PRP Records

Probable Primes Top 10000

(301723 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 ?
65013^242337-4042115625Enzo Doria05/2014
6502(17699*31^77516-29)/30115608Eric Chen05/2024
6503(2^383931+674)/2115575Stefano Morozzi09/2020
65047*10^115561+79115562Robert Price07/2019
6505(2^383872+3046)/2115557Stefano Morozzi09/2020
6506(11*2^383859-13)/15115553Renaud Lifchitz03/2011
65072^383780-3149115530Yves Minet10/2014
6508(41*10^115523-383)/9115524Robert Price11/2018
650927316^16923+16923^27316115506Hans Havermann02/2021
6510(2^383618+618)/2115481Stefano Morozzi09/2020
65112^383560-455115464Yves Minet03/2012
6512(2^383544+5)/3115458Lelio R Paula03/2014
6513(22*10^115454+119)/3115455Robert Price04/2021
651489^59221-88^59221115445Robert Price06/2015
6515(7^136559-5^136559)/2115406Jon Grantham08/2023
65162^383347+1869413115399Enzo Doria05/2016
6517(103*10^115366+17)/3115368Robert Price08/2020
6518(2^383232+750)/2115365Stefano Morozzi09/2020
6519(2^383130-7)/131793115329Lelio R Paula03/2014
6520(12^106859+1)/13115320Paul Bourdelais02/2010
652129961^7060+7060^29961115315Hans Havermann01/2021
65232^383039+1869509115307Enzo Doria05/2016
652232918^3183+3183^32918115307Hans Havermann01/2021
6524(109^56597-1)/90183471012115302Paul Vanderveen06/2025
652536964^1315+1315^36964115288Hans Havermann02/2021
6526(13*2^382968+1)/7115286Lelio R Paula04/2014
6527(22*10^115282+29)/3115283Robert Price02/2021
6528(2^382945+2046)/2115278Stefano Morozzi09/2020
6529(2^382789+3182)/2115231Stefano Morozzi09/2020
653030416^6141+6141^30416115224Hans Havermann02/2021
65316*10^115211+79115212Robert Price09/2020
6532(2^382722+3598)/2115211Stefano Morozzi09/2020
653327987^13078+13078^27987115210Hans Havermann02/2021
6534(2^382699+2090)/2115204Stefano Morozzi09/2020
6535(22*10^115188-193)/9115189Robert Price07/2022
65362^382633+73697115185Enzo Doria04/2016
65372^382509-113593115147Enzo Doria08/2014
65382^382502-2791721115145Enzo Doria03/2016
6539(2^382495+1274)/2115143Stefano Morozzi01/2021
65402^382464+22741115134Enzo Doria09/2023
654126752^20065+20065^26752115099Hans Havermann02/2021
654226383^23008+23008^26383115080Hans Havermann02/2021
65439^120590-120590115073Robert Price03/2014
654428203^12016+12016^28203115062Hans Havermann02/2021
65452^382198+9115054Lelio R Paula03/2013
654618268*31^77131+22839115035Eric Chen05/2024
654730101^6630+6630^30101115032Hans Havermann01/2021
6548(89*10^115030-179)/9115031Robert Price12/2019
654925554^26089-26089^25554114987Frank Doornink02/2024
655025142^26129-26129^25142114979Frank Doornink12/2023
6551(2^381935+2774)/2114974Stefano Morozzi02/2021
655227300^16271+16271^27300114972Hans Havermann02/2021
6553(23*10^114962+7)/3114963Robert Price05/2023
65542^381883-59197114959Enzo Doria10/2015
655527423^15542+15542^27423114944Hans Havermann02/2021
6556(2^381820+1626)/2114939Stefano Morozzi09/2020
65582^381806-4481114936Yves Minet07/2011
65572^381808-1851507114936Enzo Doria08/2015
6559(2^381792+2502)/2114931Stefano Morozzi09/2020
65602^381774-112373114926Enzo Doria06/2014
656126341^22980+22980^26341114883Hans Havermann01/2021
6562(79^60539-1)/61747564999146114867Paul Vanderveen05/2025
65632^381555-109051114860Enzo Doria04/2014
65642^381551+213683114859Enzo Doria09/2023
65652^381546-113501114857Enzo Doria08/2014
6566(7*10^114845-19)/3114846Robert Price10/2020
656726675^20178+20178^26675114833Hans Havermann02/2021
6568(2^381436+1182)/2114824Stefano Morozzi09/2020
65693^240644+16114817Robert Price04/2020
6570(13^114814)%(10^114814)114814Henri Lifchitz05/2025
65712^381360-110429114801Enzo Doria05/2014
6572(17*10^114795+79)/3114796Robert Price04/2019
6573(66^63079+1)/67114774Paul Bourdelais09/2017
65742^381252-115079114769Enzo Doria06/2015
6575(2^381251+3186)/2114768Stefano Morozzi09/2020
65762^381209-29323114756Enzo Doria07/2015
65772^381207-111546435114755Paul Bourdelais10/2021
6578569^41651-568^41651114754Jean-Louis Charton11/2009
65792^381201+1873205114753Enzo Doria06/2016
6581(85*10^114737+293)/9114738Robert Price12/2019
6582(265*10^114736+17)/3114738Robert Price03/2020
6580379*10^114735+9114738Jason Yuen01/2025
6583(2^381062+2170)/2114711Stefano Morozzi09/2020
65842^380974-112991114685Enzo Doria07/2014
658537097^1234+1234^37097114679Hans Havermann02/2021
6586(26*10^114658-119)/3114659Robert Price07/2023
658788^58949-87114626Norbert Schneider11/2015
6588(2^380773+662)/2114624Stefano Morozzi09/2020
6589Phi(155285,10)/242674820198201114610Makoto Kamada02/2024
6590(10^155285-1)*(10^2389-1)*(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201114610Anonymous04/2025
659129913^6782+6782^29913114608Hans Havermann02/2021
6592(331*10^114605-7)/9114607Robert Price04/2022
65932^380700+91114603Lelio R Paula03/2013
6594(2^380632+2578)/2114582Stefano Morozzi09/2020
65957*10^114577+27114578Robert Price11/2020
659710^114575+3^114576114576Mike Oakes09/2010
659610^114575+66561114576Patrick De Geest02/2017
659810^114575-581081114575Patrick De Geest02/2017
65992^380587-115315114569Enzo Doria06/2015
660031874^3927+3927^31874114558Hans Havermann02/2021
66012^380513-216925114546Enzo Doria05/2014
66022^380451-1840087114528Enzo Doria06/2015
6603(2^380426+1510)/2114520Stefano Morozzi09/2020
6604(15*2^380388-1)/539114507Lelio R Paula04/2014
66052^380279-461347114476Enzo Doria07/2015
6606(331*10^114454-7)/9114456Robert Price04/2022
660727121^16590+16590^27121114447Hans Havermann01/2021
660825966^25555+25555^25966114445Hans Havermann01/2021
6609(611*32^76029-53)/31114437Eric Chen11/2023
6610(11*10^114400+529)/9114401Robert Price09/2021
66112^380021+1871147114398Enzo Doria05/2016
66122^380005+1869707114393Enzo Doria05/2016
66132^379958-113297114379Enzo Doria07/2014
6614(2^379897+1274)/2114361Stefano Morozzi01/2021
66152^379881-109105114356Enzo Doria04/2014
6616(21*2^379857-1)/13114349Lelio R Paula03/2014
6617(4*10^114340+83)/3114341Robert Price02/2018
6618(26*10^114317-77)/3114318Robert Price11/2019
6619(4*10^114296+149)/9114296Robert Price04/2018
662088^58773-87114284Norbert Schneider11/2015
662127764^13065+13065^27764114280Hans Havermann01/2021
6622(132^53891-1)/131114278Anonymous06/2024
66232^379529-2790283114250Enzo Doria03/2016
66242^379522+1869115114248Enzo Doria05/2016
6625(145*10^114226-1)/9114228Serge Batalov12/2014
66262^379317-115033114186Enzo Doria06/2015
6627(22*10^114178+47)/3114179Robert Price06/2021
6628(17*2^379246-1)/17407114162Lelio R Paula03/2014
6629(2^379192+226)/2114148Stefano Morozzi09/2020
6630(228^48407-1)/227114139Alexander Zhirkov03/2023
66316*10^114091+23114092Robert Price09/2020
6632(4*10^114076+143)/3114077Robert Price03/2018
6633332*25^81584+12357114053Eric Chen10/2023
6634(2^378820+3226)/2114036Stefano Morozzi01/2021
6635(2^378754+2058)/2114017Stefano Morozzi09/2020
663613643^27572-27572^13643114008Norbert Schneider12/2022
6638(46*10^113969+683)/9113970Robert Price03/2019
6637(83*10^113969+133)/9113970Robert Price08/2021
663932226^3439+3439^32226113966Hans Havermann02/2021
6640(77*10^113963-149)/9113964Robert Price03/2022
664178*10^113954-7113956Robert Price10/2020
66422*10^113941+9113942Dmitry Domanov11/2010
664310^113933+145897113934Patrick De Geest02/2021
6646(2^378478+1642)/2113933Stefano Morozzi09/2020
664410^113933-8000000001113933Robert Price11/2020
664510^113933-66167113933Patrick De Geest02/2021
66472339662057597*10^113903+9113916Robert Price03/2021
66484*10^113905+91113906Robert Price08/2018
664910^113894+76609113895Patrick De Geest02/2021
665110^113894-10000001113894Robert Price09/2020
665010^113894-373947113894Patrick De Geest02/2021
665233933^2270+2270^33933113881Hans Havermann02/2021
66534*10^113874-21113875Robert Price09/2018
66542^378272-16565113872Enzo Doria04/2013
66552^378217-109075113855Enzo Doria04/2014
66562^378198+67113849Lelio R Paula03/2013
66572^378173-3249113842Yves Minet12/2014
6658(2^378155-5)/6597113833Lelio R Paula03/2014
66592^378137+1334025113831Henri Lifchitz10/2024
666092941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
666130030^6173+6173^30030113829Hans Havermann01/2021
66622^378128-262977113828Enzo Doria05/2014
66632^378123-113215113827Enzo Doria07/2014
66646^146274-18893113824Enzo Doria03/2013
666534596^1949+1949^34596113815Hans Havermann02/2021
66662^378078+75113813Lelio R Paula03/2013
6667(28*10^113810+449)/9113811Robert Price11/2021
666826273^21448+21448^26273113799Hans Havermann02/2021
66692^377966+255255113780Paul Bourdelais10/2021
66702^377940+63113772Lelio R Paula03/2013
66712^377941-2785843113772Enzo Doria04/2016
6672(7*10^113757+11)/9113757Tyler Busby01/2023
66732^377810+1875109113733Enzo Doria09/2016
66742^377803-1838635113731Enzo Doria05/2015
66752^377799+52223113729Yves Minet08/2010
6676(2^377791+3258)/2113727Stefano Morozzi02/2021
667711^109190-270113710Enzo Doria12/2012
667828206^10739+10739^28206113698Hans Havermann01/2021
66797*10^113693+9113694Robert Price09/2015
668013899^27442+27442^13899113692Norbert Schneider12/2020
6681(82*10^113681+161)/9113682Robert Price10/2019
668226121^22478+22478^26121113673Hans Havermann01/2021
66834*10^113658+49113659Robert Price01/2019
6684(10^113656+7)/40231/6439001113645Alfred Reich06/2021
6685(2*10^113631+529)/9113631Robert Price01/2018
66862^377408-2798279113612Enzo Doria04/2016
6687(292^46336+1)/(292^256+1)113605Martin Hopf12/2023
668813706^27459+27459^13706113596Norbert Schneider12/2020
66895*10^113586+57113587Robert Price12/2018
6690(2^377242+2794)/2113561Stefano Morozzi02/2021
66912^377222+93679113556Yves Minet02/2011
6693262147#+316847113552Makoto Morimoto02/2016
669227172^15101+15101^27172113552Hans Havermann01/2021
6694(2^377131+2018)/2113528Stefano Morozzi09/2020
66952^377026-458903113497Enzo Doria04/2015
6696(2^377014+2202)/2113493Stefano Morozzi09/2020
669734791^1828+1828^34791113488Hans Havermann02/2021
6698(2^376967+258)/2113479Stefano Morozzi09/2020
6699(29*10^113468-17)/3113469Robert Price09/2019
670035^73477-34^73477113454Robert Price05/2012
6701(14*10^113451-89)/3113452Robert Price05/2020
67022^376790+27113426Lelio R Paula03/2013
67032^376786-112701113424Enzo Doria06/2014
67042^376731+21113408Lelio R Paula03/2013
67059*10^113394-73113395Robert Price01/2021
670629660^6651+6651^29660113387Hans Havermann01/2021
67082^376634+1871245113379Enzo Doria05/2016
6707(4^188318+17)/3113379Robert Price02/2017
6709E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
67102^376576-344369113361Enzo Doria07/2015
67112^376549-4543113353Yves Minet03/2019
6712(17*2^376526-1)/223113345Lelio R Paula03/2014
6713(27*2^376441-1)/811113319Lelio R Paula03/2014
6714(2^376350+3538)/2113293Stefano Morozzi09/2020
671527265^14272+14272^27265113273Hans Havermann02/2021
671632174^3315+3315^32174113269Hans Havermann02/2021
6717(2*10^113248+73)/3113248Robert Price09/2020
67182^376128-21237113226Enzo Doria06/2013
67195*10^113224-81113225Robert Price01/2019
672010^113220+51409113221Patrick De Geest02/2021
672210^113220-1000001113220Robert Price08/2020
672110^113220-61779113220Patrick De Geest02/2021
6723(2^376102+1578)/2113218Stefano Morozzi09/2020
6724(2^375996+3102)/2113186Stefano Morozzi09/2020
672537258^1091+1091^37258113184Hans Havermann02/2021
6726(94*10^113176+11)/3113178Robert Price04/2020
6727(46*10^113162+521)/9113163Robert Price02/2019
672814*29^77375+17875113155Eric Chen06/2025
6729(2^375885+3614)/2113153Stefano Morozzi09/2020
6730(2^375873+2006)/2113149Stefano Morozzi09/2020
67313*10^113137+23113138Robert Price03/2022
6732(8*10^113135-269)/9113135Robert Price09/2021
6733(2^375726+694)/2113105Stefano Morozzi09/2020
673426050^21959+21959^26050113100Hans Havermann02/2021
67352^375638-1787171113079Enzo Doria03/2016
6736(2^375563+2178)/2113056Stefano Morozzi09/2020
67372^375537+4847113048Yves Minet02/2011
6738(17^91837+16^91837)/33113000Robert Price08/2013
67395*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
67402^375350-3221112992Yves Minet07/2011
6741(13*2^375306+1)/7112979Lelio R Paula03/2014
67422^375305+76757112979Enzo Doria05/2016
67432^375258+1874989112964Enzo Doria07/2016
6744(29^77237-1)/28112950Robert Price04/2012
674526620^17483+17483^26620112939Hans Havermann01/2021
67462^375154+74959112933Enzo Doria04/2016
6747(266*10^112930-17)/3112932Robert Price07/2020
6748(2^375134+778)/2112927Stefano Morozzi09/2020
6749(85*10^112919+293)/9112920Robert Price12/2019
675029412^6899+6899^29412112907Hans Havermann02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 10 2025 14:11 (Time in France)

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