PRP Records

Probable Primes Top 10000

(277034 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 ?
32516*10^115211+79115212Robert Price09/2020
3252(2^382722+3598)/2115211Stefano Morozzi09/2020
3253(2^382699+2090)/2115204Stefano Morozzi09/2020
32542^382633+73697115185Enzo Doria04/2016
32552^382509-113593115147Enzo Doria08/2014
32562^382502-2791721115145Enzo Doria03/2016
3257(2^382495+1274)/2115143Stefano Morozzi01/2021
32589^120590-120590115073Robert Price03/2014
32592^382198+9115054Lelio R Paula03/2013
3260(89*10^115030-179)/9115031Robert Price12/2019
32612^381883-59197114959Enzo Doria10/2015
3262(2^381820+1626)/2114939Stefano Morozzi09/2020
32642^381806-4481114936Yves Minet07/2011
32632^381808-1851507114936Enzo Doria08/2015
3265(2^381792+2502)/2114931Stefano Morozzi09/2020
32662^381774-112373114926Enzo Doria06/2014
32672^381555-109051114860Enzo Doria04/2014
32682^381546-113501114857Enzo Doria08/2014
3269(7*10^114845-19)/3114846Robert Price10/2020
3270(2^381436+1182)/2114824Stefano Morozzi09/2020
32713^240644+16114817Robert Price04/2020
32722^381360-110429114801Enzo Doria05/2014
3273(17*10^114795+79)/3114796Robert Price04/2019
3274(66^63079+1)/67114774Paul Bourdelais09/2017
32752^381252-115079114769Enzo Doria06/2015
3276(2^381251+3186)/2114768Stefano Morozzi09/2020
32772^381209-29323114756Enzo Doria07/2015
3278569^41651-568^41651114754Jean-Louis Charton11/2009
32792^381201+1873205114753Enzo Doria06/2016
3280(85*10^114737+293)/9114738Robert Price12/2019
3281(265*10^114736+17)/3114738Robert Price03/2020
3282(2^381062+2170)/2114711Stefano Morozzi09/2020
32832^380974-112991114685Enzo Doria07/2014
328488^58949-87114626Norbert Schneider11/2015
3285(2^380773+662)/2114624Stefano Morozzi09/2020
32862^380700+91114603Lelio R Paula03/2013
3287(2^380632+2578)/2114582Stefano Morozzi09/2020
32887*10^114577+27114578Robert Price11/2020
329010^114575+3^114576114576Mike Oakes09/2010
328910^114575+66561114576Patrick De Geest02/2017
329110^114575-581081114575Patrick De Geest02/2017
32922^380587-115315114569Enzo Doria06/2015
32932^380513-216925114546Enzo Doria05/2014
32942^380451-1840087114528Enzo Doria06/2015
3295(2^380426+1510)/2114520Stefano Morozzi09/2020
3296(15*2^380388-1)/539114507Lelio R Paula04/2014
32972^380279-461347114476Enzo Doria07/2015
32982^380021+1871147114398Enzo Doria05/2016
32992^380005+1869707114393Enzo Doria05/2016
33002^379958-113297114379Enzo Doria07/2014
3301(2^379897+1274)/2114361Stefano Morozzi01/2021
33022^379881-109105114356Enzo Doria04/2014
3303(21*2^379857-1)/13114349Lelio R Paula03/2014
3304(4*10^114340+83)/3114341Robert Price02/2018
3305(26*10^114317-77)/3114318Robert Price11/2019
3306(4*10^114296+149)/9114296Robert Price04/2018
330788^58773-87114284Norbert Schneider11/2015
33082^379529-2790283114250Enzo Doria03/2016
33092^379522+1869115114248Enzo Doria05/2016
3310(145*10^114226-1)/9114228Serge Batalov12/2014
33112^379317-115033114186Enzo Doria06/2015
3312(17*2^379246-1)/17407114162Lelio R Paula03/2014
3313(2^379192+226)/2114148Stefano Morozzi09/2020
33146*10^114091+23114092Robert Price09/2020
3315(4*10^114076+143)/3114077Robert Price03/2018
3316(2^378820+3226)/2114036Stefano Morozzi01/2021
3317(2^378754+2058)/2114017Stefano Morozzi09/2020
3318(46*10^113969+683)/9113970Robert Price03/2019
331978*10^113954-7113956Robert Price10/2020
33202*10^113941+9113942Dmitry Domanov11/2010
3322(2^378478+1642)/2113933Stefano Morozzi09/2020
332110^113933-8000000001113933Robert Price11/2020
33234*10^113905+91113906Robert Price08/2018
332410^113894-10000001113894Robert Price09/2020
33254*10^113874-21113875Robert Price09/2018
33262^378272-16565113872Enzo Doria04/2013
33272^378217-109075113855Enzo Doria04/2014
33282^378198+67113849Lelio R Paula03/2013
33292^378173-3249113842Yves Minet12/2014
3330(2^378155-5)/6597113833Lelio R Paula03/2014
333192941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
33322^378128-262977113828Enzo Doria05/2014
33332^378123-113215113827Enzo Doria07/2014
33346^146274-18893113824Enzo Doria03/2013
33352^378078+75113813Lelio R Paula03/2013
33362^377940+63113772Lelio R Paula03/2013
33372^377941-2785843113772Enzo Doria04/2016
33382^377810+1875109113733Enzo Doria09/2016
33392^377803-1838635113731Enzo Doria05/2015
33402^377799+52223113729Yves Minet08/2010
334111^109190-270113710Enzo Doria12/2012
33427*10^113693+9113694Robert Price09/2015
334313899^27442+27442^13899113692Norbert Schneider12/2020
3344(82*10^113681+161)/9113682Robert Price10/2019
33454*10^113658+49113659Robert Price01/2019
3346(2*10^113631+529)/9113631Robert Price01/2018
33472^377408-2798279113612Enzo Doria04/2016
334813706^27459+27459^13706113596Norbert Schneider12/2020
33495*10^113586+57113587Robert Price12/2018
33502^377222+93679113556Yves Minet02/2011
3351262147#+316847113552Makoto Morimoto02/2016
3352(2^377131+2018)/2113528Stefano Morozzi09/2020
33532^377026-458903113497Enzo Doria04/2015
3354(2^377014+2202)/2113493Stefano Morozzi09/2020
3355(2^376967+258)/2113479Stefano Morozzi09/2020
3356(29*10^113468-17)/3113469Robert Price09/2019
335735^73477-34^73477113454Robert Price05/2012
3358(14*10^113451-89)/3113452Robert Price05/2020
33592^376790+27113426Lelio R Paula03/2013
33602^376786-112701113424Enzo Doria06/2014
33612^376731+21113408Lelio R Paula03/2013
33629*10^113394-73113395Robert Price01/2021
33632^376634+1871245113379Enzo Doria05/2016
3364(4^188318+17)/3113379Robert Price02/2017
3365E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
33662^376576-344369113361Enzo Doria07/2015
33672^376549-4543113353Yves Minet03/2019
3368(17*2^376526-1)/223113345Lelio R Paula03/2014
3369(27*2^376441-1)/811113319Lelio R Paula03/2014
3370(2^376350+3538)/2113293Stefano Morozzi09/2020
3371(2*10^113248+73)/3113248Robert Price09/2020
33722^376128-21237113226Enzo Doria06/2013
33735*10^113224-81113225Robert Price01/2019
337410^113220-1000001113220Robert Price08/2020
3375(2^376102+1578)/2113218Stefano Morozzi09/2020
3376(2^375996+3102)/2113186Stefano Morozzi09/2020
3377(94*10^113176+11)/3113178Robert Price04/2020
3378(46*10^113162+521)/9113163Robert Price02/2019
3379(2^375885+3614)/2113153Stefano Morozzi09/2020
3380(2^375873+2006)/2113149Stefano Morozzi09/2020
3381(2^375726+694)/2113105Stefano Morozzi09/2020
33822^375638-1787171113079Enzo Doria03/2016
3383(2^375563+2178)/2113056Stefano Morozzi09/2020
33842^375537+4847113048Yves Minet02/2011
3385(17^91837+16^91837)/33113000Robert Price08/2013
33865*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
33872^375350-3221112992Yves Minet07/2011
3388(13*2^375306+1)/7112979Lelio R Paula03/2014
33892^375305+76757112979Enzo Doria05/2016
33902^375258+1874989112964Enzo Doria07/2016
3391(29^77237-1)/28112950Robert Price04/2012
33922^375154+74959112933Enzo Doria04/2016
3393(266*10^112930-17)/3112932Robert Price07/2020
3394(2^375134+778)/2112927Stefano Morozzi09/2020
3395(85*10^112919+293)/9112920Robert Price12/2019
3396(2^375022+1210)/2112893Stefano Morozzi09/2020
33972^374993-2787163112885Enzo Doria11/2015
339813699^27268+27268^13699112800Norbert Schneider12/2020
3399123^53970+2112793Lelio R Paula06/2013
34002^374640-4685112778Yves Minet05/2019
3401(2^374556+682)/2112753Stefano Morozzi09/2020
3402p(22852)#/2+512112745Robert Price05/2017
3403(11*10^112742-131)/3112743Robert Price09/2018
34042^374441-21049112718Enzo Doria06/2013
34054*10^112706-93112707Robert Price07/2020
3406(2^374321+1)/3112682H.&R. Lifchitz12/2000
3407(2^374213+1766)/2112650Stefano Morozzi09/2020
3408(2^374094+2674)/2112614Stefano Morozzi09/2020
3409(13^101089-1)/12112607Paul Bourdelais03/2010
34103^236011-8828112606Enzo Doria05/2014
3411(2^373748+1090)/2112510Stefano Morozzi09/2020
3412(2^373727+1806)/2112503Stefano Morozzi01/2021
341339^70666+2112435Lelio R Paula11/2013
3414(134*10^112400+7)/3112402Robert Price02/2020
3415(2^373365+326)/2112394Stefano Morozzi09/2020
3416(2^373350-7)/3112390Lelio R Paula03/2014
34172^373306-1840931112377Enzo Doria06/2015
3418(2^373262+270)/2112363Stefano Morozzi09/2020
3419(142*10^112352-7)/9112354Robert Price12/2019
34202^373117+1872107112320Enzo Doria05/2016
3421(2^373083+2226)/2112309Stefano Morozzi01/2021
34222^373040+2792761112297Enzo Doria03/2016
3423EPrime(112280)112280Eric W. Weisstein10/2010
34242^372950+7112270Lelio R Paula03/2013
34252^372945+1872167112268Enzo Doria05/2016
3426(2^372754+3094)/2112210Stefano Morozzi09/2020
34276*10^112208+43112209Robert Price07/2020
3428(2^372728+3058)/2112203Stefano Morozzi09/2020
34292^372695+72113112193Enzo Doria04/2016
34302^372689-2563112191Yves Minet07/2014
34312^372638-1859441112176Enzo Doria03/2016
34323^235074-113056112159Enzo Doria07/2014
3433-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
3434(2^372428+3742)/2112112Stefano Morozzi01/2021
3435131^52949-130112108Norbert Schneider02/2019
3436(91*10^112098-1)/9112100Robert Price04/2015
34372^372310-85061112077Paul Bourdelais02/2012
3438(10^112067+53)/9112067Serge Batalov07/2015
3439(2^372237+2082)/2112055Stefano Morozzi09/2020
344075^59760+2112054Lelio R Paula08/2013
3441(2^372200+1710)/2112044Stefano Morozzi09/2020
3442(2^372181+2250)/2112038Stefano Morozzi01/2021
3443(2^372161+2574)/2112032Stefano Morozzi09/2020
34448*10^112018-49112019Robert Price08/2019
34462^372108+74221112016Enzo Doria04/2016
3445(2^372109+2046)/2112016Stefano Morozzi09/2020
3447(184*10^112007-1)/3112009Robert Price02/2020
34485*10^112003+81112004Robert Price03/2019
3449215^48018+48018^215112000Norbert Schneider10/2018
34502^371970-459491111975Enzo Doria05/2015
345141^69427-40^69427111971Robert Price07/2012
3452(2^371782+358)/2111918Stefano Morozzi01/2021
3453(10^111902+71)/9111902Serge Batalov07/2015
3454(2^371625+1610)/2111870Stefano Morozzi09/2020
34552^371440-112865111815Enzo Doria06/2014
34562^371426-459161111811Enzo Doria05/2015
3457(94*10^111770+11)/3111772Robert Price04/2020
34582^371276-461267111766Enzo Doria07/2015
34596*10^111760+43111761Robert Price07/2020
346098079!4-1024111747Robert Price11/2019
3461(2^371186+3162)/2111738Stefano Morozzi09/2020
34622^371098-113261111712Enzo Doria07/2014
3463(7*10^111706-61)/9111706Erik Branger01/2011
34642^371044+1869391111696Enzo Doria05/2016
346588^57416+87111645Norbert Schneider11/2015
34662^370829-109693111631Enzo Doria04/2014
346715^94906-2111619Lelio R Paula11/2013
3468(2^370726+1198)/2111600Stefano Morozzi09/2020
34692^370695-4627111591Yves Minet05/2019
34707*10^111579-87111580Robert Price06/2020
34722^370643-37111575Yves Minet01/2012
3471(2^370655-5)/2439111575Lelio R Paula03/2014
34732^370610-3911111565Yves Minet04/2017
3474286^45405+45405^286111532Norbert Schneider04/2015
34754*5^159563-9111531Lelio R Paula11/2014
3476(4^185225+23)/3111517Robert Price10/2018
34772^370393-2797093111500Enzo Doria03/2016
3478(21*2^370382-1)/629111495Lelio R Paula03/2014
3479(2^370371+554)/2111493Stefano Morozzi09/2020
34802^370292-2791979111469Enzo Doria03/2016
34812^370177-461551111435Enzo Doria07/2015
3482(2^370169+1706)/2111432Stefano Morozzi09/2020
3483109^54683-108111413Norbert Schneider02/2017
3484(2^370043+1010)/2111394Stefano Morozzi09/2020
348532961^2396+2396^32961111392Hans Havermann10/2020
3486numbpart(10^10+76282)111391Serge Batalov04/2015
34872^369974+733111374Lelio R Paula05/2013
3488121^53470+120111367Norbert Schneider10/2018
34892^369915-286267111356Enzo Doria07/2015
34902^369855-1615111338Lelio R Paula05/2017
34917*10^111325+3111326Robert Price08/2015
349251^65176+2111293Lelio R Paula08/2013
34932^369643-1865767111274Enzo Doria03/2016
34942^369603+885111262Lelio R Paula05/2017
349525555^22564+22564^25555111252Hans Havermann10/2020
3496L(532277)111240Renaud Lifchitz03/2004
3497105^55033-2111233Lelio R Paula10/2017
3498(35*10^111232-737)/9111233Robert Price07/2018
349926970^13307+13307^26970111227Hans Havermann10/2020
350025419^23716+23716^25419111210Hans Havermann10/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 18 2021 19:57 (Time in France)

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