PRP Records

Probable Primes Top 10000

(290751 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 ?
45016^146274-18893113824Enzo Doria03/2013
450234596^1949+1949^34596113815Hans Havermann02/2021
45032^378078+75113813Lelio R Paula03/2013
4504(28*10^113810+449)/9113811Robert Price11/2021
450526273^21448+21448^26273113799Hans Havermann02/2021
45062^377966+255255113780Paul Bourdelais10/2021
45072^377940+63113772Lelio R Paula03/2013
45082^377941-2785843113772Enzo Doria04/2016
45092^377810+1875109113733Enzo Doria09/2016
45102^377803-1838635113731Enzo Doria05/2015
45112^377799+52223113729Yves Minet08/2010
4512(2^377791+3258)/2113727Stefano Morozzi02/2021
451311^109190-270113710Enzo Doria12/2012
451428206^10739+10739^28206113698Hans Havermann01/2021
45157*10^113693+9113694Robert Price09/2015
451613899^27442+27442^13899113692Norbert Schneider12/2020
4517(82*10^113681+161)/9113682Robert Price10/2019
451826121^22478+22478^26121113673Hans Havermann01/2021
45194*10^113658+49113659Robert Price01/2019
4520(10^113656+7)/40231/6439001113645Alfred Reich06/2021
4521(2*10^113631+529)/9113631Robert Price01/2018
45222^377408-2798279113612Enzo Doria04/2016
452313706^27459+27459^13706113596Norbert Schneider12/2020
45245*10^113586+57113587Robert Price12/2018
4525(2^377242+2794)/2113561Stefano Morozzi02/2021
45262^377222+93679113556Yves Minet02/2011
4528262147#+316847113552Makoto Morimoto02/2016
452727172^15101+15101^27172113552Hans Havermann01/2021
4529(2^377131+2018)/2113528Stefano Morozzi09/2020
45302^377026-458903113497Enzo Doria04/2015
4531(2^377014+2202)/2113493Stefano Morozzi09/2020
453234791^1828+1828^34791113488Hans Havermann02/2021
4533(2^376967+258)/2113479Stefano Morozzi09/2020
4534(29*10^113468-17)/3113469Robert Price09/2019
453535^73477-34^73477113454Robert Price05/2012
4536(14*10^113451-89)/3113452Robert Price05/2020
45372^376790+27113426Lelio R Paula03/2013
45382^376786-112701113424Enzo Doria06/2014
45392^376731+21113408Lelio R Paula03/2013
45409*10^113394-73113395Robert Price01/2021
454129660^6651+6651^29660113387Hans Havermann01/2021
45432^376634+1871245113379Enzo Doria05/2016
4542(4^188318+17)/3113379Robert Price02/2017
4544E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
45452^376576-344369113361Enzo Doria07/2015
45462^376549-4543113353Yves Minet03/2019
4547(17*2^376526-1)/223113345Lelio R Paula03/2014
4548(27*2^376441-1)/811113319Lelio R Paula03/2014
4549(2^376350+3538)/2113293Stefano Morozzi09/2020
455027265^14272+14272^27265113273Hans Havermann02/2021
455132174^3315+3315^32174113269Hans Havermann02/2021
4552(2*10^113248+73)/3113248Robert Price09/2020
45532^376128-21237113226Enzo Doria06/2013
45545*10^113224-81113225Robert Price01/2019
455510^113220+51409113221Patrick De Geest02/2021
455710^113220-1000001113220Robert Price08/2020
455610^113220-61779113220Patrick De Geest02/2021
4558(2^376102+1578)/2113218Stefano Morozzi09/2020
4559(2^375996+3102)/2113186Stefano Morozzi09/2020
456037258^1091+1091^37258113184Hans Havermann02/2021
4561(94*10^113176+11)/3113178Robert Price04/2020
4562(46*10^113162+521)/9113163Robert Price02/2019
4563(2^375885+3614)/2113153Stefano Morozzi09/2020
4564(2^375873+2006)/2113149Stefano Morozzi09/2020
45653*10^113137+23113138Robert Price03/2022
4566(8*10^113135-269)/9113135Robert Price09/2021
4567(2^375726+694)/2113105Stefano Morozzi09/2020
456826050^21959+21959^26050113100Hans Havermann02/2021
45692^375638-1787171113079Enzo Doria03/2016
4570(2^375563+2178)/2113056Stefano Morozzi09/2020
45712^375537+4847113048Yves Minet02/2011
4572(17^91837+16^91837)/33113000Robert Price08/2013
45735*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
45742^375350-3221112992Yves Minet07/2011
4575(13*2^375306+1)/7112979Lelio R Paula03/2014
45762^375305+76757112979Enzo Doria05/2016
45772^375258+1874989112964Enzo Doria07/2016
4578(29^77237-1)/28112950Robert Price04/2012
457926620^17483+17483^26620112939Hans Havermann01/2021
45802^375154+74959112933Enzo Doria04/2016
4581(266*10^112930-17)/3112932Robert Price07/2020
4582(2^375134+778)/2112927Stefano Morozzi09/2020
4583(85*10^112919+293)/9112920Robert Price12/2019
458429412^6899+6899^29412112907Hans Havermann02/2021
4585(191*10^112903-17)/3112905Robert Price11/2021
4586(2^375022+1210)/2112893Stefano Morozzi09/2020
458725992^22039+22039^25992112889Hans Havermann02/2021
45882^374993-2787163112885Enzo Doria11/2015
4589(697*10^112869+23)/9112871Robert Price04/2021
459030420^5111+5111^30420112813Hans Havermann02/2021
459113699^27268+27268^13699112800Norbert Schneider12/2020
4592123^53970+2112793Lelio R Paula06/2013
459328942^7887+7887^28942112785Hans Havermann01/2021
45942^374640-4685112778Yves Minet05/2019
459557290^93+93^57290112775Hans Havermann01/2021
4596(2^374556+682)/2112753Stefano Morozzi09/2020
4597p(22852)#/2+512112745Robert Price05/2017
4598(11*10^112742-131)/3112743Robert Price09/2018
45992^374441-21049112718Enzo Doria06/2013
46004*10^112706-93112707Robert Price07/2020
4601(2^374321+1)/3112682H.&R. Lifchitz12/2000
4602(2^374213+1766)/2112650Stefano Morozzi09/2020
4603(2^374094+2674)/2112614Stefano Morozzi09/2020
4604(13^101089-1)/12112607Paul Bourdelais03/2010
46053^236011-8828112606Enzo Doria05/2014
460631854^3427+3427^31854112602Hans Havermann02/2021
4607(85*10^112530-373)/9112531Robert Price05/2021
4608(2^373748+1090)/2112510Stefano Morozzi09/2020
4609(2^373727+1806)/2112503Stefano Morozzi01/2021
461027618^11821+11821^27618112479Hans Havermann01/2021
461126343^18580+18580^26343112460Hans Havermann01/2021
461239^70666+2112435Lelio R Paula11/2013
4613(134*10^112400+7)/3112402Robert Price02/2020
4614(2^373365+326)/2112394Stefano Morozzi09/2020
4615(2^373350-7)/3112390Lelio R Paula03/2014
46162^373306-1840931112377Enzo Doria06/2015
46178*10^112371-37112372Robert Price03/2022
4618(2^373262+270)/2112363Stefano Morozzi09/2020
46196*10^112359-79112360Robert Price03/2022
462034409^1842+1842^34409112356Hans Havermann02/2021
4621(142*10^112352-7)/9112354Robert Price12/2019
462225580^24633+24633^25580112336Hans Havermann01/2021
46232^373117+1872107112320Enzo Doria05/2016
4624(2^373083+2226)/2112309Stefano Morozzi01/2021
4625(35*10^112308+37)/9112309Robert Price05/2022
462627963^10376+10376^27963112301Hans Havermann01/2021
46272^373040+2792761112297Enzo Doria03/2016
4628EPrime(112280)112280Eric W. Weisstein10/2010
46292^372950+7112270Lelio R Paula03/2013
46302^372945+1872167112268Enzo Doria05/2016
463136274^1243+1243^36274112249Hans Havermann02/2021
4632(55*10^112246+629)/9112247Robert Price01/2022
4633(2^372872+3798)/2112246Stefano Morozzi02/2021
463425513^25060+25060^25513112232Hans Havermann02/2021
4635(53*10^112229-611)/9112230Robert Price02/2022
4636(2^372754+3094)/2112210Stefano Morozzi09/2020
46376*10^112208+43112209Robert Price07/2020
4638(2^372728+3058)/2112203Stefano Morozzi09/2020
463932061^3158+3158^32061112195Hans Havermann02/2021
46402^372695+72113112193Enzo Doria04/2016
46412^372689-2563112191Yves Minet07/2014
46422^372638-1859441112176Enzo Doria03/2016
46433^235074-113056112159Enzo Doria07/2014
4644-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
4645(2^372514+1822)/2112138Stefano Morozzi02/2021
464629468^6387+6387^29468112135Hans Havermann02/2021
4647(2^372428+3742)/2112112Stefano Morozzi01/2021
464825375^25454-25454^25375112110Norbert Schneider01/2021
4649131^52949-130112108Norbert Schneider02/2019
4650(91*10^112098-1)/9112100Robert Price04/2015
46512^372310-85061112077Paul Bourdelais02/2012
4652(10^112067+53)/9112067Serge Batalov07/2015
4653(2^372237+2082)/2112055Stefano Morozzi09/2020
465475^59760+2112054Lelio R Paula08/2013
4655(2^372200+1710)/2112044Stefano Morozzi09/2020
4656(10^112048+7)/8747/373157112039Alfred Reich06/2021
4657(2^372181+2250)/2112038Stefano Morozzi01/2021
4658(2^372161+2574)/2112032Stefano Morozzi09/2020
46598*10^112018-49112019Robert Price08/2019
46612^372108+74221112016Enzo Doria04/2016
4660(2^372109+2046)/2112016Stefano Morozzi09/2020
46628*10^112011-73112012Robert Price01/2022
4663(184*10^112007-1)/3112009Robert Price02/2020
46645*10^112003+81112004Robert Price03/2019
4665215^48018+48018^215112000Norbert Schneider10/2018
466625549^24148+24148^25549111979Hans Havermann02/2021
46672^371970-459491111975Enzo Doria05/2015
466841^69427-40^69427111971Robert Price07/2012
4669(2^371782+358)/2111918Stefano Morozzi01/2021
4670(34*10^111902-547)/9111903Robert Price03/2021
4671(10^111902+71)/9111902Serge Batalov07/2015
4672(2^371625+1610)/2111870Stefano Morozzi09/2020
467329080^7027+7027^29080111865Hans Havermann01/2021
467431307^3730+3730^31307111820Hans Havermann02/2021
46752^371440-112865111815Enzo Doria06/2014
46762^371426-459161111811Enzo Doria05/2015
467725768^21771+21771^25768111779Hans Havermann02/2021
467828022^9747+9747^28022111777Hans Havermann02/2021
4679(94*10^111770+11)/3111772Robert Price04/2020
46802^371276-461267111766Enzo Doria07/2015
46816*10^111760+43111761Robert Price07/2020
468298079!4-1024111747Robert Price11/2019
4683(2^371186+3162)/2111738Stefano Morozzi09/2020
46842^371098-113261111712Enzo Doria07/2014
4685(7*10^111706-61)/9111706Erik Branger01/2011
46862^371044+1869391111696Enzo Doria05/2016
468726310^17581+17581^26310111688Hans Havermann01/2021
468888^57416+87111645Norbert Schneider11/2015
46892^370829-109693111631Enzo Doria04/2014
469015^94906-2111619Lelio R Paula11/2013
469125835^20904+20904^25835111614Hans Havermann02/2021
4692(2^370726+1198)/2111600Stefano Morozzi09/2020
469327758^10479+10479^27758111597Hans Havermann02/2021
46942^370695-4627111591Yves Minet05/2019
46957*10^111579-87111580Robert Price06/2020
46962^370643-37111575Yves Minet01/2012
4697(2^370655-5)/2439111575Lelio R Paula03/2014
46982^370610-3911111565Yves Minet04/2017
4699(154*10^111549+17)/9111551Robert Price06/2022
470026200^18097+18097^26200111550Hans Havermann01/2021
4701286^45405+45405^286111532Norbert Schneider04/2015
47024*5^159563-9111531Lelio R Paula11/2014
47035*10^111528-21111529Robert Price12/2021
4704(4^185225+23)/3111517Robert Price10/2018
47052^370393-2797093111500Enzo Doria03/2016
4706(21*2^370382-1)/629111495Lelio R Paula03/2014
4707(2^370371+554)/2111493Stefano Morozzi09/2020
47086^143273-5111489Paul Bourdelais01/2021
47092^370292-2791979111469Enzo Doria03/2016
47102^370177-461551111435Enzo Doria07/2015
4711(2^370169+1706)/2111432Stefano Morozzi09/2020
4712109^54683-108111413Norbert Schneider02/2017
4713(83*10^111406-173)/9111407Robert Price04/2021
4714(2^370043+1010)/2111394Stefano Morozzi09/2020
471532961^2396+2396^32961111392Hans Havermann10/2020
4716numbpart(10^10+76282)111391Serge Batalov04/2015
4717(23*10^111380-29)/3111381Robert Price03/2022
47182^369974+733111374Lelio R Paula05/2013
4719121^53470+120111367Norbert Schneider10/2018
47202^369915-286267111356Enzo Doria07/2015
4721(62*10^111347-629)/9111348Robert Price07/2021
47222^369855-1615111338Lelio R Paula05/2017
47237*10^111325+3111326Robert Price08/2015
472451^65176+2111293Lelio R Paula08/2013
47252^369643-1865767111274Enzo Doria03/2016
47262^369603+885111262Lelio R Paula05/2017
472725555^22564+22564^25555111252Hans Havermann10/2020
4728L(532277)111240Renaud Lifchitz03/2004
4729105^55033-2111233Lelio R Paula10/2017
4730(35*10^111232-737)/9111233Robert Price07/2018
473126970^13307+13307^26970111227Hans Havermann10/2020
473225419^23716+23716^25419111210Hans Havermann10/2020
47339*10^111201-29111202Robert Price09/2019
47342^369392+29835111199Lelio R Paula05/2017
47353^233059+16111198Robert Price03/2020
47362^369354-3413111187Yves Minet12/2016
47372^369296-27111170Lelio R Paula02/2013
47382^369239-109837111153Enzo Doria05/2014
47392^369224-291839111148Enzo Doria07/2015
47402^369216+2798881111146Enzo Doria04/2016
474126842^13817+13817^26842111137Hans Havermann11/2020
4742(5*10^111119-191)/3111120Robert Price05/2021
4743(29*10^111112-23)/3111113Robert Price03/2022
474410^111111+163849111112Patrick De Geest03/2017
474510^111111-312911111111Patrick De Geest03/2017
47462^369092-216923111108Enzo Doria05/2014
47472^369081-55111105Lelio R Paula02/2013
4748(2^369047+3618)/2111094Stefano Morozzi09/2020
474988^57124-87111077Norbert Schneider11/2015
47502^368980+753111075Lelio R Paula05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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