload? What is the optimal amount of choice? - [[UserGeorgiaFairweather|GeorgiaFairweather]] # [[/Chunking and goal pursuit/]] - How does chunking affect goal pursuit? - [[User:MyUserName|MyUserName]] # [[/Cognitive entrenchment/]] - What is cognitive entrenchment and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[/Climate change helplessness/]] - How does learned helpless impact motivation to engage in behaviours to limit climate change? - [[User:MyUserName|MyUserName]] # [[/Closeness communication bias/]] - What is the CCB, why does it occur, and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Commitment bias/]] - What motivates escalation of commitment even it does not lead to desirably outcomes? - [[User:MyUserName|MyUserName]] # [[/Conspiracy theory motivation/]] - What motivates people to believe in conspiracy theories? - [[User:KingMob221|KingMob221]] # [[/Construal level theory/]] - What is construal level theory and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Courage motivation/]] - What is courage, what motivates courage, and how can courage be enhanced? -[[User:Hanarose123|Hanarose123]] # [[/Death drive/]] - What is the death drive and how can it be negotiated? - [[User:U3086459|U3086459]] # [[Motivation and emotion/Book/2022/Drugs-violence nexus and motivation Atu3202070|Drugs-violence nexus and motivation]] - What is the role of motivation in the drugs-violence nexus? - [[Atu3202070|Atu3202070]] # [[/Episodic future thinking and delay discounting/]] - What is the relationship between between EFT and DD? - [[User:MyUserName|MyUserName]] # [[/Episodic memory and planning/]] - What role does episodic memory play in planning? - [[User:MyUserName|U3246310]] # [[/Equity theory/]] - What is equity theory and how can it be applied? - [[EKS2001|EKS2001]] # [[/ERG theory/]] - What is Alderfer's ERG theory? - [[User:MyUserName|MyUserName]] # [[/Frame of reference and motivation/]] - How does frame of reference affect motivation? - [[User:MyUserName|MyUserName]] # [[/Freedom and motivation/]] - What is the effect of freedom on motivation? - [[Cedevlin9|Cedevlin9]] # [[/Fully functioning person/]] - What is a FFP and how can full functioning be developed? - [[User:Sebastian Armstrong|Sebastian Armstrong]] # [[/Functional fixedness/]] - What is functional fixedness and how can it be overcome? - [[User:U3214117|U3214117]] # [[/Functional imagery training/]] - What is FIT and how can it be applied? - [[User:MyUserName|MyUserName]] # [[/Gamification and work motivation/]] - How can gamification enhance work motivation? - [[U3211125|U3211125]] # [[/Giving up goals/]] - When should we give up goals and when should we persist? - [[User:MyUserName|U3161584]] # [[/Green prescription motivation/]] - What motivates green prescription compliance? - [[User:Earthxangel|Earthxangel]] # [[/Health belief model/]] - What is the HBM and how can it be used to enhance motivation for health-promoting behaviour? - [[SoSilverLibby]] # [[/Help-seeking among boys/]] - What are the barriers to help-seeking for boys and what motivates them to seek help? - [[User:BradMcGrath|BradMcGrath]] # [[/Hidden costs of reward/]] - What are the hidden costs of motivating by reward? - [[User:MyUserName|MyUserName]] # [[/Hijack hypothesis of drug addiction/]] - What is the hijack hypothesis, what is the evidence, and how does it help to understand drug addiction? - [[U3218292|U3218292]] # [[/Honesty motivation/]] - What motivates honesty? - [[User:U3200859|U3200859]] # [[/Humour, leadership, and work/]] - What role does humour play in effective leadership in the workplace? - [[User:U3210264|U3210264]] # [[/IKEA effect/]] - What is the IKEA effect and how can it be applied? - [[U3216963|U]]3216963 # [[/Intertemporal choice/]] - What are intertemporal choices and how can they be effectively negotiated? - [[User:MyUserName|MyUserName]] # [[/Kindness motivation/]] - What motivates kindness? - u3205429 # [[/Motivational music and exercise/]] - How can music be used to help motivate exercise? - [[User:MyUserName|U3183466]] # [[/Novelty-variety as a psychological need/]] - What is novelty-variety and what are its implications as a psychological need? - [[User:MyUserName|MyUserName]] # [[/Nucleus accumbens and motivation/]] - What role does the nucleus accumbens play in motivation? - [[User:U3213250|U3213250]] # [[/Perfectionism/]] - What motivates perfectionism? Is perfectionism good or bad? How can it be managed? - [[User:AEMOR|AEMOR]] # [[/Physiological needs/]] - How do human's physiological needs affect motivation? - [[U3203655]] # [[/Protection motivation theory and COVID-19/]] - How does PMT apply to managing COVID-19? - [[User:U3200956|U3200956]] # [[/Relative deprivation and motivation/]] - What is the effect of relative deprivation on motivation? - [[User:U3191574 (PHP)|U3191574 (PHP)]] # [[/Retrospective regret/]] - What is the motivational role of retrospective regret? - [[User:Will-U3214082|Will-U3214082]] # [[/Revenge motivation/]] - What motivates revenge and how does it affect us? - [[User:U3216654|U3216654]] # [[/Self-efficacy and academic achievement/]] - What role does self-efficacy play in academic achievement? - [[User:U943292|U943292]]a # [[/Self-efficacy and achievement/]] - What role does self-efficacy play in achievement outcomes? - [[User:U3216513mt|U3216513mt]] # [[/Sexual harassment at work motivation/]] - What motivates sexual harassment at work and what can be done about it? - [[User:U3037979|U3037979]] # [[/Signature strengths/]] - What are signature strengths and how can they be applied? - [[User:MyUserName|MyUserName]] # [[/Social cure/]] - What is the social cure and how can it be applied? - [[User:U3215976|U3215976]] # [[/System justification theory/]] - What is SJT, how does it affect our lives, and what can be done about it? - [[User:MyUserName|MyUserName]] # [[/Stretch goals/]] - What are stretch goals? Do they work? - [[User:MyUserName|MyUserName]] # [[/Sublimation/]] - What is sublimation and how can it be fostered? - [[User:MyUserName|MyUserName]] # [[/Survival needs and motivation/]] - What are survival needs and how do they influence motivation? - [[User:U3148161|U3148161]] # [[/Task initiation/]] - What are the challenges with task initiation and how to get get started? - [[User:MyUserName|MyUserName]] # [[/Theoretical domains framework/]] - What is the TDF and how can be used to guide behaviour change? - [[User:MyUserName|MyUserName]] # [[/Time and motivation/]] - What is the effect of time on motivation? - [[User:Lturner2311|Lturner2311]] # [[/Time management/]] - How can one's time be managed effectively? - [[User:CNK.20|CNK.20]] # [[/To-do lists/]] - Are to-do lists a good idea? What are their pros and cons? How can they be used effectively? - [[User:U3207458|U3207458]] # [[/Uncertainty avoidance/]] - What is uncertainty avoidance, why does it occur, and what are its consequences? - [[User:Franklin Brightt|Franklin Brightt]] # [[/Urgency bias and productivity/]] - What is the impact of urgency bias on productivity and what can be done about it? - U3055143 # [[/Vocational identity/]] - What is vocational identity and how does it develop? - [[User:MyUserName|MyUserName]] # [[/Volunteer tourism motivation/]] - What motivates volunteer tourism? - [[User:U962051|U962051]] # [[/Wanting and liking/]] - What are the similarities and differences between wanting and liking, and what are the implications? - [[User:MyUserName|MyUserName]] # [[/Work breaks, well-being, and productivity/]] - How do work breaks affect well-being and productivity? - [[User:MyUserName|U3215603]] # [[/Work and flow/]] - What characteristics of work can produce flow and how can flow at work be fostered? - [[User:U3213441|U3213441]] ==Emotion== # [[/Animal emotion/]] - What is the emotional experience of animals? - [[U3216502]] # [[/Attributions and emotion/]] - How do attributions affect emotion? - [[User:MyUserName|MyUserName]] # [[/Autonomous sensory meridian response and emotion/]] - What emotions are involved in ASMR experiences and why do they occur? - [[User:U3186959|U3186959]] # [[/Benzodiazepines and emotion/]] - What are the effects of benzodiazepines on emotion? - [[User:FulaAjeo22|FulaAjeo22]] # [[/Bewilderment/]] - What is bewilderment and how can it be dealt with? - [[User:MyUserName|MyUserName]] # [[/Burnout/]] - What is burnout and how can be it be managed and prevented? - [[User:MyUserName|MyUserName]] # [[/Cognitive dissonance reduction/]] - What strategies do people use to reduce cognitive dissonance and how effective are they? - [[User:Tatjurate|Tatjurate]] # [[/Colonisation and emotion in Australia/]] - What are the emotional responses to colonisation in Australia? - [[User:Micabaker1|Micabaker1]] # [[/Compassion/]] - What is compassion, what are its pros and cons, and how can it be fostered? - u3203545 # [[/Connection to country and well-being/]] - What is the relationship between connection to country and well-being? - [[User:MyUserName|MyUserName]] # [[/Contempt/]] - What is contempt, what causes it, and how can it be managed? - [[User:MyUserName|u3219905]] # [[/Core emotions/]] - What are the core emotions and what is their function? U3203140 # [[/Creative arts and trauma/]] - How can creative arts help in dealing with trauma? - [[MyUserName|SashaBrooksby]] # [[/Cultural influences on shame, guilt, and pride/]] - How does culture influence shame, guilt, and pride? - [[User:Tamika Afeaki|Tamika Afeaki]] # [[/Default mode network and the self/]] - What is the relationship between the DMN and the self? - [[User:MyUserName|MyUserName]] # [[/Difficult conversations and emotion/]] - What communication and emotional skills are needed to successfully negotiate difficult conversations? - [[User:u3158968|u3158968]] # [[/Disappointment/]] - What is disappointment, what causes disappointment, and how can disappointment be managed? - [[User:U3216256|U3216256]] # [[/DMT and spirituality/]] - How can DMT facilitate spiritual experiences? - [[DenniseSoleymani]] # [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? - [[User:MyUserName|MyUserName]] # [[/Ecological grief/]] - What is ecological grief and what can be done about it? - [[User:Brewerjr|Brewerjr]] # [[/Ecopsychology and stress/]] - How can ecopsychology help to explain and deal with stress? - [[User:MyUserName|MyUserName]] # [[/Embarrassment/]] - What is embarrassment, what causes it, and how can it be managed? - u3190353 # [[/Emotional intelligence training/]] - How can emotional intelligence be trained? - Eimilerous22 # [[/Emotion knowledge/]] - What is emotion knowledge and how can it be developed? - [[User:GabbieUC|GabbieUC]] # [[/Emotion across the lifespan/]] - How does emotion develop across the lifespan? - u3230861 # [[/Endocannabinoid system and emotion/]] - What is the role of the endocannabinoid system in emotion? - [[User:RWilliams12|Rwilliams12]] # [[/Environmental grief/]] - What is eco-grief, its causes and consequences, and what can be done? - [[User:Gabrielle Eagling|Gabrielle Eagling]] # [[/Exercise and endocannabinoids/]] - What is the relationship between exercise and the endocannabinoid system? - [[User:MyUserName|MyUserName]] # [[/Expressive suppression and emotion regulation/]] - What is the role of expressive suppression in emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Fairness and emotion/]] - What is the relation between fairness and emotion? - [[User:MyUserName|MyUserName]] # [[/Fatigue and emotion/]] - What is the effect of fatigue on emotion and what can be done about it? - [[User:Lewis.Kusk|Lewis.Kusk]] # [[/Fear/]] - What is fear, what causes it, and how can it be managed? - [[User:Icantchooseone|Icantchooseone]] # [[/Fear of working out/]] - What is FOWO and how can it be overcome? - [[User:MyUserName|MyUserName]] # [[/Fundamental attribution error and emotion/]] - What is the relationship between the FAE and emotion? - [[User:MyUserName|MyUserName]] # [[/Gratitude and subjective wellbeing/]] - What is the relationship between gratitude and subjective wellbeing? - [[User:MyUserName|MyUserName]] # [[/Gloatrage/]] - What is gloatrage, what causes it, and what are its consequences? - [[User:MyUserName|MyUserName]] # [[/Heart rate variability and emotion regulation/]] - What is the relationship between HRV and emotion regulation? - [[User:MyUserName|MyUserName]] # [[/Hedonic adaptation prevention model/]] - What is the HAP model and how can it be applied? - [[User:Lyndel Lemon|Lyndel Lemon]] # [[/Humility/]] - What is humility, what causes it, and is it desirable? - [[User:MyUserName|MyUserName]] # [[/Hypomania and emotion/]] - What are the emotional characteristics of hypomania? - [[User:Alec.cortez|Alec.cortez]] # [[/Impact bias/]] - What is impact bias, what causes it, what are its consequences, and how can it be avoided? - [[User:MyUserName|MyUserName]] # [[Indigenous Australian emotionality]] - In what ways is emotionality experienced by Indigenous Australian people? - [[User:MyUserName|MyUserName]] # [[/Indigenous Australian mindfulness/]] - How has Indigenous Australian culture traditionally conceived of, and practiced, mindfulness? - [[User:MyUserName|MyUserName]] # [[/Inspiration/]] - What is inspiration, what causes it, what are its consequences, and how can it be fostered? - [[User:MyUserName|u3227354]] # [[/Insular cortex and emotion/]] - What role does the insular cortex play in emotion? - [[User:U3190094|U3190094]] # [[/Interoception and emotion/]] - What is the relationship between interoception and emotion? - [[User:MyUserName|MyUserName]] # [[/Kama muta/]] - What is kama muta, what are its effects, and how can it be fostered? - [[User:U3183521|U3183521]] # [[/Linguistic relativism and emotion/]] - What is the role of linguistic relativism in emotion? - [[User:U3119310|U3119310]] # [[/Menstrual cycle mood disorders/]] - What causes menstrual cycle mood disorders and how can they be managed? - [[User:MyUserName|U3217109]] # [[/Mindfulness and creativity/]] - How can mindfulness enhance creativity? - [[CaityDcr1603]] # [[/Mindful self-care/]] - What is mindful self-care, why does it matter, and how can it be developed? - [[User:clairelogan|clairelogan]] # [[/Mixed emotions/]] - What are mixed emotions, what causes them, and how can they be managed? - [[User:MyUserName|u3210490]] # [[/Mudita/]] - What is mudita and how can it be developed? - [[User:MyUserName|MyUserName]] # [[/Natural disasters and emotion/]] - How do people respond emotionally to natural disasters and how can they be supported? -[[User:U3148366_Chris|U3148366_Chris]] # [[/Nature therapy/]] - What is nature therapy and how can it be applied? - Ana028 # [[/Narcissism and emotion/]] - What is the relationship between narcissism and emotion? - [[User:A Super Villain|A Super Villain]] # [[/Narrative therapy and emotion/]] - What is the role of emotion in narrative therapy? - [[User:MyUserName|MyUserName]] # [[/Needle fear/]] - How does needle fear develop, what are its consequences, and what can be done about it? - [[User:U3166273|U3166273]] # [[/Positivity ratio/]] - What is the positivity ratio and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Post-traumatic stress disorder and emotion/]] - What is the effect of PTSD on emotion? - [[User:JorjaFive|JorjaFive]] # [[/Psychological distress/]] - What is PD, what are the main types, and how can they be managed? - [[User:U3190773|U3190773]] # [[/Psychological trauma/]] - What causes psychological trauma, what are the consequences, and how can people recover from psychological trauma? - [[User:U3210431|U3210431]] # [[/Psilocybin assisted psychotherapy/]] - How can psilocybin be used to assist psychotherapy? - [[User:U3083720|U3083720]] # [[/Rational compassion/]] - What is rational compassion and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? - [[User:MyUserName|MyUserName]] # [[/Religiosity and coping/]] - What is the relationship between religiosity and coping? - [[User:MyUserName|MyUserName]] # [[/Resentment/]] - What is resentment, what causes it, and what are its consequences? - [[User:U3216389|U3216389]] # [[/Risk-as-feelings/]] - What is the emotional experience of risk and how does it influence decision-making and behaviour? - [[User:MyUserName|MyUserName]] # [[/Self-esteem and culture/]] - What are the cultural influences on self-esteem? - [[User:MyUserName|MyUserName]] # [[/Smiling and emotion/]] - What is the relationship between smiling and emotion? - U3200902 # [[/Social media and suicide prevention/]] - How can social media be used to help prevent suicide? - [[JaimeTegan|JaimeTegan]] # [[/Sorry business/]] - What is sorry business and what role does it play in Indigenous communities in Australia? - Isaacem13 # [[/Stress control mindset/]] - What is a SCM, why does it matter, and how can it be cultivated? - [[User:MyUserName|MyUserName]] # [[/Suffering as emotion/]] - What is the emotional experience of suffering and how can people cope with suffering? - [[User:Brookewin|Brookewin]] # [[/Telemental health/]] - What are the pros and cons of TMH and what are the key ingredients for effective TMH practices? - [[User:MyUserName|MyUserName]] # [[/Topophilia/]] - What is topophilia, how does it develop, and what are the psychological impacts? - [[User:RSPMeredith|RSPMeredith]] # [[/Triumph/]] - What is triumph, what causes it, and how can it be managed? - [[User:Bill.miosge|Bill.miosge]] # [[/Unemployment and mental health/]]: What is the relationship between unemployment and mental health? - [[User:MyUserName|U3216958 - Tiarna.Wilson-Ginn]] # [[/Viewing natural scenes and emotion/]] - What is the effect of viewing natural scenes on emotion and how can this be applied? - [[User:MyUserName|MyUserName]] # [[/Wave metaphor for emotion/]] - In what respects is an ocean wave a helpful metaphor for understanding human emotions? - [[jamieepiper]] # [[/Window of tolerance/]] - What is the window of tolerance and how this concept be used? - [[User:U3223109|U3223109]] # [[/Workplace mental health training/]] - What is WMHT, what techniques are used, and what are the impacts? - [[ArtOfHappiness]] # [[/Zoom fatigue/]] - What is Zoom fatigue, what causes it, what are its consequences, and what can be done about it? - [[User:u3211603|U3211603]] ==Motivation and emotion== # [[/Financial investing, motivation, and emotion/]] - What role does motivation and emotion play in financial investing? - [[U3217287|U3217287]] # [[/Hostage negotiation, motivation, and emotion/]] - What role does motivation and emotion play in hostage negotiation? - [[User:U3213549|U3213549]] # [[/Money priming, motivation, and emotion/]] - What is the effect of money priming on motivation and emotion? - [[User:MyUserName|MyUserName]] # [[/Motivational dimensional model of affect/]] - What is the motivational dimensional model of affect and what are its implications? - [[User:MyUserName|MyUserName]] # [[/Napping, motivation, and emotion/]] - What are the motivational and emotional effects of napping? - [[User:MyUserName|MyUserName]] # [[/Overchoice, emotion, and motivation/]] - What are the emotional and motivational effects of overchoice? - [[User:MyUserName|MyUserName]] # [[/Patience and impatience/]] - What are the psychological causes and consequences of patience and impatience? - [[User:MyUserName|MyUserName]] # [[/Reward system, motivation, and emotion/]] - What role does the reward system play in motivation and emotion? - [[User:U3162201|U3162201]] [[Category:Motivation and emotion/Book/2022]] t1az1y6ragzijkaow4pdkswqd9jcyd5 2 277730 2412404 2410594 2022-08-06T20:17:13Z Jtwsaddress42 234843 wikitext text/x-wiki {{User:Jtwsaddress42/People}} '''[[User:Jtwsaddress42/Bibliography_A|<big>A</big>]]''' {{User:Jtwsaddress42/People/Agre, Peter}} {{User:Jtwsaddress42/People/Arendt,_Detlev}} {{User:Jtwsaddress42/People/Arrehenius,_Svante}} {{User:Jtwsaddress42/People/Aston,_Francis_W.}} {{User:Jtwsaddress42/People/Axelrod, Julius}} {{User:Jtwsaddress42/Includes/Notes_&_Citations}} {{User:Jtwsaddress42/Navigation/Footer Navbar}} bez41snhbsie6nrg93zi8e97mfu4io6 0 279847 2412423 2411252 2022-08-06T22:30:41Z Tamika Afeaki 2947781 title wikitext text/x-wiki {{METP}} {{title|Cultural influences on shame, guilt, and pride - Tamika Afeaki}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] ==See also== * [[Motivation and emotion/Book/2021/Cultural influences on shame, guilt, and pride|Cultural influences on shame, guilt, and pride]] (Book chapter, 2021) tcikqzdyethyuour4ygvivilumd2tsb 2412425 2412423 2022-08-06T22:45:48Z Tamika Afeaki 2947781 wikitext text/x-wiki {{METP}} {{title|Cultural influences on shame, guilt, and pride - Tamika Afeaki}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] ==See also== * [[Motivation and emotion/Book/2021/Cultural influences on shame, guilt, and pride|Cultural influences on shame, guilt, and pride]] (Book chapter, 2021) {{DEFAULTSORT:Motivation_and_emotion/Book/2022/Cultural_influences_on_shame,_guilt,_and_pride - Tamika Afeaki}} pfzr2prgjqotmdozbe9jrxg522bbzvo 2412426 2412425 2022-08-06T22:48:52Z Tamika Afeaki 2947781 wikitext text/x-wiki {{METP}} [[User:Tamika Afeaki|Tamika Afeaki]] {{title|Cultural influences on shame, guilt, and pride - Tamika Afeaki}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] ==See also== * [[Motivation and emotion/Book/2021/Cultural influences on shame, guilt, and pride|Cultural influences on shame, guilt, and pride]] (Book chapter, 2021) {{DEFAULTSORT:Motivation_and_emotion/Book/2022/Cultural_influences_on_shame,_guilt,_and_pride - Tamika Afeaki}} i56gwfjlqutivhfu2l13pt9vtnxfiz9 2412429 2412426 2022-08-06T23:05:59Z Tamika Afeaki 2947781 wikitext text/x-wiki [[User:Tamika Afeaki|Tamika Afeaki]] {{METP}} {{title|Cultural influences on shame, guilt, and pride - Tamika Afeaki}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] ==See also== * [[Motivation and emotion/Book/2021/Cultural influences on shame, guilt, and pride|Cultural influences on shame, guilt, and pride]] (Book chapter, 2021) {{DEFAULTSORT:Motivation_and_emotion/Book/2022/Cultural_influences_on_shame,_guilt,_and_pride -[[User:Tamika Afeaki|Tamika Afeaki]]} 4m0rh4a1rri0lr6gawmv5n2zuv0mnxh 2412433 2412429 2022-08-06T23:09:54Z Tamika Afeaki 2947781 wikitext text/x-wiki {{title|Cultural influences on shame, guilt, and pride - Tamika Afeaki}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] ==See also== * [[Motivation and emotion/Book/2021/Cultural influences on shame, guilt, and pride|Cultural influences on shame, guilt, and pride]] (Book chapter, 2021) {{DEFAULTSORT:Motivation_and_emotion/Book/2022/Cultural_influences_on_shame,_guilt,_and_pride -[[User:Tamika Afeaki|Tamika Afeaki]]} 1ludw7em35n9au69z9cchs8fjxl4pjr 0 279849 2412491 2349032 2022-08-07T06:38:29Z 139.168.115.116 Added template wikitext text/x-wiki {{METP}} ==See also== * [[Motivation and emotion/Book/2021/Gamification and work motivation|Gamification and work motivation]] (Book chapter, 2021) {{title|Chapter title:<br>Subtitle?}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] cs2lqkd0wohnh10wpon4bdevbpd6uap 2412492 2412491 2022-08-07T06:39:38Z 139.168.115.116 wikitext text/x-wiki ==See also== * [[Motivation and emotion/Book/2021/Gamification and work motivation|Gamification and work motivation]] (Book chapter, 2021) {{title|Chapter title:<br>Subtitle?}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] q42iplv3t6lthppkrac4stoenp6xz2u 2412493 2412492 2022-08-07T06:40:39Z 139.168.115.116 changed title wikitext text/x-wiki ==See also== * [[Motivation and emotion/Book/2021/Gamification and work motivation|Gamification and work motivation]] (Book chapter, 2021) {{title|Gamification and Workplace Motivation:<br>Subtitle?}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] 31itouea2aoeag7t9c5rbi25h30z72q 2 280897 2412367 2412339 2022-08-06T13:56:49Z Guy vandegrift 813252 wikitext text/x-wiki Journals: [[User:Guy vandegrift/2021|2021]] [[:Category:Guy vandegrift/Yearbook|Pageviews]]: [[User:Guy_vandegrift/2020#2020 and before|2020]] · [[User:Guy_vandegrift/2021#2021 Pageviews|2021]] · [[User:Guy_vandegrift/2022#Pageviews|2022]]· ----- BIG PROBLEM AT [[User:Guy vandegrift/AAAListen]] ----- *[[Information_theory/Permutations_and_combinations]]. If this works well, send a link to [[User:Guy vandegrift/2022/Proposal]] *[[w:Talk:Permutation#A_nasty_organization_problem_we_need_to_fix]] *[[Sing free]] **[[Sing free/Amazing Grace]] **[[Sing_free/Great_Gate_of_Kiev_(ear_training)]] Go to readme at spreadsheet folder '''audacity file organ''' *[[Special:PrefixIndex/Draft:Sing_free]] **[[Draft:Sing free/Voice training]] *[[Draft:Beat (acoustics)]] **[[w:User:Guy_vandegrift/sandbox/02#List]] **[[Sing_free/List_of_musical_intervals_(ear_training)]] <big>'''START HERE'''</big> DON'T LOSE [[special:Permalink/2383304#Backup_LilyPond_Great_Gate_Kiev]] DON'T FORGET ABOUT [[Python/Prime factorization]] ----- ===Bi- and Multi-nomial pages to write=== ====[[Information theory/Permutations and combinations]] ... [[Draft:Information theory/Permutations and combinations|(see Draft]] ... [[Template:Information theory/Permutations and combinations|& Template)]]==== *{{Doing}} =====[[Template:Information_theory/Shannon_entropy]]===== {{:Special:PrefixIndex/Information_theory}} [https://en.wikiversity.org/wiki/Special:PrefixIndex?prefix=Draft%3AInformation+theory&namespace=0 PrefixIndex = Draft:Information theory]: *[[Draft:Information theory/Permutations and combinations]] *[[Draft:Information theory/Shannon entropy]] *[[Draft:Information theory/Shannon entropy/a]] ----- ====[[Combinatorics/Multinomial coefficients]]==== Mention two interpretations (only 2!). Provide simplest (related to information theory). Briefly present the conventional using rule of product. Link to images and other proofs all over wikiworld. OR DELETE!!! {{:Special:PrefixIndex/Combinatorics}} ----- #{{See also|w:Combinatorial principles|b:Probability/Combinatorics#What_is_combinatorics?}} #{{See also|w:Rule of product|b:Probability/The Counting Principle|w:Tree diagram (probability theory)}} #{{See also|w:Binomial theorem|w:Multinomial theorem|b:Probability/Combinatorics#Binomial_and_multinomial_coefficients}} :::{{See also|w:Catalan number|w:Lattice path|w:Binomial theorem}} ====[[Combinatorics/Stars & Bars]]==== [https://math.stackexchange.com/questions/3758836/stars-and-bars-but-with-distinct-objects/3758849 colored balls stackexchange] [https://math.stackexchange.com/questions/2593565/stars-and-bars-approach red and blue] *[[Combinatorics/Binomial coefficients]]{{done|Not written by me. Is advanced.}} {{cot|stars bars and beyond (draft)}} :<math>\binom N K =\binom{N\text{ objects}}{K\text{ bars}}</math> Since there is one more bin than bars, <math>k=K-1</math>Example with <math>N=7,\quad K=2</math>:<br>{{spaces|2}} {{Huge|{{spaces|2}}&#124;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}&#124;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}}} ====Other to do==== *[[Mathematical induction]] needs major work. ====[[Combinatorics/Images]]==== Image collection. Include link to text alternative. ====Allow zero "things" in a bin==== Put <math>n_0</math> into <math>k</math> with bins a minimum of <math>0</math> things per bin. <math>K=k-1</math> and <math>N=K+n_0\Rightarrow N=n_0+k-1</math> <math>\Rightarrow</math><math>\binom N K =\binom{n_0+k-1}{k-1}</math> ====Demand at least 1 "thing" in a bin==== :*Put <math>n_1</math> into <math>k</math> with bins a minimum of <math>1</math> thing per bin. <math>n_1=n_0+k</math> <math>\binom N K = \binom{n_1-1}{k-1}</math> {{Huge|{{spaces|2}}&deg; &#124;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}&deg; &#124;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}&bull; &deg;{{spaces|2}}}} {{cob}} ===Other links=== [[MyOpenMath/Three types of test questions]] *[[:Category:User:Guy vandegrift/Drafts]] *[[:Category:User:Guy vandegrift/Navigation]] ----- A well developed resource I should add to: {{:Special:PrefixIndex/Tensors}} ----- *[https://en.wikiversity.org/w/index.php?target=Guy+vandegrift&namespace=10&tagfilter=&newOnly=1&start=&end=&limit=50&title=Special%3AContributions My templates] ==TO DO== #[[:File:Klaviatur-wIKI.jpg]] needs conversion into two svg files. Use to improve [[w:Piano_key_frequencies]]. From [[w:Musical_keyboard]] and [[w:Keyboard matrix circuit]] it looks like we need a 5 octave version. But which octaves? #[[Free singing lessons]] # Jot ideas for proposal at [[/Proposal]] perhaps link it to Problem at end of [[Information theory/Permutations and combinations]] #*[[:File:5-choose-3 product rule.svg]] would make a good project with an advanced undergraduate student. # Finish [[Information theory/Permutations and combinations]] . Unfortunately, sister link at [[w:Permutations]] is already taken by . # [[Combinatorics]] needs [[Template:BookCat]] enhancement # [[Combinatorics/Rule of product]] needs to be finished # [[Combinatorics/Multinomials]] will have formal proofs and a collection of images # [[Mathematical induction]] needs to have two examples of induction: permutations and combinations #Finish the phasor/poynting sequence at [[:Category:MyOpenMath/Electromagnetism]] #Write essay for and setup transclusion for [[:category:Quizbank/Unfinished]] #After 2022 check images on [[w:Stars and bars (combinatorics)]] #Finish [[w:simple:Radiation pressure]] #[[Draft:Introduction_to_quantum_mechanics]] #Go back to the beginning of E&M and get one unit of TF reading questions completed. ==Done== *3 Jan 2022 [[Combinatorics/Binomial_coefficients]]^{[https://en.wikiversity.org/w/index.php?title=Combinatorics%2FBinomial_coefficients&type=revision&diff=2366084&oldid=1834808 Cleanup]} *8 Jan 2022 [[w:Mathematical induction]]^{[https://simple.wikipedia.org/w/index.php?title=Mathematical_induction&type=revision&diff=7953423&oldid=7120309 Cleanup]}{{Partly done|still needs cleaning up}} *24 Jan 2022 Created table to replace the deprecated image, [[:File:Tabela de Relações Trigonométricas.PNG]] See also: [[w:simple:special:permalink/7984902]], [[w:ca:special:permalink/29331416]], and [[c:special:permalink/624159454]] *2 Feb 2022 Added comment that Cocolmelon's "Ants and the Grasshopper" is to the tune of [https://en.wikipedia.org/w/index.php?title=Red_River_Valley_(song)&diff=prev&oldid=1070383055 w:Red River Valley] *20 Feb 2022 Imported [[Template:Magnify icon]] *26 Feb 2022 Simplified Red River Valley from [[special:permalink/2378796]] *4 Mar 2022 [https://simple.wikipedia.org/w/index.php?title=Hertz&type=revision&diff=8087736&oldid=7897066 Simple English Hz, cps table] *5 Mar 2022 Added [https://en.wikipedia.org/w/index.php?title=Red_River_Valley_(song)&diff=prev&oldid=1075389296 Red River Valley] lilypond and sister link to [[Wikipedia:Red River Valley (song)]]. *6 Mar 2022 [[Sing free/Prelude and Fugue in C major (ear training)]] with sister link to [[w:Just intonation]] *7 Mar 2022 Amazing Grace Lilypond script posted at [https://en.wikipedia.org/w/index.php?title=Amazing_Grace&oldid=1075696156 Amazing_Grace&oldid=1075696156]. Added sister link/ *3 Jun 2022 [https://en.wikipedia.org/w/index.php?title=Stand_by_Me_%28Ben_E._King_song%29&type=revision&diff=1091412161&oldid=1091349828 Minor copyedit] on [[w:Stand by Me (Ben E. King song)]] *7 July 2022 [https://en.wikipedia.org/w/index.php?title=Dyad_%28music%29&type=revision&diff=1096992061&oldid=994729869 Added trivial '''See also:''' to [[w:Dyad (music)]]] *29 July 2022 [[Python/Prime factorization]] with sister link posted on [[w:Trial division]]. ==Pageviews== ===[https://pageviews.toolforge.org/?project=en.wikibooks.org&platform=all-access&agent=user&redirects=0&range=latest-90&pages=Statics/Moment_of_Inertia_(contents)|Probability/Combinatorics|Probability/Conditional_Probability Wikibooks Pageviews:]=== [[b:Statics/Moment of Inertia (contents)]]^{[https://en.wikibooks.org/w/index.php?title=Statics%2FMoment_of_Inertia_%28contents%29&type=revision&diff=3355995&oldid=2674427 added-2-figures]}{{spaces|3}}[[b:Probability/Conditional Probability]]^{[[b:special:permalink/1658724|modified-this-version]]}{{spaces|3}} [[b:Probability/Combinatorics]]^{[[b:special:permalink/3547462|modified-this-version]]} ===[https://pageviews.wmcloud.org/?project=simple.wikipedia.org&platform=all-access&agent=user&redirects=0&range=latest-90&pages=Weighted_average|Radiation_pressure|Pascal%27s_Triangle|Hertz Simple Wikipedia Pageviews:]=== Constructing-[[w:simple:Radiation pressure]]{{spaces|3}} [[w:simple:Weighted average]]{{spaces|3}} [[w:simple:Pascal's Triangle]]{{spaces|3}} [[w:simple:Hertz]] ===[https://pageviews.wmcloud.org/?project=en.wikiversity.org&platform=all-access&agent=user&redirects=0&range=latest-90&pages=Sing_free|Sing_free/Twinkle|Sing_free/Red_River_Valley|Sing_free/Major_sixth_M6|Sing_free/Prelude_and_Fugue_in_C_major_(ear_training)|Sing_free/Four_octave_scale|Sing_free/Amazing_Grace|Python/Prime_factorization Wikiversity Pageviews:]=== [[Sing free]]{{spaces|3}} [[Sing free/Red River Valley]]{{spaces|3}} [[Sing free/Twinkle]]{{spaces|3}} [[Sing free/Major sixth M6]]{{spaces|3}} [[Sing free/Four octave scale]]{{spaces|3}} [[Sing free/Prelude and Fugue in C major (ear training)]]{{spaces|3}} [[Sing free/Amazing Grace]]{{spaces|3}} [[Python/Prime_factorization]]{{spaces|3}} [[]]{{spaces|3}} [[]]{{spaces|3}} [[Category:Guy vandegrift/Yearbook]] ==Subpages== {{Subpages/List}} {{Seealso|Sing free}} lpo5yni0gwmdmwjkmfenfbq8zw87bgx 2412373 2412367 2022-08-06T14:02:12Z Guy vandegrift 813252 wikitext text/x-wiki Journals: [[User:Guy vandegrift/2021|2021]] [[:Category:Guy vandegrift/Yearbook|Pageviews]]: [[User:Guy_vandegrift/2020#2020 and before|2020]] · [[User:Guy_vandegrift/2021#2021 Pageviews|2021]] · [[User:Guy_vandegrift/2022#Pageviews|2022]]· ----- '''[[WikiJournal Preprints/Displaying roughness in musical intervals]]''' BIG PROBLEM AT [[User:Guy vandegrift/AAAListen]] ----- *[[Information_theory/Permutations_and_combinations]]. If this works well, send a link to [[User:Guy vandegrift/2022/Proposal]] *[[w:Talk:Permutation#A_nasty_organization_problem_we_need_to_fix]] *[[Sing free]] **[[Sing free/Amazing Grace]] **[[Sing_free/Great_Gate_of_Kiev_(ear_training)]] Go to readme at spreadsheet folder '''audacity file organ''' *[[Special:PrefixIndex/Draft:Sing_free]] **[[Draft:Sing free/Voice training]] *[[Draft:Beat (acoustics)]] **[[w:User:Guy_vandegrift/sandbox/02#List]] **[[Sing_free/List_of_musical_intervals_(ear_training)]] <big>'''START HERE'''</big> DON'T LOSE [[special:Permalink/2383304#Backup_LilyPond_Great_Gate_Kiev]] DON'T FORGET ABOUT [[Python/Prime factorization]] ----- ===Bi- and Multi-nomial pages to write=== ====[[Information theory/Permutations and combinations]] ... [[Draft:Information theory/Permutations and combinations|(see Draft]] ... [[Template:Information theory/Permutations and combinations|& Template)]]==== *{{Doing}} =====[[Template:Information_theory/Shannon_entropy]]===== {{:Special:PrefixIndex/Information_theory}} [https://en.wikiversity.org/wiki/Special:PrefixIndex?prefix=Draft%3AInformation+theory&namespace=0 PrefixIndex = Draft:Information theory]: *[[Draft:Information theory/Permutations and combinations]] *[[Draft:Information theory/Shannon entropy]] *[[Draft:Information theory/Shannon entropy/a]] ----- ====[[Combinatorics/Multinomial coefficients]]==== Mention two interpretations (only 2!). Provide simplest (related to information theory). Briefly present the conventional using rule of product. Link to images and other proofs all over wikiworld. OR DELETE!!! {{:Special:PrefixIndex/Combinatorics}} ----- #{{See also|w:Combinatorial principles|b:Probability/Combinatorics#What_is_combinatorics?}} #{{See also|w:Rule of product|b:Probability/The Counting Principle|w:Tree diagram (probability theory)}} #{{See also|w:Binomial theorem|w:Multinomial theorem|b:Probability/Combinatorics#Binomial_and_multinomial_coefficients}} :::{{See also|w:Catalan number|w:Lattice path|w:Binomial theorem}} ====[[Combinatorics/Stars & Bars]]==== [https://math.stackexchange.com/questions/3758836/stars-and-bars-but-with-distinct-objects/3758849 colored balls stackexchange] [https://math.stackexchange.com/questions/2593565/stars-and-bars-approach red and blue] *[[Combinatorics/Binomial coefficients]]{{done|Not written by me. Is advanced.}} {{cot|stars bars and beyond (draft)}} :<math>\binom N K =\binom{N\text{ objects}}{K\text{ bars}}</math> Since there is one more bin than bars, <math>k=K-1</math>Example with <math>N=7,\quad K=2</math>:<br>{{spaces|2}} {{Huge|{{spaces|2}}&#124;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}&#124;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}}} ====Other to do==== *[[Mathematical induction]] needs major work. ====[[Combinatorics/Images]]==== Image collection. Include link to text alternative. ====Allow zero "things" in a bin==== Put <math>n_0</math> into <math>k</math> with bins a minimum of <math>0</math> things per bin. <math>K=k-1</math> and <math>N=K+n_0\Rightarrow N=n_0+k-1</math> <math>\Rightarrow</math><math>\binom N K =\binom{n_0+k-1}{k-1}</math> ====Demand at least 1 "thing" in a bin==== :*Put <math>n_1</math> into <math>k</math> with bins a minimum of <math>1</math> thing per bin. <math>n_1=n_0+k</math> <math>\binom N K = \binom{n_1-1}{k-1}</math> {{Huge|{{spaces|2}}&deg; &#124;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}&deg; &#124;{{spaces|2}}&bull;{{spaces|2}}&bull;{{spaces|2}}&bull; &deg;{{spaces|2}}}} {{cob}} ===Other links=== [[MyOpenMath/Three types of test questions]] *[[:Category:User:Guy vandegrift/Drafts]] *[[:Category:User:Guy vandegrift/Navigation]] ----- A well developed resource I should add to: {{:Special:PrefixIndex/Tensors}} ----- *[https://en.wikiversity.org/w/index.php?target=Guy+vandegrift&namespace=10&tagfilter=&newOnly=1&start=&end=&limit=50&title=Special%3AContributions My templates] ==TO DO== #[[:File:Klaviatur-wIKI.jpg]] needs conversion into two svg files. Use to improve [[w:Piano_key_frequencies]]. From [[w:Musical_keyboard]] and [[w:Keyboard matrix circuit]] it looks like we need a 5 octave version. But which octaves? #[[Free singing lessons]] # Jot ideas for proposal at [[/Proposal]] perhaps link it to Problem at end of [[Information theory/Permutations and combinations]] #*[[:File:5-choose-3 product rule.svg]] would make a good project with an advanced undergraduate student. # Finish [[Information theory/Permutations and combinations]] . Unfortunately, sister link at [[w:Permutations]] is already taken by . # [[Combinatorics]] needs [[Template:BookCat]] enhancement # [[Combinatorics/Rule of product]] needs to be finished # [[Combinatorics/Multinomials]] will have formal proofs and a collection of images # [[Mathematical induction]] needs to have two examples of induction: permutations and combinations #Finish the phasor/poynting sequence at [[:Category:MyOpenMath/Electromagnetism]] #Write essay for and setup transclusion for [[:category:Quizbank/Unfinished]] #After 2022 check images on [[w:Stars and bars (combinatorics)]] #Finish [[w:simple:Radiation pressure]] #[[Draft:Introduction_to_quantum_mechanics]] #Go back to the beginning of E&M and get one unit of TF reading questions completed. ==Done== *3 Jan 2022 [[Combinatorics/Binomial_coefficients]]^{[https://en.wikiversity.org/w/index.php?title=Combinatorics%2FBinomial_coefficients&type=revision&diff=2366084&oldid=1834808 Cleanup]} *8 Jan 2022 [[w:Mathematical induction]]^{[https://simple.wikipedia.org/w/index.php?title=Mathematical_induction&type=revision&diff=7953423&oldid=7120309 Cleanup]}{{Partly done|still needs cleaning up}} *24 Jan 2022 Created table to replace the deprecated image, [[:File:Tabela de Relações Trigonométricas.PNG]] See also: [[w:simple:special:permalink/7984902]], [[w:ca:special:permalink/29331416]], and [[c:special:permalink/624159454]] *2 Feb 2022 Added comment that Cocolmelon's "Ants and the Grasshopper" is to the tune of [https://en.wikipedia.org/w/index.php?title=Red_River_Valley_(song)&diff=prev&oldid=1070383055 w:Red River Valley] *20 Feb 2022 Imported [[Template:Magnify icon]] *26 Feb 2022 Simplified Red River Valley from [[special:permalink/2378796]] *4 Mar 2022 [https://simple.wikipedia.org/w/index.php?title=Hertz&type=revision&diff=8087736&oldid=7897066 Simple English Hz, cps table] *5 Mar 2022 Added [https://en.wikipedia.org/w/index.php?title=Red_River_Valley_(song)&diff=prev&oldid=1075389296 Red River Valley] lilypond and sister link to [[Wikipedia:Red River Valley (song)]]. *6 Mar 2022 [[Sing free/Prelude and Fugue in C major (ear training)]] with sister link to [[w:Just intonation]] *7 Mar 2022 Amazing Grace Lilypond script posted at [https://en.wikipedia.org/w/index.php?title=Amazing_Grace&oldid=1075696156 Amazing_Grace&oldid=1075696156]. Added sister link/ *3 Jun 2022 [https://en.wikipedia.org/w/index.php?title=Stand_by_Me_%28Ben_E._King_song%29&type=revision&diff=1091412161&oldid=1091349828 Minor copyedit] on [[w:Stand by Me (Ben E. King song)]] *7 July 2022 [https://en.wikipedia.org/w/index.php?title=Dyad_%28music%29&type=revision&diff=1096992061&oldid=994729869 Added trivial '''See also:''' to [[w:Dyad (music)]]] *29 July 2022 [[Python/Prime factorization]] with sister link posted on [[w:Trial division]]. ==Pageviews== ===[https://pageviews.toolforge.org/?project=en.wikibooks.org&platform=all-access&agent=user&redirects=0&range=latest-90&pages=Statics/Moment_of_Inertia_(contents)|Probability/Combinatorics|Probability/Conditional_Probability Wikibooks Pageviews:]=== [[b:Statics/Moment of Inertia (contents)]]^{[https://en.wikibooks.org/w/index.php?title=Statics%2FMoment_of_Inertia_%28contents%29&type=revision&diff=3355995&oldid=2674427 added-2-figures]}{{spaces|3}}[[b:Probability/Conditional Probability]]^{[[b:special:permalink/1658724|modified-this-version]]}{{spaces|3}} [[b:Probability/Combinatorics]]^{[[b:special:permalink/3547462|modified-this-version]]} ===[https://pageviews.wmcloud.org/?project=simple.wikipedia.org&platform=all-access&agent=user&redirects=0&range=latest-90&pages=Weighted_average|Radiation_pressure|Pascal%27s_Triangle|Hertz Simple Wikipedia Pageviews:]=== Constructing-[[w:simple:Radiation pressure]]{{spaces|3}} [[w:simple:Weighted average]]{{spaces|3}} [[w:simple:Pascal's Triangle]]{{spaces|3}} [[w:simple:Hertz]] ===[https://pageviews.wmcloud.org/?project=en.wikiversity.org&platform=all-access&agent=user&redirects=0&range=latest-90&pages=Sing_free|Sing_free/Twinkle|Sing_free/Red_River_Valley|Sing_free/Major_sixth_M6|Sing_free/Prelude_and_Fugue_in_C_major_(ear_training)|Sing_free/Four_octave_scale|Sing_free/Amazing_Grace|Python/Prime_factorization Wikiversity Pageviews:]=== [[Sing free]]{{spaces|3}} [[Sing free/Red River Valley]]{{spaces|3}} [[Sing free/Twinkle]]{{spaces|3}} [[Sing free/Major sixth M6]]{{spaces|3}} [[Sing free/Four octave scale]]{{spaces|3}} [[Sing free/Prelude and Fugue in C major (ear training)]]{{spaces|3}} [[Sing free/Amazing Grace]]{{spaces|3}} [[Python/Prime_factorization]]{{spaces|3}} [[]]{{spaces|3}} [[]]{{spaces|3}} [[Category:Guy vandegrift/Yearbook]] ==Subpages== {{Subpages/List}} {{Seealso|Sing free}} o18zj91n5a0o479wbap8ltvljauhiex 0 281095 2412488 2411365 2022-08-07T06:27:39Z Hamish84 1362807 Moving text wikitext text/x-wiki = <ref>'''William Shakespeare''' (bapt. 26 April 1564 – 23 April 1616</ref>A message. = What humanity needs is not any individual approach but a governance powerful body of excellence that has modern technology, knowledge, and freedom they can use to disseminate clear information. Clear information about a new language structure of absolutes beneficial to an International forum, and eventually to reach a Universal status.Its benefits reach toward conceptual language on a planet that speaks more than 7,000 languages. No matter the language spoken the concepts of: Air - Food - Water are recognised. The overall development of conceptual language can only be beneficial and will be as appropriate to Absolutes definitions. Reaching for the Stars might show us the way. Universal Language of Absolutes. "A very grand title but it took many years to explain its value" = Our history. = Born in Scotland in 1927 left school at 14 years of age. Married at 21 years of age and we had two children. We emigrated to New Zealand in 1953 and lived there for approximately thirty years. During our stay there I did a Liberal Studies Course at Canterbury University Christchurch and graduated. We have since had ten books published through Google books on the subject matter at hand and my wife Jean Caldwell McMillan is the co-author to most of the work presented here. My wife Jean was an avid reader of many works on philosophy and psychology. She was influenced by the works of Erich Fromm. Jean died 9th of January 2011. To refresh the original purpose of  our  earlier writings my wife and I  went on an odyssey  looking for any data, ancient or otherwise, on human consciousness, specifically related to Alzheimer’s disease. Now at 95 years of age (well past my used by date) it may well be that I am a candidate with a focus on my own pending dementia. If so, then the theory and the method I now write about is holding it at bay. To address the health of my mind in this way could be the catalyst that retains its own functional activity. The creation of a  semantic template is well documented below. No semantic definition of absolutes or principles can be ill-defined. They are always interconnected, interdependent and infinite. Each configuration constructed by anyone has meaning particular to them, although its value is universal. That  is why it is never personal property! [[File:JimNJean.png|center|thumb|228x228px|Jim and Jean]] = The Beginning. = "The road's half traveled when you know the way" [[File:Tree lined path - geograph.org.uk - 2269906.jpg|center|thumb]] Oxford dictionary definitions: Principle: "A fundamental truth used as a basis of reasoning". Absolute: " Complete - Entire - Perfect - Pure. These particular dictionary given definitions offers us guidelines to ‘existing conditions’ necessary for complementary understanding, and experience. We can only examine that which is real, basic evidence, that is fundamentally true, and we must ‘use’ it, to establish that which is reasonable. The general consensus is that there are no Absolutes. The following material is set out to show the very reverse is true and that everything that is is Absolute. Establish that there are no dichotomies that will leave the primary terms alone to create a semantic template. There are no dichotomies. Mythical dichotomies distort Reality. Everything is: The computer you use today has always existed, it is the arrangement of particles that have materialized it. The subject matter "Universal Language of Absolutes' is promoted to provide a new understanding of spoken language. This understanding was initially constructed by the cognitive experiences of both my wife and myself many years ago. Just like the principle of a jigsaw puzzle, meaning lies significantly in the fact that all pieces of the puzzle are interdependent and interconnected. When completed they provide a picture of the whole. We have endeavoured to produce a picture of the evolutionary process of language in human history because the evolution of language prefixes all modes of thought in human culture. The material directs the reader towards a new view that all that evolves is in a vertical direction, not the linear direction commonly understood. Human consciousness is of itself the phenomenon of evolution and to recognize its existence is part of the process. Shakespeare expressed this succinctly through the voice of Juliet who proclaimed, “a rose by any other name- would smell as sweet.” [[File:Comestible rose in the Laquenexy orchard garden, Moselle, France (01).jpg|thumb|center|237x237px]] === Conceptual language. === My wife and I recognized how profound the extension of this observation would mean conceptually. Of all the languages spoken on this planet, it would be fair to say that all of them would contain the properties of, air, food, and water conceptually, etc. This is a form of consciousness equality that is available to us all. It points to the reality of our constant relation to each other and our existence. We can never exist in a world of individuality, but only in relation to the consciousness of one another. Consequently, that exceptional experience can only be shared superficially. We cannot ‘know’ any other life experiences other than our own introspection. <gallery> File:Einstein 1921 by F Schmutzer - restoration.jpg </gallery>" ''Albert Einstein 1921. We experience our thoughts and feelings as something separate from the rest. A kind of optical delusion of consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us."'' ''Albert Einstein, in One Home, One Family, One Future,p.99'' Einstein came very close. In reality, every human being has a backpack from the day they were conceived. In the backpack every experience in their mother’s womb is experienced. At birth and throughout their lives, everything that happens to them in life is registered and creates their personality. That life with all its experiences can never be known to anyone else, consequently, we can never “know” another person. It creates equality of consciousness that we must understand. We can know details about a person, but that is all. That life is sacrosanct. Who we are really goes beyond normal human experience and into the realm of the Absolute. Werner Karl Heisenberg (physicist). The Heisenberg Uncertainty Principle. As a young layman with no knowledge of Heisenberg but interested in principles it seemed to me that the Uncertainty Principle was just a contradiction in terms. In later years I found that Heraclitus describes life as being in a state of flux a replica of the Uncertainty Principle which in fact can be defined as an absolute state. Within the context of knowing who we are and the backpack we carry our life in, we can never know each individual life as that life experience is singularly their own and sacrosanct. It now seems that the Heisenberg Uncertainty Principle can fall into the category of being an Absolute. Evolution proceeds in advance of our need to evolve. In our pure active state, we are.There is no static end (an abomination) - only beginning. As we cannot know what tomorrow will bring, living with expectations is rather futile. Nature has its own agenda. Zen Koan recorded 1228: 'An instant realization sees endless time. Endless time is as one moment. When one comprehends the endless moment He, or she, realizes the person who is seeing it.' We do not own Space. We do not own Time We do not own Energy We do not own Matter [[File:Universum.jpg|center|thumb]] "What we call the beginning is often the end And to make an end is to make a beginning. The end is where we start from We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time" T.S Eliot = Everything is in scale. = The present moment is the point in which Eternity has placed us – we all live in that moment, and whether we like it or not, we exist in it, experience it, have knowledge of it, and we all share it, measure by measure. There are no dichotomies. Illusion is a measure of Reality, as Stupidity is a measure of Intelligence If one keeps measuring illusion it is an attempted downward spiral to nothingness.There is no opposite to Reality – that illusion is a measure of Reality. There is no such thing as ‘nothing’ in the elemental construction of Homo sapiens. All the innate ‘something’s’ are the fundamentals of our being human and all our experiences. The correct use, and understanding of who we are, is an extension therefrom. Does it require any interpretation on anyones part to say ‘we are? Any attempted denial of that statement would be perverse use of the language, and delusional. === Try saying ‘we are not” === ‘We are’ is the foundation of all affirmation, and within that spectrum, we can know, and be. ‘We are’ is self-evident Truth. We can neither know, nor experience what isn’t. Eternity is the here and now, that is why it is possible to explain the experience of Eternity. Nothing is ever lost in Time. We are located in expansion. ‘twas a moment’s pause,- All that took place within me came and went As in a moment; yet with Time it dwells, And grateful memory, as a thing divine. Wordsworth Prelude, Book V111 We already know – the ''basic'' condition that must exist for us to re-cognise. It is at that moment of pure affirmation, when all that is, is manifest. Unless there was mutual identity we could not know anything. It is why we are urged to evacuate the Platonic cave. Sadly most prefer the shadows rather than confront who they are. We already know – the basic condition that must exist for us to recognise. It is at that moment of pure affirmation, when all that is, is manifest. == Lost Shadows == [[File:People Shadow.JPG|left|thumb]] The shadows move Lost in confusion Lost in despair Imagination shrouds the real Looking back Looking forward Is this the Centre? James Brines. = Basic Principles. = We are all in the business of living and attempting to understand the principles involved in that human process up to the end of life. The implicit principles necessary for life eventually disappear and all measurable criteria pronounce a body to be devoid of life. Throughout historical agreement we know what that means, and we act accordingly on *common knowledge*. We know that dying is a necessary factor of life. It is a Natural law that if we live - we also die. Natural law is Universal, for us to *know* that a body lives; we also *know* that a body’s life will end. Albeit that reports tell us that today millions of people die of disease, starvation, wars, we of necessity accept that as the ongoing reality because again we are universally connected and know the results of such carnage. Because it is in our realm of common knowledge we have graveyards, crematoriums, undertakers, doctors who pronounce bodies to have died. We understand the consequences of leaving such bodies unburied, the diseases that would prevail. Again, please explore the definition of principle (Universal principle) and try to go to the limitations of the definition without using mythical dichotomies. [[File:( A great picture of outer space ).jpg|center|thumb]] Principle: A fundamental truth used as a basis of reasoning. All of these questions are based on singularity (the Cartesian dogma)… If Descartes had only introduced inclusion into his musings (they were taken as conservative singularity) he may have realized the difficulty of addressing thought as reality. He then may have quite easily concluded that universally - *We are!!* That pronouncement is inclusive, and conclusive in every way, *we are - and we know!!* Because my knowledge is not a private, personal piece of property concerning principles, but Universal (Archimedes et al), then that innate knowledge has completeness we can share. Whatever identical resonance we may be able to share (concerning completeness), that can only be accomplished by understanding the principles involved and their constant relationship to each of us. Clearly the plethora of present and past discoveries establishes the existence of that which is fundamentally true, and the foundation for law. The principles are established, and always have been, we are in the business of making them transparent and complete. However tenuous the link we are all connected through communication, the air we breathe, the ground we walk on, the universe we live in, the common principles we live by. We all must have sustenance to survive, or we will not live. (See above) <nowiki>*</nowiki>There is nothing else to experience.* When we actively explore the reality of anything, all principles involved in that exploration are complementary, and honest, and we understand the wasteful divisive mythology that people attempt to attach to them. We cannot */partially know/* the truth, it must be complete. Dichotomies attempt to deny the existence of truth, and are misleading. How do we more reasonably completely know anything? === Naturaly. === How do we completely know? The complexity of language systems with contemporary usage requires new and creative structures to provide clear information. Internal and external reasoning capacities can only develop in concert with Man’s recognition of the principles that essentially form our lives. The inevitability of human consciousness rising beyond its historical beginnings posits a future outside our normal perceptions, and  a factual reality that points to the existence of new perceptions that are infinite.   It is natural to know when we are no longer trapped in any mythical ideologies that gives credence to dichotomies that stifle the recognition of simple principles. There was no cause for knowledge to be established - it has always existed.* Ask yourself - ‘how do you know to ask any questions at all?’ There is no hidden dimension or mystical world. The only philosophical reality is ‘that which is’. To access that we need a new structure to explore ‘knowledge’, a new transformational language. Real knowledge is not amassed information, nor is it the establishment of dogmas, isms, or mythical belief systems. Basic principles are the source and foundation of all /*knowledge*/e. Until that is recognized, extension from mythical sources only leads to a denial of one’s own senses. Trying to conceive of a contemporary world without principles is to posit a world without reason, or intelligence. The principle of pure knowledge could be said to exist in another dimension given the present state of human understanding. To progress that mistaken belief there would be strong support in the need for a comparative reality. Curiously it seems that philosophy (the seeking of knowledge) constantly discounts any knowledge that does not come within the sphere of established philosophy, and the comparative reality dictum. That consequence profoundly distils the purity of any experience and alienates the observer in their confrontation of that which is real. The measure of that ‘comparative reality’ knowledge bounded by dichotomies is so restrictive that it lies in a mythical dimension where denial of its very purpose is the order of the day. Evidently it will not allow doubt to undermine its own denials. A basic principle of Nature is /*knowledge*/ and it constantly communicates innately in every living structure. How to grow, develop, and disseminate. Knowledge is reciprocal truth that depends on our relationship and the recognition of principles operating. Knowledge (unlike information) is not stored in an individual box; it is ubiquitously manifest in everything we do. Knowledge is the experience of a positive reality, and its true construction is a dependable source of secure information (not to be misused). We daily have the opportunity of witnessing ‘knowledge’ in action as expressed by the ‘the principles of knowledge’, namely the principles themselves. The questions lie in a continuing mythical belief in a mystical unknown (the Cartesian stance) which because of its non-existence can never be known. It is a belief that is detrimental (because it attempts to deny all existing factual knowledge) to dealing with Nature and Reality and the fundamental necessity of our relationship with them. Making that relationship transparent is our basic obligation and the ongoing evolutionary activity. Although there is an obvious avoidance to address the definition of principle itself, it is a factor that must be paid attention to, to realize that ‘common knowledge’ is the only reality that exists. Amazingly although there is avoidance of principles - truth - reason etc, there is acceptance of the Cartesian dogma,. Paradoxically this determined acceptance of Descartes supports the reality of innate knowledge existing (I think - therefore I am) which establishes for him innate knowledge; however mistaken he is concerning the interpretation of his experience. = Leverage. = Long before I read of Archimedes and his various principle discoveries I was using the principle of leverage in a variety of ways, prying lids off boxes, moving articles with a lever well beyond my physical strength to do so without said lever, and I knew how to do it. Transferring that knowledge to a student or apprentice is relatively easy because innately they also /*know*/ how to do it. Every aspect of human industry uses the principle in a myriad of ways because it is our obligation to constantly progress the principle and confirm the constant utilization of knowledge. We wholeheartedly adopted Archimedes principles (et al) because we recognized their fundamental utility. It is preposterous to question the widespread /*factual knowledge*/ of all principles, more especially so when we cannot escape their ubiquitous daily existence in all our lives - Nature and Reality do not lie. One may abstain from admitting their existence. To do so is simply attempting the impossible, and is devoid of all reason. Real knowledge has been put into the realm of the mystical unknowable even to the point that knowledge practitioners go to the outer extremes and deny the gift of their natural senses. With their adherence to what they consider is knowledge they become captive automatons to any prescription for life that is expressed in that ’knowledge medium’, which then becomes the authority. When ’knowledge’ is addressed as having a collective source in Universal principles then we have the potential to experience its complete reality (microcosm - macrocosm) without any imaginary, or divisive comparative content. There is then a re-orientation process toward our true being and recognition of our own reality in relation to the natural processes we share. Real knowledge is elementary and Natural. We know, because that which is knowable is constantly expressed by the principles involved. We all share those principles and can correctly infer the most simple and obvious truths. All social life functions by our adherence to the implicit laws operating within them. Seeking experimental contradiction to a fact of life offers us nothing but proof which is the establishing of ‘complete knowledge’ however ‘more reasonably’ one wishes to extend the exercise. The construction of new philosophies must seek a mandate to fully explore the relationship between experience and innate knowledge as the foundation for pure knowledge to emerge. To repeat, knowledge or truth do not reside in any individual domain, nor are they the private possession of any human being. We know, because ’knowledge’ is an innate natural possession that we constantly share - otherwise civilization could not exist. == Knowledge: Evident facts about mutual standards that provide us with security. == We do not become human beings because we can ‘think’; we become more human because we learn to conform to the implicit principles in Nature and Reality. Denying them - denies our being. It is natural to know. There was no cause for knowledge to be established - it has always existed. Knowledge is an evolutionary process. Human beings developed from primitive innate instinctual knowledge to contemporary cultures. Some know more than others through experience, and make that knowledge transparent. Insistence on how we can ’completely’ know is an ephemeral philosophical question that attempts to deny that we can have ’knowledge’ at all, as you understand it. Knowing that we ’know’ the inherent completeness of everything through the existence of principles, is the natural catalyst to make ’that which is’ transparent. Heraclitus: "No man steps in the same river twice " He believed in the "Unity of Opposites (Absolutes). He cried for the needless unconsciousness of mankind.. “Exploration of a mythical dichotomy below for the purpose of establishing principles. Principles that are not a 'mind' construct, but the very essence of our being. Independence, is the curious and dangerous malady where humanity has lionized negative mythology in denial of its own reality. The human fundamental reality has at its base the simple natural law that we are dependent beings. From conception, the human embryo is entirely dependent on the health and well-being of its mother to provide it adequate healthy sustenance to enable its entry into the world. That form of innate dependability the human species carries with it throughout its spectrum of life. Every aspect of human activity is premised on the availability of air, food, and water without which the organism cannot survive (this would be an incontrovertible 'more reasonable' truism or an Absolute). In a perverse way, that which is our natural state has become the target for what appears to be open defiance of the laws that govern our behavior. When a basic premise is either used mistakenly, or deliberately, its consequences can be socially far reaching, for any deviation however far it is extended is a distortion of the truth, and a denial of who we are. The erroneous conclusion through exercising responsibility that we can confer independence to our actions has gained a distorting and ubiquitous influence which paradoxically undermines the very responsibility practiced. Within the context of being dependent we can correctly be responsible for our own actions but with the surety of knowledge that that responsibility is contingent on the measure of life giving forces available that we are dependent on. The mythical dichotomy 'independence' connotes with the myth of separateness, division, alienation, and the force of these particular myths is expressed in wars, genocide, criminality. Alarmingly the mythological term has become a residual in our lexicon and is used more widely with acclaim than its true counterpart. To uphold delusional 'independence' as a value to strive for erodes our human heritage by diverting useless energy toward a dubious goal, and consequences that leave us questioning our means of arrival. Sadly it is a loss of being with the paradoxical view that the energy expended will deliver up a personal reality. The cult of independent individuality with its mythical ideology based on personal intimacy is now taken for granted, which then passes into the acceptance of the spurious dichotomy as a tangible reality. This in turn disposes the adherents to discredit the very essence of their being, and in the process dehumanizes many cultures. The presumption of independent individuality leading hopefully to a superior future is in fact counter-productive to the purpose, and leads eventually to corrupt power, and subsequently the invention of immoral policies that continue the negative spiral, which in the end has no ethical base to extend from. The alienation from our substantial being creates inevitable tension anxiety, and the need to somehow relieve that anxiety with any artificial means available. = Responsibility. = Being responsible for any social activity would best be enacted with regard to the effect it will have (directly or indirectly) on the lives of those who are dependent on a beneficial outcome. To recognize with some significance the basic structure of our being in turn significantly increases the measure of our understanding of human relationships. Being dependent is not a mental construct choice - it is a state of being, and there can be no being-ness without at least one other being, there is then the possibility that the principle of true egalitarianism becomes the manifest reality. Being-ness can only be identified and expressed in relationship. This is why the cult of 'independence' is eventually so socially destructive, as it creates that alienation which attempts to deny each real human need, and leads to a depravation of honesty. Human relationships between children and adults where independence is the accepted norm is severely undermined when the educational process predominantly teaches an unnatural form of living (either intentionally or unintentionally). The educational process is then reduced to the adoption of a fiction, which in turn puts at risk any educational program. The effect of interpreting mythical dichotomies as described here is symptomatically ascribed to the existence of all other principles that govern life. The construction of any ethological debate should not be premised on comparative perspectives, based on human thought, but rather on the issues that we can recognize as being universally compatible, therein lies the common denominator point of extension. The focus of attention on comparative perspectives denies justice to 'what is'. To contemplate the 'right or wrong' of any circumstance is a deviation from the truth. The correctness of any debate (however minute the finding), is the justifiable extension, and the only true trajectory we are morally obliged to travel. Truth is not defined, nor experienced by comparison, but by 'what we are'. An orange is to an orange, what an orange is to an orange. To define correctly there should be careful and disciplined action toward establishing 'true factors' that we constantly use to promote reasonable standards. = Time. = In that moment of time, we have the potential to merge on an equal basis with the reality that exists, and to know what true interaction is. That is the point of 'direct experience'. It is then that we know the truth about ourselves and the beauty of this Universe which also reveals to us the folly of our present conditioning. In that experience, it becomes very clear that all so called cerebral activity has nothing to do with reality. The fundamental repository of our knowledge and relationship with life is our being-ness, which is not located inside a mental box to be analyzed, accepted, or discarded at will, but the very privileged natural gift of being. What some scholars deal with is the appearance of life prescribed by the illusion of comparative perspective which functions on the basis of dichotomous ideology. It is in effect a denial of our humanity to conclude that all things that exist [from our perspective] exist only in the mind, that is, they are purely notional. It compounds the denial of 'what is', and an extraordinary refusal to observe transparent life. It should be noted that there is ample contemporary exposure to the Cartesian doctrine, and in this regard, I would refer you to the works of Professor Gilbert Ryle, notably his publication The Concept of Mind. The heuristic principle applies throughout when establishing our connectedness with reality. It is only through our contact with reality that we can discover, and equate with the mutual structure of the principles that govern all existence. Have already noted that it is also a peculiar form of arrogance that presumes that life is only a notional existence beyond the boundaries of the 'mind in a box' assertion. It would be foolish of anyone to assert that ice cream has a cold smooth satisfying texture and taste on a warm summers day unless they had actually experienced it, preferably on more than one occasion. For anyone who has never enjoyed that experience, it would be foolish of them to discount the very numerous accounts of such an experience that is available just because they had not been party to that event. From a logical point of view, given the avowed experiences of ice cream eaters, we could reasonably ascertain the validity of each experience by documenting their separate opinions. Each participant would have 'direct experience' in the consumption of ice cream, which at that point in time has the potential for that participant to experience the full measure of that factual reality. We have the natural capacity to experience coldness, smoothness, which equates with the reality that exists, and the potential for those realities to unify. It is not a question of how to get outside of our minds (mind in a box position); we are constantly outside our so-called minds performing acts of transparency throughout our entire existence. The belief that our constant engagement with reality can never be based on a rational acceptance of 'what is', is at the least, very sad. The Platonic Cave shadows are a metaphor for the (mind in a box) syndrome. The need to reach simple, and obvious conclusions and accept them for the reality they are provides the opportunity to engage the complete reality of the moment. It is indeed going too far beyond the reality of the moment searching for philosophical profoundness which does not exist, that fails to establish the constant principles that always operate. Pure principles are not amorphous shadowy ideals; they are represented in everything that exists. The only way we can equate our inner knowledge of reality is through direct experience of its truth. Within that context then, life cannot take on a notional existence but is an existence that is very real, and that we continually share through our innate knowledge. That our so-called minds are defined by comparison - incompleteness - dualism would have extreme difficulty in pursuing the proposition that we are defined by our direct relationship with reality which is expressed in our innate ability to directly interact with 'what is'. The reality of interconnection, and interaction, are not idealistic concepts of a notional nature, but actual and consistent transparent realities. We do not live in a shadowy world that is hidden from our direct experience, but we are constantly engaged in the process of life, and we do not have the right, nor the choice, to deny it. The man whose book is filled with quotations has been said to creep along the shore of authors as if he were afraid to trust himself to the free compass of reasoning. I would rather defend such authors by a different allusion and ask whether honey is the worse for being gathered from many flowers. Anonymous, quoted in Tryon Edwards (1853) The World’s Laconics: Or, The Best Thoughts of the Best Authors. p. 232 == Create your own semantic template. == That will consist of an alphabetical list of Absolutes that are all interdependent and interconnected. Their unifying construction creates a ‘new’ consciousness meaning. That ‘meaning’ is yours specifically. The greatest knowledge you can ever have is your own! That meaning also creates its own moral construction that cannot be misused . The semantic template is available to everyone, and its dissemination is our responsibility. “Consider that the language structure, concepts, and definitions now in use no longer always deliver, accurate, reasonable, and responsible information. Indeed at times, they can be quite ambiguous. The statement ‘mutual agreement’, and its physical manifestation in whatever form, is its own dialectic, and will carry within it all other principles necessary for the activity to proceed. Given the Socratic assertion that if something is true then it cannot lead to false consequences no matter how circular any argument may be. Then extrapolating the statement into extended definitions must only lead to a better understanding of the inherent truths available. This can promote recognition of the underlying essence of all things, which can become more real than our conventional understanding of Reality. There is a contemporary need to find new definitions, new paradigms to explore the concepts that govern our existence. Where a circular argument is based on an untruth, then it cannot lead to a truth. The reverse of that is that when the truth is established, it cannot be denied. Establishing ‘mutual agreement’ as a center from which we can reach out for extended knowledge in its ever-evolving radius, is not a limitation, or a stop, it is only a beginning! When any concept is truly established the superficial exemplification ceases to dominate, and we can truly experience the apparent essence of ‘what is’. Paradoxically to resource innate knowledge, we must recognize our profound ignorance of Nature, and Reality. Completeness does not lie in individuality. This is an extreme form of monastic expectation. There can be no individuality (or completeness) unless there is at least one other individual. This is the true foundation of completeness. Whenever we are privileged to experience that instantaneous essence of one other, then we know in that moment that we experience ourselves. It is complete complementation with the knowledge paradoxically that it is an endless process. There are many paradoxes we live within that strain our conventional views of what is ‘more reasonable’. Any true relationship experience is not based on a causality premise, but on an experience that is necessarily complementation. Individuality in terms of completeness is a fundamental circular argument back to one, which in its form of denial excludes any form of reasonable argument to the contrary. It is a non sequitur, which denies the pressure of facts that are in abundance, despite the evidence of their reality. To observe ‘mutual agreement’ is looking at things as they are. True observation of ‘mutual agreement’ in action is observing essence transparency – it is knowing ‘who we are’. That form of recognition is essence duplication. The proposition that we can observe the Truth may well be the highest attainment of Realities properties, for Truth is knowledge. Consider the hypothesis of a human entity (an individual) being born in a black space with no other form of life in that environment. How could there be Agreement? How could there be Intelligence? How could there be Understanding? How could there be Recognition? How could there be Love? How could there be Law? How could there be Reason? All of the above principles are the transparent manifestation of Nature and Realities properties that are constantly evolving. They are ethical imperatives, and we have developed the positive properties of language to establish them for our use. We can only be defined through relationship principles for they offer us the best hope to recognize the factors that lead to complementation. There is a fundamental need to grasp simple common-sense essentials. The Here and Now is not a temporary transitional time phase that we move in and out of. It is a constant certainty that is essential to recognize, so that our focus of attention has a foundation. Centrism can imply a fixation, which also implies vulnerability, which can be perfectly true if it does not lead to extension. To understand who we are, it is essential that we recognize and become aware of the very principles that we operate from. They encapsulate all the measure of any human societies ethics, morals, and laws, which is a continuous evolutionary educational process within which the realization of its total essence is always available. To use the doctrine that reason is a reliable tool to discover Truth – therefore ‘mutual agreement’ in the context ‘correct information’ translates to the Truth to reason! Evolution is a constant dynamic process. The human phenomena of ‘who we are’ is only understood in our union with each other, and ‘what is’. The paradox again is that there never is any separation. Separation is a mythical non-existent. The principles that are our necessities have continuous expansion properties that as humans we are privileged to assist their propagation. The human constellation in its evolutionary march must use these fundamental principles to ensure continuity. To maintain coherence and consistency our source is centered in the principles and factors that we have interpreted from our association with Nature, and Reality. Whatever we write that is of any consequence, or at any other time, is written with the hope that stronger interpreters than us overtake what we present. To ‘see’ Reality as we have seen, and be intoxicated by it, as we have been, will ensure its progression.” == Discovery == The consciousness whole is the sum of all its parts and experiences. As we are all on an evolutionary path, our life and knowledge hopefully develop in the right direction. The exploration took us through a plethora of data and opinions about reality from authorities on science, religion, philosophy and metaphysics. Nowhere could we find a definitive conclusive argument, or agreement, that met our needs. For us, the question came down to “Is there anything at all that provides some form of construction, and certainty?” Something that has its own inherent ethical standards. The alternative proposition to that is a nihilistic “nothingness”. A pathological proposition that makes no sense. Heraclitus’s “unity of opposites” seemed the most promising. Our understanding of that now made dichotomies a semantic illusion. If achieved in a mindful way it is the act of uniting them, providing a conscious correct experience of ‘what is’. We live our lives with secondary knowledge that everything that is – is always interconnected and interdependent. Yet our illusory experience belies that form of knowledge. It is here that we understood Heraclitus and his “unity of opposites”. Mentally uniting opposites replaces the existing illusion of their existence – there are no dichotomies! Once the illusion is gone a new solution manifests that is peculiar to the mindfulness operator, and belongs to a higher form of consciousness. Heraclitus was known as “The Weeping Philosopher”. He wept for the needless unconsciousness of mankind when the ‘unity of opposites” was always available. He was also known as Heraclitus The Obscure. A title we suspect that came about because the successful conclusion to uniting opposites and replacing the illusion, opened a door to a new dimension. Semantic description at this time may not have been available. This brings us to the ancient Yin and Yang symbol of the ‘unity of opposites’. As separate entities in Chinese philosophy, they are complementary, and in fusion they represent the whole. So as dichotomies they don’t exist. The whole is the elemental answer to any fusion of opposites, whatever that may be. Symbolize a line as being infinite in the sense that any line can be categorised as being infinite. Apply an infinite number of points in any line. Intersect any line through any point by another line then we have a specific identifiable point at the intersection, which at that point in time has an infinite quality, yet constant and complete. Any such point has Matter, Energy, Space, and Time, the epitome of the microcosm. We may locate a Reality point that establishes the Truth. Conventional mechanical ‘thought processes’ deal with dichotomies that are based on a comparative perspective ideology, and consequently, skew any real experience of that which is real. We must use correct ‘measuring sticks’ to secure proper standards, but from the point of view that there is a belief in dichotomies, it will always be a compelling argument that aspects of reality can be contradictory. The element of denial within human historical memory accumulates to establishing dichotomies as being real. We are defined not by how ‘different’ we are, but by our commonality of existence. When we locate that Reality point we will then know that the definition in itself has a whole, and complete explanation of ‘reason” in all possible senses. All the reality we can deal with is here, and now. There is no possibility that ‘infinite regress’ (an imagined reality) is any part of our immediate experience. Infinite regress through thought processes, deals with questionable imponderables. It is a descending spiral, which further removes one from reality, which only produces illusion, and correct meanings are always deferred. It is making a holy virtue out of complexity. The epitome of completeness is the active realization of the operational principle. Conclusion: A brick – a house. Each complete in themselves. A house is not composed of one single brick, but each brick in its composition is complete, and whole in itself in that it has matter, energy, space, and time. In that context, it is a microscopic whole which has implicit within it the macrocosmic whole, a house. We cannot define that which isn’t. We constantly use negative dichotomous terms in language, which are in essence factually indefinable, and therefore non-existent, but they are used as though we can support a view as to their existence. At this time we constantly use mythical concepts as though they had real substance. That erroneous belief in turn diminishes that which is real and compounds the problem of recognition of Reality. The flat earth society no doubt had to be persuaded of the mythical nature of their beliefs. This dictates that we must research ‘that which is” to achieve an understanding that supports that reality. Separation is the mythical measure we use in an attempt to justify the real identity of either ‘relationship’ or ‘completion’, but it has no substance in fact.That we are connected, that we are related, that we are communicating, that we agree that ‘mutual agreement’ exists, all of these factors fall into the category of ‘that which is. There is nothing that is real that is not immediately available to us, there is ‘mutual agreement’. Attempting to view true relationships as having a necessary separation link, or dichotomy is a clear misunderstanding of the nature and completeness of all that we are related to. == Connectedness. == A relationship is defined as we are by the measure of contact (especially homo sapiens) that is apparent. It would be true to say that I have a measure of relationship with everyone who reads this material. No matter how tenuous the link we have a measure of relationship with all life – we are related! Depending on the strength of that relationship defines ‘who we are’. ‘Who we are’ is not defined by any spurious separation from life, quite simply because we cannot be separated from it, we are engaged in it at every moment in time. Any attempt to establish ‘separation’ as a reality is an attempt to deny ‘who we are’, and another exercise in futility! Again artificial interioralisation of concepts or principles leads only to a denial of their external reality. We are all connected by the very simple fact that we all exist on this planet. It is a very simple axiom that all life on this planet is supported by the conditional properties this planet provides. It is also a very simple, and more reasonable axiom to conclude that no matter how tenuous the link that all life in this regard has very concrete and definitive forms of relationship. We all must breathe, we all must eat, and we all must drink, and if you need any further certainty of ‘completion’ relationships, we certainly, all must die! [[File:Wikimedia|thumb|center|]Arcimedes] To set in qualifications from the premise that there is a ‘separate mind’ (a kind of Platonic cave) to get outside of. This premise precludes either in part or in whole the evidence and experience of Nature, and Reality, within which our beingness is located. It would all be beyond our grasp if indeed our conventional concepts of consciousness was adhered to, which in effect attempts to deny us that direct ‘relationship’ to ‘what is’, and the completeness of that experience. Knowing or being, despite solipsistic theories to the contrary, does not exist in penetrating one other mind, but in the democratic recognition that we know and have our being in relationship, and the mutual, and natural convergence of everything there is. Homo sapiens (race, color, or creed aside) necessarily conduct themselves in ways that extend recognition, and understanding at every level, without the constant need of ‘completion’ recognition that is inherent in all our interrelated actions. The notion of completion may be beyond what you call your ‘conscious grasp’, and therein I suspect lays the difficulty in recognition. The flat earth society eventually moved on to a realization that their visionary scope was shrunken, and severely limited. They were deprived of a planetary (never mind a universal) relationship that one can only imagine severely curtailed the very expansion of consciousness necessary for humanity to progress. We have evolved some little way because of our understanding of the natural relationship. The centered in the mind condition - which connotes with the separation ideology - screams to be released from that mythology, and engage itself directly in real relationship with everything that is. = Relationship. = Separation is the mythical tool we attempt to use to maintain a false continuity of an imaginary individuality that does not exist. The taking for granted conditional mythologies (the flat earth society) engage the victims in what can best be described as serious problems in recognizing the very limitations that restrict their development. We must learn to view wholes, which equates with viewing ‘completeness’. The whole is greater than the sum of its parts, but the parts are not necessarily separate conceptual parts. We can ‘see’ the whole when we are able to identify the factors that constitute their existence as a complete reality. That which is complete in Law = Agreements that produce secure and dependent outcomes. We know in essence the concept of ‘completeness’, and we demonstrate the evidence in myriad ways. Each act is a microcosm of the whole – view from the other end of the telescope! In the traffic analogy the driver, and all other drivers, conform to the law by driving off when the light turns green. There is an implicit agreement about the value of traffic laws, and traffic lights that control the flow of traffic. At that moment there is a complete relationship understanding of those values. The ‘complete’ or ‘wholesome’ activity of motorists waiting at traffic lights for the green signal to go, and they then move off, validates all the factors implicit within the properties of ‘mutual agreement’. Throw a ball from one side of the room to the other. The ‘whole’ or complete traverse of the ball is the instant it leaves your hand until it arrives at the other side of the room. You have already given credence to the concept of ‘mutual agreement’ as a reality. When there is a correct definition made in terms of ‘necessary factors’, then it has implicit within it the concepts of ‘completeness’ or ‘wholeness’ within the measure in which it is used. Whatever we communicate for the benefit of future generations should not be based on mythical assumptions, but should be based on necessary factors. It is ordinary life that portrays all the dignity, honor, and the complementary wonder of the human species. We are here – we are present – we are communicating. We have an obligation (which we necessarily fulfill) to make transparent the basic principles that govern our existence. That, which is factual, provides us with a correct motive for behavior, and we do a disservice to Reality when we attempt to deny it. We exist and live in a world where acts of ‘completeness’ expressed in one form as ‘mutual agreement’, are continually enacted. It is the form of expression, and continuance of processes that we constantly use to arrive at reasonable solutions, and we employ factors that are necessary to provide us with a clear, and unambiguous understanding. They motivate reasonable behavior toward activity that we can accept as being a logical process. == Natural Experience: == No form of life can exist in and of itself, it is brought into existence through a relationship with its own environment, or its species. The obvious egotistical monistic nature of oneness (if there was such an entity) could not leave any room for the realization of anything that might disturb its comfort zone. There is no real knowledge where any concentration is on the “I am” syndrome. "No man is an island, entire of itself; Every man is a piece of the continent, a part of the main." - John Donne, 'No Man Is An Island, Meditation XVII - Devotion Upon Emergent Occasion. “We are’ is an inclusive affirmation that deals with “what is’. There is no constructive dialogue, no real understanding, without a relationship. Based on personal experience, we are a distinct, and unique species born of Nature and Reality that has combined to provide us with the innate ability to recognize the very properties that created us, and utilize them through an evolutionary process toward ever-increasing transparency. That transparency can only become available through a matching process between innate knowledge, and the reality we share, a reality that is our heritage. We like all other forms of life are the product of Nature, and subject to its laws, and principles. Necessity created a language that evaluated Reality, and provided us with guidelines to emulate its constant properties. The measure, and quality of knowledge is dependent on the realization of ‘what is’. The crux of correct knowledge is to know the base that we function from. The principles that are implicit within Nature, and Reality we have now translated through the evolved language systems with symbols and definitions that we now use to share the experience. When principles are fundamentally true and recognized for what they are, misguided belief systems will evaporate. To ask what is the source of the principles we present is ipso facto to ask what is the source of Nature, and Reality, and we repeat, that is an exercise in futility, but that does not mean that we cannot recognize that which is natural to us, and express it, as best we can through language. The experience of ‘who we are’ is the Ultimate transparency that transcends all doubt, or denial. We can know with an understanding that is pure and indisputable, that is the motivational drive for evolutionary continuance. To understand who we are we must address Nature, and Reality, and ask ‘what is’ Here, and Now, with an understanding of the dichotomies that exist in language. The ‘Eureka’ moments, epiphanies, enlightenments, etc, are all evolutionary evidence of who we are, and when we can translate them into principles, and concepts, then the assertions of an Archimedes (and many others) are recognized, and properly used. Through Nature, and Reality we can establish what Truth is! Is it true to say that most people conform to the rules of the road? It would be more reasonable to assert that the answer is yes! Consequently, we can say that we have ‘Mutual agreement’, and ‘Co-operative Understanding’ as observable realities. There is no conceptual source through Time, or history where there is an end. There is only ‘beginning’. Here and Now is always the ‘beginning’, and a more reasonable platform to explore than any exploration into the past concerning our true identity. Contemporary terms like Absolute, Complete, End, we use to match our conditional understanding of ‘what is’. When we use contemporary conditional language to address concepts like Truth, Knowledge, Understanding, they are limited by the measure of our progression, but we use them all as stepping-stones. Language is a constantly evolving process. When we agree that there is ‘some certainty’ and ‘limited knowledge’ you have agreed to the concepts of certainty and knowledge as factors that are part of our natural reality. All of us function within the framework of certainty, and knowledge, to some degree. Given that we agree to their existence, these are the factors that can lead us to the experience of ‘who we are’. They are a part of us that can lead us to recognition of ‘what is’, and make a transparent reality of the very things we do on a daily basis. We do not need absolute and certain knowledge to perform everyday tasks, but those performances are structured contemporarily because of our advanced understanding of the things we do, based on our own innate reality. To honestly perceive the consistency of ‘what is’ (to be interdependent, and mutually connected) in interaction, can and does promote the visible reality of ‘who we are’. That visible evidence translates into the knowledge of our complete presence. We know with certainty that our beingness is of pure essence, and from that experience, we are obliged to formulate, as best we can, the structures that are responsible for making that transparent (witness the explosion of human progression, without the necessity in Time of experiencing fully ‘who we are’). To take a more reasonable stand please observe the multiplicity of human action where interdependence, and connection naturally proliferate. To realize that we are ‘interdependent, and mutually connected’ is the realization of a consistent fundamental truth – ‘what is’. Through identifying ‘what is’ as an internal reality we can make transparent the factors that are our natural construct. It is only through sharing this reality that we recognize it!! These factors are not based on any ideology, belief systems, or opinions; they are composed of the Reality that is available to us all. We are unique in that we have the opportunity to be able to use their value in the manner that is implicit within their structure. That use is evidence of our understanding of Reality. What could have happened without the assertion that traffic lights are a safe way to control crossroads, or the assertion that the rules of the road are beneficial for our safety? Any true experience, epiphany, enlightenment, etc, of ‘who we are’ provides fundamental, and indisputable knowledge of that Reality. Applying the recognized principles provided by Nature, and Reality consistently advances the evolutionary process, hence we have Science, Philosophy, Religion, Education, Art, and Law. When there is a Pure Realization of who ‘we are’ through relationship recognition, it is unquestionably the recognition of the encapsulated, and innate principles we all share, and there is no place for the dissolving of another Real identity through that recognition. Indeed it is a privileged insight into the epitome of purity. Nature and Reality can give us direction and guidance to our human existence, and we repeat, it is an exercise in futility to seek any cause to their beginnings. We have proffered the concept of two as a basis from which human reality can be ‘experienced’. To recognize through, and equate with the true substance, and essence of one other is to automatically experience the totality of ‘who we are’ in full measure. This does not mean that the terms ‘totality’ and ‘full measure’ convey an ‘end’ to ‘what is’. We have consistently offered recognizable facts (not assertions) that are part of our natural human activity, and give correct direction and meaning to our basic essence. We do function within the structure of ‘mutual agreement’, and we do communicate and ‘make known’ – basic obligations. These are evident simple examples of innate knowledge, and our understanding of ‘what is’ made transparent. To repeat we could not recognize anything without innate knowledge. All knowledge is a continual matching process 1 + 1 = 2. toward the realization of ‘who we are’ the development of language structures that correctly establish basic reality as it is, provides continuous knowledge that makes transparent the very nature of that reality. It is vitally important to recognize that we have active communal agreements concerning the existence of basic principles and concepts that form the very foundation of our lives. Constant change and movement in Space-Time - Energy - Matter are applicable absolutes to be recognised, which equates to evolution. There never will be a static property involved in the evolution advance. Evolution encompasses its own absolute properties to provide cognitive connection confirmation. The evolution of conceptual language exists to provide natural equality and to promote cognition between language states. No matter the languages spoken the concepts of air - food- water is the same and can provide a gateway to explore the future dynamics of human relationships. === Knowing. === Knowing what all the truth is is not some miraculous state of perception. Nor is it a high academic achievement of amassed information. It is simply an objective common-sense view of ‘what is” and in reality what must be. It is what must be for life to function within the principles that exist that are its natural foundation. We are always of necessity the living expression of a reality that must be experienced in the whole. Our recognition of the same principles operating universally is also our recognition of who we are. That proliferate ‘sameness’ is an evident easily recognizable identity. When a child is afraid of an imaginary monster in the dark, we generally do not accuse them of being absurd, or that they are lying. Appeasement comes with an explanation of reality at that level which is truthful. An explanation, which the child can grow up with, and find comfort. It is simply introducing a child to a level of truth that is more real to them. In every instance, the only reality that ever exists is truth. However, distorted it may be expressed. One of the major distortions as the result of thought processes is to consider that we can manufacture something other than the reality that exists. The ‘fact’ that you recognize contradictory or absurd statements is that behind them there is a measure of truth. The habitual liar lives in a world in which he or she imagines that truth is something they can manufacture. Where human ‘thought’ constructs its reality in terms of dichotomies it can never deal with the truth because it continually makes those comparative perception judgments. Those judgments are always in question because again they cannot deal with reality as it is. No matter how absurd or contradictory any statement is, that is the measure of truth expressed. Ergo whatever it is that is expressed, or made manifest, is the truth to some degree. Ergo everything that is, is the truth. It is our responsibility to recognize it for what it is. It may be appropriate to review previous observations on dichotomies and gradient scale. Consistently we have contended that there are no dichotomies, which then properly puts each principle into the category of an absolute. To identify ‘truth’ as an absolute in that category then everything that is must have a measure of truth. It is a very simple and sensible approach to establish ‘what is’. It is the means of identifying a reality that must have truth as a base – whatever it is, and however nonsensical it may appear. All principles have an elementary gradient scale that we must use to identify knowledge that is honest. That gradation scale knows no dichotomies. Dichotomies are always the imaginary properties of pseudo subjective reasoning. Necessary factors establish that gradient scale where only objective realities exist to furnish a healthy subjective reason with truth, and so we learn to apply the conjunction to address reality for what it is. Truth comes in an abundant variety of ways in its commonality – and therein lays its overall ‘complete’ power, despite any denial to the contrary. Embedded knowledge as we see it is neither experience nor knowledge without principle content. A person may be well educated in all aspects of the geography of a beautiful South Sea island, but have no practical experience at all of its beauty. Being clever about a subject does not necessarily equate to an understanding of the subject. Nor should it lend itself to posing as adjudicators on a proposition preset we imagine by the same adjudicators, or essentially the same school of embedded thought processes. Long before human evolution, the principle of leverage has always existed in all Nature (as have all other principles, wherever there is space – time – energy – matter). Our adaptation to the existence of principles has added to the sum total of ‘knowledge’ as we know it, including the concept of knowledge itself. That form of ‘knowledge’, and our ‘knowing’ is natural and not any personal or esoteric acquisition. Just as a fish knows what its natural habitat is, or a bird to fly in the air, the human species uses all available principles it recognizes to add to its knowledge (already said). Any valid theory of knowledge must have as its base constructive definitive principles to support it, and it is evident that our accumulated common knowledge equates to our common experience. No matter how erudite or convoluted any argument may be, if in the end it is reduced to inane observations that have no factual basis in principle, then it is time to abandon them. Do try to consider the sort of ‘mind’ processes that offers us up a world that knows nothing but separation. How can we possibly evaluate what ‘wholesomeness’ really is? How can we possibly evaluate ‘who we are’? How can there be any theory of knowledge without addressing Nature or our innate and biological relationship with it? Any attempt to debate ‘who we are’ and the completeness of that concept must have some sense of reality on the real meaning of ‘completeness’, and some understanding of the principles that are the nucleus of human society. To wrap any argument around a non-existent concept that can never be realized is apropos to attaching oneself to a system of belief in things that do not exist. One can make ponderous and convoluted statements about those beliefs but in reality, they are morally and ethically misguided. The ability to correlate correct definitions to the reality of life offers up that direct link to the truths that are common to us all. It corrects the presumptive notion that there can be ‘different’ perspectives on the same reality. There can be ‘differences’ but there can not be ‘different’ measuring sticks for the same reality. No matter the multiplicity of perspectives, they can never alter the core principle of ‘what is’. Historically evolutionary progress can best be measured by the adoption of recognized principles. Reality at whatever level we find it can only be understood by addressing ‘what is’. Nothing can be understood by attempting to relegate it to a non-entity through questionable theories of ‘knowledge’, which in essence negate the very content of knowledge itself. The perpetuation of any theory of knowledge, which cannot recognize the principles that are its foundation, can only be a shadow of its own reality. Construct the ‘necessary factors’ around the skeleton and a body will take form. If any particular theory of knowledge cannot identify simple truths, how can we possibly question how anyone ‘knows’? A dichotomy is the human attempt to deny the existence of a whole reality of a principle. We have the principle of leverage and its necessary gradient scale. Mutual agreements of a consistent reality, at a communal level, are a passive form of the Eureka moment, which recognizes fundamental principles that relates to truth. In every social structure, there are varying degrees of recognition, which determine social use. The mosaics of differences, which make up the rich pattern of life, are a testament to human creativity. Principles offer up a form of predictability in which our brain forms knowledge through the process of interaction. The experience accumulated through each moment, forms exponentially in use, or becomes transparent immediately in a Eureka moment, in which we know. Real knowledge is through the constant interaction with natural principles, much more than the transference of divided embedded information. The problem we face is that ‘knowing’ or ‘how we know” is never a personal possession. Any theory of knowledge no matter how in that respect, is true interaction. Peeling a potato and ‘knowing’ it, is rewarding enough! All principles are the repository of pure erudite knowledge. We recognize Universal principles in play at all times in Nature and its by-product – human societies. The correlation between determined interdependence to objective reality requires our intellect to ‘honestly observe ‘what is’, and assimilate that subjectively. Then the equality of the external and the internal becomes a reality and we ‘know’. Knowledge is the process of natural action, reaction, and interaction. It is nonsensical to ask how do we ‘know’.Every moment in time is complete because it must contain all the principles that form its nucleus. It can only be like that to facilitate the immediate experience of Eternity, or the wholesomeness of any of its principles. On the gradient scale of experience, we all exist somewhere on that scale. It is called life. === Relativism: === Relativism can be consistent with interconnectedness and a gradient scale of knowledge. What it cannot do is confuse the relationship that correct gradient scales of principles have in reality. Hot and cold would be on a temperature scale – no dichotomy! Leverage could only be measured by its own scale (say a child’s sea-saw to a high-rise industrial crane) – no dichotomy! The human being is a human being whether it is a child or an adult – no dichotomy! The domestic cat is the same animal species as a wild lion – no dichotomy! The domestic dog is the same animal species as a wolf – no dichotomy! How can we manage to classify these as dichotomies? Gradient scales are the natural human mechanisms used to recognize constant principles. They ensure the human perspective is aligned correctly to identify ‘what is’. The distorted human perspective is the result of human thought processes unable to establish constants that must exist in each moment of time. The problem with embedded information is that it becomes stultified and it can stifle healthy reaction. The injection of recognizable principles invigorates and brings new life that offers countless avenues for human energy to be released. More importantly, those energies are used to enhance the evolutionary process. We are collectively gifted with the potential to elevate life itself. We can correctly use such information by transforming its content so that its inherent truth is made recognizable. It would be impossible for life to function if it was composed of ‘different’ opposite realities. All theories of knowledge are in essence interconnected and can only contain validity when the principles that are the coalescent mechanisms are recognized. The unification of the truth that must exist in any theory needs to be harvested and used to offer up a body of ‘knowledge’ that has commonality of meaning. The identification of principles, truth, knowledge, and their subsequent establishment can only be achieved through direct interaction with Nature and life. Gifted with life we have an obligation to demonstrate its capacity to use every resource to sustain and nourish its own environment. We all know through the constant natural process of action – re-action – interaction. Depending on the quality of that process, knowledge will take its appropriate place on the gradient scale. That we ‘know’ is natural. It is not some extraordinary esoteric attainment, posited by a body of theories that, by their very nature, look for difficulties where none exists. Universal belief systems based on mythologies can have an entrenched view of good principles being established because of their beliefs. Indeed the perpetuation of the beliefs throughout history offers a dynamic that is counterproductive to the ‘realization’ of principles that are necessarily true. Principles used in this approximate way, paradoxically hold no real meaning, and in fact, impose unhealthy dysfunctionality. When there is a critical change toward establishing correct principles, it is axiomatic that the diffusion of mythologies becomes an automatic process. True interaction lies in the knowledge that correct action is its own reward Any other interpretation is less than tangible. The accuracy in interpreting basic principles, and the alternate knowledge implicit in the interpretation, will always establish the primary principle sought. Archimedes et al. Truth can be found in the oddest places. (Archimedes bath image here please) Archimedes cognition on how to weigh metals in water through displacement. === Truth. === Language is the construct of human action and the word “truth” seems to hold pride of place by the power of its usage and the meanings it evokes. It is preferable if we could turn our attention to the unity of principles (including truth) that are the construct of every language we use. By uniting the principal terms we can elevate the meanings we desire. Reasonable constructs and the correct duality of established principles always lead toward meaning. It is the only form of meaning that leads to its own extension eg. how to weigh metals – how else could it be? All principles have reciprocal value one to the other. No foundation principle can stand alone. They can only exist in a union, one with the other, the source of reciprocity. All absolutes are universal. There is no hierarchy beyond the meanings they evoke in their joint construction. The binary connotations, however, one may express them, provide a constant reality beyond conventional consciousness. That experience is the immediate reward through disciplined application of their use. That discipline takes the form in all human action (such as the bathing scene above) disposed toward the correct functionality of basic principles. The daily connections we make always include the distinct possibility of their recognition, when we make those connections in a mindful state. From any common sense, or ‘more reasonable’ position, it would be more productive to view reality as possessing at every level the same innate values or principles consistent with our ability to measure, or recognize them. To view reality as having ‘different’, or antagonistic properties, is simply a misguided view of ‘what is’. That form of perspective is counter productive when it attempts to establish mythical dichotomies as realities in their own right. When the realities of principles are made transparent, we can then ‘more reasonably’ make use of them to further their basic existence. Here we use reason to exemplify their necessary function, and once established it becomes (if necessary), ‘more reasonable’ to locate them in all things. ‘More reasonable’ seems to have the particular philosophical motivation, not toward simple, sensible, and reasonable evidence, but more likely toward that ‘immaterialism’ ideology, and continually seeking for an elusive protracted answer is hardly ‘more reasonable'. Since we are apparently confined to a human perspective, we must settle with the latter position: the apparent state of representation of the world. The de-materializing of any object through the practice of ‘perceptual illusion’ is an attempt to deny the reality that exists. Where perceptual illusions are concerned, innate direct communion with that which is, suspends the effect of such illusions. All the properties in a chair are recognized as the reality that exists. That is materialism. A chair does have the principles of form, design, structure, colour, substance, etc. However it is analysed – it is a quantifiable reality. === Truth and Reason. === The reason could easily be defined, and validated, as the correct application of common sense. More expressions of common sense can only endorse the completeness of any concept. A true experience of reality does not require endless explanations as to its ‘wholeness’. It just is. Truth is in reality a network of implicit principles in which it is the predominant energy in each of them. They are identifiable by their interdependent nature (see network below) not the least of which is common sense. Dictionary given definitions of ‘truth’ place it in a very common sense acceptable category. One of which is ‘accuracy of representation’. Note how the two definitions in this paragraph coalesce. The human drive toward recognizing and understanding the place of principles (constants) correlates to the energy we expend on questioning ‘who we are". The constant principles of action, reaction, interaction, are the automated natural impulse toward ‘establishing’ a human reality, and human identity. The process of evolving within that process has an egalitarian dynamic that powers it. In essence, it is a natural gift that we must accept. Each life and its identity contains all its personal experiences which can never be known to anyone else. In a sense, we can never “know” another person. Their life is sacrosanct. We can know a lot about them, and there it ends. Truth is at the top of the gradient scale that measures the veracity of all things that are complete and related and paradoxically all reality is the truth. It gets back squarely to ‘who we are” and where we exist on that scale. To view gradient scales as having no truth to their structures is denying truth itself. For the entire interconnected, interdependent network of principles, each of them has a gradient scale whereby each measure expresses truth in its own manner. All forms of leverage, from the minuscule to the lever that will move the world, are in of themselves, true and exact at that point. It is the only way we can recognize their existence, and use that complete truth at that time, to move up the scale. Time is the relative measuring stick that determines the amount of knowledge we can absorb. Consider the advanced extensions to the Archimedes principle of leverage throughout time. Network scale example. Truth Knowledge Common sense Responsibility Reason Understanding Intelligence All interdependent, and interconnected with all other principles and absolutes. No ‘thought processes’ or ‘mind’ constructs can create reality. All we can ever do to gain knowledge is ‘act’ react’ and ‘interact’ within the confines of our immediate reality. The quality of that action is determined by the nature of available information. When there is freedom from embedded thought processes, there is a natural human ability to relate to the existence of truth as it is expressed in reality, and our brain records it accordingly. Thus, the principles of civilized societies evolve. Where there are predominant belief systems, the implicit energy will naturally direct itself toward human standards that blend all ethics together. That implicit energy will find its true home in the principles it seeks. The connected strength of those principles offers sanctity of experience that demands no sacrifice. Everything that is, must of necessity, have a true comparative value (not a distorted dichotomy value) for honest recognition to be realized. which is to ‘know’. All things are relative but only within their own true scale. It is the process by which we can identify reality, as it is. Principles cannot operate on any scale practicing negative discrimination. Thus a healthy individual can be at the top of the scale and someone with various health issues can be near the bottom of the scale. But that is how Healthy they are. There can be no relativity when ‘mind’ or ‘thought processes’ believe in mythical dichotomies. When human perception is distorted by such beliefs, they create a false reality and deny access to the true state. Where there is a network of connected basic standards that are universal, then it is possible to use them and be nourished accordingly. The scale of natural human progression provides recognizable evidence that we are constantly developing. Reality is the direct and conclusive evidence of possibilities realized. Therefore, the reality is always the source of all possibilities where truth exists. When the truth is used as the universal measure of ‘what is" there can be no discord as to its accuracy. It can only measure the principles that are implicit in everything there is, its natural milieu! Truth can only deal with ‘something’, it cannot measure an imaginative negative counterpart. Truth is the constant implicit property in every universal scale of principles. Thus, reality becomes transparent. Have writ large on the value of distorted comparative perception judgments. The standard of correct knowledge always carries with it, its own appraisal. Where principles are concerned there is an obvious scale of identification (e.g., leverage and the numerous references) that is all-inclusive and provides us with evidence of its existence. We could say with some truth, that the industrial crane has more leverage than a child’s see-saw, but we cannot deny the truth at the lower level or the reason applied. Where principles are concerned, truth is not a possibility, it is a constant reality (e.g., leverage). When mythological dichotomies are recognized and established for what they are, the process of ‘ironing’ them out and experiencing their constant reality will translate into the reality, which they are, and used accordingly. To evoke that new sense of reality, the mechanisms of ‘selective immaterialism’ need to be dismantled. Where human experience is presented with something it does not understand and is unable to appreciate the principles involved, the reaction can invoke a sense of fear. That condition can be a primary breeding ground to establish a language of dichotomies and put a selective name to something it does not deserve. The diffusion of a false singular dichotomy into the natural healthy state of the common good puts responsibility into its proper place. Within the process of diffusion, there is the natural and equal absorption of our true reality. The transition between separation and inclusion will be a seamless process because it is our natural state. Objectivity and Commonsense: Explore the plethora of principles - truths - constants that are the mark and phenomena of Homo sapiens. We cannot have any doubt about our existence in this present reality. The truth of reality is and can be experienced wholly and completely by anyone at any point in time. All human progress is the result of such experiences, manifest in principles throughout time and their subsequent ‘use’ evolves exponentially. The overwhelming evidence is our reality, now. A simple analogy of objectivity and commonsense. Somewhere in our early development, someone put the ingredients of a loaf of bread together, somehow baked it, and hey presto, the first experience of a loaf of bread. It is now a form of sustenance, which feeds billions of people. We no longer need to experience that ‘truth’ that ‘knowledge’. It is unnecessary because it is subjective assimilation and the act of external and internal activity. Because ‘our’ brain functions in a manner that can identify the natural elements it exists in –space, time, energy, matter, we learn to ‘know’ and recognize ‘completely’ a child’s see-saw. Knowing is a natural evolutionary function. The quality of ‘knowing’ has its own natural determinants which of necessity contain the measure of principles required for universal recognition. An Archimedes insight (or anyone else’s) could not become a universal reality unless those determinants were in play. I know the very same way we all know – by experience via action, reaction, and interaction. Truth persists and what Archimedes experienced was true and complete. Any experience of any truth, principle, or constant can be as ‘complete’ within a grain of sand, or knowledge of a pyramid. All experience of that nature is an experience in ‘time’, and when it is the truth, we use it accordingly. There is no mechanical translation, or opinion of ‘necessary factors’ as they are constant universals. That, which is ‘complete’, is transparent universal knowledge e.g., the principle of leverage. The precision of terms must include ‘necessary factors’. Necessary factors translate into a common universal language so there is no loss of meaning. All truth – principles-constants – absolutes, that stands the test of time we use accordingly. Thus, human societies evolve, and we evolve without the necessity of having to re-experience any of the principles we recognize and establish. That simply would not be a ‘natural’ commonsense proposition and an entire waste of unnecessary energy. The truth of any principle at any point in time, and at that point in time, can be experienced completely by anyone. Whatever it may be if the principle is established – from then on, it will evolve. There are some misguided notions that ‘truth’ ‘knowledge’ and ‘experience’ have some secret value that is unattainable by ordinary experience. It is a ‘natural’ evolutionary reality that what we ‘know’ becomes useful. We have a mutual responsibility to recognize, use and honor the principles, which are the common property we share. = Human consciousness. = [[File:Lane past Coombshead Farm - geograph.org.uk - 589598.jpg|center|thumb|369x369px|"The roads half travelled when you know the way"]] [[File:Sombrero Galaxy in infrared light (Hubble Space Telescope and Spitzer Space Telescope).jpg|center|300x300px]] === The Universe === ''<big>We do not own Space</big>'' ''<big>We do not own Time</big>'' ''<big>We do not own Energy</big>'' ''<big>We do not own Matter</big>'' The human capacity to understand the question of sovereignty or ownership of Space - Time - Energy - or Matter can only be accepted when any basis of dispute includes two dispositions - human and spiritual indigenous ties throughtout history. With the evolutionary appearance of indigenous peoples throughout this planet, their way of life should make it paramount that their existence be recognised as a natural law that has providence! Their culture and way of life has its own identity in which Space - Time - Energy - Matter is expressed as they experience it. That proof also lies in the existence of caves thousands of years old, and the existence their art and culture. So the constructs defined below are a new approach to understanding the concept of ‘knowledge’ and its proper place in an evolutionary expanding universe. Knowledge acquisition requires appropriate recognition through action, reaction, interaction, in which proper perception and comsciousnessvalues are applied. That form of construction requires the dismantling of previously embedded information. This requires a new direction to formulate a sound basis from which to extend. Construction of an analytical methodology to establish a form of ‘knowledge’ that is best suited to distinguish in a contemporary reality. A reality that adequately conforms to common notions of that which is true, and can only exist without any false relation to that which does not exist. All science needs the certainty that established absolutes provide. A pragmatic construction of real knowledge would propose that all reality expresses a form of evidence or proof and that the observer and the observed contain innate properties necessary to establish a foundational agreement. That form of agreement would necessarily function on the basis that everything that is – is truth. Any other interpretation would be a disconnect from reality, and the interdependent correspondence that must exist for true recognition of any absolute. Controversy will always emerge when the discourse on bifurcation and the introduction of non-existent dichotomies are used as arguments to be explored. Pragmatism would say that the human species would need basic properties to formulate any form of reliable epistemological analysis to explain and simplify the reality that forms their existence. That reality could well be recognized initially as the absolutes of space-time - energy-matter, through innate perceptual data that corresponds to an outward structure that is constantly evolving. That which is absolute is the determinative factor in establishing the existence of truth. When a chair, is a chair, is a chair, its recognition is established when we ‘commonly’ apply subjective and objective measures to that which is truly external to that which is truly internal. That which does exist becomes ‘common’ knowledge, and accepted as being true. Thus, the distinction between a priori knowledge and a posteriori knowledge no longer exists. Where there is consensus, everything is. The formulation of absolute criteria that offers ‘simplicity’ as a tool to measure all and everything, dispenses with the confusion of ‘difficulties’ historical philosophies engage in. It also offers an observable synthesis that clarifies the confusion. Within the combined properties of those absolutes then everything potentially would be. Everything that is by that definition is original, ipso facto, everything that has no false relationship, and therefore true (no dichotomies). Given contemporary human development, it would be ‘common’ pragmatism to accept the proposition that we exist within the absolutes of space-time – energy-matter. Within those absolutes and their innate properties, it would also be pragmatic to assert that ‘everything then is’ (whatever everything may be). Pragmatism would also dictate that ‘everything that is, is its own form of truth, and must contain available constructs of meaning. Therefore knowledge and understanding would be obtainable to that common experience, and at whatever level that experience is activated it is in interdependent unison with the source. The continuing establishment of basic absolute principles (their generalities and their specifics) forms our reason. 1+1= 2 is a ‘simple’ but true universal constant generality. That form of generality is used because we recognize the specific principles of a balanced equation that adds up and makes sense. Simple generalities with their inclusive specifics form the foundation of human reason and its constant evolution. Simplicity is the bane of a ‘mind’ that must have difficulties. = Availability. = The unifying feature that makes ‘knowledge’ available to us all, are the innate universal principles in all things. Archimedes established the principle of leverage. To paraphrase - ‘give me a lever, and I will move the world’. Once the law is established it can then be put to good use. The principle of leverage is manifest in countless ways, and put to good use! The principle of leverage is a constant available to us all, and always has been. Through his application Archimedes conveyed his insight in practical terms, and made aware of the principle and the laws governing it. We now use those laws. We no longer need to philosophise on its existence as a truth. Similarly whenever 2+2 = 4.  Whatever we use to make the equation – apples, oranges, bricks, the mathematical equation is a constant, and the principle of correctness applies. Here 2+2 =4 is empirical proof that the principle of correctness and agreement exist. Principle, or law: ‘a fundamental truth used as a basis of reasoning’.           If it were otherwise we could not measure anything. That which appears abstract then, requires no implausible argument as to its non-existence. Such is the nature of all universal principles, they exist whether the notion of a ‘mind’ can perceive their existence, or not. Because ‘thought’ does not create the reality of principles – universals- truth, it cannot from its mythical standpoint understand the simplicity of a Reality where ‘everything is’, nor the simple and factual conclusion – how could it be otherwise! Where ‘everything is’ evidently encompasses the whole evolutionary dimension. It is not an ideological enclosed static that stultifies expansion of an unfolding Reality. Any pure knowledge experience that ‘everything is’ ,(quite apart from the common-sense truth of the statement) is to experience the Absolute in any immediate part of anything that exists, which establishes its own truth forever. To examine a road code of law with that knowledge, and view the actions of drivers at traffic lights, it is more than reasonable to conclude with some conviction that there is  to some degree, Agreement – Knowledge – Understanding, and Conformity to that code of law. It becomes a ‘more reasonable’ proposition within Reality to understand that that code of law is multiplied exponentially, and the principles practised,  wherever drivers, motorcars, and traffic lights exist. It is the nature of the type of knowledge we are measuring that determines the measure of reason that can be applied to any given form of Reality. We can conclude that 2+2 = 4 is a reasonable mathematical calculation that contains the principles of Agreement – Understanding – Conformity. Given the accepted knowledge of these innate principles we can with more reason apply such a calculation Universally. Knowing is agreement with ‘what is’. Knowledge is not the attempted denial of any existing reality. That is a contradiction in terms. Mechanistic observation is akin to viewing from the outside, a straw in a glass of water. The straw always looks bent, but when removed from the glass we realise it is straight. To claim an experience of that which is Absolute, is not a claim of an experience from a higher domain, or an  isolated incident – it is common-place, numbered by just how many we are. Attempting to denigrate such experience is denying the everyday actions that contain the innate principles of a constant Reality. All life functions within the constraints of the laws that are the constructs of Nature and Reality. All life is an expression of the Absolute. It is when that expression is realised, not only in an instinctive sense, but in a real sense, that we penetrate reality beyond a comparative framework of mythology. To claim that you ‘know’ intrinsically what the principle of leverage is, or the principle behind the mathematical equation 2+2=4 is to claim experience of the Absolute. The Absolute is not some abstract esoteric truth – it is that which is immediate. Whether in awareness or not, we constantly comply, to some degree, with the laws of a constant reality. Therein lies the difficulty for a comparative framework mythology – the Absolute is everything! = Basic Equation. = However much the simplicity of the equation is, it contains the properties of correctness – balance – equality – mutual identity – meaning, which in its ‘simplicity’ presages all future mathematical equations. In that universal meaning, there is particular knowledge of consistent truth. That form of ‘simple’ consistency, creates its own natural equilibrium, and its ‘usefulness’ evolves exponentially up the reality scale. Here is where we need to give proper credence to ‘that which is’. All generalities have profound and specific principles as their ‘common’ identity, which are absolute. Unless those components are recognized, both objectively and subjectively, they are reduced to a comparative value spectrum (using dichotomies) as a misguided ‘simplistic’ factor. Deductive reasoning is then deprived of all value, and leads to the inevitable spurious question ‘how do we know? Given the above criteria to establish a correct basis for knowledge that is recognizable, and of a kind that can be used universally, ‘simplicity’ can be recognized as a tool that promotes its own established formula. That which we constantly use. Everything is the truth with regard to the methodology. How that truth or generality is expressed denotes the measure of the principle that is at its core, and forms that measure of reasoning we enjoy. Fortunately, although the truth is an innate property, it is not a ‘personal’ property per se, nor is the ‘experience’ of its reality. Its natural evolution is progressive. In that progression we are in common, the beneficent recipients that ‘evidently’ conform to its constant existence. Philosophical dissertations have become a monopolistic form of opinions that always seem to presume the ‘rightness’ of difficulties in establishing the source of our being, and are unable to put in ‘simple’ terms the question of ‘who we are’. There comes with that the denial of evidence that permeates human history, which establishes the principles of our ‘common’ reality. Those opinions carry with them a colossal library of questionable erudition that becomes embedded, using questionable values to support their argument. The most distinguished opponent of such arguments (Ludwig Wittgenstein 1889-1951<ref>{{Cite book|url=http://worldcat.org/oclc/1203018418|title=Tractatus logico-philosophicus|last=author.|first=Wittgenstein, Ludwig, 1889-1951,|isbn=978-1-78527-656-9|oclc=1203018418}}</ref>) proposed that language logic was a necessary tool to dismantle the convoluted ‘mind’ propositions that have permeated the philosophical hierarchy. Those ‘mind’ propositions only served to construct meaningless concepts as to ‘who we are’. Although he gained prominence in philosophical circles, his work was directed more toward academia. In his Tractatus Logico – Philosophies he quotes: “The limits of my language mean the limits of my world - What cannot be shown cannot be said”, and “There can be no representation of the logic of facts”. Having a belief in mystical truths that were inexpressible, his statements above are indicative of the embedded language of dichotomies. His form of ‘knowledge’ ‘philosophy’ gave (without question) the concept of ‘mind’ credence to formulate its own logic to clarify its own form of reasoning. Wittgenstein, by not recognizing within the language the distortion that dichotomies create, was unable to approach the evident constructs of true meaning that lie within the interdependent relationship of absolutes, and their constant existence. Evidential reality is all there ever is. The ‘meaning’ or ‘knowledge’ that becomes evident in reality is ‘commonly’ accepted and used accordingly. To repeat, the evidential reality is all there ever is. In that regard, the exponential drive toward ‘difficulties’ amassed a historical discourse of misinformation, which is used to address the very ‘difficulties’ created by spurious value systems. In effect, dealing with ‘nothingness’. We have managed to turn ‘truth’ into a problem, into a difficulty, when the truth is simplicity itself. An oxymoron of gargantuan proportions. This contemporary malady solidifies a diversion that discounts the reality of continuous progression. Progression in which ‘common sense’ is a motivating principle that promotes human evolution. The consistency of specific principles allows us to achieve correspondence. Real knowledge is not a fabrication of convoluted prescriptions. It is the ‘coalescence’ of ‘what is’ to internal reality. That established, evolutionary progress is assured, and reality factors are recognized for what they are. True meaning can best be attained by the interaction and interdependence of natural principles and so recognized as such. That meaning which contains all the specific components of reality is experienced as ‘true knowledge’, measure by measure by anyone. That form of ‘experience’ is not a ‘mind’ process, but a very natural state of realization consistent with our level of action, reaction, and interaction. A correct and pragmatically form of knowledge-seeking foundational answers to perennial questions would seek a direct passage to our ‘commonality’, the beacon that offers guidance. Consider the quantity and quality of knowledge we all pursue that has meaning and usefulness. To posit the notion that there are no dichotomies is a cataclysmic proposition that seems nonsensical to established embedded constructs of knowledge. Constructs of knowledge that offer only confusion, and continually pose impossible questions, whose absence would provide clarity. That absence of confusion would dispel and dismantle a reality of ‘mind’, which functions on its own selection of problems. To address reality as having only absolute constructs dispels the confusion of duality and its inability to ‘use’ relativism in its proper fashion. All general absolutes contain specific principles representing facts; the essential properties that confirm reality. This reference directs the observer to observe, and go beyond the restrictions of a ‘mind’ governed by dualism, monism, or any other spurious form of philosophy that distorts the very reality it exists in. Where there are no dichotomies, all we can deal with is ‘what is’, and the logic of ‘necessary factors’ thus destroying the possible inclusion of anything described as a “paradox”. = Pure Experience. = To design a chair our brain requires to exercise the qualities and properties necessary for its manifestation e.g., strength, balance , design, functionality etc, etc. A chair, is a chair, is a chair, the product of innate knowledge.   If we did address any tentative agreement that ‘I’  is a ‘fiction’, could not our ‘conscious experience’ of that ‘fiction’ be just as fictitious. It would follow that whatever perception of Reality we experience must also be fiction. Our contention, as always, has been that ’I think - therefore I am’ by Descartes is the greater fiction for reasons already explained. To consider to whatever degree that we can function on the basis of a fictional ’I’ precludes any attempt to honestly address ’who we are’. Saying that ‘conscious perspectives’ are limited and inconsistent with apparent reality are quite correct. It then brings into question the validity of ‘conscious perspectives’ to guide us toward ‘what is’. The entangled fictional relationship between ‘mind’ ‘I’ ‘thought’ ‘consciousness’ impose formidable barriers to that which is evident. Base observations on the construct and interpretation of what ‘knowledge’ is. Human experience is limited by its mechanical interpretation of Reality, especially ‘cogito ergo sum’. If everything that is, is its own measure of Reality (the differences) then everything must be measured, at whatever level, as being that part of the whole with all principles intact, making that measure available to be experienced as the Absolute. With absolutes there is no antagonism. We cannot exist or experience anything without a Universal complementary source of identification. It is notable that within the structure of Cartesian dualism, Descartes' personal address to innate knowledge he attributed to ‘thought’ which he identified as being distinct from his body. How different Western philosophy may have been if his attribution had been toward his brain and the existence and evidence of other physical entities that functioned every bit as efficiently as he did. The premise that Descartes operated from ‘never to accept anything as true’, was simply a wrong ended approach which brought him into conflict with his passing acceptance of innate knowledge, that the idea of God was innate to his being. To view the proposition that ‘everything is true’ allows reason to seek and identify that measure of truth. No quest can be productively based on cynicism or denial, nor adherence to belief systems that separate experience, knowledge, and Reality. We have the obligation to question whatever reality has placed before us , but if we constantly deny its existence and attempt to ‘disappear’ it from our experience, then we are in danger of never experiencing that reality. Not experiencing Reality as it is, is equivalent to not experiencing ‘who we are’, and is indeed the only human source and validity of truth, although Descartes held the erroneous belief that such knowledge was independent of any experience. That belief we suspect was some form of impetus toward his ’cogito ergo sum’.                   Knowledge and experience are co-existing ‘necessary factors’ So long as anyone believes that human experience is based solely on indirect conscious interpretation (mechanical disposition), therefore any ‘knowledge’ derived from experience will be incomplete. Clearly it is the quality of ‘knowledge’ that one experiences (e.g., Archimedes) that leads to a common certainty of evidence realised through direct experience. That quality of knowledge can be available when we observe directly the activity of drivers at traffic lights with the knowledge that it is a very common activity recognized internationally. In every case we can logically pronounce the premises to be true, therefore we have a conclusion that is also true - whether that conclusion is defined as Mutual Agreement, or Common Acceptance, it does not matter - they are mutual principles. It is this form of logical knowledge of innate principles that is the precursor to knowledge of the Absolute logically defined within all reason for ‘what it is’ . Where the basic premise is true that there is ‘Mutual Agreement’ between a multiplicity of drivers at traffic lights then we can with certainty conclude that the same principles exist Universally. We can also draw concrete conclusions, and establish knowledge, that it is not ‘absolutely necessary’ to experience by observation the multiplicity of drivers conforming to their particular road code. We have already established that knowledge. Knowledge and experience are not separate philosophical theories. One cannot be without the other.. Everyone has the potential to experience the Absolute paradoxically, in part or in whole. Everything that is, must contain the properties of the Absolute, otherwise nothing could be. To ask questions about human experience based solely and inevitably on our interpretation of ‘knowledge’, and co-existing with that, its particular meaning in human existence. So long as we can only deal with our conscious interpretation as representing Reality then we derive functionally less meaning than we are entitled to. When we see other humans consistently using levers to open crates then we can recognize a ‘social intelligence’ operating which equates to understanding that is not based on opinion, but is a clear expression of human activity that has correspondence. All of the principles involved in that experience can coalesce to provide that form of Reality that requires no interpretation. It becomes recognizable knowledge. How we understand that knowledge is through the realisation and identification of the principles involved, which become immediately transparent. The Absolute could be categorised as a knowledge experience that encompasses all and everything. Whatever is manifest is that measure (complete in itself) of the Whole with all its principles intact. Where there are at least two actions that are identical we can reach a common-sense conclusion that a definitive principle is operating. When that corresponds with innate knowledge then we have the complete cycle. The definition itself is language opening the door to an experience of Reality. No one can know in isolation. An imaginary ‘I’ restricts any experience of who “we are”,  and is not a necessary part of human experience.   Explaining experience beyond imaginary thought processes requires a definitive language that deals with the principles of Reality itself. Pure experience. The world-wide disposition that has no grounding in Nature and Reality becomes captive to any mythical fear that  offers a target to give some form of direction or stability. There is nothing more simple than to make Reality transparent - its evidence abounds. We can pronounce the principle properties that provide guidelines to its existence whereby the reality is made apparent. = Expansion. = To address concerns on ‘negativity’. Negativity is in essence the inability to establish a measure of Reality. Mechanistic processes of denial are the attempt to understand and make transparent that which is apparently unexplainable, and resolve a condition whose energy is driven toward finding that core of affirmation. The evolutionary principle from all available evidence is that human beings as a species progress. This seems a paradoxical contradiction to the embedded proposition that we can never know the ‘truth’. The consequence of such a traditional premise is that denial and negativity both hold paramount positions. We are conditioned to accept the premise that there is in fact no premise that will enable us to go beyond presently accepted norms of experience. We are conditioned to accept that the ‘truth’ is inexpressible. The evolution of the human species is constantly subject to contemporary ingrained social habits, which give some kind of credence to that particular point of existence. Indirect conscious interpretation classifies itself as a solid perspective to govern and justify human activity, which in many historical ways has proved disastrous.                   Our continued intention is to expose detrimental barriers to the realisation of ‘who we are’, and in that process establish a smoother, more realistic approach to ‘who we are’. The Archimedes legacy. When we establish knowledge of something that exists through a multiplicity of experience and evidence, then from every reasonable standard we can establish that it is true, ergo that which is true is Absolute. The principle of leverage is well grounded in social intelligence, and our natural knowledge of that does not need erudite explanations of its presence, nor any ‘conscious interpretation’ to realise its existence, or its practice. Evolution eventually removes restrictive passages to direct experience, the very purpose of evolution. The principle of leverage is not a matter of opinion, it is the realisation of actuality and our continued ‘more reasonable’ response each time the principle is applied. Children learn to speak their language primarily through experience without any direct, or indirect conscious interpretation, and so, universally we ‘know’ the most powerful means to communicate. Were we to move 50 miles in any compass direction from the town we live in, there is a certain predictability that we will meet others who speak the same English language that we do. If in that experience we find that these premises we have drawn about our travels were true, then the conclusion we would come to in particular, is that when we communicate we make known what we know. …………………………………………………………. '''Please note the date:''' '''Oct 2005.''' I am offering up this older material below to provide insight as to the progression of this work. There may well be some duplication to date. During this period my wife and I worked in collaboration to ensure an equality of experience. = Stepping Stones 1. = There is nothing other than what is – there is no hidden Reality that we need to seek, it embraces us at every turn. The Archimedes experience is the pure experience of Ultimate Reality, which provides indisputable knowledge. Reality is the source of complete knowledge, it is the constant source that has provided us with all human development, from the writings of William Shakespeare, to the computer development of Bill Gates. What they have produced is now an evident part of our reality that we can engage in. We can experience ‘mutual agreement’ through epiphanies, insights, enlightenment , understanding, Eureka moments etc, they are all one and the same. Implicit within the macrocosm is the microcosm – it cannot be otherwise. The more we conform within the microcosm the more we begin to appreciate that Reality contains everything, and that we can realise through experience its manifestation. Each Eureka moment is that personal point of experience that connects us with the Truth. The principle of leverage was always available, it took an Archimedes to explain it to us. Each Eureka moment necessarily engages with the reality of complete knowledge, and utilises its share at that time. When we have complete knowledge of who we are in that personal moment, then we understand that these, egalitarian properties, are rightfully shared by everyone and that we have experienced that which is infinite. It does not mean that the process of evolution is over – it has only just begun. It does mean that we can no longer continue coasting through this existence in a near comatose state. If there is a hypnotic fixation in holding the principles of Reality as being separate, and different, then the potential realisation of their immediate unity, and communion, becomes problematic. Knowledge, and experience are one and the same – they are not different!! Experience = Immediate knowledge of basic reality that is factually correct, and that we can reasonably use. Knowledge = Immediate experience of secure, and accurate information that is constantly stable, and sustains principles. Reality = Complete Knowledge. As the microcosmic part of the total macrocosm we are immersed in reality. The real question should be, ‘how can one not know Reality, or ‘who we are’. Mutual agreement is evident when we know we can go to the bank, and deal with money transactions. Mutual agreement is evident when we know we can go to the supermarket and exchange money for goods. Mutual agreement is evident when we know we can send our children to school to enhance their education. Evident proof is validation of what is – it is not a matter of anyone’s opinion, nor is it an assumption of ours. Neither do we assume, or offer any opinion, on the Universal Reality that there is ‘mutual agreement’ that we need air, food, and water to sustain us. Evident proof is also the basis for the mechanics toward realisation of ‘complete knowledge ‘ of who we are. Reality can be realised through concentration on its basic principles. We use language to express our understanding of who we are.It is relatively easy, it is reasonable, and it is responsible. We convey through language our measure of intelligence, and to the best of our ability conform to the basic rule of communication – ‘we make known’ Implicit within that exercise is ‘mutual agreement’. We may differ in some specifics, but we meet the basic obligation of communication – ‘we make known’, and always we progress to some degree. Simultaneity is one of the constant principles that we all share and they come from Here, Now, the Present, where they have always been. Everything is. Our being is always engaged in the present, and we each have an obligation to understand our relationship to what is. The present is the only point of contact we can ever have with Reality. To some degree or another, each one of us is directly connected to Reality (we do not have any choice in the matter), and we can potentially evaluate ‘what is’ through the utilisation, and examination of factual reality. We are the microcosmic part of that Universal Macrocosm, and because we already have that innate information it is a matching process when we have a Eureka moment, an epiphany, an understanding beyond question. Nothing enters our minds - we already know! Everyone has innate knowledge of the principle of leverage. It requires correct examination of ‘what is’ for realisation to occur. It is then a relief to have ‘mutual agreement’ on the things we would wish to make transparent to others. To use a traffic analogy, it is evident that there is ‘en masse’ mutual agreement when we know to drive off when the traffic light turns green. Mutual agreement is translated into people obeying traffic rules (otherwise chaos). Two cars, two drivers, sitting directly alongside each other at traffic lights, discuss their understanding of their Road Code in this particular position, and what they should do. When the light turns green there are a myriad of principles that apply when they drive off simultaneously. They have both demonstrated their ‘complete knowledge’ of the significance of the green light from this perspective. There is Mutual Agreement. There is Predictable Conformity. There is Common Ground. Each one complements the other. They are both right. One more remove: From an outsider’s point of view – they both know! The green light could be categorised as a Eureka moment, it sets in play all the above principles, whether the drivers are aware of it or not. From the perspective of two outside objective observers who know the traffic rules, if asked, did the two drivers at the lights obey the rules – the answer would be yes, there would be mutual agreement. They have complete knowledge of this particular circumstance concerning drivers, and green lights. Could it be that certain schools of thought are curtailed by a questionable refusal to recognize what is, and have a preference for creating a difficulty where none exists! No one can examine what isn’t! There is no such thing as ‘nothing’. Something is – what is it? A Scottish engineer functions on the same principles as an Italian Pope. Because Archimedes was prominent as a mathematician, his realisation of the principle of leverage, and his understanding of the difference in water displacement between silver and gold was widely reported. This does not mean that realisation of ‘what is’ is an exclusive experience. As said previously Archimedes did not realise something new – it has always existed, and all forms of life would have utilised the leverage principle to some degree or another (watch a bird build a nest). At that time there were probably many thousands of people who had some understanding of the principle, but Archimedes was the one who made statements about it. As in any Eureka moment, we can experience infinity and who we are. It is mutual agreement (an understanding) between the part, and the whole. It is when the principles are in unison Eureka! Reality is there to be examined, and experienced, it is not separate from us, nor should we try to make it so. = Stepping stones 2. = Knowledge is not conditional by the activities of what may be called ‘thought’ or ‘consciousness processes’. Real knowledge is that which is available to all, and to be shared by all. It cannot be contained by the ‘experiencer’ and then not ‘known’ by the accident of experience. It is the actual innate experience itself which conclusively establishes the truth. It can only deal in the truth which is its modus operandi of dissemination. For me to say that ‘everything is’, is a statement of fact which cannot be denied, and an intellectual dishonesty to attempt to deny the evidence by philosophical machinations. Hostility toward the truth leads inevitably toward attempted negation - looking for nothingness! ‘Being here’ demands its own recognition - attempting to deny it is simply perverse. Knowledge is the realisation of ‘what is’.. Rene Descartes ‘I think - therefore I am ‘did no service to human evolution, or education. It established in Western societies especially, the culture of individualism, with the precursor that so-called ‘thought’ was the inward evidence for existence, and for the following unfortunate claim that we have a ‘mind’, or to use the euphemism, a soul! Experience is true knowledge. When that experience marries up with its innate counterpart then recognition is realised (cognition). In simple terms, a light goes on in the brain. There can be no real knowledge without truth. All thought qualifies experience and attempts to reduce truth to near nothingness which is a widespread conditional activity. We cannot manufacture knowledge, or the principles which are its properties. No matter the amount of correct information anyone can ingest, it does not become knowledge until there is tripartite coalescence between inherent knowledge - ingested correct information - and ‘what is’. Then we truly recognize that which is Absolute. Within Nature we have the distinct privilege of evolving in a Universe that can only recognize the attributes of social cohesion. Knowledge is not anyone’s personal possession. Whatever measure of experience we may have of it, it is only available as a Universal sharing experience to be beneficially used. Human activity whereby we witness people using tools for leverage, or drivers at traffic lights obeying the rules of the road, are observable markers that contain the properties for understanding our own reality. Unless seen for what they are, they are only mechanical platitudes with an equally mechanical response. We could rightly claim that that at least is some response, but of no real value. The natural process that operates when we see that which is innate, overrides any erudite explanation from an academic base however intellectual its original source. ‘Thinking’ for oneself cannot make judgments about a ‘natural’ experience. When we see human duplicate functions in operation then we are in communion, and at another level we recognize who we are. When we actively see the activities of the human brain in action we are not dealing with any internal ‘will - o’ - the wisp’ that no one can ever experience. We exercise that prerogative (human activity) at every moment in time, but quite apparently without that focus of attention that denotes realistic recognition. To seek identity in sectarian, or secular belief systems to overcome the contemporary feeling of loss of identity leads to the acceptance of anything that offers some form of stability. That is then used to strengthen that which is euphemistically addressed as the ’self’. To retain that security the acceptance of information transmitted throughout generations, is absorbed into the culture, and defended to the death against those who would question that belief system. The greatest knowledge we can ever have is our own and it has the potential to transcend all else and provide insight into infinity. The most tragic human condition is the lack of experience of identity in a multiplicity of identities in which we all share. The real problem is not one of ‘identity’, but a lack of ’communion’. Whether we like it or not, whether we are aware of it or not, the principle of ’communion’ must always exist to some degree for evolution to proceed. It is within the experience of that principle that we understand the fallaciousness of that much heralded ‘self’ which draws down so much energy in an attempt to establish itself as a reality. Within positive language structure possibilities (no dichotomies), there should be the disposition toward the realisation that our relationships to cognize into ‘communion’ must be addressed as specifically dependent. Social attempts to be ‘independent’ are the very remove from reality and signify reduction attempts toward nothingness. Adherence to, and the cultivation of faith and belief systems give little elbow room for any factual occurrence to be anything other than a comparison to the myths that are held. The cultural and educational socialisation of generations of children must carry with it, its historical belief systems that overwhelm the natural instincts. Observe an animal out of its natural habitat and locked in a cage for its entire life. It would be a salutary exercise if we could dispense with the term ‘mind’ from our vocabulary and magnify the use of the word brain to promote a realistic discussion on ‘who we are’. My action of levering open a wooden crate and knowledge of it is one and the same. Our remarkable brain functions like that, the purpose of a brain, the natural repository of innate knowledge. The assertion of principles is critical to avoid all activity being submerged by questioning their very existence, and being unable to see directly. It would be a rarity today, if anyone using a lever to pry open a wooden crate would have the same enormity of experience that Archimedes had, nor the need to make pronouncements about it. It has all been done prior to our awareness of its value with the accompanying data attached. Our brain knows the value of a lever and activates our body accordingly when needed. It could be categorised as evolutionary transmission. The observance of someone prying open a crate with a lever, or drivers conforming to the road code at traffic lights, is a function of the brain in action, not a mythical entity in a singular locality that denies its own senses. When the brain is not burdened by distorted belief systems it then has the potential to experience ’that which is’, which is always constant. When we understand the function of a lever, or the presence of traffic lights, then we can activate the principles involved because we already know how! The negative impact in the use of dichotomies in language lies in their distraction from the truth, as our brain processes the words we use in relation to Reality. The tendency to attempt to separate inherent truths through the words we use disrupts that natural correspondence necessary for identification. A chair, is a chair, is a chair. = Stepping stones 3. = Where principles are concerned the constituent linkages in language are identity markers to that which is real - reference points. Without dichotomies there is no separation, or ambiguity between what we experience, and ‘what is’. Philosophy in its attempt to address something through denial is an elementary confusion. To say that that is a chair, and then attempt to deny it invoking philosophical theorems concerning the human ability to experience it, is a severe contradiction on the existence of the object , and the observer. When this form of contradiction is then taken as a constant, it then precludes any common-sense and definitive answer to the existence of a chair. '''For philosophers, George Orwell’s ’to see what is in front of one’s nose needs a constant struggle’ would be apt.''' Real concepts cannot exist in any mythology, therefore all that we experience is inevitably the truth that is there to beproperly categorised for what it is. The proper use of language in this context will identify whatever it is to correspond with present reality. Misuse of language (dichotomies and mythologies) leads only to the acceptance of a fractured state where nothing is whole and represents confusion. The dissipation of the supposed problem is never realised. Fiction has been elevated to the status of an accepted reality. Very early evolutionary physical dangers allowed the development of fictions that offered some form of imaginary protection beyond limited physical ability. That contemporary humanity endorses the mythology of ‘I’ is testament to the psychological fear that still exists and requires its proper recognition. Emphasis must be placed in the relationship between language and reality for understanding to proceed. The persistence of dichotomies has their own persistent confusion which then promotes a false reality through misleading information. Microcosm and macrocosm are one and the same in a Universe where ‘everything is’. Isolated viewpoints are exactly that, and are unable to view the expanse in which we are encompassed. We must learn to view reality through both ends of the same telescope. When we understand the extensive scope of ‘truth’, then we know that its values and properties do not change - which relates to ‘completeness’. Philosophical, ideological, and intellectual endeavour , try to shape the structure of ‘what is’ based on pre-dispositional knowledge, which can only ask the same questions, and look for the same answers. Not to experience that which is absolute or whole is the normal result of the confusion of language which has no correspondence to that which is real. To discuss with a philosopher the possibility that ’mind’ per se does not exist, and to dissolve it as a concept would place them in a realistic position, would indeed be a difficult proposition. The strength of that difficulty lies in another imaginary concept, that that ‘mind’ represents ’I’, and it is anathema to that fiction to consider its own demise! = Stepping stones 4. = There are no dichotomies. Everything is, and everything that is, is complete, everything is an Absolute complete Reality. You are experiencing your measure of that reality. It cannot be otherwise that you are experiencing that measure of completeness. When we come to terms with it we have the innate capacity to see the Absolute in a grain of sand. That is knowledge. Belief in dichotomies is the mythical barrier to that particular experience - which is only denial, supported by erudite protestations that human construct dichotomies exist. At a mechanical level Intelligence and Stupidity appear to be separate identifiable conditions, and they appear to be antagonistic. Stupidity is in Reality a measure of the Intelligence which is always constant. If someone was in a state of mythical utter and complete stupidity we would not attempt any form of emancipation from that condition. We know that that is misguided and proceed with techniques to advance intelligence. Consider the proposition that there are no dichotomies, and within that possibility all questions become irrelevant. Presuming that there are no dichotomies allows the process of establishing ‘necessary factors’ to proceed, and allows each measure of wholesomeness to be realised. Experience is the criteria for knowledge. Some Reality experiences were simply transposed into particular belief systems and elevated into a pseudo spiritual dimension, or a philosophical conundrum. Where there is a belief in a divisive fiction (dichotomies) there is automatic mechanistic restriction to that which is Real. There is a capacity beyond ego and intellect which can commune with ‘what is’, and recognize its properties. Reality is constant. Within the accepted comparative framework there is the view of principles as having different divisive categories e.g., as above, Intelligence and Stupidity, and classify them within ‘thought’ structure as dichotomies and give credence to them as being an antagonistic reality. The consequence of that, is, that one is always a remove from recognizing the structural properties of immediate existence. Any construct of knowledge necessary to evaluate ’what is’ will address the properties (principles) that are the constituent constant markers available in that which is the microcosm and the macrocosm. That identity (the Absolute) is found in any sphere of Reality.Everything is - and everything that is, must be experienced for what it is, and not for what anyone denies it to be. There is no mythical human construction that can deny ’what is”. Everything is - without dichotomies. To repeat, we do not have the ability to create ‘nothingness’ - ‘that which is’ has no imaginary comparative human construct. To attempt to deal with such constructs, and give credence to them is always the denial of ‘what is’, and adherence to ‘thought’ processes whose only purpose is to cement that activity. Indeed realising that the concepts of dichotomies are human mythical constructs, denying true perspective, is the beginning of insight. The dissipation of such processes through addressing the principles of Reality allows us the potential to experience directly ‘what is’, in simple terms -the truth! Intelligence is a ‘necessary factor’. Addressing stupidity is a denial of reality at whatever level we find it. Intelligence and Stupidity are not antagonistic, they are one and the same principle with measurable degrees of existence. Only from a comparative framework standpoint is credence given to any mythical form. The above observation is not negating the process, it is questioning the markers which evolve into imaginary separation (trapped in a comparative framework mythology). That particular process can and does create a false mythical reality that appears divisive. We cannot exist within a divisive reality! Reality must be complete for us to recognize its existence. Where there are no dichotomies within the premise that ‘everything is’, there exists no antagonistic position. The distinction between human constructs of positive and negative are matters of mythical perspective wherein no experience of the Absolute is available. It is because the human ’mind’ per se places its own construction on its immediate experience, and must have its particular interpretation based on what it considers ’knowledge’. There is a difference between ’mechanical knowledge’, and ’pure knowledge’. From the mechanical knowledge standpoint which can only deal ‘in indirect conscious interpretation’, it is quite correct to say that that form of knowledge is incomplete, and it always will be. Pure knowledge experienced via our brain knows no separation, nor antagonism, and is responsible for our ability to recognize the actions of others who may pry open wooden crates with a lever, or drive off uniformly at traffic lights. Within that cohesive activity it precludes ’a matter of opinion’ and by themselves can become subjects of a pure knowledge experience. To repeat, it is a form of ’communion’ with ’what is’, and available to all. Where drivers at traffic lights universally conform to their particular road code, and where universally there is a language which identifies their activity as Mutual Agreement, or any other logical definition, we can concur with the common-sense conclusion that we have universally established that within language and common activity, there is indeed a truth formed. The coalescence between universal language and universal activity are the logical constructs that create civilizations. There is a vast social network of common activity that solidifies the logic into an honest and persuasive conclusion that confirms innate common principles –knowledge. = Stepping stones 5. = The Art of making sense of everything. How to understand principles. # Principle. A fundamental truth or proposition that serves as the foundation for a system of belief or behaviour or for a chain of reasoning. # All principles are interdependent, interconnected, and infinite. # Each one is dependent on the other two. Examples of a principles template and how to define them without dichotomies. Communication. Truth. Standard. Proof. Express. Contribute. Mutual. Direction. Advance. Comfort. Organize. Certain. Immediate. Interest. Improve. Present. Constructive. Gain. Trust. Progress. Source. Knowledge. Basic. Original Reality. Awareness.Freedom. Purpose. Connect. Understand. Support. Peace. Cause. Unity. Ability. Rights. Honest. Discover. Positive. Energy. Balance. Good. Courage. Willing.  Control. Use. Association.  Observe. Reason. Easy. Wealth. Simple. Law. Increase. Order. Flow.Co-operation. Exact. Quality. Accuracy. Strength. Responsible. Operating. Creative. Measure. Recognition. Accept. Constant. Obligation. Include. Dependence. Relationship. Value. Success. Principle. Equality. Stable. Share. Love. Sustenance. Action. Identity. Intelligence. Education. Secure. Facts. Agreement. Information. For. Rules.Clear. Yield. Example: Success = Securing facts                = Responsible co-operation               = Constructive knowledge So success by definition is : Securing facts through constructive knowledge and cooperating  responsibly. All definitions of success from your template are infinite. You will find your own suitable definition. ==== There are no dichotomies! ==== Any principle is correctly defined by any two other principles. You create a new language of Absolutes. Using conjunctions you can write your own book. The man whose book is filled with quotations has been said to creep along the shore of authors as if he were afraid to trust himself to the free compass of reasoning. I would rather defend such authors by a different allusion and ask whether honey is the worse for being gathered from many flowers. Anonymous, quoted in Tryon Edwards (1853) The World’s Laconics: Or, The Best Thoughts of the Best Authors. p. 232 Amen to that! “One is not born, but rather becomes a woman” Simone de Beauvoir. “Time does not change us. It just unfolds us” Max Frisch. We experience ourselves our thoughts and feelings as something separate from the rest. A kind of optical delusion of consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Albert Einstein, in One Home, One Family, One Future. = Who we are. =   It is notable that within the structure of Cartesian dualism, Descartes' personal address to innate knowledge he attributed to ‘thought’ which he identified as being distinct from his body. How different Western philosophy may have been if his attribution had been toward his brain and the existence and evidence of other physical entities that functioned every bit as efficiently as he did. The premise that Descartes operated from ‘never to accept anything as true’, was simply a wrong ended approach which brought him into conflict with his passing acceptance of innate knowledge, that the idea of God was innate to his being. To view the proposition that ‘everything is true’ allows reason to seek and identify that measure of truth. No quest can be productively based on cynicism or denial, nor adherence to belief systems that separate experience, knowledge, and Reality. We have the obligation to question whatever reality has placed before us , but if we constantly deny its existence and attempt to ‘disappear’ it from our experience, then we are in danger of never experiencing that reality for what it is..   For anyone to say that ‘everything is’ is a simple linguistic absolute that no amount of ‘more reasonable’ requests (above) can deny. Those requests only appear to be governed by the difficulties of ‘mental complexities’, and embedded ideologies. To accept that ‘everything is’ as an absolute, is a realistic basis to establish any reality, and comprises the basis for reason to be activated. If there is ‘nothing’, nothing can be achieved. Within that which is Absolute there are no dichotomies. Therefore there are no antagonistic positions available. Everything that is, is a measure of the Absolute.  We are always in the present, everyone and everything. Instant elementary ‘knowledge’ which we all share, and must admit to. In being alive, we do not have the ability to not be here, and we do not have the ability to not know! To have a problem in addressing what Truth and Knowledge are, to the point of denying their existence, then that problem exists well below the scale of Reality. To repeat knowledge is not the proprietary right of any individual, it is enshrined in the principle of agreement that we mutually exercise to establish its own reality. The reality of experience is not, nor ever will be, a personal possession that we can have and hold. Its reality becomes more alive when we see the same activity being practised by others. Then we know we are sharing that reality, and that experience. We cannot "have" the principles that exist, but when we undrestand them then we are obliged to use them with integrity. That form of integrity in any language, is an added foundation stone to any belief system Mechanistic ‘I’ has no concept or understanding of ‘pure knowledge’. Only when we break free of the myth that some clarity becomes apparent, and we have the opportunity to engage with what is real. Philosophy it appears to me is constrained by individual ‘thought’ processes, which (without experience) cannot escape from that individuality. Those ‘thought’ processes conjure up a human history of inflexible, and impossible propositions which only serve to protect that individuality. Descartes ‘cogito ergo sum’ has compounded the difficulties by strengthening the incorrect premise of a false individuality. ‘I’ is a phantom consciousness much like a phantom pain experienced after a limb is amputated. The brain registers the pain signifying that something should be there. Likewise our brain has that same relationship with Nature and Reality. It is analogous to our brain dealing with a ‘phantom reality’ knowing that something is missing but is continuing to evolve to establish the whole. There exists a ‘phantom chasm’ between our brain and Reality and an understanding of its properties. We are robbed of real meaning. Evidence, recognition, and the truth are the principles it uses to reform. Within their structure is the meaning of reforms. Nature does not impose any morality on us, the principles implied in morality are there for us to understand and use. Our brain has the capacity, once reality is correctly examined, to recognize ‘that which is’. Once realised it becomes embedded. That ‘phantom consciousness’ is an experience removed from its proper environment. It takes its proper place when we experience reality for ‘what it is’, which provides the totality of meaning. True experience allows us entry to the quality of knowledge that is a continuous reality. So long as anyone believes that human experience is based solely on indirect conscious interpretation (mechanical disposition), any ‘knowledge’ derived from that experience will be incomplete. That form of philosophical negative conclusion can come down to not believing that Reality exists (a chair is not a chair, is not a chair etc,), or that our experience of ourselves and others is real, and discount any other form of knowledge that threatens that belief. There is an intellectual dishonesty in denying the existence of principles. Hostility towards the truth leads inevitably to negativity. Being here demands, not denial, but the right to be recognized. We are the recipients of a ubiquitous communication system – making known. We can only understand that which we know. We make known all the time. Knowledge of Reality – Truth – the Absolute is a collective inclusive experience of the principles we share, and never the property of any individual. To ‘know’ ‘who we are’ is an inclusive experience of the principles involved. Never ‘cogito ergo sum’.   Philosophers in investigating the nature of knowledge and the Universe, firmly established for themselves that the source of reason and logic was located in a mythical concept ‘the mind’. From the wrong basis evolved elaborate and metaphysical constructions which removed the investigations further, and further, from the truth. To comprehend the material world, and give it credibility, the recognition of implicit principles is paramount. We need to construct a language that provides that form of recognition. Any philosophical theory of ‘mind’ that will deny the evident structure of solid objects is misguided by the injection of a mythical entity (mind) that determines that seeing solid objects is a ‘perceptual illusion’. That form of determination is singularly narcissistic, empowered by the self-induced threat that venturing into a ‘materialistic’ world is a loss of that illusory self, and all the belief systems it has constructed to protect it. That erroneous established view that not addressing ‘materialism’ as a profound Reality, and as only a ‘perceptual illusion, is compounded by the belief that that form of illusion is implicit in every human view available. We cannot manufacture knowledge that leads to a mechanistic understanding of ‘what is’ , nor the principles which are its properties – however much dogma is practised. We can only aspire to relate to ‘necessary factors’ that are the implicit fundamentals of existence. For me to use a lever to open a crate is a form of communion with Archimedes through the principle he enunciated. It is now not ‘necessary’ for me to go through the same experience as Archimedes to establish that ‘necessary factor’ or ‘principle’. It is now common-place, and common-sense to utilise the principle. The extract below provides some explanation of the brain processes in action Universally, and coincides with any reasoning on the observance of the leverage principle, and the actions of motorists conforming to the Road Code wherever traffic lights exist. ''The right-to-left shift of mental control looked increasingly like a universal phenomenon, capturing the essence of every learning process on every time scale, from hours to years. An individual faced with a truly novel situation or problem tackles it mostly with the right hemisphere. But once the situation becomes familiar and is mastered, the dominant role of the left hemisphere becomes evident. It looked like the empowering patterns capturing the essence of the situations (or rather the whole class of similar situations) were, once formed, stored in the left hemisphere. (The Wisdom Paradox. Professor Elkhonon Goldberg. P202)<ref>{{Cite journal|last=Vandermeulen|first=Jo|date=2008-08|title=Verstand komt met de jaren|url=http://dx.doi.org/10.1007/bf03077135|journal=Neuropraxis|volume=12|issue=4|pages=137–139|doi=10.1007/bf03077135|issn=1387-5817}}</ref>'' = Limitations. = However limited our view of connectedness is, or however tenuous the reality our experience is, ‘everything is’, and everything is connected. Innate knowledge and the fundamental nature of Man is the prior source of knowledge that seeks and identifies that connectedness. Attempting to address what we don’t know is that mythical infinite regress toward that parallel mythical ‘nothingness’. To always address what we know establishes Reality. To establish knowledge of principles, start from ‘we are here’. The natural principles within the diversity of human culture and activity when recognized as mutual ‘necessary factors’ will have the effect of enhancing and directing vital energy toward the very process of  the communion we seek, and the gradual penetration of a reality that always exists. Knowledge of Reality is not ‘different’ in other locales. The fundamental principles are the same. Addressing ‘what is’ instead of denying ‘what is’ is the basic construction of real knowledge. Within the structure of the Absolute we are all the same with a magnificent differential in our expression of the principles of necessity. That expression is our ongoing effort toward its own experience which gives it life and meaning. That experience in turn exposes us to an immediate Reality that is in communion with the fundamental structure of our being. All that we can contribute toward that is 50%, the other half is in our momentary relationship with Reality – then we know! That form of knowledge is always available through that form of experience, and it always comes in the form of confirmation which reforms. Until that experience our prior condition appears mechanistic, without direction, or understanding. Reality, life, is not mechanistic. We are the recipients of innate principles with the constant potential to experience those principles in action (Archimedes et al). Dogmas, ideologies, are the restrictive practices used to blur the recognition of principles operating to a level that understanding of that common and constant activity is virtually denied. Our natural capital (principles) is degraded to the point that their factual evidence is reduced even to the point that they are categorised as a ‘perceptual illusion”. We can trust facts 2+2=4. Simplicity has its own majesty. Anything circumscribed by reason requires control of our emotions. To comprehend the material world, bring it alive, and give it credibility, the recognition of its implicit principles is paramount. We need to construct the language that provides evidence of that Reality. Any philosophical theory of ‘mind’ that will deny the evident structure of solid objects, is misinformed by the injection of that mythical entity (mind) that determines that seeing solid objects is a ‘perceptual illusion’. That form of determination is singularly narcissistic, empowered by the self-induced threat that venturing into a ‘materialistic’ world is a loss of that illusory self, and all the belief systems it has constructed to protect it. The erroneous established view that not addressing ‘materialism’ as a profound reality, and as only a ‘perceptual illusion’, is paradoxically compounded by the belief that that form of illusion is implicit in every other human view available, thus it then makes its own sense, form and justification to the illusion! The evident question we must ask, ‘how does a ‘mind’ conclude that ‘immaterialism’ exists universally? Surely it is a simple but massive contradiction in terms. If there is nothing there but ‘perceptual illusion’, how can you attribute it to other ‘minds’. The oxymoronic effect of narcissism is that it is the very denial of ‘who we are’. Man is not composed of an overwhelming self-love. That mythical embedded belief cannot consider the possibility of underlying principles that are the real life force of Man in his relationship with Reality. The truth of that, is that humankind (in spite of itself), evolves towards its own Reality. The only human values that exist, lie in Man’s recognition of the principles involved that provide human direction. Our ‘material brain’ is a product of Nature's evolutionary process, and has innate within it the same principles that exist in all matter. That ‘which is’, is the truth, and our brain evolves to process that at every level, and we constantly manifest that in every action we take – whether we like it or not. The fundamental similarities between human beings is that we are not only evidently human, but that we also function and construct societies that we recognize as beneficial to our immediate well-being. All social function is determined by our brain capacity and its ability to postulate the relationship it has with Universal principles. = Illusion. = Considering that we can contradict things is an illusion. We can never contradict the truth. We do not have the ability to create proprietary constructs of reality. That ‘which is’, can only make its basic properties transparent to us through direct experience. Imaginary concepts must in the end conform to a measurable construct that we can identify. Within the structure of any philosophical theory of ‘knowledge’ it must contain the basic elements of truth at all times, or there is nothing!! To say that ‘everything is’ is motivated by pure reason experience as an objective, and subjective reality and as an axiomatic grammatical premise that no amount of mental acrobatics can deny. We can only deal with ‘something’, whatever it may be. There is no metaphysical construct that can provide evidence that ‘nothing’ exists, outside a mythical mind. Explaining experience beyond ‘thought’ processes requires a definitive language that deals with the reality itself. We all Know. It is innate. The ‘difference’ between us is only the measure of the knowledge that is made manifest, and that knowledge continually proliferates. The ‘individual perspective’, and the illusory ‘I’ which dominates, is the barrier to any relation to ‘what is’, and the malady of never experiencing the truth directly!   Truth, knowledge, agreement are the abundant and embedded Absolutes that form the structure of human evolution. That we constantly utilise and improve on their use is evidence of their reality, and the material transparency within every social structure. The survival and proliferation of such realities should be the evidence to establish that ‘that which is’ is Absolute. When we focus our ‘perspective’, opinion, or a hypothetical consideration of a space, time, or identity to question a Universally accepted fact, it is hardly a categorical argument to dismiss that which is true as nonsensical. Any denial that 2+2=4 is a fundamental truth hardly takes into account that the reality of such basics are vital to the success of higher mathematics. Unless the basics are continually correct, and evidently so, then no correct solutions could evolve. We know that within any basic structural ‘use’ that the calculation is correct. We commonly accept its correctness as an embedded reality. All forms of lower or higher mathematics would have the axiomatic principle of ‘correctness’ as their basis to extend from. Also, they would have as an axiom that the reverse is true. The 2+2=4 is, in its reality, the epitome of balance and construction. The 2+2 reality forms its correct conclusion when the principles of mathematics are propounded and they conform to transparent truth and arrive at 4. Only when it ‘adds up’, does it become a truth that we all recognize. Our greatest ignorance is taking for granted the proliferation of such truths through an ideological blinkered perspective. Because truth takes a commonplace form it is no less fundamental. Unless there is correct knowledge as to the existence of fundamental truth, that ‘which is’, goes unrecognised. That form of truth must be applicable to all. Truth exists in everything – it is an evidential reality. Searching for an esoteric truth is chasing shadows. Every truth is a ‘necessary factor’, and fundamental to our existence. Because of the imposed limited perspectives (via education, ideology, beliefs) that which is evidently true, and transparent, is delegated to a position of simple practicality with conditions placed on it which further deletes its substance, and we have the awful predilection of conforming to the attempted destruction of that which is true. Do we have a problem with seeing something, which is correct, as also being true? All truths are fundamental. They are not subject to attempted denial because of any diminished realisation at any point in time. Where there is reasonable evidence of balance, equity, and agreement we can conclude that a truth exists. Once innate information of that truth becomes transparent, it becomes an embedded useful human utility that must have some measure of fundamental truth as their starting point. From any common-sense, or ‘more reasonable’ position, it would be more productive to view reality as possessing at every level the same innate values or principles consistent with our ability to measure, or recognize them. To view reality as having ‘different’, or antagonistic properties, is simply a misguided view of ‘what is’.  That form of perspective is counter productive when it attempts to establish mythical dichotomies as realities in their own right. When the reality of principles are made transparent, we can then ‘more reasonably’ make use of them to further their basic existence. Here we use reason to exemplify their necessary function, and once established it becomes (if necessary), ‘more reasonable’ to locate them in all things. The dematerialization of any object through the practice of ‘perceptual illusion’ is an attempt to deny the reality that exists. Where perceptual illusions are concerned, innate direct communion with that which is, suspends the effect of such illusions. All the properties in a chair are recognized as the reality that exists. That is materialism. A chair does have the principles of form, design, structure, colour, substance etc.  However it is analysed – it is a quantifiable reality.   = Human representation. When we understand the validity and existence of principles in all things, it is easy to understand that ideological dogmas are never the foundation for real knowledge, or that direct experience of ‘what is’. Our real perspective is not some individualistic experience that confines us, it is that expanse in which we exist that offers us the view of that expanse. Everyone has the potential to go beyond their ‘apparent’ human perspective limitations. Shifting our sense of perception toward that which is basic, paradoxically extends the experience of that which is true. Let general knowledge be directed toward the performance that identifies the measure of principles that are enacted. Therein lies the production of knowledge that offers a sustainable growth of that vital universal aspect of knowledge, where, reason and truth, can prevail. Any correct definition is language itself, opening the door to that reality experience which is critical. Only when we know and experience that the same reality (with all its principles intact) exists for all of us can we then recognize the mythical distinctions that are taken as being real. The majestic experience of that reality goes well beyond historical beliefs. Exploring simple ‘necessities’ is not based on any sacred text, but the privilege of recognizing a sensible evolutionary path through life. Whatever may be in the future, is implicit in the material world now, and it has always been so. f0rrk4hcnk4w1eru1feb1107o16ge2z 2412497 2412488 2022-08-07T09:11:19Z Hamish84 1362807 /* Everything is in scale. */ Changing historical text wikitext text/x-wiki = <ref>'''William Shakespeare''' (bapt. 26 April 1564 – 23 April 1616</ref>A message. = What humanity needs is not any individual approach but a governance powerful body of excellence that has modern technology, knowledge, and freedom they can use to disseminate clear information. Clear information about a new language structure of absolutes beneficial to an International forum, and eventually to reach a Universal status.Its benefits reach toward conceptual language on a planet that speaks more than 7,000 languages. No matter the language spoken the concepts of: Air - Food - Water are recognised. The overall development of conceptual language can only be beneficial and will be as appropriate to Absolutes definitions. Reaching for the Stars might show us the way. Universal Language of Absolutes. "A very grand title but it took many years to explain its value" = Our history. = Born in Scotland in 1927 left school at 14 years of age. Married at 21 years of age and we had two children. We emigrated to New Zealand in 1953 and lived there for approximately thirty years. During our stay there I did a Liberal Studies Course at Canterbury University Christchurch and graduated. We have since had ten books published through Google books on the subject matter at hand and my wife Jean Caldwell McMillan is the co-author to most of the work presented here. My wife Jean was an avid reader of many works on philosophy and psychology. She was influenced by the works of Erich Fromm. Jean died 9th of January 2011. To refresh the original purpose of  our  earlier writings my wife and I  went on an odyssey  looking for any data, ancient or otherwise, on human consciousness, specifically related to Alzheimer’s disease. Now at 95 years of age (well past my used by date) it may well be that I am a candidate with a focus on my own pending dementia. If so, then the theory and the method I now write about is holding it at bay. To address the health of my mind in this way could be the catalyst that retains its own functional activity. The creation of a  semantic template is well documented below. No semantic definition of absolutes or principles can be ill-defined. They are always interconnected, interdependent and infinite. Each configuration constructed by anyone has meaning particular to them, although its value is universal. That  is why it is never personal property! [[File:JimNJean.png|center|thumb|228x228px|Jim and Jean]] = The Beginning. = "The road's half traveled when you know the way" [[File:Tree lined path - geograph.org.uk - 2269906.jpg|center|thumb]] Oxford dictionary definitions: Principle: "A fundamental truth used as a basis of reasoning". Absolute: " Complete - Entire - Perfect - Pure. These particular dictionary given definitions offers us guidelines to ‘existing conditions’ necessary for complementary understanding, and experience. We can only examine that which is real, basic evidence, that is fundamentally true, and we must ‘use’ it, to establish that which is reasonable. The general consensus is that there are no Absolutes. The following material is set out to show the very reverse is true and that everything that is is Absolute. Establish that there are no dichotomies that will leave the primary terms alone to create a semantic template. There are no dichotomies. Mythical dichotomies distort Reality. Everything is: The computer you use today has always existed, it is the arrangement of particles that have materialized it. The subject matter "Universal Language of Absolutes' is promoted to provide a new understanding of spoken language. This understanding was initially constructed by the cognitive experiences of both my wife and myself many years ago. Just like the principle of a jigsaw puzzle, meaning lies significantly in the fact that all pieces of the puzzle are interdependent and interconnected. When completed they provide a picture of the whole. We have endeavoured to produce a picture of the evolutionary process of language in human history because the evolution of language prefixes all modes of thought in human culture. The material directs the reader towards a new view that all that evolves is in a vertical direction, not the linear direction commonly understood. Human consciousness is of itself the phenomenon of evolution and to recognize its existence is part of the process. Shakespeare expressed this succinctly through the voice of Juliet who proclaimed, “a rose by any other name- would smell as sweet.” [[File:Comestible rose in the Laquenexy orchard garden, Moselle, France (01).jpg|thumb|center|237x237px]] === Conceptual language. === My wife and I recognized how profound the extension of this observation would mean conceptually. Of all the languages spoken on this planet, it would be fair to say that all of them would contain the properties of, air, food, and water conceptually, etc. This is a form of consciousness equality that is available to us all. It points to the reality of our constant relation to each other and our existence. We can never exist in a world of individuality, but only in relation to the consciousness of one another. Consequently, that exceptional experience can only be shared superficially. We cannot ‘know’ any other life experiences other than our own introspection. <gallery> File:Einstein 1921 by F Schmutzer - restoration.jpg </gallery>" ''Albert Einstein 1921. We experience our thoughts and feelings as something separate from the rest. A kind of optical delusion of consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us."'' ''Albert Einstein, in One Home, One Family, One Future,p.99'' Einstein came very close. In reality, every human being has a backpack from the day they were conceived. In the backpack every experience in their mother’s womb is experienced. At birth and throughout their lives, everything that happens to them in life is registered and creates their personality. That life with all its experiences can never be known to anyone else, consequently, we can never “know” another person. It creates equality of consciousness that we must understand. We can know details about a person, but that is all. That life is sacrosanct. Who we are really goes beyond normal human experience and into the realm of the Absolute. Werner Karl Heisenberg (physicist). The Heisenberg Uncertainty Principle. As a young layman with no knowledge of Heisenberg but interested in principles it seemed to me that the Uncertainty Principle was just a contradiction in terms. In later years I found that Heraclitus describes life as being in a state of flux a replica of the Uncertainty Principle which in fact can be defined as an absolute state. Within the context of knowing who we are and the backpack we carry our life in, we can never know each individual life as that life experience is singularly their own and sacrosanct. It now seems that the Heisenberg Uncertainty Principle can fall into the category of being an Absolute. Evolution proceeds in advance of our need to evolve. In our pure active state, we are.There is no static end (an abomination) - only beginning. As we cannot know what tomorrow will bring, living with expectations is rather futile. Nature has its own agenda. Zen Koan recorded 1228: 'An instant realization sees endless time. Endless time is as one moment. When one comprehends the endless moment He, or she, realizes the person who is seeing it.' We do not own Space. We do not own Time We do not own Energy We do not own Matter [[File:Universum.jpg|center|thumb]] "What we call the beginning is often the end And to make an end is to make a beginning. The end is where we start from We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time" T.S Eliot = Everything is in scale. = The present moment is the point in which Eternity has placed us – we all live in that moment, and whether we like it or not, we exist in it, experience it, have knowledge of it, and we all share it, measure by measure. There are no dichotomies. Illusion is a measure of Reality, as Stupidity is a measure of Intelligence If one keeps measuring illusion it is an attempted downward spiral to nothingness.There is no opposite to Reality – that illusion is a measure of Reality. There is no such thing as ‘nothing’ in the elemental construction of Homo sapiens. All the innate ‘something’s’ are the fundamentals of our being human and all our experiences. The correct use, and understanding of who we are, is an extension therefrom. Does it require any interpretation on anyones part to say ‘we are? Any attempted denial of that statement would be perverse use of the language, and delusional. === Try saying ‘we are not” === ‘We are’ is the foundation of all affirmation, and within that spectrum, we can know, and be. ‘We are’ is self-evident Truth. We can neither know, nor experience what isn’t. Eternity is the here and now, that is why it is possible to explain the experience of Eternity. Nothing is ever lost in Time. We are located in a vast Universe. ‘twas a moment’s pause,- All that took place within me came and went As in a moment; yet with Time it dwells, And grateful memory, as a thing divine. Wordsworth Prelude, Book V111 We already know – the ''basic'' condition that must exist for us to re-cognise. It is at that moment of pure affirmation, when all that is, is manifest. Unless there was mutual identity we could not know anything. It is why we are urged to evacuate the Platonic cave. Sadly most prefer the shadows rather than confront who they are. We already know – the basic condition that must exist for us to recognise. It is at that moment of pure affirmation, when all that is, is manifest. == Lost Shadows == [[File:People Shadow.JPG|left|thumb]] The shadows move Lost in confusion Lost in despair Imagination shrouds the real Looking back Looking forward Is this the Centre? James Brines. = Basic Principles. = We are all in the business of living and attempting to understand the principles involved in that human process up to the end of life. The implicit principles necessary for life eventually disappear and all measurable criteria pronounce a body to be devoid of life. Throughout historical agreement we know what that means, and we act accordingly on *common knowledge*. We know that dying is a necessary factor of life. It is a Natural law that if we live - we also die. Natural law is Universal, for us to *know* that a body lives; we also *know* that a body’s life will end. Albeit that reports tell us that today millions of people die of disease, starvation, wars, we of necessity accept that as the ongoing reality because again we are universally connected and know the results of such carnage. Because it is in our realm of common knowledge we have graveyards, crematoriums, undertakers, doctors who pronounce bodies to have died. We understand the consequences of leaving such bodies unburied, the diseases that would prevail. Again, please explore the definition of principle (Universal principle) and try to go to the limitations of the definition without using mythical dichotomies. [[File:( A great picture of outer space ).jpg|center|thumb]] Principle: A fundamental truth used as a basis of reasoning. All of these questions are based on singularity (the Cartesian dogma)… If Descartes had only introduced inclusion into his musings (they were taken as conservative singularity) he may have realized the difficulty of addressing thought as reality. He then may have quite easily concluded that universally - *We are!!* That pronouncement is inclusive, and conclusive in every way, *we are - and we know!!* Because my knowledge is not a private, personal piece of property concerning principles, but Universal (Archimedes et al), then that innate knowledge has completeness we can share. Whatever identical resonance we may be able to share (concerning completeness), that can only be accomplished by understanding the principles involved and their constant relationship to each of us. Clearly the plethora of present and past discoveries establishes the existence of that which is fundamentally true, and the foundation for law. The principles are established, and always have been, we are in the business of making them transparent and complete. However tenuous the link we are all connected through communication, the air we breathe, the ground we walk on, the universe we live in, the common principles we live by. We all must have sustenance to survive, or we will not live. (See above) <nowiki>*</nowiki>There is nothing else to experience.* When we actively explore the reality of anything, all principles involved in that exploration are complementary, and honest, and we understand the wasteful divisive mythology that people attempt to attach to them. We cannot */partially know/* the truth, it must be complete. Dichotomies attempt to deny the existence of truth, and are misleading. How do we more reasonably completely know anything? The complexity of language systems with contemporary usage requires new and creative structures to provide clear information. Internal and external reasoning capacities can only develop in concert with Man’s recognition of the principles that essentially form our lives. The inevitability of human consciousness rising beyond its historical beginnings posits a future outside our normal perceptions, and  a factual reality that points to the existence of new perceptions that are infinite.   It is natural to know when we are no longer trapped in any mythical ideologies that gives credence to dichotomies that stifle the recognition of simple principles. There was no cause for knowledge to be established - it has always existed.* Ask yourself - ‘how do you know to ask any questions at all?’ There is no hidden dimension or mystical world. The only philosophical reality is ‘that which is’. To access that we need a new structure to explore ‘knowledge’, a new transformational language. Real knowledge is not amassed information, nor is it the establishment of dogmas, isms, or mythical belief systems. Basic principles are the source and foundation of all /*knowledge*/e. Until that is recognized, extension from mythical sources only leads to a denial of one’s own senses. Trying to conceive of a contemporary world without principles is to posit a world without reason, or intelligence. The principle of pure knowledge could be said to exist in another dimension given the present state of human understanding. To progress that mistaken belief there would be strong support in the need for a comparative reality. Curiously it seems that philosophy (the seeking of knowledge) constantly discounts any knowledge that does not come within the sphere of established philosophy, and the comparative reality dictum. That consequence profoundly distils the purity of any experience and alienates the observer in their confrontation of that which is real. The measure of that ‘comparative reality’ knowledge bounded by dichotomies is so restrictive that it lies in a mythical dimension where denial of its very purpose is the order of the day. Evidently it will not allow doubt to undermine its own denials. A basic principle of Nature is /*knowledge*/ and it constantly communicates innately in every living structure. How to grow, develop, and disseminate. Knowledge is reciprocal truth that depends on our relationship and the recognition of principles operating. Knowledge (unlike information) is not stored in an individual box; it is ubiquitously manifest in everything we do. Knowledge is the experience of a positive reality, and its true construction is a dependable source of secure information (not to be misused). We daily have the opportunity of witnessing ‘knowledge’ in action as expressed by the ‘the principles of knowledge’, namely the principles themselves. The questions lie in a continuing mythical belief in a mystical unknown (the Cartesian stance) which because of its non-existence can never be known. It is a belief that is detrimental (because it attempts to deny all existing factual knowledge) to dealing with Nature and Reality and the fundamental necessity of our relationship with them. Making that relationship transparent is our basic obligation and the ongoing evolutionary activity. Although there is an obvious avoidance to address the definition of principle itself, it is a factor that must be paid attention to, to realize that ‘common knowledge’ is the only reality that exists. Amazingly although there is avoidance of principles - truth - reason etc, there is acceptance of the Cartesian dogma,. Paradoxically this determined acceptance of Descartes supports the reality of innate knowledge existing (I think - therefore I am) which establishes for him innate knowledge; however mistaken he is concerning the interpretation of his experience. = Leverage. = Long before I read of Archimedes and his various principle discoveries I was using the principle of leverage in a variety of ways, prying lids off boxes, moving articles with a lever well beyond my physical strength to do so without said lever, and I knew how to do it. Transferring that knowledge to a student or apprentice is relatively easy because innately they also /*know*/ how to do it. Every aspect of human industry uses the principle in a myriad of ways because it is our obligation to constantly progress the principle and confirm the constant utilization of knowledge. We wholeheartedly adopted Archimedes principles (et al) because we recognized their fundamental utility. It is preposterous to question the widespread /*factual knowledge*/ of all principles, more especially so when we cannot escape their ubiquitous daily existence in all our lives - Nature and Reality do not lie. One may abstain from admitting their existence. To do so is simply attempting the impossible, and is devoid of all reason. Real knowledge has been put into the realm of the mystical unknowable even to the point that knowledge practitioners go to the outer extremes and deny the gift of their natural senses. With their adherence to what they consider is knowledge they become captive automatons to any prescription for life that is expressed in that ’knowledge medium’, which then becomes the authority. When ’knowledge’ is addressed as having a collective source in Universal principles then we have the potential to experience its complete reality (microcosm - macrocosm) without any imaginary, or divisive comparative content. There is then a re-orientation process toward our true being and recognition of our own reality in relation to the natural processes we share. Real knowledge is elementary and Natural. We know, because that which is knowable is constantly expressed by the principles involved. We all share those principles and can correctly infer the most simple and obvious truths. All social life functions by our adherence to the implicit laws operating within them. Seeking experimental contradiction to a fact of life offers us nothing but proof which is the establishing of ‘complete knowledge’ however ‘more reasonably’ one wishes to extend the exercise. The construction of new philosophies must seek a mandate to fully explore the relationship between experience and innate knowledge as the foundation for pure knowledge to emerge. To repeat, knowledge or truth do not reside in any individual domain, nor are they the private possession of any human being. We know, because ’knowledge’ is an innate natural possession that we constantly share - otherwise civilization could not exist. == Knowledge: Evident facts about mutual standards that provide us with security. == We do not become human beings because we can ‘think’; we become more human because we learn to conform to the implicit principles in Nature and Reality. Denying them - denies our being. It is natural to know. There was no cause for knowledge to be established - it has always existed. Knowledge is an evolutionary process. Human beings developed from primitive innate instinctual knowledge to contemporary cultures. Some know more than others through experience, and make that knowledge transparent. Insistence on how we can ’completely’ know is an ephemeral philosophical question that attempts to deny that we can have ’knowledge’ at all, as you understand it. Knowing that we ’know’ the inherent completeness of everything through the existence of principles, is the natural catalyst to make ’that which is’ transparent. Heraclitus: "No man steps in the same river twice " He believed in the "Unity of Opposites (Absolutes). He cried for the needless unconsciousness of mankind.. “Exploration of a mythical dichotomy below for the purpose of establishing principles. Principles that are not a 'mind' construct, but the very essence of our being. Independence, is the curious and dangerous malady where humanity has lionized negative mythology in denial of its own reality. The human fundamental reality has at its base the simple natural law that we are dependent beings. From conception, the human embryo is entirely dependent on the health and well-being of its mother to provide it adequate healthy sustenance to enable its entry into the world. That form of innate dependability the human species carries with it throughout its spectrum of life. Every aspect of human activity is premised on the availability of air, food, and water without which the organism cannot survive (this would be an incontrovertible 'more reasonable' truism or an Absolute). In a perverse way, that which is our natural state has become the target for what appears to be open defiance of the laws that govern our behavior. When a basic premise is either used mistakenly, or deliberately, its consequences can be socially far reaching, for any deviation however far it is extended is a distortion of the truth, and a denial of who we are. The erroneous conclusion through exercising responsibility that we can confer independence to our actions has gained a distorting and ubiquitous influence which paradoxically undermines the very responsibility practiced. Within the context of being dependent we can correctly be responsible for our own actions but with the surety of knowledge that that responsibility is contingent on the measure of life giving forces available that we are dependent on. The mythical dichotomy 'independence' connotes with the myth of separateness, division, alienation, and the force of these particular myths is expressed in wars, genocide, criminality. Alarmingly the mythological term has become a residual in our lexicon and is used more widely with acclaim than its true counterpart. To uphold delusional 'independence' as a value to strive for erodes our human heritage by diverting useless energy toward a dubious goal, and consequences that leave us questioning our means of arrival. Sadly it is a loss of being with the paradoxical view that the energy expended will deliver up a personal reality. The cult of independent individuality with its mythical ideology based on personal intimacy is now taken for granted, which then passes into the acceptance of the spurious dichotomy as a tangible reality. This in turn disposes the adherents to discredit the very essence of their being, and in the process dehumanizes many cultures. The presumption of independent individuality leading hopefully to a superior future is in fact counter-productive to the purpose, and leads eventually to corrupt power, and subsequently the invention of immoral policies that continue the negative spiral, which in the end has no ethical base to extend from. The alienation from our substantial being creates inevitable tension anxiety, and the need to somehow relieve that anxiety with any artificial means available. = Responsibility. = Being responsible for any social activity would best be enacted with regard to the effect it will have (directly or indirectly) on the lives of those who are dependent on a beneficial outcome. To recognize with some significance the basic structure of our being in turn significantly increases the measure of our understanding of human relationships. Being dependent is not a mental construct choice - it is a state of being, and there can be no being-ness without at least one other being, there is then the possibility that the principle of true egalitarianism becomes the manifest reality. Being-ness can only be identified and expressed in relationship. This is why the cult of 'independence' is eventually so socially destructive, as it creates that alienation which attempts to deny each real human need, and leads to a depravation of honesty. Human relationships between children and adults where independence is the accepted norm is severely undermined when the educational process predominantly teaches an unnatural form of living (either intentionally or unintentionally). The educational process is then reduced to the adoption of a fiction, which in turn puts at risk any educational program. The effect of interpreting mythical dichotomies as described here is symptomatically ascribed to the existence of all other principles that govern life. The construction of any ethological debate should not be premised on comparative perspectives, based on human thought, but rather on the issues that we can recognize as being universally compatible, therein lies the common denominator point of extension. The focus of attention on comparative perspectives denies justice to 'what is'. To contemplate the 'right or wrong' of any circumstance is a deviation from the truth. The correctness of any debate (however minute the finding), is the justifiable extension, and the only true trajectory we are morally obliged to travel. Truth is not defined, nor experienced by comparison, but by 'what we are'. An orange is to an orange, what an orange is to an orange. To define correctly there should be careful and disciplined action toward establishing 'true factors' that we constantly use to promote reasonable standards. = Time. = In that moment of time, we have the potential to merge on an equal basis with the reality that exists, and to know what true interaction is. That is the point of 'direct experience'. It is then that we know the truth about ourselves and the beauty of this Universe which also reveals to us the folly of our present conditioning. In that experience, it becomes very clear that all so called cerebral activity has nothing to do with reality. The fundamental repository of our knowledge and relationship with life is our being-ness, which is not located inside a mental box to be analyzed, accepted, or discarded at will, but the very privileged natural gift of being. What some scholars deal with is the appearance of life prescribed by the illusion of comparative perspective which functions on the basis of dichotomous ideology. It is in effect a denial of our humanity to conclude that all things that exist [from our perspective] exist only in the mind, that is, they are purely notional. It compounds the denial of 'what is', and an extraordinary refusal to observe transparent life. It should be noted that there is ample contemporary exposure to the Cartesian doctrine, and in this regard, I would refer you to the works of Professor Gilbert Ryle, notably his publication The Concept of Mind. The heuristic principle applies throughout when establishing our connectedness with reality. It is only through our contact with reality that we can discover, and equate with the mutual structure of the principles that govern all existence. Have already noted that it is also a peculiar form of arrogance that presumes that life is only a notional existence beyond the boundaries of the 'mind in a box' assertion. It would be foolish of anyone to assert that ice cream has a cold smooth satisfying texture and taste on a warm summers day unless they had actually experienced it, preferably on more than one occasion. For anyone who has never enjoyed that experience, it would be foolish of them to discount the very numerous accounts of such an experience that is available just because they had not been party to that event. From a logical point of view, given the avowed experiences of ice cream eaters, we could reasonably ascertain the validity of each experience by documenting their separate opinions. Each participant would have 'direct experience' in the consumption of ice cream, which at that point in time has the potential for that participant to experience the full measure of that factual reality. We have the natural capacity to experience coldness, smoothness, which equates with the reality that exists, and the potential for those realities to unify. It is not a question of how to get outside of our minds (mind in a box position); we are constantly outside our so-called minds performing acts of transparency throughout our entire existence. The belief that our constant engagement with reality can never be based on a rational acceptance of 'what is', is at the least, very sad. The Platonic Cave shadows are a metaphor for the (mind in a box) syndrome. The need to reach simple, and obvious conclusions and accept them for the reality they are provides the opportunity to engage the complete reality of the moment. It is indeed going too far beyond the reality of the moment searching for philosophical profoundness which does not exist, that fails to establish the constant principles that always operate. Pure principles are not amorphous shadowy ideals; they are represented in everything that exists. The only way we can equate our inner knowledge of reality is through direct experience of its truth. Within that context then, life cannot take on a notional existence but is an existence that is very real, and that we continually share through our innate knowledge. That our so-called minds are defined by comparison - incompleteness - dualism would have extreme difficulty in pursuing the proposition that we are defined by our direct relationship with reality which is expressed in our innate ability to directly interact with 'what is'. The reality of interconnection, and interaction, are not idealistic concepts of a notional nature, but actual and consistent transparent realities. We do not live in a shadowy world that is hidden from our direct experience, but we are constantly engaged in the process of life, and we do not have the right, nor the choice, to deny it. The man whose book is filled with quotations has been said to creep along the shore of authors as if he were afraid to trust himself to the free compass of reasoning. I would rather defend such authors by a different allusion and ask whether honey is the worse for being gathered from many flowers. Anonymous, quoted in Tryon Edwards (1853) The World’s Laconics: Or, The Best Thoughts of the Best Authors. p. 232 == Create your own semantic template. == That will consist of an alphabetical list of Absolutes that are all interdependent and interconnected. Their unifying construction creates a ‘new’ consciousness meaning. That ‘meaning’ is yours specifically. The greatest knowledge you can ever have is your own! That meaning also creates its own moral construction that cannot be misused . The semantic template is available to everyone, and its dissemination is our responsibility. “Consider that the language structure, concepts, and definitions now in use no longer always deliver, accurate, reasonable, and responsible information. Indeed at times, they can be quite ambiguous. The statement ‘mutual agreement’, and its physical manifestation in whatever form, is its own dialectic, and will carry within it all other principles necessary for the activity to proceed. Given the Socratic assertion that if something is true then it cannot lead to false consequences no matter how circular any argument may be. Then extrapolating the statement into extended definitions must only lead to a better understanding of the inherent truths available. This can promote recognition of the underlying essence of all things, which can become more real than our conventional understanding of Reality. There is a contemporary need to find new definitions, new paradigms to explore the concepts that govern our existence. Where a circular argument is based on an untruth, then it cannot lead to a truth. The reverse of that is that when the truth is established, it cannot be denied. Establishing ‘mutual agreement’ as a center from which we can reach out for extended knowledge in its ever-evolving radius, is not a limitation, or a stop, it is only a beginning! When any concept is truly established the superficial exemplification ceases to dominate, and we can truly experience the apparent essence of ‘what is’. Paradoxically to resource innate knowledge, we must recognize our profound ignorance of Nature, and Reality. Completeness does not lie in individuality. This is an extreme form of monastic expectation. There can be no individuality (or completeness) unless there is at least one other individual. This is the true foundation of completeness. Whenever we are privileged to experience that instantaneous essence of one other, then we know in that moment that we experience ourselves. It is complete complementation with the knowledge paradoxically that it is an endless process. There are many paradoxes we live within that strain our conventional views of what is ‘more reasonable’. Any true relationship experience is not based on a causality premise, but on an experience that is necessarily complementation. Individuality in terms of completeness is a fundamental circular argument back to one, which in its form of denial excludes any form of reasonable argument to the contrary. It is a non sequitur, which denies the pressure of facts that are in abundance, despite the evidence of their reality. To observe ‘mutual agreement’ is looking at things as they are. True observation of ‘mutual agreement’ in action is observing essence transparency – it is knowing ‘who we are’. That form of recognition is essence duplication. The proposition that we can observe the Truth may well be the highest attainment of Realities properties, for Truth is knowledge. Consider the hypothesis of a human entity (an individual) being born in a black space with no other form of life in that environment. How could there be Agreement? How could there be Intelligence? How could there be Understanding? How could there be Recognition? How could there be Love? How could there be Law? How could there be Reason? All of the above principles are the transparent manifestation of Nature and Realities properties that are constantly evolving. They are ethical imperatives, and we have developed the positive properties of language to establish them for our use. We can only be defined through relationship principles for they offer us the best hope to recognize the factors that lead to complementation. There is a fundamental need to grasp simple common-sense essentials. The Here and Now is not a temporary transitional time phase that we move in and out of. It is a constant certainty that is essential to recognize, so that our focus of attention has a foundation. Centrism can imply a fixation, which also implies vulnerability, which can be perfectly true if it does not lead to extension. To understand who we are, it is essential that we recognize and become aware of the very principles that we operate from. They encapsulate all the measure of any human societies ethics, morals, and laws, which is a continuous evolutionary educational process within which the realization of its total essence is always available. To use the doctrine that reason is a reliable tool to discover Truth – therefore ‘mutual agreement’ in the context ‘correct information’ translates to the Truth to reason! Evolution is a constant dynamic process. The human phenomena of ‘who we are’ is only understood in our union with each other, and ‘what is’. The paradox again is that there never is any separation. Separation is a mythical non-existent. The principles that are our necessities have continuous expansion properties that as humans we are privileged to assist their propagation. The human constellation in its evolutionary march must use these fundamental principles to ensure continuity. To maintain coherence and consistency our source is centered in the principles and factors that we have interpreted from our association with Nature, and Reality. Whatever we write that is of any consequence, or at any other time, is written with the hope that stronger interpreters than us overtake what we present. To ‘see’ Reality as we have seen, and be intoxicated by it, as we have been, will ensure its progression.” == Discovery == The consciousness whole is the sum of all its parts and experiences. As we are all on an evolutionary path, our life and knowledge hopefully develop in the right direction. The exploration took us through a plethora of data and opinions about reality from authorities on science, religion, philosophy and metaphysics. Nowhere could we find a definitive conclusive argument, or agreement, that met our needs. For us, the question came down to “Is there anything at all that provides some form of construction, and certainty?” Something that has its own inherent ethical standards. The alternative proposition to that is a nihilistic “nothingness”. A pathological proposition that makes no sense. Heraclitus’s “unity of opposites” seemed the most promising. Our understanding of that now made dichotomies a semantic illusion. If achieved in a mindful way it is the act of uniting them, providing a conscious correct experience of ‘what is’. We live our lives with secondary knowledge that everything that is – is always interconnected and interdependent. Yet our illusory experience belies that form of knowledge. It is here that we understood Heraclitus and his “unity of opposites”. Mentally uniting opposites replaces the existing illusion of their existence – there are no dichotomies! Once the illusion is gone a new solution manifests that is peculiar to the mindfulness operator, and belongs to a higher form of consciousness. Heraclitus was known as “The Weeping Philosopher”. He wept for the needless unconsciousness of mankind when the ‘unity of opposites” was always available. He was also known as Heraclitus The Obscure. A title we suspect that came about because the successful conclusion to uniting opposites and replacing the illusion, opened a door to a new dimension. Semantic description at this time may not have been available. This brings us to the ancient Yin and Yang symbol of the ‘unity of opposites’. As separate entities in Chinese philosophy, they are complementary, and in fusion they represent the whole. So as dichotomies they don’t exist. The whole is the elemental answer to any fusion of opposites, whatever that may be. Symbolize a line as being infinite in the sense that any line can be categorised as being infinite. Apply an infinite number of points in any line. Intersect any line through any point by another line then we have a specific identifiable point at the intersection, which at that point in time has an infinite quality, yet constant and complete. Any such point has Matter, Energy, Space, and Time, the epitome of the microcosm. We may locate a Reality point that establishes the Truth. Conventional mechanical ‘thought processes’ deal with dichotomies that are based on a comparative perspective ideology, and consequently, skew any real experience of that which is real. We must use correct ‘measuring sticks’ to secure proper standards, but from the point of view that there is a belief in dichotomies, it will always be a compelling argument that aspects of reality can be contradictory. The element of denial within human historical memory accumulates to establishing dichotomies as being real. We are defined not by how ‘different’ we are, but by our commonality of existence. When we locate that Reality point we will then know that the definition in itself has a whole, and complete explanation of ‘reason” in all possible senses. All the reality we can deal with is here, and now. There is no possibility that ‘infinite regress’ (an imagined reality) is any part of our immediate experience. Infinite regress through thought processes, deals with questionable imponderables. It is a descending spiral, which further removes one from reality, which only produces illusion, and correct meanings are always deferred. It is making a holy virtue out of complexity. The epitome of completeness is the active realization of the operational principle. Conclusion: A brick – a house. Each complete in themselves. A house is not composed of one single brick, but each brick in its composition is complete, and whole in itself in that it has matter, energy, space, and time. In that context, it is a microscopic whole which has implicit within it the macrocosmic whole, a house. We cannot define that which isn’t. We constantly use negative dichotomous terms in language, which are in essence factually indefinable, and therefore non-existent, but they are used as though we can support a view as to their existence. At this time we constantly use mythical concepts as though they had real substance. That erroneous belief in turn diminishes that which is real and compounds the problem of recognition of Reality. The flat earth society no doubt had to be persuaded of the mythical nature of their beliefs. This dictates that we must research ‘that which is” to achieve an understanding that supports that reality. Separation is the mythical measure we use in an attempt to justify the real identity of either ‘relationship’ or ‘completion’, but it has no substance in fact.That we are connected, that we are related, that we are communicating, that we agree that ‘mutual agreement’ exists, all of these factors fall into the category of ‘that which is. There is nothing that is real that is not immediately available to us, there is ‘mutual agreement’. Attempting to view true relationships as having a necessary separation link, or dichotomy is a clear misunderstanding of the nature and completeness of all that we are related to. == Connectedness. == A relationship is defined as we are by the measure of contact (especially homo sapiens) that is apparent. It would be true to say that I have a measure of relationship with everyone who reads this material. No matter how tenuous the link we have a measure of relationship with all life – we are related! Depending on the strength of that relationship defines ‘who we are’. ‘Who we are’ is not defined by any spurious separation from life, quite simply because we cannot be separated from it, we are engaged in it at every moment in time. Any attempt to establish ‘separation’ as a reality is an attempt to deny ‘who we are’, and another exercise in futility! Again artificial interioralisation of concepts or principles leads only to a denial of their external reality. We are all connected by the very simple fact that we all exist on this planet. It is a very simple axiom that all life on this planet is supported by the conditional properties this planet provides. It is also a very simple, and more reasonable axiom to conclude that no matter how tenuous the link that all life in this regard has very concrete and definitive forms of relationship. We all must breathe, we all must eat, and we all must drink, and if you need any further certainty of ‘completion’ relationships, we certainly, all must die! [[File:Wikimedia|thumb|center|]Arcimedes] To set in qualifications from the premise that there is a ‘separate mind’ (a kind of Platonic cave) to get outside of. This premise precludes either in part or in whole the evidence and experience of Nature, and Reality, within which our beingness is located. It would all be beyond our grasp if indeed our conventional concepts of consciousness was adhered to, which in effect attempts to deny us that direct ‘relationship’ to ‘what is’, and the completeness of that experience. Knowing or being, despite solipsistic theories to the contrary, does not exist in penetrating one other mind, but in the democratic recognition that we know and have our being in relationship, and the mutual, and natural convergence of everything there is. Homo sapiens (race, color, or creed aside) necessarily conduct themselves in ways that extend recognition, and understanding at every level, without the constant need of ‘completion’ recognition that is inherent in all our interrelated actions. The notion of completion may be beyond what you call your ‘conscious grasp’, and therein I suspect lays the difficulty in recognition. The flat earth society eventually moved on to a realization that their visionary scope was shrunken, and severely limited. They were deprived of a planetary (never mind a universal) relationship that one can only imagine severely curtailed the very expansion of consciousness necessary for humanity to progress. We have evolved some little way because of our understanding of the natural relationship. The centered in the mind condition - which connotes with the separation ideology - screams to be released from that mythology, and engage itself directly in real relationship with everything that is. = Relationship. = Separation is the mythical tool we attempt to use to maintain a false continuity of an imaginary individuality that does not exist. The taking for granted conditional mythologies (the flat earth society) engage the victims in what can best be described as serious problems in recognizing the very limitations that restrict their development. We must learn to view wholes, which equates with viewing ‘completeness’. The whole is greater than the sum of its parts, but the parts are not necessarily separate conceptual parts. We can ‘see’ the whole when we are able to identify the factors that constitute their existence as a complete reality. That which is complete in Law = Agreements that produce secure and dependent outcomes. We know in essence the concept of ‘completeness’, and we demonstrate the evidence in myriad ways. Each act is a microcosm of the whole – view from the other end of the telescope! In the traffic analogy the driver, and all other drivers, conform to the law by driving off when the light turns green. There is an implicit agreement about the value of traffic laws, and traffic lights that control the flow of traffic. At that moment there is a complete relationship understanding of those values. The ‘complete’ or ‘wholesome’ activity of motorists waiting at traffic lights for the green signal to go, and they then move off, validates all the factors implicit within the properties of ‘mutual agreement’. Throw a ball from one side of the room to the other. The ‘whole’ or complete traverse of the ball is the instant it leaves your hand until it arrives at the other side of the room. You have already given credence to the concept of ‘mutual agreement’ as a reality. When there is a correct definition made in terms of ‘necessary factors’, then it has implicit within it the concepts of ‘completeness’ or ‘wholeness’ within the measure in which it is used. Whatever we communicate for the benefit of future generations should not be based on mythical assumptions, but should be based on necessary factors. It is ordinary life that portrays all the dignity, honor, and the complementary wonder of the human species. We are here – we are present – we are communicating. We have an obligation (which we necessarily fulfill) to make transparent the basic principles that govern our existence. That, which is factual, provides us with a correct motive for behavior, and we do a disservice to Reality when we attempt to deny it. We exist and live in a world where acts of ‘completeness’ expressed in one form as ‘mutual agreement’, are continually enacted. It is the form of expression, and continuance of processes that we constantly use to arrive at reasonable solutions, and we employ factors that are necessary to provide us with a clear, and unambiguous understanding. They motivate reasonable behavior toward activity that we can accept as being a logical process. == Natural Experience: == No form of life can exist in and of itself, it is brought into existence through a relationship with its own environment, or its species. The obvious egotistical monistic nature of oneness (if there was such an entity) could not leave any room for the realization of anything that might disturb its comfort zone. There is no real knowledge where any concentration is on the “I am” syndrome. "No man is an island, entire of itself; Every man is a piece of the continent, a part of the main." - John Donne, 'No Man Is An Island, Meditation XVII - Devotion Upon Emergent Occasion. “We are’ is an inclusive affirmation that deals with “what is’. There is no constructive dialogue, no real understanding, without a relationship. Based on personal experience, we are a distinct, and unique species born of Nature and Reality that has combined to provide us with the innate ability to recognize the very properties that created us, and utilize them through an evolutionary process toward ever-increasing transparency. That transparency can only become available through a matching process between innate knowledge, and the reality we share, a reality that is our heritage. We like all other forms of life are the product of Nature, and subject to its laws, and principles. Necessity created a language that evaluated Reality, and provided us with guidelines to emulate its constant properties. The measure, and quality of knowledge is dependent on the realization of ‘what is’. The crux of correct knowledge is to know the base that we function from. The principles that are implicit within Nature, and Reality we have now translated through the evolved language systems with symbols and definitions that we now use to share the experience. When principles are fundamentally true and recognized for what they are, misguided belief systems will evaporate. To ask what is the source of the principles we present is ipso facto to ask what is the source of Nature, and Reality, and we repeat, that is an exercise in futility, but that does not mean that we cannot recognize that which is natural to us, and express it, as best we can through language. The experience of ‘who we are’ is the Ultimate transparency that transcends all doubt, or denial. We can know with an understanding that is pure and indisputable, that is the motivational drive for evolutionary continuance. To understand who we are we must address Nature, and Reality, and ask ‘what is’ Here, and Now, with an understanding of the dichotomies that exist in language. The ‘Eureka’ moments, epiphanies, enlightenments, etc, are all evolutionary evidence of who we are, and when we can translate them into principles, and concepts, then the assertions of an Archimedes (and many others) are recognized, and properly used. Through Nature, and Reality we can establish what Truth is! Is it true to say that most people conform to the rules of the road? It would be more reasonable to assert that the answer is yes! Consequently, we can say that we have ‘Mutual agreement’, and ‘Co-operative Understanding’ as observable realities. There is no conceptual source through Time, or history where there is an end. There is only ‘beginning’. Here and Now is always the ‘beginning’, and a more reasonable platform to explore than any exploration into the past concerning our true identity. Contemporary terms like Absolute, Complete, End, we use to match our conditional understanding of ‘what is’. When we use contemporary conditional language to address concepts like Truth, Knowledge, Understanding, they are limited by the measure of our progression, but we use them all as stepping-stones. Language is a constantly evolving process. When we agree that there is ‘some certainty’ and ‘limited knowledge’ you have agreed to the concepts of certainty and knowledge as factors that are part of our natural reality. All of us function within the framework of certainty, and knowledge, to some degree. Given that we agree to their existence, these are the factors that can lead us to the experience of ‘who we are’. They are a part of us that can lead us to recognition of ‘what is’, and make a transparent reality of the very things we do on a daily basis. We do not need absolute and certain knowledge to perform everyday tasks, but those performances are structured contemporarily because of our advanced understanding of the things we do, based on our own innate reality. To honestly perceive the consistency of ‘what is’ (to be interdependent, and mutually connected) in interaction, can and does promote the visible reality of ‘who we are’. That visible evidence translates into the knowledge of our complete presence. We know with certainty that our beingness is of pure essence, and from that experience, we are obliged to formulate, as best we can, the structures that are responsible for making that transparent (witness the explosion of human progression, without the necessity in Time of experiencing fully ‘who we are’). To take a more reasonable stand please observe the multiplicity of human action where interdependence, and connection naturally proliferate. To realize that we are ‘interdependent, and mutually connected’ is the realization of a consistent fundamental truth – ‘what is’. Through identifying ‘what is’ as an internal reality we can make transparent the factors that are our natural construct. It is only through sharing this reality that we recognize it!! These factors are not based on any ideology, belief systems, or opinions; they are composed of the Reality that is available to us all. We are unique in that we have the opportunity to be able to use their value in the manner that is implicit within their structure. That use is evidence of our understanding of Reality. What could have happened without the assertion that traffic lights are a safe way to control crossroads, or the assertion that the rules of the road are beneficial for our safety? Any true experience, epiphany, enlightenment, etc, of ‘who we are’ provides fundamental, and indisputable knowledge of that Reality. Applying the recognized principles provided by Nature, and Reality consistently advances the evolutionary process, hence we have Science, Philosophy, Religion, Education, Art, and Law. When there is a Pure Realization of who ‘we are’ through relationship recognition, it is unquestionably the recognition of the encapsulated, and innate principles we all share, and there is no place for the dissolving of another Real identity through that recognition. Indeed it is a privileged insight into the epitome of purity. Nature and Reality can give us direction and guidance to our human existence, and we repeat, it is an exercise in futility to seek any cause to their beginnings. We have proffered the concept of two as a basis from which human reality can be ‘experienced’. To recognize through, and equate with the true substance, and essence of one other is to automatically experience the totality of ‘who we are’ in full measure. This does not mean that the terms ‘totality’ and ‘full measure’ convey an ‘end’ to ‘what is’. We have consistently offered recognizable facts (not assertions) that are part of our natural human activity, and give correct direction and meaning to our basic essence. We do function within the structure of ‘mutual agreement’, and we do communicate and ‘make known’ – basic obligations. These are evident simple examples of innate knowledge, and our understanding of ‘what is’ made transparent. To repeat we could not recognize anything without innate knowledge. All knowledge is a continual matching process 1 + 1 = 2. toward the realization of ‘who we are’ the development of language structures that correctly establish basic reality as it is, provides continuous knowledge that makes transparent the very nature of that reality. It is vitally important to recognize that we have active communal agreements concerning the existence of basic principles and concepts that form the very foundation of our lives. Constant change and movement in Space-Time - Energy - Matter are applicable absolutes to be recognised, which equates to evolution. There never will be a static property involved in the evolution advance. Evolution encompasses its own absolute properties to provide cognitive connection confirmation. The evolution of conceptual language exists to provide natural equality and to promote cognition between language states. No matter the languages spoken the concepts of air - food- water is the same and can provide a gateway to explore the future dynamics of human relationships. === Knowing. === Knowing what all the truth is is not some miraculous state of perception. Nor is it a high academic achievement of amassed information. It is simply an objective common-sense view of ‘what is” and in reality what must be. It is what must be for life to function within the principles that exist that are its natural foundation. We are always of necessity the living expression of a reality that must be experienced in the whole. Our recognition of the same principles operating universally is also our recognition of who we are. That proliferate ‘sameness’ is an evident easily recognizable identity. When a child is afraid of an imaginary monster in the dark, we generally do not accuse them of being absurd, or that they are lying. Appeasement comes with an explanation of reality at that level which is truthful. An explanation, which the child can grow up with, and find comfort. It is simply introducing a child to a level of truth that is more real to them. In every instance, the only reality that ever exists is truth. However, distorted it may be expressed. One of the major distortions as the result of thought processes is to consider that we can manufacture something other than the reality that exists. The ‘fact’ that you recognize contradictory or absurd statements is that behind them there is a measure of truth. The habitual liar lives in a world in which he or she imagines that truth is something they can manufacture. Where human ‘thought’ constructs its reality in terms of dichotomies it can never deal with the truth because it continually makes those comparative perception judgments. Those judgments are always in question because again they cannot deal with reality as it is. No matter how absurd or contradictory any statement is, that is the measure of truth expressed. Ergo whatever it is that is expressed, or made manifest, is the truth to some degree. Ergo everything that is, is the truth. It is our responsibility to recognize it for what it is. It may be appropriate to review previous observations on dichotomies and gradient scale. Consistently we have contended that there are no dichotomies, which then properly puts each principle into the category of an absolute. To identify ‘truth’ as an absolute in that category then everything that is must have a measure of truth. It is a very simple and sensible approach to establish ‘what is’. It is the means of identifying a reality that must have truth as a base – whatever it is, and however nonsensical it may appear. All principles have an elementary gradient scale that we must use to identify knowledge that is honest. That gradation scale knows no dichotomies. Dichotomies are always the imaginary properties of pseudo subjective reasoning. Necessary factors establish that gradient scale where only objective realities exist to furnish a healthy subjective reason with truth, and so we learn to apply the conjunction to address reality for what it is. Truth comes in an abundant variety of ways in its commonality – and therein lays its overall ‘complete’ power, despite any denial to the contrary. Embedded knowledge as we see it is neither experience nor knowledge without principle content. A person may be well educated in all aspects of the geography of a beautiful South Sea island, but have no practical experience at all of its beauty. Being clever about a subject does not necessarily equate to an understanding of the subject. Nor should it lend itself to posing as adjudicators on a proposition preset we imagine by the same adjudicators, or essentially the same school of embedded thought processes. Long before human evolution, the principle of leverage has always existed in all Nature (as have all other principles, wherever there is space – time – energy – matter). Our adaptation to the existence of principles has added to the sum total of ‘knowledge’ as we know it, including the concept of knowledge itself. That form of ‘knowledge’, and our ‘knowing’ is natural and not any personal or esoteric acquisition. Just as a fish knows what its natural habitat is, or a bird to fly in the air, the human species uses all available principles it recognizes to add to its knowledge (already said). Any valid theory of knowledge must have as its base constructive definitive principles to support it, and it is evident that our accumulated common knowledge equates to our common experience. No matter how erudite or convoluted any argument may be, if in the end it is reduced to inane observations that have no factual basis in principle, then it is time to abandon them. Do try to consider the sort of ‘mind’ processes that offers us up a world that knows nothing but separation. How can we possibly evaluate what ‘wholesomeness’ really is? How can we possibly evaluate ‘who we are’? How can there be any theory of knowledge without addressing Nature or our innate and biological relationship with it? Any attempt to debate ‘who we are’ and the completeness of that concept must have some sense of reality on the real meaning of ‘completeness’, and some understanding of the principles that are the nucleus of human society. To wrap any argument around a non-existent concept that can never be realized is apropos to attaching oneself to a system of belief in things that do not exist. One can make ponderous and convoluted statements about those beliefs but in reality, they are morally and ethically misguided. The ability to correlate correct definitions to the reality of life offers up that direct link to the truths that are common to us all. It corrects the presumptive notion that there can be ‘different’ perspectives on the same reality. There can be ‘differences’ but there can not be ‘different’ measuring sticks for the same reality. No matter the multiplicity of perspectives, they can never alter the core principle of ‘what is’. Historically evolutionary progress can best be measured by the adoption of recognized principles. Reality at whatever level we find it can only be understood by addressing ‘what is’. Nothing can be understood by attempting to relegate it to a non-entity through questionable theories of ‘knowledge’, which in essence negate the very content of knowledge itself. The perpetuation of any theory of knowledge, which cannot recognize the principles that are its foundation, can only be a shadow of its own reality. Construct the ‘necessary factors’ around the skeleton and a body will take form. If any particular theory of knowledge cannot identify simple truths, how can we possibly question how anyone ‘knows’? A dichotomy is the human attempt to deny the existence of a whole reality of a principle. We have the principle of leverage and its necessary gradient scale. Mutual agreements of a consistent reality, at a communal level, are a passive form of the Eureka moment, which recognizes fundamental principles that relates to truth. In every social structure, there are varying degrees of recognition, which determine social use. The mosaics of differences, which make up the rich pattern of life, are a testament to human creativity. Principles offer up a form of predictability in which our brain forms knowledge through the process of interaction. The experience accumulated through each moment, forms exponentially in use, or becomes transparent immediately in a Eureka moment, in which we know. Real knowledge is through the constant interaction with natural principles, much more than the transference of divided embedded information. The problem we face is that ‘knowing’ or ‘how we know” is never a personal possession. Any theory of knowledge no matter how in that respect, is true interaction. Peeling a potato and ‘knowing’ it, is rewarding enough! All principles are the repository of pure erudite knowledge. We recognize Universal principles in play at all times in Nature and its by-product – human societies. The correlation between determined interdependence to objective reality requires our intellect to ‘honestly observe ‘what is’, and assimilate that subjectively. Then the equality of the external and the internal becomes a reality and we ‘know’. Knowledge is the process of natural action, reaction, and interaction. It is nonsensical to ask how do we ‘know’.Every moment in time is complete because it must contain all the principles that form its nucleus. It can only be like that to facilitate the immediate experience of Eternity, or the wholesomeness of any of its principles. On the gradient scale of experience, we all exist somewhere on that scale. It is called life. === Relativism: === Relativism can be consistent with interconnectedness and a gradient scale of knowledge. What it cannot do is confuse the relationship that correct gradient scales of principles have in reality. Hot and cold would be on a temperature scale – no dichotomy! Leverage could only be measured by its own scale (say a child’s sea-saw to a high-rise industrial crane) – no dichotomy! The human being is a human being whether it is a child or an adult – no dichotomy! The domestic cat is the same animal species as a wild lion – no dichotomy! The domestic dog is the same animal species as a wolf – no dichotomy! How can we manage to classify these as dichotomies? Gradient scales are the natural human mechanisms used to recognize constant principles. They ensure the human perspective is aligned correctly to identify ‘what is’. The distorted human perspective is the result of human thought processes unable to establish constants that must exist in each moment of time. The problem with embedded information is that it becomes stultified and it can stifle healthy reaction. The injection of recognizable principles invigorates and brings new life that offers countless avenues for human energy to be released. More importantly, those energies are used to enhance the evolutionary process. We are collectively gifted with the potential to elevate life itself. We can correctly use such information by transforming its content so that its inherent truth is made recognizable. It would be impossible for life to function if it was composed of ‘different’ opposite realities. All theories of knowledge are in essence interconnected and can only contain validity when the principles that are the coalescent mechanisms are recognized. The unification of the truth that must exist in any theory needs to be harvested and used to offer up a body of ‘knowledge’ that has commonality of meaning. The identification of principles, truth, knowledge, and their subsequent establishment can only be achieved through direct interaction with Nature and life. Gifted with life we have an obligation to demonstrate its capacity to use every resource to sustain and nourish its own environment. We all know through the constant natural process of action – re-action – interaction. Depending on the quality of that process, knowledge will take its appropriate place on the gradient scale. That we ‘know’ is natural. It is not some extraordinary esoteric attainment, posited by a body of theories that, by their very nature, look for difficulties where none exists. Universal belief systems based on mythologies can have an entrenched view of good principles being established because of their beliefs. Indeed the perpetuation of the beliefs throughout history offers a dynamic that is counterproductive to the ‘realization’ of principles that are necessarily true. Principles used in this approximate way, paradoxically hold no real meaning, and in fact, impose unhealthy dysfunctionality. When there is a critical change toward establishing correct principles, it is axiomatic that the diffusion of mythologies becomes an automatic process. True interaction lies in the knowledge that correct action is its own reward Any other interpretation is less than tangible. The accuracy in interpreting basic principles, and the alternate knowledge implicit in the interpretation, will always establish the primary principle sought. Archimedes et al. Truth can be found in the oddest places. (Archimedes bath image here please) Archimedes cognition on how to weigh metals in water through displacement. === Truth. === Language is the construct of human action and the word “truth” seems to hold pride of place by the power of its usage and the meanings it evokes. It is preferable if we could turn our attention to the unity of principles (including truth) that are the construct of every language we use. By uniting the principal terms we can elevate the meanings we desire. Reasonable constructs and the correct duality of established principles always lead toward meaning. It is the only form of meaning that leads to its own extension eg. how to weigh metals – how else could it be? All principles have reciprocal value one to the other. No foundation principle can stand alone. They can only exist in a union, one with the other, the source of reciprocity. All absolutes are universal. There is no hierarchy beyond the meanings they evoke in their joint construction. The binary connotations, however, one may express them, provide a constant reality beyond conventional consciousness. That experience is the immediate reward through disciplined application of their use. That discipline takes the form in all human action (such as the bathing scene above) disposed toward the correct functionality of basic principles. The daily connections we make always include the distinct possibility of their recognition, when we make those connections in a mindful state. From any common sense, or ‘more reasonable’ position, it would be more productive to view reality as possessing at every level the same innate values or principles consistent with our ability to measure, or recognize them. To view reality as having ‘different’, or antagonistic properties, is simply a misguided view of ‘what is’. That form of perspective is counter productive when it attempts to establish mythical dichotomies as realities in their own right. When the realities of principles are made transparent, we can then ‘more reasonably’ make use of them to further their basic existence. Here we use reason to exemplify their necessary function, and once established it becomes (if necessary), ‘more reasonable’ to locate them in all things. ‘More reasonable’ seems to have the particular philosophical motivation, not toward simple, sensible, and reasonable evidence, but more likely toward that ‘immaterialism’ ideology, and continually seeking for an elusive protracted answer is hardly ‘more reasonable'. Since we are apparently confined to a human perspective, we must settle with the latter position: the apparent state of representation of the world. The de-materializing of any object through the practice of ‘perceptual illusion’ is an attempt to deny the reality that exists. Where perceptual illusions are concerned, innate direct communion with that which is, suspends the effect of such illusions. All the properties in a chair are recognized as the reality that exists. That is materialism. A chair does have the principles of form, design, structure, colour, substance, etc. However it is analysed – it is a quantifiable reality. === Truth and Reason. === The reason could easily be defined, and validated, as the correct application of common sense. More expressions of common sense can only endorse the completeness of any concept. A true experience of reality does not require endless explanations as to its ‘wholeness’. It just is. Truth is in reality a network of implicit principles in which it is the predominant energy in each of them. They are identifiable by their interdependent nature (see network below) not the least of which is common sense. Dictionary given definitions of ‘truth’ place it in a very common sense acceptable category. One of which is ‘accuracy of representation’. Note how the two definitions in this paragraph coalesce. The human drive toward recognizing and understanding the place of principles (constants) correlates to the energy we expend on questioning ‘who we are". The constant principles of action, reaction, interaction, are the automated natural impulse toward ‘establishing’ a human reality, and human identity. The process of evolving within that process has an egalitarian dynamic that powers it. In essence, it is a natural gift that we must accept. Each life and its identity contains all its personal experiences which can never be known to anyone else. In a sense, we can never “know” another person. Their life is sacrosanct. We can know a lot about them, and there it ends. Truth is at the top of the gradient scale that measures the veracity of all things that are complete and related and paradoxically all reality is the truth. It gets back squarely to ‘who we are” and where we exist on that scale. To view gradient scales as having no truth to their structures is denying truth itself. For the entire interconnected, interdependent network of principles, each of them has a gradient scale whereby each measure expresses truth in its own manner. All forms of leverage, from the minuscule to the lever that will move the world, are in of themselves, true and exact at that point. It is the only way we can recognize their existence, and use that complete truth at that time, to move up the scale. Time is the relative measuring stick that determines the amount of knowledge we can absorb. Consider the advanced extensions to the Archimedes principle of leverage throughout time. Network scale example. Truth Knowledge Common sense Responsibility Reason Understanding Intelligence All interdependent, and interconnected with all other principles and absolutes. No ‘thought processes’ or ‘mind’ constructs can create reality. All we can ever do to gain knowledge is ‘act’ react’ and ‘interact’ within the confines of our immediate reality. The quality of that action is determined by the nature of available information. When there is freedom from embedded thought processes, there is a natural human ability to relate to the existence of truth as it is expressed in reality, and our brain records it accordingly. Thus, the principles of civilized societies evolve. Where there are predominant belief systems, the implicit energy will naturally direct itself toward human standards that blend all ethics together. That implicit energy will find its true home in the principles it seeks. The connected strength of those principles offers sanctity of experience that demands no sacrifice. Everything that is, must of necessity, have a true comparative value (not a distorted dichotomy value) for honest recognition to be realized. which is to ‘know’. All things are relative but only within their own true scale. It is the process by which we can identify reality, as it is. Principles cannot operate on any scale practicing negative discrimination. Thus a healthy individual can be at the top of the scale and someone with various health issues can be near the bottom of the scale. But that is how Healthy they are. There can be no relativity when ‘mind’ or ‘thought processes’ believe in mythical dichotomies. When human perception is distorted by such beliefs, they create a false reality and deny access to the true state. Where there is a network of connected basic standards that are universal, then it is possible to use them and be nourished accordingly. The scale of natural human progression provides recognizable evidence that we are constantly developing. Reality is the direct and conclusive evidence of possibilities realized. Therefore, the reality is always the source of all possibilities where truth exists. When the truth is used as the universal measure of ‘what is" there can be no discord as to its accuracy. It can only measure the principles that are implicit in everything there is, its natural milieu! Truth can only deal with ‘something’, it cannot measure an imaginative negative counterpart. Truth is the constant implicit property in every universal scale of principles. Thus, reality becomes transparent. Have writ large on the value of distorted comparative perception judgments. The standard of correct knowledge always carries with it, its own appraisal. Where principles are concerned there is an obvious scale of identification (e.g., leverage and the numerous references) that is all-inclusive and provides us with evidence of its existence. We could say with some truth, that the industrial crane has more leverage than a child’s see-saw, but we cannot deny the truth at the lower level or the reason applied. Where principles are concerned, truth is not a possibility, it is a constant reality (e.g., leverage). When mythological dichotomies are recognized and established for what they are, the process of ‘ironing’ them out and experiencing their constant reality will translate into the reality, which they are, and used accordingly. To evoke that new sense of reality, the mechanisms of ‘selective immaterialism’ need to be dismantled. Where human experience is presented with something it does not understand and is unable to appreciate the principles involved, the reaction can invoke a sense of fear. That condition can be a primary breeding ground to establish a language of dichotomies and put a selective name to something it does not deserve. The diffusion of a false singular dichotomy into the natural healthy state of the common good puts responsibility into its proper place. Within the process of diffusion, there is the natural and equal absorption of our true reality. The transition between separation and inclusion will be a seamless process because it is our natural state. Objectivity and Commonsense: Explore the plethora of principles - truths - constants that are the mark and phenomena of Homo sapiens. We cannot have any doubt about our existence in this present reality. The truth of reality is and can be experienced wholly and completely by anyone at any point in time. All human progress is the result of such experiences, manifest in principles throughout time and their subsequent ‘use’ evolves exponentially. The overwhelming evidence is our reality, now. A simple analogy of objectivity and commonsense. Somewhere in our early development, someone put the ingredients of a loaf of bread together, somehow baked it, and hey presto, the first experience of a loaf of bread. It is now a form of sustenance, which feeds billions of people. We no longer need to experience that ‘truth’ that ‘knowledge’. It is unnecessary because it is subjective assimilation and the act of external and internal activity. Because ‘our’ brain functions in a manner that can identify the natural elements it exists in –space, time, energy, matter, we learn to ‘know’ and recognize ‘completely’ a child’s see-saw. Knowing is a natural evolutionary function. The quality of ‘knowing’ has its own natural determinants which of necessity contain the measure of principles required for universal recognition. An Archimedes insight (or anyone else’s) could not become a universal reality unless those determinants were in play. I know the very same way we all know – by experience via action, reaction, and interaction. Truth persists and what Archimedes experienced was true and complete. Any experience of any truth, principle, or constant can be as ‘complete’ within a grain of sand, or knowledge of a pyramid. All experience of that nature is an experience in ‘time’, and when it is the truth, we use it accordingly. There is no mechanical translation, or opinion of ‘necessary factors’ as they are constant universals. That, which is ‘complete’, is transparent universal knowledge e.g., the principle of leverage. The precision of terms must include ‘necessary factors’. Necessary factors translate into a common universal language so there is no loss of meaning. All truth – principles-constants – absolutes, that stands the test of time we use accordingly. Thus, human societies evolve, and we evolve without the necessity of having to re-experience any of the principles we recognize and establish. That simply would not be a ‘natural’ commonsense proposition and an entire waste of unnecessary energy. The truth of any principle at any point in time, and at that point in time, can be experienced completely by anyone. Whatever it may be if the principle is established – from then on, it will evolve. There are some misguided notions that ‘truth’ ‘knowledge’ and ‘experience’ have some secret value that is unattainable by ordinary experience. It is a ‘natural’ evolutionary reality that what we ‘know’ becomes useful. We have a mutual responsibility to recognize, use and honor the principles, which are the common property we share. = Human consciousness. = [[File:Lane past Coombshead Farm - geograph.org.uk - 589598.jpg|center|thumb|369x369px|"The roads half travelled when you know the way"]] [[File:Sombrero Galaxy in infrared light (Hubble Space Telescope and Spitzer Space Telescope).jpg|center|300x300px]] === The Universe === ''<big>We do not own Space</big>'' ''<big>We do not own Time</big>'' ''<big>We do not own Energy</big>'' ''<big>We do not own Matter</big>'' The human capacity to understand the question of sovereignty or ownership of Space - Time - Energy - or Matter can only be accepted when any basis of dispute includes two dispositions - human and spiritual indigenous ties throughtout history. With the evolutionary appearance of indigenous peoples throughout this planet, their way of life should make it paramount that their existence be recognised as a natural law that has providence! Their culture and way of life has its own identity in which Space - Time - Energy - Matter is expressed as they experience it. That proof also lies in the existence of caves thousands of years old, and the existence their art and culture. So the constructs defined below are a new approach to understanding the concept of ‘knowledge’ and its proper place in an evolutionary expanding universe. Knowledge acquisition requires appropriate recognition through action, reaction, interaction, in which proper perception and comsciousnessvalues are applied. That form of construction requires the dismantling of previously embedded information. This requires a new direction to formulate a sound basis from which to extend. Construction of an analytical methodology to establish a form of ‘knowledge’ that is best suited to distinguish in a contemporary reality. A reality that adequately conforms to common notions of that which is true, and can only exist without any false relation to that which does not exist. All science needs the certainty that established absolutes provide. A pragmatic construction of real knowledge would propose that all reality expresses a form of evidence or proof and that the observer and the observed contain innate properties necessary to establish a foundational agreement. That form of agreement would necessarily function on the basis that everything that is – is truth. Any other interpretation would be a disconnect from reality, and the interdependent correspondence that must exist for true recognition of any absolute. Controversy will always emerge when the discourse on bifurcation and the introduction of non-existent dichotomies are used as arguments to be explored. Pragmatism would say that the human species would need basic properties to formulate any form of reliable epistemological analysis to explain and simplify the reality that forms their existence. That reality could well be recognized initially as the absolutes of space-time - energy-matter, through innate perceptual data that corresponds to an outward structure that is constantly evolving. That which is absolute is the determinative factor in establishing the existence of truth. When a chair, is a chair, is a chair, its recognition is established when we ‘commonly’ apply subjective and objective measures to that which is truly external to that which is truly internal. That which does exist becomes ‘common’ knowledge, and accepted as being true. Thus, the distinction between a priori knowledge and a posteriori knowledge no longer exists. Where there is consensus, everything is. The formulation of absolute criteria that offers ‘simplicity’ as a tool to measure all and everything, dispenses with the confusion of ‘difficulties’ historical philosophies engage in. It also offers an observable synthesis that clarifies the confusion. Within the combined properties of those absolutes then everything potentially would be. Everything that is by that definition is original, ipso facto, everything that has no false relationship, and therefore true (no dichotomies). Given contemporary human development, it would be ‘common’ pragmatism to accept the proposition that we exist within the absolutes of space-time – energy-matter. Within those absolutes and their innate properties, it would also be pragmatic to assert that ‘everything then is’ (whatever everything may be). Pragmatism would also dictate that ‘everything that is, is its own form of truth, and must contain available constructs of meaning. Therefore knowledge and understanding would be obtainable to that common experience, and at whatever level that experience is activated it is in interdependent unison with the source. The continuing establishment of basic absolute principles (their generalities and their specifics) forms our reason. 1+1= 2 is a ‘simple’ but true universal constant generality. That form of generality is used because we recognize the specific principles of a balanced equation that adds up and makes sense. Simple generalities with their inclusive specifics form the foundation of human reason and its constant evolution. Simplicity is the bane of a ‘mind’ that must have difficulties. = Availability. = The unifying feature that makes ‘knowledge’ available to us all, are the innate universal principles in all things. Archimedes established the principle of leverage. To paraphrase - ‘give me a lever, and I will move the world’. Once the law is established it can then be put to good use. The principle of leverage is manifest in countless ways, and put to good use! The principle of leverage is a constant available to us all, and always has been. Through his application Archimedes conveyed his insight in practical terms, and made aware of the principle and the laws governing it. We now use those laws. We no longer need to philosophise on its existence as a truth. Similarly whenever 2+2 = 4.  Whatever we use to make the equation – apples, oranges, bricks, the mathematical equation is a constant, and the principle of correctness applies. Here 2+2 =4 is empirical proof that the principle of correctness and agreement exist. Principle, or law: ‘a fundamental truth used as a basis of reasoning’.           If it were otherwise we could not measure anything. That which appears abstract then, requires no implausible argument as to its non-existence. Such is the nature of all universal principles, they exist whether the notion of a ‘mind’ can perceive their existence, or not. Because ‘thought’ does not create the reality of principles – universals- truth, it cannot from its mythical standpoint understand the simplicity of a Reality where ‘everything is’, nor the simple and factual conclusion – how could it be otherwise! Where ‘everything is’ evidently encompasses the whole evolutionary dimension. It is not an ideological enclosed static that stultifies expansion of an unfolding Reality. Any pure knowledge experience that ‘everything is’ ,(quite apart from the common-sense truth of the statement) is to experience the Absolute in any immediate part of anything that exists, which establishes its own truth forever. To examine a road code of law with that knowledge, and view the actions of drivers at traffic lights, it is more than reasonable to conclude with some conviction that there is  to some degree, Agreement – Knowledge – Understanding, and Conformity to that code of law. It becomes a ‘more reasonable’ proposition within Reality to understand that that code of law is multiplied exponentially, and the principles practised,  wherever drivers, motorcars, and traffic lights exist. It is the nature of the type of knowledge we are measuring that determines the measure of reason that can be applied to any given form of Reality. We can conclude that 2+2 = 4 is a reasonable mathematical calculation that contains the principles of Agreement – Understanding – Conformity. Given the accepted knowledge of these innate principles we can with more reason apply such a calculation Universally. Knowing is agreement with ‘what is’. Knowledge is not the attempted denial of any existing reality. That is a contradiction in terms. Mechanistic observation is akin to viewing from the outside, a straw in a glass of water. The straw always looks bent, but when removed from the glass we realise it is straight. To claim an experience of that which is Absolute, is not a claim of an experience from a higher domain, or an  isolated incident – it is common-place, numbered by just how many we are. Attempting to denigrate such experience is denying the everyday actions that contain the innate principles of a constant Reality. All life functions within the constraints of the laws that are the constructs of Nature and Reality. All life is an expression of the Absolute. It is when that expression is realised, not only in an instinctive sense, but in a real sense, that we penetrate reality beyond a comparative framework of mythology. To claim that you ‘know’ intrinsically what the principle of leverage is, or the principle behind the mathematical equation 2+2=4 is to claim experience of the Absolute. The Absolute is not some abstract esoteric truth – it is that which is immediate. Whether in awareness or not, we constantly comply, to some degree, with the laws of a constant reality. Therein lies the difficulty for a comparative framework mythology – the Absolute is everything! = Basic Equation. = However much the simplicity of the equation is, it contains the properties of correctness – balance – equality – mutual identity – meaning, which in its ‘simplicity’ presages all future mathematical equations. In that universal meaning, there is particular knowledge of consistent truth. That form of ‘simple’ consistency, creates its own natural equilibrium, and its ‘usefulness’ evolves exponentially up the reality scale. Here is where we need to give proper credence to ‘that which is’. All generalities have profound and specific principles as their ‘common’ identity, which are absolute. Unless those components are recognized, both objectively and subjectively, they are reduced to a comparative value spectrum (using dichotomies) as a misguided ‘simplistic’ factor. Deductive reasoning is then deprived of all value, and leads to the inevitable spurious question ‘how do we know? Given the above criteria to establish a correct basis for knowledge that is recognizable, and of a kind that can be used universally, ‘simplicity’ can be recognized as a tool that promotes its own established formula. That which we constantly use. Everything is the truth with regard to the methodology. How that truth or generality is expressed denotes the measure of the principle that is at its core, and forms that measure of reasoning we enjoy. Fortunately, although the truth is an innate property, it is not a ‘personal’ property per se, nor is the ‘experience’ of its reality. Its natural evolution is progressive. In that progression we are in common, the beneficent recipients that ‘evidently’ conform to its constant existence. Philosophical dissertations have become a monopolistic form of opinions that always seem to presume the ‘rightness’ of difficulties in establishing the source of our being, and are unable to put in ‘simple’ terms the question of ‘who we are’. There comes with that the denial of evidence that permeates human history, which establishes the principles of our ‘common’ reality. Those opinions carry with them a colossal library of questionable erudition that becomes embedded, using questionable values to support their argument. The most distinguished opponent of such arguments (Ludwig Wittgenstein 1889-1951<ref>{{Cite book|url=http://worldcat.org/oclc/1203018418|title=Tractatus logico-philosophicus|last=author.|first=Wittgenstein, Ludwig, 1889-1951,|isbn=978-1-78527-656-9|oclc=1203018418}}</ref>) proposed that language logic was a necessary tool to dismantle the convoluted ‘mind’ propositions that have permeated the philosophical hierarchy. Those ‘mind’ propositions only served to construct meaningless concepts as to ‘who we are’. Although he gained prominence in philosophical circles, his work was directed more toward academia. In his Tractatus Logico – Philosophies he quotes: “The limits of my language mean the limits of my world - What cannot be shown cannot be said”, and “There can be no representation of the logic of facts”. Having a belief in mystical truths that were inexpressible, his statements above are indicative of the embedded language of dichotomies. His form of ‘knowledge’ ‘philosophy’ gave (without question) the concept of ‘mind’ credence to formulate its own logic to clarify its own form of reasoning. Wittgenstein, by not recognizing within the language the distortion that dichotomies create, was unable to approach the evident constructs of true meaning that lie within the interdependent relationship of absolutes, and their constant existence. Evidential reality is all there ever is. The ‘meaning’ or ‘knowledge’ that becomes evident in reality is ‘commonly’ accepted and used accordingly. To repeat, the evidential reality is all there ever is. In that regard, the exponential drive toward ‘difficulties’ amassed a historical discourse of misinformation, which is used to address the very ‘difficulties’ created by spurious value systems. In effect, dealing with ‘nothingness’. We have managed to turn ‘truth’ into a problem, into a difficulty, when the truth is simplicity itself. An oxymoron of gargantuan proportions. This contemporary malady solidifies a diversion that discounts the reality of continuous progression. Progression in which ‘common sense’ is a motivating principle that promotes human evolution. The consistency of specific principles allows us to achieve correspondence. Real knowledge is not a fabrication of convoluted prescriptions. It is the ‘coalescence’ of ‘what is’ to internal reality. That established, evolutionary progress is assured, and reality factors are recognized for what they are. True meaning can best be attained by the interaction and interdependence of natural principles and so recognized as such. That meaning which contains all the specific components of reality is experienced as ‘true knowledge’, measure by measure by anyone. That form of ‘experience’ is not a ‘mind’ process, but a very natural state of realization consistent with our level of action, reaction, and interaction. A correct and pragmatically form of knowledge-seeking foundational answers to perennial questions would seek a direct passage to our ‘commonality’, the beacon that offers guidance. Consider the quantity and quality of knowledge we all pursue that has meaning and usefulness. To posit the notion that there are no dichotomies is a cataclysmic proposition that seems nonsensical to established embedded constructs of knowledge. Constructs of knowledge that offer only confusion, and continually pose impossible questions, whose absence would provide clarity. That absence of confusion would dispel and dismantle a reality of ‘mind’, which functions on its own selection of problems. To address reality as having only absolute constructs dispels the confusion of duality and its inability to ‘use’ relativism in its proper fashion. All general absolutes contain specific principles representing facts; the essential properties that confirm reality. This reference directs the observer to observe, and go beyond the restrictions of a ‘mind’ governed by dualism, monism, or any other spurious form of philosophy that distorts the very reality it exists in. Where there are no dichotomies, all we can deal with is ‘what is’, and the logic of ‘necessary factors’ thus destroying the possible inclusion of anything described as a “paradox”. = Pure Experience. = To design a chair our brain requires to exercise the qualities and properties necessary for its manifestation e.g., strength, balance , design, functionality etc, etc. A chair, is a chair, is a chair, the product of innate knowledge.   If we did address any tentative agreement that ‘I’  is a ‘fiction’, could not our ‘conscious experience’ of that ‘fiction’ be just as fictitious. It would follow that whatever perception of Reality we experience must also be fiction. Our contention, as always, has been that ’I think - therefore I am’ by Descartes is the greater fiction for reasons already explained. To consider to whatever degree that we can function on the basis of a fictional ’I’ precludes any attempt to honestly address ’who we are’. Saying that ‘conscious perspectives’ are limited and inconsistent with apparent reality are quite correct. It then brings into question the validity of ‘conscious perspectives’ to guide us toward ‘what is’. The entangled fictional relationship between ‘mind’ ‘I’ ‘thought’ ‘consciousness’ impose formidable barriers to that which is evident. Base observations on the construct and interpretation of what ‘knowledge’ is. Human experience is limited by its mechanical interpretation of Reality, especially ‘cogito ergo sum’. If everything that is, is its own measure of Reality (the differences) then everything must be measured, at whatever level, as being that part of the whole with all principles intact, making that measure available to be experienced as the Absolute. With absolutes there is no antagonism. We cannot exist or experience anything without a Universal complementary source of identification. It is notable that within the structure of Cartesian dualism, Descartes' personal address to innate knowledge he attributed to ‘thought’ which he identified as being distinct from his body. How different Western philosophy may have been if his attribution had been toward his brain and the existence and evidence of other physical entities that functioned every bit as efficiently as he did. The premise that Descartes operated from ‘never to accept anything as true’, was simply a wrong ended approach which brought him into conflict with his passing acceptance of innate knowledge, that the idea of God was innate to his being. To view the proposition that ‘everything is true’ allows reason to seek and identify that measure of truth. No quest can be productively based on cynicism or denial, nor adherence to belief systems that separate experience, knowledge, and Reality. We have the obligation to question whatever reality has placed before us , but if we constantly deny its existence and attempt to ‘disappear’ it from our experience, then we are in danger of never experiencing that reality. Not experiencing Reality as it is, is equivalent to not experiencing ‘who we are’, and is indeed the only human source and validity of truth, although Descartes held the erroneous belief that such knowledge was independent of any experience. That belief we suspect was some form of impetus toward his ’cogito ergo sum’.                   Knowledge and experience are co-existing ‘necessary factors’ So long as anyone believes that human experience is based solely on indirect conscious interpretation (mechanical disposition), therefore any ‘knowledge’ derived from experience will be incomplete. Clearly it is the quality of ‘knowledge’ that one experiences (e.g., Archimedes) that leads to a common certainty of evidence realised through direct experience. That quality of knowledge can be available when we observe directly the activity of drivers at traffic lights with the knowledge that it is a very common activity recognized internationally. In every case we can logically pronounce the premises to be true, therefore we have a conclusion that is also true - whether that conclusion is defined as Mutual Agreement, or Common Acceptance, it does not matter - they are mutual principles. It is this form of logical knowledge of innate principles that is the precursor to knowledge of the Absolute logically defined within all reason for ‘what it is’ . Where the basic premise is true that there is ‘Mutual Agreement’ between a multiplicity of drivers at traffic lights then we can with certainty conclude that the same principles exist Universally. We can also draw concrete conclusions, and establish knowledge, that it is not ‘absolutely necessary’ to experience by observation the multiplicity of drivers conforming to their particular road code. We have already established that knowledge. Knowledge and experience are not separate philosophical theories. One cannot be without the other.. Everyone has the potential to experience the Absolute paradoxically, in part or in whole. Everything that is, must contain the properties of the Absolute, otherwise nothing could be. To ask questions about human experience based solely and inevitably on our interpretation of ‘knowledge’, and co-existing with that, its particular meaning in human existence. So long as we can only deal with our conscious interpretation as representing Reality then we derive functionally less meaning than we are entitled to. When we see other humans consistently using levers to open crates then we can recognize a ‘social intelligence’ operating which equates to understanding that is not based on opinion, but is a clear expression of human activity that has correspondence. All of the principles involved in that experience can coalesce to provide that form of Reality that requires no interpretation. It becomes recognizable knowledge. How we understand that knowledge is through the realisation and identification of the principles involved, which become immediately transparent. The Absolute could be categorised as a knowledge experience that encompasses all and everything. Whatever is manifest is that measure (complete in itself) of the Whole with all its principles intact. Where there are at least two actions that are identical we can reach a common-sense conclusion that a definitive principle is operating. When that corresponds with innate knowledge then we have the complete cycle. The definition itself is language opening the door to an experience of Reality. No one can know in isolation. An imaginary ‘I’ restricts any experience of who “we are”,  and is not a necessary part of human experience.   Explaining experience beyond imaginary thought processes requires a definitive language that deals with the principles of Reality itself. Pure experience. The world-wide disposition that has no grounding in Nature and Reality becomes captive to any mythical fear that  offers a target to give some form of direction or stability. There is nothing more simple than to make Reality transparent - its evidence abounds. We can pronounce the principle properties that provide guidelines to its existence whereby the reality is made apparent. = Expansion. = To address concerns on ‘negativity’. Negativity is in essence the inability to establish a measure of Reality. Mechanistic processes of denial are the attempt to understand and make transparent that which is apparently unexplainable, and resolve a condition whose energy is driven toward finding that core of affirmation. The evolutionary principle from all available evidence is that human beings as a species progress. This seems a paradoxical contradiction to the embedded proposition that we can never know the ‘truth’. The consequence of such a traditional premise is that denial and negativity both hold paramount positions. We are conditioned to accept the premise that there is in fact no premise that will enable us to go beyond presently accepted norms of experience. We are conditioned to accept that the ‘truth’ is inexpressible. The evolution of the human species is constantly subject to contemporary ingrained social habits, which give some kind of credence to that particular point of existence. Indirect conscious interpretation classifies itself as a solid perspective to govern and justify human activity, which in many historical ways has proved disastrous.                   Our continued intention is to expose detrimental barriers to the realisation of ‘who we are’, and in that process establish a smoother, more realistic approach to ‘who we are’. The Archimedes legacy. When we establish knowledge of something that exists through a multiplicity of experience and evidence, then from every reasonable standard we can establish that it is true, ergo that which is true is Absolute. The principle of leverage is well grounded in social intelligence, and our natural knowledge of that does not need erudite explanations of its presence, nor any ‘conscious interpretation’ to realise its existence, or its practice. Evolution eventually removes restrictive passages to direct experience, the very purpose of evolution. The principle of leverage is not a matter of opinion, it is the realisation of actuality and our continued ‘more reasonable’ response each time the principle is applied. Children learn to speak their language primarily through experience without any direct, or indirect conscious interpretation, and so, universally we ‘know’ the most powerful means to communicate. Were we to move 50 miles in any compass direction from the town we live in, there is a certain predictability that we will meet others who speak the same English language that we do. If in that experience we find that these premises we have drawn about our travels were true, then the conclusion we would come to in particular, is that when we communicate we make known what we know. …………………………………………………………. '''Please note the date:''' '''Oct 2005.''' I am offering up this older material below to provide insight as to the progression of this work. There may well be some duplication to date. During this period my wife and I worked in collaboration to ensure an equality of experience. = Stepping Stones 1. = There is nothing other than what is – there is no hidden Reality that we need to seek, it embraces us at every turn. The Archimedes experience is the pure experience of Ultimate Reality, which provides indisputable knowledge. Reality is the source of complete knowledge, it is the constant source that has provided us with all human development, from the writings of William Shakespeare, to the computer development of Bill Gates. What they have produced is now an evident part of our reality that we can engage in. We can experience ‘mutual agreement’ through epiphanies, insights, enlightenment , understanding, Eureka moments etc, they are all one and the same. Implicit within the macrocosm is the microcosm – it cannot be otherwise. The more we conform within the microcosm the more we begin to appreciate that Reality contains everything, and that we can realise through experience its manifestation. Each Eureka moment is that personal point of experience that connects us with the Truth. The principle of leverage was always available, it took an Archimedes to explain it to us. Each Eureka moment necessarily engages with the reality of complete knowledge, and utilises its share at that time. When we have complete knowledge of who we are in that personal moment, then we understand that these, egalitarian properties, are rightfully shared by everyone and that we have experienced that which is infinite. It does not mean that the process of evolution is over – it has only just begun. It does mean that we can no longer continue coasting through this existence in a near comatose state. If there is a hypnotic fixation in holding the principles of Reality as being separate, and different, then the potential realisation of their immediate unity, and communion, becomes problematic. Knowledge, and experience are one and the same – they are not different!! Experience = Immediate knowledge of basic reality that is factually correct, and that we can reasonably use. Knowledge = Immediate experience of secure, and accurate information that is constantly stable, and sustains principles. Reality = Complete Knowledge. As the microcosmic part of the total macrocosm we are immersed in reality. The real question should be, ‘how can one not know Reality, or ‘who we are’. Mutual agreement is evident when we know we can go to the bank, and deal with money transactions. Mutual agreement is evident when we know we can go to the supermarket and exchange money for goods. Mutual agreement is evident when we know we can send our children to school to enhance their education. Evident proof is validation of what is – it is not a matter of anyone’s opinion, nor is it an assumption of ours. Neither do we assume, or offer any opinion, on the Universal Reality that there is ‘mutual agreement’ that we need air, food, and water to sustain us. Evident proof is also the basis for the mechanics toward realisation of ‘complete knowledge ‘ of who we are. Reality can be realised through concentration on its basic principles. We use language to express our understanding of who we are.It is relatively easy, it is reasonable, and it is responsible. We convey through language our measure of intelligence, and to the best of our ability conform to the basic rule of communication – ‘we make known’ Implicit within that exercise is ‘mutual agreement’. We may differ in some specifics, but we meet the basic obligation of communication – ‘we make known’, and always we progress to some degree. Simultaneity is one of the constant principles that we all share and they come from Here, Now, the Present, where they have always been. Everything is. Our being is always engaged in the present, and we each have an obligation to understand our relationship to what is. The present is the only point of contact we can ever have with Reality. To some degree or another, each one of us is directly connected to Reality (we do not have any choice in the matter), and we can potentially evaluate ‘what is’ through the utilisation, and examination of factual reality. We are the microcosmic part of that Universal Macrocosm, and because we already have that innate information it is a matching process when we have a Eureka moment, an epiphany, an understanding beyond question. Nothing enters our minds - we already know! Everyone has innate knowledge of the principle of leverage. It requires correct examination of ‘what is’ for realisation to occur. It is then a relief to have ‘mutual agreement’ on the things we would wish to make transparent to others. To use a traffic analogy, it is evident that there is ‘en masse’ mutual agreement when we know to drive off when the traffic light turns green. Mutual agreement is translated into people obeying traffic rules (otherwise chaos). Two cars, two drivers, sitting directly alongside each other at traffic lights, discuss their understanding of their Road Code in this particular position, and what they should do. When the light turns green there are a myriad of principles that apply when they drive off simultaneously. They have both demonstrated their ‘complete knowledge’ of the significance of the green light from this perspective. There is Mutual Agreement. There is Predictable Conformity. There is Common Ground. Each one complements the other. They are both right. One more remove: From an outsider’s point of view – they both know! The green light could be categorised as a Eureka moment, it sets in play all the above principles, whether the drivers are aware of it or not. From the perspective of two outside objective observers who know the traffic rules, if asked, did the two drivers at the lights obey the rules – the answer would be yes, there would be mutual agreement. They have complete knowledge of this particular circumstance concerning drivers, and green lights. Could it be that certain schools of thought are curtailed by a questionable refusal to recognize what is, and have a preference for creating a difficulty where none exists! No one can examine what isn’t! There is no such thing as ‘nothing’. Something is – what is it? A Scottish engineer functions on the same principles as an Italian Pope. Because Archimedes was prominent as a mathematician, his realisation of the principle of leverage, and his understanding of the difference in water displacement between silver and gold was widely reported. This does not mean that realisation of ‘what is’ is an exclusive experience. As said previously Archimedes did not realise something new – it has always existed, and all forms of life would have utilised the leverage principle to some degree or another (watch a bird build a nest). At that time there were probably many thousands of people who had some understanding of the principle, but Archimedes was the one who made statements about it. As in any Eureka moment, we can experience infinity and who we are. It is mutual agreement (an understanding) between the part, and the whole. It is when the principles are in unison Eureka! Reality is there to be examined, and experienced, it is not separate from us, nor should we try to make it so. = Stepping stones 2. = Knowledge is not conditional by the activities of what may be called ‘thought’ or ‘consciousness processes’. Real knowledge is that which is available to all, and to be shared by all. It cannot be contained by the ‘experiencer’ and then not ‘known’ by the accident of experience. It is the actual innate experience itself which conclusively establishes the truth. It can only deal in the truth which is its modus operandi of dissemination. For me to say that ‘everything is’, is a statement of fact which cannot be denied, and an intellectual dishonesty to attempt to deny the evidence by philosophical machinations. Hostility toward the truth leads inevitably toward attempted negation - looking for nothingness! ‘Being here’ demands its own recognition - attempting to deny it is simply perverse. Knowledge is the realisation of ‘what is’.. Rene Descartes ‘I think - therefore I am ‘did no service to human evolution, or education. It established in Western societies especially, the culture of individualism, with the precursor that so-called ‘thought’ was the inward evidence for existence, and for the following unfortunate claim that we have a ‘mind’, or to use the euphemism, a soul! Experience is true knowledge. When that experience marries up with its innate counterpart then recognition is realised (cognition). In simple terms, a light goes on in the brain. There can be no real knowledge without truth. All thought qualifies experience and attempts to reduce truth to near nothingness which is a widespread conditional activity. We cannot manufacture knowledge, or the principles which are its properties. No matter the amount of correct information anyone can ingest, it does not become knowledge until there is tripartite coalescence between inherent knowledge - ingested correct information - and ‘what is’. Then we truly recognize that which is Absolute. Within Nature we have the distinct privilege of evolving in a Universe that can only recognize the attributes of social cohesion. Knowledge is not anyone’s personal possession. Whatever measure of experience we may have of it, it is only available as a Universal sharing experience to be beneficially used. Human activity whereby we witness people using tools for leverage, or drivers at traffic lights obeying the rules of the road, are observable markers that contain the properties for understanding our own reality. Unless seen for what they are, they are only mechanical platitudes with an equally mechanical response. We could rightly claim that that at least is some response, but of no real value. The natural process that operates when we see that which is innate, overrides any erudite explanation from an academic base however intellectual its original source. ‘Thinking’ for oneself cannot make judgments about a ‘natural’ experience. When we see human duplicate functions in operation then we are in communion, and at another level we recognize who we are. When we actively see the activities of the human brain in action we are not dealing with any internal ‘will - o’ - the wisp’ that no one can ever experience. We exercise that prerogative (human activity) at every moment in time, but quite apparently without that focus of attention that denotes realistic recognition. To seek identity in sectarian, or secular belief systems to overcome the contemporary feeling of loss of identity leads to the acceptance of anything that offers some form of stability. That is then used to strengthen that which is euphemistically addressed as the ’self’. To retain that security the acceptance of information transmitted throughout generations, is absorbed into the culture, and defended to the death against those who would question that belief system. The greatest knowledge we can ever have is our own and it has the potential to transcend all else and provide insight into infinity. The most tragic human condition is the lack of experience of identity in a multiplicity of identities in which we all share. The real problem is not one of ‘identity’, but a lack of ’communion’. Whether we like it or not, whether we are aware of it or not, the principle of ’communion’ must always exist to some degree for evolution to proceed. It is within the experience of that principle that we understand the fallaciousness of that much heralded ‘self’ which draws down so much energy in an attempt to establish itself as a reality. Within positive language structure possibilities (no dichotomies), there should be the disposition toward the realisation that our relationships to cognize into ‘communion’ must be addressed as specifically dependent. Social attempts to be ‘independent’ are the very remove from reality and signify reduction attempts toward nothingness. Adherence to, and the cultivation of faith and belief systems give little elbow room for any factual occurrence to be anything other than a comparison to the myths that are held. The cultural and educational socialisation of generations of children must carry with it, its historical belief systems that overwhelm the natural instincts. Observe an animal out of its natural habitat and locked in a cage for its entire life. It would be a salutary exercise if we could dispense with the term ‘mind’ from our vocabulary and magnify the use of the word brain to promote a realistic discussion on ‘who we are’. My action of levering open a wooden crate and knowledge of it is one and the same. Our remarkable brain functions like that, the purpose of a brain, the natural repository of innate knowledge. The assertion of principles is critical to avoid all activity being submerged by questioning their very existence, and being unable to see directly. It would be a rarity today, if anyone using a lever to pry open a wooden crate would have the same enormity of experience that Archimedes had, nor the need to make pronouncements about it. It has all been done prior to our awareness of its value with the accompanying data attached. Our brain knows the value of a lever and activates our body accordingly when needed. It could be categorised as evolutionary transmission. The observance of someone prying open a crate with a lever, or drivers conforming to the road code at traffic lights, is a function of the brain in action, not a mythical entity in a singular locality that denies its own senses. When the brain is not burdened by distorted belief systems it then has the potential to experience ’that which is’, which is always constant. When we understand the function of a lever, or the presence of traffic lights, then we can activate the principles involved because we already know how! The negative impact in the use of dichotomies in language lies in their distraction from the truth, as our brain processes the words we use in relation to Reality. The tendency to attempt to separate inherent truths through the words we use disrupts that natural correspondence necessary for identification. A chair, is a chair, is a chair. = Stepping stones 3. = Where principles are concerned the constituent linkages in language are identity markers to that which is real - reference points. Without dichotomies there is no separation, or ambiguity between what we experience, and ‘what is’. Philosophy in its attempt to address something through denial is an elementary confusion. To say that that is a chair, and then attempt to deny it invoking philosophical theorems concerning the human ability to experience it, is a severe contradiction on the existence of the object , and the observer. When this form of contradiction is then taken as a constant, it then precludes any common-sense and definitive answer to the existence of a chair. '''For philosophers, George Orwell’s ’to see what is in front of one’s nose needs a constant struggle’ would be apt.''' Real concepts cannot exist in any mythology, therefore all that we experience is inevitably the truth that is there to beproperly categorised for what it is. The proper use of language in this context will identify whatever it is to correspond with present reality. Misuse of language (dichotomies and mythologies) leads only to the acceptance of a fractured state where nothing is whole and represents confusion. The dissipation of the supposed problem is never realised. Fiction has been elevated to the status of an accepted reality. Very early evolutionary physical dangers allowed the development of fictions that offered some form of imaginary protection beyond limited physical ability. That contemporary humanity endorses the mythology of ‘I’ is testament to the psychological fear that still exists and requires its proper recognition. Emphasis must be placed in the relationship between language and reality for understanding to proceed. The persistence of dichotomies has their own persistent confusion which then promotes a false reality through misleading information. Microcosm and macrocosm are one and the same in a Universe where ‘everything is’. Isolated viewpoints are exactly that, and are unable to view the expanse in which we are encompassed. We must learn to view reality through both ends of the same telescope. When we understand the extensive scope of ‘truth’, then we know that its values and properties do not change - which relates to ‘completeness’. Philosophical, ideological, and intellectual endeavour , try to shape the structure of ‘what is’ based on pre-dispositional knowledge, which can only ask the same questions, and look for the same answers. Not to experience that which is absolute or whole is the normal result of the confusion of language which has no correspondence to that which is real. To discuss with a philosopher the possibility that ’mind’ per se does not exist, and to dissolve it as a concept would place them in a realistic position, would indeed be a difficult proposition. The strength of that difficulty lies in another imaginary concept, that that ‘mind’ represents ’I’, and it is anathema to that fiction to consider its own demise! = Stepping stones 4. = There are no dichotomies. Everything is, and everything that is, is complete, everything is an Absolute complete Reality. You are experiencing your measure of that reality. It cannot be otherwise that you are experiencing that measure of completeness. When we come to terms with it we have the innate capacity to see the Absolute in a grain of sand. That is knowledge. Belief in dichotomies is the mythical barrier to that particular experience - which is only denial, supported by erudite protestations that human construct dichotomies exist. At a mechanical level Intelligence and Stupidity appear to be separate identifiable conditions, and they appear to be antagonistic. Stupidity is in Reality a measure of the Intelligence which is always constant. If someone was in a state of mythical utter and complete stupidity we would not attempt any form of emancipation from that condition. We know that that is misguided and proceed with techniques to advance intelligence. Consider the proposition that there are no dichotomies, and within that possibility all questions become irrelevant. Presuming that there are no dichotomies allows the process of establishing ‘necessary factors’ to proceed, and allows each measure of wholesomeness to be realised. Experience is the criteria for knowledge. Some Reality experiences were simply transposed into particular belief systems and elevated into a pseudo spiritual dimension, or a philosophical conundrum. Where there is a belief in a divisive fiction (dichotomies) there is automatic mechanistic restriction to that which is Real. There is a capacity beyond ego and intellect which can commune with ‘what is’, and recognize its properties. Reality is constant. Within the accepted comparative framework there is the view of principles as having different divisive categories e.g., as above, Intelligence and Stupidity, and classify them within ‘thought’ structure as dichotomies and give credence to them as being an antagonistic reality. The consequence of that, is, that one is always a remove from recognizing the structural properties of immediate existence. Any construct of knowledge necessary to evaluate ’what is’ will address the properties (principles) that are the constituent constant markers available in that which is the microcosm and the macrocosm. That identity (the Absolute) is found in any sphere of Reality.Everything is - and everything that is, must be experienced for what it is, and not for what anyone denies it to be. There is no mythical human construction that can deny ’what is”. Everything is - without dichotomies. To repeat, we do not have the ability to create ‘nothingness’ - ‘that which is’ has no imaginary comparative human construct. To attempt to deal with such constructs, and give credence to them is always the denial of ‘what is’, and adherence to ‘thought’ processes whose only purpose is to cement that activity. Indeed realising that the concepts of dichotomies are human mythical constructs, denying true perspective, is the beginning of insight. The dissipation of such processes through addressing the principles of Reality allows us the potential to experience directly ‘what is’, in simple terms -the truth! Intelligence is a ‘necessary factor’. Addressing stupidity is a denial of reality at whatever level we find it. Intelligence and Stupidity are not antagonistic, they are one and the same principle with measurable degrees of existence. Only from a comparative framework standpoint is credence given to any mythical form. The above observation is not negating the process, it is questioning the markers which evolve into imaginary separation (trapped in a comparative framework mythology). That particular process can and does create a false mythical reality that appears divisive. We cannot exist within a divisive reality! Reality must be complete for us to recognize its existence. Where there are no dichotomies within the premise that ‘everything is’, there exists no antagonistic position. The distinction between human constructs of positive and negative are matters of mythical perspective wherein no experience of the Absolute is available. It is because the human ’mind’ per se places its own construction on its immediate experience, and must have its particular interpretation based on what it considers ’knowledge’. There is a difference between ’mechanical knowledge’, and ’pure knowledge’. From the mechanical knowledge standpoint which can only deal ‘in indirect conscious interpretation’, it is quite correct to say that that form of knowledge is incomplete, and it always will be. Pure knowledge experienced via our brain knows no separation, nor antagonism, and is responsible for our ability to recognize the actions of others who may pry open wooden crates with a lever, or drive off uniformly at traffic lights. Within that cohesive activity it precludes ’a matter of opinion’ and by themselves can become subjects of a pure knowledge experience. To repeat, it is a form of ’communion’ with ’what is’, and available to all. Where drivers at traffic lights universally conform to their particular road code, and where universally there is a language which identifies their activity as Mutual Agreement, or any other logical definition, we can concur with the common-sense conclusion that we have universally established that within language and common activity, there is indeed a truth formed. The coalescence between universal language and universal activity are the logical constructs that create civilizations. There is a vast social network of common activity that solidifies the logic into an honest and persuasive conclusion that confirms innate common principles –knowledge. = Stepping stones 5. = The Art of making sense of everything. How to understand principles. # Principle. A fundamental truth or proposition that serves as the foundation for a system of belief or behaviour or for a chain of reasoning. # All principles are interdependent, interconnected, and infinite. # Each one is dependent on the other two. Examples of a principles template and how to define them without dichotomies. Communication. Truth. Standard. Proof. Express. Contribute. Mutual. Direction. Advance. Comfort. Organize. Certain. Immediate. Interest. Improve. Present. Constructive. Gain. Trust. Progress. Source. Knowledge. Basic. Original Reality. Awareness.Freedom. Purpose. Connect. Understand. Support. Peace. Cause. Unity. Ability. Rights. Honest. Discover. Positive. Energy. Balance. Good. Courage. Willing.  Control. Use. Association.  Observe. Reason. Easy. Wealth. Simple. Law. Increase. Order. Flow.Co-operation. Exact. Quality. Accuracy. Strength. Responsible. Operating. Creative. Measure. Recognition. Accept. Constant. Obligation. Include. Dependence. Relationship. Value. Success. Principle. Equality. Stable. Share. Love. Sustenance. Action. Identity. Intelligence. Education. Secure. Facts. Agreement. Information. For. Rules.Clear. Yield. Example: Success = Securing facts                = Responsible co-operation               = Constructive knowledge So success by definition is : Securing facts through constructive knowledge and cooperating  responsibly. All definitions of success from your template are infinite. You will find your own suitable definition. ==== There are no dichotomies! ==== Any principle is correctly defined by any two other principles. You create a new language of Absolutes. Using conjunctions you can write your own book. The man whose book is filled with quotations has been said to creep along the shore of authors as if he were afraid to trust himself to the free compass of reasoning. I would rather defend such authors by a different allusion and ask whether honey is the worse for being gathered from many flowers. Anonymous, quoted in Tryon Edwards (1853) The World’s Laconics: Or, The Best Thoughts of the Best Authors. p. 232 Amen to that! “One is not born, but rather becomes a woman” Simone de Beauvoir. “Time does not change us. It just unfolds us” Max Frisch. We experience ourselves our thoughts and feelings as something separate from the rest. A kind of optical delusion of consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Albert Einstein, in One Home, One Family, One Future. = Who we are. =   It is notable that within the structure of Cartesian dualism, Descartes' personal address to innate knowledge he attributed to ‘thought’ which he identified as being distinct from his body. How different Western philosophy may have been if his attribution had been toward his brain and the existence and evidence of other physical entities that functioned every bit as efficiently as he did. The premise that Descartes operated from ‘never to accept anything as true’, was simply a wrong ended approach which brought him into conflict with his passing acceptance of innate knowledge, that the idea of God was innate to his being. To view the proposition that ‘everything is true’ allows reason to seek and identify that measure of truth. No quest can be productively based on cynicism or denial, nor adherence to belief systems that separate experience, knowledge, and Reality. We have the obligation to question whatever reality has placed before us , but if we constantly deny its existence and attempt to ‘disappear’ it from our experience, then we are in danger of never experiencing that reality for what it is..   For anyone to say that ‘everything is’ is a simple linguistic absolute that no amount of ‘more reasonable’ requests (above) can deny. Those requests only appear to be governed by the difficulties of ‘mental complexities’, and embedded ideologies. To accept that ‘everything is’ as an absolute, is a realistic basis to establish any reality, and comprises the basis for reason to be activated. If there is ‘nothing’, nothing can be achieved. Within that which is Absolute there are no dichotomies. Therefore there are no antagonistic positions available. Everything that is, is a measure of the Absolute.  We are always in the present, everyone and everything. Instant elementary ‘knowledge’ which we all share, and must admit to. In being alive, we do not have the ability to not be here, and we do not have the ability to not know! To have a problem in addressing what Truth and Knowledge are, to the point of denying their existence, then that problem exists well below the scale of Reality. To repeat knowledge is not the proprietary right of any individual, it is enshrined in the principle of agreement that we mutually exercise to establish its own reality. The reality of experience is not, nor ever will be, a personal possession that we can have and hold. Its reality becomes more alive when we see the same activity being practised by others. Then we know we are sharing that reality, and that experience. We cannot "have" the principles that exist, but when we undrestand them then we are obliged to use them with integrity. That form of integrity in any language, is an added foundation stone to any belief system Mechanistic ‘I’ has no concept or understanding of ‘pure knowledge’. Only when we break free of the myth that some clarity becomes apparent, and we have the opportunity to engage with what is real. Philosophy it appears to me is constrained by individual ‘thought’ processes, which (without experience) cannot escape from that individuality. Those ‘thought’ processes conjure up a human history of inflexible, and impossible propositions which only serve to protect that individuality. Descartes ‘cogito ergo sum’ has compounded the difficulties by strengthening the incorrect premise of a false individuality. ‘I’ is a phantom consciousness much like a phantom pain experienced after a limb is amputated. The brain registers the pain signifying that something should be there. Likewise our brain has that same relationship with Nature and Reality. It is analogous to our brain dealing with a ‘phantom reality’ knowing that something is missing but is continuing to evolve to establish the whole. There exists a ‘phantom chasm’ between our brain and Reality and an understanding of its properties. We are robbed of real meaning. Evidence, recognition, and the truth are the principles it uses to reform. Within their structure is the meaning of reforms. Nature does not impose any morality on us, the principles implied in morality are there for us to understand and use. Our brain has the capacity, once reality is correctly examined, to recognize ‘that which is’. Once realised it becomes embedded. That ‘phantom consciousness’ is an experience removed from its proper environment. It takes its proper place when we experience reality for ‘what it is’, which provides the totality of meaning. True experience allows us entry to the quality of knowledge that is a continuous reality. So long as anyone believes that human experience is based solely on indirect conscious interpretation (mechanical disposition), any ‘knowledge’ derived from that experience will be incomplete. That form of philosophical negative conclusion can come down to not believing that Reality exists (a chair is not a chair, is not a chair etc,), or that our experience of ourselves and others is real, and discount any other form of knowledge that threatens that belief. There is an intellectual dishonesty in denying the existence of principles. Hostility towards the truth leads inevitably to negativity. Being here demands, not denial, but the right to be recognized. We are the recipients of a ubiquitous communication system – making known. We can only understand that which we know. We make known all the time. Knowledge of Reality – Truth – the Absolute is a collective inclusive experience of the principles we share, and never the property of any individual. To ‘know’ ‘who we are’ is an inclusive experience of the principles involved. Never ‘cogito ergo sum’.   Philosophers in investigating the nature of knowledge and the Universe, firmly established for themselves that the source of reason and logic was located in a mythical concept ‘the mind’. From the wrong basis evolved elaborate and metaphysical constructions which removed the investigations further, and further, from the truth. To comprehend the material world, and give it credibility, the recognition of implicit principles is paramount. We need to construct a language that provides that form of recognition. Any philosophical theory of ‘mind’ that will deny the evident structure of solid objects is misguided by the injection of a mythical entity (mind) that determines that seeing solid objects is a ‘perceptual illusion’. That form of determination is singularly narcissistic, empowered by the self-induced threat that venturing into a ‘materialistic’ world is a loss of that illusory self, and all the belief systems it has constructed to protect it. That erroneous established view that not addressing ‘materialism’ as a profound Reality, and as only a ‘perceptual illusion, is compounded by the belief that that form of illusion is implicit in every human view available. We cannot manufacture knowledge that leads to a mechanistic understanding of ‘what is’ , nor the principles which are its properties – however much dogma is practised. We can only aspire to relate to ‘necessary factors’ that are the implicit fundamentals of existence. For me to use a lever to open a crate is a form of communion with Archimedes through the principle he enunciated. It is now not ‘necessary’ for me to go through the same experience as Archimedes to establish that ‘necessary factor’ or ‘principle’. It is now common-place, and common-sense to utilise the principle. The extract below provides some explanation of the brain processes in action Universally, and coincides with any reasoning on the observance of the leverage principle, and the actions of motorists conforming to the Road Code wherever traffic lights exist. ''The right-to-left shift of mental control looked increasingly like a universal phenomenon, capturing the essence of every learning process on every time scale, from hours to years. An individual faced with a truly novel situation or problem tackles it mostly with the right hemisphere. But once the situation becomes familiar and is mastered, the dominant role of the left hemisphere becomes evident. It looked like the empowering patterns capturing the essence of the situations (or rather the whole class of similar situations) were, once formed, stored in the left hemisphere. (The Wisdom Paradox. Professor Elkhonon Goldberg. P202)<ref>{{Cite journal|last=Vandermeulen|first=Jo|date=2008-08|title=Verstand komt met de jaren|url=http://dx.doi.org/10.1007/bf03077135|journal=Neuropraxis|volume=12|issue=4|pages=137–139|doi=10.1007/bf03077135|issn=1387-5817}}</ref>'' = Limitations. = However limited our view of connectedness is, or however tenuous the reality our experience is, ‘everything is’, and everything is connected. Innate knowledge and the fundamental nature of Man is the prior source of knowledge that seeks and identifies that connectedness. Attempting to address what we don’t know is that mythical infinite regress toward that parallel mythical ‘nothingness’. To always address what we know establishes Reality. To establish knowledge of principles, start from ‘we are here’. The natural principles within the diversity of human culture and activity when recognized as mutual ‘necessary factors’ will have the effect of enhancing and directing vital energy toward the very process of  the communion we seek, and the gradual penetration of a reality that always exists. Knowledge of Reality is not ‘different’ in other locales. The fundamental principles are the same. Addressing ‘what is’ instead of denying ‘what is’ is the basic construction of real knowledge. Within the structure of the Absolute we are all the same with a magnificent differential in our expression of the principles of necessity. That expression is our ongoing effort toward its own experience which gives it life and meaning. That experience in turn exposes us to an immediate Reality that is in communion with the fundamental structure of our being. All that we can contribute toward that is 50%, the other half is in our momentary relationship with Reality – then we know! That form of knowledge is always available through that form of experience, and it always comes in the form of confirmation which reforms. Until that experience our prior condition appears mechanistic, without direction, or understanding. Reality, life, is not mechanistic. We are the recipients of innate principles with the constant potential to experience those principles in action (Archimedes et al). Dogmas, ideologies, are the restrictive practices used to blur the recognition of principles operating to a level that understanding of that common and constant activity is virtually denied. Our natural capital (principles) is degraded to the point that their factual evidence is reduced even to the point that they are categorised as a ‘perceptual illusion”. We can trust facts 2+2=4. Simplicity has its own majesty. Anything circumscribed by reason requires control of our emotions. To comprehend the material world, bring it alive, and give it credibility, the recognition of its implicit principles is paramount. We need to construct the language that provides evidence of that Reality. Any philosophical theory of ‘mind’ that will deny the evident structure of solid objects, is misinformed by the injection of that mythical entity (mind) that determines that seeing solid objects is a ‘perceptual illusion’. That form of determination is singularly narcissistic, empowered by the self-induced threat that venturing into a ‘materialistic’ world is a loss of that illusory self, and all the belief systems it has constructed to protect it. The erroneous established view that not addressing ‘materialism’ as a profound reality, and as only a ‘perceptual illusion’, is paradoxically compounded by the belief that that form of illusion is implicit in every other human view available, thus it then makes its own sense, form and justification to the illusion! The evident question we must ask, ‘how does a ‘mind’ conclude that ‘immaterialism’ exists universally? Surely it is a simple but massive contradiction in terms. If there is nothing there but ‘perceptual illusion’, how can you attribute it to other ‘minds’. The oxymoronic effect of narcissism is that it is the very denial of ‘who we are’. Man is not composed of an overwhelming self-love. That mythical embedded belief cannot consider the possibility of underlying principles that are the real life force of Man in his relationship with Reality. The truth of that, is that humankind (in spite of itself), evolves towards its own Reality. The only human values that exist, lie in Man’s recognition of the principles involved that provide human direction. Our ‘material brain’ is a product of Nature's evolutionary process, and has innate within it the same principles that exist in all matter. That ‘which is’, is the truth, and our brain evolves to process that at every level, and we constantly manifest that in every action we take – whether we like it or not. The fundamental similarities between human beings is that we are not only evidently human, but that we also function and construct societies that we recognize as beneficial to our immediate well-being. All social function is determined by our brain capacity and its ability to postulate the relationship it has with Universal principles. = Illusion. = Considering that we can contradict things is an illusion. We can never contradict the truth. We do not have the ability to create proprietary constructs of reality. That ‘which is’, can only make its basic properties transparent to us through direct experience. Imaginary concepts must in the end conform to a measurable construct that we can identify. Within the structure of any philosophical theory of ‘knowledge’ it must contain the basic elements of truth at all times, or there is nothing!! To say that ‘everything is’ is motivated by pure reason experience as an objective, and subjective reality and as an axiomatic grammatical premise that no amount of mental acrobatics can deny. We can only deal with ‘something’, whatever it may be. There is no metaphysical construct that can provide evidence that ‘nothing’ exists, outside a mythical mind. Explaining experience beyond ‘thought’ processes requires a definitive language that deals with the reality itself. We all Know. It is innate. The ‘difference’ between us is only the measure of the knowledge that is made manifest, and that knowledge continually proliferates. The ‘individual perspective’, and the illusory ‘I’ which dominates, is the barrier to any relation to ‘what is’, and the malady of never experiencing the truth directly!   Truth, knowledge, agreement are the abundant and embedded Absolutes that form the structure of human evolution. That we constantly utilise and improve on their use is evidence of their reality, and the material transparency within every social structure. The survival and proliferation of such realities should be the evidence to establish that ‘that which is’ is Absolute. When we focus our ‘perspective’, opinion, or a hypothetical consideration of a space, time, or identity to question a Universally accepted fact, it is hardly a categorical argument to dismiss that which is true as nonsensical. Any denial that 2+2=4 is a fundamental truth hardly takes into account that the reality of such basics are vital to the success of higher mathematics. Unless the basics are continually correct, and evidently so, then no correct solutions could evolve. We know that within any basic structural ‘use’ that the calculation is correct. We commonly accept its correctness as an embedded reality. All forms of lower or higher mathematics would have the axiomatic principle of ‘correctness’ as their basis to extend from. Also, they would have as an axiom that the reverse is true. The 2+2=4 is, in its reality, the epitome of balance and construction. The 2+2 reality forms its correct conclusion when the principles of mathematics are propounded and they conform to transparent truth and arrive at 4. Only when it ‘adds up’, does it become a truth that we all recognize. Our greatest ignorance is taking for granted the proliferation of such truths through an ideological blinkered perspective. Because truth takes a commonplace form it is no less fundamental. Unless there is correct knowledge as to the existence of fundamental truth, that ‘which is’, goes unrecognised. That form of truth must be applicable to all. Truth exists in everything – it is an evidential reality. Searching for an esoteric truth is chasing shadows. Every truth is a ‘necessary factor’, and fundamental to our existence. Because of the imposed limited perspectives (via education, ideology, beliefs) that which is evidently true, and transparent, is delegated to a position of simple practicality with conditions placed on it which further deletes its substance, and we have the awful predilection of conforming to the attempted destruction of that which is true. Do we have a problem with seeing something, which is correct, as also being true? All truths are fundamental. They are not subject to attempted denial because of any diminished realisation at any point in time. Where there is reasonable evidence of balance, equity, and agreement we can conclude that a truth exists. Once innate information of that truth becomes transparent, it becomes an embedded useful human utility that must have some measure of fundamental truth as their starting point. From any common-sense, or ‘more reasonable’ position, it would be more productive to view reality as possessing at every level the same innate values or principles consistent with our ability to measure, or recognize them. To view reality as having ‘different’, or antagonistic properties, is simply a misguided view of ‘what is’.  That form of perspective is counter productive when it attempts to establish mythical dichotomies as realities in their own right. When the reality of principles are made transparent, we can then ‘more reasonably’ make use of them to further their basic existence. Here we use reason to exemplify their necessary function, and once established it becomes (if necessary), ‘more reasonable’ to locate them in all things. The dematerialization of any object through the practice of ‘perceptual illusion’ is an attempt to deny the reality that exists. Where perceptual illusions are concerned, innate direct communion with that which is, suspends the effect of such illusions. All the properties in a chair are recognized as the reality that exists. That is materialism. A chair does have the principles of form, design, structure, colour, substance etc.  However it is analysed – it is a quantifiable reality.   = Human representation. When we understand the validity and existence of principles in all things, it is easy to understand that ideological dogmas are never the foundation for real knowledge, or that direct experience of ‘what is’. Our real perspective is not some individualistic experience that confines us, it is that expanse in which we exist that offers us the view of that expanse. Everyone has the potential to go beyond their ‘apparent’ human perspective limitations. Shifting our sense of perception toward that which is basic, paradoxically extends the experience of that which is true. Let general knowledge be directed toward the performance that identifies the measure of principles that are enacted. Therein lies the production of knowledge that offers a sustainable growth of that vital universal aspect of knowledge, where, reason and truth, can prevail. Any correct definition is language itself, opening the door to that reality experience which is critical. Only when we know and experience that the same reality (with all its principles intact) exists for all of us can we then recognize the mythical distinctions that are taken as being real. The majestic experience of that reality goes well beyond historical beliefs. Exploring simple ‘necessities’ is not based on any sacred text, but the privilege of recognizing a sensible evolutionary path through life. Whatever may be in the future, is implicit in the material world now, and it has always been so. t80drmiud9nb2incmrqrp6z9durl2vv 0 281971 2412448 2401252 2022-08-07T02:04:58Z Guy vandegrift 813252 /* Appendix */ wikitext text/x-wiki {{share}} ==Partially completed songs== Every song needs to be improved and we need a more songs. If you wish to contribute, leave a message at {{font|size=115%|[[User talk:Guy vandegrift]]}} ;Songs :[[/Twinkle/]] :[[/Red River Valley/]] :[[/Amazing Grace/]] ;Scales and exercises :[[/Major sixth M6/]] :[[/Prelude and Fugue in C major (ear training)/]] :[[/Great_Gate_of_Kiev_(ear_training)/]] UNDER CONSTRUCTION ;For editors of this project :[[Draft:Sing free/Tables and images]] :[[Draft:Sing free/Transclusions]] ==All you need to "sing free" is ...== *A computer with [[w:Loudspeaker|speaker]] and [[w:Microphone|microphone]]. [[w:Headphones|Headphones]] are recommended but not required. *Acces to a tuner. {{#section:Draft:Sing free/Transclusions|tuners}} *When this resource is more developed, we need to supplement this page with something like [[w:Audacity|Audacity]]. [[File:LilyPond wikimedia Playback speed.png|thumb|LilyPond wikimedia Playback speed]] ===How to change tempo (fast/slow)=== Many people like to learn a song by practicing it at different [[w:tempo|tempo]]s. The easiest way to do this is to click on the three vertical dots, as shown to the right. Then select "Playback speed". For those interested in editing or creating songs, it is generally not difficult modify the script for the [[mw:Extension:Score|Score extension]]. Generally speaking, this should always be done by first copying into your sandbox, or creating a version of the song in the [[Draft:Sing free]]. ===Two ways to change the key (pitch) of a song=== #Request a key change of any song by leaving a message at [[user talk:Guy vandegrift]]. #Modify the {{font|\transpose|font=Georgia|size=16px|color=green}} command in the source code as shown below: <score vorbis="1">\language "english" \transpose c c \relative c'' {\key c \major a4 <d, f a>2 } </score> <div class="thumb tright"><div style="width:370px;"> <syntaxhighlight lang="text"> <score vorbis="1">\language "english" \transpose c c \relative c'' {\key c \major a4 <d, f a>2 } </score> </syntaxhighlight></div></div> {{clear}} <score vorbis="1">\language "english" \transpose c f \relative c'' {\key c \major a4 <d, f a>2 } </score> <div class="thumb tright"><div style="width:370px;"> <syntaxhighlight lang="text"> <score vorbis="1">\language "english" \transpose c f \relative c'' {\key c \major a4 <d, f a>2 } </score> </syntaxhighlight></div></div> ==Appendix== '''Help:''' [[w:Help:Score]] | [[s:Help:Sheet music]] | [https://lilypond.org/doc/v2.22/Documentation/learning/aligning-lyrics-to-a-melody.html lyrics] | [https://lilypond.org/doc/v2.21/Documentation/notation/chord-mode chords] | [https://lilypond.org/doc/v2.23/Documentation/notation/midi-instruments instruments] *https://itsybitsykidsmusic.com/index.php/portfolio/free-lead-sheet-with-chords-twinkle-twinkle-little-star/ *[[Ear training]] *[[w:User:Guy vandegrift/Lectures/Just and equal tuning]] *[[w:Vocal_range]] and [[w:Piano_key_frequencies#List]] {{cot|For editors of this page}} ;Subpages: Draft space {{Special:Prefixindex/Draft:Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ;Subpages: Main {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> {{cob}} k198jy2t8fiaolgw4mswk7wf6dz4m7a 2412449 2412448 2022-08-07T02:06:04Z Guy vandegrift 813252 /* Appendix */ wikitext text/x-wiki {{share}} ==Partially completed songs== Every song needs to be improved and we need a more songs. If you wish to contribute, leave a message at {{font|size=115%|[[User talk:Guy vandegrift]]}} ;Songs :[[/Twinkle/]] :[[/Red River Valley/]] :[[/Amazing Grace/]] ;Scales and exercises :[[/Major sixth M6/]] :[[/Prelude and Fugue in C major (ear training)/]] :[[/Great_Gate_of_Kiev_(ear_training)/]] UNDER CONSTRUCTION ;For editors of this project :[[Draft:Sing free/Tables and images]] :[[Draft:Sing free/Transclusions]] ==All you need to "sing free" is ...== *A computer with [[w:Loudspeaker|speaker]] and [[w:Microphone|microphone]]. [[w:Headphones|Headphones]] are recommended but not required. *Acces to a tuner. {{#section:Draft:Sing free/Transclusions|tuners}} *When this resource is more developed, we need to supplement this page with something like [[w:Audacity|Audacity]]. [[File:LilyPond wikimedia Playback speed.png|thumb|LilyPond wikimedia Playback speed]] ===How to change tempo (fast/slow)=== Many people like to learn a song by practicing it at different [[w:tempo|tempo]]s. The easiest way to do this is to click on the three vertical dots, as shown to the right. Then select "Playback speed". For those interested in editing or creating songs, it is generally not difficult modify the script for the [[mw:Extension:Score|Score extension]]. Generally speaking, this should always be done by first copying into your sandbox, or creating a version of the song in the [[Draft:Sing free]]. ===Two ways to change the key (pitch) of a song=== #Request a key change of any song by leaving a message at [[user talk:Guy vandegrift]]. #Modify the {{font|\transpose|font=Georgia|size=16px|color=green}} command in the source code as shown below: <score vorbis="1">\language "english" \transpose c c \relative c'' {\key c \major a4 <d, f a>2 } </score> <div class="thumb tright"><div style="width:370px;"> <syntaxhighlight lang="text"> <score vorbis="1">\language "english" \transpose c c \relative c'' {\key c \major a4 <d, f a>2 } </score> </syntaxhighlight></div></div> {{clear}} <score vorbis="1">\language "english" \transpose c f \relative c'' {\key c \major a4 <d, f a>2 } </score> <div class="thumb tright"><div style="width:370px;"> <syntaxhighlight lang="text"> <score vorbis="1">\language "english" \transpose c f \relative c'' {\key c \major a4 <d, f a>2 } </score> </syntaxhighlight></div></div> ==Appendix== '''Help:''' [[w:Help:Score]] | [[s:Help:Sheet music]] | [https://lilypond.org/doc/v2.22/Documentation/learning/aligning-lyrics-to-a-melody.html lyrics] | [https://lilypond.org/doc/v2.21/Documentation/notation/chord-mode chords] | [https://lilypond.org/doc/v2.23/Documentation/notation/midi-instruments instruments] *https://itsybitsykidsmusic.com/index.php/portfolio/free-lead-sheet-with-chords-twinkle-twinkle-little-star/ *[[Ear training]] *[[w:User:Guy vandegrift/Lectures/Just and equal tuning]] *[[w:Vocal_range]] and [[w:Piano_key_frequencies#List]] {{cot|For editors of this page}} ;Subpages: [[Draft:Sing free]] {{Special:Prefixindex/Draft:Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ;Subpages: [[Sing free]] {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> {{cob}} t6q3lqq0qwyxy601k802281xkhzgz4u 2412450 2412449 2022-08-07T02:06:56Z Guy vandegrift 813252 /* Appendix */ wikitext text/x-wiki {{share}} ==Partially completed songs== Every song needs to be improved and we need a more songs. If you wish to contribute, leave a message at {{font|size=115%|[[User talk:Guy vandegrift]]}} ;Songs :[[/Twinkle/]] :[[/Red River Valley/]] :[[/Amazing Grace/]] ;Scales and exercises :[[/Major sixth M6/]] :[[/Prelude and Fugue in C major (ear training)/]] :[[/Great_Gate_of_Kiev_(ear_training)/]] UNDER CONSTRUCTION ;For editors of this project :[[Draft:Sing free/Tables and images]] :[[Draft:Sing free/Transclusions]] ==All you need to "sing free" is ...== *A computer with [[w:Loudspeaker|speaker]] and [[w:Microphone|microphone]]. [[w:Headphones|Headphones]] are recommended but not required. *Acces to a tuner. {{#section:Draft:Sing free/Transclusions|tuners}} *When this resource is more developed, we need to supplement this page with something like [[w:Audacity|Audacity]]. [[File:LilyPond wikimedia Playback speed.png|thumb|LilyPond wikimedia Playback speed]] ===How to change tempo (fast/slow)=== Many people like to learn a song by practicing it at different [[w:tempo|tempo]]s. The easiest way to do this is to click on the three vertical dots, as shown to the right. Then select "Playback speed". For those interested in editing or creating songs, it is generally not difficult modify the script for the [[mw:Extension:Score|Score extension]]. Generally speaking, this should always be done by first copying into your sandbox, or creating a version of the song in the [[Draft:Sing free]]. ===Two ways to change the key (pitch) of a song=== #Request a key change of any song by leaving a message at [[user talk:Guy vandegrift]]. #Modify the {{font|\transpose|font=Georgia|size=16px|color=green}} command in the source code as shown below: <score vorbis="1">\language "english" \transpose c c \relative c'' {\key c \major a4 <d, f a>2 } </score> <div class="thumb tright"><div style="width:370px;"> <syntaxhighlight lang="text"> <score vorbis="1">\language "english" \transpose c c \relative c'' {\key c \major a4 <d, f a>2 } </score> </syntaxhighlight></div></div> {{clear}} <score vorbis="1">\language "english" \transpose c f \relative c'' {\key c \major a4 <d, f a>2 } </score> <div class="thumb tright"><div style="width:370px;"> <syntaxhighlight lang="text"> <score vorbis="1">\language "english" \transpose c f \relative c'' {\key c \major a4 <d, f a>2 } </score> </syntaxhighlight></div></div> ==Appendix== '''Help:''' [[w:Help:Score]] | [[s:Help:Sheet music]] | [https://lilypond.org/doc/v2.22/Documentation/learning/aligning-lyrics-to-a-melody.html lyrics] | [https://lilypond.org/doc/v2.21/Documentation/notation/chord-mode chords] | [https://lilypond.org/doc/v2.23/Documentation/notation/midi-instruments instruments] *https://itsybitsykidsmusic.com/index.php/portfolio/free-lead-sheet-with-chords-twinkle-twinkle-little-star/ *[[Ear training]] *[[w:User:Guy vandegrift/Lectures/Just and equal tuning]] *[[w:Vocal_range]] and [[w:Piano_key_frequencies#List]] {{cot|For editors of this page}} ;Subpages: [[Sing free]] {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ;Subpages: [[Draft:Sing free]] {{Special:Prefixindex/Draft:Sing free/|hideredirects=1|stripprefix=1}}<noinclude> {{cob}} onj40hamsl1st91lhoju759m7v9rt6h 2412455 2412450 2022-08-07T02:10:29Z Guy vandegrift 813252 /* Appendix */ wikitext text/x-wiki {{share}} ==Partially completed songs== Every song needs to be improved and we need a more songs. If you wish to contribute, leave a message at {{font|size=115%|[[User talk:Guy vandegrift]]}} ;Songs :[[/Twinkle/]] :[[/Red River Valley/]] :[[/Amazing Grace/]] ;Scales and exercises :[[/Major sixth M6/]] :[[/Prelude and Fugue in C major (ear training)/]] :[[/Great_Gate_of_Kiev_(ear_training)/]] UNDER CONSTRUCTION ;For editors of this project :[[Draft:Sing free/Tables and images]] :[[Draft:Sing free/Transclusions]] ==All you need to "sing free" is ...== *A computer with [[w:Loudspeaker|speaker]] and [[w:Microphone|microphone]]. [[w:Headphones|Headphones]] are recommended but not required. *Acces to a tuner. {{#section:Draft:Sing free/Transclusions|tuners}} *When this resource is more developed, we need to supplement this page with something like [[w:Audacity|Audacity]]. [[File:LilyPond wikimedia Playback speed.png|thumb|LilyPond wikimedia Playback speed]] ===How to change tempo (fast/slow)=== Many people like to learn a song by practicing it at different [[w:tempo|tempo]]s. The easiest way to do this is to click on the three vertical dots, as shown to the right. Then select "Playback speed". For those interested in editing or creating songs, it is generally not difficult modify the script for the [[mw:Extension:Score|Score extension]]. Generally speaking, this should always be done by first copying into your sandbox, or creating a version of the song in the [[Draft:Sing free]]. ===Two ways to change the key (pitch) of a song=== #Request a key change of any song by leaving a message at [[user talk:Guy vandegrift]]. #Modify the {{font|\transpose|font=Georgia|size=16px|color=green}} command in the source code as shown below: <score vorbis="1">\language "english" \transpose c c \relative c'' {\key c \major a4 <d, f a>2 } </score> <div class="thumb tright"><div style="width:370px;"> <syntaxhighlight lang="text"> <score vorbis="1">\language "english" \transpose c c \relative c'' {\key c \major a4 <d, f a>2 } </score> </syntaxhighlight></div></div> {{clear}} <score vorbis="1">\language "english" \transpose c f \relative c'' {\key c \major a4 <d, f a>2 } </score> <div class="thumb tright"><div style="width:370px;"> <syntaxhighlight lang="text"> <score vorbis="1">\language "english" \transpose c f \relative c'' {\key c \major a4 <d, f a>2 } </score> </syntaxhighlight></div></div> ==Appendix== '''Help:''' [[w:Help:Score]] | [[s:Help:Sheet music]] | [https://lilypond.org/doc/v2.22/Documentation/learning/aligning-lyrics-to-a-melody.html lyrics] | [https://lilypond.org/doc/v2.21/Documentation/notation/chord-mode chords] | [https://lilypond.org/doc/v2.23/Documentation/notation/midi-instruments instruments] *https://itsybitsykidsmusic.com/index.php/portfolio/free-lead-sheet-with-chords-twinkle-twinkle-little-star/ *[[Ear training]] *[[w:User:Guy vandegrift/Lectures/Just and equal tuning]] *[[w:Vocal_range]] and [[w:Piano_key_frequencies#List]] ;Subpages of [[Sing free]]: {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ;Subpages of [[Draft:Sing free]]: {{Special:Prefixindex/Draft:Sing free/|hideredirects=1|stripprefix=1}}<noinclude> m2zl0jfu45du35ty74zb2ohxjb776z2 118 282128 2412442 2382104 2022-08-07T01:57:35Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- ;Subpages {{Subpages/List}} ----- Back to [[Sing_free]] {{Special:PrefixIndex?prefix=Sing+free}} j591y0c8kaszh47hol3ja2g9ejhg7tk 2412443 2412442 2022-08-07T01:57:50Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- ;Subpages {{Subpages/List}} ----- Back to [[Sing_free]] {{:Special:PrefixIndex?prefix=Sing+free}} c8g1hk0fxeotylvimlpnxbwhnnpssxi 2412444 2412443 2022-08-07T01:58:49Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- ;Subpages {{Subpages/List}} ----- Back to [[Sing_free]] {{:Special:PrefixInde/Sing+free}} fx4qfq7j1baluyv6gl8713mwx3a47b4 2412445 2412444 2022-08-07T01:59:05Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- ;Subpages {{Subpages/List}} ----- Back to [[Sing_free]] {{:Special:PrefixIndex/Sing+free}} ddbww69a8hbonrr0eq6tm1cmjdxc32p 2412446 2412445 2022-08-07T02:02:54Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- ;Subpages: Draft space {{Subpages/List}} ----- Back to [[Sing_free]] ;Subpages: Main {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> g2u9cvrwsfpa4djzsywk00b1lf186b1 2412447 2412446 2022-08-07T02:03:33Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- ;Subpages: Draft space {{Special:Prefixindex/Draft:Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ----- Back to [[Sing_free]] ;Subpages: Main {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> 54sigbamfqzq1zkl7vdi6sxzz5n5pt1 2412451 2412447 2022-08-07T02:07:35Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ;Subpages: [[Draft:Sing free]] {{Special:Prefixindex/Draft:Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ----- 8rlh7tqu25n743i1vdergse8bg1pl98 2412452 2412451 2022-08-07T02:08:19Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- ;Subpages: [[Sing free]] {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ;Subpages: [[Draft:Sing free]] {{Special:Prefixindex/Draft:Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ----- 4qzrr1u1xngdh69yotag8o68909i6z1 2412453 2412452 2022-08-07T02:08:57Z Guy vandegrift 813252 wikitext text/x-wiki <small>Back to [[Sing_free]]</small> ----- Welcome to this project's draft space. If you want a place to modify a [[mw:Extension:Score|LilyPond score script]], go to the following page: *[[/Guest/]] ----- ;Subpages of [[Sing free]]: {{Special:Prefixindex/Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ;Subpages of [[Draft:Sing free]]: {{Special:Prefixindex/Draft:Sing free/|hideredirects=1|stripprefix=1}}<noinclude> ----- 70t22q0puu4ogzpde9kjqevr3pficyy 0 285113 2412436 2412181 2022-08-07T01:22:02Z Marshallsumter 311529 /* Reflections */ wikitext text/x-wiki <imagemap> Image:Space station size comparison.svg|270px|thumb|[[File:interactive icon.svg|left|18px|link=|The image above contains clickable links|alt=The image above contains clickable links]] Size comparisons between current and past space stations as they appeared most recently. Solar panels in blue, heat radiators in red. Note that stations have different depths not shown by silhouettes. Credit: [[w:user:Evolution and evolvability|Evolution and evolvability]].{{tlx|free media}} rect 0 0 550 420 [[International Space Station]] rect 550 0 693 420 [[Tiangong Space Station]] rect 0 420 260 700 [[Mir]] rect 260 420 500 700 [[Skylab]] rect 500 420 693 700 [[Tiangong-2]] rect 0 700 160 921 [[Salyut 1]] rect 160 700 280 921 [[Salyut 2]] rect 280 700 420 921 [[Salyut 4]] rect 420 700 550 921 [[Salyut 6]] rect 550 700 693 921 [[Salyut 7]] </imagemap> '''Def.''' a "manned [crewed] artificial satellite designed for long-term habitation, research, etc."<ref name=SpaceStationWikt>{{ cite book |author=[[wikt:User:SemperBlotto|SemperBlotto]] |title=space station |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=20 June 2005 |url=https://en.wiktionary.org/wiki/space_station |accessdate=6 July 2022 }}</ref> is called a '''space station'''. '''Def.''' "a space station, generally constructed for one purpose, that orbits a celestial body such as a planet, asteroid, or star"<ref name=OrbitalPlatform>{{ cite web |author=Roberts |title=Orbital platform |publisher=Roberts Space Industries |location= |date=2021 |url=https://robertsspaceindustries.com/galactapedia/article/box5vnAx5w-orbital-platform |accessdate=6 July 2022 }}</ref> is called an '''orbital platform'''. {{clear}} ==Apollo-Soyuz== [[Image:Apollo-Soyuz-Test-Program-artist-rendering.jpg|thumb|right|250px|A 1973 artist's conception of the docking of the two spacecraft is shown. Credit: R. Bruneau, NASA.{{tlx|free media}}]] [[Image:Apollo-Soyuz Test Project Saturn IB launch.jpg|thumb|left|A Saturn IB launch vehicle lifts the American ASTP crew into orbit. Credit: NASA.{{tlx|free media}}]] [[Image:Soyuz Spacecraft in Orbit - GPN-2002-000155.jpg|thumb|right|250px|This scene was photographed with a handheld 70mm camera from a rendezvous window of the American Apollo spacecraft. Credit: NASA.{{tlx|free media}}]] An artist's concept illustrates an Apollo-type spacecraft (on left) about to dock with a Soviet Soyuz-type spacecraft. A recent agreement between the United States and the Union of Soviet Socialist Republics provides for the docking in space of the Soyuz and Apollo-type spacecraft in Earth orbit in 1975. The joint venture is called the Apollo-Soyuz Test Project. The three American astronauts, Thomas P. Stafford, Vance D. Brand, and Deke Slayton, and two Soviet cosmonauts, Alexei Leonov and Valeri Kubasov, performed both joint and separate scientific experiments, including an arranged eclipse of the Sun by the Apollo module to allow instruments on the Soyuz to take photographs of the solar corona. The photo on the left depicts the liftoff of the Saturn IB launch vehicle (SA-210), for the Apollo/Soyuz Test Project (ASTP) mission, from the Launch Complex 39B, Kennedy Space Center. The Apollo-Soyuz Test Project (ASTP) was the first international docking of the U.S.'s Apollo spacecraft and the U.S.S.R.'s Soyuz spacecraft in space. The objective of the ASTP mission was to provide the basis for a standardized international system for docking of manned spacecraft. The Soyuz spacecraft, with Cosmonauts Alexei Leonov and Valeri Kubasov aboard, was launched from the Baikonur Cosmodrome near Tyuratam in the Kazakh, Soviet Socialist Republic, at 8:20 a.m. (EDT) on July 15, 1975. The Apollo spacecraft, with Astronauts Thomas Stafford, Vance Brand, and Donald Slayton aboard, was launched from Launch Complex 39B, Kennedy Space Center, Florida, at 3:50 p.m. (EDT) on July 15, 1975. The Primary objectives of the ASTP were achieved. They performed spacecraft rendezvous, docking and undocking, conducted intervehicular crew transfer, and demonstrated the interaction of U.S. and U.S.S.R. control centers and spacecraft crews. The mission marked the last use of a Saturn launch vehicle. The Marshall Space Flight Center was responsible for development and sustaining engineering of the Saturn IB launch vehicle during the mission. This scene (second image down on the right) was photographed with a handheld 70 mm camera from a rendezvous window of the American Apollo spacecraft in Earth orbit during the Apollo-Soyuz Test Project (ASTP) mission. It shows the Soviet Soyuz spacecraft contrasted against a black-sky background with the Earth's horizon below. The American Docking Mechanism (DM) is visible at the top of the picture. {{clear}} ==International Space Station== [[Image:STS-134 International Space Station after undocking.jpg|thumb|right|250px|The International Space Station is featured in this image photographed by an STS-134 crew member on the space shuttle Endeavour after the station and shuttle began their post-undocking relative separation. Credit: NASA.{{tlx|free media}}]] [[Image:ISS August06.jpg|thumb|left|250px|The Space Shuttle Endeavor crew captured this shot of the International Space Station (ISS) against the backdrop of Planet Earth. Credit: NASA.{{tlx|free media}}]] [[Image:539956main ISS466.jpg|thumb|right|250px|The MISSE are usually loaded on the outside of International Space Station. The inset image shows where. Credit: NASA.{{tlx|fairuse}}]] [[Image:STS-134 the starboard truss of the ISS with the newly-installed AMS-02.jpg|thumb|left|250px|In this image, the Alpha Magnetic Spectrometer-2 (AMS-02) is visible at center left on top of the starboard truss of the International Space Station. Credit: STS-134 crew member and NASA.{{tlx|free media}}]] [[Image:Nasasupports.jpg|thumb|right|250px|This is a computer-generated image of the Extreme Universe Space Observatory (EUSO) as part of the Japanese Experiment Module (JEM) on the International Space Station (ISS). Credit: JEM-EUSO, Angela Olinto.{{tlx|fairuse}}]] [[Image:BBND1.jpg|thumb|right|250px|This image shows a Bonner Ball Neutron Detector which is housed inside the small plastic ball when the top is put back on. Credit: NASA.{{tlx|free media}}]] On the right is the International Space Station after the undocking of STS-134 Space Shuttle. The Space Shuttle Endeavor crew captured this shot [on the left] of the International Space Station (ISS) against the backdrop of Planet Earth. "Since 2001, NASA and its partners have operated a series of flight experiments called Materials International Space Station Experiment, or MISSE [on the second right]. The objective of MISSE is to test the stability and durability of materials and devices in the space environment."<ref name=Sheldon>{{ cite book |author=Sheldon |title=Materials: Out of This World |publisher=NASA News |location=Washington DC USA |date=April 29, 2011 |url=http://spacestationinfo.blogspot.com/2011_04_01_archive.html |accessdate=2014-01-08 }}</ref> The '''Alpha Magnetic Spectrometer''' on the second left is designed to search for various types of unusual matter by measuring cosmic rays. The '''Extreme Universe Space Observatory''' ('''EUSO''') [on the third right] is the first Space mission concept devoted to the investigation of cosmic rays and neutrinos of [[w:Ultra-high-energy cosmic ray|extreme energy]] ({{nowrap|E > {{val|5|e=19|u=eV}}}}). Using the Earth's atmosphere as a giant detector, the detection is performed by looking at the streak of [[w:fluorescence|fluorescence]] produced when such a particle interacts with the Earth's atmosphere. The Space Environment Data Acquisition equipment-Attached Payload (SEDA-AP) aboard the Kibo (International Space Station module) measures neutrons, plasma, heavy ions, and high-energy light particles in ISS orbit. On the lower right is a Bonner Ball Neutron Detector "BBND ... determined that galactic cosmic rays were the major cause of secondary neutrons measured inside ISS. The neutron energy spectrum was measured from March 23, 2001 through November 14, 2001 in the U.S. Laboratory Module of the ISS. The time frame enabled neutron measurements to be made during a time of increased solar activity (solar maximum) as well as observe the results of a solar flare on November 4, 2001."<ref name=Choy>{{ cite book |author=Tony Choy |title=Bonner Ball Neutron Detector (BBND) |publisher=NASA |location=Johnson Space Center, Human Research Program, Houston, TX, United States |date=July 25, 2012 |url=http://www.nasa.gov/mission_pages/station/research/experiments/BBND.html |accessdate=2012-08-17 }}</ref> "Bonner Ball Neutron Detector (BBND) [shown with its cap off] measures neutron radiation (low-energy, uncharged particles) which can deeply penetrate the body and damage blood forming organs. Neutron radiation is estimated to be 20 percent of the total radiation on the International Space Station (ISS). This study characterizes the neutron radiation environment to develop safety measures to protect future ISS crews."<ref name=Choy>{{ cite book |author=Tony Choy |title=Bonner Ball Neutron Detector (BBND) |publisher=NASA |location=Johnson Space Center, Human Research Program, Houston, TX, United States |date=July 25, 2012 |url=http://www.nasa.gov/mission_pages/station/research/experiments/BBND.html |accessdate=2012-08-17 }}</ref> Six BBND detectors were distributed around the International Space Station (ISS) to allow data collection at selected points. "The six BBND detectors provided data indicating how much radiation was absorbed at various times, allowing a model of real-time exposure to be calculated, as opposed to earlier models of passive neutron detectors which were only capable of providing a total amount of radiation received over a span of time. Neutron radiation information obtained from the Bonner Ball Neutron Detector (BBND) can be used to develop safety measures to protect crewmembers during both long-duration missions on the ISS and during interplanetary exploration."<ref name=Choy/> "The Bonner Ball Neutron Detector (BBND) developed by Japan Aerospace and Exploration Agency (JAXA) was used inside the International Space Station (ISS) to measure the neutron energy spectrum. It consisted of several neutron moderators enabling the device to discriminate neutron energies up to 15 MeV (15 mega electron volts). This BBND characterized the neutron radiation on ISS during Expeditions 2 and 3."<ref name=Choy/> "BBND results show the overall neutron environment at the ISS orbital altitude is influenced by highly energetic galactic cosmic rays, except in the South Atlantic Anomaly (SAA) region where protons trapped in the Earth's magnetic field cause a more severe neutron environment. However, the number of particles measured per second per square cm per MeV obtained by BBND is consistently lower than that of the precursor investigations. The average dose-equivalent rate observed through the investigation was 3.9 micro Sv/hour or about 10 times the rate of radiological exposure to the average US citizen. In general, radiation damage to the human body is indicated by the amount of energy deposited in living tissue, modified by the type of radiation causing the damage; this is measured in units of Sieverts (Sv). The background radiation dose received by an average person in the United States is approximately 3.5 milliSv/year. Conversely, an exposure of 1 Sv can result in radiation poisoning and a dose of five Sv will result in death in 50 percent of exposed individuals. The average dose-equivalent rate observed through the BBND investigation is 3.9 micro Sv/hour, or about ten times the average US surface rate. The highest rate, 96 microSv/hour was observed in the SAA region."<ref name=Choy/> "The November 4, 2001 solar flare and the associated geomagnetic activity caused the most severe radiation environment inside the ISS during the BBND experiment. The increase of neutron dose-equivalent due to those events was evaluated to be 0.19mSv, which is less than 1 percent of the measured neutron dose-equivalent measured over the entire 8-month period."<ref name=Choy/> {{clear}} ==Mir== [[Image:Mir Space Station viewed from Endeavour during STS-89.jpg|thumb|right|250px|Approach view is of the Mir Space Station viewed from Space Shuttle Endeavour during the STS-89 rendezvous. Credit: NASA.{{tlx|free media}}]] In the image on the right, a Progress cargo ship is attached on the left, a Soyuz manned spacecraft attached on the right. Mir is seen on the right from Space Shuttle Endeavour during STS-89 (28 January 1998). Mir was a space station that operated in low Earth orbit from 1986 to 2001, operated by the Soviet Union and later by Russia. Mir was the first modular space station and was assembled in orbit from 1986 to 1996. It had a greater mass than any previous spacecraft. At the time it was the largest artificial satellite in orbit, succeeded by the International Space Station (ISS) after Mir's orbit decayed. ''Mir'' was the first continuously inhabited long-term research station in orbit and held the record for the longest continuous human presence in space at 3,644 days, until it was surpassed by the ISS on 23 October 2010.<ref name=Jackman>{{cite journal|last=Jackman|first=Frank|title=ISS Passing Old Russian Mir In Crewed Time|url=http://www.aviationweek.com/aw/generic/story_channel.jsp?channel=space&id=news/asd/2010/10/28/11.xml|Journal=Aviation Week|date=29 October 2010}}</ref> The first module of the station, known as the Mir Core Module or base block, was launched in 1986 and followed by six further modules. Proton rockets were used to launch all of its components except for the Mir Docking Module, which was installed by US Space Shuttle mission STS-74 in 1995. When complete, the station consisted of seven pressurised modules and several unpressurised components. Power was provided by several photovoltaic arrays attached directly to the modules. The station was maintained at an orbit between {{convert|296|km|mi|0|abbr=on}} and {{convert|421|km|mi|0|abbr=on}} altitude and travelled at an average speed of 27,700&nbsp;km/h (17,200&nbsp;mph), completing 15.7 orbits per day.<ref name="MirBIS">{{cite book|title=The History of Mir 1986–2000|publisher=British Interplanetary Society|{{isbn|978-0-9506597-4-9}}|editor=Hall, R.|url=https://archive.org/details/historyofmir19860000unse |date=February 2021}}</ref><ref name="FinalBIS">{{cite book|title=Mir: The Final Year|publisher=British Interplanetary Society|{{isbn|978-0-9506597-5-6}}|editor=Hall, R. |date=February 2021}}</ref><ref name="OrbitCalc">{{cite web|title=Orbital period of a planet|publisher=CalcTool|accessdate=12 September 2010|url=https://web.archive.org/web/20191112095042/http://www.calctool.org/CALC/phys/astronomy/planet_orbit }}</ref> {{clear}} ==Polar Satellite 4== [[Image:PSLV C45 EMISAT campaign 09.jpg|right|thumb|375x375px|Third and fourth stages of PSLV-C45. Credit: Indian Space Research Organisation.{{tlx|free media}}]] PS4 has carried hosted payloads like AAM on PSLV-C8,<ref name=":6">{{cite web|url=https://www.isro.gov.in/sites/default/files/flipping_book/PSLV-C8/files/assets/common/downloads/publication.pdf|title=PSLV C8 / AGILE brochure}}</ref> Luxspace (Rubin 9.1)/(Rubin 9.2) on PSLV-C14<ref>{{cite web|url=https://www.isro.gov.in/sites/default/files/flipping_book/PSLV-C14/files/assets/common/downloads/publication.pdf|title=PSLV C14/Oceansat-2 brochure}}</ref> and mRESINS on PSLV-C21.<ref>{{cite web |url=https://www.dos.gov.in/sites/default/files/flipping_book/Space%20India%20July%2012-Aug%2013/files/assets/common/downloads/Space%20India%20July%2012-Aug%2013.pdf|title=Space-India July 2012 to August 2013 }}</ref> PS4 is being augmented to serve as a long duration orbital platform after completion of its primary mission. PS4 Orbital Platform (PS4-OP) will have its own power supply, telemetry package, data storage and attitude control for hosted payloads.<ref>{{cite web|url=http://www.unoosa.org/documents/pdf/copuos/stsc/2019/tech-55E.pdf|title=Opportunities for science experiments in the fourth stage of India's PSLV|date=21 February 2019}}</ref><ref>{{cite web|url=https://www.isro.gov.in/sites/default/files/orbital_platform-_ao.pdf|title=Announcement of Opportunity (AO) for Orbital platform: an avenue for in-orbit scientific experiments|date=15 June 2019}}</ref><ref>{{cite web|url=https://timesofindia.indiatimes.com/india/2-days-after-space-station-news-isro-calls-for-docking-experiments-on-pslv-stage-4/articleshow/69800354.cms|title=2 days after Space Station news, Isro calls for "docking experiments" on PSLV stage-4|first=Chethan|last=Kumar|work=The Times of India|accessdate=23 February 2020}}</ref> On PSLV-C37 and PSLV-C38 campaigns,<ref>{{Cite web |title=''In-situ'' observations of rocket burn induced modulations of the top side ionosphere using the IDEA payload on-board the unique orbiting experimental platform (PS4) of the Indian Polar Orbiting Satellite Launch Vehicle mission - ISRO |url=https://www.isro.gov.in/situ-observations-of-rocket-burn-induced-modulations-of-top-side-ionosphere-using-idea-payload-board |accessdate=2022-06-27 |website=www.isro.gov.in |language=en}}</ref> as a demonstration PS4 was kept operational and monitored for over ten orbits after delivering spacecraft.<ref>{{cite web |title=Department of Space Annual Report 2017-18|url=https://web.archive.org/web/20180213093132/https://www.isro.gov.in/sites/default/files/article-files/node/9805/annualreport2017-18.pdf }}</ref><ref name=Singh>{{cite web |url=https://timesofindia.indiatimes.com/india/in-a-first-isro-will-make-dead-rocket-stage-alive-in-space-for-experiments/articleshow/67067817.cms|title=In a first, ISRO will make dead rocket stage "alive" in space for experiments|first=Surendra|last=Singh|work=The Times of India|date=16 December 2018|accessdate=23 February 2020}}</ref><ref name=Rajasekhar>{{cite web|url=https://www.deccanchronicle.com/science/science/200617/isro-to-lower-rockets-altitude.html|title=Isro to lower rocket's altitude|last=rajasekhar|first=pathri|publisher=Deccan Chronicle|date=2017-06-20|accessdate=23 February 2020}}</ref> PSLV-C44 was the first campaign where PS4 functioned as independent orbital platform for short duration as there was no on-board power generation capacity.<ref name=Rajwi>{{cite news|last=Rajwi|first=Tiki |url=https://www.thehindu.com/news/national/kerala/pslv-lift-off-with-added-features/article25981654.ece|title=PSLV lift-off with added features|date=2019-01-12|newspaper=The Hindu|issn=0971-751X|accessdate=23 February 2020}}</ref> It carried KalamSAT-V2 as a fixed payload, a 1U cubesat by Space Kidz India based on Interorbital Systems kit.<ref>{{cite web|title=PSLV-C44 - ISRO |url=https://www.isro.gov.in/launcher/pslv-c44|accessdate=26 June 2020|website=isro.gov.in}}</ref><ref>{{cite web |title=Congratulations to ISRO and SpaceKidzIndia on getting their CubeSat into orbit! The students modified their IOS CubeSat kit, complete w/ their own experiments!|author=Interorbital Systems|date=25 January 2019|url=https://twitter.com/interorbital/status/1088526772109422592 }}</ref> On PSLV-C45 campaign, the fourth stage had its own power generation capability as it was augmented with an array of fixed solar cells around PS4 propellant tank.<ref name=Clark>{{cite web |url=https://spaceflightnow.com/2019/04/01/indian-military-satellite-20-more-planet-imaging-cubesats-aboard-successful-pslv-launch/|title=Indian military satellite, 20 more Planet imaging CubeSats launched by PSLV|last=Clark|first=Stephen|publisher=Spaceflight Now|accessdate=2020-02-23}}</ref> Three payloads hosted on PS4-OP were, Advanced Retarding Potential Analyzer for Ionospheric Studies (ARIS 101F) by IIST,<ref>{{cite web|url=https://www.iist.ac.in/avionics/sudharshan.kaarthik|title=Department of Avionics, R. Sudharshan Kaarthik, Ph.D (Assistant Professor)}}</ref> experimental Automatic identification system (AIS) payload by ISRO and AISAT by Satellize.<ref>{{cite web|url=https://satellize.com/index.php/exseed-sat-2/|title=Exseed Sat-2|publisher=Satellize|accessdate=23 February 2020}}</ref> To function as orbital platform, fourth stage was put in spin-stabilized mode using its RCS thrusters.<ref>{{Cite web |date=16 June 2021 |title=Opportunity for Scientific Experiments on PSLV Upper Stage Orbital Platform |url=https://www.unoosa.org/documents/pdf/psa/hsti/Hyper-Microgravity_Webinar2021/Hyper-Microgravity_Webinar2021/9_RegionalActivities/R._Senan_Hypermicrogravity_ISRO.pdf}}</ref> ==Salyut 1== [[Image:Salyut 1.jpg|thumb|right|250px|Salyut 1 is photographed from the departing Soyuz 11. Credit: [[w:user:Viktor Patsayev|Viktor Patsayev]].{{tlx|fairuse}}]] Salyut 1 (DOS-1) was the world's first space station launched into low Earth orbit by the Soviet Union on April 19, 1971. The Soyuz 11 crew achieved successful hard docking and performed experiments in Salyut 1 for 23 days. Civilian Soviet space stations were internally referred to as DOS (the Russian acronym for "Long-duration orbital station"), although publicly, the Salyut name was used for the first six DOS stations (''Mir'' was internally known as DOS-7).<ref>Portree, David S. F. (March 1995). "Part 2 – Almaz, Salyut, and Mir" . Mir Hardware Heritage . Johnson Space Center Reference Series. NASA. NASA Reference Publication 1357 – via Wikisource.</ref> The astrophysical Orion 1 Space Observatory designed by Grigor Gurzadyan of Byurakan Observatory in Armenia, was installed in Salyut 1. Ultraviolet spectrograms of stars were obtained with the help of a mirror telescope of the Mersenne Three-mirror_anastigmat system and a spectrograph of the Wadsworth system using film sensitive to the far ultraviolet. The dispersion of the spectrograph was 32&nbsp;Å/mm (3.2&nbsp;nm/mm), while the resolution of the spectrograms derived was about 5&nbsp;Å at 2600&nbsp;Å (0.5&nbsp;nm at 260&nbsp;nm). Slitless spectrograms were obtained of the stars ''Vega'' and ''Beta Centauri'' between 2000 and 3800&nbsp;Å (200 and 380&nbsp;nm).<ref name=Gurzadyan>{{cite journal |title=Observed Energy Distribution of α Lyra and β Cen at 2000–3800 Å |journal=Nature |first1=G. A. |last1=Gurzadyan |first2=J. B. |last2=Ohanesyan |volume=239 |issue=5367 |page=90 |date=September 1972 |doi=10.1038/239090a0 |bibcode=1972Natur.239...90G|s2cid=4265702 }}</ref> The telescope was operated by crew member Viktor Patsayev, who became the first man to operate a telescope outside of the Earth's atmosphere.<ref name="Marett-Crosby2013">{{cite book|last=Marett-Crosby|first=Michael|title=Twenty-Five Astronomical Observations That Changed the World: And How To Make Them Yourself|url=https://books.google.com/books?id=0KRSphlvsqgC&pg=PA282|accessdate=2018-04-18|date=2013-06-28|publisher=Springer Science & Business Media|{{isbn|9781461468004}}|page=282 }}</ref> {{clear}} ==Salyut 3== [[Image:Salyut 3 paper model.JPG|thumb|right|250px|Salyut 3 (Almaz 2) Soviet military space station model shows Soyuz 14 docked. Credit: [[c:user:Godai|Godai]].{{tlx|free media}}]] Salyut 3; also known as OPS-2<ref name=Zak>{{cite web|url=http://www.russianspaceweb.com/almaz_ops2.html|title=OPS-2 (Salyut-3)|author=Anatoly Zak|publisher=RussianSpaceWeb.com}}</ref> or Almaz 2<ref name=Portree1995>D.S.F. Portree (March 1995). "Mir Hardware Heritage" (PDF). NASA. Archived from the original (PDF) on 2009-09-07.</ref>) was a Soviet Union space station launched on 25 June 1974. It was the second Almaz military space station, and the first such station to be launched successfully.<ref name=Portree1995/> It was included in the Salyut program to disguise its true military nature.<ref name=Hall>Rex Hall, David Shayler (2003). Soyuz: a universal spacecraft. Springer. p. 459. ISBN 1-85233-657-9.</ref> Due to the military nature of the station, the Soviet Union was reluctant to release information about its design, and about the missions relating to the station.<ref name=Zimmerman>Robert Zimmerman (September 3, 2003). Leaving Earth: Space Stations, Rival Superpowers, and the Quest for Interplanetary Travel. Joseph Henry Press. pp. 544. ISBN 0-309-08548-9.</ref> It attained an altitude of 219 to 270&nbsp;km on launch<ref name=Bond>Peter Bond (20 June 2002). The continuing story of the International Space Station. Springer. p. 416. {{ISBN|1-85233-567-X}}.</ref> and NASA reported its final orbital altitude was 268 to 272&nbsp;km.<ref name=NASAcat>{{cite web|url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1974-046A|title=Salyut 3 - NSSDC ID: 1974-046A|publisher=NASA}}</ref> The space stations funded and developed by the military, known as ''Almaz'' stations, were roughly similar in size and shape to the civilian DOS stations.<ref name=Zimmerman/> But the details of their design, which is attributed to Vladimir Chelomey, are considered to be significantly different from the DOS stations.<ref name=Zimmerman/> The first Almaz station was Salyut 2, which launched in April 1973, but failed only days after reaching orbit, and hence it was never manned.<ref name=Portree1995/> Salyut 3 consisted of an airlock chamber, a large-diameter work compartment, and a small diameter living compartment, giving a total habitable volume of 90 m³.<ref name=Portree/> It had two solar arrays, one docking port, and two main engines, each of which could produce 400 kgf (3.9 kN) of thrust.<ref name=Portree/> Its launch mass was 18,900 kg.<ref name=Portree1995/> The station came equipped with a shower, a standing sleeping station, as well as a foldaway bed.<ref name=Portree1995/> The floor was covered with hook and loop fastener (Velcro) to assist the cosmonauts moving around the station. Some entertainment on the station included a magnetic chess set, a small library, and a cassette deck with some audio compact Cassette tapes.<ref name=Portree/> Exercise equipment included a treadmill and Pingvin exercise suit.<ref name=Portree/> The first water-recycling facilities were tested on the station; the system was called Priboy.<ref name=Portree1995/> The work compartment was dominated by the ''Agat-1'' Earth-observation telescope, which had a focal length of 6.375 metres and an optical resolution better than three metres, according to post-Soviet sources;<ref name=Siddiqi/>. Another NASA source<ref name=Portree1995/> states the focal length was 10 metres; but Portree's document preceded Siddiqi's by several years, during which time more information about the specifications was gathered. NASA historian Siddiqi has speculated that given the size of the telescope's mirror, it likely had a resolution better than one metre.<ref name=Siddiqi>{{cite book|title=Challenge to Apollo: The Soviet Union and the Space Race, 1945-1974|author=Siddiqi, Asif A.|publisher=NASA|year=2000}} SP-2000-4408. [https://history.nasa.gov/SP-4408pt1.pdf Part 2 (page 1-499)], [https://history.nasa.gov/SP-4408pt2.pdf Part 1 (page 500-1011)]</ref> The telescope was used in conjunction with a wide-film camera, and was used primarily for military reconnaissance purposes.<ref name=Siddiqi/> The cosmonauts are said to have observed targets set out on the ground at Baikonur. Secondary objectives included study of water pollution, agricultural land, possible ore-bearing landforms, and oceanic ice formation.<ref name=Portree1995/> The Salyut 3, although called a "civilian" station, was equipped with a "self-defence" gun which had been designed for use aboard the station, and whose design is attributed to Alexander Nudelman.<ref name=Zak/> Some accounts claim the station was equipped with a Nudelman-Rikhter "Vulkan" gun, which was a variant of the Nudelman-Rikhter NR-23 (23 mm Nudelman) aircraft cannon, or possibly a Nudelman-Rikhter NR-30 (Nudelman NR-30) 30&nbsp;mm gun.<ref name=Olberg>[http://space.au.af.mil/books/oberg/ch02.pdf James Olberg, ''Space Power Theory'', Ch. 2]</ref> Later Russian sources indicate that the gun was the virtually unknown (in the West) Rikhter R-23.<ref>Широкоград А.Б. (2001) ''История авиационного вооружения'' Харвест (Shirokograd A.B. (2001) ''Istorya aviatsionnogo vooruzhenia'' Harvest. {{ISBN|985-433-695-6}}) (''History of aircraft armament'') p. 162</ref> These claims have reportedly been verified by Pavel Popovich, who had visited the station in orbit, as commander of Soyuz 14.<ref name=Olberg/> Due to potential shaking of the station, in-orbit tests of the weapon with cosmonauts in the station were ruled out.<ref name=Zak/> The gun was fixed to the station in such a way that the only way to aim would have been to change the orientation of the entire station.<ref name=Zak/><ref name=Olberg/> Following the last manned mission to the station, the gun was commanded by the ground to be fired; some sources say it was fired to depletion,<ref name=Olberg/> while other sources say three test firings took place during the Salyut 3 mission.<ref name=Zak/> {{clear}} ==Salyut 4== [[Image:Salyut-4 diagram.gif|thumb|right|250px|Diagram shows the orbital configuration of the Soviet space station Salyut 4 with a docked Soyuz 7K-T spacecraft. Credit: [[c:user:Bricktop|Bricktop]].{{tlx|free media}}]] Installed on the Salyut 4 were OST-1 (Orbiting Solar Telescope) 25&nbsp;cm solar telescope with a focal length of 2.5m and spectrograph shortwave diffraction spectrometer for far ultraviolet emissions, designed at the Crimean Astrophysical Observatory, and two X-ray telescopes.<ref>[http://www.friends-partners.org/partners/mwade/craft/salyut4.htm Salyut 4<!-- Bot generated title -->]</ref><ref>[http://adsabs.harvard.edu/abs/1979IzKry..59...31B The design of the Salyut-4 orbiting solar telescope]</ref> One of the X-ray telescopes, often called the ''Filin telescope'', consisted of four gas flow proportional counters, three of which had a total detection surface of 450&nbsp;cm² in the energy range 2–10 keV, and one of which had an effective surface of 37&nbsp;cm² for the range 0.2 to 2 keV (32 to 320 Attojoule (aJ)). The field of view was limited by a slit collimator to 3 in × 10 in full width at half maximum. The instrumentation also included optical sensors which were mounted on the outside of the station together with the X-ray detectors, and power supply and measurement units which were inside the station. Ground-based calibration of the detectors was considered along with in-flight operation in three modes: inertial orientation, orbital orientation, and survey. Data could be collected in 4 energy channels: 2 to 3.1 keV (320 to 497 aJ), 3.1 to 5.9 keV (497 to 945 aJ), 5.9 to 9.6 keV (945 to 1,538 aJ), and 2 to 9.6 keV (320 to 1,538 aJ) in the larger detectors. The smaller detector had discriminator levels set at 0.2 keV (32 aJ), 0.55 keV (88 aJ), and 0.95 keV (152 aJ).<ref name=Salyut4>{{cite web |title=Archived copy |accessdate=2012-05-05|url=https://web.archive.org/web/20120504183030/http://www.astronautix.com/craft/salyut4.htm }}</ref> Other instruments include a swivel chair for vestibular function tests, lower body negative pressure gear for cardiovascular studies, bicycle ergometer integrated physical trainer (electrically driven running track 1 m X .3 m with elastic cords providing 50&nbsp;kg load), penguin suits and alternate athletic suit, sensors for temperature and characteristics of upper atmosphere, ITS-K infrared telescope spectrometer and ultraviolet spectrometer for study of earth's infrared radiation, multispectral earth resources camera, cosmic ray detector, embryological studies, new engineering instruments tested for orientation of station by celestial objects and in darkness and a teletypewriter.<ref name=Salyut4/> {{clear}} ==Salyut 5== [[Image:Salyut 5.jpeg|thumb|right|250px|Image was obtained from the Almaz OPS page. Credit: [[c:user:Mpaoper|Mpaoper]].{{tlx|free media}}]] Salyut 5 carried Agat, a camera which the crews used to observe the Earth. The first manned mission, Soyuz 21, was launched from Baikonur on 6 July 1976, and docked at 13:40 UTC the next day.<ref name=Anikeev>{{cite web|last=Anikeev|first=Alexander|title=Soyuz-21|work=Manned Astronautics, Figures and Facts|accessdate=31 December 2010|url=https://web.archive.org/web/20110319191201/http://space.kursknet.ru/cosmos/english/machines/s21.sht }}</ref> On 14 October 1976, Soyuz 23 was launched carrying Vyacheslav Zudov and Valery Rozhdestvensky to the space station. During approach for docking the next day, a faulty sensor incorrectly detected an unexpected lateral motion. The spacecraft's Igla automated docking system fired the spacecraft's maneuvering thrusters in an attempt to stop the non-existent motion. Although the crew was able to deactivate the Igla system, the spacecraft had expended too much fuel to reattempt the docking under manual control. Soyuz 23 returned to Earth on 16 October without completing its mission objectives. The last mission to Salyut 5, Soyuz 24, was launched on 7 February 1977. Its crew consisted of cosmonauts Viktor Gorbatko and Yury Glazkov, who conducted repairs aboard the station and vented the air which had been reported to be contaminated. Scientific experiments were conducted, including observation of the sun. The Soyuz 24 crew departed on 25 February. The short mission was apparently related to Salyut 5 starting to run low on propellant for its main engines and attitude control system.<ref name=Zak/> {{clear}} ==Salyut 6== [[Image:Salyut 6.jpg|thumb|right|250px|Salyut 6 is photographed with docked Soyuz (right) and Progress (left). Credit: A cosmonaut of the Soviet space programme.{{tlx|fairuse}}]] Salyut 6 aka DOS-5, was a Soviet orbital space station, the eighth station of the Salyut programme. It was launched on 29 September 1977 by a Proton rocket. Salyut 6 was the first space station to receive large numbers of crewed and uncrewed spacecraft for human habitation, crew transfer, international participation and resupply, establishing precedents for station life and operations which were enhanced on Mir and the International Space Station. Salyut 6 was the first "second generation" space station, representing a major breakthrough in capabilities and operational success. In addition to a new propulsion system and its primary scientific instrument—the BST-1M multispectral telescope—the station had two docking ports, allowing two craft to visit simultaneously. This feature made it possible for humans to remain aboard for several months.<ref name=Chiara>{{cite book |title=Spacecraft: 100 Iconic Rockets, Shuttles, and Satellites that put us in Space |last1=De Chiara |first1=Giuseppe |last2=Gorn |first2=Michael H. |publisher=Quarto/Voyageur |date=2018 |location=Minneapolis |{{ISBN|9780760354186}} |pages=132–135}}</ref> Six long-term resident crews were supported by ten short-term visiting crews who typically arrived in newer Soyuz craft and departed in older craft, leaving the newer craft available to the resident crew as a return vehicle, thereby extending the resident crew's stay past the design life of the Soyuz. Short-term visiting crews routinely included international cosmonauts from Warsaw pact countries participating in the Soviet Union's Intercosmos programme. These cosmonauts were the first spacefarers from countries other than the Soviet Union or the United States. Salyut 6 was visited and resupplied by twelve uncrewed Progress spacecraft including Progress 1, the first instance of the series. Additionally, Salyut 6 was visited by the first instances of the new Soyuz-T spacecraft. {{clear}} ==Salyut 7== [[Image:Salyut7 with docked spacecraft.jpg|thumb|right|250px|A view of the Soviet orbital station Salyut 7, with a docked Soyuz spacecraft in view. Credit:NASA.{{tlx|fairuse}}]] Salyut 7 a.k.a. DOS-6, short for Durable Orbital Station<ref name=Portree1995/>) was a space station in low Earth orbit from April 1982 to February 1991.<ref name=Portree1995/> It was first crewed in May 1982 with two crew via Soyuz T-5, and last visited in June 1986, by Soyuz T-15.<ref name=Portree1995/> Various crew and modules were used over its lifetime, including 12 crewed and 15 uncrewed launches in total.<ref name=Portree1995/> Supporting spacecraft included the Soyuz T, Progress, and TKS spacecraft.<ref name=Portree1995/> {{clear}} ==Skylab== [[Image:Skylab (SL-4).jpg|thumb|right|250px|Skylab is an example of a manned observatory in orbit. Credit: NASA.{{tlx|free media}}]] Skylab included an Apollo Telescope Mount, which was a multi-spectral solar observatory. Numerous scientific experiments were conducted aboard Skylab during its operational life, and crews were able to confirm the existence of coronal holes in the Sun. The Earth Resources Experiment Package (EREP), was used to view the Earth with sensors that recorded data in the visible, infrared, and microwave spectral regions. {{clear}} ==Skylab 2== [[Image:40 Years Ago, Skylab Paved Way for International Space Station.jpg|thumb|right|250px|Skylab is photographed from the departing Skylab 2 spacecraft. Credit: NASA Skylab 2 crew.{{tlx|free media}}]] As the crew of Skylab 2 departs, the gold sun shield covers the main portion of the space station. The solar array at the top was the one freed during a spacewalk. The four, windmill-like solar arrays are attached to the Apollo Telescope Mount used for solar astronomy. {{clear}} ==Skylab 3== [[Image:Skylab 3 Close-Up - GPN-2000-001711.jpg|thumb|right|250px|Skylab is photographed by the arriving Skylab 3 crew. Credit: NASA Skylab 3 crew.{{tlx|free media}}]] A close-up view of the Skylab space station photographed against an Earth background from the Skylab 3 Command/Service Module during station-keeping maneuvers prior to docking. The Ilha Grande de Gurupá area of the Amazon River Valley of Brazil can be seen below. Aboard the command module were astronauts Alan L. Bean, Owen K. Garriott, and Jack R. Lousma, who remained with the Skylab space station in Earth's orbit for 59 days. This picture was taken with a hand-held 70mm Hasselblad camera using a 100mm lens and SO-368 medium speed Ektachrome film. Note the one solar array system wing on the Orbital Workshop (OWS) which was successfully deployed during extravehicular activity (EVA) on the first manned Skylab flight. The parasol solar shield which was deployed by the Skylab 2 crew can be seen through the support struts of the Apollo Telescope Mount. {{clear}} ==Skylab 4== [[Image:Skylab and Earth Limb - GPN-2000-001055.jpg|thumb|right|250px|The final view of Skylab, from the departing mission 4 crew, with Earth in the background. Credit: NASA Skylab 4 crew.{{tlx|free media}}]] An overhead view of the Skylab Orbital Workshop in Earth orbit as photographed from the Skylab 4 Command and Service Modules (CSM) during the final fly-around by the CSM before returning home. During launch on May 14, 1973, 63 seconds into flight, the micrometeor shield on the Orbital Workshop (OWS) experienced a failure that caused it to be caught up in the supersonic air flow during ascent. This ripped the shield from the OWS and damaged the tie-downs that secured one of the solar array systems. Complete loss of one of the solar arrays happened at 593 seconds when the exhaust plume from the S-II's separation rockets impacted the partially deployed solar array system. Without the micrometeoroid shield that was to protect against solar heating as well, temperatures inside the OWS rose to 126°F. The rectangular gold "parasol" over the main body of the station was designed to replace the missing micrometeoroid shield, to protect the workshop against solar heating. The replacement solar shield was deployed by the Skylab I crew. {{clear}} ==Spacelabs== [[Image:STS-42 view of payload bay.jpg|thumb|upright=1.0|right|300px|STS-42 is shown with Spacelab hardware in the orbiter bay overlooking Earth. Credit: NASA STS-42 crew.{{tlx|free media}}]] OSS-l (named for the NASA Office of Space Science and Applications) onboard STS-3 consisted of a number of instruments mounted on a Spacelab pallet, intended to obtain data on the near-Earth environment and the extent of contamination caused by the orbiter itself. Among other experiments, the OSS pallet contained a X-ray detector for measuring the polarization of X-rays emitted by solar flares.<ref name=Tramiel1984>{{cite journal|author=Tramiel, Leonard J.|author2=Chanan, Gary A. |author3=Novick, R.|title=Polarization evidence for the isotropy of electrons responsible for the production of 5-20 keV X-rays in solar flares|bibcode=1984ApJ...280..440T|date=1 May 1984|journal=The Astrophysical Journal|doi=10.1086/162010|volume=280|page=440}}</ref> Spacelab was a reusable laboratory developed by European Space Agency (ESA) and used on certain spaceflights flown by the Space Shuttle. The laboratory comprised multiple components, including a pressurized module, an unpressurized carrier, and other related hardware housed in the Shuttle's cargo bay. The components were arranged in various configurations to meet the needs of each spaceflight. "Spacelab is important to all of us for at least four good reasons. It expanded the Shuttle's ability to conduct science on-orbit manyfold. It provided a marvelous opportunity and example of a large international joint venture involving government, industry, and science with our European allies. The European effort provided the free world with a really versatile laboratory system several years before it would have been possible if the United States had had to fund it on its own. And finally, it provided Europe with the systems development and management experience they needed to move into the exclusive manned space flight arena."<ref>[https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19880009991.pdf ''Spacelab: An International Success Story'' Foreword by NASA Administrator James C. Fletcher]</ref> NASA shifted its focus from the Lunar missions to the Space Shuttle, and also space research.<ref name=Portree>{{cite web |url=https://spaceflighthistory.blogspot.com/2017/03/nasa-seeks-to-pep-up-shuttlespacelab.html |title=Spaceflight History: NASA Johnson's Plan to PEP Up Shuttle/Spacelab (1981) |last=Portree |first=David S.F. |date=2017 |website=Spaceflight History}}</ref> Spacelab consisted of a variety of interchangeable components, with the major one being a crewed laboratory that could be flown in Space Shuttle orbiter's bay and returned to Earth.<ref name="Angelo">{{cite book |author=Joseph Angelo |title=Dictionary of Space Technology |url=https://books.google.com/books?id=wSzfAQAAQBAJ&pg=PA393 |year=2013 |publisher=Routledge |{{isbn|978-1-135-94402-5}} |page=393}}</ref> However, the habitable module did not have to be flown to conduct a Spacelab-type mission and there was a variety of pallets and other hardware supporting space research.<ref name="Angelo"/> The habitable module expanded the volume for astronauts to work in a shirt-sleeve environment and had space for equipment racks and related support equipment.<ref name="Angelo"/> When the habitable module was not used, some of the support equipment for the pallets could instead be housed in the smaller Igloo, a pressurized cylinder connected to the Space Shuttle orbiter crew area.<ref name="Angelo"/> {| class="wikitable" |- ! Mission name ! Space Shuttle orbiter ! Launch date ! Spacelab <br>mission name ! Pressurized <br>module ! Unpressurized <br>modules |- | STS-2 | ''Columbia'' | November 12, 1981 | OSTA-1 | | 1 Pallet (E002)<ref name=STS2>{{cite web |url=https://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-2.html |title=STS-2 |publisher=NASA |accessdate=23 November 2010}}</ref> |- | STS-3 | ''Columbia'' | March 22, 1982 | OSS-1 | | 1 Pallet (E003)<ref name=STS3>{{cite web |url=https://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-3.html |title=STS-3 |publisher=NASA |accessdate=23 November 2010}}</ref> |- | STS-9 | ''Columbia'' | November 28, 1983 | Spacelab 1 | Module LM1 | 1 Pallet (F001) |- | STS-41-G | ''Challenger'' | October 5, 1984 | OSTA-3 | | 1 Pallet (F006)<ref name=NASA28>{{cite web |url=https://science.nasa.gov/science-news/science-at-nasa/1999/msad15mar99_1/ |title=Spacelab joined diverse scientists and disciplines on 28 Shuttle missions |publisher=NASA |date=15 March 1999 |accessdate=23 November 2010}}</ref> |- | STS-51-A | ''Discovery'' | November 8, 1984 | Retrieval of 2 satellites | | 2 Pallets (F007+F008) |- | STS-51-B | ''Challenger'' | April 29, 1985 | Spacelab 3 | Module LM1 | Multi-Purpose Experiment Support Structure (MPESS) |- | STS-51-F | ''Challenger'' | July 29, 1985 | Spacelab 2 | Igloo | 3 Pallets (F003+F004+F005) + IPS |- | STS-61-A | ''Challenger'' | October 30, 1985 | Spacelab D1 | Module LM2 | MPESS |- | STS-35 | ''Columbia'' | December 2, 1990 | ASTRO-1 | Igloo | 2 Pallets (F002+F010) + IPS |- | STS-40 | ''Columbia'' | June 5, 1991 | SLS-1 | Module LM1 | |- | STS-42 | ''Discovery'' | January 22, 1992 | IML-1 | Module LM2 | |- | STS-45 | ''Atlantis'' | March 24, 1992 | ATLAS-1 | Igloo | 2 Pallets (F004+F005) |- | STS-50 | ''Columbia'' | June 25, 1992 | USML-1 | Module LM1 | Extended Duration Orbiter (EDO) |- | STS-46 | ''Atlantis'' | July 31, 1992 | TSS-1 | | 1 Pallet (F003)<ref name=ESA-STS46>{{cite web |url=https://www.esa.int/Enabling_Support/Operations/ESA_hands_over_a_piece_of_space_history |title=ESA hands over a piece of space history |publisher=ESA}}</ref> |- | STS-47 (J) | ''Endeavour'' | September 12, 1992 | Spacelab-J | Module LM2 | |- | STS-56 | ''Discovery'' | April 8, 1993 | ATLAS-2 | Igloo | 1 Pallet (F008) |- | STS-55 (D2) | ''Columbia'' | April 26, 1993 | Spacelab D2 | Module LM1 | Unique Support Structure (USS) |- | STS-58 | ''Columbia'' | October 18, 1993 | SLS-2 | Module LM2 | EDO |- | STS-61 | ''Endeavour'' | December 2, 1993 | HST SM 01 | | 1 Pallet (F009) |- | STS-59 | ''Endeavour'' | April 9, 1994 | SRL-1 | | 1 Pallet (F006) |- | STS-65 | ''Columbia'' | July 8, 1994 | IML-2 | Module LM1 | EDO |- | STS-64 | ''Discovery'' | September 9, 1994 | LITE | | 1 Pallet (F007)<ref name=PraxisLog>{{cite book |title=Manned Spaceflight Log 1961–2006 |author=Tim Furniss |author2=David Shayler |author3=Michael Derek Shayler |publisher=Springer Praxis |page=829 |date=2007}}</ref> |- | STS-68 | ''Endeavour'' | September 30, 1994 | SRL-2 | | 1 Pallet (F006) |- | STS-66 | ''Atlantis'' | November 3, 1994 | ATLAS-3 | Igloo | 1 Pallet (F008) |- | STS-67 | ''Endeavour'' | March 2, 1995 | ASTRO-2 | Igloo | 2 Pallets (F002+F010) + IPS + EDO |- | STS-71 | ''Atlantis'' | June 27, 1995 | Spacelab-Mir | Module LM2 | |- | STS-73 | ''Columbia'' | October 20, 1995 | USML-2 | Module LM1 | EDO |- | STS-75 | ''Columbia'' | February 22, 1996 | TSS-1R / USMP-3 | | 1 Pallet (F003)<ref name=NASA28/> + 2 MPESS + EDO |- | STS-78 | ''Columbia'' | June 20, 1996 | LMS | Module LM2 | EDO |- | STS-82 | ''Discovery'' | February 21, 1997 | HST SM 02 | | 1 Pallet (F009)<ref name=NASA28/> |- | STS-83 | ''Columbia'' | April 4, 1997 | MSL-1 | Module LM1 | EDO |- | STS-94 | ''Columbia'' | July 1, 1997 | MSL-1R | Module LM1 | EDO |- | STS-90 | ''Columbia'' | April 17, 1998 | Neurolab | Module LM2 | EDO |- | STS-103 | ''Discovery'' | December 20, 1999 | HST SM 03A | | 1 Pallet (F009) |- | STS-99 | ''Endeavour'' | February 11, 2000 | SRTM | | 1 Pallet (F006) |- | STS-92 | ''Discovery'' | Oktober 11, 2000 | ISS assembly | | 1 Pallet (F005) |- | STS-100 | ''Endeavour'' | April 19, 2001 | ISS assembly | | 1 Pallet (F004) |- | STS-104 | ''Atlantis'' | July 12, 2001 | ISS assembly | | 2 Pallets (F002+F010) |- | STS-109 | ''Columbia'' | March 1, 2002 | HST SM 03B | | 1 Pallet (F009) |- | STS-123 | ''Endeavour'' | March 11, 2008 | ISS assembly | | 1 Pallet (F004) |- | STS-125 | ''Atlantis'' | May 11, 2009 | HST SM 04 | | 1 Pallet (F009) |} {{clear}} ==Spacelab 1== [[Image:Spacelab1 flight columbia.jpg|thumb|right|250px|Spacelab 1 was carried into space onboard STS-9. Credit: NASA STS-9 crew.{{tlx|free media}}]] The Spacelab 1 mission had experiments in the fields of space plasma physics, solar physics, atmospheric physics, astronomy, and Earth observation.<ref name=Shayler>{{cite book |url=https://books.google.com/books?id=TweEC3h633AC&pg=PA433 |title=NASA's Scientist-Astronauts |first1=David |last1=Shayler |last2=Burgess |first2=Colin |date=2007 |publisher=Springer Science & Business Media |{{isbn|978-0-387-49387-9}} |page=433 |bibcode=2006nasa.book.....S }}</ref> {{clear}} ==Spacelab 2== [[Image:STS-51-F Instrument Pointing System.jpg|thumb|right|250px|Spacelab 2 pallet is shown in the open payload bay of Space Shuttle ''Challenger''. Credit: NASA STS-19 crew.{{tlx|free media}}]] View of the Spacelab 2 pallet in the open payload bay. The solar telescope on the Instrument Pointing System (IPS) is fully deployed. The Solar UV high resolution Telescope and Spectrograph are also visible. The Spacelab Infrared Telescope (IRT) was also flown on the mission.<ref name=Kent/> The IRT was a {{cvt|15.2|cm}} aperture liquid helium-cooled infrared telescope, observing light between wavelengths of 1.7 to 118 μm.<ref name=Kent>[http://adsabs.harvard.edu/full/1992ApJS...78..403K Kent, et al. – '''Galactic structure from the Spacelab infrared telescope''' (1992)]</ref> It was thought heat emissions from the Shuttle corrupting long-wavelength data, but it still returned useful astronomical data.<ref name=Kent/> Another problem was that a piece of mylar insulation broke loose and floated in the line-of-sight of the telescope.<ref name=Kent/> IRT collected infrared data on 60% of the galactic plane.<ref name="ipac.caltech.edu">{{cite web |title=Archived copy of Infrared Astronomy From Earth Orbit|accessdate=2016-12-10|url=https://web.archive.org/web/20161221020839/http://www.ipac.caltech.edu/outreach/Edu/orbit.html }}</ref> A later space mission that experienced a stray light problem from debris was ''Gaia'' astrometry spacecraft launch in 2013 by the ESA - the source of the stray light was later identified as the fibers of the sunshield, protruding beyond the edges of the shield.<ref>{{cite news|url=http://www.cosmos.esa.int/web/gaia/news_20141217|title=STATUS OF THE GAIA STRAYLIGHT ANALYSIS AND MITIGATION ACTIONS|publisher=ESA|date=2014-12-17|accessdate=5 February 2022}}</ref> {{clear}} ==Spacelab 3== [[Image:Spacelab Module in Cargo Bay.jpg|thumb|right|250px|Spacelab Module is photographed in the Cargo Bay. Credit: NASA STS-17 crew.{{tlx|free media}}]] [[Image:Crystal in VCGS furnace.jpg|thumb|upright=1.0|left|250px|Mercuric iodide crystals were grown on STS-51-B, Spacelab 3. Credit: [[w:user:Lodewijk van den Berg|Lodewijk van den Berg]] and Marshall Space Flight Center, NASA.{{tlx|free media}}]] [[Image:Vapor Crystal Growth System Furnace.jpg|thumb|right|250px|The Vapor Crystal Growth System Furnace experiment is shown on STS-51-B. Credit: STS-17 crew.{{tlx|free media}}]] [[Image:STS-51B launch.jpg|thumb|left|250px|Space Shuttle ''Challenger'' launches on STS-51B. Credit: NASA.{{tlx|free media}}]] [[Image:STS51B-06-010.jpg|thumb|right|250px|Lodewijk van den Berg observes the crystal growth aboard Spacelab. Credit: NASA STS-17 crew.{{tlx|free media}}]] Van den Berg and his colleagues designed the EG&G Vapor Crystal Growth System experiment apparatus for a Space Shuttle flight. The experiment required an in-flight operator and NASA decided that it would be easier to train a crystal growth scientist to become an astronaut, than it would be the other way around. NASA asked EG&G and Van den Berg to compile a list of eight people who would qualify to perform the science experiments in space and to become a Payload Specialist. Van den Berg and his chief, Dr. Harold A. Lamonds could only come up with seven names. Lamonds subsequently proposed adding Van den Berg to the list, joking with Van den Berg that due to his age, huge glasses and little strength, he would probably be dropped during the first selection round; but at least they would have eight names. Van den Berg agreed to be added to the list, but didn't really consider himself being selected to be a realistic scenario.<ref name=Engelen>{{Cite news |title=Niet Wubbo maar Lodewijk van den Berg was de eerste |last=van Engelen |first=Gert |periodical=Delft Integraal |year=2005 |issue=3 |pages=23–26 |language=nl |accessdate=2017-08-24 |url=https://web.archive.org/web/20170824215339/http://actueel.tudelft.nl/fileadmin/UD/MenC/Support/Internet/TU_Website/TU_Delft_portal/Actueel/Magazines/Delft_Integraal/archief/2005_DI/2005-3/doc/DI05-3-5LodewijkvdBerg.pdf }}</ref><ref name="netwerk">{{cite video |title=De `vergeten astronaut` |url=https://web.archive.org/web/20091014203252/http://www.netwerk.tv/node/3884 |medium=documentary |publisher=Netwerk, NCRV and Evangelische Omroep (EO)|accessdate=2008-04-09 }}</ref> The first selection round consisted of a selection based on science qualifications in the field in question, which Van den Berg easily passed. The final four candidates were tested on physical and mental qualifications which he also passed, while two of the others failed due to possible heart issues. He was now part of the final two, and NASA always trains two astronauts, a prime and a back-up. In 1983 he started to train as an astronaut and six months before the launch he was told that he would be the prime astronaut, much to his own surprise. When he went into space he was 53 years old, making him one of the oldest rookie astronauts.<ref name=Engelen/><ref name="netwerk" /> {{clear}} ==Space Transportation Systems (STSs)== [[Image:Space Shuttle, Nuclear Shuttle, and Space Tug.jpg|thumb|right|250px|This artist's concept illustrates the use of the Space Shuttle, Nuclear Shuttle, and Space Tug in NASA's Integrated Program. Credit: NASA.{{tlx|free media}}]] The purpose of the system was two-fold: to reduce the cost of spaceflight by replacing the current method of launching capsules on expendable rockets with reusable spacecraft; and to support ambitious follow-on programs including permanent orbiting space stations around Earth and the Moon, and a human landing mission to Mars. The Space Shuttles were often used as short term orbital platforms. {{clear}} ==STS-1== [[Image:Space Shuttle Columbia launching.jpg|thumb|left|250px|The April 12, 1981, launch at Pad 39A of STS-1, just seconds past 7 a.m., carries astronauts John Young and Robert Crippen into an Earth orbital mission scheduled to last for 54 hours, ending with unpowered landing at Edwards Air Force Base in California. Credit: NASA.{{tlx|free media}}]] [[Image:Columbia STS-1 training.jpg|thumb|right|250px|STS-1 crew is shown in Space Shuttle Columbia's cabin. Credit: NASA.{{tlx|free media}}]] STS-1 (Space Transportation System-1) was the first orbital spaceflight of NASA's Space Shuttle program. The first orbiter, ''Columbia'', launched on April 12, 1981, and returned on April 14, 1981, 54.5 hours later, having orbited the Earth 36 times. The majority of the ''Columbia'' crew's approximately 53 hours in low Earth orbit was spent conducting systems tests including Crew Optical Alignment Sight (COAS) calibration, star tracker performance, Inertial Measurement Unit (IMU) performance, manual and automatic Reaction Control System (RCS) testing, radiation measurement, propellant crossfeeding, hydraulics functioning, fuel cell purging and Earth photography. {{clear}} ==STS-2== [[Image:Aerial View of Columbia Launch - GPN-2000-001358.jpg|thumb|upright=1.0|left|250px|Aerial view shows ''Columbia'' launch from Pad 39A at the Kennedy Space Center in Florida. Credit: NASA / John Young aboard NASA's Shuttle Training Aircraft (STA).{{tlx|free media}}]] [[Image:STS-2 Canadarm debut.jpg|thumb|right|250px|On Space Shuttle mission STS-2, Nov. 1981, the Canadarm is flown in space for the first time. Credit: NASA.{{tlx|free media}}]] STS-2 was the second Space Shuttle mission conducted by NASA, and the second flight of the orbiter ''Columbia''. It launched on November 12, 1981, and landed two days later on November 14, 1981.<ref name="NASA - STS-2">{{cite web|publisher=NASA|title=NASA – STS-2 |url=http://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-2.html|accessdate=May 9, 2008}}</ref> On a Spacelab pallet were a number of remote-sensing instruments for environmental quality, and ocean and weather conditions.<ref>{{cite web |url=https://web.archive.org/web/19970208115640/http://southport.jpl.nasa.gov/scienceapps/sira.html |title=SIR-A: 1982|publisher=NASA|accessdate= 22 June 2013}}</ref> The second launch of ''Columbia'' also included an onboard camera for Earth photography. Other experiments or tests included Shuttle Multispectral Infrared Radiometer, Feature Identification and Location Experiment, Measurement of Air Pollution from Satellites, Ocean Color Experiment, Night/Day optical Survey of Lightning, Heflex Bioengineering Test, and Aerodynamic Coefficient Identification Package (ACIP).<ref name=Becker>{{cite web |url=http://www.spacefacts.de/mission/english/sts-2.htm|title=Spaceflight mission report: STS-2|first=Joachim|last=Becker|website=spacefacts.de|accessdate=December 30, 2017}}</ref> {{clear}} ==STS-3== [[Image:STS-3 launch.jpg|thumb|upright=1.0|left|250px|STS-3 lifts off from Launch Complex-39A at Kennedy Space Center. Credit: NASA.{{tlx|free media}}]] [[Image:STS-3 infrared on reentry.jpg|thumb|upright=1.0|right|250px|The Kuiper Airborne Observatory took an infrared image of the orbiter's heat shield to study its operational temperatures. In this image, ''Columbia'' is travelling at Mach{{nbsp}}15.6 at an altitude of {{cvt|56|km}}. Credit: .{{tlx|free media}}]] STS-3 was NASA's third Space Shuttle mission, and was the third mission for the Space Shuttle Columbia. It launched on March 22, 1982, and landed eight days later on March 30, 1982. In its payload bay, ''Columbia'' again carried the Development Flight Instrumentation (DFI) package, and a test canister for the Small Self-Contained Payload program – also known as the Getaway Special (GAS) – was mounted on one side of the payload bay. {{clear}} ==STS-4== [[Image:STS-4 launch.jpg|thumb|left|250px|Launch view of the Space Shuttle ''Columbia'' for the STS-4 mission. Credit: NASA.{{tlx|free media}}]] [[Image:STS-4 Induced Environment Contaminant Monitor.jpg|thumb|right|250px|View shows the Space Shuttle's RMS grappling the Induced Environment Contaminant Monitor (IECM) experiment. Credit: NASA STS-4 crew.{{tlx|free media}}]] STS-4 was the fourth NASA Space Shuttle mission, and also the fourth for Space Shuttle ''Columbia''. The mission launched on June 27, 1982,<ref name=oomops>{{cite book|url=https://news.google.com/newspapers?id=OvlLAAAAIBAJ&pg=4930%2C5770829|newspaper=The Spokesman-Review |location=Spokane, Washington|agency=Associated Press|title=Shuttle off on military operations|date=June 28, 1982 }}</ref> and landed a week later on July 4, 1982.<ref name=owastwrd>{{cite book |url=https://news.google.com/newspapers?id=QflLAAAAIBAJ&pg=6186%2C1692654|newspaper=The Spokesman-Review|location=Spokane, Washington|agency=Associated Press|title=Shuttle test: 'Outstanding' was the word |date=July 5, 1982 }}</ref> The North Atlantic Ocean southeast of the Bahamas is in the background as ''Columbia'''s remote manipulator system (RMS) arm and end effector grasp a multi-instrument monitor for detecting contaminants. The experiment is called the induced environment contaminant monitor (IECM). Below the IECM the tail of the orbiter can be seen. In the shuttle's mid-deck, a Continuous Flow Electrophoresis System and the Mono-disperse Latex Reactor flew for the second time. The crew conducted a lightning survey with hand-held cameras, and performed medical experiments on themselves for two student projects. They also operated the Remote Manipulator System (Canadarm) with an instrument called the Induced Environment Contamination Monitor mounted on its end, designed to obtain information on gases or particles being released by the orbiter in flight.<ref name=JSC>{{cite web|url=http://www.jsc.nasa.gov/history/shuttle_pk/pk/Flight_004_STS-004_Press_Kit.pdf|title=STS-004 Press Kit|publisher=NASA|accessdate=4 July 2013}}</ref> {{clear}} ==STS-5== [[Image:STS-5 Launch (18277306658).jpg|thumb|left|250px|''Columbia'' is launched from Launch Pad 39A on its fifth flight and first operational mission. Credit: NASA.{{tlx|free media}}]] STS-5 was the fifth NASA Space Shuttle mission and the fifth flight of the Space Shuttle ''Columbia''. It launched on November 11, 1982, and landed five days later on November 16, 1982. STS-5 carried a West German-sponsored microgravity Getaway Special (GAS) experiment canister in the payload bay. The crew also conducted three student-designed experiments during the flight. {{clear}} ==STS-6== [[Image:Space Shuttle Challenger (04-04-1983).JPEG|thumb|left|250px|STS-6 was launched. Credit: NASA.{{tlx|free media}}]] STS-6 was the sixth NASA Space Shuttle mission and the maiden flight of the Space Shuttle ''Challenger''. Launched from Kennedy Space Center on April 4, 1983, ''Challenger'' returned to Earth on April 9, 1983, at 10:53:42 a.m. PST. Names: Space Transportation System-6, NSSDCA/COSPAR ID: 1982-110A. STS-6 payloads included three Getaway Special (GAS) canisters and the continuation of the Mono-disperse Latex Reactor and Continuous Flow Electrophoresis experiments. {{clear}} ==STS-7== [[Image:Challenger launch on STS-7.jpg|thumb|left|250px|Space Shuttle Challenger launches on STS-7. Credit: NASA.{{tlx|free media}}]] [[Image:Space debris impact on Space Shuttle window.jpg|thumb|right|250px|An impact crater is in one of the windows of the Space Shuttle ''Challenger'' following a collision with a paint chip during STS-7. Credit: NASA STS-7 crew.{{tlx|free media}}]] STS-7 was NASA's seventh Space Shuttle mission, and the second mission for the Space Shuttle ''Challenger''. The shuttle launched from Kennedy Space Center on June 18, 1983, and landed at Edwards Air Force Base on June 24, 1983. Norman Thagard, a mission specialist, conducted medical tests concerning Space adaptation syndrome, a bout of nausea frequently experienced by astronauts during the early phase of a space flight. The mission carried the first Shuttle pallet satellite (SPAS-1), built by Messerschmitt-Bölkow-Blohm (MBB). SPAS-1 was unique in that it was designed to operate in the payload bay or be deployed by the Remote Manipulator System (Canadarm) as a free-flying satellite. It carried 10 experiments to study formation of metal alloys in microgravity, the operation of heat pipes, instruments for remote sensing observations, and a mass spectrometer to identify various gases in the payload bay. It was deployed by the Canadarm and flew alongside and over ''Challenger'' for several hours, performing various maneuvers, while a U.S.-supplied camera mounted on SPAS-1 took pictures of the orbiter. The Canadarm later grappled the pallet and returned it to the payload bay. STS-7 also carried seven Getaway Special (GAS) canisters, which contained a wide variety of experiments, as well as the OSTA-2 payload, a joint U.S.-West Germany scientific pallet payload. The orbiter's Ku-band antenna was able to relay data through the U.S. tracking and data relay satellite (TDRS) to a ground terminal for the first time. {{clear}} ==STS-8== [[Image:STS_8_Launch.jpg|thumb|left|250|Space Shuttle ''Challenger'' begins its third mission on 30 August 1983, conducting the first night launch of the shuttle program. Credit: NASA.{{tlx|free media}}]] STS-8 was the eighth NASA Space Shuttle mission and the third flight of the Space Shuttle ''Challenger''. It launched on August 30, 1983, and landed on September 5, 1983. The secondary payload, replacing a delayed NASA communications satellite, was a four-metric-ton dummy payload, intended to test the use of the shuttle's Canadarm (remote manipulator system). Scientific experiments carried on board ''Challenger'' included the environmental testing of new hardware and materials designed for future spacecraft, the study of biological materials in electric fields under microgravity, and research into space adaptation syndrome (also known as "space sickness"). The Payload Flight Test Article (PFTA) had been scheduled for launch in June 1984 on STS-16 in the April 1982 manifest,<ref name="news 82-46">{{cite press release|url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19820014425.pdf|hdl=2060/19820014425|title=Space Shuttle payload flight manifest / News Release 82-46|date=April 14, 1982|publisher=NASA |last1=McCormack |first1= Dick |last2=Hess |first2=Mark |archive-url=https://web.archive.org/web/20220412163838/https://ntrs.nasa.gov/citations/19820014425 |archive-date=2022-04-12 |url-status=live }}</ref> but by May 1983 it had been brought forward to STS-11. That month, when the TDRS missions were delayed, it was brought forward to STS-8 to fill the hole in the manifest.<ref name="STS-8 Press Information, p. i">''STS-8 Press Information'', p. i</ref> It was an aluminum structure resembling two wheels with a {{cvt|6|m}} long central axle, ballasted with lead to give it a total mass of {{cvt|3855|kg}}, which could be lifted by the Canadarm Remote Manipulator System – the Shuttle's "robot arm" – and moved around to help astronauts gain experience in using the system. It was stored in the midsection of the payload bay.<ref>Press kit, p. 32</ref> The orbiter carried the Development Flight Instrumentation (DFI) pallet in its forward payload bay; this had previously flown on ''Columbia'' to carry test equipment. The pallet was not outfitted with any flight instrumentation, but was used to mount two experiments. The first studied the interaction of ambient atomic oxygen with the structural materials of the orbiter and payload, while the second tested the performance of a heat pipe designed for use in the heat rejection systems of future spacecraft.<ref>Press kit, pp. 38–39. The first experiment was formally designated "Evaluation of Oxygen Interaction with Materials" (DSO-0301) while the second was the High Capacity Heat Pipe Demonstration (DSO-0101)</ref> Four Getaway Special (GAS) payloads were carried. One studied the effects of cosmic rays on electronic equipment. The second studied the effect of the gas environment around the orbiter using ultraviolet absorption measurements, as a precursor to ultraviolet equipment being designed for Spacelab 2. A third, sponsored by the Japanese ''Asahi Shimbun'' newspaper, tried to use water vapor in two tanks to create snow crystals. This was a second attempt at an experiment first flown on STS-6, which had had to be redesigned after the water in the tanks froze solid. The last was similar to an experiment flown on STS-3, and studied the ambient levels of atomic oxygen by measuring the rates at which small carbon and osmium wafers oxidized.<ref>Press kit, pp. 40–41. In order, these were designated the Cosmic Ray Upset Experiment (CRUX) (G-0346); the Ultraviolet-Sensitive Photographic Emulsion Experiment (G-0347); the Japanese snow crystal experiment (G-0475), and the Contamination Monitor Package (G-0348).</ref> The mission, in cooperation with the United States Postal Service (USPS), also carried 260,000 postal covers franked with US$9.35 express postage stamps, which were to be sold to collectors, with the profits divided between the USPS and NASA. Two storage boxes were attached to the DFI pallet, with more stored in six of the Getaway Special canisters.<ref>Press kit, p. 37</ref> A number of other experiments were to be performed inside the orbiter crew compartment. Among these was the Continuous Flow Electrophoresis System, being flown for the fourth time. This separated solutions of biological materials by passing electric fields through them; the experiment aimed at supporting research into diabetes treatments.<ref>Press kit, p. 38</ref> A small animal cage was flown containing six rats; no animal experiment was carried out on the flight, but a student involvement project was planned for a later mission which would use the cage, and NASA wanted to ensure it was flight-tested.<ref name="Press kit, p. 39">Press kit, p. 39</ref> The student involvement project carried out on STS-8 involved William E. Thornton using biofeedback techniques, to try to determine if they worked in microgravity.<ref name="Press kit, p. 39"/> A photography experiment would attempt to study the spectrum of a luminous atmospheric glow which had been reported around the orbiter, and determine how this interacted with firings of the reaction control system (RCS).<ref>''STS-9 Press Information'', p. 60. This was formally designated as "Investigation of STS Atmospheric Luminosities".</ref> {{clear}} ==STS-9== [[Image:Sts-9lift.jpg|thumb|left|250px|Columbia launches on mission STS-9 from Launch Pad 39-A. Credit: NASA.{{tlx|free media}}]] STS-9 (also referred to Spacelab 1) <ref>"Fun facts about STS numbering"|url=https://web.archive.org/web/20100527232806/http://enterfiringroom.ksc.nasa.gov/funFactsSTSNumbers.htm|date=2010-05-27 |NASA/KSC 29 October 2004. Retrieved 20 July 2013</ref> was the ninth NASA Space Shuttle mission and the sixth mission of the Space Shuttle ''Columbia''. Launched on 28 November 1983, the ten-day mission carried the first Spacelab laboratory module into orbit. The mission was devoted entirely to Spacelab 1, a joint NASA/European Space Agency (ESA) program designed to demonstrate the ability to conduct advanced scientific research in space. Both the mission specialists and payload specialists worked in the Spacelab module and coordinated their efforts with scientists at the Marshall Space Flight Center (MSFC) Payload Operations Control Center (POCC), which was then located at the Johnson Space Center (JSC) in Texas. Funding for Spacelab 1 was provided by the ESA. Over the course of the mission, 72 scientific experiments were carried out, spanning the fields of atmospheric and plasma physics, astronomy, solar physics, material sciences, technology, astrobiology and Earth observations. The Spacelab effort went so well that the mission was extended an additional day to 10 days, making it the longest-duration shuttle flight at that time. {{clear}} ==STS-10== [[Image:STS-41-B Launch (20071535339).jpg|thumb|upright=1.0|left|250px|STS-41B was launched. Credit: NASA.{{tlx|free media}}]] [[Image:EVAtion - GPN-2000-001087.jpg|thumb|upright=1.0|right|250px|McCandless approaches his maximum distance from ''Challenger''. Credit: NASA STS-10 crew.{{tlx|free media}}]] STS-41-B was the tenth (STS-10) NASA Space Shuttle mission and the fourth flight of the Space Shuttle ''Challenger''. It launched on 3 February 1984, and landed on 11 February 1984. The mission carried five Get Away Special (GAS) canisters, six live rats in the middeck area, a Cinema-360 camera and a continuation of the Continuous Flow Electrophoresis System and Monodisperse Latex Reactor experiments.<ref name=Ency>{{cite web |url=https://web.archive.org/web/20020415042717/http://www.astronautix.com/flights/sts41b.htm |title=STS-41-B|publisher=Encyclopedia Astronautica|accessdate=July 20, 2013 }}</ref> Included in one of the GAS canisters was the first experiment designed and built by a high school team to fly in space. The experiment, on seed germination and growth in zero gravity, was created and built by a team of four students from Brighton High School, Cottonwood Heights, Utah, through a partnership with Utah State University.<ref name=Ency/> {{clear}} ==STS-11== [[Image:SMMS repair by STS-41C Astronauts.jpg|thumb|right|250px|Mission Specialists George Nelson and James D. A. van Hoften repair the captured Solar Maximum Mission satellite on 11 April 1984. Credit: NASA STS-13 (STS-41-C) crew.{{tlx|free media}}]] [[Image:EL-1994-00475.jpeg|thumb|left|250px|The launch of STS-41-C on 6 April 1984 is shown. Credit: NASA.{{tlx|free media}}]] [[Image:STS-41-C-LDEF-deploy-small.jpg|thumb|left|250px|The deployed Long Duration Exposure Facility (LDEF) became an important source of information on the small-particle space debris environment. Credit: NASA STS-13 (STS-41-C) crew.{{tlx|free media}}]] STS-41-C (formerly STS-13) was NASA's eleventh Space Shuttle mission, and the fifth mission of Space Shuttle ''Challenger''.<ref name=Hoften>[http://www.jsc.nasa.gov/history/oral_histories/vanHoftenJD/vanHoftenJDA_12-5-07.pdf James D. A. van Hoften] NASA Johnson Space Center Oral History Project. 5 December 2007 Retrieved 20 July 2013</ref><ref name=Hart>[http://www.jsc.nasa.gov/history/oral_histories/HartTJ/HartTJ_4-10-03.pdf Terry J. Hart] NASA Johnson Space Center Oral History Project. April 10, 2003 Retrieved July 20, 2013</ref> The launch took place on 6 April 1984 and the landing on 13 April 1984 took place at Edwards Air Force Base. On the second day of the flight, the LDEF was grappled by the Remote Manipulator System (Canadarm) and successfully released into orbit. Its 57 experiments, mounted in 86 removable trays, were contributed by 200 researchers from eight countries. Retrieval of the passive LDEF was initially scheduled for 1985, but schedule delays and the ''Challenger'' disaster of 1986 postponed the retrieval until 12 January 1990, when ''Columbia'' retrieved the LDEF during STS-32. {{clear}} ==STS-12== [[Image:STS-41-D launch August 30, 1984.jpg|thumb|left|250px|The launch of Space Shuttle ''Discovery'' on its first mission on 30 August 1984. Credit: NASA.{{tlx|free media}}]] [[Image:STS41D-01-021.jpg|thumb|right|250px|View of the OAST-1 solar array on STS-41-D is shown. Credit: NASA STS-14 crew.{{tlx|free media}}]] STS-41-D (formerly STS-14) was the 12th flight of NASA's Space Shuttle program, and the first mission of Space Shuttle ''Discovery''. It was launched from Kennedy Space Center, Florida, on 30 August 1984, and landed at Edwards Air Force Base, California, on 5 September 1984. A number of scientific experiments were conducted, including a prototype electrical system of the International Space Station, or extendable solar array, that would eventually form the basis of the main solar arrays on the International Space Station (ISS). The OAST-1 photovoltaic module (solar array), a device {{cvt|4|m}} wide and {{cvt|31|m}} high, folded into a package {{cvt|18|cm}} deep. The array carried a number of different types of experimental solar cells and was extended to its full height several times during the mission. At the time, it was the largest structure ever extended from a crewed spacecraft, and it demonstrated the feasibility of large lightweight solar arrays for use on future orbital installations, such as the International Space Station (ISS). A student experiment to study crystal growth in microgravity was also carried out. {{clear}} ==STS-13== STS-41-G (formerly STS-17) was the 13th flight of NASA's Space Shuttle program and the sixth flight of Space Shuttle ''Challenger''. ''Challenger'' launched on 5 October 1984 and landed at the Shuttle Landing Facility (SLF) at Kennedy Space Center – becoming the second shuttle mission to land there – on 13 October 1984, at 12:26 p.m. EDT.<ref name=mis41g>{{cite web|url=https://science.ksc.nasa.gov/shuttle/missions/41-g/mission-41-g.html|title=41-G (13) |publisher=NASA|accessdate=13 February 2018}}</ref>. The OSTA-3 experiment package (Spacelab) in the payload bay included the Large Format Camera (LFC) to photograph the Earth, another camera called MAPS which measured air pollution, and a feature identification and location experiment called FILE, which consisted of two TV cameras and two {{cvt|70|mm}} still cameras. Payload Specialist Scully-Power, an employee of the U.S. Naval Research Laboratory (NRL), performed a series of oceanography observations during the mission. Garneau conducted a series of experiments sponsored by the Canadian government, called CANEX, which were related to medical, atmospheric, climatic, materials and robotic science. A number of Getaway Special (GAS) canisters, covering a wide variety of materials testing and physics experiments, were also flown. {{clear}} ==STS-14== STS-51-A (formerly STS-19) was the 14th flight of NASA's Space Shuttle program, and the second flight of Space Shuttle ''Discovery''. The mission launched from Kennedy Space Center on 8 November 1984, and landed just under eight days later on 16 November 1984. STS-51-F (also known as Spacelab 2) was the 19th flight of NASA's Space Shuttle program and the eighth flight of Space Shuttle ''Challenger''. It launched from Kennedy Space Center, Florida, on 29 July 1985, and landed just under eight days later on 6 August 1985. Names: Space Transportation System-19 and Spacelab 2. {{clear}} ==STS-15== STS-51-C (formerly STS-20) was the 15th flight of NASA's Space Shuttle program, and the third flight of Space Shuttle ''Discovery''. It launched on 24 January 1985, and made the fourth shuttle landing at Kennedy Space Center, Florida, on 27 January 1985. ==STS-16== STS-51-D was the 16th flight of NASA's Space Shuttle program, and the fourth flight of Space Shuttle ''Discovery''.<ref name=PressKitit51D>{{cite web |url=http://www.shuttlepresskit.com/STS-51D/STS51D.pdf|title=STS-51D Press Kit|author=NASA|accessdate=December 16, 2009}}</ref> The launch of STS-51-D from Kennedy Space Center (KSC), Florida, on 12 April 1985, and landed on 19 April 1985, at KSC. ''Discovery''s other mission payloads included the Continuous Flow Electrophoresis System III (CFES-III), which was flying for sixth time; two Shuttle Student Involvement Program (SSIP) experiments; the American Flight Echo-cardiograph (AFE); two Getaway specials (GASs); a set of Phase Partitioning Experiments (PPE); an astronomical photography verification test; various medical experiments; and "Toys in Space", an informal study of the behavior of simple toys in a microgravity environment, with the results being made available to school students upon the shuttle's return.<ref>{{cite web |url=https://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-51D.html|title=STS-51D|publisher=NASA|accessdate=January 16, 2018|date=February 18, 2010}}</ref> ==STS-17== [[Image:STS-51-B crew in Spacelab.jpg|thumb|right|250px|Space Transportation System-17, Spacelab 3, Overmyer, Lind, van den Berg, and Thornton are in the Spacelab Module LM1 during flight. Credit: NASA STS-17 crew.{{tlx|free media}}]] [[Image:STS-51B launch.jpg|thumb|upright=1.0|left|250px|Launch of STS-51B is shown. Credit:NASA.{{tlx|free media}}]] STS-51B was the 17th flight of NASA's Space Shuttle program, and the seventh flight of Space Shuttle ''Challenger''. The launch of ''Challenger'' was on April 29, 1985, and it landed successfully on May 6, 1985. STS-51B was the second flight of the European Space Agency (ESA)'s Spacelab pressurized module, and the first with the Spacelab module in a fully operational configuration. Spacelab's capabilities for multi-disciplinary research in microgravity were successfully demonstrated. The gravity gradient attitude of the orbiter proved quite stable, allowing the delicate experiments in materials processing and fluid mechanics to proceed normally. The crew operated around the clock in two 12-hour shifts. Two squirrel monkeys and 24 Brown rats were flown in special cages,<ref>|url=https://web.archive.org/web/20110719061203/http://lis.arc.nasa.gov/lis/Programs/STS/STS_51B/STS_51B.html|date=July 19, 2011</ref> the second time American astronauts flew live non-human mammals aboard the shuttle. The crew members in orbit were supported 24 hours a day by a temporary Payload Operations Control Center, located at the Johnson Space Center. On the mission, Spacelab carried 15 primary experiments, of which 14 were successfully performed. Two Getaway Special (GAS) experiments required that they be deployed from their canisters, a first for the program. These were NUSAT (Northern Utah Satellite) and GLOMR (Global Low Orbiting Message Relay satellite). NUSAT deployed successfully, but GLOMR did not deploy, and was returned to Earth. {{clear}} ==STS-18== [[Image:STS-51-G Morelos 1 deployment.jpg|thumb|right|250px|Mexico's Morelos satellite deploys from Discovery's payload bay. Credit: NASA STS-18 crew.{{tlx|free media}}]] [[Image:STS-51-G Spartan 1.jpg|thumb|left|250px|Spartan 1 is shown after deployment on STS-51-G. Credit: NASA STS-18 crew.{{tlx|free media}}]] STS-51-G was the 18th flight of NASA's Space Shuttle program, and the fifth flight of Space Shuttle ''Discovery''. The SPARTAN-1 (Shuttle Pointed Autonomous Research Tool for AstroNomy) a deployable/retrievable carrier module, was designed to be deployed from the orbiter and fly free in space before being retrieved. SPARTAN-1 included {{cvt|140|kg}} of astronomy experiments. It was deployed and operated successfully, independent of the orbiter, before being retrieved. ''Discovery'' furthermore carried an experimental materials-processing furnace, two French biomedical experiments (French Echocardiograph Experiment (FEE) and French Postural Experiment (FPE)),<ref name=SF51G>{{cite web|title=STS-51G|url=http://spacefacts.de/mission/english/sts-51g.htm|publisher=Spacefacts|accessdate=23 January 2021}}</ref> and six Getaway Special (GAS) experiments, which were all successfully performed, although the GO34 Getaway Special shut down prematurely. This mission was also the first flight test of the OEX advanced autopilot which gave the orbiter capabilities above and beyond those of the baseline system. The mission's final payload element was a High Precision Tracking Experiment (HPTE) for the Strategic Defense Initiative (SDI) (nicknamed "Star Wars"); the HPTE successfully deployed on orbit 64. {{clear}} ==STS-19== [[Image:STS-51-F shuttle.jpg|thumb|upright=1.0|left|250px|Aborted launch attempt is at T-3 seconds on 12 July 1985. Credit: NASA.{{tlx|free media}}]] [[Image:STS-51-F Plasma Diagnostics Package.jpg|thumb|upright=1.0|right|250px|The Plasma Diagnostics Package (PDP) is grappled by the Canadarm. Credit: NASA STS-19 crew.{{tlx|free media}}]] [[Image:Isabella lake STS51F-42-34.jpg|thumb|upright=1.0|right|250px|A view of the Sierra Nevada mountains and surroundings from Earth orbit was taken on the STS-51-F mission. Credit: NASA STS-19 crew.{{tlx|free media}}]] STS-51-F (also known as Spacelab 2) was the 19th flight of NASA's Space Shuttle program and the eighth flight of Space Shuttle ''Challenger''. STS-51-F's primary payload was the laboratory module Spacelab 2. A special part of the modular Spacelab system, the "Spacelab igloo", which was located at the head of a three-pallet train, provided on-site support to instruments mounted on pallets. The main mission objective was to verify performance of Spacelab systems, determine the interface capability of the orbiter, and measure the environment created by the spacecraft. Experiments covered life sciences, plasma physics, astronomy, high-energy astrophysics, solar physics, atmospheric physics and technology research. Despite mission replanning necessitated by ''Challenger''s abort to orbit trajectory, the Spacelab mission was declared a success. The flight marked the first time the European Space Agency (ESA) Instrument Pointing System (IPS) was tested in orbit. This unique pointing instrument was designed with an accuracy of one arcsecond. Initially, some problems were experienced when it was commanded to track the Sun, but a series of software fixes were made and the problem was corrected. In addition, Anthony W. England became the second amateur radio operator to transmit from space during the mission. The Plasma Diagnostics Package (PDP), which had been previously flown on STS-3, made its return on the mission, and was part of a set of plasma physics experiments designed to study the Earth's ionosphere. During the third day of the mission, it was grappled out of the payload bay by the Remote Manipulator System (Canadarm) and released for six hours.<ref name=report>{{cite web|title=STS-51F National Space Transportation System Mission Report|url=https://www.scribd.com/doc/52621059/STS-51F-National-Space-Transportation-System-Mission-Report|publisher=NASA Lyndon B. Johnson Space Center|accessdate=March 1, 2014|page=2|date=September 1985}}</ref> During this time, ''Challenger'' maneuvered around the PDP as part of a targeted proximity operations exercise. The PDP was successfully grappled by the Canadarm and returned to the payload bay at the beginning of the fourth day of the mission.<ref name=report/> In an experiment during the mission, thruster rockets were fired at a point over Tasmania and also above Boston to create two "holes" – plasma depletion regions – in the ionosphere. A worldwide group collaborated with the observations made from Spacelab 2.<ref>{{cite web|url=http://harveycohen.net/essex/index.htm|title=Elizabeth A. Essex-Cohen Ionospheric Physics Papers |date=2007|accessdate=5 February 2022}}</ref> {{clear}} ==STS-20== STS-51-I was the 20th mission of NASA's Space Shuttle program and the sixth flight of Space Shuttle ''Discovery''. The mission launched from Kennedy Space Center, Florida, on August 27, 1985, and landed at Edwards Air Force Base, California, on September 3, 1985. ==STS-21== STS-51-J was the 21st NASA Space Shuttle mission and the first flight of Space Shuttle ''Atlantis''. It launched from Kennedy Space Center, Florida, on 3 October 1985, and landed at Edwards Air Force Base, California, on 7 October 1985. ==STS-22== STS-61-A (also known as Spacelab D-1) was the 22nd mission of NASA's Space Shuttle program. It was a scientific Spacelab mission, funded and directed by West Germany – hence the non-NASA designation of D-1 (for Deutschland-1). STS-61-A was the ninth and last successful flight of Space Shuttle ''Challenger''. ==STS-23== STS-61-B was NASA's 23rd Space Shuttle mission, and its second using Space Shuttle ''Atlantis''. The shuttle was launched from Kennedy Space Center, Florida, on 26 November 1985. ''Atlantis'' landed at Edwards Air Force Base, California, at 16:33:49 EST on 3 December 1985. ==STS-24== STS-61-C was the 24th mission of NASA's Space Shuttle program, and the seventh mission of Space Shuttle ''Columbia''. The mission launched from Florida's Kennedy Space Center on 12 January 1986, and landed six days later on 18 January 1986. ==STS-26== [[Image:Return_to_Flight_Launch_of_Discovery_-_GPN-2000-001871.jpg|thumb|upright=1.0|left|250px|''Discovery'' lifts off from KSC, the first shuttle mission after the Challenger disaster. Credit: NASA.{{tlx|free media}}]] [[Image:ISD highres STS026 STS026-43-82.JPG|thumb|right|250px|This 70mm southward-looking view over the Pacific Ocean features the Hawaiian Islands chain. Credit: NASA STS-26 crew.{{tlx|free media}}]] [[Image:EFS highres STS026 STS026-43-98.JPG|thumb|right|250px|Chad is photographed from orbit on STS-26. Credit: NASA STS-26 crew.{{tlx|free media}}]] [[Image:EFS highres STS026 STS026-42-23.JPG|thumb|right|250px|Jebel Marra, Sudan, is photographed from Discovery, STS-26. Credit: NASA STS-26 crew.{{tlx|free media}}]] STS-26 was the 26th NASA Space Shuttle mission and the seventh flight of the orbiter Discovery. The mission launched from Kennedy Space Center, Florida, on 29 September 1988, and landed four days later on 3 October 1988. The materials processing experiments included two Shuttle Student Involvement Projects, one on titanium grain formation and the other on controlling crystal growth with a membrane. Another materials science experiment, the Physical Vapor Transport of Organic Solids-2 (PVTOS-2), was a joint project of NASA's Office of Commercial Programs and the 3M company. Three life sciences experiments were conducted, including one on the aggregation of red blood cells, intended to help determine if microgravity can play a beneficial role in clinical research and medical diagnostic tests. Two further experiments involved atmospheric sciences, while one was in communications research. * Physical Vapor Transport of Organic Solids (PVTOS-2) * Protein Crystal Growth (PCG) * Infrared Communications Flight Experiment (IRCFE) * Aggregation of Red Blood Cells (ARC) * Isoelectric Focusing Experiment (IFE) * Mesoscale Lightning Experiment (MLE) * Phase Partitioning Experiment (PPE) * Earth-Limb Radiance Experiment (ELRAD) * Automated Directional Solidification Furnace (ADSF) * Two Shuttle Student Involvement Program (SSIP) experiments * Voice Control Unit test and evaluation (VCU) The Hawaiian Islands shown in the image on the right perturb the prevailing northeasterly winds producing extensive cloud wakes in the lee of the islands. The atmospheric haze in the Hawaii wake is probably a result of the continuing eruptions of Kilauea volcano on the southeast coast. From the lower right corner in a diagonal directed upward to the north are the islands of Nihau (1), Kauai (2), Oahu (3), Molokai (4), Lanai (5), Maui (6), Kahoolawe (7), and Hawaii (8). {{clear}} ==STS-27== [[Image:STS-27 liftoff.jpg|thumb|upright=1.0|left|250px|''Atlantis'' launches on STS-27. Credit: NASA.{{tlx|free media}}]] [[Image:Scanned highres STS027 STS027-33-79 2.jpg|thumb|right|250px|The Brahmaputra River was imaged from orbit. Credit: NASA STS-27 crew.{{tlx|free media}}]] [[Image:ReefBase highres STS027 STS027-32-34.jpg|thumb|right|250px|Fiji was imaged from orbit. Credit: NASA STS-27 crew.{{tlx|free media}}]] STS-27 was the 27th NASA Space Shuttle mission, and the third flight of Space Shuttle ''Atlantis''. Launching on 2 December 1988, 14:30:34 UTC, and landing on 6 December 1988, 23:36:11 UTC, at Edwards Air Force Base, Runway 17. {{clear}} ==STS-28== [[Image:STS-29 Launch.jpg|thumb|left|250px|Liftoff shows mission STS-29 with shuttle ''Discovery''. Credit: NASA.{{tlx|free media}}]] [[Image:EFS highres STS029 STS029-92-38.jpg|thumb|right|250px|Lake Natron, Tanzania, was photographed from ''Discovery'' on mission STS-29. Credit: NASA STS-28 crew.{{tlx|free media}}]] STS-29 was the 28th NASA Space Shuttle mission, the eighth flight of Discovery and the 28th Space Shuttle mission overall. It launched from Kennedy Space Center, Florida, on 13 March 1989,<ref name="LATimes 1989-03-14">{{cite news|last1=Dye|first1=Lee|title=Space Shuttle Launched, Puts Satellite in Orbit|newspaper=Los Angeles Times|url-status=live|date=1989-03-14|url=https://www.latimes.com/archives/la-xpm-1989-03-14-mn-650-story.html|archive-url=https://web.archive.org/web/20210106132036/https://www.latimes.com/archives/la-xpm-1989-03-14-mn-650-story.html|archive-date=2021-01-06}}</ref> and landed on 18 March 1989, 14:35:50 UTC, at Edwards Air Force Base, Runway 22. ''Discovery'' carried eight secondary payloads, including two Shuttle Student Involvement Program (SSIP) experiments. One student experiment, using four live rats with tiny pieces of bone removed from their bodies, was to test whether the environmental effects of space flight inhibit bone healing. The other student experiment was to fly 32 chicken eggs to determine the effects of space flight on fertilized chicken embryos.<ref name=Brown1990>{{cite journal|title=NASA's Educational Programs|journal=Government Information Quarterly|date=1990|last=Brown|first=Robert W. |volume=7|issue=2|pages=185–195|issn=0740-624X|doi=10.1016/0740-624X(90)90054-R |url=https://web.archive.org/web/20210106181752/https://ntrs.nasa.gov/api/citations/19900019131/downloads/19900019131.pdf }}</ref> One experiment, mounted in the payload bay, was only termed "partially successful". The Space Station Heat Pipe Advanced Radiator Element (SHARE), a potential cooling system for the planned Space Station ''Freedom'', operated continuously for less than 30 minutes under powered electrical loads. The failure was blamed on the faulty design of the equipment, especially the manifold section.<ref name=Kosson>{{cite book|last1=Kosson|first1=Robert|last2=Brown|first2=Richard|last3=Ungar|first3=Eugene|title=Space Station heat pipe advanced radiator element (SHARE) flight test results and analysis, In: ''28th Aerospace Sciences Meeting''|publisher=American Institute of Aeronautics and Astronautics|location=Reston, Virginia|date=1990-01-11|doi=10.2514/6.1990-59|url=https://arc.aiaa.org/doi/10.2514/6.1990-59|accessdate=2021-01-06}}</ref> All other experiments operated successfully. Crystals were obtained from all the proteins in the Protein Crystal Growth (PCG) experiment. The Chromosomes and Plant Cell Division in Space (CHROMEX), a life sciences experiment, was designed to show the effects of microgravity on root development. An IMAX (70 mm) camera was used to film a variety of scenes for the 1990 IMAX film ''Blue Planet'',<ref name=Venant>{{cite web|last1=Venant|first1=Elizabeth|title=Astronauts Play Film Makers for IMAX 'Blue Planet' |date=1989-03-18|url=https://web.archive.org/web/20210106175224/https://www.latimes.com/archives/la-xpm-1989-03-18-ca-273-story.html }}</ref> including the effects of floods, hurricanes, wildfires and volcanic eruptions on Earth. A ground-based United States Air Force experiment used the orbiter as a calibration target for the Air Force Maui Optical and Supercomputing observatory (AMOS) in Hawaii.<ref name=Viereck>{{cite book|last1=Viereck|first1=R. A.|last2=Murad|first2=E.|last3=Pike|first3=C. P.|last4=Kofsky|first4=I. L.|last5=Trowbridge|first5=C. A.|last6=Rall|first6=D. L. A.|last7=Satayesh|first7=A.|last8=Berk|first8=A.|last9=Elgin|first9=J. B. |title=Photometric analysis of a space shuttle water venting, In: ''Fourth Annual Workshop on Space Operations Applications and Research (SOAR 90)'' |url=https://ntrs.nasa.gov/api/citations/19910011413/downloads/19910011413.pdf|publisher=NASA|location=Houston, Texas|date=1990|pages=676–680}}</ref> {{clear}} ==STS-29== [[Image:STS-30 launch.jpg|thumb|upright=1.0|left|250px|The launch of ''Atlantis'' is as STS-30. Credit: NASA.{{tlx|free media}}]] [[Image:ISD highres STS030 STS030-89-59.jpg|thumb|right|250px|Thunderstorms are imaged from orbit. Credit: NASA STS-29 crew.{{tlx|free media}}]] STS-30 was the 29th NASA Space Shuttle mission and the fourth mission for the Space Shuttle ''Atlantis''. The mission launched from Kennedy Space Center, Florida, on 4 May 1989, and landed four days later on 8 May 1989 at Edwards Air Force Base, Runway 22. Three mid-deck experiments were included on the mission. All had flown before. Mission Specialist Cleave used a portable laptop computer to operate and monitor the Fluids Experiment Apparatus (FEA).<ref name="MSER STS-30"/> [[Image:ISD highres STS030 STS030-76-31.jpg|thumb|right|250px|Ocean waves off the coast of Mexico are imaged from orbit. Credit: NASA STS-29 crew.{{tlx|free media}}]] An {{cvt|8|mm}} video camcorder, flown for the first time on the Shuttle, provided the opportunity for the crew to record and downlink on-orbit activities such as the FEA, which was a joint endeavor between Rockwell International and NASA. Payload bay video cameras were used to record storm systems from orbit as part of the Mesoscale Lightning Experiment.<ref name="MSER STS-30">{{cite book|author1=Office of Safety, Reliability, Maintainability and Quality Assurance|title=Misson Safety Evaluation Report for STS-30 - Postflight Edition |publisher=NASA|url=https://web.archive.org/web/20210106192422/https://ntrs.nasa.gov/api/citations/19920013999/downloads/19920013999.pdf|location=Washington, D.C.|date=1989-08-25 }}</ref> {{clear}} ==STS-30== [[Image:1989_s28_Liftoff.jpg|thumb|upright=1.0|left|250px|Launch of STS-28 is shown. Credit: NASA.{{tlx|free media}}]] [[Image:SILTS Image.jpg|thumb|right|250px|SILTS camera infrared image shows the flight surfaces of Columbia during STS-28 reentry. Credit: NASA.{{tlx|free media}}]] [[Image:Skull1.jpg|thumb|left|250px|Human skull is flown as part of DSO-469 on Space Shuttle missions STS-28, 36, and 31 during a study of radiation doses in space. Credit: NASA.{{tlx|free media}}]] [[Image:EFS highres STS028 STS028-89-83.JPG|thumb|right|250px|Alaska and the vast Malaspina Glacier were photographed from Columbia on mission STS-28. Credit: NASA STS-30 crew.{{tlx|free media}}]] STS-28 was the 30th NASA Space Shuttle mission, the fourth shuttle mission dedicated to United States Department of Defense (DoD) purposes, and the eighth flight of Space Shuttle ''Columbia''. The mission launched on 8 August 1989 and landed on runway 17 of Edwards Air Force Base, California, on 13 August 1989. The mission marked the first flight of an {{cvt|5|kg}} human skull, which served as the primary element of "Detailed Secondary Objective 469", also known as the In-flight Radiation Dose Distribution (IDRD) experiment. This joint NASA/DoD experiment was designed to examine the penetration of radiation into the human cranium during spaceflight. The female skull was seated in a plastic matrix, representative of tissue, and sliced into ten layers. Hundreds of thermoluminescent dosimeters were mounted in the skull's layers to record radiation levels at multiple depths. This experiment, which also flew on STS-36 and STS-31, was located in the shuttle's mid-deck lockers on all three flights, recording radiation levels at different orbital inclinations.<ref name=Macknight/> The Shuttle Lee-side Temperature Sensing (SILTS) infrared camera package made its second flight aboard ''Columbia'' on this mission. The cylindrical pod and surrounding black tiles on the orbiter's vertical stabilizer housed an imaging system, designed to map thermodynamic conditions during reentry, on the surfaces visible from the top of the tail fin. Ironically, the camera faced the port wing of ''Columbia'', which was breached by superheated plasma on STS-107 (its disastrous final flight), destroying the wing and, later, the orbiter. The SILTS system was used for only six missions before being deactivated, but the pod remained for the duration of ''Columbia''s career.<ref>[http://spaceflight.nasa.gov/shuttle/reference/shutref/orbiter/comm/inst/silts.ht Shuttle Infrared Leeside Temperature Sensing]</ref> ''Columbia's'' thermal protection system was also upgraded to a similar configuration as ''Discovery'' and ''Atlantis'' in between the loss of ''Challenger'' and STS-28, with many of the white LRSI tiles replaced with felt insulation blankets in order to reduce weight and turnaround time. One other minor modification that debuted on STS-28 was the move of ''Columbia's'' name from its payload bay doors to the fuselage, allowing the orbiter to be easily recognized while in orbit. {{clear}} ==STS-31== [[Image:STS-34 Launch (Low).jpg|thumb|left|250px|The launch was viewed from below. Credit: NASA.{{tlx|free media}}]] [[Image:EFS highres STS034 STS034-86-96.jpg|thumb|right|Greece was imaged from orbit. Credit: NASA STS-31 crew.{{tlx|free media}}]] [[Image:ReefBase highres STS034 STS034-86-65.jpg|thumb|right|250px|The Mekong River delta was imaged from orbit. Credit: NASA STS-31 crew.{{tlx|free media}}]] STS-34 was a NASA Space Shuttle mission using ''Atlantis''. It was the 31st shuttle mission overall, launched from Kennedy Space Center, Florida, on 18 October 1989, and landed at Edwards Air Force Base, Runway 23, California, on 23 October 1989. ''Atlantis''' payload bay held two canisters containing the Shuttle Solar Backscatter Ultraviolet (SSBUV) experiment. SSBUV, which made its first flight on STS-34, was developed by NASA to check the calibration of the ozone sounders on free-flying satellites, and to verify the accuracy of atmospheric ozone and solar irradiance data. The experiment operated successfully. STS-34 carried a further five mid-deck experiments, all of which were deemed successful, including the Polymer Morphology (PM) experiment, sponsored by the 3M company under a joint endeavor agreement with NASA. The PM experiment was designed to observe the melting and resolidifying of different types of polymers while in orbit. The Mesoscale Lightning Experiment (MLE), which had been flown on previous shuttle missions, observed the visual characteristics of large-scale lightning in the upper atmosphere. Chang-Díaz and Baker, a medical doctor, performed a detailed supplementary objective by photographing and videotaping the veins and arteries in the retinal wall of Baker's eyeball to provide detailed measurements which might give clues about a possible relationship between cranial pressure and motion sickness. Baker also tested the effectiveness of anti-motion sickness medication in space. {{clear}} ==STS-32== [[Image:1989 s33 Liftoff.jpg|thumb|upright=1.0|left|250px|Launch shows STS-32. Credit: NASA.{{tlx|free media}}]] STS-33 was NASA Space Shuttle mission 32 using the Space Shuttle ''Discovery'' that lifted off from Launch Complex 39B at Kennedy Space Center (KSC), Florida, on 22 November 1989 at 7:23:30 p.m. EST; and landed at Edwards Air Force Base, California, on 27 November 1989 at 7:30:16 p.m. EST. STS-33 was observed by the {{cvt|1.6|m}} telescope of the United States Air Force, Air Force Maui Optical and Supercomputing observatory (AMOS) during five passes over Hawaii. Spectrographic and infrared images of the shuttle obtained with the Enhanced Longwave Spectral Imager (ELSI) were aimed at studying the interactions between gases released by the shuttle's primary reaction control system (RCS) and residual atmospheric oxygen and nitrogen species in orbit.<ref name=Knecht>{{cite web|title=Recovery of Images from the AMOS ELSI Data for STS-33|date=19 April 1990|first=David J. |last=Knecht|publisher=Geophysics Laboratory (PHK), Hanscom AFB|url=https://web.archive.org/web/20121007213434/http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA225653&Location=U2&doc=GetTRDoc.pdf }}</ref><ref name=Kofsky>{{cite web|title=Measurements and Interpretation of Contaminant Radiations in the Spacecraft Environment|date=28 June 1991|author1=I.L. Kofsky|author2=D.L.A. Rall|author3=R.B. Sluder|publisher=Phillips Laboratory, Hanscom AFB |url=https://web.archive.org/web/20121007213711/http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA241756 }}</ref> {{clear}} ==STS-33== [[Image:1990 s32 Liftoff.jpg|thumb|upright=1.0|left|250px|The launch show STS-32 from LC-39A. Credit: NASA.{{tlx|free media}}]] STS-32 was the 33rd mission of NASA's Space Shuttle program, and the ninth launch of Space Shuttle ''Columbia'', that launched on 9 January 1990, 12:35:00 UTC, from the Kennedy Space Center, LC-39A, and landed on 20 January 1990, 09:35:36 UTC, at Edwards Air Force Base, Runway 22. A primary objective was to retrieve NASA's Long Duration Exposure Facility (LDEF) on the fourth day of the flight using the shuttle's Remote Manipulator System (Canadarm). The crew performed a 41⁄2-hour photographic survey of the free-flying structure, which held 57 science, technology and applications experiments. The 12-sided cylinder, about the size of a small satellite bus, was then berthed in the orbiter's payload bay for return to Earth. LDEF had dropped to such a low altitude that the orbiter could not do the usual lower-orbit catch-up because of the thicker atmosphere, and had to reach the LDEF from above. Earth observation footage from the IMAX camera was retrieved. STS-32 carried a number of mid-deck scientific payloads, some of which had already been flown on previous shuttle missions. The experiments included: * Characterization of ''Neurospora crassa'' Circadian Rhythms (CNCR) * Protein Crystal Growth (PCG) * Fluid Experiment Apparatus (FEA) * American Flight Echocardiograph (AFE) * Latitude / Longitude Locator (L3) * Mesoscale Lightning Experiment (MLE) * IMAX camera * Air Force Maui Optical Site (AMOS) experiment. {{clear}} ==STS-34== [[Image:STS-36 Launch.jpg|thumb|left|250px|Launch shows ''Atlantis''. Credit: NASA.{{tlx|free media}}]] STS-36 was a NASA Space Shuttle mission using ''Atlantis'', the sixth flight, launched from Kennedy Space Center, Florida, on 28 February 1990, and landed on 4 March 1990 at Edwards Air Force Base Runway 23. The mission marked another flight of a {{cvt|5|kg}} human skull, which served as the primary element of "Detailed Secondary Objective 469", also known as the In-flight Radiation Dose Distribution (IDRD) experiment. This joint NASA/DoD experiment was designed to examine the penetration of radiation into the human cranium during spaceflight. The female skull was seated in a plastic matrix, representative of tissue, and sliced into ten layers. Hundreds of thermo-luminescent dosimeters were mounted in the skull's layers to record radiation levels at multiple depths. This experiment, which also flew on STS-28 and STS-31, was located in the shuttle's mid-deck lockers on all three flights, recording radiation levels at different orbital inclinations.<ref name=Macknight/> {{clear}} ==STS-35== [[Image:STS-31 Launch - GPN-2000-000684.jpg|thumb|upright=1.0|left|250px|Space Shuttle ''Discovery'' launches from LC-39B for STS-31 with ''Columbia'' on LC-39A in preparation for STS-35. Credit: NASA.{{tlx|free media}}]] [[Image:HST over Bahamas.jpg|thumb|right|250px|''Columbia'' is high over Cuba. Credit: NASA STS-35 crew.{{tlx|free media}}]] [[Image:Scanned highres STS031 STS031-76-39 copy.jpg|thumb|right|250px|Hubble drifts away over Peru. Credit: NASA STS-35 crew.{{tlx|free media}}]] [[Image:Florida from STS-31.jpg|thumb|right|250px|Florida and The Bahamas are photographed. Credit: NASA STS-35 crew.{{tlx|free media}}]] STS-31 was the 35th mission of the NASA Space Shuttle program, launch date: 24 April 1990, 12:33:51 UTC, spacecraft: Space Shuttle ''Discovery'', launch site: Kennedy Space Center, LC-39B, landing date: 29 April 1990, 13:49:57 UTC, landing site: Edwards Air Force Base, Runway 22. The mission was devoted to photography and onboard experiments. At one point during the mission, ''Discovery'' briefly reached an apsis (apogee) of {{cvt|621|km}}, the highest altitude ever reached by a Shuttle orbiter.<ref name=McDowell>{{cite web|author=Jonathan McDowell |title=Here is a comparison of the STS-31 and STS-82 TLE data (apogee and perigee given in 'conventional height', i.e. geocentric radius minus 6378 km) |url=https://twitter.com/planet4589/status/1438322692097286151|accessdate=2021-09-16 }}</ref> The record height also permitted the crew to photograph Earth's large-scale geographic features not apparent from lower orbits. Experiments on the mission included a biomedical technology study, advanced materials research, particle contamination and ionizing radiation measurements, and a student science project studying zero gravity effects on electronic arcs. ''Discovery''{{'}}s reentry from its higher than usual orbit required a deorbit burn of 4 minutes and 58 seconds, the longest in Shuttle history up to that time.<ref name="STS-31 SSMR">{{cite web |author1=Lyndon B. Johnson Space Center |date=May 1990 |title=STS-31 Space Shuttle Mission Report |url=https://web.archive.org/web/20210107114538/https://ntrs.nasa.gov/api/citations/19920008146/downloads/19920008146.pdf |publisher=NASA}}</ref> Secondary payloads included the IMAX Cargo Bay Camera (ICBC) to document operations outside the crew cabin, and a handheld IMAX camera for use inside the orbiter. Also included were the Ascent Particle Monitor (APM) to detect particulate matter in the payload bay; a Protein Crystal Growth (PCG) experiment to provide data on growing protein crystals in microgravity, [[Radiation]] Monitoring Equipment III (RME III) to measure gamma ray levels in the crew cabin; Investigations into Polymer Membrane Processing (IPMP) to determine porosity control in the microgravity environment, and an Air Force Maui Optical and Supercomputing observatory (Air Force Maui Optical Site, or AMOS) experiment.<ref name="STS-31 SSMR"/> The mission marked the flight of a {{cvt|5|kg}} human skull, which served as the primary element of "Detailed Secondary Objective 469", also known as the In-flight Radiation Dose Distribution (IDRD) experiment. This joint NASA/DoD experiment was designed to examine the penetration of [[radiation]] into the human cranium during spaceflight. The female skull was seated in a plastic matrix, representative of tissue, and sliced into ten layers. Hundreds of thermo-luminescent dosimeters were mounted in the skull's layers to record radiation levels at multiple depths. This experiment, which also flew on STS-28 and STS-36, was located in the shuttle's mid-deck lockers on all three flights, recording radiation levels at different orbital inclinations.<ref name=Macknight>{{cite book|last1=MacKnight|first1=Nigel|title=Space Year 1991: The Complete Record of the Year's Space Events|date=1991-12-31|publisher=Motorbooks International|location=Osceola, Wisconsin|{{isbn|978-0879384821}}|page=41}}</ref> {{clear}} ==STS-36== [[Image:STS-41 launch.jpg|thumb|upright=1.0|left|250px|STS-41 launches from Kennedy Space Center, on 6 October 1990. Credit: NASA.{{tlx|free media}}]] STS-41 was the 36th Space Shuttle mission, and the eleventh mission of the Space Shuttle ''Discovery''. Instruments: # Air Force Maui Optical Site (AMOS) # Chromosome and Plant Cell Division Experiment (CHROMEX) # INTELSAT Solar Array Coupon (ISAC) # Investigations into Polymer Membrane Processing (IPMP) # Physiological Systems Experiment (PSE) # Radiation Monitoring Experiment (RME III) # Shuttle Solar Backscatter Ultraviolet (SSBUV) # Solid Surface Combustion Experiment (SSCE) # Shuttle Student Involvement Program (SSIP) # Voice Command System (VCS). By comparing ''Discovery''{{'}}s measurements with coordinated satellite observations, scientists were able to calibrate their satellite instruments to insure the most accurate readings possible. Until STS-41, previous research had shown that during the process of adapting to microgravity, animals and humans experienced loss of bone mass, cardiac deconditioning, and after prolonged periods (over 30 days), developed symptoms similar to that of terrestrial disuse osteoporosis. The goal of the STS-41 Physiological Systems Experiment (PSE), sponsored by the Ames Research Center and Pennsylvania State University's Center for Cell Research, was to determine if pharmacological treatments would be effective in reducing or eliminating some of these disorders. Proteins, developed by Genentech of San Francisco, California, were administered to eight rats during the flight while another eight rats accompanying them on the flight did not receive the treatment. {{clear}} ==STS-37== [[Image:STS-38 shuttle.jpg|thumb|left|250px|Launch shows STS-38. Credit: NASA.{{tlx|free media}}]] [[Image:ISD highres STS038 STS038-76-68.jpg|thumb|right|250px|Sunlight on the ocean is shown. Credit: NASA STS-37 crew.{{tlx|free media}}]] STS-38 was a Space Shuttle mission by NASA using the Space Shuttle ''Atlantis'', launch date: 15 November 1990, 23:48:15 UTC, launch site: Kennedy Space Center, LC-39A, landing date: 20 November 1990, 21:42:46 UTC, landing site: Kennedy Space Center, SLF Runway 33. {{clear}} ==STS-38== [[Image:STS-35 shuttle.jpg|thumb|upright=1.0|left|250px|''Columbia'' finally heads aloft on 2 December 1990. Credit: NASA.{{tlx|free media}}]] [[Image:Onboard Photo - Astro-1 Ultraviolet Telescope in Cargo Bay.jpg|thumb|right|250px|ASTRO-1 is in ''Columbia''{{'}}s payload bay. Credit: NASA STS-38 crew.{{tlx|free media}}]] [[Image:S035 Parker.jpg|thumb|upright=1.0|right|250px|MS Robert A. Parker manually points ASTRO-1's instruments using a toggle on the aft flight deck. Credit: NASA STS-38 crew.{{tlx|free media}}]] [[Image:STS035-502-4.jpg|thumb|upright=1.0|right|250px|''Columbia'' passes over Lake Eyre, Australia. Credit: NASA STS-38 crew.{{tlx|free media}}]] [[Image:STS035-602-24.jpg|thumb|right|250px|Namibia is photographed from orbit. Credit: NASA STS-38 crew.{{tlx|free media}}]] STS-35 was the tenth flight of Space Shuttle ''Columbia'', the 38th shuttle flight, and a mission devoted to astronomical observations with ASTRO-1, a Spacelab observatory consisting of four telescopes. The mission launched from Kennedy Space Center in Florida on 2 December 1990, 06:49:01 UTC, launch site: Kennedy Space Center, LC-39B, landing date: 11 December 1990, 05:54:09 UTC, landing site: Edwards Air Force Base, Runway 22. The primary payload of mission STS-35 was ASTRO-1, the fifth flight of the Spacelab system and the second with the Igloo and two pallets train configuration. The primary objectives were round-the-clock observations of the celestial sphere in ultraviolet and X-ray spectral wavelengths with the ASTRO-1 observatory, consisting of four telescopes: Hopkins Ultraviolet Telescope (HUT); Wisconsin Ultraviolet Photo-Polarimeter Experiment (WUPPE); Ultraviolet Imaging Telescope (UIT), mounted on the Instrument Pointing System (IPS). The Instrument Pointing System consisted of a three-axis gimbal system mounted on a gimbal support structure connected to a Spacelab pallet at one end and the aft end of the payload at the other, a payload clamping system for support of the mounted experiment during launch and landing, and a control system based on the inertial reference of a three-axis gyro package and operated by a gimbal-mounted microcomputer.<ref>STS-35 Press Kit, p.31, PAO, 1990</ref> The Broad-Band X-Ray Telescope (BBXRT) and its Two-Axis Pointing System (TAPS) rounded out the instrument complement in the aft payload bay. The crew split into shifts after reaching orbit, with Gardner, Parker, and Parise comprising the Red Team; the Blue Team consisted of Hoffman, Durrance, and Lounge. Commander Brand was unassigned to either team and helped coordinate mission activities. The telescopes were powered up and raised from their stowed position by the Red Team 11 hours into the flight. Observations began under the Blue Team 16 hours into the mission after the instruments were checked out.<ref>Space Shuttle Columbia: Her Missions and Crews, p.129, Ben Evans, 2005</ref> In a typical ASTRO-1 ultraviolet observation, the flight crew member on duty maneuvered the Shuttle to point the cargo bay in the general direction of the astronomical object to be observed. The mission specialist commanded the pointing system to aim the telescopes toward the target. They also locked on to guide stars to help the pointing system remain stable despite orbiter thruster firings. The payload specialist set up each instrument for the upcoming observation, identified the celestial target on the guide television, and provided the necessary pointing corrections for placing the object precisely in the telescope's field of view. He then started the instrument observation sequences and monitored the data being recorded. Because the many observations created a heavy workload, the payload and mission specialists worked together to perform these complicated operations and evaluate the quality of observations. Each observation took between 10 minutes to a little over an hour.<ref>STS-35 Press Kit, p.35, PAO, 1990.</ref> Issues with the pointing precision of the IPS and the sequential overheating failures of both data display units (used for pointing telescopes and operating experiments) during the mission impacted crew-aiming procedures and forced ground teams at Marshall Space Flight Center (MSFC) to aim the telescopes with fine-tuning by the flight crew. BBXRT-01 was directed from the outset by ground-based operators at Goddard Space Flight Center (GSFC) and was not affected. The X-ray telescope required little attention from the crew. A crew member would turn on the BBXRT and the TAPS at the beginning of operations and then turn them off when the operations concluded. After the telescope was activated, researchers at Goddard could "talk" to the telescope via computer. Before science operations began, stored commands were loaded into the BBXRT computer system. Then, when the astronauts positioned the Shuttle in the general direction of the source, the TAPS automatically pointed the BBXRT at the object. Since the Shuttle could be oriented in only one direction at a time, X-ray observations had to be coordinated carefully with ultraviolet observations. Despite the pointing problems, the full suite of telescopes obtained 231 observations of 130 celestial objects over a combined span of 143 hours. Science teams at Marshall and Goddard estimated that 70% of the mission objectives were completed.<ref>Space Shuttle Columbia: Her Missions and Crews, p. 133, Ben Evans, 2005</ref> ASTRO-1 was the first shuttle mission controlled in part from the Spacelab Mission Operations Control facility at MSFC in Huntsville, Alabama. Conducting short-wave radio transmissions between ground-based amateur radio operators and a Shuttle-based amateur radio operator was the basis for the Shuttle Amateur Radio Experiment (SAREX-II). SAREX communicated with amateur stations in line-of-sight of the orbiter in one of four transmission modes: voice, Slow-scan television (SSTV), data or (uplink only) amateur television (Fast scan television) (FSTV). The voice mode was operated in the attended mode while SSTV, data or FSTV could be operated in either attended or unattended modes. During the mission, SAREX was operated by Payload Specialist Ron Parise, a licensed operator (WA4SIR), during periods when he was not scheduled for orbiter or other payload activities.<ref>STS-35 Press Kit, p. 41, PAO, 1990.</ref> A ground-based experiment to calibrate electro-optical sensors at Air Force Maui Optical and Supercomputing observatory (Air Force Maui Optical Site, AMOS) in Hawaii was also conducted during the mission. The Space Classroom Program, Assignment: The Stars project was carried out to spark student interest in science, mathematics and technology. Mission Specialist Hoffman conducted the first classroom lesson taught from space on 7 December 1990 in support of this objective, covering material on the electromagnetic spectrum and the ASTRO-1 observatory. A supporting lesson was taught from the ASTRO-1 control center in Huntsville. {{clear}} ==STS-39== [[Image:STS-37 Launch.jpg|thumb|upright=1.0|left|250px|Launch shows ''Atlantis'' on STS-37. Credit: NASA.{{tlx|free media}}]] [[Image:KuwaitiOilFires-STS037-152-91-(2).jpg|thumb|upright=1|right|250px|Smoke plumes from aKuwaiti Oil Fires were seen during STS-37. Credit: NASA STS-39 crew.{{tlx|free media}}]] STS-37, the thirty-ninth NASA Space Shuttle mission and the eighth flight of the Space Shuttle ''Atlantis'', launch date: 5 April 1991, 14:22:45 UTC, launch site: Kennedy Space Center, LC-39B, landing date: 11 April 1991, 13:55:29 UTC, landing site Edwards Air Force Base, Runway 33. During the spaceflight, the crew was additionally able to photograph the Kuwaiti oil fires on 7 April 1991, as the Gulf War was ongoing during the spaceflight.<ref>{{cite web |url=https://nara.getarchive.net/media/s37-73-047-sts-037-kuwait-oil-fires-kuwait-taken-during-the-sts-37-mission-bef582|title= "S37-73-047 - STS-037 - Kuwait Oil Fires, Kuwait taken during the STS-37 mission" |accessdate= May 8, 2022}}</ref> Smoke plumes from a few of the Kuwaiti Oil Fires on April 7, 1991, are seen during STS-37.<ref name="gulflink.osd.mil">{{cite web |url=https://eol.jsc.nasa.gov/SearchPhotos/photo.pl?mission=STS037&roll=152&frame=91|title=Astronaut Photo STS037-152-91 }}</ref> Instruments: # Air Force Maui Optical Site (AMOS) # Ascent Particle Monitor (APM) # Bioserve/Instrumentation Technology Associates Materials Dispersion Apparatus (BIMDA) to explore the commercial potential of experiments in the biomedical, manufacturing processes and fluid sciences fields # Crew and Equipment Translation Aid (CETA), which involved scheduled six-hour spacewalk by astronauts Ross and Apt # Protein Crystal Growth (PCG), which has flown eight times before in various forms # Radiation Monitoring Equipment (RME Ill) # Shuttle Amateur Radio Experiment (SAREX II). {{clear}} ==STS-40== [[Image:STS-39 launch.jpg|thumb|left|250px|Launch shows STS-39. Credit: NASA.{{tlx|free media}}]] [[Image:Critical-ionization-velocity.jpg|thumb|right|250px|The Critical ionization velocity (CIV) experiment is shown in ''Discovery''{{'}}s payload bay. Credit: NASA STS-40 crew.{{tlx|free media}}]] [[Image:Aurora-SpaceShuttle-EO.jpg|thumb|upright=1.0|right|250px|STS-39 observes Aurora australis. Credit: NASA STS-40 crew,{{tlx|free media}}]] STS-39 was the twelfth mission of the NASA Space Shuttle ''Discovery'', and the 40th orbital shuttle mission overall, launch date: 28 April 1991, 11:33:14 UTC, launch site: Kennedy Space Center, LC-39A, landing date: 6 May 1991, 18:55:37 UTC, landing site: Kennedy Space Center, SLF Runway 15. The high orbital inclination of the mission, 57.01° with respect to the equator, allowed the crew to fly over most of Earth's large land masses and observe and record environmental resources and problem areas. Instruments: # Chemical Release Observation (CRO) # Cryogenic Infrared Radiance Instrumentation for Shuttle (CIRRIS) # Cloud Logic to Optimize Use of Defense Systems (CLOUDS-1A) # Infrared Background Signature Survey (IBSS) # Multi-Purpose Release Canister (MPEC) # Shuttle pallet satellite (SPAS-II) # Space Test Program (STP-01) # Radiation Monitoring Equipment (RME-III). {{clear}} ==STS-41== [[Image:STS-040 shuttle.jpg|thumb|upright=1.0|left|Launch shows STS-40. Credit: NASA.{{tlx|free media}}]] [[Image:STS-40 Spacelab.jpg|thumb|right|250px|Spacelab Module LM1 in ''Columbia''{{'}}s payload bay, served as the Spacelab Life Sciences laboratory. Credit: NASA STS-41 crew.{{tlx|free media}}]] STS-40, the eleventh launch of Space Shuttle Columbia, was a nine-day mission in June 1991. It carried the Spacelab module for Spacelab Life Sciences 1 (SLS-1), the fifth Spacelab mission and the first dedicated solely to biology. The mission featured the most detailed and interrelated physiological measurements in space since 1973-1974 Skylab missions. Subjects were humans, 30 rodents and thousands of tiny jellyfish. Primary SLS-1 experiments studied six body systems; of 18 investigations, ten involved humans, seven involved rodents, and one used jellyfish. Six body systems investigated were cardiovascular/cardiopulmonary (heart, lungs and blood vessels); renal/endocrine (kidneys and hormone-secreting organs and glands); blood (blood plasma); immune system (white blood cells); musculoskeletal (muscles and bones); and neurovestibular (brains and nerves, eyes and inner ear). Other payloads included twelve Getaway Special (GAS) canisters installed on GAS bridge in cargo bay for experiments in materials science, plant biology and cosmic radiation; Middeck Zero-Gravity Dynamics Experiment (MODE); and seven Orbiter Experiments (OEXs). {{clear}} ==STS-42== [[Image:STS-43 Launch - GPN-2000-000731.jpg|thumb|upright=1.0|left|250px|Launch shows Space Shuttle ''Atlantis'' from the Kennedy Space Center. Credit: NASA.{{tlx|free media}}]] [[Image:Sts-43crew.jpg|thumb|upright=1.0|right|250px|Crew members pose for on-orbit portrait in the middeck of ''Atlantis''. Credit: NASA STS-43 crew.{{tlx|free media}}]] [[Image:1991 s43 Atlantis over Florida.jpg|thumb|upright=1.0|right|250px|''Atlantis'' passes over Florida. SHARE-II is prominent on the left. Credit: NASA STS-43 crew.{{tlx|free media}}]] STS-43, the forty-second space shuttle mission overall, the ninth mission for Space Shuttle ''Atlantis'', was a nine-day mission to test an advanced heatpipe radiator for potential use on the then-future space station, conduct a variety of medical and materials science investigations, and conduct astronaut photography of Earth. Launch date: 2 August 1991, 15:01:59 UTC, launch site Kennedy Space Center, LC-39A, landing date: 11 August 1991, 12:23:25 UTC, landing site: Kennedy Space Center, SLF Runway 15. On the left, the Space Shuttle ''Atlantis'' streaks skyward as sunlight pierces through the gap between the orbiter and ET assembly. ''Atlantis'' lifted off on the 42nd space shuttle flight at 11:02 a.m. EDT on August 2, 1991 carrying a crew of five and TDRS-E. A remote camera at the 275-foot level of the Fixed Surface Structure took this picture. STS-43 crewmembers pose for on-orbit (in space) portrait on the middeck of ''Atlantis'', Orbiter Vehicle (OV) 104. At the left side of the frame are the forward lockers and at the right is the open airlock hatch. In between and in front of the starboard wall-mounted sleep restraints are (left to right) Mission Specialist (MS) G. David Low, MS Shannon W. Lucid, MS James C. Adamson, Commander John E. Blaha, and Pilot Michael A. Baker. Other experiments included Auroral Photography Experiment (APE-B) Protein Crystal Growth Ill (PCG Ill); Bioserve / Instrumentation Technology Associates Materials Dispersion Apparatus (BIMDA); Investigations into Polymer Membrane Processing (IPMP); Space Acceleration Measurement System (SAMS); Solid Surface Combustion Experiment (SSCE); Ultraviolet Plume imager (UVPI); and the Air Force Maui Optical Site (AMOS) experiment.<ref>{{Cite web|url=http://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-43.html|title=NASA - STS-43}}</ref> Instruments: # Optical Communications Through Windows (OCTW) # Solid Surface Combustion Experiment (SSCE) # Space Station Heat Pipe Advanced Radiator Element (SHARE II) # Shuttle Solar Backscatter Ultra-Violet (SSBUV) # Tank Pressure Control Equipment (TPCE) {{clear}} ==STS-43== [[Image:STS48 launch.jpg|thumb|upright=1.0|left|250px|Liftoff shows STS-48. Credit: NASA.{{tlx|free media}}]] STS-48 was a Space Shuttle mission that launched on 12 September 1991, 23:11:04 UTC, from Kennedy Space Center, Florida. The orbiter was Space Shuttle ''Discovery''. The mission landed on 18 September at 12:38 a.m. EDT at Edwards Air Force Base on runway 22. Names: Space Transportation System-43. NSSDCA ID: 1991-063A, launch date: 1991-09-12. Instruments: # Air Force Maui Optical Site (AMOS) # Ascent Particle Monitor (APM) # Cosmic Ray Effects and Activation Monitor (CREAM) # Investigations into Polymer Membrane Processing (IPMP) # Middeck 0-Gravity Dynamics Experiment (MODE) # Physiological and Anatomical Rodent Experiment (PARE) # Protein Crystal Growth (PCG II-2) # Shuttle Activation Monitor (SAM) {{clear}} ==STS-44== [[Image:STS-044 shuttle.jpg|thumb|left|250px|STS-44 ''Atlantis'', Orbiter Vehicle (OV) 104, soars into the evening darkness after liftoff from Kennedy Space Center (KSC) Launch Complex (LC) Pad at 6:44 pm (Eastern Standard Time (EST)). Credit: NASA.{{tlx|free media}}]] [[Image:S44-72-084 - STS-044 - Earth observations taken during the STS-44 mission - DPLA - 6072e1427cecd676cbb4906ffa68900f.jpg|thumb|right|250px|Low oblique photograph was taken from ''Atlantis'' of clouds over the Indian Ocean. Credit: NASA STS-44 crew.{{tlx|free media}}]] [[Image:Typhoon Yuri eye.jpg|thumb|right|250px|This spectacular, low-oblique photograph shows the bowl-shaped eye (center of photograph) of Typhoon Yuri in the western Pacific Ocean just west of the Northern Mariana Islands. Credit: NASA STS-44 crew.{{tlx|free media}}]] STS-44 was a NASA Space Shuttle mission using ''Atlantis'' that launched on 24 November 1991, 23:44:00 UTC, launch site: Kennedy Space Center, LC-39A, landing date: 1 December 1991, 22:34:12 UTC, landing site: Edwards Air Force Base, Runway 5. NSSDCA ID: 1991-080A, launch date: 1991-11-24. Names: Space Transportation System-44. The clouds over the Indian Ocean were photographed at tilt: Low Oblique cldp: 50, -24.2°N latitude, 89.8°N longitude, azimuth: 103°, 198 km altitude, elevation: 52°. In the second image down on the right, the eye wall descends almost to the sea surface, a distance of nearly 45 000 feet (13 800 meters). In this case the eye is filled with clouds, but in many cases the sea surface can be seen through the eye. Yuri grew to super typhoon status, packing maximum sustained winds estimated at 165 miles (270 kilometers) per hour, with gusts reaching an estimated 200 miles (320 kilometers) per hour. The storm moved west toward the Philippine Islands before turning northeast into the north Pacific Ocean, thus avoiding any major landmass. Instruments: # Air Force Maui Optical Site (AMOS) # Bioreactor Flow # Cosmic Radiation Effects and Activation Monitor (CREAM) # Extended Duration Orbiter Medical Project # Extended Duration Orbiter (EDO) # Interim Operational Contamination Monitor (IOCM) # Military Man in Space (M88-1) # Radiation Monitoring Equipment (RME III) # Shuttle Activation Monitor (SAM) # Terra-Scout # Ultraviolet Plume Instrument (UVPI) # Visual Function Tester (VFT-1) {{clear}} ==STS-45== [[Image:S42-50-022 - STS-042 - STS-42 Earth observations - DPLA - 89f59f2368ab90105ca9847ed651ae57.jpg|thumb|right|250px|Kunlun Mountains are in Tibet at lat: 36°N lon: 91°E. Credit: NASA STS-45 crew.{{tlx|free media}}]] STS-42/IML 1, NSSDCA ID: 1992-002A. launch date: 1992-01-22. Space Shuttle Mission STS-42 was the 45th Shuttle flight and the 15th flight of ''Discovery''. "The main objective of STS-42 was to carry out the International Microgravity Laboratory-1 (IML-1) mission, a collection of life science and microgravity experiments developed by more than 200 scientists from 16 countries. The IML-1 was the first in a series of IML missions planned to fly aboard the Space Shuttle this decade. In addition the the IML-1 module, STS-42 also carried 12 Get Away Special containers containing experiments ranging from materials processing work to investigations into the development of animal life in weightlessness. Two experiments from the Space Shuttle Student Involvement Program, Convection in Zero Gravity and Zero-G Capillary Rise of Liquid Through Granular Porous Media, were also flown. On ''Discovery'''s lower deck, the Investigation into Polymer Membrane Processing investigated advances in filtering technologies in microgravity, and the Radiation Monitoring Equipment-III recorded radiation levels in the crew cabin. The spacecraft maintained a gravity gradient orientation with its nose pointed to space and its tail to Earth in order to minimize firings of the Shuttle's small steering thrusters, thus avoiding disturbances to onboard experiments."<ref name=Williams>{{ cite web |author=David R. Williams |title=STS 42/IML 1 |publisher=Goddard Spaceflight Center |location=Greenbelt, MD USA |date=27 April 2022 |url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1992-002A |accessdate=25 July 2022 }}</ref> {{clear}} ==STS-46== [[Image:STS-45 payload.jpg|thumb|right|250px|Components of the Spacelab (ATLAS-1 laboratory) in the payload bay of ''Atlantis'' is shown. Credit: NASA STS-46 crew.{{tlx|free media}}]] STS-45 was a 1992 NASA Space Shuttle mission using the Space Shuttle ''Atlantis'', Names: Space Transportation System-46. It was the 46th Space Shuttle mission and the 11th for ''Atlantis''. Launch date: 24 March 1992, 13:13:39 UTC, launch site: Kennedy Space Center, LC-39A, lLanding date: 2 April 1992, 11:23 UTC, landing site Kennedy Space Center, SLF Runway 33. NSSDCA ID: 1992-015A.<ref name=STS-45>https://nssdc.gsfc.nasa.gov/nmc/spacecraft/query</ref> STS-45 carried the first Spacelab (Atmospheric Laboratory for Applications and Science) (ATLAS-1) experiments, placed on Spacelab pallets mounted in the orbiter's payload bay. The non-deployable payload, equipped with 12 instruments from the United States, France, Germany, Belgium, Switzerland, the Netherlands and Japan, conducted studies in atmospheric chemistry, solar radiation, space plasma physics and ultraviolet astronomy. ATLAS-1 instruments included the Atmospheric Trace Molecule Spectroscopy (ATMOS); Grille Spectrometer; Millimeter Wave Atmospheric Sounder (MAS); Imaging Spectrometric Observatory (ISO); Atmospheric Lyman-Alpha Emissions (ALAE); Atmospheric Emissions Photometric Imager (AEPI); Space Experiments with Particle Accelerators (SEPAC); Active Cavity Radiometer (ACR); Measurement of Solar Constant (SOLCON); Solar Spectrum;<ref>{{cite web |title=Background |url=http://solspec.projet.latmos.ipsl.fr/SOLSPEC_GB/Background.html |website=SOLSPEC |publisher=Institut Pierre Simon Laplace |accessdate=26 March 2022 }}</ref> Solar Ultraviolet Spectral Irradiance Monitor (SUSIM); and Far Ultraviolet Space Telescope (FAUST). Other payloads included the Shuttle Solar Backscatter Ultraviolet (SSBUV) experiment, a Get Away Special (GAS) experiment and six mid-deck experiments. {{clear}} ==STS-47== STS-49 was the NASA maiden flight of the Space Shuttle ''Endeavour'', which launched on 7 May 1992, Names: Space Transportation System-47. NSSDCA ID: 1992-026A, launch date: 1992-05-07. Other "payloads of opportunity" experiments conducted included: Commercial Protein Crystal Growth (CPCG), Ultraviolet Plume Imager (UVPI) and the Air Force Maui Optical Station (AMOS) investigation. Mission was extended two days to complete objectives. ==STS-48== [[Image:Spacelab Module in Cargo Bay.jpg|thumb|right|250px|Spacelab Module LM1 in ''Columbia'''s payload bay, served as the United States Microgravity Laboratory. Credit: NASA STS-48 crew.{{tlx|free media}}]] STS-50 (U.S. Microgravity Laboratory-1) was a NASA Space Shuttle mission, the 12th mission of the ''Columbia'' orbiter. Names: Space Transportation System-48. NSSDCA ID: 1992-034A, launch date: 1992-06-25. "Space Shuttle Mission STS 50 was the 48th Shuttle flight and the 12th flight of Columbia. [...] STS 50 carried the United States Microgravity Laboratory (USML 1), a Spacelab long module with an Extended Duration Orbiter (EDO) pallet in the aft cargo bay. The USML 1 consisted of 31 experiments ranging from the manufacture of crystals for possible semiconductor use to the study of the behavior of weightless fluids. STS 50 also carried the Investigations into Polymer Membrane Processing experiment and the Space Shuttle Amature Radio Experiment-II. Columbia landed July 9, 1992, at 11:43 a.m. UT on KSC's Shuttle Landing Facility Runway 33."<ref name=WiiliamsSTS50>{{ cite web |author=David R. Williams |title=STS 50/USML 1 |publisher=NASA Goddard Spaceflight Center |location=Greenbelt, MD USA |date=27 April 2022 |url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1992-034A |accessdate=25 July 2022 }}</ref> ''Columbia'''s "stand-up" orbital attitude, although ideal for microgravity experiments, was very far from optimal from the point of view of D&M (Debris and Micrometeoroid) vulnerability. The orbiter received 40 radiation debris impacts, impacts on eight windows, and three impacts on the carbon-carbon wing leading edges.<ref name=Young>{{cite book|last=Young|first=John W.|title=Forever Young: A Life of Adventure in Air and Space|publisher=University Press of Florida|date=16 September 2012|chapter=22|page=432|{{isbn|978-0813042091}} }}</ref> {{clear}} ==STS-49== [[Image:STS-46 Launch (19919136345).jpg|thumb|left|250px|Space Shuttle ''Atlantis''' STS-46 mission was launched on July 31, 1992, from the Kennedy Space Center. Credit: NASA.{{tlx|free media}}]] [[Image:S46-86-073 - STS-046 - Earth observations from the shuttle orbiter Atlantis during STS-46 - DPLA - accaf9e431417caa6b584443309329cb.jpg|thumb|right|250px|Earth observation is from the shuttle orbiter ''Atlantis'' during STS-46 of Dominican Republic, lat. 20°, lon. -71°. Credit: NASA STS-49 crew.{{tlx|free media}}]] [[Image:S46-93-064 - STS-046 - Earth observations from the shuttle orbiter Atlantis during STS-46 - DPLA - 41e6ccb6ebaff54dbc92eb925055ae3c.jpg|thumb|right|250px|Vietnam, Dong Hoi coastal area is at lat: 17.5° lon: 105.8°, tilt: 15°, dir: N, azi: 83, alt: 124, elev: 34. Credit: NASA STS-49 crew.{{tlx|free media}}]] NSSDCA ID: 1992-049A for STS-46 launch date 1992-07-31. STS-46 was a NASA Space Shuttle mission using Space Shuttle ''Atlantis'' and was launched on July 31, 1992, 13:56:48 UTC, and landed on August 8, 1992, 13:11:50 UTC, at Kennedy Space Center, SLF Runway 33. Names: Space Transportation System-49. Secondary payloads included the Evaluation of Oxygen Integration with Materials/Thermal Management Processes (EOIM-III/TEMP 2A), Consortium for Materials Development in Space Complex Autonomous Payload (CONCAP II and CONCAP III), IMAX Cargo Bay Camera (ICBC), Limited Duration Space Environment Candidate Materials Exposure (LDCE), Pituitary Growth Hormone Cell Function (PHCF), and the Ultraviolet Plume Instrument (UVPI). {{clear}} ==STS-50== [[Image:STS-047 shuttle.jpg|thumb|left|250px|STS-47 Endeavour, Orbiter Vehicle (OV) 105, lifts off from KSC. Credit: NASA.{{tlx||free media}}]] [[Image:STS-47 payloadbay.jpg|thumb|right|250px|Part of Space Shuttle ''Endeavour'''s payload bay and the Spacelab-J science module are shown. Credit: NASA STS-50 crew.{{tlx|free media}}]] [[Image:Bosten-Lake (Bosten-See), Xinjiang, China, 87.00E, 42.00N.jpg|thumb|right|250px|Bosten Lake area in East Turkestan (Xinjiang) is shown. Credit: NASA STS-50 crew.{{tlx|free media}}]] STS-47 was the 50th NASA Space Shuttle mission of the program, as well as the second mission of the Space Shuttle ''Endeavour''. NSSDCA ID: 1992-061A. "STS 47 was the 50th Shuttle mission and flew as its primary payload Spacelab-J (SL-J), utilized pressurized Spacelab module. Jointly sponsored by NASA and the National Space Development Agency (NASDA) of Japan, SL-J included 24 material science and 19 life sciences experiments, of which 34 were sponsored by NASDA, seven by NASA, and two collaborative efforts. The mission was extended one day to further science objectives. The materials science investigations covered such fields as biotechnology, electronic materials, fluid dynamics and transport phenomena, glasses and ceramics, metals and alloys, and acceleration measurements. The life sciences investigations covered human health, cell separation and biology, development biology, animal and human physiology and behavior, space radiation, and biological rhythms. Test subjects included the crew, Japanese koi fish, cultured animal and plant cells, chicken embryos, fruit flies, fungi and plant seeds, and frogs and frog eggs."<ref name=WilliamsSTS47>{{ cite web |author=David R. Williams |title=STS 47 |publisher=NASA GSFC |location=Greenbelt, MD USA |date=27 April 2022 |url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1992-061A |accessdate=26 July 2022 }}</ref> "Also flown in the payload bay were 12 Get Away Special (GAS) canisters (10 holding experiments, two for ballast) attached to a GAS Bridge Assembly. Middeck experiments included Israeli Space Agency Investigation about Hornets (USAIAH); Solid Surface Combustion Experiment (SSCE); Shuttle Amateur Radio Experiment (SAREX II); Air Force Maui Optical Site (AMOS); and Ultraviolet Plume Instrument (UVPI)."<ref name=WilliamsSTS47/> Camera location for the second image on the right was 42° 00′ 00″ N, 87° 00′ 00″ E, taken on 13 September 1992, 04:07:31. {{clear}} ==STS-51== [[Image:STS 52 Launch.jpg|thumb|upright=1.0|left|250px|Liftoff shows STS-51. Credit: NASA.{{tlx|free media}}]] STS-52 was a ''Space Transportation System'' (NASA Space Shuttle) mission using Space Shuttle ''Columbia'', and was launched on 22 October 1992.<ref name=Ryba1992>{{cite web|last1=Ryba|first1=Jeanne|title=STS-52|work=Space Shuttle - Mission Archives |publisher=NASA|accessdate=22 April 2021|url=https://web.archive.org/web/20210422171154/https://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-52.html|date=31 March 2010 }}</ref> NSSDCA ID: 1992-070A, launch date: 1992-10-22. Names: Space Transportation System-51. "It carried the US Microgravity Payload-2 (USMP-2) which contained several microgravity experimental packages. Among them were the growth of cadmium telluride crystals from vapor phase, growth of protein/enzyme crystals, and a number of high school experiments such as the clotting action of snake venom on blood plasma proteins, germination of Florida's official flower seeds, and microgravity effect on dry mustard seeds that were germinated after return. Also on-board were 6 rats that had been given anti-osteoporotic treatment with an experimental drug."<ref name=WilliamsSTS52>{{ cite web |author=David R. Williams |title=STS 52/USMP 1 |publisher=NASA Goddard Spaceflight Center |location=Greenbelt, MD USA |date=27 April 2022 |url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1992-070A |accessdate=25 July 2022 }}</ref> {{clear}} ==STS-52== [[Image:STS-053 shuttle.jpg|thumb|left|250px|Launch of ''Discovery'' is for a United States Department of Defense (DoD) mission. Credit: NASA.{{tlx|free media}}]] STS-53 was a NASA Space Shuttle ''Discovery'' mission in support of the United States Department of Defense (DoD). The mission was launched on 2 December 1992 from Kennedy Space Center, Florida. Launch Site: Cape Canaveral, United States. NSSDCA/COSPAR ID: 1992-086A. "The secondary unclassified experiments include: (1) Shuttle Glow (GLO), to investigate Shuttle/space environment interactions; (2) Cryogenic Heat Pipe Experiment (CRYOHP), a joint DoD and NASA Hitchhiker experiment to test advanced technology to regect excess heat generated by infrared sensors; [...] (4) Battlefield Laser Acquisition Sensor Test (BLAST), an Army space project to demonstrate the use of spaceborne laser receivers to detect laser energy from ground test locations; (5) Cloud Logic to Optimize Use of Defense System (CLOUDS), a meteorological experiment to quantify the variation in apparent cloud cover as a function of orbital view angle; (6) Cosmic Radiation Effects and Activation Monitor (CREAM), an experiment designed to collect cosmic ray energy loss spectra, neutron fluxes, and induced radioactivity; (7) Fluid Acquisition and Resupply Equipment (FARE), an experimen t to investigate the dynamics of fluid transfer in space; (8) Hand-held, earth-oriented, Real-time, Cooperative, User-friendly, Location-targeting and Environmental System (HERCULES), a Naval Research Lab (NRL) experiment to enable a Shuttle astrionaut to point a camera at an Earth feature, record the image and determine the latitude and longitude of the feature; (10) Microencapsulation In Space (MIS), designed to incresae the knowledge of microencapsulated drug technology; (11) Radiation Monitoring Equipment -III (RME-III), an instrument to measure the exposure to ionizing radiation on the Shuttle; (12) Space Tissue Loss (STL), to study the effects of space on fragile life systems; and (13) Visual Function Tester - Model II (VFT-2), a series of vision performance experiments in space."<ref name=WilliamsSTS53>{{ cite web |author=David R. Williams |title=STS 53 |publisher=NASA Goddard Spaceflight Center |location=Greenbelt, MD USA |date=27 April 2022 |url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1992-086A |accessdate=25 July 2022 }}</ref> Names: Space Transportation System-52. {{clear}} ==STS-53== STS-54 was a NASA Space Transportation System (Space Shuttle) mission using Space Shuttle ''Endeavour''. This was the third flight for ''Endeavour'', and was launched on 13 January 1993. Names: Space Transportation System-53. NSSDCA/COSPAR ID: 1993-003A. {{clear}} ==STS-54== [[Image:STS056-91-054 - Payload bay view with ATLAS pallet (Retouched).jpg|thumb|right|250px|Components of the Spacelab ATLAS-2 laboratory are shown in the payload bay of ''Discovery''. Credit: NASA STS-53 crew.{{tlx|free media}}]] [[Image:STS-56 Launch - GPN-2000-000748.jpg|thumb|left|250px|Launch shows STS-56. Credit: NASA.{{tlx|free media}}]] [[Image:STS056-90-034 - SPARTAN-201 free-flying (Retouched).jpg|thumb|right|250px|SPARTAN-201 free-flying near STS-56. Credit: NASA STS-53 crew retouched by [[c:user:Askeuhd|Askeuhd]].{{tlx|free media}}]] Names: Space Transportation System-54. STS-56 was a NASA Space Shuttle Discovery mission to perform special experiments. The mission was launched from Kennedy Space Center, Florida, on 8 April 1993. NSSDCA/COSPAR ID: 1993-023A. The primary payload of the flight was the Spacelab Atmospheric Laboratory for Applications and Science-2 (ATLAS-2), designed to collect data on the relationship between the Sun's energy output and Earth's middle atmosphere and how these factors affect the ozone layer. It included six instruments mounted on a Spacelab pallet in the cargo bay, with the seventh mounted on the wall of the bay in two Get Away Special (GAS) canisters. Atmospheric instruments included the Atmospheric Trace Molecule Spectroscopy (ATMOS) experiment, the Millimeter Wave Atmospheric Sounder (MAS), and the Shuttle Solar Backscatter Ultraviolet (SSBUV/A) spectrometer (on the cargo bay wall). Solar science instruments were the solar spectrometry instrument SOLSPEC,<ref name="SOLSPEC">{{cite web |title=Background |url=http://solspec.projet.latmos.ipsl.fr/SOLSPEC_GB/Background.html |website=SOLSPEC |publisher=Institut Pierre Simon Laplace |accessdate=11 March 2022 }}</ref> the Solar Ultraviolet Irradiance Monitor (SUSIM), and the Active Cavity Radiometer (ACR) and Solar Constant (SOLCON) experiments.<ref name=Ryba>{{cite web|last1=Ryba|first1=Jeanne|title=STS-56|url=https://www.nasa.gov/mission_pages/shuttle/shuttlemissions/archives/sts-56.html|publisher=NASA|accessdate=11 March 2022}}</ref> ATLAS-2 is one element of NASA's Mission to Planet Earth program. All seven ATLAS-2 instruments first flew on Spacelab ATLAS-1 during STS-45, and flew a third time in late 1994 on STS-66.<ref name=Ryba/> On 11 April 1993, the crew used the remote manipulator arm (Canadarm) to deploy the Shuttle Point Autonomous Research Tool for Astronomy-201 (SPARTAN-201), a free-flying science instrument platform designed to study velocity and acceleration of the solar wind and observe the sun's corona. Collected data was stored on tape for playback after return to Earth. SPARTAN-201 was retrieved on 13 April 1993.<ref name=Ryba/> {{clear}} ==STS-55== [[Image:STS-55 Spacelab.jpg|thumb|right|250px|Spacelab Module LM1 in ''Columbia'''s payload bay, serves as the Spacelab D-2 laboratory. Credit: NASA STS-55 crew.{{tlx|free media}}]] Names: Space Transportation System-55. NSSDCA/COSPAR ID: 1993-027A. Columbia carried to orbit the second reusable German Spacelab D-2 and demonstrated the shuttle's ability for international cooperation, exploration, and scientific research in space. The Spacelab module and an exterior experiment support structure contained in Columbia's payload bay comprised the Spacelab D-2 payload. The first German Spacelab flight, D-1, flew Shuttle mission STS-61-A in October 1985. The crew worked in two shifts around-the-clock to complete investigations into the areas of fluid physics, materials sciences, life sciences, biological sciences, technology, Earth observations, atmospheric physics, and astronomy. Many of the experiments advanced the research of the D-1 mission by conducting similar tests, using upgraded processing hardware, or implementing methods that took full advantage of the technical advancements since 1985. {{clear}} ==STS-56== [[Image:STS057-89-042.jpg|thumb|right|250px|''Endeavour'''s payload bay, with the Space habitat (SpaceHab) module (foreground), European Retrievable Carrier (EURECA) (background), and astronauts David Low and Peter Wisoff performing an Extravehicular activity (EVA) (centre). Credit: NASA STS-56 crew.{{tlx|free media}}]] [[Image:1993 s57 Liftoff.jpg|thumb|upright=1.0|left|Liftoff shows STS-51. Credit: NASA.{{tlx|free media}}]] [[Image:EURECA berth STS-57.jpg|thumb|upright=1.0|right|250px|European Retrievable Carrier (EURECA) is stowed by ''Endeavour'''s remote manipulator system (Canadarm). Credit: NASA STS-56 crew.{{tlx|free media}}]] STS-57 was a NASA Space Shuttle-Spacehab mission of Space Shuttle ''Endeavour'' that launched 21 June 1993 from Kennedy Space Center, Florida. Names: Space Transportation System-56. NSSDCA/COSPAR ID: 1993-037A. EURECA had been deployed from the Space Shuttle ''Atlantis'' in August 1992 (STS-46) and contained several experiments to study the long-term effects of exposure to microgravity. {{clear}} ==STS-57== [[Image:1993 s51 IMAX view of Discovery from Spas.JPG|thumb|right|250px|IMAX photography of ''Discovery'' in orbit, was viewed from the free-flying SPAS-ORFEUS astronomy platform. Credit: NASA STS-57 crew.{{tlx|free media}}]] [[Image:1993 s51 Liftoff.jpg|thumb|upright=1.0|left|250px|Launch was seen from the RSS. Credit: NASA.{{tlx|free media}}]] [[Image:51 SPAS 04.jpg|thumb|upright=1.0|right|250px|The ORFEUS/SPAS platform is captured by the Canadarm. Credit: NASA STS-57 crew.{{tlx|free media}}]] STS-51 was a NASA Space Shuttle ''Discovery'' mission. The flight featured the deployment and retrieval of the SPAS-ORFEUS satellite and its IMAX camera, which captured spectacular footage of ''Discovery'' in space. Names: Space Transportation System-57. NSSDCA/COSPAR ID: 1993-058A. {{clear}} ==STS-58== [[Image:STS058-92-064.jpg|thumb|right|250px|Spacelab module LM2 is in ''Columbia'''s payload bay, serving as the Spacelab Life Sciences-2 laboratory. Credit: NASA STS-58 crew.{{tlx|free media}}]] [[Image:Sts-58 pad.jpg|thumb|upright=1.0|left|250px|''Columbia'' is on Pad 39B ready for launch. Credit: NASA.{{tlx|free media}}]] STS-58 was a NASA mission flown by Space Shuttle ''Columbia'' launched from Kennedy Space Center, Florida, on 18 October 1993. Names: Space Transportation System-58. NSSDCA/COSPAR ID: 1993-065A. {{clear}} ==STS-59== [[Image:STS061-98-050 - Astronauts Musgrave and Hoffman during servicing of HST (Retouched).jpg|thumb|right|250px|Musgrave is being raised to the top of ''Hubble'' by Canadarm, as it sits in ''Endeavour'''s payload bay. Credit: NASA STS-59 crew.{{tlx|free media}}]] [[Image:1993 sts61 liftoff.jpg|thumb|upright=1.0|left|250px|Launch shows the first ''Hubble'' servicing mission. Credit: NASA.{{tlx|free media}}]] STS-61 was the first NASA Hubble Space Telescope servicing mission, and the fifth flight of the Space Shuttle Endeavour. The mission launched on 2 December 1993 from Kennedy Space Center (KSC) in Florida. Names: Space Transportation System-59. NSSDCA/COSPAR ID: 1993-075A. {{clear}} ==STS-60== [[Image:Wake Shield Facility on STS-60 (STS060-74-054).jpg|thumb|right|250px|The Astrotech Corporation SPACEHAB-2 in ''Discovery'''s payload bay, as Canadarm grapples the Wake Shield Facility (WSF-1). Credit: NASA STS-60 crew.{{tlx|free media}}]] STS-60 was the first mission of the U.S./Russian Shuttle-Mir Program. The mission used NASA Space Shuttle ''Discovery'', which lifted off from Launch Pad 39A on 3 February 1994 from Kennedy Space Center, Florida. The mission carried the Wake Shield Facility experiment and a SPACEHAB module, developed by SPACEHAB Inc., into orbit. NSSDCA/COSPAR ID: 1994-006A. Names: Space Transportation System-60. {{clear}} ==STS-61== [[Image:1994_s62_Liftoff.jpg|thumb|left|250px|Liftoff shows ''Columbia'' on STS-62. Credit: NASA.{{tlx|free media}}]] [[Image:Typhoon Owen, STS-62.jpg|thumb|right|250px|''Columbia'' passes over Typhoon Owen. Credit: NASA STS-61 crew.{{tlx|free media}}]] STS-62 was a Space Shuttle program mission flown aboard Space Shuttle Columbia. The primary payloads were the USMP-02 microgravity experiments package and the OAST-2 engineering and technology payload, both in the orbiter's cargo bay. The two-week mission also featured a number of biomedical experiments focusing on the effects of long duration spaceflight. NSSDCA/COSPAR ID: 1994-015A Names: Space Transportation System-61. {{clear}} ==STS-62== [[Image:EndeavourPayloadBaySTS59.jpg|thumb|right|250px|Space Shuttle ''Endeavour'' is in orbit with SIR-C in its payload bay. Credit: NASA STS-61 crew.{{tlx|free media}}]] STS-59 was a Space Shuttle program mission that took place in 1994. The launch was chronicled by the 1994 Discovery Channel special about the Space Shuttle program. NSSDCA/COSPAR ID: 1994-020A. Names: Space Transportation System-62. {{clear}} ==STS-63== [[Image:STS-65 spacelab.jpg|thumb|right|250px|Spacelab Module LM1 in ''Columbia'''s payload bay, serving as the International Microgravity Laboratory. Credit: NASA STS-63 crew.{{tlx|free media}}]] NSSDCA/COSPAR ID: 1994-039A. Names: Space Transportation System-63. {{clear}} ==Tiangong space stations== [[Image:Tiangong Space Station Rendering 2022.07.jpg|thumb|center|400px|Rendering of Tiangong Space Station in late July 2022, is as of June 2022 with Tianhe core module in the middle, Wentian lab module on the left, Tianzhou cargo spacecrafts on right, and Shenzhou-14 crewed spacecraft at nadir. Credit: [[c:user:Shujianyang|Shujianyang]].{{tlx|free media}}]]. The Tiangong space station is a space station being constructed by China in low Earth orbit between 340 and 450 km (210 and 280 mi) above the surface. Being China's first long-term space station, it is the goal of the "Third Step" of the China Manned Space Program. Once completed, Tiangong will have a mass between 80 and 100 t (180,000 and 220,000 lb), roughly one-fifth the mass of the International Space Station and about the size of the decommissioned Russian Mir space station. {{clear}} ==Reflections== {{main|Radiation astronomy/Reflections}} [[Image:Ash and Steam Plume, Soufriere Hills Volcano, Montserrat.jpg|thumb|right|250px|This oblique astronaut photograph from the International Space Station (ISS) captures a white-to-grey volcanic ash and steam plume extending westwards from the Soufriere Hills volcano. Credit: NASA Expedition 21 crew.{{tlx|free media}}]] The Soufrière Hills, a volcano on the island of Montserrat, in the Lesser Antilles island chain in the Caribbean Sea, has been active since 1995. The most recent eruptive phase of the volcano began with a short swarm of volcano-tectonic earthquakes—earthquakes thought to be caused by movement of magma beneath a volcano—on October 4, 2009, followed by a series of ash-venting events that have continued through October 13, 2009. These venting events create plumes that can deposit ash at significant distances from the volcano. In addition to ash plumes, pyroclastic flows and lava dome growth have been reported as part of the current eruptive activity. This oblique astronaut photograph from the International Space Station (ISS) captures a white-to-gray ash and steam plume extending westwards from the volcano on October 11, 2009. Oblique images are taken by astronauts looking out from the ISS at an angle, rather than looking straight downward toward the Earth (a perspective called a nadir view), as is common with most remotely sensed data from satellites. An oblique view gives the scene a more three-dimension quality, and provides a look at the vertical structure of the volcanic plume. While much of the island is covered in green vegetation, gray deposits that include pyroclastic flows and volcanic mudflows (lahars) are visible extending from the volcano toward the coastline. When compared to its extent in earlier views, the volcanic debris has filled in more of the eastern coastline. Urban areas are visible in the northern and western portions of the island; they are recognizable by linear street patterns and the presence of bright building rooftops. The silver-gray appearance of the Caribbean Sea surface is due to sunglint, which is the mirror-like reflection of sunlight off the water surface back towards the handheld camera onboard the ISS. The sunglint highlights surface wave patterns around the island. {{clear}} ==Visuals== {{main|Radiation astronomy/Visuals}} [[Image:El Misti Volcano and Arequipa, Peru.jpg|thumb|right|250px|This mosaic of two astronaut photographs illustrates the closeness of Arequipa, Peru, to the 5,822-meter-high El Misti Volcano. Credit: This image was taken by the NASA Expedition 21 crew.{{tlx|free media}}]] This mosaic on the right of two astronaut photographs illustrates the closeness of Arequipa, Peru, to the 5,822-meter-high El Misti Volcano. The city centre of Arequipa, Peru, lies only 17 kilometres away from the summit of El Misti; the grey urban area is bordered by green agricultural fields (image left). Much of the building stone for Arequipa, known locally as sillar, is quarried from nearby pyroclastic flow deposits that are white. Arequipa is known as “the White City” because of the prevalence of this building material. The Chili River extends north-eastwards from the city centre and flows through a canyon (image right) between El Misti volcano and Nevado Chachani to the north. {{clear}} ==Blues== {{main|Radiation astronomy/Blues}} [[Image:Ifalik ISS021.png|thumb|right|250px|NASA astronaut image is of Ifalik Atoll, Yap State, Federated States of Micronesia. Credit: ISS Expedition 21 Crew Earth Observations.{{tlx|free media}}]] Ifalik is a coral atoll of four islands in the central Caroline Islands in the Pacific Ocean, and forms a legislative district in Yap State in the Federated States of Micronesia. Ifalik is located approximately {{convert|40|km|mi}} east of Woleai and {{convert|700|km|mi}} southeast of the island of Yap. The population of Ifalik was 561 in 2000,<ref>{{cite web|website=The Pacific Community|url=https://web.archive.org/web/20100924233537/http://www.spc.int/prism/country/fm/stats/Census%20%26%20Surveys/2000/Yap-BT.pdf |title=Census & Surveys: 2000: Yap|accessdate=4 September 2020}}</ref> living on 1.5&nbsp;km². The primary islets of Ifalik are called Ella, Elangelap, Rawaii, and Falalop, which is the atoll's main island.<ref>[http://www.pacificweb.org/DOCS/fsm/Yap2000Census/2000%20Yap%20Census%20Report_Final.pdf Pacificweb]</ref> The total land area of Ifalik is only {{convert|1.47 |km2|sqmi}}, but it encloses a {{convert|20|m|ft}} deep lagoon of {{convert|2.43|km2|sqmi}}.<ref>Otis W. Freeman, ed., Geography of the Pacific, Wiley 1953</ref> The total area is about six square kilometers.<ref>[ftp://rock.geosociety.org/pub/reposit/2001/2001075.pdf Geosociety], January 2020, InternetArchiveBot</ref> Ifalik is known as a “warrior island”. Prior to European contact, its warriors invaded the outer islands in Yap as well as some of the outer islands in Chuuk. Atolls under the attack included, Lamotrek, Faraulep, Woleai, Elato, Satawal, Ulithi, and Poluwat (outer islet of Chuuk). {{clear}} ==Greens== {{main|Radiation astronomy/Greens}} [[Image:ISS021-E-15710 Pearl Harbor, Hawaii.jpg|thumb|right|250px|This detailed astronaut photograph illustrates the southern coastline of the Hawaiian island Oahu, including Pearl Harbor. Credit: ISS Expedition 21 Crew Earth Observations.{{tlx|free media}}]] A comparison between this image and a 2003 astronaut photograph of Pearl Harbor suggests that little observable land use or land cover change has occurred in the area over the past six years. The most significant difference is the presence of more naval vessels in the Reserve Fleet anchorage in Middle Loch (image center). The urban areas of Waipahu, Pearl City, and Aliamanu border the harbor to the northwest, north, and east. The built-up areas, recognizable by linear streets and white rooftops, contrast sharply with the reddish volcanic soils and green vegetation on the surrounding hills. {{clear}} ==Oranges== {{main|Radiation astronomy/Oranges}} [[Image:Northern Savage Island, Atlantic Ocean.jpg|thumb|right|250px|Selvagem Grande, with an approximate area of 4 square kilometres, is the largest of the Savage Islands. Credit: NASA Expedition 21 crew.{{tlx|free media}}]] [[Image:Ounianga Lakes from ISS.jpg|thumb|left|250px|This astronaut photograph features one of the largest of a series of ten mostly fresh water lakes in the Ounianga Basin in the heart of the Sahara Desert of northeastern Chad. Credit: NASA Expedition 21 crew.{{tlx|free media}}]] [[Image:Southern Savage Islands, Atlantic Ocean.jpg|thumb|right|250px|The irregularly-shaped Ilhéus do Norte, Ilhéu de Fora, and Selvagem Pequena are visible in the centre of the image. Credit: NASA Expedition 21 crew.{{tlx|free media}}]] Selvagem Grande Island is part of the Savage Islands archipelago, which themselves are part of the Portuguese Autonomous Region of Madeira in the North Atlantic Ocean. The island ({{convert|2000|x|1700|m}}) belongs to the northeast group of the Savage Islands, which comprises in addition three islets: Sinho Islet, Palheiro de Terra and Palheiro do Mar.<ref name="NatGeoReport" /> It is generally flat, but has three summits, remnants of former volcanic cones appropriately named Atalaia, Tornozelos and Inferno, Atalaia being the highest of the three, reaching {{convert|163|m|ft|0|abbr=on}} in altitude.<ref name="NatGeoReport">{{cite web |title=Marine Biodiversity and Ecosystem Health of Ilhas Selvagens, Portugal |url=https://media.nationalgeographic.org/assets/file/PristineSeasSelvagensScientificReport.pdf |publisher=National Geographic Society |accessdate=4 November 2020}}</ref> The lakes in the image on the left are remnants of a single large lake, probably tens of kilometers long, that once occupied this remote area approximately 14,800 to 5,500 years ago. As the climate dried out during the subsequent millennia, the lake shrank, and large, wind-driven sand dunes invaded the original depression, dividing it into several smaller basins. The area shown in this image is approximately 11 by 9 kilometers. The lakes’ dark surfaces are almost completely segregated by linear, orange sand dunes that stream into the depression from the northeast. The almost-year-round northeast winds and cloudless skies make for very high evaporation rates; an evaporation rate of more than 6 meters per year has been measured in one of the nearby lakes. Despite this, only one of the ten lakes is saline. In the second image down on the right, the other Savage islands are ringed by bright white breaking waves along the fringing beaches. {{clear}} ==Reds== {{main|Radiation astronomy/Reds}} [[Image:Ankara, Turkey.jpg|thumb|right|250px|The central portion of the capital city of Turkey, Ankara, is featured in this astronaut photograph. Credit: NASA Expedition 19 crew.{{tlx|free media}}]] The central portion of the capital city of Turkey, Ankara, is featured in this astronaut photograph. Hill slopes around the city (image left and right) are fairly green due to spring rainfall. One of the most striking aspects of the urban area is the almost uniform use of red brick roofing tiles, which contrast with lighter-coloured roads; the contrast is particularly evident in the northern (image lower left) and southern (image upper right) portions of the city. Numerous parks are visible as green patches interspersed within the red-roofed urban region. A region of cultivated fields in the western portion of the city (image centre) is a recreational farming area known as the Atatürk Forest Farm and Zoo—an interesting example of intentional preservation of a former land use within an urban area. {{clear}} ==Radars== {{main|Radiation astronomy/Radars}} [[Image:SIR-B Sudbury Impact Crater.jpg|thumb|upright=1.0|right|250px|Sample image was taken using the SIR-B over Canada. Credit: NASA STS-13 (STS-17, STS-41-G) crew.{{tlx|free media}}]] [[Image:STS-41-G SIR-B antenna.jpg|thumb|upright=1.0|left|250px|SIR-B antenna deployment is shown. Credit: NASA STS-13 (STS-17, STS-41-G) crew.{{tlx|free media}}]] [[Image:TEIDE.JPG|thumb|right|250px|A Synthetic aperture radar (SAR) radar image acquired by the SIR-C/X-SAR radar on board the Space Shuttle ''Endeavour'' shows the Teide volcano. Credit: NASA STS-65 (STS-68) crew.{{tlx|free media}}]] The Shuttle Imaging Radar-A (SIR-A) was for remote sensing of Earth's resources. Experiments were conducted by Shuttle missions: STS-2. The Shuttle Imaging Radar-B (SIR-B) was part of the OSTA-3 experiment package (Spacelab) in the payload bay of STS-13. The SIR-B was an improved version of a similar device flown on the OSTA-1 package during STS-2. It had an eight-panel antenna array measuring {{cvt|11|xx|2|m}}. It operated throughout the flight, but much of the data had to be recorded on board the orbiter rather than transmitted to Earth in real-time as was originally planned. {{clear}} ==Capes== [[Image:Cape canaveral.jpg|thumb|right|250px|Cape Canaveral, Florida, and the NASA John F. Kennedy Space Center are shown in this near-vertical photograph. Credit: NASA STS-43 crew.{{tlx|free media}}]] '''Def.''' a "piece or point of land, extending beyond the adjacent coast into a sea or lake"<ref name=CapeWikt>{{ cite book |title=cape |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=15 December 2014 |url=https://en.wiktionary.org/wiki/cape |accessdate=2014-12-20 }}</ref> is called a '''cape'''. {{clear}} ==Coastlines== [[Image:Dalmatian Coastline near Split, Croatia.jpg|thumb|right|250px|Dalmatian Coastline near Split, Croatia, is shown. Credit: NASA Expedition 19 crew.{{tlx|free media}}]] In this image on the right, a thin zone of disturbed water (tan patches) marking a water boundary appears in the Adriatic Sea between Split and the island of Brač. It may be a plankton bloom or a line of convergence between water masses, which creates rougher water. {{clear}} ==Craters== {{main|Radiation astronomy/Craters}} [[Image:ISS020-E-026195 Aorounga Impact Crater Chad.jpg|thumb|right|250px|The concentric ring structure of the Aorounga crater—renamed Aorounga South in the multiple-crater interpretation of SIR data—is clearly visible in this detailed astronaut photograph. Credit: NASA Expedition 20 crew.{{tlx|free media}}]] [[Image:Mount Tambora Volcano, Sumbawa Island, Indonesia.jpg|thumb|left|250px|This detailed astronaut photograph depicts the summit caldera of the Mount Tambora. Credit: NASA ISS Expedition 20 crew.{{tlx|free media}}]] The concentric ring structure of the Aorounga crater—renamed Aorounga South in the multiple-crater interpretation of SIR data—is clearly visible in this detailed astronaut photograph on the right. The central highland, or peak, of the crater is surrounded by a small sand-filled trough; this in turn is surrounded by a larger circular trough. Linear rock ridges alternating with light orange sand deposits cross the image from upper left to lower right; these are called yardangs by geomorphologists. Yardangs form by wind erosion of exposed rock layers in a unidirectional wind field. The wind blows from the northeast at Aorounga, and sand dunes formed between the yardangs are actively migrating to the southwest. Aorounga Impact Crater is located in the Sahara Desert, in north-central Chad, and is one of the best preserved impact structures in the world. The crater is thought to be middle or upper Devonian to lower Mississippian (approximately 345–370 million years old) based on the age of the sedimentary rocks deformed by the impact. Spaceborne Imaging Radar (SIR) data collected in 1994 suggests that Aorounga is one of a set of three craters formed by the same impact event. The other two suggested impact structures are buried by sand deposits. The concentric ring structure of the Aorounga crater—renamed Aorounga South in the multiple-crater interpretation of SIR data—is clearly visible in this detailed astronaut photograph. The central highland, or peak, of the crater is surrounded by a small sand-filled trough; this in turn is surrounded by a larger circular trough. Linear rock ridges alternating with light orange sand deposits cross the image from upper left to lower right; these are called yardangs by geomorphologists. Yardangs form by wind erosion of exposed rock layers in a unidirectional wind field. The wind blows from the northeast at Aorounga, and sand dunes formed between the yardangs are actively migrating to the southwest. {{clear}} ==Glaciology== {{main|Radiation astronomy/Cryometeors}} [[Image:Upsala Glacier, Argentina.jpg|thumb|right|250px|The Southern Patagonian Icefield of Argentina and Chile is the southern remnant of the Patagonia Ice Sheet that covered the southern Andes Mountains during the last ice age. Credit: NASA Expedition 21 crew.{{tlx|free media}}]] The Southern Patagonian Icefield of Argentina and Chile is the southern remnant of the Patagonia Ice Sheet that covered the southern Andes Mountains during the last ice age. This detailed astronaut photograph on the right illustrates the terminus of one of the ice-field’s many spectacular glaciers—Upsala Glacier, located on the eastern side of the ice-field. This image was taken during spring in the Southern Hemisphere, and icebergs were calving from the glacier terminus into the waters of Lago Argentino (Lake Argentina, image right). Two icebergs are especially interesting because they retain fragments of the moraine (rock debris) that forms a dark line along the upper surface of the glacier. The inclusion of the moraine illustrates how land-based rocks and sediment may wind up in ocean sediments far from shore. Moraines are formed from rock and soil debris that accumulate along the front and sides of a flowing glacier. The glacier is like a bulldozer that pushes soil and rock in front of it, leaving debris on either side. When two glaciers merge (image centre), moraines along their edges can join to form a medial moraine that is drawn out along the upper surface of the new glacier. {{clear}} ==Lakes== [[Image:STS001-012-0363 - View of China (Retouched).tif|thumb|right|250px|View shows the lake Jieze Caka in Tibet. Credit: NASA STS-1 crew, [[c:user:Askeuhd|Askeuhd]].{{tlx|free media}}]] [[Image:STS002-13-274 - View of China.jpg|thumb|left|250px|The image shows Bangong Lake in Himalaya, China. Credit: STS-2 crew.{{tlx|free media}}]] '''Def.''' a "large, [landlocked]<ref name=LakeWikt1>{{ cite book |author=[[wikt:User:Paul G|Paul G]] |title=lake |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=15 December 2003 |url=https://en.wiktionary.org/wiki/lake |accessdate=15 July 2022 }}</ref> stretch of water"<ref name=LakeWikt>{{ cite book |author=[[wikt:User:Polyglot|Polyglot]] |title=lake |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=11 July 2003 |url=https://en.wiktionary.org/wiki/lake |accessdate=15 July 2022 }}</ref> is called a '''lake'''. The image on the right show the Tibetan plateau containing lake Jieze Caka. {{clear}} ==Mountains== [[Image:Saint Helena Island.jpg|thumb|250px|right|This astronaut photograph shows the island’s sharp peaks and deep ravines; the rugged topography results from erosion of the volcanic rocks that make up the island. Credit: NASA Expedition 19 crew.{{tlx|free media}}]] '''Def.''' a "large mass of earth and rock, rising above the common level of the earth or adjacent land, usually given by geographers as above 1000 feet in height (or 304.8 metres), though such masses may still be described as hills in comparison with larger mountains"<ref name=MountainWikt>{{ cite book |author=[[wikt:User:92.7.198.35|92.7.198.35]] |title=mountain |publisher=Wikimedia Foundation, Inc |location=San Francisco, California |date=9 January 2011 |url=https://en.wiktionary.org/wiki/mountain |accessdate=2014-12-14 }}</ref> is called a '''mountain'''. The image on the right was acquired by astronauts onboard the International Space Station as part of an ongoing effort (the HMS Beagle Project) to document current biodiversity in areas visited by Charles Darwin. Saint Helena Island, located in the South Atlantic Ocean approximately 1,860 kilometers (1,156 miles) west of Africa, was one of the many isolated islands that naturalist Charles Darwin visited during his scientific voyages in the nineteenth century. He visited the island in 1836 aboard the HMS Beagle, recording observations of the plants, animals, and geology that would shape his theory of evolution. The astronaut photograph shows the island’s sharp peaks and deep ravines; the rugged topography results from erosion of the volcanic rocks that make up the island. The change in elevation from the coast to the interior creates a climate gradient. The higher, wetter center is covered with green vegetation, whereas the lower coastal areas are drier and hotter, with little vegetation cover. Human presence on the island has also caused dramatic changes to the original plants and animals of the island. Only about 10 percent of the forest cover observed by the first explorers now remains in a semi-natural state, concentrated in the interior highlands. {{clear}} ==Rock structures== {{main|Radiation astronomy/Rocks}} [[Image:Big Thomson Mesa, Capitol Reef National Park, Utah.jpg|thumb|right|250px|This detailed astronaut photograph shows part of Big Thomson Mesa, near the southern end of Capitol Reef National Park. Credit: NASA Expedition 20 crew.{{tlx|free media}}]] This detailed astronaut photograph on the right shows part of Big Thomson Mesa, near the southern end of Capitol Reef National Park. Capitol Reef National Park is located on the Colorado Plateau, which occupies the adjacent quarters of Arizona, Colorado, New Mexico, and Utah. Big Thomson Mesa (image left) is part of a large feature known as the en:Waterpocket Fold. The Fold is a geologic structure called a monocline—layers of generally flat-lying sedimentary rock with a steep, one-sided bend, like a carpet runner draped over a stair step. Geologists think that monoclines on the Colorado Plateau result from faulting (cracking) of deeper and more brittle crystalline rocks under tectonic pressure; while the crystalline rocks were broken into raised or lowered blocks, the overlaying, less brittle sedimentary rocks were flexed without breaking. The portion of the Waterpocket Fold illustrated in this image includes layered rocks formed during the Mesozoic Era (about 250 – 65 million years ago). The oldest layers are at the bottom of the sequence, with each successive layer younger than the preceding one going upwards in the sequence. Not all of the formation’s rock layers are clearly visible, but some of the major layers (units to geologists) can be easily distinguished. The top half of the image includes the oldest rocks in the view: dark brown and dark green Moenkopi and Chinle Formations. Moving toward the foot of the mesa, two strikingly coloured units are visible near image centre: light red to orange Wingate Sandstone and white Navajo Sandstone. Beyond those units, reddish brown to brown Carmel Formation and Entrada Sandstone occupy a topographic bench at the foot of a cliff. The top of the cliff face above this bench—Big Thomson Mesa—is comprised of brown Dakota Sandstone. This sequence represents more than 100 million years of sediments being deposited and turned into rock. Much younger Quaternary (2-million- to approximately 10,000-year-old) deposits are also present in the view. The area shown in this astronaut photograph is located approximately 65 kilometers to the southeast of Fruita, UT near the southern end of Capitol Reef National Park. {{clear}} ==Volcanoes== [[Image:Mount Hood, Oregon.jpg|thumb|right|250px|Gray volcanic deposits from Mount Hood extend southwards along the banks of the White River (image lower left). Credit: NASA Expedition 20 crew.{{tlx|free media}}]] [[Image:Teide Volcano, Canary Islands, Spain.jpg|thumb|left|250px|This detailed astronaut photograph features two stratovolcanoes—Pico de Teide and Pico Viejo—located on Tenerife Island. Credit: NASA Expedition 20 crew.{{tlx|free media}}]] Gray volcanic deposits extend southwards along the banks of the White River (image lower left) and form several prominent ridges along the south-east to south-west flanks of the volcano. The deposits contrast sharply with the green vegetation on the lower flanks of the volcano. North is to the right. The detailed astronaut photograph on the left features two stratovolcanoes—Pico de Teide and Pico Viejo—located on Tenerife Island, part of the Canary Islands of Spain. Stratovolcanoes are steep-sided, typically conical volcanoes formed by interwoven layers of lava and fragmented rock material from explosive eruptions. Pico de Teide has a relatively sharp peak, whereas an explosion crater forms the summit of Pico Viejo. The two stratovolcanoes formed within an even larger volcanic structure known as the Las Cañadas caldera. A caldera is a large collapse depression usually formed when a major eruption completely empties the magma chamber underlying a volcano. The last eruption of Teide occurred in 1909. Sinuous flow levees marking individual lava flows are perhaps the most striking volcanic features visible in the image. Flow levees are formed when the outer edges of a channelized lava flow cool and harden while the still-molten interior continues to flow downhill. Numerous examples radiate outwards from the peaks of both Pico de Teide and Pico Viejo. Brown to tan overlapping lava flows and domes are visible to the east-south-east of the Teide stratovolcano. {{clear}} ==See also== {{div col|colwidth=20em}} * [[Radiation astronomy/Gravitationals|Gravitational astronomy]] * [[Radiation astronomy/Infrareds|Infrared astronomy]] * [[Radiation astronomy/Radars|Radar astronomy]] * [[Radio astronomy]] * [[Submillimeter astronomy]] * [[Radiation astronomy/Superluminals|Superluminal astronomy]] {{Div col end}} ==References== {{reflist|2}} ==External links== * [http://www.iau.org/ International Astronomical Union] * [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED] * [http://nssdc.gsfc.nasa.gov/ NASA's National Space Science Data Center] * [http://www.ncbi.nlm.nih.gov/sites/gquery NCBI All Databases Search] * [http://www.osti.gov/ Office of Scientific & Technical Information] * [http://www.ncbi.nlm.nih.gov/pccompound PubChem Public Chemical Database] * [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System] * [http://www.scirus.com/srsapp/advanced/index.jsp?q1= Scirus for scientific information only advanced search] * [http://cas.sdss.org/astrodr6/en/tools/quicklook/quickobj.asp SDSS Quick Look tool: SkyServer] * [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database] * [http://simbad.harvard.edu/simbad/ SIMBAD Web interface, Harvard alternate] * [http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp Spacecraft Query at NASA] * [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl Universal coordinate converter] <!-- footer templates --> {{tlx|Principles of radiation astronomy}}{{Radiation astronomy resources}}{{Sisterlinks|Orbital platforms}} <!-- categories --> [[Category:Spaceflight]] jmifhwsjy61tteprs83vuoeykoxunbw 118 285152 2412456 2411079 2022-08-07T02:18:08Z Guy vandegrift 813252 /* Images+ links */ wikitext text/x-wiki '''Physics of music''', or ''[[w:Musical acoustics|musical acoustics]]'' is an effort to understand music from a scientific point of view. Here the goal is to understand musical consonance and dissonance using basic concepts. ===Sound waves and frequency=== <gallery mode="packed" heights="150px" style="text-align:left"> File:Drum vibration mode01.gif|Sound is created by a moving object, like this membrane. To create sound that humans can hear, the membrane will typically make hundreds of vibrations each second. File:CPT-sound-physical-manifestation.svg|Regions of air compression and [[wikt:rarefraction|rarefraction]] move at the "[[w:simple:Speed of sound|speed of sound]]". The sine wave illustrates the variation in air density. File:Sound wave physics.gif|The pressure fluctuations of a travelling sound wave can be graphed as a function of either distance or time (click image to expand). </gallery> {| class="wikitable floatright" !Other ways to<br> to say <u>hertz</u> |- |inverse-seconds |- |cycles per second |- |cps |} ==wikitable== {| class="wikitable floatright" style="text-align:center"; |+ 8 consonant intervals |- ! rank !! name !! half<br>tones!!ratio |- | 1 || P1 (unison) || 0 || 1/1 |- | 2 || P8 (octave) || 12 || 2/1 |- | 3 || P5 (fifth) || 7 || 3/2 |- | 4 || P4 (fourth) || 5 || 4/3 |- | 5 || M6 (maj 6th) || 9 || 5/3 |- | 6 || M3 (maj 3rd) || 4 || 5/4 |- | 7 || m6 (min 6th) || 8 || 8/5 |- | 8 || m3 (min 3rd) || 3 || 6/5 |} ==Terminology== The words used to describe something often depend on who is speaking, and things can get tricky when musicians and scientists are involved. The '''pitch''' of a musical note is measured by it's '''frequency''', or the number of cycles that occur each second. While musicians often refer to a notes pitch by a number (e.g., "440A"), scientists and engineers prefer to attach units to everything (e.g., "440 Hertz" or simply: 440Hz). One "Hertz" is defined as one cycle per second. The term '''[[wikt:musical interval|musical interval]]''' can refer to the difference between two pitches. [[w:Encyclopædia Britannica|Encyclopædia Britannica]] distinguishes between the '''melodic interval''' (two consecutive notes played consecutively), and the '''harmonic interval'''<ref>https://www.google.com/search?q=musical+interval+meaning&rlz=1C1CHBF_enUS1007US1007&oq=musical+interval+meaning&aqs=chrome..69i57j0i15i22i30j0i22i30l3j0i15i22i30j0i22i30j0i15i22i30j0i390l2.5708j0j7&sourceid=chrome&ie=UTF-8</ref><ref>https://www.britannica.com/art/interval-music</ref> (two pitches played simultaneously). While one is allowed to refer interval as a chord, calling it an "harmonic interval" precisely states that we are talking about <u>two pitches sounded at the same time</u>. An excellent alternative to "harmonic interval" would be to call it a '''[[w:Dyad (music)| dyad]]'''.<ref>[[Wiktionary:dyad]] informs us that "dyad" is a general-purpose word for "two things".</ref> An important distinction between different intervals is '''consonance''' versus '''dissonance''', which might be expressed as a distinction between ''smoothness'' and ''roughness''. By no means is dissonance "bad". In his Ninth Symphony, Beethoven famously interrupts an extremely dissonant passage by a singer who announces Ode to Joy with these words: ::Oh friends, not these sounds! ::Let us instead strike up more pleasing ::and more joyful ones! These terms are not always absolute: While some might argue that the [[w:Tritone|tritone]] is consonant, all would agree that it is more dissonant than the established consonant intervals. ==Stackexchange ranking== *[https://music.stackexchange.com/questions/46509/what-is-the-list-of-intervals-in-order-of-dissonance stackexchange] ranked them as follows: 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 1:1 (unison); 2:1 (octave); 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 9:5 (m7); 9:8 (M2); 15:8 (M7); 16:15 (m2); 45:32 (A4) *Note that 5*45-7*32=1= 5*10-7*7 *The exact ranking of consonance among the intervals is not fully agreed on.<ref>https://kb.osu.edu/bitstream/handle/1811/24077/1/EMR000007a-mashinter.pdf</ref> <score sound="1" lang="lilypond">\language "english" {\set Staff.midiInstrument = #"reed organ" \tempo "" 4 = 40 \time 15/4 \hide Staff.TimeSignature <c' g'> <c' f'> <c' a'> <c' e'> <c' ef'> <c' af'> <c' fs'>2 <c' af'>4 <c' ef'> <c' e'> <c' a'> <c' f'> <c' g'>} \addlyrics{"P5" "P4" "M6" "M3" "m3" "m6" "TT" "m6" "m3" "M3" "M6" "P4" "P5"} </score> ==List== [[w:List of pitch intervals]] --- [[w:Interval_(music)#Size_of_intervals_used_in_different_tuning_systems]] --- [[w:Pythagorean_tuning]] --- [[w:Music_and_mathematics]] -- [[w:Musical_temperament]] ===new=== [[Sing_free/List_of_musical_intervals_(ear_training)]] ==Links== *https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/ <gallery> File:Major_triad.svg </gallery> '''<big>[https://trainer.thetamusic.com/en/content/html5-harmonic-intervals check this out!!!]</big>''' *[[Sing free]] [[Draft:Sing free/Tables and images]] ===intervals=== [[File:Intervals.png|thumb|429x429px|All dyads within an octave on C. {{audio|Intervals.mid|Play}}]] == 4s2u6s9hrruuu57t16v4iy8idc1fr3a 2412457 2412456 2022-08-07T02:18:48Z Guy vandegrift 813252 /* Links */ wikitext text/x-wiki '''Physics of music''', or ''[[w:Musical acoustics|musical acoustics]]'' is an effort to understand music from a scientific point of view. Here the goal is to understand musical consonance and dissonance using basic concepts. ===Sound waves and frequency=== <gallery mode="packed" heights="150px" style="text-align:left"> File:Drum vibration mode01.gif|Sound is created by a moving object, like this membrane. To create sound that humans can hear, the membrane will typically make hundreds of vibrations each second. File:CPT-sound-physical-manifestation.svg|Regions of air compression and [[wikt:rarefraction|rarefraction]] move at the "[[w:simple:Speed of sound|speed of sound]]". The sine wave illustrates the variation in air density. File:Sound wave physics.gif|The pressure fluctuations of a travelling sound wave can be graphed as a function of either distance or time (click image to expand). </gallery> {| class="wikitable floatright" !Other ways to<br> to say <u>hertz</u> |- |inverse-seconds |- |cycles per second |- |cps |} ==wikitable== {| class="wikitable floatright" style="text-align:center"; |+ 8 consonant intervals |- ! rank !! name !! half<br>tones!!ratio |- | 1 || P1 (unison) || 0 || 1/1 |- | 2 || P8 (octave) || 12 || 2/1 |- | 3 || P5 (fifth) || 7 || 3/2 |- | 4 || P4 (fourth) || 5 || 4/3 |- | 5 || M6 (maj 6th) || 9 || 5/3 |- | 6 || M3 (maj 3rd) || 4 || 5/4 |- | 7 || m6 (min 6th) || 8 || 8/5 |- | 8 || m3 (min 3rd) || 3 || 6/5 |} ==Terminology== The words used to describe something often depend on who is speaking, and things can get tricky when musicians and scientists are involved. The '''pitch''' of a musical note is measured by it's '''frequency''', or the number of cycles that occur each second. While musicians often refer to a notes pitch by a number (e.g., "440A"), scientists and engineers prefer to attach units to everything (e.g., "440 Hertz" or simply: 440Hz). One "Hertz" is defined as one cycle per second. The term '''[[wikt:musical interval|musical interval]]''' can refer to the difference between two pitches. [[w:Encyclopædia Britannica|Encyclopædia Britannica]] distinguishes between the '''melodic interval''' (two consecutive notes played consecutively), and the '''harmonic interval'''<ref>https://www.google.com/search?q=musical+interval+meaning&rlz=1C1CHBF_enUS1007US1007&oq=musical+interval+meaning&aqs=chrome..69i57j0i15i22i30j0i22i30l3j0i15i22i30j0i22i30j0i15i22i30j0i390l2.5708j0j7&sourceid=chrome&ie=UTF-8</ref><ref>https://www.britannica.com/art/interval-music</ref> (two pitches played simultaneously). While one is allowed to refer interval as a chord, calling it an "harmonic interval" precisely states that we are talking about <u>two pitches sounded at the same time</u>. An excellent alternative to "harmonic interval" would be to call it a '''[[w:Dyad (music)| dyad]]'''.<ref>[[Wiktionary:dyad]] informs us that "dyad" is a general-purpose word for "two things".</ref> An important distinction between different intervals is '''consonance''' versus '''dissonance''', which might be expressed as a distinction between ''smoothness'' and ''roughness''. By no means is dissonance "bad". In his Ninth Symphony, Beethoven famously interrupts an extremely dissonant passage by a singer who announces Ode to Joy with these words: ::Oh friends, not these sounds! ::Let us instead strike up more pleasing ::and more joyful ones! These terms are not always absolute: While some might argue that the [[w:Tritone|tritone]] is consonant, all would agree that it is more dissonant than the established consonant intervals. ==Stackexchange ranking== *[https://music.stackexchange.com/questions/46509/what-is-the-list-of-intervals-in-order-of-dissonance stackexchange] ranked them as follows: 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 1:1 (unison); 2:1 (octave); 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 9:5 (m7); 9:8 (M2); 15:8 (M7); 16:15 (m2); 45:32 (A4) *Note that 5*45-7*32=1= 5*10-7*7 *The exact ranking of consonance among the intervals is not fully agreed on.<ref>https://kb.osu.edu/bitstream/handle/1811/24077/1/EMR000007a-mashinter.pdf</ref> <score sound="1" lang="lilypond">\language "english" {\set Staff.midiInstrument = #"reed organ" \tempo "" 4 = 40 \time 15/4 \hide Staff.TimeSignature <c' g'> <c' f'> <c' a'> <c' e'> <c' ef'> <c' af'> <c' fs'>2 <c' af'>4 <c' ef'> <c' e'> <c' a'> <c' f'> <c' g'>} \addlyrics{"P5" "P4" "M6" "M3" "m3" "m6" "TT" "m6" "m3" "M3" "M6" "P4" "P5"} </score> ==List== [[w:List of pitch intervals]] --- [[w:Interval_(music)#Size_of_intervals_used_in_different_tuning_systems]] --- [[w:Pythagorean_tuning]] --- [[w:Music_and_mathematics]] -- [[w:Musical_temperament]] ===new=== [[Sing_free/List_of_musical_intervals_(ear_training)]] ==Links== *https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/ Lott and Stone: Perception of musical consonance and dissonance: an outcome of neural synchronization <gallery> File:Major_triad.svg </gallery> '''<big>[https://trainer.thetamusic.com/en/content/html5-harmonic-intervals check this out!!!]</big>''' *[[Sing free]] [[Draft:Sing free/Tables and images]] ===intervals=== [[File:Intervals.png|thumb|429x429px|All dyads within an octave on C. {{audio|Intervals.mid|Play}}]] == dkqamf70b1atlmcx2hj7dycwj0a3aws 2412459 2412457 2022-08-07T02:29:14Z Guy vandegrift 813252 /* Links */ wikitext text/x-wiki '''Physics of music''', or ''[[w:Musical acoustics|musical acoustics]]'' is an effort to understand music from a scientific point of view. Here the goal is to understand musical consonance and dissonance using basic concepts. ===Sound waves and frequency=== <gallery mode="packed" heights="150px" style="text-align:left"> File:Drum vibration mode01.gif|Sound is created by a moving object, like this membrane. To create sound that humans can hear, the membrane will typically make hundreds of vibrations each second. File:CPT-sound-physical-manifestation.svg|Regions of air compression and [[wikt:rarefraction|rarefraction]] move at the "[[w:simple:Speed of sound|speed of sound]]". The sine wave illustrates the variation in air density. File:Sound wave physics.gif|The pressure fluctuations of a travelling sound wave can be graphed as a function of either distance or time (click image to expand). </gallery> {| class="wikitable floatright" !Other ways to<br> to say <u>hertz</u> |- |inverse-seconds |- |cycles per second |- |cps |} ==wikitable== {| class="wikitable floatright" style="text-align:center"; |+ 8 consonant intervals |- ! rank !! name !! half<br>tones!!ratio |- | 1 || P1 (unison) || 0 || 1/1 |- | 2 || P8 (octave) || 12 || 2/1 |- | 3 || P5 (fifth) || 7 || 3/2 |- | 4 || P4 (fourth) || 5 || 4/3 |- | 5 || M6 (maj 6th) || 9 || 5/3 |- | 6 || M3 (maj 3rd) || 4 || 5/4 |- | 7 || m6 (min 6th) || 8 || 8/5 |- | 8 || m3 (min 3rd) || 3 || 6/5 |} ==Terminology== The words used to describe something often depend on who is speaking, and things can get tricky when musicians and scientists are involved. The '''pitch''' of a musical note is measured by it's '''frequency''', or the number of cycles that occur each second. While musicians often refer to a notes pitch by a number (e.g., "440A"), scientists and engineers prefer to attach units to everything (e.g., "440 Hertz" or simply: 440Hz). One "Hertz" is defined as one cycle per second. The term '''[[wikt:musical interval|musical interval]]''' can refer to the difference between two pitches. [[w:Encyclopædia Britannica|Encyclopædia Britannica]] distinguishes between the '''melodic interval''' (two consecutive notes played consecutively), and the '''harmonic interval'''<ref>https://www.google.com/search?q=musical+interval+meaning&rlz=1C1CHBF_enUS1007US1007&oq=musical+interval+meaning&aqs=chrome..69i57j0i15i22i30j0i22i30l3j0i15i22i30j0i22i30j0i15i22i30j0i390l2.5708j0j7&sourceid=chrome&ie=UTF-8</ref><ref>https://www.britannica.com/art/interval-music</ref> (two pitches played simultaneously). While one is allowed to refer interval as a chord, calling it an "harmonic interval" precisely states that we are talking about <u>two pitches sounded at the same time</u>. An excellent alternative to "harmonic interval" would be to call it a '''[[w:Dyad (music)| dyad]]'''.<ref>[[Wiktionary:dyad]] informs us that "dyad" is a general-purpose word for "two things".</ref> An important distinction between different intervals is '''consonance''' versus '''dissonance''', which might be expressed as a distinction between ''smoothness'' and ''roughness''. By no means is dissonance "bad". In his Ninth Symphony, Beethoven famously interrupts an extremely dissonant passage by a singer who announces Ode to Joy with these words: ::Oh friends, not these sounds! ::Let us instead strike up more pleasing ::and more joyful ones! These terms are not always absolute: While some might argue that the [[w:Tritone|tritone]] is consonant, all would agree that it is more dissonant than the established consonant intervals. ==Stackexchange ranking== *[https://music.stackexchange.com/questions/46509/what-is-the-list-of-intervals-in-order-of-dissonance stackexchange] ranked them as follows: 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 1:1 (unison); 2:1 (octave); 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 9:5 (m7); 9:8 (M2); 15:8 (M7); 16:15 (m2); 45:32 (A4) *Note that 5*45-7*32=1= 5*10-7*7 *The exact ranking of consonance among the intervals is not fully agreed on.<ref>https://kb.osu.edu/bitstream/handle/1811/24077/1/EMR000007a-mashinter.pdf</ref> <score sound="1" lang="lilypond">\language "english" {\set Staff.midiInstrument = #"reed organ" \tempo "" 4 = 40 \time 15/4 \hide Staff.TimeSignature <c' g'> <c' f'> <c' a'> <c' e'> <c' ef'> <c' af'> <c' fs'>2 <c' af'>4 <c' ef'> <c' e'> <c' a'> <c' f'> <c' g'>} \addlyrics{"P5" "P4" "M6" "M3" "m3" "m6" "TT" "m6" "m3" "M3" "M6" "P4" "P5"} </score> ==List== [[w:List of pitch intervals]] --- [[w:Interval_(music)#Size_of_intervals_used_in_different_tuning_systems]] --- [[w:Pythagorean_tuning]] --- [[w:Music_and_mathematics]] -- [[w:Musical_temperament]] ===new=== [[Sing_free/List_of_musical_intervals_(ear_training)]] ==Links== *https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/ Lott and Stone: Perception of musical consonance and dissonance: an outcome of neural synchronization *https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00381/full Computational Approach to Musical Consonance and Dissonance Lluis L. Trulla1, Nicola Di Stefano and Alessandro Giuliani THIS ONE LOOKS ESSENTIAL TO MY EFFORTS <gallery> File:Major_triad.svg </gallery> '''<big>[https://trainer.thetamusic.com/en/content/html5-harmonic-intervals check this out!!!]</big>''' *[[Sing free]] [[Draft:Sing free/Tables and images]] ===intervals=== [[File:Intervals.png|thumb|429x429px|All dyads within an octave on C. {{audio|Intervals.mid|Play}}]] == 2ik21e6211fybe1641t93kovdpcghnj 2412465 2412459 2022-08-07T02:48:28Z Guy vandegrift 813252 /* Links */ wikitext text/x-wiki '''Physics of music''', or ''[[w:Musical acoustics|musical acoustics]]'' is an effort to understand music from a scientific point of view. Here the goal is to understand musical consonance and dissonance using basic concepts. ===Sound waves and frequency=== <gallery mode="packed" heights="150px" style="text-align:left"> File:Drum vibration mode01.gif|Sound is created by a moving object, like this membrane. To create sound that humans can hear, the membrane will typically make hundreds of vibrations each second. File:CPT-sound-physical-manifestation.svg|Regions of air compression and [[wikt:rarefraction|rarefraction]] move at the "[[w:simple:Speed of sound|speed of sound]]". The sine wave illustrates the variation in air density. File:Sound wave physics.gif|The pressure fluctuations of a travelling sound wave can be graphed as a function of either distance or time (click image to expand). </gallery> {| class="wikitable floatright" !Other ways to<br> to say <u>hertz</u> |- |inverse-seconds |- |cycles per second |- |cps |} ==wikitable== {| class="wikitable floatright" style="text-align:center"; |+ 8 consonant intervals |- ! rank !! name !! half<br>tones!!ratio |- | 1 || P1 (unison) || 0 || 1/1 |- | 2 || P8 (octave) || 12 || 2/1 |- | 3 || P5 (fifth) || 7 || 3/2 |- | 4 || P4 (fourth) || 5 || 4/3 |- | 5 || M6 (maj 6th) || 9 || 5/3 |- | 6 || M3 (maj 3rd) || 4 || 5/4 |- | 7 || m6 (min 6th) || 8 || 8/5 |- | 8 || m3 (min 3rd) || 3 || 6/5 |} ==Terminology== The words used to describe something often depend on who is speaking, and things can get tricky when musicians and scientists are involved. The '''pitch''' of a musical note is measured by it's '''frequency''', or the number of cycles that occur each second. While musicians often refer to a notes pitch by a number (e.g., "440A"), scientists and engineers prefer to attach units to everything (e.g., "440 Hertz" or simply: 440Hz). One "Hertz" is defined as one cycle per second. The term '''[[wikt:musical interval|musical interval]]''' can refer to the difference between two pitches. [[w:Encyclopædia Britannica|Encyclopædia Britannica]] distinguishes between the '''melodic interval''' (two consecutive notes played consecutively), and the '''harmonic interval'''<ref>https://www.google.com/search?q=musical+interval+meaning&rlz=1C1CHBF_enUS1007US1007&oq=musical+interval+meaning&aqs=chrome..69i57j0i15i22i30j0i22i30l3j0i15i22i30j0i22i30j0i15i22i30j0i390l2.5708j0j7&sourceid=chrome&ie=UTF-8</ref><ref>https://www.britannica.com/art/interval-music</ref> (two pitches played simultaneously). While one is allowed to refer interval as a chord, calling it an "harmonic interval" precisely states that we are talking about <u>two pitches sounded at the same time</u>. An excellent alternative to "harmonic interval" would be to call it a '''[[w:Dyad (music)| dyad]]'''.<ref>[[Wiktionary:dyad]] informs us that "dyad" is a general-purpose word for "two things".</ref> An important distinction between different intervals is '''consonance''' versus '''dissonance''', which might be expressed as a distinction between ''smoothness'' and ''roughness''. By no means is dissonance "bad". In his Ninth Symphony, Beethoven famously interrupts an extremely dissonant passage by a singer who announces Ode to Joy with these words: ::Oh friends, not these sounds! ::Let us instead strike up more pleasing ::and more joyful ones! These terms are not always absolute: While some might argue that the [[w:Tritone|tritone]] is consonant, all would agree that it is more dissonant than the established consonant intervals. ==Stackexchange ranking== *[https://music.stackexchange.com/questions/46509/what-is-the-list-of-intervals-in-order-of-dissonance stackexchange] ranked them as follows: 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 1:1 (unison); 2:1 (octave); 3:2 (P5); 4:3 (P4); 5:3 (M6); 5:4 (M3); 6:5 (m3); 8:5 (m6); 9:5 (m7); 9:8 (M2); 15:8 (M7); 16:15 (m2); 45:32 (A4) *Note that 5*45-7*32=1= 5*10-7*7 *The exact ranking of consonance among the intervals is not fully agreed on.<ref>https://kb.osu.edu/bitstream/handle/1811/24077/1/EMR000007a-mashinter.pdf</ref> <score sound="1" lang="lilypond">\language "english" {\set Staff.midiInstrument = #"reed organ" \tempo "" 4 = 40 \time 15/4 \hide Staff.TimeSignature <c' g'> <c' f'> <c' a'> <c' e'> <c' ef'> <c' af'> <c' fs'>2 <c' af'>4 <c' ef'> <c' e'> <c' a'> <c' f'> <c' g'>} \addlyrics{"P5" "P4" "M6" "M3" "m3" "m6" "TT" "m6" "m3" "M3" "M6" "P4" "P5"} </score> ==List== [[w:List of pitch intervals]] --- [[w:Interval_(music)#Size_of_intervals_used_in_different_tuning_systems]] --- [[w:Pythagorean_tuning]] --- [[w:Music_and_mathematics]] -- [[w:Musical_temperament]] ===new=== [[Sing_free/List_of_musical_intervals_(ear_training)]] <gallery> File:Major_triad.svg </gallery> '''<big>[https://trainer.thetamusic.com/en/content/html5-harmonic-intervals check this out!!!]</big>''' *[[Sing free]] [[Draft:Sing free/Tables and images]] ===intervals=== [[File:Intervals.png|thumb|429x429px|All dyads within an octave on C. {{audio|Intervals.mid|Play}}]] == 9ji5k71qulblxjexv21avl89z9bkfq6 0 285380 2412351 2412120 2022-08-06T13:37:46Z Young1lim 21186 /* Handling Series of Data */ wikitext text/x-wiki === Introduction === * Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]]) * Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]]) * Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]]) === Handling Repetition === * Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]]) * Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]]) === Handling a Big Work === * Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]]) * Functions & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]]) === Handling Series of Data === ==== Background ==== * Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]]) ==== Basics ==== * Arrays ([[Media:C04.Series1.Array.1.A.20220805.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]]) * Pointers ([[Media:C04.Series2.Pointer.1.A.20180726.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]]) * Array Pointers ([[Media:C04.Series3.ArrayPointer.1.A.20220805.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20220418.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.11.pdf |B.pdf]]) * Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]]) ==== Applications ==== * Applications of Arrays ([[Media:C04.Series1App.Array.1.A.20220805.pdf |A.pdf]]) * Applications of Pointers ([[Media:C04.Series7.AppPoint.1.A.20200424.pdf |A.pdf]]) * Applications of Array Pointers ([[Media:C04.Series3App.ArrayPointer.1.A.2022024.pdf |A.pdf]]) * Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]]) * Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]]) * Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]]) ==== Examples ==== * Spreadsheet Example Programs :: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]]) :: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]]) :: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]]) :: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]]) === Handling Various Kinds of Data === * Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]]) * Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]]) * Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]]) * Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]]) === Handling Low Level Operations === * Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]]) * Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]]) * Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]]) * Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]]) === Declarations === * Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]]) * Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]]) * Scope === Class Notes === * TOC ([[Media:TOC.20171007.pdf |TOC.pdf]]) * Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library * Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements * Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers * Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts * Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops * Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control * Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions * Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope * Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion * Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions * Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications * Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions * Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications * Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) * Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2) * Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO * Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions * Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications * Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum * Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List * Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing * Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing <!----------------------------------------------------------------------> </br> See also https://cprogramex.wordpress.com/ == '''Old Materials '''== until 201201 * Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]]) * Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]]) * Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]]) * Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]]) * Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]]) * Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]]) * Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]]) * Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]]) * Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]]) * Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]]) * Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]]) * Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]]) * Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]]) <br> until 201107 * Intro.1.A ([[Media:Intro.1.A.pdf |pdf]]) * Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]]) * Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]]) * Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]]) * Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]]) * Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]]) * Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]]) * Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]]) * Array.1.A ([[Media:Array.1.A.pdf |pdf]]) * Type.1.A ([[Media:Type.1.A.pdf |pdf]]) * Structure.1.A ([[Media:Structure.1.A.pdf |pdf]]) go to [ [[C programming in plain view]] ] [[Category:C programming]] </br> nutqdsklaj2nwrvej4gqplur7y8yadm 2412355 2412351 2022-08-06T13:41:14Z Young1lim 21186 /* Handling Series of Data */ wikitext text/x-wiki === Introduction === * Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]]) * Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]]) * Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]]) === Handling Repetition === * Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]]) * Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]]) === Handling a Big Work === * Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]]) * Functions & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]]) === Handling Series of Data === ==== Background ==== * Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]]) ==== Basics ==== * Arrays ([[Media:C04.Series1.Array.1.A.20220806.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]]) * Pointers ([[Media:C04.Series2.Pointer.1.A.20180726.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]]) * Array Pointers ([[Media:C04.Series3.ArrayPointer.1.A.20220806.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20220418.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.11.pdf |B.pdf]]) * Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]]) ==== Applications ==== * Applications of Arrays ([[Media:C04.Series1App.Array.1.A.20220806.pdf |A.pdf]]) * Applications of Pointers ([[Media:C04.Series7.AppPoint.1.A.20200424.pdf |A.pdf]]) * Applications of Array Pointers ([[Media:C04.Series3App.ArrayPointer.1.A.2022024.pdf |A.pdf]]) * Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]]) * Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]]) * Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]]) ==== Examples ==== * Spreadsheet Example Programs :: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]]) :: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]]) :: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]]) :: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]]) === Handling Various Kinds of Data === * Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]]) * Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]]) * Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]]) * Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]]) === Handling Low Level Operations === * Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]]) * Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]]) * Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]]) * Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]]) === Declarations === * Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]]) * Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]]) * Scope === Class Notes === * TOC ([[Media:TOC.20171007.pdf |TOC.pdf]]) * Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library * Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements * Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers * Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts * Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops * Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control * Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions * Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope * Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion * Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions * Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications * Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions * Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications * Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) * Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2) * Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO * Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions * Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications * Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum * Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List * Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing * Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing <!----------------------------------------------------------------------> </br> See also https://cprogramex.wordpress.com/ == '''Old Materials '''== until 201201 * Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]]) * Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]]) * Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]]) * Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]]) * Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]]) * Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]]) * Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]]) * Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]]) * Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]]) * Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]]) * Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]]) * Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]]) * Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]]) <br> until 201107 * Intro.1.A ([[Media:Intro.1.A.pdf |pdf]]) * Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]]) * Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]]) * Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]]) * Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]]) * Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]]) * Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]]) * Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]]) * Array.1.A ([[Media:Array.1.A.pdf |pdf]]) * Type.1.A ([[Media:Type.1.A.pdf |pdf]]) * Structure.1.A ([[Media:Structure.1.A.pdf |pdf]]) go to [ [[C programming in plain view]] ] [[Category:C programming]] </br> 8z5pva3damnjeib49t0n44wvmv12xq2 0 285385 2412422 2412278 2022-08-06T22:29:50Z Young1lim 21186 /* Object Files */ wikitext text/x-wiki === Executable and Linkable Format === ==== Object Files ==== * Introduction * ELF Header ([[Media:ELF1.1B.Header.20220211.pdf |pdf]]) * Group section ([[Media:ELF1.1C.Group.20220426.pdf |pdf]]) * String table section ([[Media:ELF1.1D.StringTbl.20220427.pdf |pdf]]) * Weak and common symbols ([[Media:ELF1.1E.WeakComm.20220806.pdf |pdf]]) * Symbol table section ([[Media:ELF1.1F.SymbolTbl.20220722.pdf |pdf]]) * Special Sections ([[Media:ELF1.7B.Section.20200511.pdf |B.pdf]]) * Relocation ([[Media:ELF1.6A.Relocation.20190413.pdf |A.pdf]]) ==== Program Loading and Dynamic Linking ==== * Introduction * Program Header ([[Media:ELF1.2B.ProgHeader.20220110.pdf |pdf]]) * Program Loading * Dynamic Linking ([[Media:ELF2.4A.DynLinking.20191028.pdf |pdf]]) ==== C Library ==== * C Library === ELF Study === ==== ELF Relocations ==== * Linking ([[Media:ELF1.7A.Linking.20200731.pdf |A.pdf]]) * Loading ([[Media:ELF1.7B.Loading.20201103.pdf |B.pdf]]) * Executing ([[Media:ELF1.7C.Executing.20201221.pdf |C.pdf]]) * Virtual Memory ([[Media:ELF2.1D.VMemory.20211227.pdf |D.pdf]]) * PIC Method ([[Media:ELF1.7B.PICMethod.20200417.pdf |C.pdf]]) * Design Cycles ([[Media:ELF1.7C.DesignCycle.20200317.pdf |D.pdf]]) * Relocs in i386 ([[Media:ELF1.7D.Reloc386.20200413.pdf |E.pdf]]) ==== Relocation Examples ==== * Relocs example introduction ([[Media:ELF1.7Ex.1Intro.20200109.pdf |E1.pdf]]) * Relocs in an object for a library ([[Media:ELF1.7Ex.2ObjectRel.20200319.pdf |E2.pdf]]) * Relocs in an object for an executable ([[Media:ELF1.7Ex.3ObjectMain.20200118.pdf |E3.pdf]]) * Relocs in a library ([[Media:ELF1.7Ex.4Library.20200320.pdf |E4.pdf]]) * Relocs in an executable ([[Media:ELF1.7Ex.5Executable.20200228.pdf |E5.pdf]]) * Result Summary ([[Media:ELF1.7Ex.6Result.20200121.pdf |E6.pdf]]) * Symbol Table Listing ([[Media:ELF1.7Ex.7Symbol.20200120.pdf |E7.pdf]]) * Relocs Listing ([[Media:ELF1.7Ex.8Relocs.20200121.pdf |E8.pdf]]) * Assembly Listing ([[Media:ELF1.7Ex.9Assembly.20200128.pdf |E9.pdf]]) * Reloc Experiments ([[Media:ELF1.7F.Experiments.20191206.pdf |F.pdf]]) </br> go to [ [[C programming in plain view]] ] [[Category:C programming]] jjbeyj54qtgr0wprwku8xc77qhplh5v 0 285677 2412400 2412150 2022-08-06T19:49:45Z ThaniosAkro 2805358 /* Right hand side positive */ wikitext text/x-wiki =Congruences= The subject of congruences is a field of mathematics that covers the integers, their relationship to each other and also the effect of arithmetic operations on their relationship to each other. Expressed mathematically: :<math>A \equiv B \pmod{N}</math> read as: A is congruent with B modulo N. {{RoundBoxTop|theme=2}} <math>A,B,N</math> are integers and <math>N > 1.</math> {{RoundBoxBottom}} This means that: * A modulo N equals B modulo N, * the difference, A-B, is exactly divisible by N, or * <math>A-B = K\cdot N.</math> where p modulo N or <code>p % N</code> is the remainder when p is divided by N. For example: <math>23 \equiv 8 \pmod{5}</math> because division <math>\frac{23-8}{5}</math> is exact without remainder, or <math>5\mid (23-8).</math> Similarly, <math>39 \not\equiv 29 \,\pmod{7}</math> because division <math>\frac{39-29}{7}</math> is not exact, or <math>7\nmid (39-29).</math> ==Law of addition== ===Adding a constant=== {{RoundBoxTop|theme=2}} If <math>A \equiv B \pmod{N}, </math> then: <math>A+q \equiv B+q \pmod{N}.</math> Proof: <math>A-B = K\cdot N</math>, therefore <math>A = B + K\cdot N.</math> <math>(A+q) - (B+q) = B + K\cdot N + q - B - q = K\cdot N</math> which is exactly divisible by N. {{RoundBoxBottom}} ===Adding 2 congruences=== {{RoundBoxTop|theme=2}} If <math>A \equiv B \pmod{N}, </math> and <math>C \equiv D \pmod{N}, </math> then: <math>A+C \equiv B+D \pmod{N}.</math> Proof: <math>A-B = K_1\cdot N</math>, therefore <math>A = B + K_1\cdot N</math> and <math>C = D + K_2\cdot N</math> <math>(A+C) - (B+D)</math> <math>= B + K_1\cdot N + D + K_2\cdot N - B - D</math> <math>= N(K_1 + K_2)</math> which is exactly divisible by N. {{RoundBoxBottom}} ==Law of Common Congruence== {{RoundBoxTop|theme=2}} If <math>A \equiv B \pmod{N} </math> and <math>C \equiv B \pmod{N},</math> then: <math>A \equiv C \pmod{N}.</math> Proof: <math>A = B + K_1\cdot N</math> and <math>C = B + K_2\cdot N.</math> <math>A - C = B + K_1\cdot N - B - K_2\cdot N = (K_1 - K_2)N</math> which is exactly divisible by N. {{RoundBoxBottom}} ==Law of Multiplication== ===by a constant=== {{RoundBoxTop|theme=2}} If <math>A \equiv B \pmod{N} </math> then: <math>A\cdot p \equiv B\cdot p \pmod{N}.</math> Proof: <math>A\cdot p - B\cdot p = p(A-B)</math> which is exactly divisible by N. {{RoundBoxBottom}} ===by another congruence=== {{RoundBoxTop|theme=2}} If <math>A \equiv B \pmod{N} </math> and <math>C \equiv D \pmod{N},</math> then: <math>A\cdot C \equiv B\cdot D \pmod{N}.</math> Proof: <math>A = B + K_1\cdot N</math> and <math>C = D + K_2\cdot N.</math> <math>A\cdot C - B\cdot D</math> <math>= (B + K_1\cdot N)( D + K_2\cdot N) - B\cdot D</math> <math>= B\cdot D + B\cdot K_2\cdot N + K_1\cdot N\cdot D + K_1\cdot N\cdot K_2\cdot N - B\cdot D</math> <math>= N( B\cdot K_2 + K_1\cdot D + K_1\cdot K_2\cdot N )</math> which is exactly divisible by N. {{RoundBoxBottom}} ==Law of squares== {{RoundBoxTop|theme=2}} If <math>A \equiv B \pmod{N} </math> then: <math>A^2 \equiv B^2 \pmod{N}.</math> Proof: <math>A^2 - B^2 = (A+B)(A-B)</math> which is exactly divisible by N. {{RoundBoxBottom}} ==Law of Division?== {{RoundBoxTop|theme=2}} A simple example shows that a "law of division" does not exist. <math>24 \equiv 14 \pmod{10}.</math> However <math>\frac{24}{2} \not\equiv \frac{14}{2} \pmod{10}</math> Because <math>12 - 7 = 5</math> is not exactly divisible by <math>10</math> {{RoundBoxBottom}} =Quadratic Congruences= A quadratic congruence is a congruence that contains at least one exact square, for example: <math>x^2 \equiv y \pmod{N}</math> or <math>x^2 \equiv y^2 \pmod{N}.</math> Initially, let us consider the congruence: <math>x^2 \equiv y \pmod{N}.</math> If <math>y = x^2 - N,</math> then: <math>x^2 \equiv y \pmod{N}.</math> Proof: <math>x^2 - y = x^2 - (x^2 - N) = N</math> which is exactly divisible by <math>N.</math> Consider an example with real numbers. Let <math>N = 257</math> and <math>26 \ge x \ge 6.</math> <syntaxhighlight> N = 257 x | x^2 - N ----|-------- 6 | -221 7 | -208 8 | -193 9 | -176 10 | -157 11 | -136 12 | -113 13 | -88 14 | -61 15 | -32 16 | -1 17 | 32 18 | 67 19 | 104 20 | 143 21 | 184 22 | 227 23 | 272 24 | 319 25 | 368 26 | 419 </syntaxhighlight> A cursory glance at the values of <math>x^2 - N</math> indicates that the value <math>x^2 - N</math> is never divisible by <math>5.</math> Proof: <math>N \equiv 2 \pmod{5}</math> therefore <math>N - 2 = k5</math> or <math>N = 5k + 2.</math> The table shows all possible values of <math>x\ %\ 5:</math> <syntaxhighlight> x | x^2 | y = x^2 - N ------ | --------------- | ----------------------------------------------- 5p + 0 | 25pp | 25pp - (5k+2) = 25pp - 5k - 2 5p + 1 | 25pp + 10p + 1 | 25pp + 10p + 1 - (5k+2) = 25pp + 10p - 5k - 1 5p + 2 | 25pp + 20p + 4 | 25pp + 20p + 4 - (5k+2) = 25pp + 20p - 5k + 2 5p + 3 | 25pp + 30p + 9 | 25pp + 30p + 9 - (5k+2) = 25pp + 30p - 5k + 7 5p + 4 | 25pp + 40p + 16 | 25pp + 40p + 16 - (5k+2) = 25pp + 40p - 5k + 14 </syntaxhighlight> As you can see, the value <math>y = x^2 - N</math> is never exactly divisible by <math>5.</math> If you look closely, you will see also that it is never exactly divisible by <math>3.</math> Why is this? An interesting question that leads us to the topic of quadratic residues. ==Quadratic Residues== Consider all the congruences for prime number <math>5:</math> <math>x^2 \equiv y \pmod{5}</math> for <math>5 > x \ge 0.</math> <syntaxhighlight> x | x^2 | (x^2) % 5 ---|---------|----------- 0 | 0 | 0 1 | 1 | 1 2 | 4 | 4 3 | 9 | 4 4 | 16 | 1 </syntaxhighlight> Quadratic residues of <math>5</math> are <math>0,1,4.</math> Values <math>2,3</math> are not quadratic residues of <math>5.</math> These values are quadratic non-residues. To calculate the quadratic residues of a small prime <math>p:</math> <syntaxhighlight lang=python> # python code: def quadResidues(p) : L1 = [] for v in range (p>>1, -1, -1) : L1 += [(v*v) % p] return L1 print (quadResidues(11)) </syntaxhighlight> <syntaxhighlight> [3, 5, 9, 4, 1, 0] </syntaxhighlight> Quadratic residues of <math>11</math> are <math>0,1,3,4,5,9.</math> The method presented here answers the question, "What are the quadratic residues of p?" If <math>p</math> is a very large prime, the question is often, "Is r a quadratic residue of p?" The answer is found in advanced number theory. Let us return to quadratic residues mod <math>N = 257.</math> <math>N\ %\ 5 = 2,</math> therefore <math>N</math> is not a quadratic residue of <math>5.</math> This is why <math>x^2 - N</math> is never divisible by <math>5</math> exactly. <math>N\ %\ 11 = 4,</math> therefore <math>N</math> is a quadratic residue of <math>11</math> and a value of <math>x</math> that satisfies the congruence <math>x^2 \equiv 4 \pmod{257}</math> has form <math>11p \pm 2.</math> From the table above: <syntaxhighlight> N = 257 x | x^2 - N ----|-------- 9 | -176 13 | -88 20 | 143 24 | 319 </syntaxhighlight> These <math>4</math> values of <math>x^2 - N</math> are exactly divisible by <math>11.</math> <math>x = 9</math> is <math>11\cdot 1 - 2.</math> <math>x = 13</math> is <math>11\cdot 1 + 2.</math> <math>x = 20</math> is <math>11\cdot 2 - 2.</math> <math>x = 24</math> is <math>11\cdot 2 + 2.</math> ===Products=== This section uses prime number <math>41</math> as an example. Using <code>quadResidues(p)</code> quadratic residues of <math>41</math> are: <syntaxhighlight> qr41 = [0, 1, 2, 4, 5, 8, 9, 10, 16, 18, 20, 21, 23, 25, 31, 32, 33, 36, 37, 39, 40] </syntaxhighlight> Quadratic non-residues of <math>41</math> are: <syntaxhighlight> qnr41 = [3, 6, 7, 11, 12, 13, 14, 15, 17, 19, 22, 24, 26, 27, 28, 29, 30, 34, 35, 38] </syntaxhighlight> ====of 2 residues==== A simple test to verify that the product of 2 residues is a residue: <syntaxhighlight lang=python> # Python code. for index1 in range (0, len(qr41)) : v1 = qr41[index1] for index2 in range (index1, len(qr41)) : v2 = qr41[index2] residue = (v1*v2) % 41 if residue not in qr41 : print ('residue',residue,'not quadratic.') </syntaxhighlight> This test shows that, at least for prime number <math>41,</math> the product of 2 residues is a residue. Advanced math proves that this is true for all primes. ====of 2 non-residues==== A simple test to verify that the product of 2 non-residues is a residue: <syntaxhighlight lang=python> # Python code. for index1 in range (0, len(qnr41)) : v1 = qnr41[index1] for index2 in range (index1, len(qnr41)) : v2 = qnr41[index2] residue = (v1*v2) % 41 if residue not in qr41 : print ('residue',residue,'not quadratic.') </syntaxhighlight> This test shows that, at least for prime number <math>41,</math> the product of 2 non-residues is a residue. Advanced math proves that this is true for all primes. ====of residue and non-residue==== A simple test to verify that the product of residue and non-residue is non-residue: <syntaxhighlight lang=python> # Python code. for index1 in range (1, len(qr41)) : v1 = qr41[index1] for index2 in range (0, len(qnr41)) : v2 = qnr41[index2] residue = (v1*v2) % 41 if residue not in qnr41 : print ('residue',residue,'quadratic.') </syntaxhighlight> This test shows that, at least for prime number <math>41,</math> the product of residue and non-residue is non-residue. Advanced math proves that this is true for all primes. {{RoundBoxTop|theme=2}} Some authors may consider <math>0</math> as not a legitimate residue. <math>0</math> is not included as a residue in the test above. {{RoundBoxBottom}} ==Euler's criterion== In number theory, '''Euler's criterion''' is a formula for determining whether or not an integer is a quadratic residue modulo a prime number. Precisely, Let ''p'' be an odd prime and ''a'' be an integer coprime to ''p''. Then :<math> a^{\tfrac{p-1}{2}} \equiv \begin{cases} \;\;\,1\pmod{p}& \text{ if there is an integer }x \text{ such that }a\equiv x^2 \pmod{p},\\ -1\pmod{p}& \text{ if there is no such integer.} \end{cases} </math> Euler's criterion can be concisely reformulated using the Legendre symbol: :<math> \left(\frac{a}{p}\right) \equiv a^{\tfrac{p-1}{2}} \pmod p. </math> :<math>\left(\frac{a}{p}\right) = \begin{cases} 1 & \text{if } a \text{ is a quadratic residue modulo } p \text{ and } a \not\equiv 0\pmod p, \\ -1 & \text{if } a \text{ is a non-quadratic residue modulo } p, \\ 0 & \text{if } a \equiv 0 \pmod p. \end{cases}</math> It is known that <math>3</math> is a quadratic residue modulo <math>11.</math> Therefore <math>(3^5)\ %\ 11</math> should be <math>1.</math> <syntaxhighlight lang=python> # python code: >>> (3**5) % 11 1 </syntaxhighlight> It is known that <math>7</math> is a quadratic non-residue modulo <math>11.</math> Therefore <math>(7^5)\ %\ 11</math> should be <math>-1.</math> <syntaxhighlight lang=python> # python code: >>> (7**5) % 11 10 </syntaxhighlight> :<math>10 \equiv -1 \pmod{11}</math> Python's decimal module provides a method for computing <math>(a^x)\ %\ p</math> very efficiently for both small and very large numbers. <syntaxhighlight lang=python> # python code: >>> import decimal >>> decimal.Context().power(3,5,11) Decimal('1') >>> decimal.Context().power(7,5,11) Decimal('10') >>> >>> a = 3456789 >>> p = 761838257287 >>> decimal.Context().power(a, p>>1, p) Decimal('761838257286') </syntaxhighlight> :<math>761838257286 \equiv -1 \pmod{761838257287}</math> Value <math>a = 3456789</math> is not a quadratic residue modulo <math>p = 761838257287.</math> {{RoundBoxTop|theme=3}} An exact square such as <math>1,4,9,16,25,\dots</math> is always a quadratic residue modulo an odd prime <math>p.</math> {{RoundBoxBottom}} ===Product of 2 residues=== Let <math>a,b</math> be quadratic residues modulo odd prime <math>p.</math> Let <math>q = \frac{p-1}{2}.</math> Then: <math>a^q \equiv 1 \pmod p</math> <math>b^q \equiv 1 \pmod p</math> By law of multiplication: <math>(a^q)(b^q) \equiv (1)(1) \pmod p</math> or <math>(a\cdot b)^q \equiv 1 \pmod p</math> Product <math>(a\cdot b)</math> of 2 quadratic residues <math>a, b</math> is quadratic residue. Similarly, product of 2 non-residues is residue, and product of residue and non-residue is non-residue. ==Factors of integer N== Several modern methods for determining the factors of a given integer attempt to create two congruent squares modulo integer <math>N.</math> <math>x^2 \equiv y^2 \pmod{N}</math> This means that the difference between the two squares is exactly divisible by <math>N</math>: <math>N\mid (x^2 - y^2).</math> Integer <math>N</math> always contains the factors <math>N,1,</math> called trivial factors. If <math>N</math> contains two non-trivial factors <math>p,q,</math> then: <math>\frac{(x+y)(x-y)}{p \cdot q}.</math> With a little luck <math>p\mid (x+y)</math> and <math>q\mid (x-y)</math> in which case: <math>p = \text{igcd}(x+y, N)</math> and <math>q = \text{igcd}(x-y, N)</math> where "<math>\text{igcd}</math>" is function "<math>\text{integer greatest common divisor.}</math>" ===A simple example:=== We will use quadratic congruences to calculate factors of <math>N = 4171</math> for <math>164 \ge x \ge 1.</math> ====Right hand side exact square==== One congruence produced an exact square for y: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 70 | 4900 | 729 |} :<math>4900 \equiv 729 \pmod{N}</math> :<math>70^2 \equiv 27^2 \pmod{N}</math> <math>p = \text{igcd}(70-27, 4171)</math> <math>= \text{igcd}(43, 4171)</math> <math>= 43.</math> <math>q = \text{igcd}(70+27, 4171)</math> <math>= \text{igcd}(97, 4171)</math> <math>= 97.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> ====Right hand side negative==== Table below contains a sample of values of <math>x</math> that produce negative <math>y:</math> {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 7 | 49 | -4122 |- | 8 | 64 | -4107 ** |- | 9 | 81 | -4090 |- | 10 | 100 | -4071 |- | 11 | 121 | -4050 !! |- | 12 | 144 | -4027 |- | 60 | 3600 | -571 |- | 61 | 3721 | -450 <math>\ \ </math>!! |- | 62 | 3844 | -327 |- | 63 | 3969 | -202 |- | 64 | 4096 | -75 <math>\ \ \ \ </math>** |- | 65 | 4225 | 54 |} =====Non-trivial result 1===== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 8 | 64 | -4107 ** |- | 64 | 4096 | -75 <math>\ \ \ \ </math>** |} :<math>64 \equiv -4107 \pmod{N}</math> :<math>4096 \equiv -75 \pmod{N}</math> :<math>64\cdot 4096 \equiv -4107\cdot (-75) \pmod{N}</math> :<math>262144 \equiv 308025 \pmod{N}</math> :<math>512^2 \equiv 555^2 \pmod{4171}</math> <math>p = \text{igcd}(555-512, 4171)</math> <math>= \text{igcd}(43, 4171)</math> <math>= 43.</math> <math>q = \text{igcd}(555+512, 4171)</math> <math>= \text{igcd}(1067, 4171)</math> <math>= 97.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> =====Non-trivial result 2===== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 11 | 121 | -4050 !! |- | 61 | 3721 | -450 <math>\ \ </math>!! |} :<math>121 \equiv -4050 \pmod{N}</math> :<math>3721 \equiv -450 \pmod{N}</math> :<math>121\cdot 3721 \equiv -4050 \cdot (-450) \pmod{N}</math> :<math>450241 \equiv 1822500 \pmod{N}</math> :<math>671^2 \equiv 1350^2 \pmod{4171}</math> <math>p = \text{igcd}(1350-671, 4171)</math> <math>= \text{igcd}(679, 4171)</math> <math>= 97.</math> <math>q = \text{igcd}(1350+671, 4171)</math> <math>= \text{igcd}(2021, 4171)</math> <math>= 43.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> ====Right hand side positive==== Table below contains a sample of values of <math>x</math> that produce positive <math>y:</math> {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 65 | 4225 | 54 <math>\ \ \ </math>** |- | 66 | 4356 | 185 |- | 88 | 7744 | 3573 |- | 89 | 7921 | 3750 **!! |- | 90 | 8100 | 3929 |- | 144 | 20736 | 16565 |- | 145 | 21025 | 16854 <math>\ </math>!! |- | 146 | 21316 | 17145 |} =====Non-trivial result===== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 65 | 4225 | 54 <math>\ \ \ </math>** |- | 89 | 7921 | 3750 **!! |} :<math>4225 \equiv 54 \pmod{N}</math> :<math>7921 \equiv 3750 \pmod{N}</math> :<math>4225\cdot 7921 \equiv 54 \cdot 3750 \pmod{N}</math> :<math>33466225 \equiv 202500 \pmod{N}</math> :<math>5785^2 \equiv 450^2 \pmod{4171}</math> <math>p = \text{igcd}(5785-450, 4171)</math> <math>= \text{igcd}(5335, 4171)</math> <math>= 97.</math> <math>q = \text{igcd}(5785+450, 4171)</math> <math>= \text{igcd}(6235, 4171)</math> <math>= 43.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> =====Trivial result===== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 89 | 7921 | 3750 **!! |- | 145 | 21025 | 16854 <math>\ </math>!! |} :<math>7921 \equiv 3750 \pmod{N}</math> :<math>21025 \equiv 16854 \pmod{N}</math> :<math>7921\cdot 21025 \equiv 3750 \cdot 16854 \pmod{N}</math> :<math>166539025 \equiv 63202500 \pmod{N}</math> :<math>12905^2 \equiv 7950^2 \pmod{4171}</math> <math>p = \text{igcd}(12905-7950, 4171)</math> <math>= \text{igcd}(4955, 4171)</math> <math>= 1.</math> <math>q = \text{igcd}(12905+7950, 4171)</math> <math>= \text{igcd}(20855, 4171)</math> <math>= 4171.</math> This congruence produced the trivial factors of <math>4171.</math> ====With 3 congruences==== The congruences: {| class="wikitable" |- ! <math>x</math> !! <math>x^2</math> !! <math>y = x^2 - N</math> |- | 56 | 3136 | -1035 |- | 59 | 3481 | -690 |- | 145 | 21025 | 16854 |} :<math>3136 \equiv -1035 \pmod{N}</math> :<math>3481 \equiv -690 \pmod{N}</math> :<math>21025 \equiv 16854 \pmod{N}</math> :<math>3136\cdot 3481 \cdot 21025 \equiv -1035 \cdot -690 \cdot 16854 \pmod{N}</math> :<math>229517646400 \equiv 12036284100 \pmod{N}</math> :<math>479080^2 \equiv 109710^2 \pmod{4171}</math> <math>p=\text{igcd}(479080-109710,4171)</math> <math>= 43.</math> <math>q = \text{igcd}(479080+109710, 4171)</math> <math>= 97.</math> Non-trivial factors of <math>4171</math> are <math>43,97.</math> =Links to related topics= [https://en.wikipedia.org/wiki/Quadratic_residue Quadratic Residue] [https://en.wikipedia.org/wiki/Modular_arithmetic Modular Arithmetic] [https://en.wikipedia.org/wiki/Leonhard_Euler Leonhard Euler,] [https://en.wikipedia.org/wiki/Euler%27s_criterion Euler's Criterion] [https://en.wikipedia.org/wiki/Adrien-Marie_Legendre Adrien-Marie Legendre,] [https://en.wikipedia.org/wiki/Legendre_symbol Legendre Symbol] [https://en.wikipedia.org/wiki/Carl_Pomerance Carl Pomerance,] [https://en.wikipedia.org/wiki/Quadratic_sieve Quadratic sieve] [https://docs.python.org/3.4/library/decimal.html?highlight=decimal#module-decimal Python's decimal Module] bv00cakfxm0aloja12n52fdn3tck57y 0 285721 2412363 2411289 2022-08-06T13:47:00Z Guy vandegrift 813252 wikitext text/x-wiki [[File:Factorization flowchart.svg|thumb|420px|Flowchart for a simple prime factorization code]] '''Topics covered:''' ''prime factorization, flowcharts, python dictionaries'' Here we learn how a [[Python Concepts/Dictionaries|python dictionary]] can help express an integer as a [[w:Integer factorization|product of prime numbers]]. There are a few things the student should know about the code we are about to examine: * A serious python programmer would instead download a package that gives you a function that performs prime factorization. Two promising candidates are [https://pypi.org/project/primefac/ pypi.org/project/primefac] and [https://www.sympy.org/en/index.html www.sympy.org/]. * A simpler version of this same program does not use the "dictionary",<ref>Outside of Python a "dictionary" is also called an [[w:Associative array]].</ref> and can be found at [[Wikipedia:Trial division#Method]].<ref>A working python script is at [[w:Special:Permalink/1086485306]]</ref>. * Lacking the mental wherewithal to seize upon either of these opportunities, I googled "python prime factorization", found many codes, and selected the [[#Python code|one we shall examine]] for two reasons:<ref>The code that follows is discussed at [https://stackoverflow.com/questions/15347174/python-finding-prime-factors stackoverflow question 15347174] and [https://scientific-python-101.readthedocs.io/_downloads/prime_factorization_solution.py scientific-python-101.readthedocs]</ref> :# I wanted a code that counts repeated factors in order to later write the factored form in wikitext with exponents.<ref>In the wikitext version, I had to add a few lines so that exponents of 1 would not appear. Example: <math>12=2^2\cdot 3^1</math> should instead read <math>12=2^2\cdot 3.</math> I ommitted the feature here in order to keep the lesson simple.</ref> :# I didn't understand the python code, and wanted master it in order to fully understand how python dictionaries are used. A good student exercise would be to modify this code so that it runs approximately twice as fast. This is accomplished by considering only odd number in the search for prime factors of N.<ref>All prime numbers are odd, except for 2</ref> The table below illustrates the present version of the code's "wasted" efforts to see if 4 and 6 might be prime factors of 1550. The table also illustrates the efficiency of dividing a candidate integer into the number <math>n</math>, which soon becomes much smaller than <math>N.</math> It took only eight (8) steps to factor {{math|1550}} into prime numbers. {| class="wikitable" style="text-align: center; vertical-align: bottom;" |+ <math>\text{Establishing } 1550=2\cdot 5^2 \cdot 31</math> |- ! n ! k ! k^2 ! k^2<n? ! n/k ! mod ! replace ! factor ! * |- | 1550 | 2 | 4 | TRUE | 775 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"|n: n/k | style="background:#ffffcc"|2 | |- | 775 | 2 | 4 | TRUE | 387 | 1 | k: k+1 | | |- | 775 | 3 | 9 | TRUE | 258 | 1 | k: k+1 | | |- | 775 | 4 | 16 | TRUE | 193 | 3 | k: k+1 | | |- | 775 | 5 | 25 | TRUE | 155 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"| n: n/k | style="background:#ffffcc"| 5 | |- | 155 | 5 | 25 | TRUE | 31 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"| n: n/k | style="background:#ffffcc"| 5 | |- | 31 | 5 | 25 | TRUE | 6 | 1 | k: k+1 | | |- | 31 | 6 | 36 | FALSE | - | - | - | | style="background:#ffffcc"| 31 |} ==Python code== ‎<syntaxhighlight lang="python" line="1"> ## In a python code, the function definitions precede the code. We need only 1 function: def prime_factorization(N): ## 12=(2**2)*(2**1)*(5**1), or equivalently, 12 = 2**2 * 3 * 5 ## The dictionary, dict, expresses k**v as a "key-value" pair. In other ## words, if we look up the key, k=5, the dictionary will return the ## value, v=1. In other words: ## k**v <=> key**value <=> base**exponent (for the factored form of N) ## Begin function: n=N #--------------------# n will change in the while loop (getting smaller.) dict = {} #--------------# Start with an empty dictionary if n==1: #---------------# The factorization of 1 is a special case. return {1: 1} # In other words 1 = 1**1 (but recall that 1 is not prime.) k = 2 #------------------# Our first candidate for factorizing any integer. while k**2 <= n: #-------# Do the following unless k is "too big": if n % k: #----------# . Equivalent to: "If k is not a factor of n:" k += 1 #---------# .. increase the value of k by 1 on next attempt. else: #--------------# . Equivalent to "If k is a factor of n:" n /= k #---------# .. Replace n by n/k (for next attempt) try: #-----------# .. If k is in the dictionary, this attempts to: dict[k] += 1 # ... increase the value of k by 1. except KeyError: # .. KeyError occurs if k is not in the dictionary dict[k] = 1 # ... Add k to dictionary and set exponent v=1 # end(while)#------------# (exits while k**2 <= n:) if n > 1: #--------------# It can be shown that n is either 1 or prime. try: #---------------# . Try to enter n into dictionary dict[n] += 1 #---# .. increase exponent v->v+1 if k in dictinary except KeyError: #---# . If n is not in the dictionary, dict[n] = 1 # .. then enter n into dictionary with v=1 return dict #------# python talk for ending function ################ End def prime_factorization | Begin program ########## #import sys again=True while again == 1: text="\nEnter a positive integer you wish to factor into prime numbers:\n" N=int(input(text)) dict=prime_factorization(N) print("\n"+str(int(N))+"=") text="(" for b in dict.keys(): text+=str(int(b))+"**"+str(int(dict.get(b)))+") * (" print(text.rstrip(" * (")+"\n") print("The dictionary is:\n") print(dict) again=int(input("\nType 1 for another integer, 0 to terminate.")) </syntaxhighlight> With one extra line a print command will display the dictionary. From the fact that python decided to print {{math|31}} as {{math|31.0}}, we know that this dictionary is taking the keys (2, 5, 31) to be floating point numbers. Python permits such a casual attitude regarding the mixing number types.<ref>"Casualness", I believe, lies at the heart of pythonic philosophy. </ref> This makes it easier to program python, but perhaps more difficult to sort out such misunderstandings after the program has been written. print(dict) {2: 1, 5: 2, 31.0: 1} ===Comments=== =====Line 15: while k**2 <= n:===== This is an important line because it permits the termination of the search before one might think. I leave it as an exercise for the student to learn why any value of k larger than square root of n will never be the next factor of N. It is also left to the student to understand the fact that the time to find the factors can be cut nearly in half if we modify line 17 and increase k by 2 (instead of 1), and why this larger step cannot be taken until after k=2 has been considered. ====Lines in the code that might seem confusing==== The code uses two cleverness tricks that might seem confusing. I lack the formal training in programming to know whether such cleverness would be perceived as a flaw. I know that programmers are allowed to be clever, and I know that clear programs are better than confusing programs. The fact that these tricks confused me does not necessarily mean they should be avoided. And the nice thing about both sources of confusion is that they taught me something about python. =====Line 16: if n%k might seem backwards===== Python follows a common practice of interpreting the number 1 to be True and 0 to be False. But python also accepts any non-zero number as True. Here n%k denotes nmod&nbsp;k, which is the remainder when on divides n by k. If there is no remainder the "if" condition is not satisfied and the code stipulates that the next value of k is attempted. Any number not equal to zero is interpreted as the "if" condition being satisfied, meaning that k is a divisor of n (in that case, we replace n by n/k.) This might be good coding, but it seems to me that it would have been better to construct it along the lines of "if n%k == 0" or even "if n%k !=0". =====Lines 21-23 and 29-31: A failed attempt to change the value of a key===== In this code fragment, we ask if a given value of k has already been identified as a factor. But instead of "asking" if k has been declared a key in the dictionary, an <u>attempt</u> is made to change the value of k. If that attempt fails (because k is not among the dictionary's keys), then k is added to the list of keys, with a value of 1 (a value of 1 indicates that at this point, k, but not k² has been established to be a factor of n.) Again, there might be nothing wrong with using a key error like this. But the code would have been easier for me to follow if the if statement simply called the question of whether k was a key in dict. ==Sample output with a large number== Sometimes you have to wait a few minutes to factor a number this large. But usually it comes out in just a few seconds. I would imagine that a number that was the product of only two roughly equal prime numbers would take forever because k=k+1 must be repeated a virtually infinite number of times. This number came quickly: {{Font color|blue|Enter a positive integer you wish to factor into prime numbers:}} 99283428376482768916467328912876456416375474272263423467896879187289499287374899 &nbsp; <span style="color:blue>99283428376482768916467328912876456416375474272263423467896879187289499287374899=</span> {{Font color|blue|(619**1) * (688**1) * (768**3) * (1024**17) * (64853**1) * (5302548928**1)}} &nbsp; {{Font color|blue|The dictionary is:}} &nbsp; <span style="color:blue>{619: 1, 688: 1, 768: 3, 1024: 17, 64853: 1, 5302548928.0: 1}</span> &nbsp; {{Font color|blue|Type 1 for another integer, 0 to terminate.}} {{center|'''DO NOT TRY TO FACTOR A NUMBER THIS LARGE UNLESS YOU ARE WILLING TO INTERUPT YOUR PYTHON PROGRAM.'''}} {{center|Keep in mind that the universe is only about <math>4.4\times10^{26}\text{nanoseconds}</math> old.<ref>http://astronomy.nmsu.edu/geas/lectures/lecture02/slide04.html</ref>}} The number shown rounds up to 10⁸⁰. It is not likely that any computer will ever count that high. If the number to be factored consists of two prime number that are close to 10⁸⁰, the code will iterate all the way up to k coming close to 10⁴⁰. The inability of any computer to perform that many iterations helps explain how cryptocurrency works. The owner of cryptocurrency can all information to be made public by posting something with the properties of the product of two very large prime numbers. The product is made public and anybody with knowledge of one of the products can claim ownership of the funds. On the other hand, if you lose that information, nobody on earth can retrieve it for you. &nbsp; cxel5cuh2on7z2ln8si212e45cp35kg 2412364 2412363 2022-08-06T13:50:23Z Guy vandegrift 813252 wikitext text/x-wiki [[File:Factorization flowchart.svg|thumb|420px|Flowchart for a simple prime factorization code]] '''Topics covered:''' ''prime factorization, flowcharts, python dictionaries'' Here we learn how a [[Python Concepts/Dictionaries|python dictionary]] can help express an integer as a [[w:Integer factorization|product of prime numbers]]. There are two things the student should know about the code we are about to examine: * A serious python programmer would instead download a package that already has a function for prime factorization. Two promising candidates are [https://pypi.org/project/primefac/ pypi.org/project/primefac] and [https://www.sympy.org/en/index.html www.sympy.org/]. * A simpler version of this same program does not use the python dictionary.<ref>Outside of Python a "dictionary" is also called an [[w:Associative array]].</ref> It can be found at [[Wikipedia:Trial division#Method]].<ref>A working python script is at [[w:Special:Permalink/1086485306]]</ref>. * * * Lacking the mental wherewithal to seize upon either of these opportunities, I googled "python prime factorization", found many codes, and selected the [[#Python code|one we shall examine]] for two reasons:<ref>The code that follows is discussed at [https://stackoverflow.com/questions/15347174/python-finding-prime-factors stackoverflow question 15347174] and [https://scientific-python-101.readthedocs.io/_downloads/prime_factorization_solution.py scientific-python-101.readthedocs]</ref> :# I wanted a code that counts repeated factors in order to later write the factored form in wikitext with exponents.<ref>In the wikitext version, I had to add a few lines so that exponents of 1 would not appear. Example: <math>12=2^2\cdot 3^1</math> should instead read <math>12=2^2\cdot 3.</math> I ommitted the feature here in order to keep the lesson simple.</ref> :# I didn't understand the python code, and wanted master it in order to fully understand how python dictionaries are used. A good student exercise would be to modify this code so that it runs approximately twice as fast. This is accomplished by considering only odd number in the search for prime factors of N.<ref>All prime numbers are odd, except for 2</ref> The table below illustrates the present version of the code's "wasted" efforts to see if 4 and 6 might be prime factors of 1550. The table also illustrates the efficiency of dividing a candidate integer into the number <math>n</math>, which soon becomes much smaller than <math>N.</math> It took only eight (8) steps to factor {{math|1550}} into prime numbers. {| class="wikitable" style="text-align: center; vertical-align: bottom;" |+ <math>\text{Establishing } 1550=2\cdot 5^2 \cdot 31</math> |- ! n ! k ! k^2 ! k^2<n? ! n/k ! mod ! replace ! factor ! * |- | 1550 | 2 | 4 | TRUE | 775 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"|n: n/k | style="background:#ffffcc"|2 | |- | 775 | 2 | 4 | TRUE | 387 | 1 | k: k+1 | | |- | 775 | 3 | 9 | TRUE | 258 | 1 | k: k+1 | | |- | 775 | 4 | 16 | TRUE | 193 | 3 | k: k+1 | | |- | 775 | 5 | 25 | TRUE | 155 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"| n: n/k | style="background:#ffffcc"| 5 | |- | 155 | 5 | 25 | TRUE | 31 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"| n: n/k | style="background:#ffffcc"| 5 | |- | 31 | 5 | 25 | TRUE | 6 | 1 | k: k+1 | | |- | 31 | 6 | 36 | FALSE | - | - | - | | style="background:#ffffcc"| 31 |} ==Python code== ‎<syntaxhighlight lang="python" line="1"> ## In a python code, the function definitions precede the code. We need only 1 function: def prime_factorization(N): ## 12=(2**2)*(2**1)*(5**1), or equivalently, 12 = 2**2 * 3 * 5 ## The dictionary, dict, expresses k**v as a "key-value" pair. In other ## words, if we look up the key, k=5, the dictionary will return the ## value, v=1. In other words: ## k**v <=> key**value <=> base**exponent (for the factored form of N) ## Begin function: n=N #--------------------# n will change in the while loop (getting smaller.) dict = {} #--------------# Start with an empty dictionary if n==1: #---------------# The factorization of 1 is a special case. return {1: 1} # In other words 1 = 1**1 (but recall that 1 is not prime.) k = 2 #------------------# Our first candidate for factorizing any integer. while k**2 <= n: #-------# Do the following unless k is "too big": if n % k: #----------# . Equivalent to: "If k is not a factor of n:" k += 1 #---------# .. increase the value of k by 1 on next attempt. else: #--------------# . Equivalent to "If k is a factor of n:" n /= k #---------# .. Replace n by n/k (for next attempt) try: #-----------# .. If k is in the dictionary, this attempts to: dict[k] += 1 # ... increase the value of k by 1. except KeyError: # .. KeyError occurs if k is not in the dictionary dict[k] = 1 # ... Add k to dictionary and set exponent v=1 # end(while)#------------# (exits while k**2 <= n:) if n > 1: #--------------# It can be shown that n is either 1 or prime. try: #---------------# . Try to enter n into dictionary dict[n] += 1 #---# .. increase exponent v->v+1 if k in dictinary except KeyError: #---# . If n is not in the dictionary, dict[n] = 1 # .. then enter n into dictionary with v=1 return dict #------# python talk for ending function ################ End def prime_factorization | Begin program ########## #import sys again=True while again == 1: text="\nEnter a positive integer you wish to factor into prime numbers:\n" N=int(input(text)) dict=prime_factorization(N) print("\n"+str(int(N))+"=") text="(" for b in dict.keys(): text+=str(int(b))+"**"+str(int(dict.get(b)))+") * (" print(text.rstrip(" * (")+"\n") print("The dictionary is:\n") print(dict) again=int(input("\nType 1 for another integer, 0 to terminate.")) </syntaxhighlight> With one extra line a print command will display the dictionary. From the fact that python decided to print {{math|31}} as {{math|31.0}}, we know that this dictionary is taking the keys (2, 5, 31) to be floating point numbers. Python permits such a casual attitude regarding the mixing number types.<ref>"Casualness", I believe, lies at the heart of pythonic philosophy. </ref> This makes it easier to program python, but perhaps more difficult to sort out such misunderstandings after the program has been written. print(dict) {2: 1, 5: 2, 31.0: 1} ===Comments=== =====Line 15: while k**2 <= n:===== This is an important line because it permits the termination of the search before one might think. I leave it as an exercise for the student to learn why any value of k larger than square root of n will never be the next factor of N. It is also left to the student to understand the fact that the time to find the factors can be cut nearly in half if we modify line 17 and increase k by 2 (instead of 1), and why this larger step cannot be taken until after k=2 has been considered. ====Lines in the code that might seem confusing==== The code uses two cleverness tricks that might seem confusing. I lack the formal training in programming to know whether such cleverness would be perceived as a flaw. I know that programmers are allowed to be clever, and I know that clear programs are better than confusing programs. The fact that these tricks confused me does not necessarily mean they should be avoided. And the nice thing about both sources of confusion is that they taught me something about python. =====Line 16: if n%k might seem backwards===== Python follows a common practice of interpreting the number 1 to be True and 0 to be False. But python also accepts any non-zero number as True. Here n%k denotes nmod&nbsp;k, which is the remainder when on divides n by k. If there is no remainder the "if" condition is not satisfied and the code stipulates that the next value of k is attempted. Any number not equal to zero is interpreted as the "if" condition being satisfied, meaning that k is a divisor of n (in that case, we replace n by n/k.) This might be good coding, but it seems to me that it would have been better to construct it along the lines of "if n%k == 0" or even "if n%k !=0". =====Lines 21-23 and 29-31: A failed attempt to change the value of a key===== In this code fragment, we ask if a given value of k has already been identified as a factor. But instead of "asking" if k has been declared a key in the dictionary, an <u>attempt</u> is made to change the value of k. If that attempt fails (because k is not among the dictionary's keys), then k is added to the list of keys, with a value of 1 (a value of 1 indicates that at this point, k, but not k² has been established to be a factor of n.) Again, there might be nothing wrong with using a key error like this. But the code would have been easier for me to follow if the if statement simply called the question of whether k was a key in dict. ==Sample output with a large number== Sometimes you have to wait a few minutes to factor a number this large. But usually it comes out in just a few seconds. I would imagine that a number that was the product of only two roughly equal prime numbers would take forever because k=k+1 must be repeated a virtually infinite number of times. This number came quickly: {{Font color|blue|Enter a positive integer you wish to factor into prime numbers:}} 99283428376482768916467328912876456416375474272263423467896879187289499287374899 &nbsp; <span style="color:blue>99283428376482768916467328912876456416375474272263423467896879187289499287374899=</span> {{Font color|blue|(619**1) * (688**1) * (768**3) * (1024**17) * (64853**1) * (5302548928**1)}} &nbsp; {{Font color|blue|The dictionary is:}} &nbsp; <span style="color:blue>{619: 1, 688: 1, 768: 3, 1024: 17, 64853: 1, 5302548928.0: 1}</span> &nbsp; {{Font color|blue|Type 1 for another integer, 0 to terminate.}} {{center|'''DO NOT TRY TO FACTOR A NUMBER THIS LARGE UNLESS YOU ARE WILLING TO INTERUPT YOUR PYTHON PROGRAM.'''}} {{center|Keep in mind that the universe is only about <math>4.4\times10^{26}\text{nanoseconds}</math> old.<ref>http://astronomy.nmsu.edu/geas/lectures/lecture02/slide04.html</ref>}} The number shown rounds up to 10⁸⁰. It is not likely that any computer will ever count that high. If the number to be factored consists of two prime number that are close to 10⁸⁰, the code will iterate all the way up to k coming close to 10⁴⁰. The inability of any computer to perform that many iterations helps explain how cryptocurrency works. The owner of cryptocurrency can all information to be made public by posting something with the properties of the product of two very large prime numbers. The product is made public and anybody with knowledge of one of the products can claim ownership of the funds. On the other hand, if you lose that information, nobody on earth can retrieve it for you. &nbsp; 3bvud4r33b2iqn7jz62vk484cbqe7ul 2412365 2412364 2022-08-06T13:53:03Z Guy vandegrift 813252 wikitext text/x-wiki [[File:Factorization flowchart.svg|thumb|420px|Flowchart for a simple prime factorization code]] '''Topics covered:''' ''prime factorization, flowcharts, python dictionaries'' Here we learn how a [[Python Concepts/Dictionaries|python dictionary]] can help express an integer as a [[w:Integer factorization|product of prime numbers]]. There are two things the student should know about the code we are about to examine: * A serious python programmer would instead download a package that already has a function for prime factorization. Two promising candidates are [https://pypi.org/project/primefac/ pypi.org/project/primefac] and [https://www.sympy.org/en/index.html www.sympy.org/]. * A simpler version of this same program does not use the python dictionary.<ref>Outside of Python a "dictionary" is also called an [[w:Associative array]].</ref> It can be found at [[Wikipedia:Trial division#Method]].<ref>A working python script is at [[w:Special:Permalink/1086485306]]</ref>. Lacking the wherewithal to seize upon either of these opportunities, I googled "python prime factorization", found many<ref>I suspect that the abundance of such codes is the result of so many educators tasking students with writing a code that performs prime factorization.</ref> codes, and selected the [[#Python code|one we shall examine]] for two reasons:<ref>The code that follows is discussed at [https://stackoverflow.com/questions/15347174/python-finding-prime-factors stackoverflow question 15347174] and [https://scientific-python-101.readthedocs.io/_downloads/prime_factorization_solution.py scientific-python-101.readthedocs]</ref> :# I wanted a code that counts repeated factors in order to later write the factored form in wikitext with exponents.<ref>In the wikitext version, I had to add a few lines so that exponents of 1 would not appear. Example: <math>12=2^2\cdot 3^1</math> should instead read <math>12=2^2\cdot 3.</math> I ommitted the feature here in order to keep the lesson simple.</ref> :# I didn't understand the python code, and wanted master it in order to fully understand how python dictionaries are used. A good student exercise would be to modify this code so that it runs approximately twice as fast. This is accomplished by considering only odd number in the search for prime factors of N.<ref>All prime numbers are odd, except for 2</ref> The table below illustrates the present version of the code's "wasted" efforts to see if 4 and 6 might be prime factors of 1550. The table also illustrates the efficiency of dividing a candidate integer into the number <math>n</math>, which soon becomes much smaller than <math>N.</math> It took only eight (8) steps to factor {{math|1550}} into prime numbers. {| class="wikitable" style="text-align: center; vertical-align: bottom;" |+ <math>\text{Establishing } 1550=2\cdot 5^2 \cdot 31</math> |- ! n ! k ! k^2 ! k^2<n? ! n/k ! mod ! replace ! factor ! * |- | 1550 | 2 | 4 | TRUE | 775 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"|n: n/k | style="background:#ffffcc"|2 | |- | 775 | 2 | 4 | TRUE | 387 | 1 | k: k+1 | | |- | 775 | 3 | 9 | TRUE | 258 | 1 | k: k+1 | | |- | 775 | 4 | 16 | TRUE | 193 | 3 | k: k+1 | | |- | 775 | 5 | 25 | TRUE | 155 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"| n: n/k | style="background:#ffffcc"| 5 | |- | 155 | 5 | 25 | TRUE | 31 | style="background:#ffffcc"| '''0''' | style="background:#ffffcc"| n: n/k | style="background:#ffffcc"| 5 | |- | 31 | 5 | 25 | TRUE | 6 | 1 | k: k+1 | | |- | 31 | 6 | 36 | FALSE | - | - | - | | style="background:#ffffcc"| 31 |} ==Python code== ‎<syntaxhighlight lang="python" line="1"> ## In a python code, the function definitions precede the code. We need only 1 function: def prime_factorization(N): ## 12=(2**2)*(2**1)*(5**1), or equivalently, 12 = 2**2 * 3 * 5 ## The dictionary, dict, expresses k**v as a "key-value" pair. In other ## words, if we look up the key, k=5, the dictionary will return the ## value, v=1. In other words: ## k**v <=> key**value <=> base**exponent (for the factored form of N) ## Begin function: n=N #--------------------# n will change in the while loop (getting smaller.) dict = {} #--------------# Start with an empty dictionary if n==1: #---------------# The factorization of 1 is a special case. return {1: 1} # In other words 1 = 1**1 (but recall that 1 is not prime.) k = 2 #------------------# Our first candidate for factorizing any integer. while k**2 <= n: #-------# Do the following unless k is "too big": if n % k: #----------# . Equivalent to: "If k is not a factor of n:" k += 1 #---------# .. increase the value of k by 1 on next attempt. else: #--------------# . Equivalent to "If k is a factor of n:" n /= k #---------# .. Replace n by n/k (for next attempt) try: #-----------# .. If k is in the dictionary, this attempts to: dict[k] += 1 # ... increase the value of k by 1. except KeyError: # .. KeyError occurs if k is not in the dictionary dict[k] = 1 # ... Add k to dictionary and set exponent v=1 # end(while)#------------# (exits while k**2 <= n:) if n > 1: #--------------# It can be shown that n is either 1 or prime. try: #---------------# . Try to enter n into dictionary dict[n] += 1 #---# .. increase exponent v->v+1 if k in dictinary except KeyError: #---# . If n is not in the dictionary, dict[n] = 1 # .. then enter n into dictionary with v=1 return dict #------# python talk for ending function ################ End def prime_factorization | Begin program ########## #import sys again=True while again == 1: text="\nEnter a positive integer you wish to factor into prime numbers:\n" N=int(input(text)) dict=prime_factorization(N) print("\n"+str(int(N))+"=") text="(" for b in dict.keys(): text+=str(int(b))+"**"+str(int(dict.get(b)))+") * (" print(text.rstrip(" * (")+"\n") print("The dictionary is:\n") print(dict) again=int(input("\nType 1 for another integer, 0 to terminate.")) </syntaxhighlight> With one extra line a print command will display the dictionary. From the fact that python decided to print {{math|31}} as {{math|31.0}}, we know that this dictionary is taking the keys (2, 5, 31) to be floating point numbers. Python permits such a casual attitude regarding the mixing number types.<ref>"Casualness", I believe, lies at the heart of pythonic philosophy. </ref> This makes it easier to program python, but perhaps more difficult to sort out such misunderstandings after the program has been written. print(dict) {2: 1, 5: 2, 31.0: 1} ===Comments=== =====Line 15: while k**2 <= n:===== This is an important line because it permits the termination of the search before one might think. I leave it as an exercise for the student to learn why any value of k larger than square root of n will never be the next factor of N. It is also left to the student to understand the fact that the time to find the factors can be cut nearly in half if we modify line 17 and increase k by 2 (instead of 1), and why this larger step cannot be taken until after k=2 has been considered. ====Lines in the code that might seem confusing==== The code uses two cleverness tricks that might seem confusing. I lack the formal training in programming to know whether such cleverness would be perceived as a flaw. I know that programmers are allowed to be clever, and I know that clear programs are better than confusing programs. The fact that these tricks confused me does not necessarily mean they should be avoided. And the nice thing about both sources of confusion is that they taught me something about python. =====Line 16: if n%k might seem backwards===== Python follows a common practice of interpreting the number 1 to be True and 0 to be False. But python also accepts any non-zero number as True. Here n%k denotes nmod&nbsp;k, which is the remainder when on divides n by k. If there is no remainder the "if" condition is not satisfied and the code stipulates that the next value of k is attempted. Any number not equal to zero is interpreted as the "if" condition being satisfied, meaning that k is a divisor of n (in that case, we replace n by n/k.) This might be good coding, but it seems to me that it would have been better to construct it along the lines of "if n%k == 0" or even "if n%k !=0". =====Lines 21-23 and 29-31: A failed attempt to change the value of a key===== In this code fragment, we ask if a given value of k has already been identified as a factor. But instead of "asking" if k has been declared a key in the dictionary, an <u>attempt</u> is made to change the value of k. If that attempt fails (because k is not among the dictionary's keys), then k is added to the list of keys, with a value of 1 (a value of 1 indicates that at this point, k, but not k² has been established to be a factor of n.) Again, there might be nothing wrong with using a key error like this. But the code would have been easier for me to follow if the if statement simply called the question of whether k was a key in dict. ==Sample output with a large number== Sometimes you have to wait a few minutes to factor a number this large. But usually it comes out in just a few seconds. I would imagine that a number that was the product of only two roughly equal prime numbers would take forever because k=k+1 must be repeated a virtually infinite number of times. This number came quickly: {{Font color|blue|Enter a positive integer you wish to factor into prime numbers:}} 99283428376482768916467328912876456416375474272263423467896879187289499287374899 &nbsp; <span style="color:blue>99283428376482768916467328912876456416375474272263423467896879187289499287374899=</span> {{Font color|blue|(619**1) * (688**1) * (768**3) * (1024**17) * (64853**1) * (5302548928**1)}} &nbsp; {{Font color|blue|The dictionary is:}} &nbsp; <span style="color:blue>{619: 1, 688: 1, 768: 3, 1024: 17, 64853: 1, 5302548928.0: 1}</span> &nbsp; {{Font color|blue|Type 1 for another integer, 0 to terminate.}} {{center|'''DO NOT TRY TO FACTOR A NUMBER THIS LARGE UNLESS YOU ARE WILLING TO INTERUPT YOUR PYTHON PROGRAM.'''}} {{center|Keep in mind that the universe is only about <math>4.4\times10^{26}\text{nanoseconds}</math> old.<ref>http://astronomy.nmsu.edu/geas/lectures/lecture02/slide04.html</ref>}} The number shown rounds up to 10⁸⁰. It is not likely that any computer will ever count that high. If the number to be factored consists of two prime number that are close to 10⁸⁰, the code will iterate all the way up to k coming close to 10⁴⁰. The inability of any computer to perform that many iterations helps explain how cryptocurrency works. The owner of cryptocurrency can all information to be made public by posting something with the properties of the product of two very large prime numbers. The product is made public and anybody with knowledge of one of the products can claim ownership of the funds. On the other hand, if you lose that information, nobody on earth can retrieve it for you. &nbsp; csjgcmtbc5wvscc5n3x2ihbx7va8ckk 2 285833 2412407 2410589 2022-08-06T20:43:04Z Jtwsaddress42 234843 wikitext text/x-wiki * {{cite AV media | last= Agre | first= Peter | year= 2003 | title= Aquaporin Water Channels (Nobel Lecture) | publisher= Nobel Prize | medium= Recorded December 8, 2003, Aula Magna, Stockholm University | publication-date= December 8, 2003 | url= https://www.nobelprize.org/prizes/chemistry/2003/agre/lecture/ }} [[File:High-contrast-camera-video.svg|24px|video]] (0:45:27) * {{cite journal | last= Agre | first= Peter | year= 2004 | title= Aquaporin Water Channels (Nobel Lecture) | journal= Angewandte Chemie International Edition | volume= 43 | number= 33| pages= 4278-4290 | publication-date= August 13, 2004| pmid= 15368374 | doi= 10.1002/anie.200460804 | url= https://www.nobelprize.org/uploads/2018/06/agre-lecture.pdf }} * {{cite journal | last1= Agre | first1= P. | last2= Preston | first2= G.M. | last3= Smith | first3= B.L. | last4= Jung | first4= J.S. | last5= Raina | first5= S. | last6= Moon | first6= C. | last7= Guggino | first7= W.B. | last8= Nielson | first8= S. | year= 1993 | title= Aquaporin CHIP: the archetypal molecular water channel | journal= American Journal of Physiology: Renal Physiology | volume= 265 | number= 4 | pages= F463-F476 | publication-date= October 1, 1993 | pmid= 7694481 | doi= 10.1152/ajprenal.1993.265.4.F463 | url= https://journals.physiology.org/doi/abs/10.1152/ajprenal.1993.265.4.F463 }} ac8srd89wzeyfbojb20uokzn3aoqosn 2412413 2412407 2022-08-06T21:03:18Z Jtwsaddress42 234843 wikitext text/x-wiki * {{cite AV media | last= Agre | first= Peter | year= 2003 | title= Aquaporin Water Channels (Nobel Lecture) | publisher= Nobel Prize | medium= Recorded December 8, 2003, Aula Magna, Stockholm University | publication-date= December 8, 2003 | url= https://www.nobelprize.org/prizes/chemistry/2003/agre/lecture/ }} [[File:High-contrast-camera-video.svg|24px|video]] (0:45:27) * {{cite journal | last= Agre | first= Peter | year= 2004 | title= Aquaporin Water Channels (Nobel Lecture) | journal= Angewandte Chemie International Edition | volume= 43 | number= 33| pages= 4278-4290 | publication-date= August 13, 2004| pmid= 15368374 | doi= 10.1002/anie.200460804 | url= https://www.nobelprize.org/uploads/2018/06/agre-lecture.pdf }} * {{cite journal | last1= Agre | first1= Peter | last2= Preston | first2= Gregory M. | last3= Smith | first3= Barbara L. | last4= Jung | first4= Jin Sup | last5= Raina | first5= Surabhi | last6= Moon | first6= Chulso | last7= Guggino | first7= William B. | last8= Nielson | first8= Søren | year= 1993 | title= Aquaporin CHIP: the archetypal molecular water channel | journal= American Journal of Physiology: Renal Physiology | volume= 265 | number= 4 | pages= F463-F476 | publication-date= October 1, 1993 | pmid= 7694481 | doi= 10.1152/ajprenal.1993.265.4.F463 | url= https://journals.physiology.org/doi/abs/10.1152/ajprenal.1993.265.4.F463 }} du8swnskolk051hn9dzf0kn10ai1ybq 2 285834 2412409 2412061 2022-08-06T20:54:16Z Jtwsaddress42 234843 /* Axelrod, Julius (1912 - 2004) */ wikitext text/x-wiki {{RoundBoxTop|theme=3}} === [[w:Julius Axelrod|Axelrod, Julius (1912 - 2004)]] === <hr/> [[File:Axelrod01.jpg|thumb|Julius Axelrod (1912 - 2004)]] [[File:Julius Axelrod 1970.jpg|thumb|Julius Axelrod 1970]] [[File:Julius Axelrod.jpg|thumb|]] '''Notable Accomplishments''' * [https://www.nobelprize.org/prizes/medicine/1970/axelrod/facts/ The Nobel Prize in Physiology or Medicine 1970] -shared with Sir Bernard Katz and Ulf von Euler “for their discoveries concerning the humoral transmittors in the nerve terminals and the mechanism for their storage, release and inactivation.” * Catecholamine Neurotransmitters & their Metabolism <br /> <hr /> {| align= center | width= 640px |'''Biosynthesis of the Catecholamine Neurotransmitters''' [[File:Biosynthese catecholaminen.png|640px|Biosynthese catecholaminen]] <br /> |}<hr /> '''Publications''' {{User:Jtwsaddress42/Bibliography/Axelrod, Julius}} <br /><hr /> {| align= center | witdh= 640px |'''Julius Axelrod at the Blackboard''' [[File:Axelrod.jpg|640px|Julius Axelrod at the Blackboard]] <br /> |} {{RoundBoxBottom}} <hr /> 1hakmy9u8m1aso0bx89k4mhtovh73g6 2412410 2412409 2022-08-06T20:55:18Z Jtwsaddress42 234843 /* Axelrod, Julius (1912 - 2004) */ wikitext text/x-wiki {{RoundBoxTop|theme=3}} === [[w:Julius Axelrod|Axelrod, Julius (1912 - 2004)]] === <hr/> [[File:Axelrod01.jpg|thumb|Julius Axelrod (1912 - 2004)]] [[File:Julius Axelrod 1970.jpg|thumb|Julius Axelrod 1970]] [[File:Julius Axelrod.jpg|thumb|]] '''Notable Accomplishments''' * [https://www.nobelprize.org/prizes/medicine/1970/axelrod/facts/ The Nobel Prize in Physiology or Medicine 1970] -shared with Sir Bernard Katz and Ulf von Euler “for their discoveries concerning the humoral transmittors in the nerve terminals and the mechanism for their storage, release and inactivation.” * Catecholamine Neurotransmitters & their Metabolism <br /> <hr /> {| align= center | width= 640px |'''Biosynthesis of the Catecholamine Neurotransmitters''' [[File:Biosynthese catecholaminen.png|640px|Biosynthese catecholaminen]] <br /> |} <hr /> '''Publications''' {{User:Jtwsaddress42/Bibliography/Axelrod, Julius}} <br /><hr /> {| align= center | witdh= 640px |'''Julius Axelrod at the Blackboard''' [[File:Axelrod.jpg|640px|Julius Axelrod at the Blackboard]] <br /> |} {{RoundBoxBottom}} <hr /> c7f9k026w9z6ll9o4xcf93tt6vxybdz 118 286028 2412366 2412114 2022-08-06T13:56:08Z Guy vandegrift 813252 Guy vandegrift moved page [[Beat (acoustics)]] to [[Draft:Beat (acoustics)]] without leaving a redirect wikitext text/x-wiki [[Image:Beating Frequency.svg|thumb|300px|Diagram of beat frequency]] A '''beat''' is an [[w:Interference (wave propagation)|interference]] pattern between two [[w:sound|sounds]] of slightly different [[w:frequency|frequencies]], ''perceived'' as a periodic variation in [[w:amplitude (music)|volume]] whose rate is the [[w:Difference (mathematics)|difference]] of the two frequencies. The fundamentals of this topic are taught at some level in virtually every introductory high school or college course. [[w:Beat (acoustics)|Wikipedia]] features the figure shown and equations like, :<math> f_\text{beat} = f_1 - f_1.</math> But topics beyond these fundamentals are rarely pursued, and for good reason. Much about how humans perceive beats in musical intervals is poorly understood. This Wikiversity resource is not so much aimed at answering difficult questions, but to offer students the the opportunity to [https://www.pinterest.com/pin/164662930098107644/ "mess around"] in a way that enhances one's understanding of mathematics and computer programming. ==Fourier analysis== ''See also'' [[w:Kramers–Kronig relations]], [[w:Cauchy principal value]], [https://wiki.seg.org/wiki/Dictionary:Hilbert_transform]and [[w:Sokhotski–Plemelj theorem]] <math> \int_\infty^\infty e^{i\omega t}d\omega=2\pi\delta(t)</math> <math>\frac{1}{X+i\epsilon} = \frac {X}{X^2+ \epsilon^2} - i \pi \delta(X)</math> <math>\frac{1}{X+i\epsilon} = \frac {X}{X^2+ \epsilon^2} - \frac {i\epsilon}{X^2+ \epsilon^2}</math> <math>\frac 1 X = \text{pp} \frac 1 X -i\pi \delta(X)</math> ==Links== '''Basic''' * <u>[[Wikipedia:Beat (acoustics)]]</u>: The fact that Wikipedia only covers the basic ideas supports my contention that material beyond these well known topics will always be murky.<ref>{{cite journal |last= Weinberger |first= Norman |date= September 2006 |title= Music And The Brain |url= https://www.scientificamerican.com/article/music-and-the-brain-2006-09/ |journal= Scientific American |volume= 16 |issue= 3 |pages= 36-43 |doi= 10.1038/scientificamerican0906-36sp |accessdate=2022-08-04 }}</ref><ref>Note the inserted footnote templates regarding "verification" and "original research?" at [[w:special:permalink/1102305761]]. </ref> * <u>[http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/beat.html Hyperphysics: Sound/beat:]</u> parallels the Wikipedia article. * [https://www.omnicalculator.com/physics/beat-frequency <u>Omnicalculator's beat frequency demonstration</u>] effectively how the 3:2 rhythm pattern is just an ultra slow version of the consonant perfect fifth in music. '''Advanced (or otherwise different)''' * <u>[https://www.violinist.com/discussion/archive/18551/ Violinist.com]</u> discussion on using beats to tune a violin ==Footnotes== im6h1q5p5toc5gbcssqdpkf8fr92b85 2412439 2412366 2022-08-07T01:55:33Z Guy vandegrift 813252 Guy vandegrift moved page [[Draft:Beat (acoustics)]] to [[Draft:Sing free/Beat (acoustics)]] wikitext text/x-wiki [[Image:Beating Frequency.svg|thumb|300px|Diagram of beat frequency]] A '''beat''' is an [[w:Interference (wave propagation)|interference]] pattern between two [[w:sound|sounds]] of slightly different [[w:frequency|frequencies]], ''perceived'' as a periodic variation in [[w:amplitude (music)|volume]] whose rate is the [[w:Difference (mathematics)|difference]] of the two frequencies. The fundamentals of this topic are taught at some level in virtually every introductory high school or college course. [[w:Beat (acoustics)|Wikipedia]] features the figure shown and equations like, :<math> f_\text{beat} = f_1 - f_1.</math> But topics beyond these fundamentals are rarely pursued, and for good reason. Much about how humans perceive beats in musical intervals is poorly understood. This Wikiversity resource is not so much aimed at answering difficult questions, but to offer students the the opportunity to [https://www.pinterest.com/pin/164662930098107644/ "mess around"] in a way that enhances one's understanding of mathematics and computer programming. ==Fourier analysis== ''See also'' [[w:Kramers–Kronig relations]], [[w:Cauchy principal value]], [https://wiki.seg.org/wiki/Dictionary:Hilbert_transform]and [[w:Sokhotski–Plemelj theorem]] <math> \int_\infty^\infty e^{i\omega t}d\omega=2\pi\delta(t)</math> <math>\frac{1}{X+i\epsilon} = \frac {X}{X^2+ \epsilon^2} - i \pi \delta(X)</math> <math>\frac{1}{X+i\epsilon} = \frac {X}{X^2+ \epsilon^2} - \frac {i\epsilon}{X^2+ \epsilon^2}</math> <math>\frac 1 X = \text{pp} \frac 1 X -i\pi \delta(X)</math> ==Links== '''Basic''' * <u>[[Wikipedia:Beat (acoustics)]]</u>: The fact that Wikipedia only covers the basic ideas supports my contention that material beyond these well known topics will always be murky.<ref>{{cite journal |last= Weinberger |first= Norman |date= September 2006 |title= Music And The Brain |url= https://www.scientificamerican.com/article/music-and-the-brain-2006-09/ |journal= Scientific American |volume= 16 |issue= 3 |pages= 36-43 |doi= 10.1038/scientificamerican0906-36sp |accessdate=2022-08-04 }}</ref><ref>Note the inserted footnote templates regarding "verification" and "original research?" at [[w:special:permalink/1102305761]]. </ref> * <u>[http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/beat.html Hyperphysics: Sound/beat:]</u> parallels the Wikipedia article. * [https://www.omnicalculator.com/physics/beat-frequency <u>Omnicalculator's beat frequency demonstration</u>] effectively how the 3:2 rhythm pattern is just an ultra slow version of the consonant perfect fifth in music. '''Advanced (or otherwise different)''' * <u>[https://www.violinist.com/discussion/archive/18551/ Violinist.com]</u> discussion on using beats to tune a violin ==Footnotes== im6h1q5p5toc5gbcssqdpkf8fr92b85 6 286110 2412348 2022-08-06T13:36:01Z Young1lim 21186 {{Information |Description=Laurent.5: Applications 6A (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} wikitext text/x-wiki == Summary == {{Information |Description=Laurent.5: Applications 6A (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} ju62xonvx6x23s6vcr9a0ytghjovaun 6 286111 2412350 2022-08-06T13:37:10Z Young1lim 21186 {{Information |Description=Laurent.5: Applications 6A (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} wikitext text/x-wiki == Summary == {{Information |Description=Laurent.5: Applications 6A (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} t61el974x13zogo22qr5ek3jx7xwefx 6 286112 2412352 2022-08-06T13:38:31Z Young1lim 21186 {{Information |Description=C04.Series.1: Arrays 1A (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=C04.Series.1: Arrays 1A (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} gi0a23b8qv85pw6l8t0adopkemjtpvj 6 286113 2412353 2022-08-06T13:39:25Z Young1lim 21186 {{Information |Description=C04.Series.3: Array Pointers 1A (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=C04.Series.3: Array Pointers 1A (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} jtwelwb3kfn6iq0s1dnsfuyam8fa8gf 6 286114 2412354 2022-08-06T13:40:40Z Young1lim 21186 {{Information |Description=C04.Series.1App: Applications of Arrays 1A (20220805- 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=C04.Series.1App: Applications of Arrays 1A (20220805- 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} k9wbrqynuvu1bxb31lyvds0tbep06vw 6 286115 2412356 2022-08-06T13:42:01Z Young1lim 21186 {{Information |Description=C04.Series.1: Arrays 1A (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=C04.Series.1: Arrays 1A (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} o9cg2ad0skd76ebbg8tx6o09deiinwr 6 286116 2412357 2022-08-06T13:43:02Z Young1lim 21186 {{Information |Description=C04.Series.3: Array Pointers 1A (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=C04.Series.3: Array Pointers 1A (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 7uusvo7xn628j9v7q77u9g5w306441m 6 286117 2412358 2022-08-06T13:43:54Z Young1lim 21186 {{Information |Description=C04.Series.1App: Applications of Arrays 1A (20220806- 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=C04.Series.1App: Applications of Arrays 1A (20220806- 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} k19rxjm7hqnzz60tzpaxd6ejlquu403 6 286118 2412360 2022-08-06T13:45:15Z Young1lim 21186 {{Information |Description=VLSI.Arith.1.A: Variable Block Adders (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=VLSI.Arith.1.A: Variable Block Adders (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} o3soz73jodynbeg930mypjxyzzpk3di 6 286119 2412362 2022-08-06T13:46:20Z Young1lim 21186 {{Information |Description=VLSI.Arith.1.A: Variable Block Adders (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=VLSI.Arith.1.A: Variable Block Adders (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} thdqbyqlwdnarigcecq89vsrn4z4gjx 3 286120 2412368 2022-08-06T13:59:59Z Dave Braunschweig 426084 Welcome wikitext text/x-wiki {{Robelbox|theme=9|title=Welcome!|width=100%}} <div style="{{Robelbox/pad}}"> '''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] Eimilerous22!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. Please remember to [[Wikiversity:Signature|sign and date]] your finished comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. The signature icon [[File:OOjs UI icon signature-ltr.svg]] above the edit window makes it simple. All users are expected to abide by our [[Wikiversity:Privacy policy|Privacy]], [[Wikiversity:Civility|Civility]], and the [[Foundation:Terms of Use|Terms of Use]] policies while at Wikiversity. To [[Wikiversity:Introduction|get started]], you may <!-- The Left column --> <div style="width:50.0%; float:left"> * [[Help:guides|Take a guided tour]] and learn [[Help:Editing|to edit]]. * Visit a (kind of) [[Wikiversity:Random|random project]]. * [[Wikiversity:Browse|Browse]] Wikiversity, or visit a portal corresponding to your educational level: [[Portal: Pre-school Education|pre-school]], [[Portal: Primary Education|primary]], [[Portal:Secondary Education|secondary]], [[Portal:Tertiary Education|tertiary]], [[Portal:Non-formal Education|non-formal education]]. * Find out about [[Wikiversity:Research|research]] activities on Wikiversity. * [[Wikiversity:Introduction explore|Explore]] Wikiversity with the links to your left. </div> <!-- The Right column --> <div style="width:50.0%; float:left"> * Enable VisualEditor under [[Special:Preferences#mw-prefsection-betafeatures|Beta]] settings to make article editing easier. * Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] and find out [[Help:How to write an educational resource|how to write an educational resource]] for Wikiversity. * Give [[Wikiversity:Feedback|feedback]] about your initial observations. * Discuss Wikiversity issues or ask questions at the [[Wikiversity:Colloquium|colloquium]]. * [[Wikiversity:Chat|Chat]] with other Wikiversitans on [[:freenode:wikiversity|<kbd>#wikiversity</kbd>]]. </div> <br clear="both"/> You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:59, 6 August 2022 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} turu9kwb2ml0jc5octjohypqzg3aspg 3 286121 2412369 2022-08-06T14:00:00Z Dave Braunschweig 426084 Welcome wikitext text/x-wiki {{Robelbox|theme=9|title=Welcome!|width=100%}} <div style="{{Robelbox/pad}}"> '''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] Lyndel Lemon!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. Please remember to [[Wikiversity:Signature|sign and date]] your finished comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. The signature icon [[File:OOjs UI icon signature-ltr.svg]] above the edit window makes it simple. All users are expected to abide by our [[Wikiversity:Privacy policy|Privacy]], [[Wikiversity:Civility|Civility]], and the [[Foundation:Terms of Use|Terms of Use]] policies while at Wikiversity. To [[Wikiversity:Introduction|get started]], you may <!-- The Left column --> <div style="width:50.0%; float:left"> * [[Help:guides|Take a guided tour]] and learn [[Help:Editing|to edit]]. * Visit a (kind of) [[Wikiversity:Random|random project]]. * [[Wikiversity:Browse|Browse]] Wikiversity, or visit a portal corresponding to your educational level: [[Portal: Pre-school Education|pre-school]], [[Portal: Primary Education|primary]], [[Portal:Secondary Education|secondary]], [[Portal:Tertiary Education|tertiary]], [[Portal:Non-formal Education|non-formal education]]. * Find out about [[Wikiversity:Research|research]] activities on Wikiversity. * [[Wikiversity:Introduction explore|Explore]] Wikiversity with the links to your left. </div> <!-- The Right column --> <div style="width:50.0%; float:left"> * Enable VisualEditor under [[Special:Preferences#mw-prefsection-betafeatures|Beta]] settings to make article editing easier. * Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] and find out [[Help:How to write an educational resource|how to write an educational resource]] for Wikiversity. * Give [[Wikiversity:Feedback|feedback]] about your initial observations. * Discuss Wikiversity issues or ask questions at the [[Wikiversity:Colloquium|colloquium]]. * [[Wikiversity:Chat|Chat]] with other Wikiversitans on [[:freenode:wikiversity|<kbd>#wikiversity</kbd>]]. </div> <br clear="both"/> You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 14:00, 6 August 2022 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} bhh99jnsnt5cdr8m9go1t4l34k93n00 3 286122 2412370 2022-08-06T14:00:01Z Dave Braunschweig 426084 Welcome wikitext text/x-wiki {{Robelbox|theme=9|title=Welcome!|width=100%}} <div style="{{Robelbox/pad}}"> '''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] GabbieUC!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. Please remember to [[Wikiversity:Signature|sign and date]] your finished comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. The signature icon [[File:OOjs UI icon signature-ltr.svg]] above the edit window makes it simple. All users are expected to abide by our [[Wikiversity:Privacy policy|Privacy]], [[Wikiversity:Civility|Civility]], and the [[Foundation:Terms of Use|Terms of Use]] policies while at Wikiversity. To [[Wikiversity:Introduction|get started]], you may <!-- The Left column --> <div style="width:50.0%; float:left"> * [[Help:guides|Take a guided tour]] and learn [[Help:Editing|to edit]]. * Visit a (kind of) [[Wikiversity:Random|random project]]. * [[Wikiversity:Browse|Browse]] Wikiversity, or visit a portal corresponding to your educational level: [[Portal: Pre-school Education|pre-school]], [[Portal: Primary Education|primary]], [[Portal:Secondary Education|secondary]], [[Portal:Tertiary Education|tertiary]], [[Portal:Non-formal Education|non-formal education]]. * Find out about [[Wikiversity:Research|research]] activities on Wikiversity. * [[Wikiversity:Introduction explore|Explore]] Wikiversity with the links to your left. </div> <!-- The Right column --> <div style="width:50.0%; float:left"> * Enable VisualEditor under [[Special:Preferences#mw-prefsection-betafeatures|Beta]] settings to make article editing easier. * Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] and find out [[Help:How to write an educational resource|how to write an educational resource]] for Wikiversity. * Give [[Wikiversity:Feedback|feedback]] about your initial observations. * Discuss Wikiversity issues or ask questions at the [[Wikiversity:Colloquium|colloquium]]. * [[Wikiversity:Chat|Chat]] with other Wikiversitans on [[:freenode:wikiversity|<kbd>#wikiversity</kbd>]]. </div> <br clear="both"/> You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 14:00, 6 August 2022 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} cs68ieqcxeokv0a1s2sru19md7b0fie 3 286123 2412371 2022-08-06T14:00:01Z Dave Braunschweig 426084 Welcome wikitext text/x-wiki {{Robelbox|theme=9|title=Welcome!|width=100%}} <div style="{{Robelbox/pad}}"> '''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] Cherie.roj!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. Please remember to [[Wikiversity:Signature|sign and date]] your finished comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. The signature icon [[File:OOjs UI icon signature-ltr.svg]] above the edit window makes it simple. All users are expected to abide by our [[Wikiversity:Privacy policy|Privacy]], [[Wikiversity:Civility|Civility]], and the [[Foundation:Terms of Use|Terms of Use]] policies while at Wikiversity. To [[Wikiversity:Introduction|get started]], you may <!-- The Left column --> <div style="width:50.0%; float:left"> * [[Help:guides|Take a guided tour]] and learn [[Help:Editing|to edit]]. * Visit a (kind of) [[Wikiversity:Random|random project]]. * [[Wikiversity:Browse|Browse]] Wikiversity, or visit a portal corresponding to your educational level: [[Portal: Pre-school Education|pre-school]], [[Portal: Primary Education|primary]], [[Portal:Secondary Education|secondary]], [[Portal:Tertiary Education|tertiary]], [[Portal:Non-formal Education|non-formal education]]. * Find out about [[Wikiversity:Research|research]] activities on Wikiversity. * [[Wikiversity:Introduction explore|Explore]] Wikiversity with the links to your left. </div> <!-- The Right column --> <div style="width:50.0%; float:left"> * Enable VisualEditor under [[Special:Preferences#mw-prefsection-betafeatures|Beta]] settings to make article editing easier. * Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] and find out [[Help:How to write an educational resource|how to write an educational resource]] for Wikiversity. * Give [[Wikiversity:Feedback|feedback]] about your initial observations. * Discuss Wikiversity issues or ask questions at the [[Wikiversity:Colloquium|colloquium]]. * [[Wikiversity:Chat|Chat]] with other Wikiversitans on [[:freenode:wikiversity|<kbd>#wikiversity</kbd>]]. </div> <br clear="both"/> You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:59, 6 August 2022 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} ik3rsnw4pc00bitsrw0666agqyrwxm4 3 286124 2412372 2022-08-06T14:00:02Z Dave Braunschweig 426084 Welcome wikitext text/x-wiki {{Robelbox|theme=9|title=Welcome!|width=100%}} <div style="{{Robelbox/pad}}"> '''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] Tiarnawilson01!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. Please remember to [[Wikiversity:Signature|sign and date]] your finished comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. The signature icon [[File:OOjs UI icon signature-ltr.svg]] above the edit window makes it simple. All users are expected to abide by our [[Wikiversity:Privacy policy|Privacy]], [[Wikiversity:Civility|Civility]], and the [[Foundation:Terms of Use|Terms of Use]] policies while at Wikiversity. To [[Wikiversity:Introduction|get started]], you may <!-- The Left column --> <div style="width:50.0%; float:left"> * [[Help:guides|Take a guided tour]] and learn [[Help:Editing|to edit]]. * Visit a (kind of) [[Wikiversity:Random|random project]]. * [[Wikiversity:Browse|Browse]] Wikiversity, or visit a portal corresponding to your educational level: [[Portal: Pre-school Education|pre-school]], [[Portal: Primary Education|primary]], [[Portal:Secondary Education|secondary]], [[Portal:Tertiary Education|tertiary]], [[Portal:Non-formal Education|non-formal education]]. * Find out about [[Wikiversity:Research|research]] activities on Wikiversity. * [[Wikiversity:Introduction explore|Explore]] Wikiversity with the links to your left. </div> <!-- The Right column --> <div style="width:50.0%; float:left"> * Enable VisualEditor under [[Special:Preferences#mw-prefsection-betafeatures|Beta]] settings to make article editing easier. * Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] and find out [[Help:How to write an educational resource|how to write an educational resource]] for Wikiversity. * Give [[Wikiversity:Feedback|feedback]] about your initial observations. * Discuss Wikiversity issues or ask questions at the [[Wikiversity:Colloquium|colloquium]]. * [[Wikiversity:Chat|Chat]] with other Wikiversitans on [[:freenode:wikiversity|<kbd>#wikiversity</kbd>]]. </div> <br clear="both"/> You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:59, 6 August 2022 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} ju2kb3kysuu7jy2pwnaslrphbtv63y3 0 286126 2412376 2022-08-06T15:00:10Z Ougurlu 2947730 New resource with "<!--CONTRIBUTOR INSTRUCTIONS 1. This text is a comment: it'll be hidden from the published lesson plan, so it's just for you! If you see unfamiliar code, look for an explanation in a comment like this. 2. Heads up: you'll find a comment at the bottom with simple instructions on adding "category tags," which will help people find this lesson plan. Please follow them :) --><!-- DON'T MESS WITH THIS BIT --> {{Eventmath draft header}} <div style="background-color: #DA..." wikitext text/x-wiki <!--CONTRIBUTOR INSTRUCTIONS 1. This text is a comment: it'll be hidden from the published lesson plan, so it's just for you! If you see unfamiliar code, look for an explanation in a comment like this. 2. Heads up: you'll find a comment at the bottom with simple instructions on adding "category tags," which will help people find this lesson plan. Please follow them :) --><!-- DON'T MESS WITH THIS BIT --> {{Eventmath draft header}} <div style="background-color: #DAF3EF; padding: 1em; overflow:hidden;"> <div style="overflow:hidden;"> <div style="width:50%; margin-right:4em; float:left;"> {{Eventmath lesson plan overview <!--EDIT BELOW THIS LINE ONLY--> <!-- The summary below is displayed as a guide for visitors and contributors. You can publish without it, but it's required for removal from draft status.--> |assumed-knowledge = <!--Below, please briefly describe any mathematical skills or background knowledge students should have before completing this lesson.--> |activities = <!--Below, please briefly summarize what students will do during this lesson and what they will learn.--> |class-time = <!--Below, please type one of the following, exactly as it appears: 00-15 minutes, 15-30 minutes, 30-45 minutes, 45-60 minutes, 60-90 minutes, more than 90 minutes. Your best guess is fine! It can be changed later.--> <!--Next, you'll provide all citation data for the source (article/social media post/video). Article example: | source-website = Huffington Post | source-title = Voters In Wyoming Have 3.6 Times The Voting Power That I Have. It’s Time To End The Electoral College. | source-date = 2016-11-10 | source-url = https://www.huffpost.com/entry/its-time-to-end-the-electoral-college_b_12891764 | source-archive-url = https://web.archive.org/web/20201210161426/https://www.huffpost.com/entry/its-time-to-end-the-electoral-college_b_12891764 | source-archive-date = 2021-10-28 Post example: | source-website = Twitter | source-title = Remember: Germany is supposed to be a SUCCESS STORY. | source-date = 2020-12-22 | source-url = https://twitter.com/Neoavatara/status/1341581271991013376 | source-archive-url = https://web.archive.org/web/20201223064324/https://twitter.com/Neoavatara/status/1341581271991013376 | source-archive-date = 2021-02-16 Notes: 1. To ensure lesson plans can be sorted by date, please enter all dates in the format YYYY-MM-DD, including leading zeros: January is 01, not 1, for example. 2. If you cannot find a date, use n.d. as the date (no date). 3. To ensure that the article/post will remain accessible for educators and students... a. Archive it at https://archive.org/web/ (use the "Save Page Now" form to generate a permanent URL). b. Paste that URL here as the source-archive-url. c. Enter the date you archived the source as the source-archive date. 4. Linking to a website helps the site. If the lesson plan is debunking disinformation, you may avoid spreading disinformation by omitting the url of the original site entirely. In that case, use the URL of the archived version as the value of source-url, and omit values for archive-url and archive-date. --> | source-website = | source-title = | source-date = | source-url = | source-archive-url = | source-archive-date = }} </div> <div style="float:left; width:20%;"> [[File:Eventmath_logo_bitmap_graphic.png|250px]] </div> </div> <div style="width:70%; float:left;"> <!--INSTRUCTIONS FOR THE BODY OF THE LESSON PLAN 1. Note that "==My heading==" is a level 2 section heading, "===My subheading===" is level 3, etc. Level 1 is reserved for the title. 2. After you fill in a section, please delete the ''italicized instructions.'' 3. Check out the "Advanced" and "Help" menus at the top of the editor if you don't know how to format lists, etc. --> ==Activities== ''This is the main content of the lesson plan. Write as much or as little as needed to convey the main objective, the activities and tasks, and any other essential information. You may organize this content however you'd like.'' ''You can use LaTeX to render mathematical symbols, such as <math>\sum_{k=1}^n k = \frac{1}{2}n(n+1)</math>. See the [https://en.wikiversity.org/wiki/Help:Formula Help:Formula] page for more details.'' ''You may also wish to include helpful materials for an instructor, such as:'' * ''solutions to problems posed by the lesson,'' * ''anticipated points of confusion and suggestions,'' * ''discussion topics that may arise when working with students, or'' * ''any other relevant ideas or materials.'' ==Assignments== ''You're welcome to suggest exercises, activities, assignments, or projects based on the material of this lesson.'' ==Resources== ''(Include these sections at your discretion, keeping in mind that you and others can always edit and add more to these sections later.)'' ===Background=== ''You're welcome to share links to openly-accessible content (e.g. from Khan Academy, YouTube, Wikiversity, etc.) about domain knowledge or math skills students should have. Likewise, you may wish to include contextual information for the instructor.'' ===Explorations=== ''You're welcome to share references for additional learning and exploration, such as links to other articles, videos, spreadsheets, or computer code. When an open-access substitute is unavailable, links to paywalled sites are acceptable in this section.'' ==Feedback== <!--PLEASE DO NOT EDIT THIS SECTION DIRECTLY.--> Have you found this lesson plan helpful? Tell us about it! Just click ''Endorse'' below to open up an editor and type your comments. When you're ready, they'll appear at the bottom of this section to help other educators looking for good lesson plans. (Alternatively, if you see a way to improve this lesson plan, be bold and make an edit! You're also welcome to discuss the lesson plan or provide constructive feedback on its [[{{TALKPAGENAME}}|Discussion page]].) <div style="float:left;"> <inputbox> type=commenttitle hidden=yes page={{FULLPAGENAME}} buttonlabel=Endorse arialabel=Endorse the lesson plan editintro=Eventmath/Lesson plan endorsement instructions preload=Template:Eventmath lesson plan endorsement </inputbox> </div> </div> <div style="width:10%; padding:4em; float:left;"> __TOC__ </div> </div> <!--CATEGORY TAG INSTRUCTIONS Please follow these instructions so that people can find this lesson plan! 1. Select a primary event type from the following list: business, culture, economics, education, finance, government, health, politics, science, technology 2. Select a primary math type from the following list: algebra, arithmetic, calculus, combinatorics, geometry, logic, probability, statistics 3. Type your category tags directly underneath "[[Category: Eventmath lesson plans]]," at the bottom of this editor. For example, if you choose calculus and economics, you would have the following category tags on consecutive lines: [[Category: Eventmath lesson plans]] [[Category: Eventmath calculus]] [[Category: Eventmath economics]] NOTE: Be sure to use sentence casing for the category names (e.g. "Eventmath calculus" not "Eventmath Calculus"). FAQ Q: Can I apply multiple event or math tags? A: Yes! For example, you might want both a probability tag and a statistics tag. Q: Can I make a new category? A: Yes! Just type it in the same format. Example: [[Category: Eventmath number theory]] However, this category will not automatically have its own display box on the Lesson plans page. If you think there should be one, you can add one. If you don't know how, leave a comment on the Lesson plans "Discuss" tab. Alternatively, you might interpret an existing category more broadly. For example, if you have a lesson plan for differential equations, you might decide to include that under the calculus category. It's up to you. --> [[Category: Eventmath lesson plans]] 8zkvqs3236i10nkkknmusott8dkbze7 2412377 2412376 2022-08-06T15:01:00Z Ougurlu 2947730 wikitext text/x-wiki <!--CONTRIBUTOR INSTRUCTIONS 1. This text is a comment: it'll be hidden from the published lesson plan, so it's just for you! If you see unfamiliar code, look for an explanation in a comment like this. 2. Heads up: you'll find a comment at the bottom with simple instructions on adding "category tags," which will help people find this lesson plan. Please follow them :) --> <!-- DON'T MESS WITH THIS BIT --> {{Eventmath draft header}} <div style="background-color: #DAF3EF; padding: 1em; overflow:hidden;"> <div style="overflow:hidden;"> <div style="width:50%; float:left;"> {{Eventmath lesson plan overview <!--EDIT BELOW THIS LINE ONLY--> <!-- The summary below is displayed as a guide for visitors and contributors. You can publish without it, but it's required for removal from draft status.--> |assumed-knowledge = <!--Below, please briefly describe any mathematical skills or background knowledge students should have before completing this lesson.--> |activities = <!--Below, please briefly summarize what students will do during this lesson and what they will learn. Using inclusion-exclusion to understand COVID reinfection--> |class-time = <!--Below, please type one of the following, exactly as it appears: 00-15 minutes, 15-30 minutes, 30-45 minutes, 45-60 minutes, 60-90 minutes, more than 90 minutes. Your best guess is fine! It can be changed later.--> <!--Next, you'll provide all citation data for the source (article/social media post/video). Article example: | source-website = NPR | source-title = The future of the pandemic is looking clearer as we learn more about infection | source-date = 2022-02-07 | source-url = https://www.npr.org/sections/goatsandsoda/2022/02/07/1057245449/the-future-of-the-pandemic-is-looking-clearer-as-we-learn-more-about-infection--> | source-website = NPR | source-title = The future of the pandemic is looking clearer as we learn more about infection | source-date = 2022-02-07 | source-url = https://www.npr.org/sections/goatsandsoda/2022/02/07/1057245449/the-future-of-the-pandemic-is-looking-clearer-as-we-learn-more-about-infection }} </div> <div style="float:left; width:20%;"> [[File:Eventmath_logo_bitmap_graphic.png|250px]] </div> </div> <div style="width:70%; float:left;"> <!--INSTRUCTIONS FOR THE BODY OF THE LESSON PLAN 1. Note that "==My heading==" is a level 2 section heading, "===My subheading===" is level 3, etc. Level 1 is reserved for the title. 2. After you fill in a section, please delete the ''italicized instructions.'' 3. Check out the "Advanced" and "Help" menus at the top of the editor if you don't know how to format lists, etc. --> ==Activities== ''This is the main content of the lesson plan. Write as much or as little as needed to convey the main objective, the activities and tasks, and any other essential information. You may organize this content however you'd like.'' ''You can use LaTeX to render mathematical symbols, such as <math>\sum_{k=1}^n k^2 = \frac{1}{6}n(n+1)(2n+1)</math>. See the [https://en.wikiversity.org/wiki/Help:Formula Help:Formula] page for more details.'' ''You may also wish to include helpful materials for an instructor, such as:'' * ''solutions to problems posed by the lesson,'' * ''anticipated points of confusion and suggestions,'' * ''discussion topics that may arise when working with students, or'' * ''any other relevant ideas or materials.'' ==Assignments== ''You're welcome to suggest any exercises, activities, assignments, or projects based on the material of this lesson.'' ==Resources== ''(Include these sections at your discretion, keeping in mind that you and others can always edit and add more to these sections later.)'' ===Background=== ''You're welcome to share links to openly-accessible content (e.g. from Khan Academy, YouTube, Wikiversity, etc.) about domain knowledge or math skills students should have. Likewise, you may wish to include contextual information for the instructor.'' ===Explorations=== ''You're welcome to share references for additional learning and exploration, such as links to other articles, videos, spreadsheets, or computer code. When an open-access substitute is unavailable, links to paywalled sites are acceptable in this section.'' ==Feedback== <!--PLEASE DO NOT EDIT THIS SECTION DIRECTLY.--> Have you found this lesson plan helpful? Tell us about it! Just click ''Endorse'' below to open up an editor and type your comments. When you're ready, they'll appear at the bottom of this section to help other educators look for good lesson plans. (Alternatively, if you see a way to improve this lesson plan, be bold and make an edit! You're also welcome to discuss the lesson plan or provide constructive feedback on its [[{{TALKPAGENAME}}|Discussion page]].) <div style="float:left;"> <inputbox> type=commenttitle hidden=yes page={{FULLPAGENAME}} buttonlabel=Endorse arialabel=Endorse the lesson plan editintro=Eventmath/Lesson plan endorsement instructions preload=Template:Eventmath lesson plan endorsement </inputbox> </div> </div> <div style="width:10%; padding:4em; float:left;"> __TOC__ </div> </div> <!--CATEGORY TAG INSTRUCTIONS Please follow these instructions so that people can find this lesson plan! 1. Select a primary event type from the following list: government, health 2. Select a primary math type from the following list: combinatorics 3. Type your category tags directly underneath "[[Category: Eventmath lesson plans]]," at the bottom of this editor. For example, if you choose calculus and economics, you would have the following category tags on consecutive lines: [[Category: Eventmath lesson plans]] [[Category: Eventmath calculus]] [[Category: Eventmath economics]] NOTE: Be sure to use sentence casing for the category names (e.g. "Eventmath calculus" not "Eventmath Calculus"). FAQ Q: Can I apply multiple event or math tags? A: Yes! For example, you might want both a probability tag and a statistics tag. Q: Can I make a new category? A: Yes! Just type it in the same format. Example: [[Category: Eventmath number theory]] However, this category will not automatically have its own display box on the Lesson plans page. If you think there should be one, you can add one. If you don't know how, leave a comment on the Lesson plans "Discuss" tab. Alternatively, you might interpret an existing category more broadly. For example, if you have a lesson plan for differential equations, you might decide to include that under the calculus category. It's up to you. --> [[Category: Eventmath lesson plans]] 1vnzwdly1oayqz8op8oj0guhvpfjb9z 0 286127 2412378 2022-08-06T15:06:07Z Ougurlu 2947730 New resource with "<!--CONTRIBUTOR INSTRUCTIONS 1. This text is a comment: it'll be hidden from the published lesson plan, so it's just for you! If you see unfamiliar code, look for an explanation in a comment like this. 2. Heads up: you'll find a comment at the bottom with simple instructions on adding "category tags," which will help people find this lesson plan. Please follow them :) --><!-- DON'T MESS WITH THIS BIT --> {{Eventmath draft header}} <div style="background-color: #DA..." wikitext text/x-wiki <!--CONTRIBUTOR INSTRUCTIONS 1. This text is a comment: it'll be hidden from the published lesson plan, so it's just for you! If you see unfamiliar code, look for an explanation in a comment like this. 2. Heads up: you'll find a comment at the bottom with simple instructions on adding "category tags," which will help people find this lesson plan. Please follow them :) --><!-- DON'T MESS WITH THIS BIT --> {{Eventmath draft header}} <div style="background-color: #DAF3EF; padding: 1em; overflow:hidden;"> <div style="overflow:hidden;"> <div style="width:50%; margin-right:4em; float:left;"> {{Eventmath lesson plan overview <!--EDIT BELOW THIS LINE ONLY--> <!-- The summary below is displayed as a guide for visitors and contributors. You can publish without it, but it's required for removal from draft status.--> |assumed-knowledge = <!--Below, please briefly describe any mathematical skills or background knowledge students should have before completing this lesson.--> |activities = <!--Below, please briefly summarize what students will do during this lesson and what they will learn.--> |class-time = <!--Below, please type one of the following, exactly as it appears: 00-15 minutes, 15-30 minutes, 30-45 minutes, 45-60 minutes, 60-90 minutes, more than 90 minutes. Your best guess is fine! It can be changed later.--> <!--Next, you'll provide all citation data for the source (article/social media post/video). Article example: | source-website = Huffington Post | source-title = Voters In Wyoming Have 3.6 Times The Voting Power That I Have. It’s Time To End The Electoral College. | source-date = 2016-11-10 | source-url = https://www.huffpost.com/entry/its-time-to-end-the-electoral-college_b_12891764 | source-archive-url = https://web.archive.org/web/20201210161426/https://www.huffpost.com/entry/its-time-to-end-the-electoral-college_b_12891764 | source-archive-date = 2021-10-28 Post example: | source-website = Twitter | source-title = Remember: Germany is supposed to be a SUCCESS STORY. | source-date = 2020-12-22 | source-url = https://twitter.com/Neoavatara/status/1341581271991013376 | source-archive-url = https://web.archive.org/web/20201223064324/https://twitter.com/Neoavatara/status/1341581271991013376 | source-archive-date = 2021-02-16 Notes: 1. To ensure lesson plans can be sorted by date, please enter all dates in the format YYYY-MM-DD, including leading zeros: January is 01, not 1, for example. 2. If you cannot find a date, use n.d. as the date (no date). 3. To ensure that the article/post will remain accessible for educators and students... a. Archive it at https://archive.org/web/ (use the "Save Page Now" form to generate a permanent URL). b. Paste that URL here as the source-archive-url. c. Enter the date you archived the source as the source-archive date. 4. Linking to a website helps the site. If the lesson plan is debunking disinformation, you may avoid spreading disinformation by omitting the url of the original site entirely. In that case, use the URL of the archived version as the value of source-url, and omit values for archive-url and archive-date. --> | source-website = | source-title = | source-date = | source-url = | source-archive-url = | source-archive-date = }} </div> <div style="float:left; width:20%;"> [[File:Eventmath_logo_bitmap_graphic.png|250px]] </div> </div> <div style="width:70%; float:left;"> <!--INSTRUCTIONS FOR THE BODY OF THE LESSON PLAN 1. Note that "==My heading==" is a level 2 section heading, "===My subheading===" is level 3, etc. Level 1 is reserved for the title. 2. After you fill in a section, please delete the ''italicized instructions.'' 3. Check out the "Advanced" and "Help" menus at the top of the editor if you don't know how to format lists, etc. --> ==Activities== ''This is the main content of the lesson plan. Write as much or as little as needed to convey the main objective, the activities and tasks, and any other essential information. You may organize this content however you'd like.'' ''You can use LaTeX to render mathematical symbols, such as <math>\sum_{k=1}^n k = \frac{1}{2}n(n+1)</math>. See the [https://en.wikiversity.org/wiki/Help:Formula Help:Formula] page for more details.'' ''You may also wish to include helpful materials for an instructor, such as:'' * ''solutions to problems posed by the lesson,'' * ''anticipated points of confusion and suggestions,'' * ''discussion topics that may arise when working with students, or'' * ''any other relevant ideas or materials.'' ==Assignments== ''You're welcome to suggest exercises, activities, assignments, or projects based on the material of this lesson.'' ==Resources== ''(Include these sections at your discretion, keeping in mind that you and others can always edit and add more to these sections later.)'' ===Background=== ''You're welcome to share links to openly-accessible content (e.g. from Khan Academy, YouTube, Wikiversity, etc.) about domain knowledge or math skills students should have. Likewise, you may wish to include contextual information for the instructor.'' ===Explorations=== ''You're welcome to share references for additional learning and exploration, such as links to other articles, videos, spreadsheets, or computer code. When an open-access substitute is unavailable, links to paywalled sites are acceptable in this section.'' ==Feedback== <!--PLEASE DO NOT EDIT THIS SECTION DIRECTLY.--> Have you found this lesson plan helpful? Tell us about it! Just click ''Endorse'' below to open up an editor and type your comments. When you're ready, they'll appear at the bottom of this section to help other educators looking for good lesson plans. (Alternatively, if you see a way to improve this lesson plan, be bold and make an edit! You're also welcome to discuss the lesson plan or provide constructive feedback on its [[{{TALKPAGENAME}}|Discussion page]].) <div style="float:left;"> <inputbox> type=commenttitle hidden=yes page={{FULLPAGENAME}} buttonlabel=Endorse arialabel=Endorse the lesson plan editintro=Eventmath/Lesson plan endorsement instructions preload=Template:Eventmath lesson plan endorsement </inputbox> </div> </div> <div style="width:10%; padding:4em; float:left;"> __TOC__ </div> </div> <!--CATEGORY TAG INSTRUCTIONS Please follow these instructions so that people can find this lesson plan! 1. Select a primary event type from the following list: business, culture, economics, education, finance, government, health, politics, science, technology 2. Select a primary math type from the following list: algebra, arithmetic, calculus, combinatorics, geometry, logic, probability, statistics 3. Type your category tags directly underneath "[[Category: Eventmath lesson plans]]," at the bottom of this editor. For example, if you choose calculus and economics, you would have the following category tags on consecutive lines: [[Category: Eventmath lesson plans]] [[Category: Eventmath calculus]] [[Category: Eventmath economics]] NOTE: Be sure to use sentence casing for the category names (e.g. "Eventmath calculus" not "Eventmath Calculus"). FAQ Q: Can I apply multiple event or math tags? A: Yes! For example, you might want both a probability tag and a statistics tag. Q: Can I make a new category? A: Yes! Just type it in the same format. Example: [[Category: Eventmath number theory]] However, this category will not automatically have its own display box on the Lesson plans page. If you think there should be one, you can add one. If you don't know how, leave a comment on the Lesson plans "Discuss" tab. Alternatively, you might interpret an existing category more broadly. For example, if you have a lesson plan for differential equations, you might decide to include that under the calculus category. It's up to you. --> [[Category: Eventmath lesson plans]] 8zkvqs3236i10nkkknmusott8dkbze7 2412379 2412378 2022-08-06T15:07:08Z Ougurlu 2947730 wikitext text/x-wiki <!--CONTRIBUTOR INSTRUCTIONS 1. This text is a comment: it'll be hidden from the published lesson plan, so it's just for you! If you see unfamiliar code, look for an explanation in a comment like this. 2. Heads up: you'll find a comment at the bottom with simple instructions on adding "category tags," which will help people find this lesson plan. Please follow them :) --> <!-- DON'T MESS WITH THIS BIT --> {{Eventmath draft header}} <div style="background-color: #DAF3EF; padding: 1em; overflow:hidden;"> <div style="overflow:hidden;"> <div style="width:50%; float:left;"> {{Eventmath lesson plan overview <!--EDIT BELOW THIS LINE ONLY--> <!-- The summary below is displayed as a guide for visitors and contributors. You can publish without it, but it's required for removal from draft status.--> |assumed-knowledge = <!--Below, please briefly describe any mathematical skills or background knowledge students should have before completing this lesson.--> |activities = <!--Below, please briefly summarize what students will do during this lesson and what they will learn. Using inclusion-exclusion to understand COVID reinfection--> |class-time = <!--Below, please type one of the following, exactly as it appears: 00-15 minutes, 15-30 minutes, 30-45 minutes, 45-60 minutes, 60-90 minutes, more than 90 minutes. Your best guess is fine! It can be changed later.--> <!--Next, you'll provide all citation data for the source (article/social media post/video). Article example: | source-website = NPR | source-title = The future of the pandemic is looking clearer as we learn more about infection | source-date = 2022-02-07 | source-url = https://www.npr.org/sections/goatsandsoda/2022/02/07/1057245449/the-future-of-the-pandemic-is-looking-clearer-as-we-learn-more-about-infection--> | source-website = NPR | source-title = The future of the pandemic is looking clearer as we learn more about infection | source-date = 2022-02-07 | source-url = https://www.npr.org/sections/goatsandsoda/2022/02/07/1057245449/the-future-of-the-pandemic-is-looking-clearer-as-we-learn-more-about-infection }} </div> <div style="float:left; width:20%;"> [[File:Eventmath_logo_bitmap_graphic.png|250px]] </div> </div> <div style="width:70%; float:left;"> <!--INSTRUCTIONS FOR THE BODY OF THE LESSON PLAN 1. Note that "==My heading==" is a level 2 section heading, "===My subheading===" is level 3, etc. Level 1 is reserved for the title. 2. After you fill in a section, please delete the ''italicized instructions.'' 3. Check out the "Advanced" and "Help" menus at the top of the editor if you don't know how to format lists, etc. --> ==Activities== ''This is the main content of the lesson plan. Write as much or as little as needed to convey the main objective, the activities and tasks, and any other essential information. You may organize this content however you'd like.'' ''You can use LaTeX to render mathematical symbols, such as <math>\sum_{k=1}^n k^2 = \frac{1}{6}n(n+1)(2n+1)</math>. See the [https://en.wikiversity.org/wiki/Help:Formula Help:Formula] page for more details.'' ''You may also wish to include helpful materials for an instructor, such as:'' * ''solutions to problems posed by the lesson,'' * ''anticipated points of confusion and suggestions,'' * ''discussion topics that may arise when working with students, or'' * ''any other relevant ideas or materials.'' ==Assignments== ''You're welcome to suggest any exercises, activities, assignments, or projects based on the material of this lesson.'' ==Resources== ''(Include these sections at your discretion, keeping in mind that you and others can always edit and add more to these sections later.)'' ===Background=== ''You're welcome to share links to openly-accessible content (e.g. from Khan Academy, YouTube, Wikiversity, etc.) about domain knowledge or math skills students should have. Likewise, you may wish to include contextual information for the instructor.'' ===Explorations=== ''You're welcome to share references for additional learning and exploration, such as links to other articles, videos, spreadsheets, or computer code. When an open-access substitute is unavailable, links to paywalled sites are acceptable in this section.'' ==Feedback== <!--PLEASE DO NOT EDIT THIS SECTION DIRECTLY.--> Have you found this lesson plan helpful? Tell us about it! Just click ''Endorse'' below to open up an editor and type your comments. When you're ready, they'll appear at the bottom of this section to help other educators look for good lesson plans. (Alternatively, if you see a way to improve this lesson plan, be bold and make an edit! You're also welcome to discuss the lesson plan or provide constructive feedback on its [[{{TALKPAGENAME}}|Discussion page]].) <div style="float:left;"> <inputbox> type=commenttitle hidden=yes page={{FULLPAGENAME}} buttonlabel=Endorse arialabel=Endorse the lesson plan editintro=Eventmath/Lesson plan endorsement instructions preload=Template:Eventmath lesson plan endorsement </inputbox> </div> </div> <div style="width:10%; padding:4em; float:left;"> __TOC__ </div> </div> <!--CATEGORY TAG INSTRUCTIONS Please follow these instructions so that people can find this lesson plan! 1. Select a primary event type from the following list: government, health 2. Select a primary math type from the following list: combinatorics 3. Type your category tags directly underneath "[[Category: Eventmath lesson plans]]," at the bottom of this editor. For example, if you choose calculus and economics, you would have the following category tags on consecutive lines: [[Category: Eventmath lesson plans]] [[Category: Eventmath calculus]] [[Category: Eventmath economics]] NOTE: Be sure to use sentence casing for the category names (e.g. "Eventmath calculus" not "Eventmath Calculus"). FAQ Q: Can I apply multiple event or math tags? A: Yes! For example, you might want both a probability tag and a statistics tag. Q: Can I make a new category? A: Yes! Just type it in the same format. Example: [[Category: Eventmath number theory]] However, this category will not automatically have its own display box on the Lesson plans page. If you think there should be one, you can add one. If you don't know how, leave a comment on the Lesson plans "Discuss" tab. Alternatively, you might interpret an existing category more broadly. For example, if you have a lesson plan for differential equations, you might decide to include that under the calculus category. It's up to you. --> [[Category: Eventmath lesson plans]] 1vnzwdly1oayqz8op8oj0guhvpfjb9z 6 286128 2412381 2022-08-06T15:32:15Z Young1lim 21186 {{Information |Description=5MRV.3B: Stationary Random Process Examples (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} wikitext text/x-wiki == Summary == {{Information |Description=5MRV.3B: Stationary Random Process Examples (20220805 - 20220804) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} eskmuhqpaqutuoxt8lvnb59kf1loycd 6 286129 2412383 2022-08-06T15:35:27Z Young1lim 21186 {{Information |Description=5MRV.3B: Stationary Random Process Examples (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} wikitext text/x-wiki == Summary == {{Information |Description=5MRV.3B: Stationary Random Process Examples (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 6vhngbk6rx1z7irj3cjvsij62u2gpm8 3 286131 2412390 2022-08-06T16:47:50Z Pathoschild 14426 create header for talk page ([[m:Synchbot|requested by MdsShakil]]) wikitext text/x-wiki <div style="display: flex; flex-wrap: wrap; justify-content: center; align-items: center; margin: 16px 0; border: 1px solid #aaaaaa;"> <div style="padding: 12px;">[[File:Circle-icons-megaphone.svg|75px|link=[[m:User_talk:MdsShakil]]]]</div> <div style="flex: 1; padding: 12px; background-color: #dddddd; color: #555555;"> <div style="font-weight: bold; font-size: 150%; color: red; font-family: 'Comic Sans MS'">Welcome to my talk page!</div> <div style="max-width: 700px">Hey! I am Shakil Hosen. I patrol many projects, and where I don't know the language I only act in cases of serious vandalism. If you think I have done anything wrong, feel free to [[m:User talk:MdsShakil|message me]] on Meta wiki. If you don't like that you can leave me messages here too, but since I do not watch all of my talk pages, your message might not get a timely response. Thanks! [[File:Face-smile.svg|18px|link=[[m:User:MdsShakil]]]]</div> </div> </div> 6ns6eellkw7iqc4yteyjnszfjmo2yio 2 286132 2412396 2022-08-06T18:40:59Z Jtwsaddress42 234843 New resource with "{{RoundBoxTop|theme=3}} === [[w:Peter Agre|Agre, Peter (1849 – )]] === <hr /> [[File:Peter Agre.jpg|thumb|Peter Agre]] [[File:Aquaporin-Sideview.png|thumb|Aquaporin (sideview)]] '''Notable Accomplishments''' * [https://www.nobelprize.org/prizes/chemistry/2003/agre/facts/ The Nobel Prize in Chemistry 2003] - “for the discovery of water channels”, shared with Roderick MacKinnon “for discoveries concerning channels in cell membranes.” * Aquaporins <br /><hr /> {|..." wikitext text/x-wiki {{RoundBoxTop|theme=3}} === [[w:Peter Agre|Agre, Peter (1849 – )]] === <hr /> [[File:Peter Agre.jpg|thumb|Peter Agre]] [[File:Aquaporin-Sideview.png|thumb|Aquaporin (sideview)]] '''Notable Accomplishments''' * [https://www.nobelprize.org/prizes/chemistry/2003/agre/facts/ The Nobel Prize in Chemistry 2003] - “for the discovery of water channels”, shared with Roderick MacKinnon “for discoveries concerning channels in cell membranes.” * Aquaporins <br /><hr /> {| align= center | width= 640px | |} <hr /> '''Publications''' {{User:Jtwsaddress42/Bibliography/Agre, Peter}} {{RoundBoxBottom}} <hr /> g5s8xjbv2hficucd6ng19kyj0ft37kd 2412402 2412396 2022-08-06T20:15:45Z Jtwsaddress42 234843 wikitext text/x-wiki {{RoundBoxTop|theme=3}} === [[w:Peter Agre|Agre, Peter (1849 – )]] === <hr /> [[File:Peter Agre.jpg|thumb|Peter Agre]] [[File:Aquaporin-Sideview.png|thumb|Aquaporin (sideview)]] '''Notable Accomplishments''' * [https://www.nobelprize.org/prizes/chemistry/2003/agre/facts/ The Nobel Prize in Chemistry 2003] - “for the discovery of water channels”, shared with Roderick MacKinnon “for discoveries concerning channels in cell membranes.” * Aquaporins <br /><hr /> {| align= center | width= 640px |{{User:Jtwsaddress42/Gallery/Aquaporins}} |} <hr /> '''Publications''' {{User:Jtwsaddress42/Bibliography/Agre, Peter}} {{RoundBoxBottom}} <hr /> bonosstifpimn0u0siapl02a5f4ma4k 2412403 2412402 2022-08-06T20:16:34Z Jtwsaddress42 234843 wikitext text/x-wiki {{RoundBoxTop|theme=3}} === [[w:Peter Agre|Agre, Peter (1949 – )]] === <hr /> [[File:Peter Agre.jpg|thumb|Peter Agre]] [[File:Aquaporin-Sideview.png|thumb|Aquaporin (sideview)]] '''Notable Accomplishments''' * [https://www.nobelprize.org/prizes/chemistry/2003/agre/facts/ The Nobel Prize in Chemistry 2003] - “for the discovery of water channels”, shared with Roderick MacKinnon “for discoveries concerning channels in cell membranes.” * Aquaporins <br /><hr /> {| align= center | width= 640px |{{User:Jtwsaddress42/Gallery/Aquaporins}} |} <hr /> '''Publications''' {{User:Jtwsaddress42/Bibliography/Agre, Peter}} {{RoundBoxBottom}} <hr /> svtfi4ilscgma7mv7wyxf6p7yy4aujo 2412406 2412403 2022-08-06T20:25:11Z Jtwsaddress42 234843 wikitext text/x-wiki {{RoundBoxTop|theme=3}} === [[w:Peter Agre|Agre, Peter (1949 – )]] === <hr /> [[File:Peter Agre.jpg|thumb|Peter Agre]] [[File:Aquaporin-Sideview.png|thumb|Aquaporin (sideview)]] [[File:NPH MRI 272 GILD.gif|thumb|Aquaporin-1 (AQP1) is found in choroid plexus, contributes to production of CSF and AQP4 is found on perivascular and ependymal cells{{efn|NPH MRI 272 GILD}}]] '''Notable Accomplishments''' * [https://www.nobelprize.org/prizes/chemistry/2003/agre/facts/ The Nobel Prize in Chemistry 2003] - “for the discovery of water channels”, shared with Roderick MacKinnon “for discoveries concerning channels in cell membranes.” * Aquaporins <br /><hr /> {| align= center | width= 640px |{{User:Jtwsaddress42/Gallery/Aquaporins}} |} <hr /> '''Publications''' {{User:Jtwsaddress42/Bibliography/Agre, Peter}} {{RoundBoxBottom}} <hr /> rvnac1gurj6ube7gu33ydlxwuq2jte1 2412408 2412406 2022-08-06T20:52:49Z Jtwsaddress42 234843 wikitext text/x-wiki {{RoundBoxTop|theme=3}} === [[w:Peter Agre|Agre, Peter (1949 – )]] === <hr /> [[File:Peter Agre.jpg|thumb|Peter Agre]] [[File:Aquaporin-Sideview.png|thumb|Aquaporin (sideview)]] [[File:NPH MRI 272 GILD.gif|thumb|Aquaporin-1 (AQP1) is found in choroid plexus, contributes to production of CSF and AQP4 is found on perivascular and ependymal cells{{efn|NPH MRI 272 GILD}}]] '''Notable Accomplishments''' * [https://www.nobelprize.org/prizes/chemistry/2003/agre/facts/ The Nobel Prize in Chemistry 2003] - “for the discovery of water channels”, shared with Roderick MacKinnon “for discoveries concerning channels in cell membranes.” * Aquaporins <br /><hr /> {| align= center | width= 640px |{{User:Jtwsaddress42/Gallery/Aquaporins}} |} <hr /> '''Publications''' {{User:Jtwsaddress42/Bibliography/Agre, Peter}} <br /><hr /> {| align= center | width= 640px |[[File:2710 Aquaporins-01.jpg|center|640px|2710 Aquaporins-01]] |} {{RoundBoxBottom}} <hr /> 8om6xesbzonst73whkdkpuqz46b3ljp 2 286133 2412401 2022-08-06T20:14:44Z Jtwsaddress42 234843 New resource with "{| align= center | style="font-size:85%" |{{Gallery | title = ''Aquaporins'' | width = 100 | height = 100 | align= center | File:173-Aquaporin 1fqy.jpg|alt1= Aquaporin illustration|Aquaporin illustration{{efn|173-Aquaporin 1fqy}} | File:AQP1.png|alt2= 2D structure of aquaporin 1 (AQP1)|2D structure of aquaporin 1 (AQP1){{efn|Depicting the six transmembrane alpha-helices and the five interhelical loop regions A-E}} }} |}" wikitext text/x-wiki {| align= center | style="font-size:85%" |{{Gallery | title = ''Aquaporins'' | width = 100 | height = 100 | align= center | File:173-Aquaporin 1fqy.jpg|alt1= Aquaporin illustration|Aquaporin illustration{{efn|173-Aquaporin 1fqy}} | File:AQP1.png|alt2= 2D structure of aquaporin 1 (AQP1)|2D structure of aquaporin 1 (AQP1){{efn|Depicting the six transmembrane alpha-helices and the five interhelical loop regions A-E}} }} |} 6wfl9x6f3xl0vm8m8n06edr24br3j51 2412405 2412401 2022-08-06T20:21:24Z Jtwsaddress42 234843 wikitext text/x-wiki {| align= center | style="font-size:85%" |{{Gallery | title = ''Aquaporins'' | width = 100 | height = 100 | align= center | File:173-Aquaporin 1fqy.jpg|alt1= Aquaporin illustration|Aquaporin illustration{{efn|173-Aquaporin 1fqy}} | File:AQP1.png|alt2= 2D structure of aquaporin 1 (AQP1)|2D structure of aquaporin 1 (AQP1){{efn|Depicting the six transmembrane alpha-helices and the five interhelical loop regions A-E}} | File:Aquaporin Z.png|alt3= Aquaporin Z| Aquaporin Z | File:AQP-channel.png|alt4= AQP-channel|AQP-channel }} |} tfrap0hiwu4cqekxbsojchhwyxvib1h 6 286134 2412415 2022-08-06T21:20:53Z Young1lim 21186 {{Information |Description=MP3.1F: Mutability - Lambda Calculus (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=MP3.1F: Mutability - Lambda Calculus (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 30p75cun7ftdnxw3mvjs44nwf5sbjwx 6 286135 2412418 2022-08-06T21:50:33Z Young1lim 21186 {{Information |Description=ARM.4ASM: UART Architecture (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} wikitext text/x-wiki == Summary == {{Information |Description=ARM.4ASM: UART Architecture (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{GFDL}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} azb25c6i3kpdgjeq7p52zrqob0cewmv 2 286136 2412420 2022-08-06T22:28:05Z AJbobcat 2947782 Who is our creator gods? wikitext text/x-wiki The illojim is our creators. gd9lg27kwr7m5lq8z7jxis6n019qy6f 6 286137 2412424 2022-08-06T22:30:58Z Young1lim 21186 {{Information |Description=ELF1.1E: Weak and Common Symbols (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} wikitext text/x-wiki == Summary == {{Information |Description=ELF1.1E: Weak and Common Symbols (20220806 - 20220805) |Source={{own|Young1lim}} |Date=2022-08-06 |Author=Young W. Lim |Permission={{cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} enve1gjg4nj4bpju5ekkrowk9fepza4 0 286138 2412427 2022-08-06T22:56:38Z Tamika Afeaki 2947781 New resource with "[[User:Tamika Afeaki|Tamika Afeaki]]" wikitext text/x-wiki [[User:Tamika Afeaki|Tamika Afeaki]] 2sxsgxyu9nlww1ao6bumiqakjgxk3tb 3 286139 2412430 2022-08-06T23:06:37Z Dave Braunschweig 426084 Welcome wikitext text/x-wiki {{Robelbox|theme=9|title=Welcome!|width=100%}} <div style="{{Robelbox/pad}}"> '''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] Tamika Afeaki!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. 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You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:06, 6 August 2022 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} rxriz980tixntdzlugu54zjlmj7l2e5 0 286140 2412431 2022-08-06T23:07:02Z Tamika Afeaki 2947781 New resource with "[[User:Tamika Afeaki|Tamika Afeaki]]" wikitext text/x-wiki [[User:Tamika Afeaki|Tamika Afeaki]] 2sxsgxyu9nlww1ao6bumiqakjgxk3tb 118 286141 2412440 2022-08-07T01:55:33Z Guy vandegrift 813252 Guy vandegrift moved page [[Draft:Beat (acoustics)]] to [[Draft:Sing free/Beat (acoustics)]] wikitext text/x-wiki #REDIRECT [[Draft:Sing free/Beat (acoustics)]] qdhsygn0274pvblbcldpdoaz918fdxg 118 286142 2412460 2022-08-07T02:33:43Z Guy vandegrift 813252 New resource with "==From== https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00381/full References Abel, M., Ahnert, K., and Bergweiler, S. (2009). Synchronization of sound sources. Phys. Rev. Lett. 103:114301. doi: 10.1103/PhysRevLett.103.114301 PubMed Abstract | CrossRef Full Text | Google Scholar Benade, A. H. (1973). The physics of brasses. Sci. Am. 229, 24–35. doi: 10.1038/scientificamerican0773-24 CrossRef Full Text | Google Scholar Bidelman, G. M., and Heinz, M. G. (20..." wikitext text/x-wiki ==From== https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00381/full References Abel, M., Ahnert, K., and Bergweiler, S. (2009). Synchronization of sound sources. Phys. Rev. Lett. 103:114301. doi: 10.1103/PhysRevLett.103.114301 PubMed Abstract | CrossRef Full Text | Google Scholar Benade, A. H. (1973). The physics of brasses. Sci. Am. 229, 24–35. doi: 10.1038/scientificamerican0773-24 CrossRef Full Text | Google Scholar Bidelman, G. M., and Heinz, M. G. (2011). Auditory-nerve responses predict pitch attributes related to musical consonance-dissonance for normal and impaired hearing. J. Acoust. Soc. 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Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity. Biol. Insp. Cong. Arch. 22, 82–94. doi: 10.1016/j.bica.2017.09.001 CrossRef Full Text | Google Scholar Park, J. Y., Park, H., Kim, J., and Park, H. J. (2011). Consonant chords stimulate higher EEG gamma activity than dissonant chords. Neurosci. Lett. 488, 101–105. doi: 10.1016/j.neulet.2010.11.011 PubMed Abstract | CrossRef Full Text | Google Scholar Parncutt, R., and Hair, G. (2011). Consonance and dissonance in theory and psychology: disentangling dissonant dichotomies. J. Interdiscip. Music Stud. 5, 119–166. Google Scholar Perani, D., Saccuman, M. C., Scifo, P., Spada, D., Andreolli, G., Rovelli, R., et al. (2010). Functional specializations for music processing in the human newborn brain. Proc. Natl. Acad. Sci. U.S.A. 107, 4758–4763. doi: 10.1073/pnas.0909074107 PubMed Abstract | CrossRef Full Text | Google Scholar Piana, G. (2007). Barlumi per una Filosofia Della Musica. Morrisville: Lulu Press. Google Scholar Plomp, R. (1976). Aspects of Tone Sensation: A Psychophysical Study. London: Academic Press. Google Scholar Plomp, R., and Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. J. Acoust. Soc. Am. 38, 548–560. doi: 10.1121/1.1909741 PubMed Abstract | CrossRef Full Text | Google Scholar Roads, C. (2001). Microsound. Cambridge, MA: The MIT Press. Google Scholar Roederer, J. G. (2008). The Physics and Psychophysics of Music. New York, NY: Springer. Google Scholar Schroeder, M. (1990). Fractals, Chaos, Power Laws. New York, NY: W.H Freeman and Co. Google Scholar Schwartz, D. A., Howe, C. Q., and Purves, D. (2003). The statistical structure of human speech sounds predicts music universals. J. Neurosci. 23, 7160–7168. PubMed Abstract | Google Scholar Serra, J., Serra, X., and Andrzejak, R. G. (2009). Cross recurrence quantification for cover song identification. New J. Phys. 11:093017. doi: 10.1088/1367-2630/11/9/093017 CrossRef Full Text | Google Scholar Trulla, L. L., Giuliani, A., Zbilut, J. P., and Webber, C. L. (1996). Recurrence quantification analysis of the logistic equation with transients. Phys. Lett. A 223, 255–260. doi: 10.1016/S0375-9601(96)00741-4 CrossRef Full Text | Google Scholar Trulla, L. L., Giuliani, A., Zimatore, G., Colosimo, A., and Zbilut, J. P. (2005). Non-linear assessment of musical consonance. Electron. J. Theor. Phys. 8, 22–34. Google Scholar Wang, X. (2013). The harmonic organization of auditory cortex. Front. Syst. Neurosci. 7:114. doi: 10.3389/fnsys.2013.00114 CrossRef Full Text | Google Scholar Webber, C. L., and Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973. doi: 10.1152/jappl.1994.76.2.965 PubMed Abstract | CrossRef Full Text | Google Scholar Zimatore, G., Giuliani, A., Hatzopoulos, S., Martini, A., and Colosimo, A. (2003). Otoacoustic emissions at different click intensities: invariant and subject-dependent features. J. Appl. Physiol. 95, 2299–2305. doi: 10.1152/japplphysiol.00667.2003 PubMed Abstract | CrossRef Full Text | Google Scholar Zimatore, G., Hatzopoulos, S., Giuliani, A., Martini, A., and Colosimo, A. (2002). Comparison of transient otoacoustic emission (TEOAE) responses from neonatal and adult ears. J. Appl. Physiol. 92, 2521–2528. doi: 10.1152/japplphysiol.01163.2001 PubMed Abstract | CrossRef Full Text | Google Scholar jpykschl5skyj1o5qx012kbg01ulw8v 2412461 2412460 2022-08-07T02:37:29Z Guy vandegrift 813252 wikitext text/x-wiki ==From== [https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00381/full Computational Approach to Musical Consonance and Dissonance: Lluis L. Trulla1, Nicola Di Stefano and Alessandro Giuliani] References Abel, M., Ahnert, K., and Bergweiler, S. (2009). Synchronization of sound sources. Phys. Rev. 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Psychol. 6:1405. doi: 10.3389/fpsyg.2015.01405 PubMed Abstract | CrossRef Full Text | Google Scholar Orsucci, F., Giuliani, A., Webber, C., Zbilut, J., Fonagy, P., and Mazza, M. (2006). Combinatorics and synchronization in natural semiotics. Phys. A Stat. Mech. Appl. 361, 665–676. doi: 10.1016/j.physa.2005.06.044 CrossRef Full Text | Google Scholar Pankovski, T., and Pankovska, E. (2017). Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity. Biol. Insp. Cong. Arch. 22, 82–94. doi: 10.1016/j.bica.2017.09.001 CrossRef Full Text | Google Scholar Park, J. Y., Park, H., Kim, J., and Park, H. J. (2011). Consonant chords stimulate higher EEG gamma activity than dissonant chords. Neurosci. Lett. 488, 101–105. doi: 10.1016/j.neulet.2010.11.011 PubMed Abstract | CrossRef Full Text | Google Scholar Parncutt, R., and Hair, G. (2011). Consonance and dissonance in theory and psychology: disentangling dissonant dichotomies. J. Interdiscip. 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Neurosci. 7:114. doi: 10.3389/fnsys.2013.00114 CrossRef Full Text | Google Scholar Webber, C. L., and Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973. doi: 10.1152/jappl.1994.76.2.965 PubMed Abstract | CrossRef Full Text | Google Scholar Zimatore, G., Giuliani, A., Hatzopoulos, S., Martini, A., and Colosimo, A. (2003). Otoacoustic emissions at different click intensities: invariant and subject-dependent features. J. Appl. Physiol. 95, 2299–2305. doi: 10.1152/japplphysiol.00667.2003 PubMed Abstract | CrossRef Full Text | Google Scholar Zimatore, G., Hatzopoulos, S., Giuliani, A., Martini, A., and Colosimo, A. (2002). Comparison of transient otoacoustic emission (TEOAE) responses from neonatal and adult ears. J. Appl. Physiol. 92, 2521–2528. doi: 10.1152/japplphysiol.01163.2001 PubMed Abstract | CrossRef Full Text | Google Scholar d7t0k1eyewq7f2xr33nhanabuup14rw 2412462 2412461 2022-08-07T02:37:55Z Guy vandegrift 813252 /* From */ wikitext text/x-wiki ==From== [https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00381/full Computational Approach to Musical Consonance and Dissonance: Lluis L. Trulla1, Nicola Di Stefano and Alessandro Giuliani] References Abel, M., Ahnert, K., and Bergweiler, S. (2009). Synchronization of sound sources. Phys. Rev. Lett. 103:114301. doi: 10.1103/PhysRevLett.103.114301 PubMed Abstract | CrossRef Full Text | Google Scholar Benade, A. H. (1973). The physics of brasses. Sci. Am. 229, 24–35. doi: 10.1038/scientificamerican0773-24 CrossRef Full Text | Google Scholar Bidelman, G. M., and Heinz, M. G. (2011). Auditory-nerve responses predict pitch attributes related to musical consonance-dissonance for normal and impaired hearing. J. Acoust. Soc. Am. 130, 1488–1502. doi: 10.1121/1.3605559 PubMed Abstract | CrossRef Full Text | Google Scholar Bidelman, G. M., and Krishnan, A. (2009). Neural correlates of consonance, dissonance, and the hierarchy of musical pitch in the human brainstem. J. Neurosci. 29, 13165–13171. doi: 10.1523/JNEUROSCI.3900-09.2009 PubMed Abstract | CrossRef Full Text | Google Scholar Bowling, D. L., Hoeschele, M., Kamraan, Z. G., and Tecumseh Fitch, W. (2017). The nature and nurture of musical consonance. Music Percept. 35, 118–121. doi: 10.1525/mp.2017.35.1.118 CrossRef Full Text | Google Scholar Bowling, D. L., and Purves, D. (2015). A biological rationale for musical consonance. Proc. Natl. Acad. Sci. U.S.A. 112, 11155–11160. doi: 10.1073/pnas.1505768112 PubMed Abstract | CrossRef Full Text | Google Scholar Cartwright, J. H. E., Douthettb, J., González, D. L., Krantzd, R., and Piro, O. (2010). Two musical paths to the Farey series and devil’s staircase. J. Math. Music 4, 57–74. doi: 10.1080/17459737.2010.485001 CrossRef Full Text | Google Scholar Cartwright, J. H. E., Gonzalez, D. L., and Piro, O. (2001). Pitch perception: a dynamical-systems perspective. Proc. Natl. Acad. Sci. U.S.A. 98, 4855–4859. doi: 10.1073/pnas.081070998 PubMed Abstract | CrossRef Full Text | Google Scholar Cartwright, J. H. E., Gonzalez, D. L., Piro, O., and Stanziali, D. (2002). Aesthetics, dynamics, and musical scales: a golden connection. J. New Music Res. 31, 51–58. doi: 10.1076/jnmr.31.1.51.8099 CrossRef Full Text | Google Scholar Cross, I. (2003). Music as a biocultural phenomenon. Ann. N. Y. Acad. Sci. 999, 106–111. doi: 10.1196/annals.1284.010 PubMed Abstract | CrossRef Full Text | Google Scholar Di Stefano, N., Focaroli, V., Giuliani, A., Formica, D., Taffoni, F., and Keller, F. (2017). A new research method to test auditory preferences in young listeners: results from a consonance versus dissonance perception study. Psychol. Music 45, 699–712. doi: 10.1177/0305735616681205 CrossRef Full Text | Google Scholar Eckmann, J. P., Kamphorst, S. O., and Ruelle, D. (1987). Recurrence plots of dynamical systems. Europhys. Lett. 4, 973–976. doi: 10.1209/0295-5075/4/9/004 CrossRef Full Text | Google Scholar Fastl, H., and Zwicker, E. (2006). Psychoacoustic. Facts and Models. Berlin: Springer. Google Scholar Foo, F., King-Stephens, D., Weber, P., Laxer, K., Parvizi, J., and Knight, R. T. (2016). Differential processing of consonance and dissonance within the human superior temporal gyrus. Front. Hum. Neurosci. 10:154. doi: 10.3389/fnhum.2016.00154 PubMed Abstract | CrossRef Full Text | Google Scholar Frova, A. (1999). Fisica nella Musica. Bologna: Zanichelli. Google Scholar González-García, N., González, M. A., and Rendón, P. L. (2016). Neural activity related to discrimination and vocal production of consonant and dissonant musical intervals. Brain Res. 1643, 59–69. doi: 10.1016/j.brainres.2016.04.065 PubMed Abstract | CrossRef Full Text | Google Scholar Helmholtz, H. (1954). On the Sensations of Tone. New York, NY: Dover Publications. Google Scholar Kameoka, A., and Kuriyagawa, M. (1969a). Consonance theory part I: consonance of dyads. J. Acoust. Soc. Am. 45, 1451–1459. doi: 10.1121/1.1911623 CrossRef Full Text | Google Scholar Kameoka, A., and Kuriyagawa, M. (1969b). Consonance theory part II: consonance of complex tones and its calculation method. J. Acoust. Soc. Am. 45, 1460–1469. doi: 10.1121/1.1911624 PubMed Abstract | CrossRef Full Text | Google Scholar Kennel, M. B., Brown, R., and Abarbanel, H. D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403. doi: 10.1103/PhysRevA.45.3403 CrossRef Full Text | Google Scholar Koelsch, S., Fritz, T., Schulze, K., Alsop, D., and Schlaug, G. (2005). Adults and children processing music: An fMRI study. Neuroimage 25, 1068–1076. doi: 10.1016/j.neuroimage.2004.12.050 PubMed Abstract | CrossRef Full Text | Google Scholar Koelsch, S., and Mulder, J. (2002). Electric brain responses to inappropriate harmonies during listening to expressive music. Clin. Neurophysiol. 113, 862–869. doi: 10.1016/S1388-2457(02)00050-0 PubMed Abstract | CrossRef Full Text | Google Scholar Large, E. W., and Almonte, F. V. (2012). Neurodynamics, tonality, and the auditory brainstem response. Ann. N. Y. Acad. Sci. 1252, E1–E7. doi: 10.1111/j.1749-6632.2012.06594.x PubMed Abstract | CrossRef Full Text | Google Scholar Large, E. W., and Tretakis, A. E. (2005). Tonality and nonlinear resonance. Ann. N. Y. Acad. Sci. 1060, 53–56. doi: 10.1196/annals.1360.046 PubMed Abstract | CrossRef Full Text | Google Scholar Lohri, A. (2016). Kombinationstöne und Tartinis “terzo suono”. Mainz: Schott Music. Google Scholar Lots, I. S., and Stone, L. (2008). Perception of musical consonance and dissonance: an outcome of neural synchronization. J. R. Soc. Interface 5, 1429–1434. doi: 10.1098/rsif.2008.0143 PubMed Abstract | CrossRef Full Text | Google Scholar Manetti, C., Ceruso, M. A., Giuliani, A., Webber, C. L. Jr., and Zbilut, J. P. (1999). Recurrence quantification analysis as a tool for characterization of molecular dynamics simulations. Phys. Rev. E 59, 992–998. doi: 10.1103/PhysRevE.59.992 CrossRef Full Text | Google Scholar Marwan, N., Romano, M. C., Thiel, M., and Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329. doi: 10.1016/j.physrep.2006.11.001 CrossRef Full Text | Google Scholar McCauley, J. L. (1994). Chaos, Dynamics and Fractals. Cambridge: Cambridge University Press. Google Scholar McDermott, J., Schultz, A. F., Undurraga, E. A., and Godoy, R. A. (2016). Indifference to dissonance in native Amazonians reveals cultural variations in music perception. Nature 535, 547–550. doi: 10.1038/nature18635 PubMed Abstract | CrossRef Full Text | Google Scholar Minati, L., Rosazza, C., D’Incerti, L., Pietrocini, E., Valentini, L., Scaioli, V., et al. (2008). FMRI/ERP of musical syntax: comparison of melodies and unstructured note sequences. Neuroreport 19, 1381–1385. doi: 10.1097/WNR.0b013e32830c694b PubMed Abstract | CrossRef Full Text | Google Scholar Nikolsky, A. (2015). Evolution of tonal organization in music mirrors symbolic representation of perceptual reality. Part-1: prehistoric. Front. Psychol. 6:1405. doi: 10.3389/fpsyg.2015.01405 PubMed Abstract | CrossRef Full Text | Google Scholar Orsucci, F., Giuliani, A., Webber, C., Zbilut, J., Fonagy, P., and Mazza, M. (2006). Combinatorics and synchronization in natural semiotics. Phys. A Stat. Mech. Appl. 361, 665–676. doi: 10.1016/j.physa.2005.06.044 CrossRef Full Text | Google Scholar Pankovski, T., and Pankovska, E. (2017). Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity. Biol. Insp. Cong. Arch. 22, 82–94. doi: 10.1016/j.bica.2017.09.001 CrossRef Full Text | Google Scholar Park, J. Y., Park, H., Kim, J., and Park, H. J. (2011). Consonant chords stimulate higher EEG gamma activity than dissonant chords. Neurosci. Lett. 488, 101–105. doi: 10.1016/j.neulet.2010.11.011 PubMed Abstract | CrossRef Full Text | Google Scholar Parncutt, R., and Hair, G. (2011). Consonance and dissonance in theory and psychology: disentangling dissonant dichotomies. J. Interdiscip. Music Stud. 5, 119–166. Google Scholar Perani, D., Saccuman, M. C., Scifo, P., Spada, D., Andreolli, G., Rovelli, R., et al. (2010). Functional specializations for music processing in the human newborn brain. Proc. Natl. Acad. Sci. U.S.A. 107, 4758–4763. doi: 10.1073/pnas.0909074107 PubMed Abstract | CrossRef Full Text | Google Scholar Piana, G. (2007). Barlumi per una Filosofia Della Musica. Morrisville: Lulu Press. Google Scholar Plomp, R. (1976). Aspects of Tone Sensation: A Psychophysical Study. London: Academic Press. Google Scholar Plomp, R., and Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. J. Acoust. Soc. Am. 38, 548–560. doi: 10.1121/1.1909741 PubMed Abstract | CrossRef Full Text | Google Scholar Roads, C. (2001). Microsound. Cambridge, MA: The MIT Press. Google Scholar Roederer, J. G. (2008). The Physics and Psychophysics of Music. New York, NY: Springer. Google Scholar Schroeder, M. (1990). Fractals, Chaos, Power Laws. New York, NY: W.H Freeman and Co. Google Scholar Schwartz, D. A., Howe, C. Q., and Purves, D. (2003). The statistical structure of human speech sounds predicts music universals. J. Neurosci. 23, 7160–7168. PubMed Abstract | Google Scholar Serra, J., Serra, X., and Andrzejak, R. G. (2009). Cross recurrence quantification for cover song identification. New J. Phys. 11:093017. doi: 10.1088/1367-2630/11/9/093017 CrossRef Full Text | Google Scholar Trulla, L. L., Giuliani, A., Zbilut, J. P., and Webber, C. L. (1996). Recurrence quantification analysis of the logistic equation with transients. Phys. Lett. A 223, 255–260. doi: 10.1016/S0375-9601(96)00741-4 CrossRef Full Text | Google Scholar Trulla, L. L., Giuliani, A., Zimatore, G., Colosimo, A., and Zbilut, J. P. (2005). Non-linear assessment of musical consonance. Electron. J. Theor. Phys. 8, 22–34. Google Scholar Wang, X. (2013). The harmonic organization of auditory cortex. Front. Syst. Neurosci. 7:114. doi: 10.3389/fnsys.2013.00114 CrossRef Full Text | Google Scholar Webber, C. L., and Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973. doi: 10.1152/jappl.1994.76.2.965 PubMed Abstract | CrossRef Full Text | Google Scholar Zimatore, G., Giuliani, A., Hatzopoulos, S., Martini, A., and Colosimo, A. (2003). Otoacoustic emissions at different click intensities: invariant and subject-dependent features. J. Appl. Physiol. 95, 2299–2305. doi: 10.1152/japplphysiol.00667.2003 PubMed Abstract | CrossRef Full Text | Google Scholar Zimatore, G., Hatzopoulos, S., Giuliani, A., Martini, A., and Colosimo, A. (2002). Comparison of transient otoacoustic emission (TEOAE) responses from neonatal and adult ears. J. Appl. Physiol. 92, 2521–2528. doi: 10.1152/japplphysiol.01163.2001 PubMed Abstract | CrossRef Full Text | Google Scholar q2uhzd38kole1b7ybbird7o6w7ek5e2 2412464 2412462 2022-08-07T02:46:22Z Guy vandegrift 813252 /* From */ wikitext text/x-wiki ==From== [https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00381/full Computational Approach to Musical Consonance and Dissonance: Lluis L. Trulla1, Nicola Di Stefano and Alessandro Giuliani] References #Abel, M., Ahnert, K., and Bergweiler, S. (2009). Synchronization of sound sources. Phys. Rev. Lett. 103:114301. doi: 10.1103/PhysRevLett.103.114301 #Benade, A. H. (1973). The physics of brasses. Sci. Am. 229, 24–35. doi: 10.1038/scientificamerican0773-24 #Bidelman, G. M., and Heinz, M. G. (2011). Auditory-nerve responses predict pitch attributes related to musical consonance-dissonance for normal and impaired hearing. J. Acoust. Soc. Am. 130, 1488–1502. doi: 10.1121/1.3605559 #Bidelman, G. M., and Krishnan, A. (2009). Neural correlates of consonance, dissonance, and the hierarchy of musical pitch in the human brainstem. J. Neurosci. 29, 13165–13171. doi: 10.1523/JNEUROSCI.3900-09.2009 #Bowling, D. L., Hoeschele, M., Kamraan, Z. G., and Tecumseh Fitch, W. (2017). The nature and nurture of musical consonance. Music Percept. 35, 118–121. doi: 10.1525/mp.2017.35.1.118 #Bowling, D. L., and Purves, D. (2015). A biological rationale for musical consonance. Proc. Natl. Acad. Sci. U.S.A. 112, 11155–11160. doi: 10.1073/pnas.1505768112 #Cartwright, J. H. E., Douthettb, J., González, D. L., Krantzd, R., and Piro, O. (2010). Two musical paths to the Farey series and devil’s staircase. J. Math. Music 4, 57–74. doi: 10.1080/17459737.2010.485001 #Cartwright, J. H. E., Gonzalez, D. L., and Piro, O. (2001). Pitch perception: a dynamical-systems perspective. Proc. Natl. Acad. Sci. U.S.A. 98, 4855–4859. doi: 10.1073/pnas.081070998 #Cartwright, J. H. E., Gonzalez, D. L., Piro, O., and Stanziali, D. (2002). Aesthetics, dynamics, and musical scales: a golden connection. J. New Music Res. 31, 51–58. doi: 10.1076/jnmr.31.1.51.8099 #Cross, I. (2003). Music as a biocultural phenomenon. Ann. N. Y. Acad. Sci. 999, 106–111. doi: 10.1196/annals.1284.010 #Di Stefano, N., Focaroli, V., Giuliani, A., Formica, D., Taffoni, F., and Keller, F. (2017). A new research method to test auditory preferences in young listeners: results from a consonance versus dissonance perception study. Psychol. Music 45, 699–712. doi: 10.1177/0305735616681205 #Eckmann, J. P., Kamphorst, S. O., and Ruelle, D. (1987). Recurrence plots of dynamical systems. Europhys. Lett. 4, 973–976. doi: 10.1209/0295-5075/4/9/004 #Fastl, H., and Zwicker, E. (2006). Psychoacoustic. Facts and Models. Berlin: Springer. #Foo, F., King-Stephens, D., Weber, P., Laxer, K., Parvizi, J., and Knight, R. T. (2016). Differential processing of consonance and dissonance within the human superior temporal gyrus. Front. Hum. Neurosci. 10:154. doi: 10.3389/fnhum.2016.00154 #Frova, A. (1999). Fisica nella Musica. Bologna: Zanichelli. #González-García, N., González, M. A., and Rendón, P. L. (2016). Neural activity related to discrimination and vocal production of consonant and dissonant musical intervals. Brain Res. 1643, 59–69. doi: 10.1016/j.brainres.2016.04.065 #Helmholtz, H. (1954). On the Sensations of Tone. New York, NY: Dover Publications. #Kameoka, A., and Kuriyagawa, M. (1969a). Consonance theory part I: consonance of dyads. J. Acoust. Soc. Am. 45, 1451–1459. doi: 10.1121/1.1911623 #Kameoka, A., and Kuriyagawa, M. (1969b). Consonance theory part II: consonance of complex tones and its calculation method. J. Acoust. Soc. Am. 45, 1460–1469. doi: 10.1121/1.1911624 #Kennel, M. B., Brown, R., and Abarbanel, H. D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403. doi: 10.1103/PhysRevA.45.3403 #Koelsch, S., Fritz, T., Schulze, K., Alsop, D., and Schlaug, G. (2005). Adults and children processing music: An fMRI study. Neuroimage 25, 1068–1076. doi: 10.1016/j.neuroimage.2004.12.050 #Koelsch, S., and Mulder, J. (2002). Electric brain responses to inappropriate harmonies during listening to expressive music. Clin. Neurophysiol. 113, 862–869. doi: 10.1016/S1388-2457(02)00050-0 #Large, E. W., and Almonte, F. V. (2012). Neurodynamics, tonality, and the auditory brainstem response. Ann. N. Y. Acad. Sci. 1252, E1–E7. doi: 10.1111/j.1749-6632.2012.06594.x #Large, E. W., and Tretakis, A. E. (2005). Tonality and nonlinear resonance. Ann. N. Y. Acad. Sci. 1060, 53–56. doi: 10.1196/annals.1360.046 #Lohri, A. (2016). Kombinationstöne und Tartinis “terzo suono”. Mainz: Schott Music. #Lots, I. S., and Stone, L. (2008). Perception of musical consonance and dissonance: an outcome of neural synchronization. J. R. Soc. Interface 5, 1429–1434. doi: 10.1098/rsif.2008.0143 #Manetti, C., Ceruso, M. A., Giuliani, A., Webber, C. L. Jr., and Zbilut, J. P. (1999). Recurrence quantification analysis as a tool for characterization of molecular dynamics simulations. Phys. Rev. E 59, 992–998. doi: 10.1103/PhysRevE.59.992 #Marwan, N., Romano, M. C., Thiel, M., and Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329. doi: 10.1016/j.physrep.2006.11.001 #McCauley, J. L. (1994). Chaos, Dynamics and Fractals. Cambridge: Cambridge University Press. #McDermott, J., Schultz, A. F., Undurraga, E. A., and Godoy, R. A. (2016). Indifference to dissonance in native Amazonians reveals cultural variations in music perception. Nature 535, 547–550. doi: 10.1038/nature18635 #Minati, L., Rosazza, C., D’Incerti, L., Pietrocini, E., Valentini, L., Scaioli, V., et al. (2008). FMRI/ERP of musical syntax: comparison of melodies and unstructured note sequences. Neuroreport 19, 1381–1385. doi: 10.1097/WNR.0b013e32830c694b #Nikolsky, A. (2015). Evolution of tonal organization in music mirrors symbolic representation of perceptual reality. Part-1: prehistoric. Front. Psychol. 6:1405. doi: 10.3389/fpsyg.2015.01405 #Orsucci, F., Giuliani, A., Webber, C., Zbilut, J., Fonagy, P., and Mazza, M. (2006). Combinatorics and synchronization in natural semiotics. Phys. A Stat. Mech. Appl. 361, 665–676. doi: 10.1016/j.physa.2005.06.044 #Pankovski, T., and Pankovska, E. (2017). Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity. Biol. Insp. Cong. Arch. 22, 82–94. doi: 10.1016/j.bica.2017.09.001 #Park, J. Y., Park, H., Kim, J., and Park, H. J. (2011). Consonant chords stimulate higher EEG gamma activity than dissonant chords. Neurosci. Lett. 488, 101–105. doi: 10.1016/j.neulet.2010.11.011 #Parncutt, R., and Hair, G. (2011). Consonance and dissonance in theory and psychology: disentangling dissonant dichotomies. J. Interdiscip. Music Stud. 5, 119–166. #Perani, D., Saccuman, M. C., Scifo, P., Spada, D., Andreolli, G., Rovelli, R., et al. (2010). Functional specializations for music processing in the human newborn brain. Proc. Natl. Acad. Sci. U.S.A. 107, 4758–4763. doi: 10.1073/pnas.0909074107 #Piana, G. (2007). Barlumi per una Filosofia Della Musica. Morrisville: Lulu Press. #Plomp, R. (1976). Aspects of Tone Sensation: A Psychophysical Study. London: Academic Press. #Plomp, R., and Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. J. Acoust. Soc. Am. 38, 548–560. doi: 10.1121/1.1909741 #Roads, C. (2001). Microsound. Cambridge, MA: The MIT Press. #Roederer, J. G. (2008). The Physics and Psychophysics of Music. New York, NY: Springer. #Schroeder, M. (1990). Fractals, Chaos, Power Laws. New York, NY: W.H Freeman and Co. #Schwartz, D. A., Howe, C. Q., and Purves, D. (2003). The statistical structure of human speech sounds predicts music universals. J. Neurosci. 23, 7160–7168. #Serra, J., Serra, X., and Andrzejak, R. G. (2009). Cross recurrence quantification for cover song identification. New J. Phys. 11:093017. doi: 10.1088/1367-2630/11/9/093017 #Trulla, L. L., Giuliani, A., Zbilut, J. P., and Webber, C. L. (1996). Recurrence quantification analysis of the logistic equation with transients. Phys. Lett. A 223, 255–260. doi: 10.1016/S0375-9601(96)00741-4 #Trulla, L. L., Giuliani, A., Zimatore, G., Colosimo, A., and Zbilut, J. P. (2005). Non-linear assessment of musical consonance. Electron. J. Theor. Phys. 8, 22–34. #Wang, X. (2013). The harmonic organization of auditory cortex. Front. Syst. Neurosci. 7:114. doi: 10.3389/fnsys.2013.00114 #Webber, C. L., and Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973. doi: 10.1152/jappl.1994.76.2.965 #Zimatore, G., Giuliani, A., Hatzopoulos, S., Martini, A., and Colosimo, A. (2003). Otoacoustic emissions at different click intensities: invariant and subject-dependent features. J. Appl. Physiol. 95, 2299–2305. doi: 10.1152/japplphysiol.00667.2003 #Zimatore, G., Hatzopoulos, S., Giuliani, A., Martini, A., and Colosimo, A. (2002). Comparison of transient otoacoustic emission (TEOAE) responses from neonatal and adult ears. J. Appl. Physiol. 92, 2521–2528. doi: 10.1152/japplphysiol.01163.2001 gpovxkcrs3rmi6nx4gx3vrly1cmuicx 2412466 2412464 2022-08-07T02:50:10Z Guy vandegrift 813252 /* From */ wikitext text/x-wiki ==From== ==Links== *[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/ Lott and Stone: Perception of musical consonance and dissonance: an outcome of neural synchronization] *[https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00381/full Computational Approach to Musical Consonance and Dissonance: Lluis L. Trulla1, Nicola Di Stefano and Alessandro Giuliani] has a long list of references: #Abel, M., Ahnert, K., and Bergweiler, S. (2009). Synchronization of sound sources. Phys. Rev. Lett. 103:114301. doi: 10.1103/PhysRevLett.103.114301 #Benade, A. H. (1973). The physics of brasses. Sci. Am. 229, 24–35. doi: 10.1038/scientificamerican0773-24 #Bidelman, G. M., and Heinz, M. G. (2011). Auditory-nerve responses predict pitch attributes related to musical consonance-dissonance for normal and impaired hearing. J. Acoust. Soc. Am. 130, 1488–1502. doi: 10.1121/1.3605559 #Bidelman, G. M., and Krishnan, A. (2009). Neural correlates of consonance, dissonance, and the hierarchy of musical pitch in the human brainstem. J. Neurosci. 29, 13165–13171. doi: 10.1523/JNEUROSCI.3900-09.2009 #Bowling, D. L., Hoeschele, M., Kamraan, Z. G., and Tecumseh Fitch, W. (2017). The nature and nurture of musical consonance. Music Percept. 35, 118–121. doi: 10.1525/mp.2017.35.1.118 #Bowling, D. L., and Purves, D. (2015). A biological rationale for musical consonance. Proc. Natl. Acad. Sci. U.S.A. 112, 11155–11160. doi: 10.1073/pnas.1505768112 #Cartwright, J. H. E., Douthettb, J., González, D. L., Krantzd, R., and Piro, O. (2010). Two musical paths to the Farey series and devil’s staircase. J. Math. Music 4, 57–74. doi: 10.1080/17459737.2010.485001 #Cartwright, J. H. E., Gonzalez, D. L., and Piro, O. (2001). Pitch perception: a dynamical-systems perspective. Proc. Natl. Acad. Sci. U.S.A. 98, 4855–4859. doi: 10.1073/pnas.081070998 #Cartwright, J. H. E., Gonzalez, D. L., Piro, O., and Stanziali, D. (2002). Aesthetics, dynamics, and musical scales: a golden connection. J. New Music Res. 31, 51–58. doi: 10.1076/jnmr.31.1.51.8099 #Cross, I. (2003). Music as a biocultural phenomenon. Ann. N. Y. Acad. Sci. 999, 106–111. doi: 10.1196/annals.1284.010 #Di Stefano, N., Focaroli, V., Giuliani, A., Formica, D., Taffoni, F., and Keller, F. (2017). A new research method to test auditory preferences in young listeners: results from a consonance versus dissonance perception study. Psychol. Music 45, 699–712. doi: 10.1177/0305735616681205 #Eckmann, J. P., Kamphorst, S. O., and Ruelle, D. (1987). Recurrence plots of dynamical systems. Europhys. Lett. 4, 973–976. doi: 10.1209/0295-5075/4/9/004 #Fastl, H., and Zwicker, E. (2006). Psychoacoustic. Facts and Models. Berlin: Springer. #Foo, F., King-Stephens, D., Weber, P., Laxer, K., Parvizi, J., and Knight, R. T. (2016). Differential processing of consonance and dissonance within the human superior temporal gyrus. Front. Hum. Neurosci. 10:154. doi: 10.3389/fnhum.2016.00154 #Frova, A. (1999). Fisica nella Musica. Bologna: Zanichelli. #González-García, N., González, M. A., and Rendón, P. L. (2016). Neural activity related to discrimination and vocal production of consonant and dissonant musical intervals. Brain Res. 1643, 59–69. doi: 10.1016/j.brainres.2016.04.065 #Helmholtz, H. (1954). On the Sensations of Tone. New York, NY: Dover Publications. #Kameoka, A., and Kuriyagawa, M. (1969a). Consonance theory part I: consonance of dyads. J. Acoust. Soc. Am. 45, 1451–1459. doi: 10.1121/1.1911623 #Kameoka, A., and Kuriyagawa, M. (1969b). Consonance theory part II: consonance of complex tones and its calculation method. J. Acoust. Soc. Am. 45, 1460–1469. doi: 10.1121/1.1911624 #Kennel, M. B., Brown, R., and Abarbanel, H. D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403. doi: 10.1103/PhysRevA.45.3403 #Koelsch, S., Fritz, T., Schulze, K., Alsop, D., and Schlaug, G. (2005). Adults and children processing music: An fMRI study. Neuroimage 25, 1068–1076. doi: 10.1016/j.neuroimage.2004.12.050 #Koelsch, S., and Mulder, J. (2002). Electric brain responses to inappropriate harmonies during listening to expressive music. Clin. Neurophysiol. 113, 862–869. doi: 10.1016/S1388-2457(02)00050-0 #Large, E. W., and Almonte, F. V. (2012). Neurodynamics, tonality, and the auditory brainstem response. Ann. N. Y. Acad. Sci. 1252, E1–E7. doi: 10.1111/j.1749-6632.2012.06594.x #Large, E. W., and Tretakis, A. E. (2005). Tonality and nonlinear resonance. Ann. N. Y. Acad. Sci. 1060, 53–56. doi: 10.1196/annals.1360.046 #Lohri, A. (2016). Kombinationstöne und Tartinis “terzo suono”. Mainz: Schott Music. #Lots, I. S., and Stone, L. (2008). Perception of musical consonance and dissonance: an outcome of neural synchronization. J. R. Soc. Interface 5, 1429–1434. doi: 10.1098/rsif.2008.0143 #Manetti, C., Ceruso, M. A., Giuliani, A., Webber, C. L. Jr., and Zbilut, J. P. (1999). Recurrence quantification analysis as a tool for characterization of molecular dynamics simulations. Phys. Rev. E 59, 992–998. doi: 10.1103/PhysRevE.59.992 #Marwan, N., Romano, M. C., Thiel, M., and Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329. doi: 10.1016/j.physrep.2006.11.001 #McCauley, J. L. (1994). Chaos, Dynamics and Fractals. Cambridge: Cambridge University Press. #McDermott, J., Schultz, A. F., Undurraga, E. A., and Godoy, R. A. (2016). Indifference to dissonance in native Amazonians reveals cultural variations in music perception. Nature 535, 547–550. doi: 10.1038/nature18635 #Minati, L., Rosazza, C., D’Incerti, L., Pietrocini, E., Valentini, L., Scaioli, V., et al. (2008). FMRI/ERP of musical syntax: comparison of melodies and unstructured note sequences. Neuroreport 19, 1381–1385. doi: 10.1097/WNR.0b013e32830c694b #Nikolsky, A. (2015). Evolution of tonal organization in music mirrors symbolic representation of perceptual reality. Part-1: prehistoric. Front. Psychol. 6:1405. doi: 10.3389/fpsyg.2015.01405 #Orsucci, F., Giuliani, A., Webber, C., Zbilut, J., Fonagy, P., and Mazza, M. (2006). Combinatorics and synchronization in natural semiotics. Phys. A Stat. Mech. Appl. 361, 665–676. doi: 10.1016/j.physa.2005.06.044 #Pankovski, T., and Pankovska, E. (2017). Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity. Biol. Insp. Cong. Arch. 22, 82–94. doi: 10.1016/j.bica.2017.09.001 #Park, J. Y., Park, H., Kim, J., and Park, H. J. (2011). Consonant chords stimulate higher EEG gamma activity than dissonant chords. Neurosci. Lett. 488, 101–105. doi: 10.1016/j.neulet.2010.11.011 #Parncutt, R., and Hair, G. (2011). Consonance and dissonance in theory and psychology: disentangling dissonant dichotomies. J. Interdiscip. Music Stud. 5, 119–166. #Perani, D., Saccuman, M. C., Scifo, P., Spada, D., Andreolli, G., Rovelli, R., et al. (2010). Functional specializations for music processing in the human newborn brain. Proc. Natl. Acad. Sci. U.S.A. 107, 4758–4763. doi: 10.1073/pnas.0909074107 #Piana, G. (2007). Barlumi per una Filosofia Della Musica. Morrisville: Lulu Press. #Plomp, R. (1976). Aspects of Tone Sensation: A Psychophysical Study. London: Academic Press. #Plomp, R., and Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. J. Acoust. Soc. Am. 38, 548–560. doi: 10.1121/1.1909741 #Roads, C. (2001). Microsound. Cambridge, MA: The MIT Press. #Roederer, J. G. (2008). The Physics and Psychophysics of Music. New York, NY: Springer. #Schroeder, M. (1990). Fractals, Chaos, Power Laws. New York, NY: W.H Freeman and Co. #Schwartz, D. A., Howe, C. Q., and Purves, D. (2003). The statistical structure of human speech sounds predicts music universals. J. Neurosci. 23, 7160–7168. #Serra, J., Serra, X., and Andrzejak, R. G. (2009). Cross recurrence quantification for cover song identification. New J. Phys. 11:093017. doi: 10.1088/1367-2630/11/9/093017 #Trulla, L. L., Giuliani, A., Zbilut, J. P., and Webber, C. L. (1996). Recurrence quantification analysis of the logistic equation with transients. Phys. Lett. A 223, 255–260. doi: 10.1016/S0375-9601(96)00741-4 #Trulla, L. L., Giuliani, A., Zimatore, G., Colosimo, A., and Zbilut, J. P. (2005). Non-linear assessment of musical consonance. Electron. J. Theor. Phys. 8, 22–34. #Wang, X. (2013). The harmonic organization of auditory cortex. Front. Syst. Neurosci. 7:114. doi: 10.3389/fnsys.2013.00114 #Webber, C. L., and Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973. doi: 10.1152/jappl.1994.76.2.965 #Zimatore, G., Giuliani, A., Hatzopoulos, S., Martini, A., and Colosimo, A. (2003). Otoacoustic emissions at different click intensities: invariant and subject-dependent features. J. Appl. Physiol. 95, 2299–2305. doi: 10.1152/japplphysiol.00667.2003 #Zimatore, G., Hatzopoulos, S., Giuliani, A., Martini, A., and Colosimo, A. (2002). Comparison of transient otoacoustic emission (TEOAE) responses from neonatal and adult ears. J. Appl. Physiol. 92, 2521–2528. doi: 10.1152/japplphysiol.01163.2001 hz0ikztirivwvkiqj6q7j6z85lrlvtp 2412467 2412466 2022-08-07T02:50:24Z Guy vandegrift 813252 /* From */ wikitext text/x-wiki ==Links== *[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/ Lott and Stone: Perception of musical consonance and dissonance: an outcome of neural synchronization] *[https://www.frontiersin.org/articles/10.3389/fpsyg.2018.00381/full Computational Approach to Musical Consonance and Dissonance: Lluis L. Trulla1, Nicola Di Stefano and Alessandro Giuliani] has a long list of references: #Abel, M., Ahnert, K., and Bergweiler, S. (2009). Synchronization of sound sources. Phys. Rev. Lett. 103:114301. doi: 10.1103/PhysRevLett.103.114301 #Benade, A. H. (1973). The physics of brasses. Sci. Am. 229, 24–35. doi: 10.1038/scientificamerican0773-24 #Bidelman, G. M., and Heinz, M. G. (2011). Auditory-nerve responses predict pitch attributes related to musical consonance-dissonance for normal and impaired hearing. J. Acoust. Soc. Am. 130, 1488–1502. doi: 10.1121/1.3605559 #Bidelman, G. M., and Krishnan, A. (2009). Neural correlates of consonance, dissonance, and the hierarchy of musical pitch in the human brainstem. J. Neurosci. 29, 13165–13171. doi: 10.1523/JNEUROSCI.3900-09.2009 #Bowling, D. L., Hoeschele, M., Kamraan, Z. G., and Tecumseh Fitch, W. (2017). The nature and nurture of musical consonance. Music Percept. 35, 118–121. doi: 10.1525/mp.2017.35.1.118 #Bowling, D. L., and Purves, D. (2015). A biological rationale for musical consonance. Proc. Natl. Acad. Sci. U.S.A. 112, 11155–11160. doi: 10.1073/pnas.1505768112 #Cartwright, J. H. E., Douthettb, J., González, D. L., Krantzd, R., and Piro, O. (2010). Two musical paths to the Farey series and devil’s staircase. J. Math. Music 4, 57–74. doi: 10.1080/17459737.2010.485001 #Cartwright, J. H. E., Gonzalez, D. L., and Piro, O. (2001). Pitch perception: a dynamical-systems perspective. Proc. Natl. Acad. Sci. U.S.A. 98, 4855–4859. doi: 10.1073/pnas.081070998 #Cartwright, J. H. E., Gonzalez, D. L., Piro, O., and Stanziali, D. (2002). Aesthetics, dynamics, and musical scales: a golden connection. J. New Music Res. 31, 51–58. doi: 10.1076/jnmr.31.1.51.8099 #Cross, I. (2003). Music as a biocultural phenomenon. Ann. N. Y. Acad. Sci. 999, 106–111. doi: 10.1196/annals.1284.010 #Di Stefano, N., Focaroli, V., Giuliani, A., Formica, D., Taffoni, F., and Keller, F. (2017). A new research method to test auditory preferences in young listeners: results from a consonance versus dissonance perception study. Psychol. Music 45, 699–712. doi: 10.1177/0305735616681205 #Eckmann, J. P., Kamphorst, S. O., and Ruelle, D. (1987). Recurrence plots of dynamical systems. Europhys. Lett. 4, 973–976. doi: 10.1209/0295-5075/4/9/004 #Fastl, H., and Zwicker, E. (2006). Psychoacoustic. Facts and Models. Berlin: Springer. #Foo, F., King-Stephens, D., Weber, P., Laxer, K., Parvizi, J., and Knight, R. T. (2016). Differential processing of consonance and dissonance within the human superior temporal gyrus. Front. Hum. Neurosci. 10:154. doi: 10.3389/fnhum.2016.00154 #Frova, A. (1999). Fisica nella Musica. Bologna: Zanichelli. #González-García, N., González, M. A., and Rendón, P. L. (2016). Neural activity related to discrimination and vocal production of consonant and dissonant musical intervals. Brain Res. 1643, 59–69. doi: 10.1016/j.brainres.2016.04.065 #Helmholtz, H. (1954). On the Sensations of Tone. New York, NY: Dover Publications. #Kameoka, A., and Kuriyagawa, M. (1969a). Consonance theory part I: consonance of dyads. J. Acoust. Soc. Am. 45, 1451–1459. doi: 10.1121/1.1911623 #Kameoka, A., and Kuriyagawa, M. (1969b). Consonance theory part II: consonance of complex tones and its calculation method. J. Acoust. Soc. Am. 45, 1460–1469. doi: 10.1121/1.1911624 #Kennel, M. B., Brown, R., and Abarbanel, H. D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403. doi: 10.1103/PhysRevA.45.3403 #Koelsch, S., Fritz, T., Schulze, K., Alsop, D., and Schlaug, G. (2005). Adults and children processing music: An fMRI study. Neuroimage 25, 1068–1076. doi: 10.1016/j.neuroimage.2004.12.050 #Koelsch, S., and Mulder, J. (2002). Electric brain responses to inappropriate harmonies during listening to expressive music. Clin. Neurophysiol. 113, 862–869. doi: 10.1016/S1388-2457(02)00050-0 #Large, E. W., and Almonte, F. V. (2012). Neurodynamics, tonality, and the auditory brainstem response. Ann. N. Y. Acad. Sci. 1252, E1–E7. doi: 10.1111/j.1749-6632.2012.06594.x #Large, E. W., and Tretakis, A. E. (2005). Tonality and nonlinear resonance. Ann. N. Y. Acad. Sci. 1060, 53–56. doi: 10.1196/annals.1360.046 #Lohri, A. (2016). Kombinationstöne und Tartinis “terzo suono”. Mainz: Schott Music. #Lots, I. S., and Stone, L. (2008). Perception of musical consonance and dissonance: an outcome of neural synchronization. J. R. Soc. Interface 5, 1429–1434. doi: 10.1098/rsif.2008.0143 #Manetti, C., Ceruso, M. A., Giuliani, A., Webber, C. L. Jr., and Zbilut, J. P. (1999). Recurrence quantification analysis as a tool for characterization of molecular dynamics simulations. Phys. Rev. E 59, 992–998. doi: 10.1103/PhysRevE.59.992 #Marwan, N., Romano, M. C., Thiel, M., and Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329. doi: 10.1016/j.physrep.2006.11.001 #McCauley, J. L. (1994). Chaos, Dynamics and Fractals. Cambridge: Cambridge University Press. #McDermott, J., Schultz, A. F., Undurraga, E. A., and Godoy, R. A. (2016). Indifference to dissonance in native Amazonians reveals cultural variations in music perception. Nature 535, 547–550. doi: 10.1038/nature18635 #Minati, L., Rosazza, C., D’Incerti, L., Pietrocini, E., Valentini, L., Scaioli, V., et al. (2008). FMRI/ERP of musical syntax: comparison of melodies and unstructured note sequences. Neuroreport 19, 1381–1385. doi: 10.1097/WNR.0b013e32830c694b #Nikolsky, A. (2015). Evolution of tonal organization in music mirrors symbolic representation of perceptual reality. Part-1: prehistoric. Front. Psychol. 6:1405. doi: 10.3389/fpsyg.2015.01405 #Orsucci, F., Giuliani, A., Webber, C., Zbilut, J., Fonagy, P., and Mazza, M. (2006). Combinatorics and synchronization in natural semiotics. Phys. A Stat. Mech. Appl. 361, 665–676. doi: 10.1016/j.physa.2005.06.044 #Pankovski, T., and Pankovska, E. (2017). Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity. Biol. Insp. Cong. Arch. 22, 82–94. doi: 10.1016/j.bica.2017.09.001 #Park, J. Y., Park, H., Kim, J., and Park, H. J. (2011). Consonant chords stimulate higher EEG gamma activity than dissonant chords. Neurosci. Lett. 488, 101–105. doi: 10.1016/j.neulet.2010.11.011 #Parncutt, R., and Hair, G. (2011). Consonance and dissonance in theory and psychology: disentangling dissonant dichotomies. J. Interdiscip. Music Stud. 5, 119–166. #Perani, D., Saccuman, M. C., Scifo, P., Spada, D., Andreolli, G., Rovelli, R., et al. (2010). Functional specializations for music processing in the human newborn brain. Proc. Natl. Acad. Sci. U.S.A. 107, 4758–4763. doi: 10.1073/pnas.0909074107 #Piana, G. (2007). Barlumi per una Filosofia Della Musica. Morrisville: Lulu Press. #Plomp, R. (1976). Aspects of Tone Sensation: A Psychophysical Study. London: Academic Press. #Plomp, R., and Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. J. Acoust. Soc. Am. 38, 548–560. doi: 10.1121/1.1909741 #Roads, C. (2001). Microsound. Cambridge, MA: The MIT Press. #Roederer, J. G. (2008). The Physics and Psychophysics of Music. New York, NY: Springer. #Schroeder, M. (1990). Fractals, Chaos, Power Laws. New York, NY: W.H Freeman and Co. #Schwartz, D. A., Howe, C. Q., and Purves, D. (2003). The statistical structure of human speech sounds predicts music universals. J. Neurosci. 23, 7160–7168. #Serra, J., Serra, X., and Andrzejak, R. G. (2009). Cross recurrence quantification for cover song identification. New J. Phys. 11:093017. doi: 10.1088/1367-2630/11/9/093017 #Trulla, L. L., Giuliani, A., Zbilut, J. P., and Webber, C. L. (1996). Recurrence quantification analysis of the logistic equation with transients. Phys. Lett. A 223, 255–260. doi: 10.1016/S0375-9601(96)00741-4 #Trulla, L. L., Giuliani, A., Zimatore, G., Colosimo, A., and Zbilut, J. P. (2005). Non-linear assessment of musical consonance. Electron. J. Theor. Phys. 8, 22–34. #Wang, X. (2013). The harmonic organization of auditory cortex. Front. Syst. Neurosci. 7:114. doi: 10.3389/fnsys.2013.00114 #Webber, C. L., and Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973. doi: 10.1152/jappl.1994.76.2.965 #Zimatore, G., Giuliani, A., Hatzopoulos, S., Martini, A., and Colosimo, A. (2003). Otoacoustic emissions at different click intensities: invariant and subject-dependent features. J. Appl. Physiol. 95, 2299–2305. doi: 10.1152/japplphysiol.00667.2003 #Zimatore, G., Hatzopoulos, S., Giuliani, A., Martini, A., and Colosimo, A. (2002). Comparison of transient otoacoustic emission (TEOAE) responses from neonatal and adult ears. J. Appl. Physiol. 92, 2521–2528. doi: 10.1152/japplphysiol.01163.2001 39nvykb8a42hjhpvnyrfb7k64mqc3sb 0 286144 2412494 2022-08-07T06:53:41Z U3219905 2947550 New resource with "Test" wikitext text/x-wiki Test bop1vj5i98maix36pjrpgep1w6hnxfe 2412496 2412494 2022-08-07T06:56:55Z U3219905 2947550 wikitext text/x-wiki {{title|Chapter title:<br>Subtitle?}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] thp5r91aziue2l80cis4wxipwwn2uzy 0 286145 2412500 2022-08-07T10:50:47Z U3211603 2947419 Added Template - {{subst:ME/BCS}} wikitext text/x-wiki {{title|Chapter title:<br>Subtitle?}} {{MECR3|1=https://yourlinkgoeshere.com}} __TOC__ ==Overview== You are underway {{smile}}! This template provides tips for [[Motivation and emotion/Assessment/Topic|topic development]]. Gradually remove these suggestions as you develop the chapter. Also consult the [[Motivation and emotion/Assessment/Chapter|author guidelines]]. At the top of the chapter, the title and sub-title should match the ''exact'' wording and casing as shown in the {{Motivation and emotion/Book}}. The sub-titles all end with a question mark. This Overview section should be concise but consist of several paragraphs which engage the reader, illustrate the problem, and outline how psychological science can help. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is the first focus question? * What is the second focus question? * What is the third focus question? {{RoundBoxBottom}} {{tip| Suggestions for this section: * What is the problem? Why is it important? * How can specific motivation and/or emotion theories and research help? * Provide an example or case study. * Conclude with Focus questions to guide the chapter. }} ==Main headings== How you are going to structure the chapter? Aim for three to six main headings between the [[#Overview|Overview]] and [[#Conclusion|Conclusion]]. {{tip|Suggestions for this section: * For the [[Motivation and emotion/Assessment/Topic|topic development]], provide at least 3 bullet-points about key content per section. Include key citations. * For the [[Motivation and emotion/Assessment/Chapter|book chapter]], expand the bullet points into paragraphs. * If a section has a lot of content, arrange it into two to five sub-headings such as in the [[#Interactive learning features|interactive learning features section]]. Avoid having sections with only one sub-heading. }} ==Learning features== What brings an online book chapter to life are its interactive learning features. Case studies, feature boxes, figures, links, tables, and quiz questions can be used throughout the chapter. ===Case studies=== Case studies describe real-world examples of concepts in action. Case studies can be real or fictional. A case could be used multiple times during a chapter to illustrate different theories or stages. It is often helpful to present case studies using [[#Feature boxes|feature boxes]]. ===Boxes=== Boxes can be used to highlight content, but don't overuse them. There are many different ways of creating boxes (e.g., see [[Help:Pretty boxes|Pretty boxes]]). Possible uses include: * Focus questions * Case studies or examples * Quiz questions * Take-home messages {{RoundBoxTop|theme=3}} ;Feature box example * Shaded background * Coloured border {{RoundBoxBottom}} ===Figures=== [[File:Monkey-typing.jpg|right|205px|thumb|''Figure 1''. Example image with descriptive caption.]] Use figures to illustrate concepts, add interest, and provide examples. Figures can be used to show photographs, drawings, diagrams, graphs, etcetera. Figures can be embedded throughout the chapter, starting with the Overview section. Figures should be captioned (using a number and a description) in order to explain their relevance to the text. Possible images can be found at [[commons:|Wikimedia Commons]]. Images can also be uploaded if they are licensed for re-use or if you created the image. Each figure should be referred to at least once in the main text (e.g., see Figure 1). ===Links=== Where key words are first used, make them into [[Help:Links|interwiki links]] such as Wikipedia links to articles about famous people (e.g., [[w:Sigmund Freud|Sigmund Freud]] and key concepts (e.g., [[w:Dreams|dreams]]) and links to book chapters about related topics (e.g., would you like to learn about how to overcome [[Motivation and emotion/Book/2020/Writer's block|writer's block]]?). ===Tables=== Tables can be an effective way to organise and summarise information. Tables should be captioned (using APA style) to explain their relevance to the text. Plus each table should be referred to at least once in the main text (e.g., see Table 1 and Table 2). Here are some [[Motivation and emotion/Wikiversity/Tables|example 3 x 3 tables]] which could be adapted. ===Quizzes=== Quizzes are a direct way to engage readers. But don't make quizzes too hard or long. It is better to have one or two review questions per major section than a long quiz at the end. Try to quiz conceptual understanding, rather than trivia. Here are some simple quiz questions which could be adapted. Choose the correct answers and click "Submit": <quiz display=simple> {Quizzes are an interactive learning feature: |type="()"} + True - False {Long quizzes are a good idea: |type="()"} - True + False </quiz> To learn about different types of quiz questions, see [[Help:Quiz|Quiz]]. ==Conclusion== The Conclusion is arguably the most important section. It should be possible for someone to read the [[#Overview|Overview]] and the Conclusion and still get a good idea of the topic. {{tip|Suggestions for this section: * What is the answer to the question in the sub-title (based on psychological theory and research)? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide up to half-a-dozen [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. For example: * [[Motivation and emotion/Book/2016/Anorexia nervosa and extrinsic motivation|Anorexia nervosa and extrinsic motivation]] (Book chapter, 2016) * [[w:David McClelland|David McClelland]] (Wikipedia) * [[Motivation and emotion/Book/2018/Loss aversion|Loss aversion]] (Book chapter, 2018) * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] (Wikipedia) {{tip|Suggestions for this section: * Present in alphabetical order. * Include the source in parentheses. }} ==References== List the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Blair, R. J. R. (2004). The roles of orbital frontal cortex in the modulation of antisocial behavior. ''Brain and Cognition'', ''55''(1), 198–208. https://doi.org/10.1016/S0278-2626(03)00276-8 Buckholtz, J. W., & Meyer-Lindenberg, A. (2008). MAOA and the neurogenetic architecture of human aggression. ''Trends in Neurosciences'', ''31''(3), 120–129. https://doi.org/10.1016/j.tins.2007.12.006 Eckardt, M., File, S., Gessa, G., Grant, K., Guerri, C., Hoffman, P., & Tabakoff, B. (1998). Effects of moderate alcohol consumption on the central nervous system. ''Alcoholism, Clinical and Experimental Research'', ''22''(5), 998–1040. https://doi.org/10.1111/j.1530-0277.1998.tb03695.x }} {{tip|Suggestions for this section: * Important aspects for APA style include: ** Wrap the set of references in the hanging indent template. Using "Edit source": <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> ** Author surname, followed by a comma, then author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case except first letter and proper names, ending in a full-stop. ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop. ** Provide the full doi as a URL and working hyperlink * Common mistakes include: ** incorrect capitalisation ** incorrect italicisation ** providing a "retrieved from" date (not part of APA 7th ed. style). ** citing sources that weren't actually read or consulted }} ==External links== Provide up to half-a-dozen [[Help:Contents/Links#External_links|external links]] to relevant resources such as presentations, news articles, and professional sites. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Present in alphabetical order * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] thp5r91aziue2l80cis4wxipwwn2uzy