PRP Records

Probable Primes Top 10000

(301421 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 ?
6251(14*10^116112-101)/3116113Robert Price02/2019
6252Phi(236354,10)/24817171116109Makoto Kamada08/2019
62533*10^116107+23116108Robert Price03/2022
625428729^10990+10990^28729116094Hans Havermann02/2021
62552^385622+71839116084Enzo Doria04/2016
62572^385564+781116067Lelio R Paula01/2012
6256(2^385565+1562)/2116067Stefano Morozzi09/2020
6258(2^385563+378)/2116066Stefano Morozzi02/2021
6259(2^385557+2214)/2116064Stefano Morozzi09/2020
626029431^8776+8776^29431116056Hans Havermann01/2021
6261(266*10^116024-17)/3116026Robert Price07/2020
626230263^6820+6820^30263116022Hans Havermann02/2021
62632^385410+71893116020Enzo Doria04/2016
626438225^1084+1084^38225116014Hans Havermann02/2021
626526548^23433+23433^26548116011Hans Havermann02/2021
626612^107422-11115928Riley Fisher12/2023
6267(25*2^385091+1)/27115924Lelio R Paula04/2014
6268(11*10^115910-131)/3115911Robert Price09/2018
62692^384953-111943115883Paul Bourdelais02/2012
627043^70942-2115882Lelio R Paula04/2014
6271(94*10^115879-7)/3115881Robert Price03/2020
62727*10^115863+3115864Robert Price08/2015
62732^384834+93115847Donovan Johnson07/2008
62742^384809+71297115840Enzo Doria04/2016
6275(55*10^115829+323)/9115830Robert Price10/2021
6276(7*2^384759-1)/5115825Lelio R Paula04/2014
627731348^4951+4951^31348115822Hans Havermann02/2021
6278(793*10^115810+53)/9115812Robert Price01/2022
6279(71*10^115810-17)/9115811Ray Chandler08/2011
6280(97*10^115794-1)/3115796Serge Batalov12/2014
628131115^5266+5266^31115115794Hans Havermann02/2021
62822*10^115784-27115785Robert Price05/2018
628310^115773+126739115774Patrick De Geest04/2018
628510^115773-1000000001115773Robert Price03/2018
628410^115773-396221115773Patrick De Geest04/2018
6286(2^384582+778)/2115771Stefano Morozzi09/2020
628730537^6178+6178^30537115762Hans Havermann01/2021
62882^384530+1874305115756Enzo Doria06/2016
6289(3*2^384524-1)/7631115750Lelio R Paula03/2014
629028275^12406+12406^28275115748Hans Havermann01/2021
6291(44*10^115697-413)/9115698Robert Price03/2019
629231408^4825+4825^31408115692Hans Havermann02/2021
6293(2^384317+1026)/2115691Stefano Morozzi09/2020
62942^384312+81091115690Yves Minet02/2010
6295(2^384265+2150)/2115675Stefano Morozzi09/2020
6296(2^384246+2182)/2115670Stefano Morozzi09/2020
6297(4*10^115668-79)/3115669Robert Price02/2018
6298(2^384193+242)/2115654Stefano Morozzi09/2020
6299(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
6300(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
630118^92125-92125^18115642Dylan Delgado08/2019
63023^242337-4042115625Enzo Doria05/2014
6303(17699*31^77516-29)/30115608Eric Chen05/2024
6304(2^383931+674)/2115575Stefano Morozzi09/2020
63057*10^115561+79115562Robert Price07/2019
6306(2^383872+3046)/2115557Stefano Morozzi09/2020
6307(11*2^383859-13)/15115553Renaud Lifchitz03/2011
63082^383780-3149115530Yves Minet10/2014
6309(41*10^115523-383)/9115524Robert Price11/2018
631027316^16923+16923^27316115506Hans Havermann02/2021
6311(2^383618+618)/2115481Stefano Morozzi09/2020
63122^383560-455115464Yves Minet03/2012
6313(2^383544+5)/3115458Lelio R Paula03/2014
6314(22*10^115454+119)/3115455Robert Price04/2021
631589^59221-88^59221115445Robert Price06/2015
6316(7^136559-5^136559)/2115406Jon Grantham08/2023
63172^383347+1869413115399Enzo Doria05/2016
6318(103*10^115366+17)/3115368Robert Price08/2020
6319(2^383232+750)/2115365Stefano Morozzi09/2020
6320(2^383130-7)/131793115329Lelio R Paula03/2014
6321(12^106859+1)/13115320Paul Bourdelais02/2010
632229961^7060+7060^29961115315Hans Havermann01/2021
63242^383039+1869509115307Enzo Doria05/2016
632332918^3183+3183^32918115307Hans Havermann01/2021
632536964^1315+1315^36964115288Hans Havermann02/2021
6326(13*2^382968+1)/7115286Lelio R Paula04/2014
6327(22*10^115282+29)/3115283Robert Price02/2021
6328(2^382945+2046)/2115278Stefano Morozzi09/2020
6329(2^382789+3182)/2115231Stefano Morozzi09/2020
633030416^6141+6141^30416115224Hans Havermann02/2021
63316*10^115211+79115212Robert Price09/2020
6332(2^382722+3598)/2115211Stefano Morozzi09/2020
633327987^13078+13078^27987115210Hans Havermann02/2021
6334(2^382699+2090)/2115204Stefano Morozzi09/2020
6335(22*10^115188-193)/9115189Robert Price07/2022
63362^382633+73697115185Enzo Doria04/2016
63372^382509-113593115147Enzo Doria08/2014
63382^382502-2791721115145Enzo Doria03/2016
6339(2^382495+1274)/2115143Stefano Morozzi01/2021
63402^382464+22741115134Enzo Doria09/2023
634126752^20065+20065^26752115099Hans Havermann02/2021
634226383^23008+23008^26383115080Hans Havermann02/2021
63439^120590-120590115073Robert Price03/2014
634428203^12016+12016^28203115062Hans Havermann02/2021
63452^382198+9115054Lelio R Paula03/2013
634618268*31^77131+22839115035Eric Chen05/2024
634730101^6630+6630^30101115032Hans Havermann01/2021
6348(89*10^115030-179)/9115031Robert Price12/2019
634925554^26089-26089^25554114987Frank Doornink02/2024
635025142^26129-26129^25142114979Frank Doornink12/2023
6351(2^381935+2774)/2114974Stefano Morozzi02/2021
635227300^16271+16271^27300114972Hans Havermann02/2021
6353(23*10^114962+7)/3114963Robert Price05/2023
63542^381883-59197114959Enzo Doria10/2015
635527423^15542+15542^27423114944Hans Havermann02/2021
6356(2^381820+1626)/2114939Stefano Morozzi09/2020
63582^381806-4481114936Yves Minet07/2011
63572^381808-1851507114936Enzo Doria08/2015
6359(2^381792+2502)/2114931Stefano Morozzi09/2020
63602^381774-112373114926Enzo Doria06/2014
636126341^22980+22980^26341114883Hans Havermann01/2021
63622^381555-109051114860Enzo Doria04/2014
63632^381551+213683114859Enzo Doria09/2023
63642^381546-113501114857Enzo Doria08/2014
6365(7*10^114845-19)/3114846Robert Price10/2020
636626675^20178+20178^26675114833Hans Havermann02/2021
6367(2^381436+1182)/2114824Stefano Morozzi09/2020
63683^240644+16114817Robert Price04/2020
6369(13^114814)%(10^114814)114814Henri Lifchitz05/2025
63702^381360-110429114801Enzo Doria05/2014
6371(17*10^114795+79)/3114796Robert Price04/2019
6372(66^63079+1)/67114774Paul Bourdelais09/2017
63732^381252-115079114769Enzo Doria06/2015
6374(2^381251+3186)/2114768Stefano Morozzi09/2020
63752^381209-29323114756Enzo Doria07/2015
63762^381207-111546435114755Paul Bourdelais10/2021
6377569^41651-568^41651114754Jean-Louis Charton11/2009
63782^381201+1873205114753Enzo Doria06/2016
6380(85*10^114737+293)/9114738Robert Price12/2019
6381(265*10^114736+17)/3114738Robert Price03/2020
6379379*10^114735+9114738Jason Yuen01/2025
6382(2^381062+2170)/2114711Stefano Morozzi09/2020
63832^380974-112991114685Enzo Doria07/2014
638437097^1234+1234^37097114679Hans Havermann02/2021
6385(26*10^114658-119)/3114659Robert Price07/2023
638688^58949-87114626Norbert Schneider11/2015
6387(2^380773+662)/2114624Stefano Morozzi09/2020
6388Phi(155285,10)/242674820198201114610Makoto Kamada02/2024
6389(10^155285-1)*(10^2389-1)*(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201114610Anonymous04/2025
639029913^6782+6782^29913114608Hans Havermann02/2021
6391(331*10^114605-7)/9114607Robert Price04/2022
63922^380700+91114603Lelio R Paula03/2013
6393(2^380632+2578)/2114582Stefano Morozzi09/2020
63947*10^114577+27114578Robert Price11/2020
639610^114575+3^114576114576Mike Oakes09/2010
639510^114575+66561114576Patrick De Geest02/2017
639710^114575-581081114575Patrick De Geest02/2017
63982^380587-115315114569Enzo Doria06/2015
639931874^3927+3927^31874114558Hans Havermann02/2021
64002^380513-216925114546Enzo Doria05/2014
64012^380451-1840087114528Enzo Doria06/2015
6402(2^380426+1510)/2114520Stefano Morozzi09/2020
6403(15*2^380388-1)/539114507Lelio R Paula04/2014
64042^380279-461347114476Enzo Doria07/2015
6405(331*10^114454-7)/9114456Robert Price04/2022
640627121^16590+16590^27121114447Hans Havermann01/2021
640725966^25555+25555^25966114445Hans Havermann01/2021
6408(611*32^76029-53)/31114437Eric Chen11/2023
6409(11*10^114400+529)/9114401Robert Price09/2021
64102^380021+1871147114398Enzo Doria05/2016
64112^380005+1869707114393Enzo Doria05/2016
64122^379958-113297114379Enzo Doria07/2014
6413(2^379897+1274)/2114361Stefano Morozzi01/2021
64142^379881-109105114356Enzo Doria04/2014
6415(21*2^379857-1)/13114349Lelio R Paula03/2014
6416(4*10^114340+83)/3114341Robert Price02/2018
6417(26*10^114317-77)/3114318Robert Price11/2019
6418(4*10^114296+149)/9114296Robert Price04/2018
641988^58773-87114284Norbert Schneider11/2015
642027764^13065+13065^27764114280Hans Havermann01/2021
6421(132^53891-1)/131114278Anonymous06/2024
64222^379529-2790283114250Enzo Doria03/2016
64232^379522+1869115114248Enzo Doria05/2016
6424(145*10^114226-1)/9114228Serge Batalov12/2014
64252^379317-115033114186Enzo Doria06/2015
6426(22*10^114178+47)/3114179Robert Price06/2021
6427(17*2^379246-1)/17407114162Lelio R Paula03/2014
6428(2^379192+226)/2114148Stefano Morozzi09/2020
6429(228^48407-1)/227114139Alexander Zhirkov03/2023
64306*10^114091+23114092Robert Price09/2020
6431(4*10^114076+143)/3114077Robert Price03/2018
6432332*25^81584+12357114053Eric Chen10/2023
6433(2^378820+3226)/2114036Stefano Morozzi01/2021
6434(2^378754+2058)/2114017Stefano Morozzi09/2020
643513643^27572-27572^13643114008Norbert Schneider12/2022
6437(46*10^113969+683)/9113970Robert Price03/2019
6436(83*10^113969+133)/9113970Robert Price08/2021
643832226^3439+3439^32226113966Hans Havermann02/2021
6439(77*10^113963-149)/9113964Robert Price03/2022
644078*10^113954-7113956Robert Price10/2020
64412*10^113941+9113942Dmitry Domanov11/2010
644210^113933+145897113934Patrick De Geest02/2021
6445(2^378478+1642)/2113933Stefano Morozzi09/2020
644310^113933-8000000001113933Robert Price11/2020
644410^113933-66167113933Patrick De Geest02/2021
64462339662057597*10^113903+9113916Robert Price03/2021
64474*10^113905+91113906Robert Price08/2018
644810^113894+76609113895Patrick De Geest02/2021
645010^113894-10000001113894Robert Price09/2020
644910^113894-373947113894Patrick De Geest02/2021
645133933^2270+2270^33933113881Hans Havermann02/2021
64524*10^113874-21113875Robert Price09/2018
64532^378272-16565113872Enzo Doria04/2013
64542^378217-109075113855Enzo Doria04/2014
64552^378198+67113849Lelio R Paula03/2013
64562^378173-3249113842Yves Minet12/2014
6457(2^378155-5)/6597113833Lelio R Paula03/2014
64582^378137+1334025113831Henri Lifchitz10/2024
645992941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
646030030^6173+6173^30030113829Hans Havermann01/2021
64612^378128-262977113828Enzo Doria05/2014
64622^378123-113215113827Enzo Doria07/2014
64636^146274-18893113824Enzo Doria03/2013
646434596^1949+1949^34596113815Hans Havermann02/2021
64652^378078+75113813Lelio R Paula03/2013
6466(28*10^113810+449)/9113811Robert Price11/2021
646726273^21448+21448^26273113799Hans Havermann02/2021
64682^377966+255255113780Paul Bourdelais10/2021
64692^377940+63113772Lelio R Paula03/2013
64702^377941-2785843113772Enzo Doria04/2016
6471(7*10^113757+11)/9113757Tyler Busby01/2023
64722^377810+1875109113733Enzo Doria09/2016
64732^377803-1838635113731Enzo Doria05/2015
64742^377799+52223113729Yves Minet08/2010
6475(2^377791+3258)/2113727Stefano Morozzi02/2021
647611^109190-270113710Enzo Doria12/2012
647728206^10739+10739^28206113698Hans Havermann01/2021
64787*10^113693+9113694Robert Price09/2015
647913899^27442+27442^13899113692Norbert Schneider12/2020
6480(82*10^113681+161)/9113682Robert Price10/2019
648126121^22478+22478^26121113673Hans Havermann01/2021
64824*10^113658+49113659Robert Price01/2019
6483(10^113656+7)/40231/6439001113645Alfred Reich06/2021
6484(2*10^113631+529)/9113631Robert Price01/2018
64852^377408-2798279113612Enzo Doria04/2016
6486(292^46336+1)/(292^256+1)113605Martin Hopf12/2023
648713706^27459+27459^13706113596Norbert Schneider12/2020
64885*10^113586+57113587Robert Price12/2018
6489(2^377242+2794)/2113561Stefano Morozzi02/2021
64902^377222+93679113556Yves Minet02/2011
6492262147#+316847113552Makoto Morimoto02/2016
649127172^15101+15101^27172113552Hans Havermann01/2021
6493(2^377131+2018)/2113528Stefano Morozzi09/2020
64942^377026-458903113497Enzo Doria04/2015
6495(2^377014+2202)/2113493Stefano Morozzi09/2020
649634791^1828+1828^34791113488Hans Havermann02/2021
6497(2^376967+258)/2113479Stefano Morozzi09/2020
6498(29*10^113468-17)/3113469Robert Price09/2019
649935^73477-34^73477113454Robert Price05/2012
6500(14*10^113451-89)/3113452Robert Price05/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 19 2025 12:52 (Time in France)

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