PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
925113736^11949+11949^1373656007Hans Havermann04/2016
9252(5*2^186036-1)/1156003Lelio R Paula01/2014
9253(299*10^55998-17)/356000Robert Price01/2017
9254p(12103)#/2-12855994Robert Price05/2017
92552^186003-17433755993Gary Barnes09/2009
9257(2^186010+78557)/12355993Lelio R Paula05/2012
925620^43037-9355993Lelio R Paula02/2013
925816375^2626+2626^1637555991Hans Havermann03/2016
925911083^13842-13842^1108355987Norbert Schneider11/2018
926015631^3816+3816^1563155985Hans Havermann03/2016
926121^42335-255977Lelio R Paula08/2013
9262Phi(64736,139)55959Enzo Doria07/2012
926315215^4762+4762^1521555958Hans Havermann03/2016
926419317^788+788^1931755953Anatoly F. Selevich12/2006
926513582^13165+13165^1358255950Hans Havermann08/2016
9266(78557*2^185842+1)/18955947Lelio R Paula06/2014
926711867^13730-13730^1186755941Norbert Schneider09/2018
926815^47562-8655938Lelio R Paula02/2013
92694*10^55932+9155933Robert Price11/2017
92703^117222+455930Lelio R Paula03/2012
927124^40519-23^4051955925Robert Price07/2012
927213636^12623+12623^1363655924Hans Havermann07/2016
92732^185767-9955922Lelio R Paula03/2011
9274(19*2^185750-1)/1555917Lelio R Paula01/2014
927515^47542-5855914Lelio R Paula02/2013
927652211!4+255914Robert Price08/2017
927720^42973-558355910Enzo Doria03/2013
92784*10^55906+2155907Robert Price08/2016
92792^185713-11155906Lelio R Paula03/2011
928013^50174+8855891Lelio R Paula01/2013
928114569^6846+6846^1456955879Hans Havermann08/2016
9282Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
92833^117087-8055865Lelio R Paula10/2012
9284(7*10^55851-43)/955851Robert Price10/2014
92852^185519-16955847Lelio R Paula03/2011
92867^66074+1055840Lelio R Paula10/2012
9287(19*10^55833-49)/355834Robert Price02/2017
9288(2*10^55834-59)/355834Robert Price05/2017
92892^185463-423755830Yves Minet08/2018
929012^51732+555829Lelio R Paula01/2013
929111252^13779-13779^1125255822Norbert Schneider10/2018
92923*2^185429+755821Lelio R Paula03/2014
9293(60^31393+1)/6155820Paul Bourdelais08/2017
9295(9787*2^185420-1)/38155819Lelio R Paula04/2015
929414427^7396+7396^1442755819Hans Havermann08/2016
929610^55811+2155812Robert Price01/2011
929710^55811-7410355811Patrick De Geest12/2012
929811^53591-153055810Enzo Doria11/2012
9299(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
93002^185355-214555798Lelio R Paula03/2011
930114531^6912+6912^1453155794Hans Havermann07/2016
93022^185327-161555789Lelio R Paula03/2011
93032^185280-1277955775Enzo Doria10/2012
930415504^3955+3955^1550455771Hans Havermann07/2016
9305(2*10^55762-59)/355762Robert Price05/2017
93065^79770-4455757Lelio R Paula10/2012
930718^44416-8555755Lelio R Paula02/2013
93082^185208-45999555754Enzo Doria06/2015
93092^185200+118555751Lelio R Paula03/2011
9310(536*10^55748-23)/955750Robert Price11/2017
93117^65964+6^(65964-1)55747Robert Price03/2016
93122^185151-23715755737Gary Barnes09/2009
9313110017^11055-10255734Enzo Doria07/2012
931514754^5987+5987^1475455729Hans Havermann07/2016
931412591^13592-13592^1259155729Norbert Schneider07/2018
931640090!3-955711Robert Price09/2014
93179*10^55707+8955708Robert Price11/2016
93182^185023-225755698Yves Minet06/2009
931918628^977+977^1862855696Anatoly F. Selevich01/2007
93202^185006-9355693Lelio R Paula03/2011
93212^185003-251555692Yves Minet07/2014
93222^184992-7855755689Jorge Menendez02/2018
93233*10^55679+3755680Robert Price10/2017
93246^71524-1955657Lelio R Paula10/2012
93252^184872-219555653Yves Minet08/2013
9326507^20572+20572^50755648Norbert Schneider06/2016
9327(86*10^55645-311)/955646Robert Price10/2017
9328134^26151-13355626Norbert Schneider03/2015
932915340^4221+4221^1534055614Hans Havermann07/2016
933027743!2+255612Robert Price01/2013
933120^42744+8155612Lelio R Paula02/2013
933214609^6406+6406^1460955611Hans Havermann07/2016
93332^184724-11288355608Enzo Doria06/2014
933413507^13074+13074^1350755601Hans Havermann07/2016
93352^184689+12955597Lelio R Paula03/2011
9336(9179*2^184672-1)/19355594Lelio R Paula03/2015
9337(22*10^55592-19)/355593Robert Price02/2017
9338Phi(59984,89)55582Enzo Doria05/2012
93398815^14088-14088^881555581Norbert Schneider11/2018
934011^53368+1655578Lelio R Paula01/2013
934120^42717-192355577Enzo Doria03/2013
9342117^26870+26870^11755573Serge Batalov05/2014
934312^51488+5555565Lelio R Paula01/2013
9345(44*10^55558-17)/955559Robert Price06/2015
9344(2*10^55559-23)/355559Robert Price09/2017
934610^55555+3285755556Patrick De Geest06/2010
934710^55555-13672155555Patrick De Geest06/2010
9348(11*2^184541-1)/35155551Lelio R Paula01/2014
934920^42696-204355549Enzo Doria03/2013
9350(35*10^55547-737)/955548Robert Price11/2017
9351(2*10^55544+1)/355544Serge Batalov06/2009
9352(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
93535003^15013-16055537Enzo Doria07/2012
935439^34896-255522Lelio R Paula08/2013
9355(6^71345-61)/555517Lelio R Paula05/2014
93562^184407-301955513Yves Minet10/2014
9357(43*10^55512-61)/955513Robert Price06/2015
935820^42667-84355512Enzo Doria03/2013
9359133^26134-13255505Norbert Schneider03/2015
9360(31*2^184378-1)/71155502Lelio R Paula01/2014
93619*7^65667-455497Lelio R Paula09/2014
93622^184342-17355493Lelio R Paula03/2011
936315^47182+9255491Lelio R Paula02/2013
93645^79378+655483Lelio R Paula10/2012
9365581^20068+20068^58155472Norbert Schneider06/2016
9366(2^184232+1)/25755457Donovan Johnson03/2005
936718^44177-141555455Enzo Doria03/2013
93682^184203-279786755451Enzo Doria04/2016
93692^184189+1755447Lelio R Paula03/2011
93702^184183+2612355445Yves Minet01/2010
9371Phi(77077,10)55441Ray Chandler05/2009
93722^184141-11325155432Enzo Doria07/2014
93732^184093-50461355418Gary Barnes09/2009
93746517^14528-14528^651755411Norbert Schneider12/2018
9375(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
93762^184044-11126955403Enzo Doria05/2014
937714051^8766+8766^1405155401Hans Havermann07/2016
937898^27819+27819^9855394Serge Batalov05/2014
9379(178*10^55390-7)/955392Robert Price08/2017
938058046^9+9^5804655390Andrey Kulsha02/2004
93817^65536+2*59232-255385Jiahao He07/2017
93822^183980+7524155384Enzo Doria04/2016
938310^55372+3755373Robert Price01/2011
938410^55372-4996755372Patrick De Geest12/2012
9385(13*10^55367+17)/355368Robert Price06/2015
93862*6^71150+755366Lelio R Paula09/2014
938719^43296-6255365Lelio R Paula02/2013
938819^43295+1055364Lelio R Paula02/2013
9389(29*10^55362-11)/955363Robert Price04/2015
9390(37*10^55359+53)/955360Robert Price05/2015
939119^43283+7255349Lelio R Paula02/2013
93922^183800-6555330Lelio R Paula03/2011
939321001^12801-11055329Enzo Doria07/2012
939433^36433-32^3643355325Robert Price04/2012
9395(17*2^183729+1)/14555308Lelio R Paula07/2012
93969932^13837-13837^993255307Norbert Schneider11/2018
93989^57952+8^(57952-1)55301Robert Price03/2016
939714872^5229+5229^1487255301Hans Havermann08/2016
939961^30972-255296Lelio R Paula08/2013
94002^183671-11253755291Enzo Doria06/2014
9401(2^183687+7)/49793974555287Lelio R Paula02/2012
94023^115873+5655286Lelio R Paula10/2012
940313^49629-8455284Lelio R Paula01/2013
94042^183632-555279Henri Lifchitz08/2005
940513981^8988+8988^1398155277Hans Havermann07/2016
940610688^13719-13719^1068855273Norbert Schneider09/2018
9407(5*2^183585+1)/1355265Lelio R Paula07/2012
94082^183576+17155262Lelio R Paula03/2011
940913^49604+8255257Lelio R Paula01/2013
9410(11*10^55254+1)/355255Erik Branger03/2014
941112609^13474-13474^1260955253Norbert Schneider05/2018
94123^115802-2655252Lelio R Paula10/2012
94132^183534-364555250Lelio R Paula01/2011
9414(15*2^183533-1)/11355249Lelio R Paula01/2014
94155^79032-1376655241Enzo Doria02/2013
94168*3^115759-755232Lelio R Paula03/2014
94186^70974-13755229Lelio R Paula10/2012
94172^183466+52428755229Paul Underwood08/2018
94192^183446-11307355223Enzo Doria07/2014
94202^183441+57729457555222Lelio R Paula03/2013
94215^79000-655219Lelio R Paula10/2012
94222^183413-90155213Yves Minet01/2012
942319^43168-5055202Lelio R Paula02/2013
94242^183340+1968355191Lelio R Paula02/2012
94256^70923+3555189Lelio R Paula10/2012
94262^183317-403555184Lelio R Paula01/2011
94272^183284-1555174Lelio R Paula03/2011
94282^183255+14955166Lelio R Paula02/2011
94294*10^55165+8755166Robert Price05/2016
9431(3^115574+4)/6303755139Lelio R Paula03/2012
94302^183165-11233355139Enzo Doria06/2014
9432(109^27061-1)/10855133Richard Fischer09/2017
94332^183142+85555132Lelio R Paula01/2011
9434(49*10^55129+383)/955130Robert Price04/2017
94352^183019+25525555095Lelio R Paula01/2011
9436(10^55084-19)/955084Robert Price10/2017
94373*10^55077+755078Erik Branger11/2013
9438(62*10^55075-71)/955076Robert Price09/2015
943927499!2-3255070Robert Price10/2015
944015307^3958+3958^1530755067Hans Havermann08/2016
9441155^25137-15455059Norbert Schneider12/2018
944270^29836-6955051Norbert Schneider10/2012
944318^43854-8355049Lelio R Paula02/2013
94447^65126+5855038Lelio R Paula10/2012
94452^182827-161555037Lelio R Paula11/2009
94467*10^55030-955031Dmitry Domanov11/2010
94479027^13912-13912^902755030Norbert Schneider08/2018
94482^182768-405555019Yves Minet02/2018
94496^70702+2355017Lelio R Paula10/2012
9450(23*2^182753+1)/15155014Lelio R Paula07/2012
94512^182743-161555012Lelio R Paula11/2009
9452(24737*2^182736+1)/39955011Lelio R Paula05/2014
94533^115280-956855003Enzo Doria02/2013
94542^182656-1284954985Enzo Doria10/2012
945512791^13388-13388^1279154984Norbert Schneider03/2018
94569*19^42995+1654981Curtis Bright05/2015
94572^182627+2842554977Lelio R Paula11/2009
94582^182597-11305354968Enzo Doria07/2014
9459(3^115213+2)/3090672554964Lelio R Paula03/2012
94602^182581-197554963Yves Minet09/2012
9461(2*10^54960-179)/354960Robert Price11/2017
946227449!!-1654959Robert Price06/2015
9463(22*10^54958-73)/354959Robert Price09/2017
94654^91283-3^9128354958Jean-Louis Charton01/2004
94642^182565+10754958Lelio R Paula11/2009
94662^182560+205354957Lelio R Paula12/2010
9467126892#-p(126892)54927Henri Lifchitz12/2018
94682^182451-18245154924Henri Lifchitz10/2004
94692^182444+8154922Henri Lifchitz10/2005
94707589^14154-14154^758954921Norbert Schneider01/2019
94712^182433+7410554918Enzo Doria04/2016
947220^42206-524354912Enzo Doria03/2013
94732^182394+8554907Lelio R Paula02/2011
94742^182374-11228754901Enzo Doria06/2014
9475(47^32833-33^32833)/1454899Serge Batalov12/2016
947610188^13697-13697^1018854899Norbert Schneider09/2018
94772^182363-11316754897Enzo Doria07/2014
94782^182359-11222154896Enzo Doria06/2014
9479(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
9480(17*2^182274+1)/146754869Lelio R Paula01/2012
948118^43698-554853Lelio R Paula02/2013
94822^182209-189354851Yves Minet09/2012
94832^182194-344354846Yves Minet12/2016
948415023^4468+4468^1502354836Hans Havermann08/2016
94852^182135+9014354829Yves Minet10/2010
94862^182119+7433354824Enzo Doria04/2016
948714289^6860+6860^1428954818Hans Havermann08/2016
94883^114892-114892^354818Norbert Schneider03/2017
94892^182070-4735554809Lelio R Paula01/2011
94903^114869+7654807Lelio R Paula10/2012
94918^60681-60681^854801Norbert Schneider12/2016
94921897^16710+16710^189754777Serge Batalov05/2014
9493Phi(61868,59)54776Enzo Doria04/2012
9494113^26679+254775Lelio R Paula05/2013
94953^114789-7454769Lelio R Paula10/2012
949615^46567+9854768Lelio R Paula02/2013
9497(2*10^54767-71)/354767Robert Price01/2017
9498(298*10^54765-7)/354767Robert Price06/2017
9499(21*2^181931-1)/16999754763Lelio R Paula01/2014
9500(31*10^54761-121)/954762Robert Price06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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