PRP Records

Probable Primes Top 10000

(301421 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 ?
65012^376790+27113426Lelio R Paula03/2013
65022^376786-112701113424Enzo Doria06/2014
65032^376731+21113408Lelio R Paula03/2013
65049*10^113394-73113395Robert Price01/2021
650529660^6651+6651^29660113387Hans Havermann01/2021
65072^376634+1871245113379Enzo Doria05/2016
6506(4^188318+17)/3113379Robert Price02/2017
6508E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
65092^376576-344369113361Enzo Doria07/2015
65102^376549-4543113353Yves Minet03/2019
6511(17*2^376526-1)/223113345Lelio R Paula03/2014
6512(27*2^376441-1)/811113319Lelio R Paula03/2014
6513(2^376350+3538)/2113293Stefano Morozzi09/2020
651427265^14272+14272^27265113273Hans Havermann02/2021
651532174^3315+3315^32174113269Hans Havermann02/2021
6516(2*10^113248+73)/3113248Robert Price09/2020
65172^376128-21237113226Enzo Doria06/2013
65185*10^113224-81113225Robert Price01/2019
651910^113220+51409113221Patrick De Geest02/2021
652110^113220-1000001113220Robert Price08/2020
652010^113220-61779113220Patrick De Geest02/2021
6522(2^376102+1578)/2113218Stefano Morozzi09/2020
6523(2^375996+3102)/2113186Stefano Morozzi09/2020
652437258^1091+1091^37258113184Hans Havermann02/2021
6525(94*10^113176+11)/3113178Robert Price04/2020
6526(46*10^113162+521)/9113163Robert Price02/2019
6527(2^375885+3614)/2113153Stefano Morozzi09/2020
6528(2^375873+2006)/2113149Stefano Morozzi09/2020
65293*10^113137+23113138Robert Price03/2022
6530(8*10^113135-269)/9113135Robert Price09/2021
6531(2^375726+694)/2113105Stefano Morozzi09/2020
653226050^21959+21959^26050113100Hans Havermann02/2021
65332^375638-1787171113079Enzo Doria03/2016
6534(2^375563+2178)/2113056Stefano Morozzi09/2020
65352^375537+4847113048Yves Minet02/2011
6536(17^91837+16^91837)/33113000Robert Price08/2013
65375*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
65382^375350-3221112992Yves Minet07/2011
6539(13*2^375306+1)/7112979Lelio R Paula03/2014
65402^375305+76757112979Enzo Doria05/2016
65412^375258+1874989112964Enzo Doria07/2016
6542(29^77237-1)/28112950Robert Price04/2012
654326620^17483+17483^26620112939Hans Havermann01/2021
65442^375154+74959112933Enzo Doria04/2016
6545(266*10^112930-17)/3112932Robert Price07/2020
6546(2^375134+778)/2112927Stefano Morozzi09/2020
6547(85*10^112919+293)/9112920Robert Price12/2019
654829412^6899+6899^29412112907Hans Havermann02/2021
6549(191*10^112903-17)/3112905Robert Price11/2021
6550(2^375022+1210)/2112893Stefano Morozzi09/2020
655125992^22039+22039^25992112889Hans Havermann02/2021
65522^374993-2787163112885Enzo Doria11/2015
6553(697*10^112869+23)/9112871Robert Price04/2021
6554(19*10^112851+377)/9112852Alfred Reich11/2022
655530420^5111+5111^30420112813Hans Havermann02/2021
655613699^27268+27268^13699112800Norbert Schneider12/2020
6557123^53970+2112793Lelio R Paula06/2013
655812308*27^78796+23112790Eric Chen07/2023
655928942^7887+7887^28942112785Hans Havermann01/2021
65602^374640-4685112778Yves Minet05/2019
656112^104501-11112776Riley Fisher12/2023
656257290^93+93^57290112775Hans Havermann01/2021
6563115^54726-54726^115112774Norman Luhn09/2024
656413608^27277-27277^13608112758Norbert Schneider12/2022
6565(2^374556+682)/2112753Stefano Morozzi09/2020
6566p(22852)#/2+512112745Robert Price05/2017
6567(11*10^112742-131)/3112743Robert Price09/2018
65682^374441-21049112718Enzo Doria06/2013
65694*10^112706-93112707Robert Price07/2020
6570(2^374321+1)/3112682H.&R. Lifchitz12/2000
6571(2^374213+1766)/2112650Stefano Morozzi09/2020
6572(2^374094+2674)/2112614Stefano Morozzi09/2020
6573(13^101089-1)/12112607Paul Bourdelais03/2010
65743^236011-8828112606Enzo Doria05/2014
657531854^3427+3427^31854112602Hans Havermann02/2021
6576(85*10^112530-373)/9112531Robert Price05/2021
6577(2^373748+1090)/2112510Stefano Morozzi09/2020
6578(2^373727+1806)/2112503Stefano Morozzi01/2021
657927618^11821+11821^27618112479Hans Havermann01/2021
6580U(602921)/4823369112479Serge Batalov07/2024
658126343^18580+18580^26343112460Hans Havermann01/2021
658239^70666+2112435Lelio R Paula11/2013
6583(134*10^112400+7)/3112402Robert Price02/2020
6584(2^373365+326)/2112394Stefano Morozzi09/2020
6585(2^373350-7)/3112390Lelio R Paula03/2014
65862^373306-1840931112377Enzo Doria06/2015
65878*10^112371-37112372Robert Price03/2022
6588(2^373262+270)/2112363Stefano Morozzi09/2020
65896*10^112359-79112360Robert Price03/2022
659034409^1842+1842^34409112356Hans Havermann02/2021
6591(142*10^112352-7)/9112354Robert Price12/2019
659225580^24633+24633^25580112336Hans Havermann01/2021
65932^373117+1872107112320Enzo Doria05/2016
6594(2^373083+2226)/2112309Stefano Morozzi01/2021
6595(35*10^112308+37)/9112309Robert Price05/2022
659627963^10376+10376^27963112301Hans Havermann01/2021
65972^373040+2792761112297Enzo Doria03/2016
6598(156^51203-1)/155112293Anonymous06/2024
6599EPrime(112280)112280Eric W. Weisstein10/2010
66002^372950+7112270Lelio R Paula03/2013
66012^372945+1872167112268Enzo Doria05/2016
660236274^1243+1243^36274112249Hans Havermann02/2021
6603(55*10^112246+629)/9112247Robert Price01/2022
6604(2^372872+3798)/2112246Stefano Morozzi02/2021
660525513^25060+25060^25513112232Hans Havermann02/2021
6606(53*10^112229-611)/9112230Robert Price02/2022
6607(2^372754+3094)/2112210Stefano Morozzi09/2020
66086*10^112208+43112209Robert Price07/2020
6609(2^372728+3058)/2112203Stefano Morozzi09/2020
661032061^3158+3158^32061112195Hans Havermann02/2021
66112^372695+72113112193Enzo Doria04/2016
66122^372689-2563112191Yves Minet07/2014
66132^372638-1859441112176Enzo Doria03/2016
66143^235074-113056112159Enzo Doria07/2014
6615-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
6616(2^372514+1822)/2112138Stefano Morozzi02/2021
661729468^6387+6387^29468112135Hans Havermann02/2021
6618(2^372428+3742)/2112112Stefano Morozzi01/2021
661925375^25454-25454^25375112110Norbert Schneider01/2021
6620131^52949-130112108Norbert Schneider02/2019
6621(91*10^112098-1)/9112100Robert Price04/2015
6622(68*10^112087-149)/9112088Robert Price07/2022
66232^372314+212419112078Enzo Doria08/2023
66242^372310-85061112077Paul Bourdelais02/2012
6625(10^112067+53)/9112067Serge Batalov07/2015
6626(2^372237+2082)/2112055Stefano Morozzi09/2020
662775^59760+2112054Lelio R Paula08/2013
6628(2^372200+1710)/2112044Stefano Morozzi09/2020
6629(10^112048+7)/8747/373157112039Alfred Reich06/2021
6630(2^372181+2250)/2112038Stefano Morozzi01/2021
6631F(536233)/825798821/1102495049/5641839306317112036Serge Batalov07/2024
6632(2^372161+2574)/2112032Stefano Morozzi09/2020
66338*10^112018-49112019Robert Price08/2019
66352^372108+74221112016Enzo Doria04/2016
6634(2^372109+2046)/2112016Stefano Morozzi09/2020
66368*10^112011-73112012Robert Price01/2022
6637(184*10^112007-1)/3112009Robert Price02/2020
66385*10^112003+81112004Robert Price03/2019
6639215^48018+48018^215112000Norbert Schneider10/2018
664025549^24148+24148^25549111979Hans Havermann02/2021
66412^371970-459491111975Enzo Doria05/2015
664241^69427-40^69427111971Robert Price07/2012
6643(2^371782+358)/2111918Stefano Morozzi01/2021
664415*25^80056+446111915Eric Chen10/2023
6645(34*10^111902-547)/9111903Robert Price03/2021
6646(10^111902+71)/9111902Serge Batalov07/2015
6647(2^371625+1610)/2111870Stefano Morozzi09/2020
664829080^7027+7027^29080111865Hans Havermann01/2021
664931307^3730+3730^31307111820Hans Havermann02/2021
66502^371440-112865111815Enzo Doria06/2014
66512^371426-459161111811Enzo Doria05/2015
665225768^21771+21771^25768111779Hans Havermann02/2021
665328022^9747+9747^28022111777Hans Havermann02/2021
6654(94*10^111770+11)/3111772Robert Price04/2020
66552^371276-461267111766Enzo Doria07/2015
66566*10^111760+43111761Robert Price07/2020
665798079!4-1024111747Robert Price11/2019
6658(2^371186+3162)/2111738Stefano Morozzi09/2020
665910^(2*55862+1)-4*10^55862-1111725Robert Price07/2023
66602^371098-113261111712Enzo Doria07/2014
6661(7*10^111706-61)/9111706Erik Branger01/2011
66622^371044+1869391111696Enzo Doria05/2016
666326310^17581+17581^26310111688Hans Havermann01/2021
666488^57416+87111645Norbert Schneider11/2015
66652^370829-109693111631Enzo Doria04/2014
666615^94906-2111619Lelio R Paula11/2013
666725835^20904+20904^25835111614Hans Havermann02/2021
6668(2^370726+1198)/2111600Stefano Morozzi09/2020
666927758^10479+10479^27758111597Hans Havermann02/2021
66702^370695-4627111591Yves Minet05/2019
66717*10^111579-87111580Robert Price06/2020
66722^370643-37111575Yves Minet01/2012
6673(2^370655-5)/2439111575Lelio R Paula03/2014
66742^370610-3911111565Yves Minet04/2017
6675(154*10^111549+17)/9111551Robert Price06/2022
667626200^18097+18097^26200111550Hans Havermann01/2021
6677286^45405+45405^286111532Norbert Schneider04/2015
66784*5^159563-9111531Lelio R Paula11/2014
66795*10^111528-21111529Robert Price12/2021
6680(4^185225+23)/3111517Robert Price10/2018
66812^370393-2797093111500Enzo Doria03/2016
6682(21*2^370382-1)/629111495Lelio R Paula03/2014
6683(2^370371+554)/2111493Stefano Morozzi09/2020
66846^143273-5111489Paul Bourdelais01/2021
66852^370292-2791979111469Enzo Doria03/2016
6686(14*10^111443-11)/3111444Robert Price08/2022
66872^370177-461551111435Enzo Doria07/2015
6688(2^370169+1706)/2111432Stefano Morozzi09/2020
6689109^54683-108111413Norbert Schneider02/2017
6691(83*10^111406-173)/9111407Robert Price04/2021
6690959^37362-37362^959111407Henri Lifchitz10/2024
6692(2^370043+1010)/2111394Stefano Morozzi09/2020
669332961^2396+2396^32961111392Hans Havermann10/2020
6694numbpart(10^10+76282)111391Serge Batalov04/2015
6695(19*10^111385+11)/3111386Robert Price07/2023
6696(23*10^111380-29)/3111381Robert Price03/2022
66972^369974+733111374Lelio R Paula05/2013
6698121^53470+120111367Norbert Schneider10/2018
66992^369915-286267111356Enzo Doria07/2015
6700(62*10^111347-629)/9111348Robert Price07/2021
67012^369855-1615111338Lelio R Paula05/2017
67027*10^111325+3111326Robert Price08/2015
670351^65176+2111293Lelio R Paula08/2013
67042^369643-1865767111274Enzo Doria03/2016
67052^369603+885111262Lelio R Paula05/2017
670625555^22564+22564^25555111252Hans Havermann10/2020
6707F(532391)/89441689/1425422598617111243Serge Batalov07/2024
6708L(532277)111240Renaud Lifchitz03/2004
6709105^55033-2111233Lelio R Paula10/2017
6710(35*10^111232-737)/9111233Robert Price07/2018
671126970^13307+13307^26970111227Hans Havermann10/2020
671225419^23716+23716^25419111210Hans Havermann10/2020
6713(26^78593-3^78593)/23111206Robert Price02/2025
67149*10^111201-29111202Robert Price09/2019
67152^369392+29835111199Lelio R Paula05/2017
67163^233059+16111198Robert Price03/2020
67172^369354-3413111187Yves Minet12/2016
67182^369296-27111170Lelio R Paula02/2013
6719(2468^40960+1)/(2468^8192+1)111161Martin Hopf08/2024
67202^369239-109837111153Enzo Doria05/2014
67212^369224-291839111148Enzo Doria07/2015
67222^369216+2798881111146Enzo Doria04/2016
672326842^13817+13817^26842111137Hans Havermann11/2020
6724(5*10^111119-191)/3111120Robert Price05/2021
6725(29*10^111112-23)/3111113Robert Price03/2022
672610^111111+163849111112Patrick De Geest03/2017
672710^111111-312911111111Patrick De Geest03/2017
67282^369092-216923111108Enzo Doria05/2014
67292^369081-55111105Lelio R Paula02/2013
6730(2^369047+3618)/2111094Stefano Morozzi09/2020
673188^57124-87111077Norbert Schneider11/2015
67322^368980+753111075Lelio R Paula05/2013
67332^368946-3623111064Yves Minet03/2017
67342^368929+29835111059Lelio R Paula05/2017
67354^184463-3^184463111058Jean-Louis Charton12/2004
6736111^54298+110111057Norbert Schneider04/2017
6737(4*10^111032-7)/3111033Ray Chandler04/2011
6738(29*10^111020-41)/3111021Tyler Busby03/2024
673935799^1262+1262^35799111015Hans Havermann10/2020
6740(298*10^111004+11)/3111006Robert Price11/2020
674127648^10349+10349^27648111004Hans Havermann11/2020
674228899^6932+6932^28899110997Hans Havermann11/2020
6743(749^38809+1)/(749^197+1)110990Martin Hopf11/2023
67442^368641-460303110972Enzo Doria06/2015
67452^368619-109087110966Enzo Doria04/2014
6746(74*10^110961+313)/9110962Robert Price06/2019
674725258^24711+24711^25258110956Hans Havermann11/2020
6748(2^368539+1290)/2110941Stefano Morozzi01/2021
67493*2^368489+7110927Lelio R Paula09/2014
6750(14*10^110922+61)/3110923Robert Price12/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 19 2025 12:52 (Time in France)

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