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 ?
5251(17*10^130695-161)/9130696Robert Price02/2021
525230513^19148+19148^30513130661Hans Havermann03/2021
525329736^24761+24761^29736130654Hans Havermann04/2021
52549*10^130638+41130639Robert Price08/2020
52552^433911-91130621Lelio R Paula06/2017
525630786^17449+17449^30786130588Hans Havermann03/2021
52572^433744-114419130570Enzo Doria02/2015
52592^433708+1869451130560Enzo Doria05/2016
52582^433710+93130560Lelio R Paula06/2017
52607*10^130535-27130536Robert Price11/2022
5261(17^130533)%(10^130533)130533Henri Lifchitz05/2025
5262(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
5263804*34^85220+713130516Eric Chen08/2023
5264(29*2^433547-1)/27130511Lelio R Paula06/2015
52653^273521+10130503Tyler NeSmith01/2021
526641659^1356+1356^41659130487Hans Havermann03/2021
52674*10^130480+9130481Robert Price05/2015
5268(23*2^433449-1)/75130481Lelio R Paula06/2015
52693*2^433422+5130474Jon Grantham07/2023
5270(23*2^433334-1)/3731130445Lelio R Paula06/2015
5271(31*10^130414-49)/9130415Robert Price11/2021
527226462^29485-29485^26462130402Frank Doornink03/2024
527333481^7848+7848^33481130401Hans Havermann03/2021
5274(17*10^130393+7)/3130394Robert Price06/2023
5275(22*10^130392+203)/9130393Robert Price10/2021
527629773^23950+23950^29773130386Hans Havermann04/2021
52772^433023-113497130353Enzo Doria08/2014
527831175^15178+15178^31175130350Hans Havermann04/2021
52792^433002+1179379130347Enzo Doria06/2016
52802^432974+19130339Robert Price08/2015
528131903^12168+12168^31903130331Hans Havermann04/2021
52822^432917+22217130322Enzo Doria09/2023
528329387^27112+27112^29387130278Hans Havermann04/2021
52842^432768+213181130277Enzo Doria09/2023
528529577^25370+25370^29577130267Hans Havermann04/2021
528631738^12685+12685^31738130231Hans Havermann03/2021
528744235^878+878^44235130206Hans Havermann04/2021
528832160^11171+11171^32160130187Hans Havermann04/2021
528929489^25956+25956^29489130172Hans Havermann04/2021
5290(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
529133005^8766+8766^33005130133Hans Havermann04/2021
5292(35*10^130132-611)/9130133Robert Price02/2022
5293(444^49408+1)/(444^256+1)130125Martin Hopf12/2023
52942^432217+41130111Lelio R Paula06/2017
5295(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
5296((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
529797^65480-2130094Lelio R Paula05/2017
529836007^4102+4102^36007130094Hans Havermann04/2021
52994*10^130088-89130089Robert Price11/2018
53002^432117-113215130081Enzo Doria07/2014
5301(4*10^130080+41)/9130080Serge Batalov11/2022
53029583*29^88890+736129997Eric Chen06/2025
53032^431804+72511129986Enzo Doria04/2016
530427902^29237-29237^27902129978Frank Doornink03/2024
5305(2313^38809-1)/(2313^197-1)129898Ryan Propper11/2023
5306(13*10^129896+137)/3129897Robert Price06/2021
5307(13*10^129890+71)/3129891Robert Price06/2021
530829048^29101-29101^29048129882Norbert Schneider03/2022
530937832^2709+2709^37832129871Hans Havermann04/2021
531031055^15184+15184^31055129853Hans Havermann04/2021
5312(3^272141-3^136071+1)/7129844Serge Batalov03/2014
5311Phi(1632846L,3)129844Anonymous03/2025
531331385^13702+13702^31385129833Hans Havermann04/2021
5314(13*10^129826+41)/9129827Tyler Busby02/2023
531528901^29102-29102^28901129822Norbert Schneider03/2022
5316(47*10^129789-119)/9129790Robert Price05/2019
5317(9*2^431141+1)/17129787Lelio R Paula06/2015
531825999^29384-29384^25999129730Frank Doornink03/2024
531925771^29408-29408^25771129723Frank Doornink02/2024
5320(166*10^129712+17)/3129714Robert Price07/2022
5321(29*2^430881-1)/21129709Lelio R Paula06/2015
53222^430807+1869563129686Enzo Doria05/2016
53232^430721-21429129660Enzo Doria07/2013
5324(4*10^129618+89)/3129619Robert Price08/2021
5325(142^60223-1)/141129616Anonymous06/2024
5326(10^129587-7^129587)/3129587Jon Grantham07/2023
53272^430415-276271129568Enzo Doria07/2015
532832282^10311+10311^32282129558Hans Havermann04/2021
532929486^24741+24741^29486129545Hans Havermann04/2021
5330(29*10^129543+313)/9129544Robert Price04/2021
533137095^3104+3104^37095129533Hans Havermann04/2021
533231132^14459+14459^31132129514Hans Havermann04/2021
533332582^9435+9435^32582129506Hans Havermann03/2021
533430442^17953+17953^30442129505Hans Havermann03/2021
5335(199*10^129487-7)/3129489Robert Price05/2020
53362^430142-2791721129486Enzo Doria03/2016
5337(7*10^129472-13)/3129473Robert Price07/2018
5338(8*10^129469+79)/3129470Robert Price10/2020
533931678^12213+12213^31678129463Hans Havermann04/2021
534010620^32143-10619^32143129412Norbert Schneider08/2023
5341(772*10^129406-7)/9129408Robert Price06/2022
5342(535^47431-1)/534129406Tom Wu09/2024
5343((3*20425-8193)*F(618977)-(20425-8193)*L(618977))/2129363Yaroslav Berezhko03/2025
534431100^14439+14439^31100129362Hans Havermann04/2021
534533009^8288+8288^33009129345Hans Havermann04/2021
534625895^29306-29306^25895129334Frank Doornink03/2024
5347(44^78697+43^78697)/87129333Aurel Gibier11/2023
534829675^22804+22804^29675129324Hans Havermann04/2021
534929068^28099+28099^29068129315Hans Havermann04/2021
53502^429568-21017129313Enzo Doria07/2013
5351(10^129295+83)/3129295Robert Price08/2021
5352(853*10^129274-7)/9129276Robert Price07/2021
535330958^14961+14961^30958129249Hans Havermann04/2021
5354(11*10^129239-179)/3129240Robert Price09/2018
535528659^28988+28988^28659129208Norbert Schneider02/2021
535629423^24616+24616^29423129203Hans Havermann03/2021
53572^429194-112685129201Enzo Doria06/2014
535831*35^83672+17398129197Eric Chen05/2025
53592^429145-2780449129186Enzo Doria04/2016
536032500^9427+9427^32500129168Hans Havermann04/2021
536133577^7014+7014^33577129136Hans Havermann03/2021
53622^428892-113453129110Enzo Doria07/2014
5363(11*2^428881-7)/15129106Renaud Lifchitz03/2011
53642^428727-113959129060Enzo Doria10/2014
5365(7*2^428725-1)/13129059Lelio R Paula05/2014
5366(10^129051-31)/3129051Serge Batalov12/2014
5367(3^732836)/(2^732836)129047Henri Lifchitz05/2025
5368(134*10^129038+7)/3129040Robert Price02/2020
53692^428564+71161129011Enzo Doria04/2016
537028781^28930+28930^28781129002Norbert Schneider02/2021
537129065^27424+27424^29065128995Hans Havermann04/2021
53722^428502-113285128992Enzo Doria07/2014
53732^428421-21373128968Enzo Doria06/2013
5374L(616787)128901Henri Lifchitz09/2008
5375(765^44701-1)/764128900Tom Wu07/2024
537620^99055-3128874Paul Bourdelais12/2020
537791^65772-2128851Lelio R Paula05/2017
53782^428022+43128848Lelio R Paula05/2017
53792^427999-459397128841Enzo Doria05/2015
53802^427993+76847128839Enzo Doria05/2016
538131059^14060+14060^31059128833Hans Havermann03/2021
538210^128805+152871128806Patrick De Geest05/2021
538310^128805-10001128805Robert Price02/2021
53842^427824-1851507128788Enzo Doria08/2015
53852^427807-21469128783Enzo Doria07/2013
538629082^26783+26783^29082128772Hans Havermann04/2021
538740055^1638+1638^40055128750Hans Havermann04/2021
5388(923^43411-1)/922128720Tom Wu07/2024
538911^123594-240128710Enzo Doria09/2012
53902^427504-21503128692Enzo Doria07/2013
539137727^2574+2574^37727128673Hans Havermann04/2021
539229686^21591+21591^29686128668Hans Havermann04/2021
539310^128668-70000000001128668Robert Price08/2021
539410^128668-350729128668Alfred Reich08/2024
53952^427420+91128667Lelio R Paula05/2017
53968*10^128651-37128652Robert Price03/2022
5397(68*10^128645-257)/9128646Robert Price07/2019
53982^427269-113635128621Enzo Doria08/2014
53992^427130+1877569128579Enzo Doria08/2016
54002^427068+20011128561Enzo Doria06/2023
54012^427016-115349128545Enzo Doria07/2015
54022^427001+1334025128541Henri Lifchitz11/2024
5403(4*10^128510+137)/3128511Robert Price03/2018
54042^426889-112879128507Enzo Doria06/2014
54052^426804+1869931128481Enzo Doria05/2016
54062^426750+77635128465Enzo Doria05/2016
540727708^28913-28913^27708128450Frank Doornink03/2024
540836988^2969+2969^36988128445Hans Havermann03/2021
540936664^3185+3185^36664128439Hans Havermann03/2021
541032618^8649+8649^32618128416Hans Havermann04/2021
541128883^27874+27874^28883128391Hans Havermann04/2021
54122^426425-91128367Lelio R Paula05/2017
5413(15*2^426398-1)/11128359Lelio R Paula05/2014
54142^426352+74971128345Enzo Doria04/2016
5415(199*10^128343-7)/3128345Robert Price05/2020
54164*10^128343-21128344Robert Price09/2018
5417(65*10^128338+493)/9128339Robert Price08/2021
541835632^3997+3997^35632128337Hans Havermann04/2021
54192^426300-1863689128330Enzo Doria03/2016
54202^426293+1881017128327Enzo Doria11/2016
5421(88*10^128324-637)/9128325Robert Price11/2020
5422(491*10^128285+31)/9128287Robert Price04/2022
542339103^1908+1908^39103128281Hans Havermann04/2021
54242^426043+35128252Robert Price11/2015
5425(4*10^128244-19)/3128245Robert Price03/2018
542626220^29021-29021^26220128234Frank Doornink03/2024
542735489^4102+4102^35489128222Hans Havermann04/2021
542834721^4926+4926^34721128208Hans Havermann04/2021
5429(305*10^128198+1)/9128200Robert Price02/2020
54302^425808-459959128181Enzo Doria06/2015
543130632^15291+15291^30632128178Hans Havermann04/2021
5432U(623603)128177Serge Batalov07/2024
543335981^3648+3648^35981128167Hans Havermann04/2021
54342^425627-113605128127Enzo Doria08/2014
5435(4*10^128109+119)/3128110Robert Price12/2021
5436(22*10^128094+53)/3128095Robert Price07/2019
5437(86*10^128086-221)/9128087Robert Price09/2019
543818565^30002-30002^18565128070Norbert Schneider01/2015
5439(2^425287-9)/2737128021Lelio R Paula05/2015
5440(3*2^425233-1)/25128007Lelio R Paula05/2014
5441Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
54422^425205+4911128000Marek Hubal02/2017
544329241^23836+23836^29241127995Hans Havermann04/2021
54442^425118-113663127974Enzo Doria08/2014
5445(86*10^127967-329)/9127968Robert Price01/2020
54462^425061+1869761127957Enzo Doria05/2016
5447746^44541+44541^746127955Norbert Schneider07/2019
544830236^17043+17043^30236127946Hans Havermann03/2021
54492^424938+212419127920Enzo Doria08/2023
54502^424918-21141127914Enzo Doria07/2013
5451(62*10^127903+91)/9127904Robert Price07/2021
54522^424864-29489127897Enzo Doria08/2015
545330438^15893+15893^30438127877Hans Havermann02/2021
5454(97*10^127858-1)/3127860Serge Batalov12/2014
545528929^26258+26258^28929127845Hans Havermann03/2021
545630563^15220+15220^30563127828Hans Havermann03/2021
54572^424632-2786639127827Enzo Doria03/2016
545810^127821-700001127821Robert Price08/2021
54592^424577-113755127811Enzo Doria09/2014
5460(7*2^424512-1)/3127792Lelio R Paula05/2014
5461(56*10^127752+691)/9127753Robert Price05/2019
546211^122629-720127705Enzo Doria11/2012
546322*10^127645+3127647Robert Price01/2020
546428715^27844+27844^28715127631Hans Havermann03/2021
5465(56*10^127612+187)/9127613Robert Price10/2021
5466(5*36^81995+821)/7127609Eric Chen01/2021
54674*10^127562-39127563Robert Price09/2020
546832595^8186+8186^32595127547Hans Havermann03/2021
54692^423696-21429127546Enzo Doria07/2013
54702^423664-1864559127536Enzo Doria03/2016
547137889^2322+2322^37889127530Hans Havermann03/2021
547237668^2429+2429^37668127523Hans Havermann03/2021
54733^267267-4127519Henri Lifchitz10/2014
5474fibonacci(610144)-2127513Jon Grantham08/2023
547526253^28852-28852^26253127503Frank Doornink03/2024
5476(103*10^127491+17)/3127493Robert Price08/2020
547729376^21869+21869^29376127487Hans Havermann03/2021
547831186^12241+12241^31186127483Hans Havermann02/2021
5479(19^99689+5^99689)/24127477Robert Price09/2013
548027069^28754-28754^27069127452Frank Doornink01/2024
5481(21*2^423372+1)/101127447Lelio R Paula05/2014
548230594^14645+14645^30594127446Hans Havermann03/2021
54832^423328-21537127435Enzo Doria07/2013
5484(67*10^127413-7)/3127415Robert Price01/2020
5485(5*34^83193+700233)/11127408Eric Chen08/2023
5486(2*10^127407+73)/3127407Robert Price09/2020
5487(2^423165-7)/25127384Lelio R Paula05/2015
5488(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
5489(4*10^127349+17)/3127350Tyler Busby01/2023
549029512^20647+20647^29512127341Hans Havermann03/2021
54912^422987-3001935127332Paul Bourdelais07/2023
5492(112*10^127324+17)/3127326Robert Price03/2020
549429565^20252+20252^29565127321Hans Havermann03/2021
5493232^232^232+1831^1831127321Henri Lifchitz03/2025
5495fibonacci(609165)-3127308Jon Grantham08/2023
5497(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
5496(5^182099-3^182099)/2127282Kellen Shenton05/2022
5498(16*10^127259+197)/3127260Robert Price04/2019
5499(26*10^127240+61)/3127241Robert Price10/2019
5500(234483*27^88884-145)/26127230Curtis Bright05/2015


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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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