PRP Records

Probable Primes Top 10000

(300935 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 ?
625110^113933+145897113934Patrick De Geest02/2021
6254(2^378478+1642)/2113933Stefano Morozzi09/2020
625210^113933-8000000001113933Robert Price11/2020
625310^113933-66167113933Patrick De Geest02/2021
62552339662057597*10^113903+9113916Robert Price03/2021
62564*10^113905+91113906Robert Price08/2018
625710^113894+76609113895Patrick De Geest02/2021
625910^113894-10000001113894Robert Price09/2020
625810^113894-373947113894Patrick De Geest02/2021
626033933^2270+2270^33933113881Hans Havermann02/2021
62614*10^113874-21113875Robert Price09/2018
62622^378272-16565113872Enzo Doria04/2013
62632^378217-109075113855Enzo Doria04/2014
62642^378198+67113849Lelio R Paula03/2013
62652^378173-3249113842Yves Minet12/2014
6266(2^378155-5)/6597113833Lelio R Paula03/2014
62672^378137+1334025113831Henri Lifchitz10/2024
626892941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
626930030^6173+6173^30030113829Hans Havermann01/2021
62702^378128-262977113828Enzo Doria05/2014
62712^378123-113215113827Enzo Doria07/2014
62726^146274-18893113824Enzo Doria03/2013
627334596^1949+1949^34596113815Hans Havermann02/2021
62742^378078+75113813Lelio R Paula03/2013
6275(28*10^113810+449)/9113811Robert Price11/2021
627626273^21448+21448^26273113799Hans Havermann02/2021
62772^377966+255255113780Paul Bourdelais10/2021
62782^377940+63113772Lelio R Paula03/2013
62792^377941-2785843113772Enzo Doria04/2016
6280(7*10^113757+11)/9113757Tyler Busby01/2023
62812^377810+1875109113733Enzo Doria09/2016
62822^377803-1838635113731Enzo Doria05/2015
62832^377799+52223113729Yves Minet08/2010
6284(2^377791+3258)/2113727Stefano Morozzi02/2021
628511^109190-270113710Enzo Doria12/2012
628628206^10739+10739^28206113698Hans Havermann01/2021
62877*10^113693+9113694Robert Price09/2015
628813899^27442+27442^13899113692Norbert Schneider12/2020
6289(82*10^113681+161)/9113682Robert Price10/2019
629026121^22478+22478^26121113673Hans Havermann01/2021
62914*10^113658+49113659Robert Price01/2019
6292(10^113656+7)/40231/6439001113645Alfred Reich06/2021
6293(2*10^113631+529)/9113631Robert Price01/2018
62942^377408-2798279113612Enzo Doria04/2016
6295(292^46336+1)/(292^256+1)113605Martin Hopf12/2023
629613706^27459+27459^13706113596Norbert Schneider12/2020
62975*10^113586+57113587Robert Price12/2018
6298(2^377242+2794)/2113561Stefano Morozzi02/2021
62992^377222+93679113556Yves Minet02/2011
6301262147#+316847113552Makoto Morimoto02/2016
630027172^15101+15101^27172113552Hans Havermann01/2021
6302(2^377131+2018)/2113528Stefano Morozzi09/2020
63032^377026-458903113497Enzo Doria04/2015
6304(2^377014+2202)/2113493Stefano Morozzi09/2020
630534791^1828+1828^34791113488Hans Havermann02/2021
6306(2^376967+258)/2113479Stefano Morozzi09/2020
6307(29*10^113468-17)/3113469Robert Price09/2019
630835^73477-34^73477113454Robert Price05/2012
6309(14*10^113451-89)/3113452Robert Price05/2020
63102^376790+27113426Lelio R Paula03/2013
63112^376786-112701113424Enzo Doria06/2014
63122^376731+21113408Lelio R Paula03/2013
63139*10^113394-73113395Robert Price01/2021
631429660^6651+6651^29660113387Hans Havermann01/2021
63162^376634+1871245113379Enzo Doria05/2016
6315(4^188318+17)/3113379Robert Price02/2017
6317E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
63182^376576-344369113361Enzo Doria07/2015
63192^376549-4543113353Yves Minet03/2019
6320(17*2^376526-1)/223113345Lelio R Paula03/2014
6321(27*2^376441-1)/811113319Lelio R Paula03/2014
6322(2^376350+3538)/2113293Stefano Morozzi09/2020
632327265^14272+14272^27265113273Hans Havermann02/2021
632432174^3315+3315^32174113269Hans Havermann02/2021
6325(2*10^113248+73)/3113248Robert Price09/2020
63262^376128-21237113226Enzo Doria06/2013
63275*10^113224-81113225Robert Price01/2019
632810^113220+51409113221Patrick De Geest02/2021
633010^113220-1000001113220Robert Price08/2020
632910^113220-61779113220Patrick De Geest02/2021
6331(2^376102+1578)/2113218Stefano Morozzi09/2020
6332(2^375996+3102)/2113186Stefano Morozzi09/2020
633337258^1091+1091^37258113184Hans Havermann02/2021
6334(94*10^113176+11)/3113178Robert Price04/2020
6335(46*10^113162+521)/9113163Robert Price02/2019
6336(2^375885+3614)/2113153Stefano Morozzi09/2020
6337(2^375873+2006)/2113149Stefano Morozzi09/2020
63383*10^113137+23113138Robert Price03/2022
6339(8*10^113135-269)/9113135Robert Price09/2021
6340(2^375726+694)/2113105Stefano Morozzi09/2020
634126050^21959+21959^26050113100Hans Havermann02/2021
63422^375638-1787171113079Enzo Doria03/2016
6343(2^375563+2178)/2113056Stefano Morozzi09/2020
63442^375537+4847113048Yves Minet02/2011
6345(17^91837+16^91837)/33113000Robert Price08/2013
63465*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
63472^375350-3221112992Yves Minet07/2011
6348(13*2^375306+1)/7112979Lelio R Paula03/2014
63492^375305+76757112979Enzo Doria05/2016
63502^375258+1874989112964Enzo Doria07/2016
6351(29^77237-1)/28112950Robert Price04/2012
635226620^17483+17483^26620112939Hans Havermann01/2021
63532^375154+74959112933Enzo Doria04/2016
6354(266*10^112930-17)/3112932Robert Price07/2020
6355(2^375134+778)/2112927Stefano Morozzi09/2020
6356(85*10^112919+293)/9112920Robert Price12/2019
635729412^6899+6899^29412112907Hans Havermann02/2021
6358(191*10^112903-17)/3112905Robert Price11/2021
6359(2^375022+1210)/2112893Stefano Morozzi09/2020
636025992^22039+22039^25992112889Hans Havermann02/2021
63612^374993-2787163112885Enzo Doria11/2015
6362(697*10^112869+23)/9112871Robert Price04/2021
6363(19*10^112851+377)/9112852Alfred Reich11/2022
636430420^5111+5111^30420112813Hans Havermann02/2021
636513699^27268+27268^13699112800Norbert Schneider12/2020
6366123^53970+2112793Lelio R Paula06/2013
636712308*27^78796+23112790Eric Chen07/2023
636828942^7887+7887^28942112785Hans Havermann01/2021
63692^374640-4685112778Yves Minet05/2019
637012^104501-11112776Riley Fisher12/2023
637157290^93+93^57290112775Hans Havermann01/2021
6372115^54726-54726^115112774Norman Luhn09/2024
637313608^27277-27277^13608112758Norbert Schneider12/2022
6374(2^374556+682)/2112753Stefano Morozzi09/2020
6375p(22852)#/2+512112745Robert Price05/2017
6376(11*10^112742-131)/3112743Robert Price09/2018
63772^374441-21049112718Enzo Doria06/2013
63784*10^112706-93112707Robert Price07/2020
6379(2^374321+1)/3112682H.&R. Lifchitz12/2000
6380(2^374213+1766)/2112650Stefano Morozzi09/2020
6381(2^374094+2674)/2112614Stefano Morozzi09/2020
6382(13^101089-1)/12112607Paul Bourdelais03/2010
63833^236011-8828112606Enzo Doria05/2014
638431854^3427+3427^31854112602Hans Havermann02/2021
6385(85*10^112530-373)/9112531Robert Price05/2021
6386(2^373748+1090)/2112510Stefano Morozzi09/2020
6387(2^373727+1806)/2112503Stefano Morozzi01/2021
638827618^11821+11821^27618112479Hans Havermann01/2021
6389U(602921)/4823369112479Serge Batalov07/2024
639026343^18580+18580^26343112460Hans Havermann01/2021
639139^70666+2112435Lelio R Paula11/2013
6392(134*10^112400+7)/3112402Robert Price02/2020
6393(2^373365+326)/2112394Stefano Morozzi09/2020
6394(2^373350-7)/3112390Lelio R Paula03/2014
63952^373306-1840931112377Enzo Doria06/2015
63968*10^112371-37112372Robert Price03/2022
6397(2^373262+270)/2112363Stefano Morozzi09/2020
63986*10^112359-79112360Robert Price03/2022
639934409^1842+1842^34409112356Hans Havermann02/2021
6400(142*10^112352-7)/9112354Robert Price12/2019
640125580^24633+24633^25580112336Hans Havermann01/2021
64022^373117+1872107112320Enzo Doria05/2016
6403(2^373083+2226)/2112309Stefano Morozzi01/2021
6404(35*10^112308+37)/9112309Robert Price05/2022
640527963^10376+10376^27963112301Hans Havermann01/2021
64062^373040+2792761112297Enzo Doria03/2016
6407(156^51203-1)/155112293Anonymous06/2024
6408EPrime(112280)112280Eric W. Weisstein10/2010
64092^372950+7112270Lelio R Paula03/2013
64102^372945+1872167112268Enzo Doria05/2016
641136274^1243+1243^36274112249Hans Havermann02/2021
6412(55*10^112246+629)/9112247Robert Price01/2022
6413(2^372872+3798)/2112246Stefano Morozzi02/2021
641425513^25060+25060^25513112232Hans Havermann02/2021
6415(53*10^112229-611)/9112230Robert Price02/2022
6416(2^372754+3094)/2112210Stefano Morozzi09/2020
64176*10^112208+43112209Robert Price07/2020
6418(2^372728+3058)/2112203Stefano Morozzi09/2020
641932061^3158+3158^32061112195Hans Havermann02/2021
64202^372695+72113112193Enzo Doria04/2016
64212^372689-2563112191Yves Minet07/2014
64222^372638-1859441112176Enzo Doria03/2016
64233^235074-113056112159Enzo Doria07/2014
6424-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
6425(2^372514+1822)/2112138Stefano Morozzi02/2021
642629468^6387+6387^29468112135Hans Havermann02/2021
6427(2^372428+3742)/2112112Stefano Morozzi01/2021
642825375^25454-25454^25375112110Norbert Schneider01/2021
6429131^52949-130112108Norbert Schneider02/2019
6430(91*10^112098-1)/9112100Robert Price04/2015
6431(68*10^112087-149)/9112088Robert Price07/2022
64322^372314+212419112078Enzo Doria08/2023
64332^372310-85061112077Paul Bourdelais02/2012
6434(10^112067+53)/9112067Serge Batalov07/2015
6435(2^372237+2082)/2112055Stefano Morozzi09/2020
643675^59760+2112054Lelio R Paula08/2013
6437(2^372200+1710)/2112044Stefano Morozzi09/2020
6438(10^112048+7)/8747/373157112039Alfred Reich06/2021
6439(2^372181+2250)/2112038Stefano Morozzi01/2021
6440F(536233)/825798821/1102495049/5641839306317112036Serge Batalov07/2024
6441(2^372161+2574)/2112032Stefano Morozzi09/2020
64428*10^112018-49112019Robert Price08/2019
64442^372108+74221112016Enzo Doria04/2016
6443(2^372109+2046)/2112016Stefano Morozzi09/2020
64458*10^112011-73112012Robert Price01/2022
6446(184*10^112007-1)/3112009Robert Price02/2020
64475*10^112003+81112004Robert Price03/2019
6448215^48018+48018^215112000Norbert Schneider10/2018
644925549^24148+24148^25549111979Hans Havermann02/2021
64502^371970-459491111975Enzo Doria05/2015
645141^69427-40^69427111971Robert Price07/2012
6452(2^371782+358)/2111918Stefano Morozzi01/2021
645315*25^80056+446111915Eric Chen10/2023
6454(34*10^111902-547)/9111903Robert Price03/2021
6455(10^111902+71)/9111902Serge Batalov07/2015
6456(2^371625+1610)/2111870Stefano Morozzi09/2020
645729080^7027+7027^29080111865Hans Havermann01/2021
645831307^3730+3730^31307111820Hans Havermann02/2021
64592^371440-112865111815Enzo Doria06/2014
64602^371426-459161111811Enzo Doria05/2015
646125768^21771+21771^25768111779Hans Havermann02/2021
646228022^9747+9747^28022111777Hans Havermann02/2021
6463(94*10^111770+11)/3111772Robert Price04/2020
64642^371276-461267111766Enzo Doria07/2015
64656*10^111760+43111761Robert Price07/2020
646698079!4-1024111747Robert Price11/2019
6467(2^371186+3162)/2111738Stefano Morozzi09/2020
646810^(2*55862+1)-4*10^55862-1111725Robert Price07/2023
64692^371098-113261111712Enzo Doria07/2014
6470(7*10^111706-61)/9111706Erik Branger01/2011
64712^371044+1869391111696Enzo Doria05/2016
647226310^17581+17581^26310111688Hans Havermann01/2021
647388^57416+87111645Norbert Schneider11/2015
64742^370829-109693111631Enzo Doria04/2014
647515^94906-2111619Lelio R Paula11/2013
647625835^20904+20904^25835111614Hans Havermann02/2021
6477(2^370726+1198)/2111600Stefano Morozzi09/2020
647827758^10479+10479^27758111597Hans Havermann02/2021
64792^370695-4627111591Yves Minet05/2019
64807*10^111579-87111580Robert Price06/2020
64812^370643-37111575Yves Minet01/2012
6482(2^370655-5)/2439111575Lelio R Paula03/2014
64832^370610-3911111565Yves Minet04/2017
6484(154*10^111549+17)/9111551Robert Price06/2022
648526200^18097+18097^26200111550Hans Havermann01/2021
6486286^45405+45405^286111532Norbert Schneider04/2015
64874*5^159563-9111531Lelio R Paula11/2014
64885*10^111528-21111529Robert Price12/2021
6489(4^185225+23)/3111517Robert Price10/2018
64902^370393-2797093111500Enzo Doria03/2016
6491(21*2^370382-1)/629111495Lelio R Paula03/2014
6492(2^370371+554)/2111493Stefano Morozzi09/2020
64936^143273-5111489Paul Bourdelais01/2021
64942^370292-2791979111469Enzo Doria03/2016
6495(14*10^111443-11)/3111444Robert Price08/2022
64962^370177-461551111435Enzo Doria07/2015
6497(2^370169+1706)/2111432Stefano Morozzi09/2020
6498109^54683-108111413Norbert Schneider02/2017
6500(83*10^111406-173)/9111407Robert Price04/2021
6499959^37362-37362^959111407Henri Lifchitz10/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 07 2025 10:37 (Time in France)

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