PRP Records

Probable Primes Top 10000

(280932 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 ?
3751(2^377131+2018)/2113528Stefano Morozzi09/2020
37522^377026-458903113497Enzo Doria04/2015
3753(2^377014+2202)/2113493Stefano Morozzi09/2020
375434791^1828+1828^34791113488Hans Havermann02/2021
3755(2^376967+258)/2113479Stefano Morozzi09/2020
3756(29*10^113468-17)/3113469Robert Price09/2019
375735^73477-34^73477113454Robert Price05/2012
3758(14*10^113451-89)/3113452Robert Price05/2020
37592^376790+27113426Lelio R Paula03/2013
37602^376786-112701113424Enzo Doria06/2014
37612^376731+21113408Lelio R Paula03/2013
37629*10^113394-73113395Robert Price01/2021
376329660^6651+6651^29660113387Hans Havermann01/2021
37652^376634+1871245113379Enzo Doria05/2016
3764(4^188318+17)/3113379Robert Price02/2017
3766E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
37672^376576-344369113361Enzo Doria07/2015
37682^376549-4543113353Yves Minet03/2019
3769(17*2^376526-1)/223113345Lelio R Paula03/2014
3770(27*2^376441-1)/811113319Lelio R Paula03/2014
3771(2^376350+3538)/2113293Stefano Morozzi09/2020
377227265^14272+14272^27265113273Hans Havermann02/2021
377332174^3315+3315^32174113269Hans Havermann02/2021
3774(2*10^113248+73)/3113248Robert Price09/2020
37752^376128-21237113226Enzo Doria06/2013
37765*10^113224-81113225Robert Price01/2019
377710^113220+51409113221Patrick De Geest02/2021
377910^113220-1000001113220Robert Price08/2020
377810^113220-61779113220Patrick De Geest02/2021
3780(2^376102+1578)/2113218Stefano Morozzi09/2020
3781(2^375996+3102)/2113186Stefano Morozzi09/2020
378237258^1091+1091^37258113184Hans Havermann02/2021
3783(94*10^113176+11)/3113178Robert Price04/2020
3784(46*10^113162+521)/9113163Robert Price02/2019
3785(2^375885+3614)/2113153Stefano Morozzi09/2020
3786(2^375873+2006)/2113149Stefano Morozzi09/2020
3787(2^375726+694)/2113105Stefano Morozzi09/2020
378826050^21959+21959^26050113100Hans Havermann02/2021
37892^375638-1787171113079Enzo Doria03/2016
3790(2^375563+2178)/2113056Stefano Morozzi09/2020
37912^375537+4847113048Yves Minet02/2011
3792(17^91837+16^91837)/33113000Robert Price08/2013
37935*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
37942^375350-3221112992Yves Minet07/2011
3795(13*2^375306+1)/7112979Lelio R Paula03/2014
37962^375305+76757112979Enzo Doria05/2016
37972^375258+1874989112964Enzo Doria07/2016
3798(29^77237-1)/28112950Robert Price04/2012
379926620^17483+17483^26620112939Hans Havermann01/2021
38002^375154+74959112933Enzo Doria04/2016
3801(266*10^112930-17)/3112932Robert Price07/2020
3802(2^375134+778)/2112927Stefano Morozzi09/2020
3803(85*10^112919+293)/9112920Robert Price12/2019
380429412^6899+6899^29412112907Hans Havermann02/2021
3805(2^375022+1210)/2112893Stefano Morozzi09/2020
380625992^22039+22039^25992112889Hans Havermann02/2021
38072^374993-2787163112885Enzo Doria11/2015
380830420^5111+5111^30420112813Hans Havermann02/2021
380913699^27268+27268^13699112800Norbert Schneider12/2020
3810123^53970+2112793Lelio R Paula06/2013
381128942^7887+7887^28942112785Hans Havermann01/2021
38122^374640-4685112778Yves Minet05/2019
381357290^93+93^57290112775Hans Havermann01/2021
3814(2^374556+682)/2112753Stefano Morozzi09/2020
3815p(22852)#/2+512112745Robert Price05/2017
3816(11*10^112742-131)/3112743Robert Price09/2018
38172^374441-21049112718Enzo Doria06/2013
38184*10^112706-93112707Robert Price07/2020
3819(2^374321+1)/3112682H.&R. Lifchitz12/2000
3820(2^374213+1766)/2112650Stefano Morozzi09/2020
3821(2^374094+2674)/2112614Stefano Morozzi09/2020
3822(13^101089-1)/12112607Paul Bourdelais03/2010
38233^236011-8828112606Enzo Doria05/2014
382431854^3427+3427^31854112602Hans Havermann02/2021
3825(2^373748+1090)/2112510Stefano Morozzi09/2020
3826(2^373727+1806)/2112503Stefano Morozzi01/2021
382727618^11821+11821^27618112479Hans Havermann01/2021
382826343^18580+18580^26343112460Hans Havermann01/2021
382939^70666+2112435Lelio R Paula11/2013
3830(134*10^112400+7)/3112402Robert Price02/2020
3831(2^373365+326)/2112394Stefano Morozzi09/2020
3832(2^373350-7)/3112390Lelio R Paula03/2014
38332^373306-1840931112377Enzo Doria06/2015
3834(2^373262+270)/2112363Stefano Morozzi09/2020
383534409^1842+1842^34409112356Hans Havermann02/2021
3836(142*10^112352-7)/9112354Robert Price12/2019
383725580^24633+24633^25580112336Hans Havermann01/2021
38382^373117+1872107112320Enzo Doria05/2016
3839(2^373083+2226)/2112309Stefano Morozzi01/2021
384027963^10376+10376^27963112301Hans Havermann01/2021
38412^373040+2792761112297Enzo Doria03/2016
3842EPrime(112280)112280Eric W. Weisstein10/2010
38432^372950+7112270Lelio R Paula03/2013
38442^372945+1872167112268Enzo Doria05/2016
384536274^1243+1243^36274112249Hans Havermann02/2021
3846(2^372872+3798)/2112246Stefano Morozzi02/2021
384725513^25060+25060^25513112232Hans Havermann02/2021
3848(2^372754+3094)/2112210Stefano Morozzi09/2020
38496*10^112208+43112209Robert Price07/2020
3850(2^372728+3058)/2112203Stefano Morozzi09/2020
385132061^3158+3158^32061112195Hans Havermann02/2021
38522^372695+72113112193Enzo Doria04/2016
38532^372689-2563112191Yves Minet07/2014
38542^372638-1859441112176Enzo Doria03/2016
38553^235074-113056112159Enzo Doria07/2014
3856-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
3857(2^372514+1822)/2112138Stefano Morozzi02/2021
385829468^6387+6387^29468112135Hans Havermann02/2021
3859(2^372428+3742)/2112112Stefano Morozzi01/2021
386025375^25454-25454^25375112110Norbert Schneider01/2021
3861131^52949-130112108Norbert Schneider02/2019
3862(91*10^112098-1)/9112100Robert Price04/2015
38632^372310-85061112077Paul Bourdelais02/2012
3864(10^112067+53)/9112067Serge Batalov07/2015
3865(2^372237+2082)/2112055Stefano Morozzi09/2020
386675^59760+2112054Lelio R Paula08/2013
3867(2^372200+1710)/2112044Stefano Morozzi09/2020
3868(2^372181+2250)/2112038Stefano Morozzi01/2021
3869(2^372161+2574)/2112032Stefano Morozzi09/2020
38708*10^112018-49112019Robert Price08/2019
38722^372108+74221112016Enzo Doria04/2016
3871(2^372109+2046)/2112016Stefano Morozzi09/2020
3873(184*10^112007-1)/3112009Robert Price02/2020
38745*10^112003+81112004Robert Price03/2019
3875215^48018+48018^215112000Norbert Schneider10/2018
387625549^24148+24148^25549111979Hans Havermann02/2021
38772^371970-459491111975Enzo Doria05/2015
387841^69427-40^69427111971Robert Price07/2012
3879(2^371782+358)/2111918Stefano Morozzi01/2021
3880(34*10^111902-547)/9111903Robert Price03/2021
3881(10^111902+71)/9111902Serge Batalov07/2015
3882(2^371625+1610)/2111870Stefano Morozzi09/2020
388329080^7027+7027^29080111865Hans Havermann01/2021
388431307^3730+3730^31307111820Hans Havermann02/2021
38852^371440-112865111815Enzo Doria06/2014
38862^371426-459161111811Enzo Doria05/2015
388725768^21771+21771^25768111779Hans Havermann02/2021
388828022^9747+9747^28022111777Hans Havermann02/2021
3889(94*10^111770+11)/3111772Robert Price04/2020
38902^371276-461267111766Enzo Doria07/2015
38916*10^111760+43111761Robert Price07/2020
389298079!4-1024111747Robert Price11/2019
3893(2^371186+3162)/2111738Stefano Morozzi09/2020
38942^371098-113261111712Enzo Doria07/2014
3895(7*10^111706-61)/9111706Erik Branger01/2011
38962^371044+1869391111696Enzo Doria05/2016
389726310^17581+17581^26310111688Hans Havermann01/2021
389888^57416+87111645Norbert Schneider11/2015
38992^370829-109693111631Enzo Doria04/2014
390015^94906-2111619Lelio R Paula11/2013
390125835^20904+20904^25835111614Hans Havermann02/2021
3902(2^370726+1198)/2111600Stefano Morozzi09/2020
390327758^10479+10479^27758111597Hans Havermann02/2021
39042^370695-4627111591Yves Minet05/2019
39057*10^111579-87111580Robert Price06/2020
39072^370643-37111575Yves Minet01/2012
3906(2^370655-5)/2439111575Lelio R Paula03/2014
39082^370610-3911111565Yves Minet04/2017
390926200^18097+18097^26200111550Hans Havermann01/2021
3910286^45405+45405^286111532Norbert Schneider04/2015
39114*5^159563-9111531Lelio R Paula11/2014
3912(4^185225+23)/3111517Robert Price10/2018
39132^370393-2797093111500Enzo Doria03/2016
3914(21*2^370382-1)/629111495Lelio R Paula03/2014
3915(2^370371+554)/2111493Stefano Morozzi09/2020
39166^143273-5111489Paul Bourdelais01/2021
39172^370292-2791979111469Enzo Doria03/2016
39182^370177-461551111435Enzo Doria07/2015
3919(2^370169+1706)/2111432Stefano Morozzi09/2020
3920109^54683-108111413Norbert Schneider02/2017
3921(2^370043+1010)/2111394Stefano Morozzi09/2020
392232961^2396+2396^32961111392Hans Havermann10/2020
3923numbpart(10^10+76282)111391Serge Batalov04/2015
39242^369974+733111374Lelio R Paula05/2013
3925121^53470+120111367Norbert Schneider10/2018
39262^369915-286267111356Enzo Doria07/2015
39272^369855-1615111338Lelio R Paula05/2017
39287*10^111325+3111326Robert Price08/2015
392951^65176+2111293Lelio R Paula08/2013
39302^369643-1865767111274Enzo Doria03/2016
39312^369603+885111262Lelio R Paula05/2017
393225555^22564+22564^25555111252Hans Havermann10/2020
3933L(532277)111240Renaud Lifchitz03/2004
3935105^55033-2111233Lelio R Paula10/2017
3934(35*10^111232-737)/9111233Robert Price07/2018
393626970^13307+13307^26970111227Hans Havermann10/2020
393725419^23716+23716^25419111210Hans Havermann10/2020
39389*10^111201-29111202Robert Price09/2019
39392^369392+29835111199Lelio R Paula05/2017
39403^233059+16111198Robert Price03/2020
39412^369354-3413111187Yves Minet12/2016
39422^369296-27111170Lelio R Paula02/2013
39432^369239-109837111153Enzo Doria05/2014
39442^369224-291839111148Enzo Doria07/2015
39452^369216+2798881111146Enzo Doria04/2016
394626842^13817+13817^26842111137Hans Havermann11/2020
394710^111111+163849111112Patrick De Geest03/2017
394810^111111-312911111111Patrick De Geest03/2017
39492^369092-216923111108Enzo Doria05/2014
39502^369081-55111105Lelio R Paula02/2013
3951(2^369047+3618)/2111094Stefano Morozzi09/2020
395288^57124-87111077Norbert Schneider11/2015
39532^368980+753111075Lelio R Paula05/2013
39542^368946-3623111064Yves Minet03/2017
39552^368929+29835111059Lelio R Paula05/2017
39564^184463-3^184463111058Jean-Louis Charton12/2004
3957111^54298+110111057Norbert Schneider04/2017
3958(4*10^111032-7)/3111033Ray Chandler04/2011
395935799^1262+1262^35799111015Hans Havermann10/2020
3960(298*10^111004+11)/3111006Robert Price11/2020
396127648^10349+10349^27648111004Hans Havermann11/2020
396228899^6932+6932^28899110997Hans Havermann11/2020
39632^368641-460303110972Enzo Doria06/2015
39642^368619-109087110966Enzo Doria04/2014
3965(74*10^110961+313)/9110962Robert Price06/2019
396625258^24711+24711^25258110956Hans Havermann11/2020
3967(2^368539+1290)/2110941Stefano Morozzi01/2021
39683*2^368489+7110927Lelio R Paula09/2014
3969(14*10^110922+61)/3110923Robert Price12/2018
397097411!4-2110913Robert Price07/2017
3971(9179*2^368330-1)/35110881Lelio R Paula05/2015
397225830^19619+19619^25830110880Hans Havermann10/2020
3973(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
397426022^18191+18191^26022110850Hans Havermann10/2020
3975(2^368211+2250)/2110843Stefano Morozzi01/2021
39762^368050-64875110795Lelio R Paula05/2017
39772^368048+25110794Lelio R Paula02/2013
3978(2^368017+2262)/2110784Stefano Morozzi02/2021
397969^60239-2110771Lelio R Paula10/2013
3980(23*2^367952+1)/15717110762Lelio R Paula03/2014
39812^367924-69110757Lelio R Paula02/2013
3982(2^367779+3750)/2110713Stefano Morozzi01/2021
39832^367709-109723110692Enzo Doria04/2014
3984(3*2^367644-1)/107110671Lelio R Paula03/2014
3985(2^367626+3514)/2110667Stefano Morozzi09/2020
3986(23*2^367398+1)/57963110595Lelio R Paula03/2014
3987140^51515-139110558Norbert Schneider04/2019
39882^367215+1879223110543Enzo Doria09/2016
398925782^19375+19375^25782110534Hans Havermann10/2020
399026117^17058+17058^26117110526Hans Havermann10/2020
39912^367141+41110521Lelio R Paula02/2013
39922^367126+29835110516Lelio R Paula05/2017
3993(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
3994(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
3995(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
3996(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
3997(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
3998(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
3999(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
4000(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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