PRP Records

Probable Primes Top 10000

(277054 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 ?
3251(2^383544+5)/3115458Lelio R Paula03/2014
325289^59221-88^59221115445Robert Price06/2015
32532^383347+1869413115399Enzo Doria05/2016
3254(103*10^115366+17)/3115368Robert Price08/2020
3255(2^383232+750)/2115365Stefano Morozzi09/2020
3256(2^383130-7)/131793115329Lelio R Paula03/2014
3257(12^106859+1)/13115320Paul Bourdelais02/2010
32582^383039+1869509115307Enzo Doria05/2016
3259(13*2^382968+1)/7115286Lelio R Paula04/2014
3260(2^382945+2046)/2115278Stefano Morozzi09/2020
3261(2^382789+3182)/2115231Stefano Morozzi09/2020
32626*10^115211+79115212Robert Price09/2020
3263(2^382722+3598)/2115211Stefano Morozzi09/2020
3264(2^382699+2090)/2115204Stefano Morozzi09/2020
32652^382633+73697115185Enzo Doria04/2016
32662^382509-113593115147Enzo Doria08/2014
32672^382502-2791721115145Enzo Doria03/2016
3268(2^382495+1274)/2115143Stefano Morozzi01/2021
32699^120590-120590115073Robert Price03/2014
32702^382198+9115054Lelio R Paula03/2013
3271(89*10^115030-179)/9115031Robert Price12/2019
32722^381883-59197114959Enzo Doria10/2015
3273(2^381820+1626)/2114939Stefano Morozzi09/2020
32752^381806-4481114936Yves Minet07/2011
32742^381808-1851507114936Enzo Doria08/2015
3276(2^381792+2502)/2114931Stefano Morozzi09/2020
32772^381774-112373114926Enzo Doria06/2014
32782^381555-109051114860Enzo Doria04/2014
32792^381546-113501114857Enzo Doria08/2014
3280(7*10^114845-19)/3114846Robert Price10/2020
3281(2^381436+1182)/2114824Stefano Morozzi09/2020
32823^240644+16114817Robert Price04/2020
32832^381360-110429114801Enzo Doria05/2014
3284(17*10^114795+79)/3114796Robert Price04/2019
3285(66^63079+1)/67114774Paul Bourdelais09/2017
32862^381252-115079114769Enzo Doria06/2015
3287(2^381251+3186)/2114768Stefano Morozzi09/2020
32882^381209-29323114756Enzo Doria07/2015
3289569^41651-568^41651114754Jean-Louis Charton11/2009
32902^381201+1873205114753Enzo Doria06/2016
3291(85*10^114737+293)/9114738Robert Price12/2019
3292(265*10^114736+17)/3114738Robert Price03/2020
3293(2^381062+2170)/2114711Stefano Morozzi09/2020
32942^380974-112991114685Enzo Doria07/2014
329588^58949-87114626Norbert Schneider11/2015
3296(2^380773+662)/2114624Stefano Morozzi09/2020
32972^380700+91114603Lelio R Paula03/2013
3298(2^380632+2578)/2114582Stefano Morozzi09/2020
32997*10^114577+27114578Robert Price11/2020
330110^114575+3^114576114576Mike Oakes09/2010
330010^114575+66561114576Patrick De Geest02/2017
330210^114575-581081114575Patrick De Geest02/2017
33032^380587-115315114569Enzo Doria06/2015
33042^380513-216925114546Enzo Doria05/2014
33052^380451-1840087114528Enzo Doria06/2015
3306(2^380426+1510)/2114520Stefano Morozzi09/2020
3307(15*2^380388-1)/539114507Lelio R Paula04/2014
33082^380279-461347114476Enzo Doria07/2015
33092^380021+1871147114398Enzo Doria05/2016
33102^380005+1869707114393Enzo Doria05/2016
33112^379958-113297114379Enzo Doria07/2014
3312(2^379897+1274)/2114361Stefano Morozzi01/2021
33132^379881-109105114356Enzo Doria04/2014
3314(21*2^379857-1)/13114349Lelio R Paula03/2014
3315(4*10^114340+83)/3114341Robert Price02/2018
3316(26*10^114317-77)/3114318Robert Price11/2019
3317(4*10^114296+149)/9114296Robert Price04/2018
331888^58773-87114284Norbert Schneider11/2015
33192^379529-2790283114250Enzo Doria03/2016
33202^379522+1869115114248Enzo Doria05/2016
3321(145*10^114226-1)/9114228Serge Batalov12/2014
33222^379317-115033114186Enzo Doria06/2015
3323(17*2^379246-1)/17407114162Lelio R Paula03/2014
3324(2^379192+226)/2114148Stefano Morozzi09/2020
33256*10^114091+23114092Robert Price09/2020
3326(4*10^114076+143)/3114077Robert Price03/2018
3327(2^378820+3226)/2114036Stefano Morozzi01/2021
3328(2^378754+2058)/2114017Stefano Morozzi09/2020
3329(46*10^113969+683)/9113970Robert Price03/2019
333078*10^113954-7113956Robert Price10/2020
33312*10^113941+9113942Dmitry Domanov11/2010
3333(2^378478+1642)/2113933Stefano Morozzi09/2020
333210^113933-8000000001113933Robert Price11/2020
33344*10^113905+91113906Robert Price08/2018
333510^113894-10000001113894Robert Price09/2020
33364*10^113874-21113875Robert Price09/2018
33372^378272-16565113872Enzo Doria04/2013
33382^378217-109075113855Enzo Doria04/2014
33392^378198+67113849Lelio R Paula03/2013
33402^378173-3249113842Yves Minet12/2014
3341(2^378155-5)/6597113833Lelio R Paula03/2014
334292941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
33432^378128-262977113828Enzo Doria05/2014
33442^378123-113215113827Enzo Doria07/2014
33456^146274-18893113824Enzo Doria03/2013
33462^378078+75113813Lelio R Paula03/2013
33472^377940+63113772Lelio R Paula03/2013
33482^377941-2785843113772Enzo Doria04/2016
33492^377810+1875109113733Enzo Doria09/2016
33502^377803-1838635113731Enzo Doria05/2015
33512^377799+52223113729Yves Minet08/2010
335211^109190-270113710Enzo Doria12/2012
33537*10^113693+9113694Robert Price09/2015
335413899^27442+27442^13899113692Norbert Schneider12/2020
3355(82*10^113681+161)/9113682Robert Price10/2019
335626121^22478+22478^26121113673Hans Havermann01/2021
33574*10^113658+49113659Robert Price01/2019
3358(2*10^113631+529)/9113631Robert Price01/2018
33592^377408-2798279113612Enzo Doria04/2016
336013706^27459+27459^13706113596Norbert Schneider12/2020
33615*10^113586+57113587Robert Price12/2018
33622^377222+93679113556Yves Minet02/2011
3363262147#+316847113552Makoto Morimoto02/2016
3364(2^377131+2018)/2113528Stefano Morozzi09/2020
33652^377026-458903113497Enzo Doria04/2015
3366(2^377014+2202)/2113493Stefano Morozzi09/2020
3367(2^376967+258)/2113479Stefano Morozzi09/2020
3368(29*10^113468-17)/3113469Robert Price09/2019
336935^73477-34^73477113454Robert Price05/2012
3370(14*10^113451-89)/3113452Robert Price05/2020
33712^376790+27113426Lelio R Paula03/2013
33722^376786-112701113424Enzo Doria06/2014
33732^376731+21113408Lelio R Paula03/2013
33749*10^113394-73113395Robert Price01/2021
33762^376634+1871245113379Enzo Doria05/2016
3375(4^188318+17)/3113379Robert Price02/2017
3377E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
33782^376576-344369113361Enzo Doria07/2015
33792^376549-4543113353Yves Minet03/2019
3380(17*2^376526-1)/223113345Lelio R Paula03/2014
3381(27*2^376441-1)/811113319Lelio R Paula03/2014
3382(2^376350+3538)/2113293Stefano Morozzi09/2020
3383(2*10^113248+73)/3113248Robert Price09/2020
33842^376128-21237113226Enzo Doria06/2013
33855*10^113224-81113225Robert Price01/2019
338610^113220-1000001113220Robert Price08/2020
3387(2^376102+1578)/2113218Stefano Morozzi09/2020
3388(2^375996+3102)/2113186Stefano Morozzi09/2020
3389(94*10^113176+11)/3113178Robert Price04/2020
3390(46*10^113162+521)/9113163Robert Price02/2019
3391(2^375885+3614)/2113153Stefano Morozzi09/2020
3392(2^375873+2006)/2113149Stefano Morozzi09/2020
3393(2^375726+694)/2113105Stefano Morozzi09/2020
33942^375638-1787171113079Enzo Doria03/2016
3395(2^375563+2178)/2113056Stefano Morozzi09/2020
33962^375537+4847113048Yves Minet02/2011
3397(17^91837+16^91837)/33113000Robert Price08/2013
33985*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
33992^375350-3221112992Yves Minet07/2011
3400(13*2^375306+1)/7112979Lelio R Paula03/2014
34012^375305+76757112979Enzo Doria05/2016
34022^375258+1874989112964Enzo Doria07/2016
3403(29^77237-1)/28112950Robert Price04/2012
34042^375154+74959112933Enzo Doria04/2016
3405(266*10^112930-17)/3112932Robert Price07/2020
3406(2^375134+778)/2112927Stefano Morozzi09/2020
3407(85*10^112919+293)/9112920Robert Price12/2019
3408(2^375022+1210)/2112893Stefano Morozzi09/2020
34092^374993-2787163112885Enzo Doria11/2015
341013699^27268+27268^13699112800Norbert Schneider12/2020
3411123^53970+2112793Lelio R Paula06/2013
34122^374640-4685112778Yves Minet05/2019
3413(2^374556+682)/2112753Stefano Morozzi09/2020
3414p(22852)#/2+512112745Robert Price05/2017
3415(11*10^112742-131)/3112743Robert Price09/2018
34162^374441-21049112718Enzo Doria06/2013
34174*10^112706-93112707Robert Price07/2020
3418(2^374321+1)/3112682H.&R. Lifchitz12/2000
3419(2^374213+1766)/2112650Stefano Morozzi09/2020
3420(2^374094+2674)/2112614Stefano Morozzi09/2020
3421(13^101089-1)/12112607Paul Bourdelais03/2010
34223^236011-8828112606Enzo Doria05/2014
3423(2^373748+1090)/2112510Stefano Morozzi09/2020
3424(2^373727+1806)/2112503Stefano Morozzi01/2021
342526343^18580+18580^26343112460Hans Havermann01/2021
342639^70666+2112435Lelio R Paula11/2013
3427(134*10^112400+7)/3112402Robert Price02/2020
3428(2^373365+326)/2112394Stefano Morozzi09/2020
3429(2^373350-7)/3112390Lelio R Paula03/2014
34302^373306-1840931112377Enzo Doria06/2015
3431(2^373262+270)/2112363Stefano Morozzi09/2020
3432(142*10^112352-7)/9112354Robert Price12/2019
34332^373117+1872107112320Enzo Doria05/2016
3434(2^373083+2226)/2112309Stefano Morozzi01/2021
343527963^10376+10376^27963112301Hans Havermann01/2021
34362^373040+2792761112297Enzo Doria03/2016
3437EPrime(112280)112280Eric W. Weisstein10/2010
34382^372950+7112270Lelio R Paula03/2013
34392^372945+1872167112268Enzo Doria05/2016
3440(2^372754+3094)/2112210Stefano Morozzi09/2020
34416*10^112208+43112209Robert Price07/2020
3442(2^372728+3058)/2112203Stefano Morozzi09/2020
34432^372695+72113112193Enzo Doria04/2016
34442^372689-2563112191Yves Minet07/2014
34452^372638-1859441112176Enzo Doria03/2016
34463^235074-113056112159Enzo Doria07/2014
3447-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
3448(2^372428+3742)/2112112Stefano Morozzi01/2021
3449131^52949-130112108Norbert Schneider02/2019
3450(91*10^112098-1)/9112100Robert Price04/2015
34512^372310-85061112077Paul Bourdelais02/2012
3452(10^112067+53)/9112067Serge Batalov07/2015
3453(2^372237+2082)/2112055Stefano Morozzi09/2020
345475^59760+2112054Lelio R Paula08/2013
3455(2^372200+1710)/2112044Stefano Morozzi09/2020
3456(2^372181+2250)/2112038Stefano Morozzi01/2021
3457(2^372161+2574)/2112032Stefano Morozzi09/2020
34588*10^112018-49112019Robert Price08/2019
34602^372108+74221112016Enzo Doria04/2016
3459(2^372109+2046)/2112016Stefano Morozzi09/2020
3461(184*10^112007-1)/3112009Robert Price02/2020
34625*10^112003+81112004Robert Price03/2019
3463215^48018+48018^215112000Norbert Schneider10/2018
34642^371970-459491111975Enzo Doria05/2015
346541^69427-40^69427111971Robert Price07/2012
3466(2^371782+358)/2111918Stefano Morozzi01/2021
3467(10^111902+71)/9111902Serge Batalov07/2015
3468(2^371625+1610)/2111870Stefano Morozzi09/2020
34692^371440-112865111815Enzo Doria06/2014
34702^371426-459161111811Enzo Doria05/2015
3471(94*10^111770+11)/3111772Robert Price04/2020
34722^371276-461267111766Enzo Doria07/2015
34736*10^111760+43111761Robert Price07/2020
347498079!4-1024111747Robert Price11/2019
3475(2^371186+3162)/2111738Stefano Morozzi09/2020
34762^371098-113261111712Enzo Doria07/2014
3477(7*10^111706-61)/9111706Erik Branger01/2011
34782^371044+1869391111696Enzo Doria05/2016
347926310^17581+17581^26310111688Hans Havermann01/2021
348088^57416+87111645Norbert Schneider11/2015
34812^370829-109693111631Enzo Doria04/2014
348215^94906-2111619Lelio R Paula11/2013
3483(2^370726+1198)/2111600Stefano Morozzi09/2020
34842^370695-4627111591Yves Minet05/2019
34857*10^111579-87111580Robert Price06/2020
34872^370643-37111575Yves Minet01/2012
3486(2^370655-5)/2439111575Lelio R Paula03/2014
34882^370610-3911111565Yves Minet04/2017
3489286^45405+45405^286111532Norbert Schneider04/2015
34904*5^159563-9111531Lelio R Paula11/2014
3491(4^185225+23)/3111517Robert Price10/2018
34922^370393-2797093111500Enzo Doria03/2016
3493(21*2^370382-1)/629111495Lelio R Paula03/2014
3494(2^370371+554)/2111493Stefano Morozzi09/2020
34952^370292-2791979111469Enzo Doria03/2016
34962^370177-461551111435Enzo Doria07/2015
3497(2^370169+1706)/2111432Stefano Morozzi09/2020
3498109^54683-108111413Norbert Schneider02/2017
3499(2^370043+1010)/2111394Stefano Morozzi09/2020
350032961^2396+2396^32961111392Hans Havermann10/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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