PRP Records

Probable Primes Top 10000

(290751 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 ?
729525206!+p(4114)100001Henri Lifchitz09/2005
729625206!-p(5447)100001Henri Lifchitz10/2005
729725206!-p(12402)100001Henri Lifchitz04/2006
729825206!-p(16290)100001Henri Lifchitz09/2006
729925206!-p(19647)100001Henri Lifchitz02/2007
73002^332194+11473100001Henri Lifchitz03/2007
729010^100000+342909100001Milton L. Brown12/2007
729110^100000+346579100001Robert Price04/2012
729210^100000+829767100001Robert Price05/2012
729310^100000+871899100001Robert Price05/2012
729410^100000+1475997100001Robert Price07/2012
728310^100000+1751769100001Robert Price08/2012
728410^100000+2155489100001Robert Price10/2012
728510^100000+2483527100001Robert Price12/2012
728610^100000+2503087100001Robert Price12/2012
728710^100000+2686179100001Robert Price12/2012
728810^100000+2688933100001Robert Price12/2012
728910^100000+3667159100001Robert Price08/2013
726310^100000+15136771100001Robert Price09/2019
726410^100000+15219873100001Robert Price10/2019
726510^100000+15274039100001Robert Price10/2019
726610^100000+15394069100001Robert Price10/2019
726710^100000+15547119100001Robert Price10/2019
726810^100000+15932923100001Robert Price11/2019
726910^100000+16345467100001Robert Price12/2019
727010^100000+16672143100001Robert Price01/2020
727110^100000+16731939100001Robert Price02/2020
727210^100000+16907049100001Robert Price03/2020
727310^100000+17652523100001Robert Price05/2020
727410^100000+18047167100001Robert Price05/2020
727510^100000+18471819100001Robert Price06/2020
727610^100000+18494793100001Robert Price07/2020
727710^100000+18762609100001Robert Price07/2020
727810^100000+19204141100001Robert Price08/2020
727910^100000+19349793100001Robert Price08/2020
728010^100000+19495699100001Robert Price09/2020
728110^100000+19668927100001Robert Price09/2020
728210^100000+19704313100001Robert Price09/2020
725110^100000+22388581100001Robert Price03/2021
725210^100000+22390933100001Robert Price03/2021
725310^100000+22436169100001Robert Price03/2021
725410^100000+22714557100001Robert Price04/2021
725510^100000+22847671100001Robert Price04/2021
725610^100000+23178567100001Robert Price05/2021
725710^100000+23332003100001Robert Price05/2021
725810^100000+23414571100001Robert Price05/2021
725910^100000+23529979100001Robert Price05/2021
726010^100000+23749243100001Robert Price06/2021
726110^100000+23821771100001Robert Price06/2021
726210^100000+24179307100001Robert Price07/2021
730110^99999+309403100000Daniel Heuer01/2004
730210^100000-260199100000Patrick De Geest01/2010
730310^99999-5951199999Patrick De Geest07/2009
730410^99998+23543799999Patrick De Geest02/2020
730510^99998-28658799998Patrick De Geest02/2020
730610^99997+7229799998Patrick De Geest02/2020
730710^99997-40262799997Patrick De Geest02/2020
730810^99996+27985399997Patrick De Geest02/2020
730910^99997-50000000199997Robert Price12/2020
731010^99996-9496199996Patrick De Geest02/2020
731110^99995+5463399996Patrick De Geest02/2020
731210^99995-10142999995Patrick De Geest02/2020
731310^99994+11727199995Patrick De Geest02/2020
731410^99994-45228999994Patrick De Geest02/2020
731510^99993+37131199994Patrick De Geest02/2020
731610^99993-18649199993Patrick De Geest02/2020
731710^99992+1743199993Patrick De Geest02/2020
731810^99992-2860799992Patrick De Geest02/2020
731910^99991+12539199992Patrick De Geest02/2020
732010^99991-20457399991Patrick De Geest02/2020
732110^99990+1389999991Patrick De Geest02/2020
732210^99990-811199990Patrick De Geest02/2020
73232^332141-11307399985Enzo Doria07/2014
73246*10^99979-7999980Robert Price03/2022
7326(3^209561+2)/72810125599978Lelio R Paula09/2013
732523827^15702+15702^2382799978Hans Havermann04/2018
73272^332085+186589799968Enzo Doria03/2016
7328(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
73292^332023+19199949Lelio R Paula02/2011
7330(6271^26321-1)/627099946Serge Batalov06/2022
73317*10^99944+2799945Robert Price11/2020
73322^331938+7114999924Enzo Doria04/2016
73332^331932-7879599922Lelio R Paula09/2016
73342^331921+77199919Lelio R Paula01/2013
7335(3^209419-2)/513275599912Lelio R Paula09/2013
73362^331860-11498999900Enzo Doria05/2015
73372^331746-1165599866Lelio R Paula09/2016
733811^95891-2899861Lelio R Paula08/2016
7339(2^331694-5)/1199849Lelio R Paula10/2013
7340(3^209246+7)/6499834Lelio R Paula09/2013
734125062^9617+9617^2506299823Hans Havermann04/2018
734215^84866-5299811Lelio R Paula08/2016
734313^89600+3099810Lelio R Paula08/2016
73442^331527+10028024506599800Paul Bourdelais10/2021
734522950^22309+22309^2295099798Hans Havermann03/2018
73465^142772-3899794Lelio R Paula08/2016
7347(7482^25759-1)/748199787Serge Batalov06/2022
7348(23*2^331459+1)/47599778Lelio R Paula11/2013
73492^331416-331416+199767Robert Price10/2014
73502^331256-5799718Lelio R Paula12/2012
735128192^3443+3443^2819299714Hans Havermann03/2018
73522^331185+73799697Lelio R Paula01/2013
7353(4*10^99693+149)/999693Robert Price03/2017
73542^331154+188052799688Enzo Doria10/2016
7356(19^77951+1)/2099679Paul Bourdelais03/2010
735524354^12385+12385^2435499679Hans Havermann03/2018
73572^331110+187045999675Enzo Doria05/2016
73585*2^331075+799665Lelio R Paula08/2014
735925776^7351+7351^2577699659Hans Havermann02/2018
7360(16*10^99656-31)/399657Robert Price03/2016
7361(6059^26347-1)/605899652Serge Batalov06/2022
7362(15544^23773-1)/1554399642Serge Batalov06/2022
73642^330968+34599632Lelio R Paula09/2016
7363(2^330969+690)/299632Stefano Morozzi09/2020
73662*5^142528-799624Lelio R Paula11/2014
73652^330942+7732999624Enzo Doria05/2016
736714^86914-9999615Lelio R Paula08/2016
7368(19*2^330902+1)/7799611Lelio R Paula11/2013
736922971^21692+21692^2297199610Hans Havermann03/2018
73702^330845+7168799595Enzo Doria04/2016
7371(26667^22501-1)/2666699585Serge Batalov06/2022
7372(23*2^330770+1)/399573Lelio R Paula11/2013
737324494^11613+11613^2449499567Hans Havermann03/2018
73742^330735+841599562Lelio R Paula09/2016
73752^330720+7407199557Enzo Doria04/2016
7376(10405^24781-1)/1040499548Serge Batalov06/2022
737831^66738-299531Lelio R Paula09/2013
7377(9002^25171-1)/900199531Serge Batalov06/2022
7379(5023^26893-1)/502299527Serge Batalov06/2022
73807*3^208567+499513Lelio R Paula08/2014
7381(15881^23689-1)/1588099511Serge Batalov06/2022
7382(13*10^99508+47)/399509Robert Price01/2017
73832^330553+77999507Lelio R Paula01/2013
738415^84606-9499505Lelio R Paula08/2016
7385(10^99497+173)/399497Robert Price05/2021
73869*10^99493-4399494Robert Price09/2021
73876^127858+4799493Lelio R Paula08/2016
73885^142337+4899490Lelio R Paula08/2016
73897^117724-2099489Lelio R Paula08/2016
7390(559^36209-1)/55899479Serge Batalov06/2022
7391(13470^24091-1)/1346999477Serge Batalov06/2022
7392(29*10^99474-17)/399475Erik Branger09/2014
7393(185*10^99466-11)/399468Robert Price10/2020
7394(2^330410+2038)/299464Stefano Morozzi09/2020
7395(9*2^330407-1)/799463Lelio R Paula03/2014
7396(2863^28771-1)/286299453Serge Batalov06/2022
7397(2^330373+2114)/299452Stefano Morozzi09/2020
7398(68*10^99441+7)/399443Robert Price03/2016
739910^99434+15557199435Patrick De Geest04/2020
740010^99434-12345678999434Robert Price02/2020
740110^99434-19123799434Patrick De Geest04/2020
740246^59791-45^5979199418Jean-Louis Charton01/2013
740323839^14802+14802^2383999417Hans Havermann02/2018
7404(2*10^99408+529)/999408Robert Price01/2017
7405(2^330216+3510)/299405Stefano Morozzi09/2020
740653^57646-299398Lelio R Paula09/2013
74072^330165+187002599390Enzo Doria05/2016
74087*10^99383+9799384Robert Price09/2021
74092^330142-15599383Lelio R Paula12/2012
74102^330088-11525999367Enzo Doria06/2015
741124216^12671+12671^2421699354Hans Havermann01/2018
7412Phi(200548,10)/320876999354Makoto Kamada04/2019
7413(746*10^99303+1)/999305Robert Price02/2017
74143^208107+4099293Lelio R Paula08/2016
7415(3939^27617-1)/393899291Serge Batalov06/2022
7416(5*2^329833-1)/36999288Lelio R Paula02/2014
74178*3^208093+599287Lelio R Paula08/2014
74185^142043+5699284Lelio R Paula08/2016
7419(13*10^99282-157)/999283Robert Price05/2021
7420(10^99284+7)/53/6799281Alfred Reich06/2021
742122*10^99275+799277Robert Price04/2016
74222^329778+187618999274Enzo Doria07/2016
7423(6580^25997-1)/657999259Serge Batalov06/2022
7424(2249^29611-1)/224899253Serge Batalov06/2022
7425(10^99239-13)/399239Robert Price02/2017
7426(1199^32233-1)/119899237Serge Batalov06/2022
74283^207987+6299236Lelio R Paula08/2016
7427(62*10^99235+91)/999236Robert Price07/2021
74292^329638+4999231Lelio R Paula12/2012
74307^117413-1899226Lelio R Paula08/2016
74312^329586-45890399216Enzo Doria04/2015
7432(6290^26119-1)/628999214Serge Batalov06/2022
74342^329553+10199206Lelio R Paula12/2012
7433(21297^22921-1)/2129699206Serge Batalov06/2022
74352^329551-11289799205Enzo Doria06/2014
7436(3^207925+7)/5099204Lelio R Paula09/2013
74376^127458-1799399182Enzo Doria03/2013
743827197^4428+4428^2719799166Hans Havermann10/2017
7439(46*10^99143-1)/999144Robert Price12/2014
74407*10^99133+6999134Robert Price10/2017
7441(21701^22861-1)/2170099132Serge Batalov06/2022
744218^78968-306599127Enzo Doria03/2013
744425927^6654+6654^2592799122Hans Havermann10/2017
744387915!4+1699122Robert Price09/2019
74452^329259+18999117Lelio R Paula12/2012
74468*10^99113+3999114Robert Price01/2017
74476^127364+7799109Lelio R Paula08/2016
7448(82*10^99103+143)/999104Robert Price06/2021
7449(11414^24421-1)/1141399083Serge Batalov06/2022
7450(2^329135+1110)/299080Stefano Morozzi09/2020
7451(22089^22807-1)/2208899074Serge Batalov06/2022
7452(59*10^99069+391)/999070Robert Price03/2021
7453(797*10^99061-41)/999063Robert Price04/2022
74542^329058-28768199057Harrison Mesh06/2022
74556^127285+1399047Lelio R Paula08/2016
7456(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
74572^329007+7328399041Enzo Doria04/2016
74585*3^207543-899024Lelio R Paula08/2014
7459(2^328930+570)/299018Stefano Morozzi09/2020
74602^328885+14999005Lelio R Paula12/2012
746223392^17075+17075^2339299004Hans Havermann09/2017
7461(7424^25579-1)/742399004Serge Batalov06/2022
7463(2^328879-9)/11999001Lelio R Paula10/2013
74645^141618+5498987Lelio R Paula08/2016
74658*10^98982+5198983Robert Price05/2017
7466(21*2^328809-1)/770998979Lelio R Paula03/2014
74672^328794-279760198977Enzo Doria04/2016
7468(88331^20011-1)/8833098972Serge Batalov06/2022
74696^127176+598963Lelio R Paula11/2014
74702*10^98961-2198962Robert Price09/2020
747124262^11989+11989^2426298960Hans Havermann09/2017
7472(60138^20707-1)/6013798958Serge Batalov06/2022
74732^328700-10970998949Enzo Doria04/2014
7474(2^328698+1810)/298948Stefano Morozzi01/2021
7475(1014^32917-1)/101398947Serge Batalov06/2022
747687771!4-12898944Robert Price11/2019
7477(4576^27031-1)/457598943Serge Batalov06/2022
7478(2^328658+3042)/298936Stefano Morozzi09/2020
7479(1933^30103-1)/193298923Serge Batalov06/2022
748046711!2-2^4671198916Robert Price09/2015
74819*7^117037+498909Lelio R Paula11/2014
7482127^47012+12698905Norbert Schneider01/2019
7483(93826^19891-1)/9382598900Serge Batalov06/2022
7484(2^328525+1250)/298896Stefano Morozzi09/2020
7485(10^98890+149)/398890Serge Batalov12/2014
748622775^21978+21978^2277598889Hans Havermann08/2017
74872^328497-21693398888Enzo Doria05/2014
74882^328487+3276998885Lelio R Paula08/2016
74893^207250-11235898884Enzo Doria06/2014
749013^88754-9098867Lelio R Paula08/2016
74912^328406+70998861Lelio R Paula02/2013
74922*10^98860-2198861Robert Price09/2020
7493(17*2^328413-1)/1617398860Lelio R Paula03/2014
74947^116976+7698857Lelio R Paula08/2016
7495(2^328378+2710)/298852Stefano Morozzi09/2020
7496(25411^22441-1)/2541098849Serge Batalov06/2022
7497(18668^23143-1)/1866798842Serge Batalov06/2022
74992^328335+115598839Lelio R Paula08/2016
74982^328333-34900398839Harrison Mesh06/2022
7500287^40210+40210^28798832Norbert Schneider11/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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