PRP Records

Probable Primes Top 10000

(295461 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 ?
57516*10^115211+79115212Robert Price09/2020
5752(2^382722+3598)/2115211Stefano Morozzi09/2020
575327987^13078+13078^27987115210Hans Havermann02/2021
5754(2^382699+2090)/2115204Stefano Morozzi09/2020
5755(22*10^115188-193)/9115189Robert Price07/2022
57562^382633+73697115185Enzo Doria04/2016
57572^382509-113593115147Enzo Doria08/2014
57582^382502-2791721115145Enzo Doria03/2016
5759(2^382495+1274)/2115143Stefano Morozzi01/2021
57602^382464+22741115134Enzo Doria09/2023
576126752^20065+20065^26752115099Hans Havermann02/2021
576226383^23008+23008^26383115080Hans Havermann02/2021
57639^120590-120590115073Robert Price03/2014
576428203^12016+12016^28203115062Hans Havermann02/2021
57652^382198+9115054Lelio R Paula03/2013
576618268*31^77131+22839115035Eric Chen05/2024
576730101^6630+6630^30101115032Hans Havermann01/2021
5768(89*10^115030-179)/9115031Robert Price12/2019
576925554^26089-26089^25554114987Frank Doornink02/2024
577025142^26129-26129^25142114979Frank Doornink12/2023
5771(2^381935+2774)/2114974Stefano Morozzi02/2021
577227300^16271+16271^27300114972Hans Havermann02/2021
5773(23*10^114962+7)/3114963Robert Price05/2023
57742^381883-59197114959Enzo Doria10/2015
577527423^15542+15542^27423114944Hans Havermann02/2021
5776(2^381820+1626)/2114939Stefano Morozzi09/2020
57782^381806-4481114936Yves Minet07/2011
57772^381808-1851507114936Enzo Doria08/2015
5779(2^381792+2502)/2114931Stefano Morozzi09/2020
57802^381774-112373114926Enzo Doria06/2014
578126341^22980+22980^26341114883Hans Havermann01/2021
57822^381555-109051114860Enzo Doria04/2014
57832^381551+213683114859Enzo Doria09/2023
57842^381546-113501114857Enzo Doria08/2014
5785(7*10^114845-19)/3114846Robert Price10/2020
578626675^20178+20178^26675114833Hans Havermann02/2021
5787(2^381436+1182)/2114824Stefano Morozzi09/2020
57883^240644+16114817Robert Price04/2020
57892^381360-110429114801Enzo Doria05/2014
5790(17*10^114795+79)/3114796Robert Price04/2019
5791(66^63079+1)/67114774Paul Bourdelais09/2017
57922^381252-115079114769Enzo Doria06/2015
5793(2^381251+3186)/2114768Stefano Morozzi09/2020
57942^381209-29323114756Enzo Doria07/2015
57952^381207-111546435114755Paul Bourdelais10/2021
5796569^41651-568^41651114754Jean-Louis Charton11/2009
57972^381201+1873205114753Enzo Doria06/2016
5798(85*10^114737+293)/9114738Robert Price12/2019
5799(265*10^114736+17)/3114738Robert Price03/2020
5800(2^381062+2170)/2114711Stefano Morozzi09/2020
58012^380974-112991114685Enzo Doria07/2014
580237097^1234+1234^37097114679Hans Havermann02/2021
5803(26*10^114658-119)/3114659Robert Price07/2023
580488^58949-87114626Norbert Schneider11/2015
5805(2^380773+662)/2114624Stefano Morozzi09/2020
5806Phi(155285,10)/242674820198201114610Makoto Kamada02/2024
580729913^6782+6782^29913114608Hans Havermann02/2021
5808(331*10^114605-7)/9114607Robert Price04/2022
58092^380700+91114603Lelio R Paula03/2013
5810(2^380632+2578)/2114582Stefano Morozzi09/2020
58117*10^114577+27114578Robert Price11/2020
581310^114575+3^114576114576Mike Oakes09/2010
581210^114575+66561114576Patrick De Geest02/2017
581410^114575-581081114575Patrick De Geest02/2017
58152^380587-115315114569Enzo Doria06/2015
581631874^3927+3927^31874114558Hans Havermann02/2021
58172^380513-216925114546Enzo Doria05/2014
58182^380451-1840087114528Enzo Doria06/2015
5819(2^380426+1510)/2114520Stefano Morozzi09/2020
5820(15*2^380388-1)/539114507Lelio R Paula04/2014
58212^380279-461347114476Enzo Doria07/2015
5822(331*10^114454-7)/9114456Robert Price04/2022
582327121^16590+16590^27121114447Hans Havermann01/2021
582425966^25555+25555^25966114445Hans Havermann01/2021
5825(611*32^76029-53)/31114437Eric Chen11/2023
5826(11*10^114400+529)/9114401Robert Price09/2021
58272^380021+1871147114398Enzo Doria05/2016
58282^380005+1869707114393Enzo Doria05/2016
58292^379958-113297114379Enzo Doria07/2014
5830(2^379897+1274)/2114361Stefano Morozzi01/2021
58312^379881-109105114356Enzo Doria04/2014
5832(21*2^379857-1)/13114349Lelio R Paula03/2014
5833(4*10^114340+83)/3114341Robert Price02/2018
5834(26*10^114317-77)/3114318Robert Price11/2019
5835(4*10^114296+149)/9114296Robert Price04/2018
583688^58773-87114284Norbert Schneider11/2015
583727764^13065+13065^27764114280Hans Havermann01/2021
5838(132^53891-1)/131114278Anonymous06/2024
58392^379529-2790283114250Enzo Doria03/2016
58402^379522+1869115114248Enzo Doria05/2016
5841(145*10^114226-1)/9114228Serge Batalov12/2014
58422^379317-115033114186Enzo Doria06/2015
5843(22*10^114178+47)/3114179Robert Price06/2021
5844(17*2^379246-1)/17407114162Lelio R Paula03/2014
5845(2^379192+226)/2114148Stefano Morozzi09/2020
5846(228^48407-1)/227114139Alexander Zhirkov03/2023
58476*10^114091+23114092Robert Price09/2020
5848(4*10^114076+143)/3114077Robert Price03/2018
5849332*25^81584+12357114053Eric Chen10/2023
5850(2^378820+3226)/2114036Stefano Morozzi01/2021
5851(2^378754+2058)/2114017Stefano Morozzi09/2020
585213643^27572-27572^13643114008Norbert Schneider12/2022
5854(46*10^113969+683)/9113970Robert Price03/2019
5853(83*10^113969+133)/9113970Robert Price08/2021
585532226^3439+3439^32226113966Hans Havermann02/2021
5856(77*10^113963-149)/9113964Robert Price03/2022
585778*10^113954-7113956Robert Price10/2020
58582*10^113941+9113942Dmitry Domanov11/2010
585910^113933+145897113934Patrick De Geest02/2021
5862(2^378478+1642)/2113933Stefano Morozzi09/2020
586010^113933-8000000001113933Robert Price11/2020
586110^113933-66167113933Patrick De Geest02/2021
58632339662057597*10^113903+9113916Robert Price03/2021
58644*10^113905+91113906Robert Price08/2018
586510^113894+76609113895Patrick De Geest02/2021
586710^113894-10000001113894Robert Price09/2020
586610^113894-373947113894Patrick De Geest02/2021
586833933^2270+2270^33933113881Hans Havermann02/2021
58694*10^113874-21113875Robert Price09/2018
58702^378272-16565113872Enzo Doria04/2013
58712^378217-109075113855Enzo Doria04/2014
58722^378198+67113849Lelio R Paula03/2013
58732^378173-3249113842Yves Minet12/2014
5874(2^378155-5)/6597113833Lelio R Paula03/2014
587592941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
587630030^6173+6173^30030113829Hans Havermann01/2021
58772^378128-262977113828Enzo Doria05/2014
58782^378123-113215113827Enzo Doria07/2014
58796^146274-18893113824Enzo Doria03/2013
588034596^1949+1949^34596113815Hans Havermann02/2021
58812^378078+75113813Lelio R Paula03/2013
5882(28*10^113810+449)/9113811Robert Price11/2021
588326273^21448+21448^26273113799Hans Havermann02/2021
58842^377966+255255113780Paul Bourdelais10/2021
58852^377940+63113772Lelio R Paula03/2013
58862^377941-2785843113772Enzo Doria04/2016
5887(7*10^113757+11)/9113757Tyler Busby01/2023
58882^377810+1875109113733Enzo Doria09/2016
58892^377803-1838635113731Enzo Doria05/2015
58902^377799+52223113729Yves Minet08/2010
5891(2^377791+3258)/2113727Stefano Morozzi02/2021
589211^109190-270113710Enzo Doria12/2012
589328206^10739+10739^28206113698Hans Havermann01/2021
58947*10^113693+9113694Robert Price09/2015
589513899^27442+27442^13899113692Norbert Schneider12/2020
5896(82*10^113681+161)/9113682Robert Price10/2019
589726121^22478+22478^26121113673Hans Havermann01/2021
58984*10^113658+49113659Robert Price01/2019
5899(10^113656+7)/40231/6439001113645Alfred Reich06/2021
5900(2*10^113631+529)/9113631Robert Price01/2018
59012^377408-2798279113612Enzo Doria04/2016
5902(292^46336+1)/(292^256+1)113605Martin Hopf12/2023
590313706^27459+27459^13706113596Norbert Schneider12/2020
59045*10^113586+57113587Robert Price12/2018
5905(2^377242+2794)/2113561Stefano Morozzi02/2021
59062^377222+93679113556Yves Minet02/2011
5908262147#+316847113552Makoto Morimoto02/2016
590727172^15101+15101^27172113552Hans Havermann01/2021
5909(2^377131+2018)/2113528Stefano Morozzi09/2020
59102^377026-458903113497Enzo Doria04/2015
5911(2^377014+2202)/2113493Stefano Morozzi09/2020
591234791^1828+1828^34791113488Hans Havermann02/2021
5913(2^376967+258)/2113479Stefano Morozzi09/2020
5914(29*10^113468-17)/3113469Robert Price09/2019
591535^73477-34^73477113454Robert Price05/2012
5916(14*10^113451-89)/3113452Robert Price05/2020
59172^376790+27113426Lelio R Paula03/2013
59182^376786-112701113424Enzo Doria06/2014
59192^376731+21113408Lelio R Paula03/2013
59209*10^113394-73113395Robert Price01/2021
592129660^6651+6651^29660113387Hans Havermann01/2021
59232^376634+1871245113379Enzo Doria05/2016
5922(4^188318+17)/3113379Robert Price02/2017
5924E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
59252^376576-344369113361Enzo Doria07/2015
59262^376549-4543113353Yves Minet03/2019
5927(17*2^376526-1)/223113345Lelio R Paula03/2014
5928(27*2^376441-1)/811113319Lelio R Paula03/2014
5929(2^376350+3538)/2113293Stefano Morozzi09/2020
593027265^14272+14272^27265113273Hans Havermann02/2021
593132174^3315+3315^32174113269Hans Havermann02/2021
5932(2*10^113248+73)/3113248Robert Price09/2020
59332^376128-21237113226Enzo Doria06/2013
59345*10^113224-81113225Robert Price01/2019
593510^113220+51409113221Patrick De Geest02/2021
593710^113220-1000001113220Robert Price08/2020
593610^113220-61779113220Patrick De Geest02/2021
5938(2^376102+1578)/2113218Stefano Morozzi09/2020
5939(2^375996+3102)/2113186Stefano Morozzi09/2020
594037258^1091+1091^37258113184Hans Havermann02/2021
5941(94*10^113176+11)/3113178Robert Price04/2020
5942(46*10^113162+521)/9113163Robert Price02/2019
5943(2^375885+3614)/2113153Stefano Morozzi09/2020
5944(2^375873+2006)/2113149Stefano Morozzi09/2020
59453*10^113137+23113138Robert Price03/2022
5946(8*10^113135-269)/9113135Robert Price09/2021
5947(2^375726+694)/2113105Stefano Morozzi09/2020
594826050^21959+21959^26050113100Hans Havermann02/2021
59492^375638-1787171113079Enzo Doria03/2016
5950(2^375563+2178)/2113056Stefano Morozzi09/2020
59512^375537+4847113048Yves Minet02/2011
5952(17^91837+16^91837)/33113000Robert Price08/2013
59535*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
59542^375350-3221112992Yves Minet07/2011
5955(13*2^375306+1)/7112979Lelio R Paula03/2014
59562^375305+76757112979Enzo Doria05/2016
59572^375258+1874989112964Enzo Doria07/2016
5958(29^77237-1)/28112950Robert Price04/2012
595926620^17483+17483^26620112939Hans Havermann01/2021
59602^375154+74959112933Enzo Doria04/2016
5961(266*10^112930-17)/3112932Robert Price07/2020
5962(2^375134+778)/2112927Stefano Morozzi09/2020
5963(85*10^112919+293)/9112920Robert Price12/2019
596429412^6899+6899^29412112907Hans Havermann02/2021
5965(191*10^112903-17)/3112905Robert Price11/2021
5966(2^375022+1210)/2112893Stefano Morozzi09/2020
596725992^22039+22039^25992112889Hans Havermann02/2021
59682^374993-2787163112885Enzo Doria11/2015
5969(697*10^112869+23)/9112871Robert Price04/2021
5970(19*10^112851+377)/9112852Alfred Reich11/2022
597130420^5111+5111^30420112813Hans Havermann02/2021
597213699^27268+27268^13699112800Norbert Schneider12/2020
5973123^53970+2112793Lelio R Paula06/2013
597412308*27^78796+23112790Eric Chen07/2023
597528942^7887+7887^28942112785Hans Havermann01/2021
59762^374640-4685112778Yves Minet05/2019
597712^104501-11112776Riley Fisher12/2023
597857290^93+93^57290112775Hans Havermann01/2021
597913608^27277-27277^13608112758Norbert Schneider12/2022
5980(2^374556+682)/2112753Stefano Morozzi09/2020
5981p(22852)#/2+512112745Robert Price05/2017
5982(11*10^112742-131)/3112743Robert Price09/2018
59832^374441-21049112718Enzo Doria06/2013
59844*10^112706-93112707Robert Price07/2020
5985(2^374321+1)/3112682H.&R. Lifchitz12/2000
5986(2^374213+1766)/2112650Stefano Morozzi09/2020
5987(2^374094+2674)/2112614Stefano Morozzi09/2020
5988(13^101089-1)/12112607Paul Bourdelais03/2010
59893^236011-8828112606Enzo Doria05/2014
599031854^3427+3427^31854112602Hans Havermann02/2021
5991(85*10^112530-373)/9112531Robert Price05/2021
5992(2^373748+1090)/2112510Stefano Morozzi09/2020
5993(2^373727+1806)/2112503Stefano Morozzi01/2021
599427618^11821+11821^27618112479Hans Havermann01/2021
599526343^18580+18580^26343112460Hans Havermann01/2021
599639^70666+2112435Lelio R Paula11/2013
5997(134*10^112400+7)/3112402Robert Price02/2020
5998(2^373365+326)/2112394Stefano Morozzi09/2020
5999(2^373350-7)/3112390Lelio R Paula03/2014
60002^373306-1840931112377Enzo Doria06/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!