PRP Records

Probable Primes Top 10000

(183432 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 (> 30000) Who ? When ?
62515*3^145129-469245Lelio R Paula04/2014
62527*3^145126+869244Lelio R Paula04/2014
625311^66480-237069232Enzo Doria12/2012
62542^229962-6569226Lelio R Paula02/2012
62552^229958-11073369225Enzo Doria05/2014
6256V(332407)69225Serge Batalov03/2015
62576^88959+769224Lelio R Paula09/2013
625815^58855-9469219Lelio R Paula09/2013
6259(2^229838+47)/1208169185Lelio R Paula04/2012
62603^144952+9869160Lelio R Paula09/2013
62615^98941-7269157Lelio R Paula06/2013
6262(17*2^229604-1)/22969117Lelio R Paula01/2014
62632^229585-106369112Yves Minet11/2012
6264(13*2^229567-1)/1969107Lelio R Paula01/2014
6265(13*2^229393-1)/569055Lelio R Paula01/2014
6266(53*10^69050-17)/969051Robert Price09/2015
62672^229305-186853369028Enzo Doria04/2016
62682^229297+138569026Lelio R Paula04/2012
626918^54986-244169023Enzo Doria03/2013
6270(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
62715^98736-1463669014Enzo Doria02/2013
6272(13^61949-5^61949)/869007Robert Price03/2013
6273(2^229227+5)/61169002Lelio R Paula04/2012
62742^229216-11327969001Enzo Doria07/2014
627510^68994+5191368995Patrick De Geest03/2016
627710^68994-10^5814-168994Serge Batalov01/2011
627610^68994-8294768994Patrick De Geest03/2016
6278(17*2^229136-1)/238168975Lelio R Paula01/2014
62792^229113+10768970Lelio R Paula02/2012
628011^66202-441068943Enzo Doria01/2013
628112^63883+568942Lelio R Paula07/2013
6282(9913*2^229002-1)/39990368935Lelio R Paula04/2015
62832^228962-11158168925Enzo Doria05/2014
62842^228944+8168920Henri Lifchitz01/2007
628511^66174-5468914Lelio R Paula09/2013
62862^228913-11126568910Enzo Doria05/2014
62872^228902+7351968907Enzo Doria04/2016
6288(47*2^228884+1)/6368901Lelio R Paula04/2015
62892^228821+7642768882Enzo Doria05/2016
62903^144340+5068868Lelio R Paula09/2013
62912^228758-11296768864Enzo Doria06/2014
62922^228743-11137968859Enzo Doria05/2014
62932^228741-11091168858Enzo Doria05/2014
6295lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
62943*5^98511-868857Lelio R Paula09/2014
62962^228717+46768851Lelio R Paula02/2011
6297Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
6298(509203*2^228665-1)/3568840Lelio R Paula04/2015
62998^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
630011^66074-105068809Enzo Doria11/2012
6301(68*10^68798-11)/368800Robert Price10/2017
63022^228484+18168781Lelio R Paula02/2012
63032^228479-5869568780Lelio R Paula04/2012
63042^228465-1585368775Enzo Doria04/2013
630511^66040-540068774Enzo Doria01/2013
6306(13*2^228441-1)/57568766Lelio R Paula01/2014
6307(17*2^228393+1)/29568752Lelio R Paula08/2012
63082*10^68744+4168745Robert Price01/2017
630911^66011-15068744Enzo Doria08/2012
6310(13*2^228304-1)/8168726Lelio R Paula01/2014
63112^228295-11107968724Enzo Doria05/2014
6312(3^144039+7)/2268723Lelio R Paula04/2012
6313(8*10^68722+49)/368723Robert Price03/2016
6314(35*10^68718+1)/968719Serge Batalov11/2010
63152^228271-22827168717Henri Lifchitz11/2004
63162^228257+8287568713Lelio R Paula02/2013
63173^144013+4068712Lelio R Paula09/2013
631813^61671-8668699Lelio R Paula09/2013
631917^55828-7268694Lelio R Paula09/2013
63206^88259+6168679Lelio R Paula09/2013
632118^54699-568663Lelio R Paula09/2013
632233^45216+268662Lelio R Paula05/2013
6323(2^228073-5)/368657Lelio R Paula04/2012
6324(2^(6*38012+1)-5)/368657Kevin Acres11/2013
63252^228055-11160768652Enzo Doria05/2014
63262^228054-11476168652Enzo Doria05/2015
63272^228041+118568648Lelio R Paula04/2012
63282^228040-103768647Yves Minet11/2012
63292*F(328450)-168642Henri Lifchitz12/2009
63305^98201-3468640Lelio R Paula06/2013
63319^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
63327*2^227780-368570Lelio R Paula04/2014
63332^227733-12168555Lelio R Paula02/2012
63342^227702-1696768546Enzo Doria05/2013
63352^227689-11165568542Enzo Doria05/2014
6336gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
63375^98051+268535Ray Chandler07/2011
63385*10^68524+5168525Robert Price01/2017
6339(11*10^68520-149)/368521Robert Price01/2017
634019^53573-7868507Lelio R Paula09/2013
6341(68*10^68504+13)/968505Ray Chandler10/2010
63429*5^98003+468503Lelio R Paula09/2014
63432^227528+5168493Lelio R Paula02/2012
63443^143497+868466Lelio R Paula04/2012
63452^227430-9568464Lelio R Paula02/2012
63463*5^97934-268454Lelio R Paula09/2014
634720^52613+7768452Lelio R Paula09/2013
63482^227371+3276968446Lelio R Paula04/2012
6349(3^143465+4)/2127042006768440Lelio R Paula04/2012
6350CopelandErdos(68433)68433Eric W. Weisstein08/2013
63512^227323+7543168432Enzo Doria04/2016
63522^227314-196568429Lelio R Paula04/2012
63532^227303-11061768426Enzo Doria05/2014
63547^80963+6668422Lelio R Paula07/2013
63552^227290+7384968422Enzo Doria04/2016
6356(14^59693-1)/1368415Paul Bourdelais06/2008
63572^227256-278624968411Enzo Doria03/2016
63598*10^68400-768401Dmitry Domanov11/2010
6358(15*2^227228-1)/58368401Lelio R Paula01/2014
63602^227210+186916968398Enzo Doria05/2016
63612^227159-183863568382Enzo Doria05/2015
636244*10^68368+368370Robert Price08/2017
63632^227115-780768369Lelio R Paula10/2009
63642^227078-4735568358Lelio R Paula04/2012
6365(2^227063-1017)/34968351Lelio R Paula04/2012
63662^227057+14809168351Lelio R Paula04/2012
63672^227046+18768348Lelio R Paula02/2012
63689*10^68331+5968332Robert Price10/2017
636911^65608-72068324Enzo Doria11/2012
637033408!2-2^33408-168315Joe McLean05/2017
63712^226894-12368302Lelio R Paula02/2012
637210^68297+14155968298Patrick De Geest05/2013
637310^68297-9368297Robert Price05/2011
6374680^24107-679^2410768284Jean-Louis Charton07/2010
637512^63267+5968277Lelio R Paula07/2013
63762^226785-115968270Yves Minet11/2012
63777^80769+9068258Lelio R Paula07/2013
6378(88*10^68256-1)/368258Robert Price10/2017
63792^226741+6658768256Yves Minet10/2010
63802^226720-11240368250Enzo Doria06/2014
6381(78557*2^226694+1)/368247Lelio R Paula06/2014
6382(83*10^68231+7)/968232Robert Price10/2015
638365^37636+1668231Lelio R Paula01/2016
63845^97615-4^(97615+1)68230Robert Price04/2016
638512^63200-4368205Lelio R Paula07/2013
6386-330*Bern(21940)/22379062073368201Serge Batalov04/2015
63873^142925+868068193Lelio R Paula06/2013
63883*2^226512-768188Lelio R Paula04/2014
638914^59484+5768177Lelio R Paula08/2013
639011^65438-219068147Enzo Doria12/2012
639191^34784-268144Lelio R Paula09/2013
6392(2^226336-3)*6-768135Gilbert Mozzo06/2016
6393(22*10^68133-37)/368134Robert Price05/2017
63945^97476+3668133Lelio R Paula06/2013
63953*5^97474-268132Lelio R Paula09/2014
639612^63130+4968129Lelio R Paula07/2013
63972^226281+538568118Lelio R Paula04/2012
63982^226257-304968111Yves Minet10/2014
6399(28*10^68107-43)/368108Robert Price04/2016
64002^226243-258768106Yves Minet07/2014
640120^52346-1168104Lelio R Paula09/2013
64022^226205-9968095Lelio R Paula02/2012
64032^226187-4968090Lelio R Paula02/2012
64043^142708+7668090Lelio R Paula06/2013
64057*10^68088-8968089Robert Price01/2017
64062^226154+7183968080Enzo Doria04/2016
6407(10^68078+59)/368078Serge Batalov12/2014
640914^59387+6968066Lelio R Paula08/2013
64082^226108-11342968066Enzo Doria07/2014
6410(24^49307-1)/2368053Robert Price04/2012
641115^57859-2868048Lelio R Paula08/2013
6412(509203*2^226003-1)/1368039Lelio R Paula04/2015
64132^226015-11136168038Enzo Doria05/2014
6414(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
6415156*(10^(4*17000)-1)/101-168001Robert Price05/2014
64162^225878-101767997Lelio R Paula04/2012
64173*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
64183*2^225865+567993Lelio R Paula04/2014
642011^65284-582067987Enzo Doria01/2013
641919^53166+7067987Lelio R Paula08/2013
64212^225837+7540767984Enzo Doria04/2016
64223^142464-11265467973Enzo Doria06/2014
64232^225777+9567966Lelio R Paula02/2012
6424(2^225641-1017)/13881567920Lelio R Paula04/2012
64252^225609-1844567916Enzo Doria05/2013
64262^225542-17767895Lelio R Paula02/2012
64272^225536-2967894Henri Lifchitz05/2005
642811^65190-339067889Enzo Doria12/2012
64293^142249-2^(142249-1)67871Robert Price01/2016
643011^65168-483067866Enzo Doria01/2013
643110^67863+5862767864Patrick De Geest01/2016
643210^67863-1167863Robert Price05/2011
6433(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
6434(19*2^225357-1)/1167840Lelio R Paula01/2014
64359*6^87164-767828Lelio R Paula09/2014
6436131^32034+13067825Norbert Schneider03/2015
6437(29*2^225314+1)/1088167824Lelio R Paula08/2012
6438(134*10^67816+7)/367818Robert Price02/2017
64392^225261+85567811Lelio R Paula04/2012
6440(29*2^225252-1)/293367806Lelio R Paula01/2014
6441(4*10^67796+23)/967796Robert Price11/2014
6442(23*2^225177+1)/3167785Lelio R Paula08/2012
6443(4*10^67784+149)/967784Robert Price03/2017
64442^225120+15167768Lelio R Paula02/2012
6445(44^41233+1)/4567763Robert Price11/2013
64468*10^67742+967743Dmitry Domanov11/2010
64472^224977+108967725Lelio R Paula04/2012
6448(2^224950+5)/1950967713Lelio R Paula04/2012
644911^65011-597067702Enzo Doria01/2013
645088*10^67691+767693Robert Price11/2016
645111^65000-714067691Enzo Doria01/2013
64522^224841+5967684Lelio R Paula02/2012
645333129!2+2^3312967684Robert Price09/2015
64542^224827+841567680Lelio R Paula02/2013
6455(9913*2^224821-1)/1982567678Lelio R Paula04/2015
64562^224815-4978967677Henri Lifchitz04/2005
6457(43*10^67664+11)/967665Robert Price06/2015
6458(292*10^67659-1)/367661Robert Price01/2017
6459(17*2^224766+1)/2900767659Lelio R Paula06/2012
64602^224744+57729457567655Lelio R Paula02/2016
6461((1+sqrt(7)+sqrt(6))^45863-1)*((1+sqrt(7)-sqrt(6))^45863-1)*((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(767653Mike Oakes05/2009
6462(2^224721+78557)/173967645Lelio R Paula05/2012
64632^224700+191567642Lelio R Paula04/2012
6464(29*2^224694-1)/19890567636Lelio R Paula01/2014
64652^224658-9367629Lelio R Paula02/2012
64662^224624-1307767619Enzo Doria10/2012
646718^53860-331967609Enzo Doria03/2013
6468(21181*2^224570+1)/567606Lelio R Paula06/2014
64692^224578-11104167605Enzo Doria05/2014
64702^224569-11323367603Enzo Doria07/2014
64712^224562-11317167600Enzo Doria07/2014
64722^224556-11312967599Enzo Doria07/2014
64736*7^79980-567592Lelio R Paula09/2014
6474(6883*2^224523-1)/1603167588Lelio R Paula04/2015
647510^67579+16477967580Patrick De Geest07/2017
6477(52*10^67578-61)/967579Robert Price09/2015
647610^67579-40167579Robert Price06/2017
6478(17^54919-1)/1667574Paul Bourdelais03/2010
6479(2^224363-9)/195167537Lelio R Paula04/2012
6480(709*10^67517-7)/967519Robert Price09/2017
648147719!3-5904967516Robert Price12/2015
6482(22^50287+1)/2367506Robert Price06/2013
648311^64811-582067494Enzo Doria01/2013
6484131^31870+31870^13167478Serge Batalov05/2014
64859*10^67468+767469Dmitry Domanov11/2010
6486(31*2^224115-1)/4772367463Lelio R Paula01/2014
6487128^32001+32001^12867433Serge Batalov05/2014
6488(89*10^67431-17)/967432Robert Price11/2015
64892^223912-11105967405Enzo Doria05/2014
64912^223913+7369767405Enzo Doria04/2016
6490(2*10^67405-23)/367405Robert Price09/2017
6492(10^67404+179)/967404Serge Batalov12/2014
649318738^3955+3955^1873867404Hans Havermann09/2016
64949*7^79728-267379Lelio R Paula09/2014
6495(28*10^67378-43)/367379Robert Price04/2016
6496(3^141234-7)/43024128267378Lelio R Paula04/2012
6497211^28988-267377Lelio R Paula09/2013
64982^223793-1806967369Enzo Doria05/2013
64992^223777-252167364Yves Minet07/2014
6500(15185*2^223775-1)/1518367363Lelio R Paula04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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