PRP Records

Probable Primes Top 10000

(295149 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
57512^379529-2790283114250Enzo Doria03/2016
57522^379522+1869115114248Enzo Doria05/2016
5753(145*10^114226-1)/9114228Serge Batalov12/2014
57542^379317-115033114186Enzo Doria06/2015
5755(22*10^114178+47)/3114179Robert Price06/2021
5756(17*2^379246-1)/17407114162Lelio R Paula03/2014
5757(2^379192+226)/2114148Stefano Morozzi09/2020
5758(228^48407-1)/227114139Alexander Zhirkov03/2023
57596*10^114091+23114092Robert Price09/2020
5760(4*10^114076+143)/3114077Robert Price03/2018
5761332*25^81584+12357114053Eric Chen10/2023
5762(2^378820+3226)/2114036Stefano Morozzi01/2021
5763(2^378754+2058)/2114017Stefano Morozzi09/2020
576413643^27572-27572^13643114008Norbert Schneider12/2022
5766(46*10^113969+683)/9113970Robert Price03/2019
5765(83*10^113969+133)/9113970Robert Price08/2021
576732226^3439+3439^32226113966Hans Havermann02/2021
5768(77*10^113963-149)/9113964Robert Price03/2022
576978*10^113954-7113956Robert Price10/2020
57702*10^113941+9113942Dmitry Domanov11/2010
577110^113933+145897113934Patrick De Geest02/2021
5774(2^378478+1642)/2113933Stefano Morozzi09/2020
577210^113933-8000000001113933Robert Price11/2020
577310^113933-66167113933Patrick De Geest02/2021
57752339662057597*10^113903+9113916Robert Price03/2021
57764*10^113905+91113906Robert Price08/2018
577710^113894+76609113895Patrick De Geest02/2021
577910^113894-10000001113894Robert Price09/2020
577810^113894-373947113894Patrick De Geest02/2021
578033933^2270+2270^33933113881Hans Havermann02/2021
57814*10^113874-21113875Robert Price09/2018
57822^378272-16565113872Enzo Doria04/2013
57832^378217-109075113855Enzo Doria04/2014
57842^378198+67113849Lelio R Paula03/2013
57852^378173-3249113842Yves Minet12/2014
5786(2^378155-5)/6597113833Lelio R Paula03/2014
578792941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
578830030^6173+6173^30030113829Hans Havermann01/2021
57892^378128-262977113828Enzo Doria05/2014
57902^378123-113215113827Enzo Doria07/2014
57916^146274-18893113824Enzo Doria03/2013
579234596^1949+1949^34596113815Hans Havermann02/2021
57932^378078+75113813Lelio R Paula03/2013
5794(28*10^113810+449)/9113811Robert Price11/2021
579526273^21448+21448^26273113799Hans Havermann02/2021
57962^377966+255255113780Paul Bourdelais10/2021
57972^377940+63113772Lelio R Paula03/2013
57982^377941-2785843113772Enzo Doria04/2016
5799(7*10^113757+11)/9113757Tyler Busby01/2023
58002^377810+1875109113733Enzo Doria09/2016
58012^377803-1838635113731Enzo Doria05/2015
58022^377799+52223113729Yves Minet08/2010
5803(2^377791+3258)/2113727Stefano Morozzi02/2021
580411^109190-270113710Enzo Doria12/2012
580528206^10739+10739^28206113698Hans Havermann01/2021
58067*10^113693+9113694Robert Price09/2015
580713899^27442+27442^13899113692Norbert Schneider12/2020
5808(82*10^113681+161)/9113682Robert Price10/2019
580926121^22478+22478^26121113673Hans Havermann01/2021
58104*10^113658+49113659Robert Price01/2019
5811(10^113656+7)/40231/6439001113645Alfred Reich06/2021
5812(2*10^113631+529)/9113631Robert Price01/2018
58132^377408-2798279113612Enzo Doria04/2016
5814(292^46336+1)/(292^256+1)113605Martin Hopf12/2023
581513706^27459+27459^13706113596Norbert Schneider12/2020
58165*10^113586+57113587Robert Price12/2018
5817(2^377242+2794)/2113561Stefano Morozzi02/2021
58182^377222+93679113556Yves Minet02/2011
5820262147#+316847113552Makoto Morimoto02/2016
581927172^15101+15101^27172113552Hans Havermann01/2021
5821(2^377131+2018)/2113528Stefano Morozzi09/2020
58222^377026-458903113497Enzo Doria04/2015
5823(2^377014+2202)/2113493Stefano Morozzi09/2020
582434791^1828+1828^34791113488Hans Havermann02/2021
5825(2^376967+258)/2113479Stefano Morozzi09/2020
5826(29*10^113468-17)/3113469Robert Price09/2019
582735^73477-34^73477113454Robert Price05/2012
5828(14*10^113451-89)/3113452Robert Price05/2020
58292^376790+27113426Lelio R Paula03/2013
58302^376786-112701113424Enzo Doria06/2014
58312^376731+21113408Lelio R Paula03/2013
58329*10^113394-73113395Robert Price01/2021
583329660^6651+6651^29660113387Hans Havermann01/2021
58352^376634+1871245113379Enzo Doria05/2016
5834(4^188318+17)/3113379Robert Price02/2017
5836E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
58372^376576-344369113361Enzo Doria07/2015
58382^376549-4543113353Yves Minet03/2019
5839(17*2^376526-1)/223113345Lelio R Paula03/2014
5840(27*2^376441-1)/811113319Lelio R Paula03/2014
5841(2^376350+3538)/2113293Stefano Morozzi09/2020
584227265^14272+14272^27265113273Hans Havermann02/2021
584332174^3315+3315^32174113269Hans Havermann02/2021
5844(2*10^113248+73)/3113248Robert Price09/2020
58452^376128-21237113226Enzo Doria06/2013
58465*10^113224-81113225Robert Price01/2019
584710^113220+51409113221Patrick De Geest02/2021
584910^113220-1000001113220Robert Price08/2020
584810^113220-61779113220Patrick De Geest02/2021
5850(2^376102+1578)/2113218Stefano Morozzi09/2020
5851(2^375996+3102)/2113186Stefano Morozzi09/2020
585237258^1091+1091^37258113184Hans Havermann02/2021
5853(94*10^113176+11)/3113178Robert Price04/2020
5854(46*10^113162+521)/9113163Robert Price02/2019
5855(2^375885+3614)/2113153Stefano Morozzi09/2020
5856(2^375873+2006)/2113149Stefano Morozzi09/2020
58573*10^113137+23113138Robert Price03/2022
5858(8*10^113135-269)/9113135Robert Price09/2021
5859(2^375726+694)/2113105Stefano Morozzi09/2020
586026050^21959+21959^26050113100Hans Havermann02/2021
58612^375638-1787171113079Enzo Doria03/2016
5862(2^375563+2178)/2113056Stefano Morozzi09/2020
58632^375537+4847113048Yves Minet02/2011
5864(17^91837+16^91837)/33113000Robert Price08/2013
58655*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
58662^375350-3221112992Yves Minet07/2011
5867(13*2^375306+1)/7112979Lelio R Paula03/2014
58682^375305+76757112979Enzo Doria05/2016
58692^375258+1874989112964Enzo Doria07/2016
5870(29^77237-1)/28112950Robert Price04/2012
587126620^17483+17483^26620112939Hans Havermann01/2021
58722^375154+74959112933Enzo Doria04/2016
5873(266*10^112930-17)/3112932Robert Price07/2020
5874(2^375134+778)/2112927Stefano Morozzi09/2020
5875(85*10^112919+293)/9112920Robert Price12/2019
587629412^6899+6899^29412112907Hans Havermann02/2021
5877(191*10^112903-17)/3112905Robert Price11/2021
5878(2^375022+1210)/2112893Stefano Morozzi09/2020
587925992^22039+22039^25992112889Hans Havermann02/2021
58802^374993-2787163112885Enzo Doria11/2015
5881(697*10^112869+23)/9112871Robert Price04/2021
5882(19*10^112851+377)/9112852Alfred Reich11/2022
588330420^5111+5111^30420112813Hans Havermann02/2021
588413699^27268+27268^13699112800Norbert Schneider12/2020
5885123^53970+2112793Lelio R Paula06/2013
588612308*27^78796+23112790Eric Chen07/2023
588728942^7887+7887^28942112785Hans Havermann01/2021
58882^374640-4685112778Yves Minet05/2019
588912^104501-11112776Riley Fisher12/2023
589057290^93+93^57290112775Hans Havermann01/2021
589113608^27277-27277^13608112758Norbert Schneider12/2022
5892(2^374556+682)/2112753Stefano Morozzi09/2020
5893p(22852)#/2+512112745Robert Price05/2017
5894(11*10^112742-131)/3112743Robert Price09/2018
58952^374441-21049112718Enzo Doria06/2013
58964*10^112706-93112707Robert Price07/2020
5897(2^374321+1)/3112682H.&R. Lifchitz12/2000
5898(2^374213+1766)/2112650Stefano Morozzi09/2020
5899(2^374094+2674)/2112614Stefano Morozzi09/2020
5900(13^101089-1)/12112607Paul Bourdelais03/2010
59013^236011-8828112606Enzo Doria05/2014
590231854^3427+3427^31854112602Hans Havermann02/2021
5903(85*10^112530-373)/9112531Robert Price05/2021
5904(2^373748+1090)/2112510Stefano Morozzi09/2020
5905(2^373727+1806)/2112503Stefano Morozzi01/2021
590627618^11821+11821^27618112479Hans Havermann01/2021
590726343^18580+18580^26343112460Hans Havermann01/2021
590839^70666+2112435Lelio R Paula11/2013
5909(134*10^112400+7)/3112402Robert Price02/2020
5910(2^373365+326)/2112394Stefano Morozzi09/2020
5911(2^373350-7)/3112390Lelio R Paula03/2014
59122^373306-1840931112377Enzo Doria06/2015
59138*10^112371-37112372Robert Price03/2022
5914(2^373262+270)/2112363Stefano Morozzi09/2020
59156*10^112359-79112360Robert Price03/2022
591634409^1842+1842^34409112356Hans Havermann02/2021
5917(142*10^112352-7)/9112354Robert Price12/2019
591825580^24633+24633^25580112336Hans Havermann01/2021
59192^373117+1872107112320Enzo Doria05/2016
5920(2^373083+2226)/2112309Stefano Morozzi01/2021
5921(35*10^112308+37)/9112309Robert Price05/2022
592227963^10376+10376^27963112301Hans Havermann01/2021
59232^373040+2792761112297Enzo Doria03/2016
5924EPrime(112280)112280Eric W. Weisstein10/2010
59252^372950+7112270Lelio R Paula03/2013
59262^372945+1872167112268Enzo Doria05/2016
592736274^1243+1243^36274112249Hans Havermann02/2021
5928(55*10^112246+629)/9112247Robert Price01/2022
5929(2^372872+3798)/2112246Stefano Morozzi02/2021
593025513^25060+25060^25513112232Hans Havermann02/2021
5931(53*10^112229-611)/9112230Robert Price02/2022
5932(2^372754+3094)/2112210Stefano Morozzi09/2020
59336*10^112208+43112209Robert Price07/2020
5934(2^372728+3058)/2112203Stefano Morozzi09/2020
593532061^3158+3158^32061112195Hans Havermann02/2021
59362^372695+72113112193Enzo Doria04/2016
59372^372689-2563112191Yves Minet07/2014
59382^372638-1859441112176Enzo Doria03/2016
59393^235074-113056112159Enzo Doria07/2014
5940-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
5941(2^372514+1822)/2112138Stefano Morozzi02/2021
594229468^6387+6387^29468112135Hans Havermann02/2021
5943(2^372428+3742)/2112112Stefano Morozzi01/2021
594425375^25454-25454^25375112110Norbert Schneider01/2021
5945131^52949-130112108Norbert Schneider02/2019
5946(91*10^112098-1)/9112100Robert Price04/2015
5947(68*10^112087-149)/9112088Robert Price07/2022
59482^372314+212419112078Enzo Doria08/2023
59492^372310-85061112077Paul Bourdelais02/2012
5950(10^112067+53)/9112067Serge Batalov07/2015
5951(2^372237+2082)/2112055Stefano Morozzi09/2020
595275^59760+2112054Lelio R Paula08/2013
5953(2^372200+1710)/2112044Stefano Morozzi09/2020
5954(10^112048+7)/8747/373157112039Alfred Reich06/2021
5955(2^372181+2250)/2112038Stefano Morozzi01/2021
5956(2^372161+2574)/2112032Stefano Morozzi09/2020
59578*10^112018-49112019Robert Price08/2019
59592^372108+74221112016Enzo Doria04/2016
5958(2^372109+2046)/2112016Stefano Morozzi09/2020
59608*10^112011-73112012Robert Price01/2022
5961(184*10^112007-1)/3112009Robert Price02/2020
59625*10^112003+81112004Robert Price03/2019
5963215^48018+48018^215112000Norbert Schneider10/2018
596425549^24148+24148^25549111979Hans Havermann02/2021
59652^371970-459491111975Enzo Doria05/2015
596641^69427-40^69427111971Robert Price07/2012
5967(2^371782+358)/2111918Stefano Morozzi01/2021
596815*25^80056+446111915Eric Chen10/2023
5969(34*10^111902-547)/9111903Robert Price03/2021
5970(10^111902+71)/9111902Serge Batalov07/2015
5971(2^371625+1610)/2111870Stefano Morozzi09/2020
597229080^7027+7027^29080111865Hans Havermann01/2021
597331307^3730+3730^31307111820Hans Havermann02/2021
59742^371440-112865111815Enzo Doria06/2014
59752^371426-459161111811Enzo Doria05/2015
597625768^21771+21771^25768111779Hans Havermann02/2021
597728022^9747+9747^28022111777Hans Havermann02/2021
5978(94*10^111770+11)/3111772Robert Price04/2020
59792^371276-461267111766Enzo Doria07/2015
59806*10^111760+43111761Robert Price07/2020
598198079!4-1024111747Robert Price11/2019
5982(2^371186+3162)/2111738Stefano Morozzi09/2020
598310^(2*55862+1)-4*10^55862-1111725Robert Price07/2023
59842^371098-113261111712Enzo Doria07/2014
5985(7*10^111706-61)/9111706Erik Branger01/2011
59862^371044+1869391111696Enzo Doria05/2016
598726310^17581+17581^26310111688Hans Havermann01/2021
598888^57416+87111645Norbert Schneider11/2015
59892^370829-109693111631Enzo Doria04/2014
599015^94906-2111619Lelio R Paula11/2013
599125835^20904+20904^25835111614Hans Havermann02/2021
5992(2^370726+1198)/2111600Stefano Morozzi09/2020
599327758^10479+10479^27758111597Hans Havermann02/2021
59942^370695-4627111591Yves Minet05/2019
59957*10^111579-87111580Robert Price06/2020
59972^370643-37111575Yves Minet01/2012
5996(2^370655-5)/2439111575Lelio R Paula03/2014
59982^370610-3911111565Yves Minet04/2017
5999(154*10^111549+17)/9111551Robert Price06/2022
600026200^18097+18097^26200111550Hans Havermann01/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!