PRP Records

Probable Primes Top 10000

(259919 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
87512*F(328450)-168642Henri Lifchitz12/2009
87525^98201-3468640Lelio R Paula06/2013
8753(2^227993+1682)/268633Stefano Morozzi01/2020
8754(2^227989+842)/268632Stefano Morozzi01/2020
8755(2^227989+2010)/268632Stefano Morozzi01/2020
8756(2^227959+3614)/268623Stefano Morozzi01/2020
8757(2^227961+2054)/268623Stefano Morozzi01/2020
87589^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
8759(2^227938+3678)/268616Stefano Morozzi01/2020
876018177^5948+5948^1817768607Hans Havermann09/2019
8761(2^227869+2822)/268596Stefano Morozzi01/2020
8762(2^227813+666)/268579Stefano Morozzi01/2020
87637*2^227780-368570Lelio R Paula04/2014
876415327^16382-16382^1532768567Norbert Schneider11/2018
8765(2^227771+2730)/268566Stefano Morozzi01/2020
87662^227733-12168555Lelio R Paula02/2012
876716460^14607+14607^1646068549Hans Havermann09/2019
87682^227702-1696768546Enzo Doria05/2013
87692^227689-11165568542Enzo Doria05/2014
8770gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
87715^98051+268535Ray Chandler07/2011
87725*10^68524+5168525Robert Price01/2017
8773(11*10^68520-149)/368521Robert Price01/2017
877416624^13235+13235^1662468520Hans Havermann09/2019
877516359^15430+15430^1635968518Hans Havermann08/2019
877619^53573-7868507Lelio R Paula09/2013
8777(68*10^68504+13)/968505Ray Chandler10/2010
87789*5^98003+468503Lelio R Paula09/2014
877921121^1750+1750^2112168497Hans Havermann10/2019
87802^227528+5168493Lelio R Paula02/2012
8781(146*28^47316+1)/368476Karsten Bonath06/2018
8782(2^227462+3102)/268473Stefano Morozzi01/2020
87833^143497+868466Lelio R Paula04/2012
87842^227430-9568464Lelio R Paula02/2012
8785(8*10^68455+13)/368456Robert Price11/2017
87863*5^97934-268454Lelio R Paula09/2014
878720^52613+7768452Lelio R Paula09/2013
87882^227371+3276968446Lelio R Paula04/2012
8789(3^143465+4)/2127042006768440Lelio R Paula04/2012
8790CopelandErdos(68433)68433Eric W. Weisstein08/2013
87912^227323+7543168432Enzo Doria04/2016
87922^227314-196568429Lelio R Paula04/2012
87932^227303-11061768426Enzo Doria05/2014
87957^80963+6668422Lelio R Paula07/2013
87942^227290+7384968422Enzo Doria04/2016
8796(14^59693-1)/1368415Paul Bourdelais06/2008
87972^227256-278624968411Enzo Doria03/2016
87998*10^68400-768401Dmitry Domanov11/2010
8798(15*2^227228-1)/58368401Lelio R Paula01/2014
88002^227210+186916968398Enzo Doria05/2016
8801(2^227176+2958)/268387Stefano Morozzi01/2020
88022^227159-183863568382Enzo Doria05/2015
880344*10^68368+368370Robert Price08/2017
88042^227115-780768369Lelio R Paula10/2009
880518469^5032+5032^1846968368Hans Havermann08/2019
88062^227078-4735568358Lelio R Paula04/2012
880716927^10920+10920^1692768355Hans Havermann10/2019
8808(2^227063-1017)/34968351Lelio R Paula04/2012
88092^227057+14809168351Lelio R Paula04/2012
88102^227046+18768348Lelio R Paula02/2012
8811(2^227030+454)/268343Stefano Morozzi01/2020
8812(2^227022+2950)/268341Stefano Morozzi01/2020
88142^227009-469368337Yves Minet05/2019
8813(2^227010+3214)/268337Stefano Morozzi01/2020
88159*10^68331+5968332Robert Price10/2017
881611^65608-72068324Enzo Doria11/2012
8817(32*10^68320+319)/968321Robert Price10/2017
881833408!2-2^33408-168315Joe McLean05/2017
88192^226894-12368302Lelio R Paula02/2012
882010^68297+14155968298Patrick De Geest05/2013
882110^68297-9368297Robert Price05/2011
8822680^24107-679^2410768284Jean-Louis Charton07/2010
882312^63267+5968277Lelio R Paula07/2013
88242^226785-115968270Yves Minet11/2012
88257^80769+9068258Lelio R Paula07/2013
8826(88*10^68256-1)/368258Robert Price10/2017
88272^226741+6658768256Yves Minet10/2010
88282^226720-11240368250Enzo Doria06/2014
8829(78557*2^226694+1)/368247Lelio R Paula06/2014
8830(2^226665+1674)/268233Stefano Morozzi01/2020
8831(83*10^68231+7)/968232Robert Price10/2015
883265^37636+1668231Lelio R Paula01/2016
88335^97615-4^(97615+1)68230Robert Price04/2016
8834(2^226634+2550)/268224Stefano Morozzi01/2020
883512^63200-4368205Lelio R Paula07/2013
8836-330*Bern(21940)/22379062073368201Serge Batalov04/2015
8837(2^226553+2246)/268199Stefano Morozzi01/2020
88383^142925+868068193Lelio R Paula06/2013
88393*2^226512-768188Lelio R Paula04/2014
8840(2^226502+442)/268184Stefano Morozzi01/2020
884114^59484+5768177Lelio R Paula08/2013
8842(2^226452+406)/268169Stefano Morozzi01/2020
884311^65438-219068147Enzo Doria12/2012
8844(2^226374+2814)/268146Stefano Morozzi01/2020
884591^34784-268144Lelio R Paula09/2013
884616589^12810+12810^1658968141Hans Havermann10/2019
8847(2^226356+2986)/268140Stefano Morozzi01/2020
8848(2^226357+3702)/268140Stefano Morozzi01/2020
8850(2^226336-3)*6-768135Gilbert Mozzo06/2016
8849(2^226340+1878)/268135Stefano Morozzi01/2020
8851(22*10^68133-37)/368134Robert Price05/2017
88525^97476+3668133Lelio R Paula06/2013
88533*5^97474-268132Lelio R Paula09/2014
885412^63130+4968129Lelio R Paula07/2013
88552^226281+538568118Lelio R Paula04/2012
88562^226257-304968111Yves Minet10/2014
8857(28*10^68107-43)/368108Robert Price04/2016
88592^226243-258768106Yves Minet07/2014
8858(2^226241+2570)/268106Stefano Morozzi01/2020
886020^52346-1168104Lelio R Paula09/2013
88612^226205-9968095Lelio R Paula02/2012
88622^226187-4968090Lelio R Paula02/2012
88633^142708+7668090Lelio R Paula06/2013
88647*10^68088-8968089Robert Price01/2017
886518562^4653+4653^1856268081Hans Havermann09/2019
88662^226154+7183968080Enzo Doria04/2016
8867(10^68078+59)/368078Serge Batalov12/2014
8868(2^226121+2822)/268069Stefano Morozzi01/2020
887014^59387+6968066Lelio R Paula08/2013
88692^226108-11342968066Enzo Doria07/2014
8871(62*10^68059-197)/968060Robert Price10/2017
8872(24^49307-1)/2368053Robert Price04/2012
8873(2^226060+1842)/268051Stefano Morozzi01/2020
887415^57859-2868048Lelio R Paula08/2013
8875(2^226029+2802)/268042Stefano Morozzi01/2020
8876(509203*2^226003-1)/1368039Lelio R Paula04/2015
88772^226015-11136168038Enzo Doria05/2014
8878(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
88794*10^68020+9168021Robert Price11/2017
888016181^15948+15948^1618168004Hans Havermann09/2019
8881156*(10^(4*17000)-1)/101-168001Robert Price05/2014
88822^225878-101767997Lelio R Paula04/2012
88833*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
88843*2^225865+567993Lelio R Paula04/2014
8885(2^225868+1662)/267993Stefano Morozzi01/2020
888611^65284-582067987Enzo Doria01/2013
888719^53166+7067987Lelio R Paula08/2013
88882^225837+7540767984Enzo Doria04/2016
88893^142464-11265467973Enzo Doria06/2014
889016851^10802+10802^1685167969Hans Havermann09/2019
88912^225777+9567966Lelio R Paula02/2012
8892(2^225643+1634)/267926Stefano Morozzi01/2020
8893(2^225644+3606)/267926Stefano Morozzi01/2020
8894(2^225642+1902)/267925Stefano Morozzi01/2020
8895(2^225641-1017)/13881567920Lelio R Paula04/2012
88962^225609-1844567916Enzo Doria05/2013
8897(2^225590+1414)/267910Stefano Morozzi01/2020
88982^225542-17767895Lelio R Paula02/2012
88992^225536-2967894Henri Lifchitz05/2005
890011^65190-339067889Enzo Doria12/2012
890162271!4-102467878Robert Price11/2019
890216971^9986+9986^1697167874Hans Havermann09/2019
89033^142249-2^(142249-1)67871Robert Price01/2016
890411^65168-483067866Enzo Doria01/2013
890510^67863+5862767864Patrick De Geest01/2016
890616258^14933+14933^1625867864Hans Havermann09/2019
890710^67863-1167863Robert Price05/2011
8908(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
8909(19*2^225357-1)/1167840Lelio R Paula01/2014
89109*6^87164-767828Lelio R Paula09/2014
8911131^32034+13067825Norbert Schneider03/2015
8912(29*2^225314+1)/1088167824Lelio R Paula08/2012
891317761^6586+6586^1776167823Hans Havermann09/2019
8914(134*10^67816+7)/367818Robert Price02/2017
89152^225261+85567811Lelio R Paula04/2012
8916(29*2^225252-1)/293367806Lelio R Paula01/2014
8917(4*10^67796+23)/967796Robert Price11/2014
891815477^16180-16180^1547767790Norbert Schneider09/2018
8919(2^225183+2318)/267787Stefano Morozzi01/2020
8920(23*2^225177+1)/3167785Lelio R Paula08/2012
8921(4*10^67784+149)/967784Robert Price03/2017
89228177^17322+17322^817767774Norbert Schneider03/2019
89232^225120+15167768Lelio R Paula02/2012
8924(2^225109+3126)/267765Stefano Morozzi01/2020
8925(44^41233+1)/4567763Robert Price11/2013
8926(2^225085+2610)/267758Stefano Morozzi01/2020
892789933!6-1667747Robert Price08/2018
89288*10^67742+967743Dmitry Domanov11/2010
8929(2^224979+3626)/267726Stefano Morozzi01/2020
89302^224977+108967725Lelio R Paula04/2012
8931(2^224971+3678)/267723Stefano Morozzi01/2020
8932(2^224950+5)/1950967713Lelio R Paula04/2012
893311^65011-597067702Enzo Doria01/2013
893488*10^67691+767693Robert Price11/2016
893511^65000-714067691Enzo Doria01/2013
89362^224841+5967684Lelio R Paula02/2012
893733129!2+2^3312967684Robert Price09/2015
89382^224827+841567680Lelio R Paula02/2013
8939(9913*2^224821-1)/1982567678Lelio R Paula04/2015
89402^224815-4978967677Henri Lifchitz04/2005
89417257^17528+17528^725767672Norbert Schneider08/2019
8942(43*10^67664+11)/967665Robert Price06/2015
8943(292*10^67659-1)/367661Robert Price01/2017
8944(17*2^224766+1)/2900767659Lelio R Paula06/2012
89452^224744+57729457567655Lelio R Paula02/2016
8946((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
8947(2^224721+78557)/173967645Lelio R Paula05/2012
89482^224700+191567642Lelio R Paula04/2012
8949(29*2^224694-1)/19890567636Lelio R Paula01/2014
8950(2^224679+2870)/267635Stefano Morozzi01/2020
89512^224658-9367629Lelio R Paula02/2012
89522^224624-1307767619Enzo Doria10/2012
8953(2^224598+2910)/267611Stefano Morozzi01/2020
895418^53860-331967609Enzo Doria03/2013
8955(21181*2^224570+1)/567606Lelio R Paula06/2014
895689762!6-367606Robert Price08/2018
89572^224578-11104167605Enzo Doria05/2014
89582^224569-11323367603Enzo Doria07/2014
89592^224562-11317167600Enzo Doria07/2014
89602^224556-11312967599Enzo Doria07/2014
89616*7^79980-567592Lelio R Paula09/2014
8962(6883*2^224523-1)/1603167588Lelio R Paula04/2015
896310^67579+16477967580Patrick De Geest07/2017
8965(52*10^67578-61)/967579Robert Price09/2015
896410^67579-40167579Robert Price06/2017
8966(17^54919-1)/1667574Paul Bourdelais03/2010
8967(2^224442+2314)/267564Stefano Morozzi01/2020
896822115^1134+1134^2211567553Hans Havermann08/2019
8969((10^33771-1)*10000/9+6389)*10^33771+(10^33771-1)/967546Hans Havermann05/2019
8970(2^224363-9)/195167537Lelio R Paula04/2012
8971(2^224327+2510)/267529Stefano Morozzi01/2020
8972(2^224303+1458)/267522Stefano Morozzi01/2020
8973(709*10^67517-7)/967519Robert Price09/2017
8974(2^224289+1370)/267518Stefano Morozzi01/2020
897547719!3-5904967516Robert Price12/2015
897616356^13411+13411^1635667509Hans Havermann09/2019
8977(22^50287+1)/2367506Robert Price06/2013
897816671^11198+11198^1667167504Hans Havermann09/2019
89793*10^67499+6767500Robert Price11/2017
898011^64811-582067494Enzo Doria01/2013
8981131^31870+31870^13167478Serge Batalov05/2014
89829*10^67468+767469Dmitry Domanov11/2010
8983(31*2^224115-1)/4772367463Lelio R Paula01/2014
8984(2^224108+1066)/267463Stefano Morozzi01/2020
8985128^32001+32001^12867433Serge Batalov05/2014
8986(89*10^67431-17)/967432Robert Price11/2015
89872^223912-11105967405Enzo Doria05/2014
89892^223913+7369767405Enzo Doria04/2016
8988(2*10^67405-23)/367405Robert Price09/2017
8990(10^67404+179)/967404Serge Batalov12/2014
899118738^3955+3955^1873867404Hans Havermann09/2016
89929*7^79728-267379Lelio R Paula09/2014
8993(28*10^67378-43)/367379Robert Price04/2016
8994(3^141234-7)/43024128267378Lelio R Paula04/2012
8995211^28988-267377Lelio R Paula09/2013
89964*10^67375+9167376Robert Price11/2017
89972^223793-1806967369Enzo Doria05/2013
89982^223777-252167364Yves Minet07/2014
8999(15185*2^223775-1)/1518367363Lelio R Paula04/2015
9000(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!