PRP Records

Probable Primes Top 10000

(291910 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 ?
475134596^1949+1949^34596113815Hans Havermann02/2021
47522^378078+75113813Lelio R Paula03/2013
4753(28*10^113810+449)/9113811Robert Price11/2021
475426273^21448+21448^26273113799Hans Havermann02/2021
47552^377966+255255113780Paul Bourdelais10/2021
47562^377940+63113772Lelio R Paula03/2013
47572^377941-2785843113772Enzo Doria04/2016
4758(7*10^113757+11)/9113757Tyler Busby01/2023
47592^377810+1875109113733Enzo Doria09/2016
47602^377803-1838635113731Enzo Doria05/2015
47612^377799+52223113729Yves Minet08/2010
4762(2^377791+3258)/2113727Stefano Morozzi02/2021
476311^109190-270113710Enzo Doria12/2012
476428206^10739+10739^28206113698Hans Havermann01/2021
47657*10^113693+9113694Robert Price09/2015
476613899^27442+27442^13899113692Norbert Schneider12/2020
4767(82*10^113681+161)/9113682Robert Price10/2019
476826121^22478+22478^26121113673Hans Havermann01/2021
47694*10^113658+49113659Robert Price01/2019
4770(10^113656+7)/40231/6439001113645Alfred Reich06/2021
4771(2*10^113631+529)/9113631Robert Price01/2018
47722^377408-2798279113612Enzo Doria04/2016
477313706^27459+27459^13706113596Norbert Schneider12/2020
47745*10^113586+57113587Robert Price12/2018
4775(2^377242+2794)/2113561Stefano Morozzi02/2021
47762^377222+93679113556Yves Minet02/2011
4778262147#+316847113552Makoto Morimoto02/2016
477727172^15101+15101^27172113552Hans Havermann01/2021
4779(2^377131+2018)/2113528Stefano Morozzi09/2020
47802^377026-458903113497Enzo Doria04/2015
4781(2^377014+2202)/2113493Stefano Morozzi09/2020
478234791^1828+1828^34791113488Hans Havermann02/2021
4783(2^376967+258)/2113479Stefano Morozzi09/2020
4784(29*10^113468-17)/3113469Robert Price09/2019
478535^73477-34^73477113454Robert Price05/2012
4786(14*10^113451-89)/3113452Robert Price05/2020
47872^376790+27113426Lelio R Paula03/2013
47882^376786-112701113424Enzo Doria06/2014
47892^376731+21113408Lelio R Paula03/2013
47909*10^113394-73113395Robert Price01/2021
479129660^6651+6651^29660113387Hans Havermann01/2021
47932^376634+1871245113379Enzo Doria05/2016
4792(4^188318+17)/3113379Robert Price02/2017
4794E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
47952^376576-344369113361Enzo Doria07/2015
47962^376549-4543113353Yves Minet03/2019
4797(17*2^376526-1)/223113345Lelio R Paula03/2014
4798(27*2^376441-1)/811113319Lelio R Paula03/2014
4799(2^376350+3538)/2113293Stefano Morozzi09/2020
480027265^14272+14272^27265113273Hans Havermann02/2021
480132174^3315+3315^32174113269Hans Havermann02/2021
4802(2*10^113248+73)/3113248Robert Price09/2020
48032^376128-21237113226Enzo Doria06/2013
48045*10^113224-81113225Robert Price01/2019
480510^113220+51409113221Patrick De Geest02/2021
480710^113220-1000001113220Robert Price08/2020
480610^113220-61779113220Patrick De Geest02/2021
4808(2^376102+1578)/2113218Stefano Morozzi09/2020
4809(2^375996+3102)/2113186Stefano Morozzi09/2020
481037258^1091+1091^37258113184Hans Havermann02/2021
4811(94*10^113176+11)/3113178Robert Price04/2020
4812(46*10^113162+521)/9113163Robert Price02/2019
4813(2^375885+3614)/2113153Stefano Morozzi09/2020
4814(2^375873+2006)/2113149Stefano Morozzi09/2020
48153*10^113137+23113138Robert Price03/2022
4816(8*10^113135-269)/9113135Robert Price09/2021
4817(2^375726+694)/2113105Stefano Morozzi09/2020
481826050^21959+21959^26050113100Hans Havermann02/2021
48192^375638-1787171113079Enzo Doria03/2016
4820(2^375563+2178)/2113056Stefano Morozzi09/2020
48212^375537+4847113048Yves Minet02/2011
4822(17^91837+16^91837)/33113000Robert Price08/2013
48235*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
48242^375350-3221112992Yves Minet07/2011
4825(13*2^375306+1)/7112979Lelio R Paula03/2014
48262^375305+76757112979Enzo Doria05/2016
48272^375258+1874989112964Enzo Doria07/2016
4828(29^77237-1)/28112950Robert Price04/2012
482926620^17483+17483^26620112939Hans Havermann01/2021
48302^375154+74959112933Enzo Doria04/2016
4831(266*10^112930-17)/3112932Robert Price07/2020
4832(2^375134+778)/2112927Stefano Morozzi09/2020
4833(85*10^112919+293)/9112920Robert Price12/2019
483429412^6899+6899^29412112907Hans Havermann02/2021
4835(191*10^112903-17)/3112905Robert Price11/2021
4836(2^375022+1210)/2112893Stefano Morozzi09/2020
483725992^22039+22039^25992112889Hans Havermann02/2021
48382^374993-2787163112885Enzo Doria11/2015
4839(697*10^112869+23)/9112871Robert Price04/2021
4840(19*10^112851+377)/9112852Alfred Reich11/2022
484130420^5111+5111^30420112813Hans Havermann02/2021
484213699^27268+27268^13699112800Norbert Schneider12/2020
4843123^53970+2112793Lelio R Paula06/2013
484428942^7887+7887^28942112785Hans Havermann01/2021
48452^374640-4685112778Yves Minet05/2019
484657290^93+93^57290112775Hans Havermann01/2021
484713608^27277-27277^13608112758Norbert Schneider12/2022
4848(2^374556+682)/2112753Stefano Morozzi09/2020
4849p(22852)#/2+512112745Robert Price05/2017
4850(11*10^112742-131)/3112743Robert Price09/2018
48512^374441-21049112718Enzo Doria06/2013
48524*10^112706-93112707Robert Price07/2020
4853(2^374321+1)/3112682H.&R. Lifchitz12/2000
4854(2^374213+1766)/2112650Stefano Morozzi09/2020
4855(2^374094+2674)/2112614Stefano Morozzi09/2020
4856(13^101089-1)/12112607Paul Bourdelais03/2010
48573^236011-8828112606Enzo Doria05/2014
485831854^3427+3427^31854112602Hans Havermann02/2021
4859(85*10^112530-373)/9112531Robert Price05/2021
4860(2^373748+1090)/2112510Stefano Morozzi09/2020
4861(2^373727+1806)/2112503Stefano Morozzi01/2021
486227618^11821+11821^27618112479Hans Havermann01/2021
486326343^18580+18580^26343112460Hans Havermann01/2021
486439^70666+2112435Lelio R Paula11/2013
4865(134*10^112400+7)/3112402Robert Price02/2020
4866(2^373365+326)/2112394Stefano Morozzi09/2020
4867(2^373350-7)/3112390Lelio R Paula03/2014
48682^373306-1840931112377Enzo Doria06/2015
48698*10^112371-37112372Robert Price03/2022
4870(2^373262+270)/2112363Stefano Morozzi09/2020
48716*10^112359-79112360Robert Price03/2022
487234409^1842+1842^34409112356Hans Havermann02/2021
4873(142*10^112352-7)/9112354Robert Price12/2019
487425580^24633+24633^25580112336Hans Havermann01/2021
48752^373117+1872107112320Enzo Doria05/2016
4876(2^373083+2226)/2112309Stefano Morozzi01/2021
4877(35*10^112308+37)/9112309Robert Price05/2022
487827963^10376+10376^27963112301Hans Havermann01/2021
48792^373040+2792761112297Enzo Doria03/2016
4880EPrime(112280)112280Eric W. Weisstein10/2010
48812^372950+7112270Lelio R Paula03/2013
48822^372945+1872167112268Enzo Doria05/2016
488336274^1243+1243^36274112249Hans Havermann02/2021
4884(55*10^112246+629)/9112247Robert Price01/2022
4885(2^372872+3798)/2112246Stefano Morozzi02/2021
488625513^25060+25060^25513112232Hans Havermann02/2021
4887(53*10^112229-611)/9112230Robert Price02/2022
4888(2^372754+3094)/2112210Stefano Morozzi09/2020
48896*10^112208+43112209Robert Price07/2020
4890(2^372728+3058)/2112203Stefano Morozzi09/2020
489132061^3158+3158^32061112195Hans Havermann02/2021
48922^372695+72113112193Enzo Doria04/2016
48932^372689-2563112191Yves Minet07/2014
48942^372638-1859441112176Enzo Doria03/2016
48953^235074-113056112159Enzo Doria07/2014
4896-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
4897(2^372514+1822)/2112138Stefano Morozzi02/2021
489829468^6387+6387^29468112135Hans Havermann02/2021
4899(2^372428+3742)/2112112Stefano Morozzi01/2021
490025375^25454-25454^25375112110Norbert Schneider01/2021
4901131^52949-130112108Norbert Schneider02/2019
4902(91*10^112098-1)/9112100Robert Price04/2015
4903(68*10^112087-149)/9112088Robert Price07/2022
49042^372310-85061112077Paul Bourdelais02/2012
4905(10^112067+53)/9112067Serge Batalov07/2015
4906(2^372237+2082)/2112055Stefano Morozzi09/2020
490775^59760+2112054Lelio R Paula08/2013
4908(2^372200+1710)/2112044Stefano Morozzi09/2020
4909(10^112048+7)/8747/373157112039Alfred Reich06/2021
4910(2^372181+2250)/2112038Stefano Morozzi01/2021
4911(2^372161+2574)/2112032Stefano Morozzi09/2020
49128*10^112018-49112019Robert Price08/2019
49142^372108+74221112016Enzo Doria04/2016
4913(2^372109+2046)/2112016Stefano Morozzi09/2020
49158*10^112011-73112012Robert Price01/2022
4916(184*10^112007-1)/3112009Robert Price02/2020
49175*10^112003+81112004Robert Price03/2019
4918215^48018+48018^215112000Norbert Schneider10/2018
491925549^24148+24148^25549111979Hans Havermann02/2021
49202^371970-459491111975Enzo Doria05/2015
492141^69427-40^69427111971Robert Price07/2012
4922(2^371782+358)/2111918Stefano Morozzi01/2021
4923(34*10^111902-547)/9111903Robert Price03/2021
4924(10^111902+71)/9111902Serge Batalov07/2015
4925(2^371625+1610)/2111870Stefano Morozzi09/2020
492629080^7027+7027^29080111865Hans Havermann01/2021
492731307^3730+3730^31307111820Hans Havermann02/2021
49282^371440-112865111815Enzo Doria06/2014
49292^371426-459161111811Enzo Doria05/2015
493025768^21771+21771^25768111779Hans Havermann02/2021
493128022^9747+9747^28022111777Hans Havermann02/2021
4932(94*10^111770+11)/3111772Robert Price04/2020
49332^371276-461267111766Enzo Doria07/2015
49346*10^111760+43111761Robert Price07/2020
493598079!4-1024111747Robert Price11/2019
4936(2^371186+3162)/2111738Stefano Morozzi09/2020
49372^371098-113261111712Enzo Doria07/2014
4938(7*10^111706-61)/9111706Erik Branger01/2011
49392^371044+1869391111696Enzo Doria05/2016
494026310^17581+17581^26310111688Hans Havermann01/2021
494188^57416+87111645Norbert Schneider11/2015
49422^370829-109693111631Enzo Doria04/2014
494315^94906-2111619Lelio R Paula11/2013
494425835^20904+20904^25835111614Hans Havermann02/2021
4945(2^370726+1198)/2111600Stefano Morozzi09/2020
494627758^10479+10479^27758111597Hans Havermann02/2021
49472^370695-4627111591Yves Minet05/2019
49487*10^111579-87111580Robert Price06/2020
49502^370643-37111575Yves Minet01/2012
4949(2^370655-5)/2439111575Lelio R Paula03/2014
49512^370610-3911111565Yves Minet04/2017
4952(154*10^111549+17)/9111551Robert Price06/2022
495326200^18097+18097^26200111550Hans Havermann01/2021
4954286^45405+45405^286111532Norbert Schneider04/2015
49554*5^159563-9111531Lelio R Paula11/2014
49565*10^111528-21111529Robert Price12/2021
4957(4^185225+23)/3111517Robert Price10/2018
49582^370393-2797093111500Enzo Doria03/2016
4959(21*2^370382-1)/629111495Lelio R Paula03/2014
4960(2^370371+554)/2111493Stefano Morozzi09/2020
49616^143273-5111489Paul Bourdelais01/2021
49622^370292-2791979111469Enzo Doria03/2016
4963(14*10^111443-11)/3111444Robert Price08/2022
49642^370177-461551111435Enzo Doria07/2015
4965(2^370169+1706)/2111432Stefano Morozzi09/2020
4966109^54683-108111413Norbert Schneider02/2017
4967(83*10^111406-173)/9111407Robert Price04/2021
4968(2^370043+1010)/2111394Stefano Morozzi09/2020
496932961^2396+2396^32961111392Hans Havermann10/2020
4970numbpart(10^10+76282)111391Serge Batalov04/2015
4971(23*10^111380-29)/3111381Robert Price03/2022
49722^369974+733111374Lelio R Paula05/2013
4973121^53470+120111367Norbert Schneider10/2018
49742^369915-286267111356Enzo Doria07/2015
4975(62*10^111347-629)/9111348Robert Price07/2021
49762^369855-1615111338Lelio R Paula05/2017
49777*10^111325+3111326Robert Price08/2015
497851^65176+2111293Lelio R Paula08/2013
49792^369643-1865767111274Enzo Doria03/2016
49802^369603+885111262Lelio R Paula05/2017
498125555^22564+22564^25555111252Hans Havermann10/2020
4982L(532277)111240Renaud Lifchitz03/2004
4983105^55033-2111233Lelio R Paula10/2017
4984(35*10^111232-737)/9111233Robert Price07/2018
498526970^13307+13307^26970111227Hans Havermann10/2020
498625419^23716+23716^25419111210Hans Havermann10/2020
49879*10^111201-29111202Robert Price09/2019
49882^369392+29835111199Lelio R Paula05/2017
49893^233059+16111198Robert Price03/2020
49902^369354-3413111187Yves Minet12/2016
49912^369296-27111170Lelio R Paula02/2013
49922^369239-109837111153Enzo Doria05/2014
49932^369224-291839111148Enzo Doria07/2015
49942^369216+2798881111146Enzo Doria04/2016
499526842^13817+13817^26842111137Hans Havermann11/2020
4996(5*10^111119-191)/3111120Robert Price05/2021
4997(29*10^111112-23)/3111113Robert Price03/2022
499810^111111+163849111112Patrick De Geest03/2017
499910^111111-312911111111Patrick De Geest03/2017
50002^369092-216923111108Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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