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 ?
502925206!+p(4114)100001Henri Lifchitz09/2005
503025206!-p(5447)100001Henri Lifchitz10/2005
503125206!-p(12402)100001Henri Lifchitz04/2006
503225206!-p(16290)100001Henri Lifchitz09/2006
503325206!-p(19647)100001Henri Lifchitz02/2007
50342^332194+11473100001Henri Lifchitz03/2007
502410^100000+342909100001Milton L. Brown12/2007
502510^100000+346579100001Robert Price04/2012
502610^100000+829767100001Robert Price05/2012
502710^100000+871899100001Robert Price05/2012
502810^100000+1475997100001Robert Price07/2012
501710^100000+1751769100001Robert Price08/2012
501810^100000+2155489100001Robert Price10/2012
501910^100000+2483527100001Robert Price12/2012
502010^100000+2503087100001Robert Price12/2012
502110^100000+2686179100001Robert Price12/2012
502210^100000+2688933100001Robert Price12/2012
502310^100000+3667159100001Robert Price08/2013
500410^100000+7867333100001Robert Price12/2016
500510^100000+8743093100001Robert Price02/2017
500610^100000+8955391100001Robert Price03/2017
500710^100000+9180019100001Robert Price03/2017
500810^100000+9225987100001Robert Price04/2017
500910^100000+9265587100001Robert Price04/2017
501010^100000+9287049100001Robert Price04/2017
501110^100000+9425053100001Robert Price05/2017
501210^100000+9450769100001Robert Price05/2017
501310^100000+9528747100001Robert Smith05/2017
501410^100000+9548071100001Robert Price06/2017
501510^100000+10064287100001Robert Price08/2017
501610^100000+10229569100001Robert Price10/2017
500110^100000+19495699100001Robert Price09/2020
500210^100000+19668927100001Robert Price09/2020
500310^100000+19704313100001Robert Price09/2020
503510^99999+309403100000Daniel Heuer01/2004
503610^100000-260199100000Patrick De Geest01/2010
503710^99999-5951199999Patrick De Geest07/2009
503810^99998+23543799999Patrick De Geest02/2020
503910^99998-28658799998Patrick De Geest02/2020
504010^99997+7229799998Patrick De Geest02/2020
504110^99997-40262799997Patrick De Geest02/2020
504210^99996+27985399997Patrick De Geest02/2020
504310^99997-50000000199997Robert Price12/2020
504410^99996-9496199996Patrick De Geest02/2020
504510^99995+5463399996Patrick De Geest02/2020
504610^99995-10142999995Patrick De Geest02/2020
504710^99994+11727199995Patrick De Geest02/2020
504810^99994-45228999994Patrick De Geest02/2020
504910^99993+37131199994Patrick De Geest02/2020
505010^99993-18649199993Patrick De Geest02/2020
505110^99992+1743199993Patrick De Geest02/2020
505210^99992-2860799992Patrick De Geest02/2020
505310^99991+12539199992Patrick De Geest02/2020
505410^99991-20457399991Patrick De Geest02/2020
505510^99990+1389999991Patrick De Geest02/2020
505610^99990-811199990Patrick De Geest02/2020
50572^332141-11307399985Enzo Doria07/2014
5059(3^209561+2)/72810125599978Lelio R Paula09/2013
505823827^15702+15702^2382799978Hans Havermann04/2018
50602^332085+186589799968Enzo Doria03/2016
5061(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
50622^332023+19199949Lelio R Paula02/2011
50637*10^99944+2799945Robert Price11/2020
50642^331938+7114999924Enzo Doria04/2016
50652^331932-7879599922Lelio R Paula09/2016
50662^331921+77199919Lelio R Paula01/2013
5067(3^209419-2)/513275599912Lelio R Paula09/2013
50682^331860-11498999900Enzo Doria05/2015
50692^331746-1165599866Lelio R Paula09/2016
507011^95891-2899861Lelio R Paula08/2016
5071(2^331694-5)/1199849Lelio R Paula10/2013
5072(3^209246+7)/6499834Lelio R Paula09/2013
507325062^9617+9617^2506299823Hans Havermann04/2018
507415^84866-5299811Lelio R Paula08/2016
507513^89600+3099810Lelio R Paula08/2016
507622950^22309+22309^2295099798Hans Havermann03/2018
50775^142772-3899794Lelio R Paula08/2016
5078(23*2^331459+1)/47599778Lelio R Paula11/2013
50792^331416-331416+199767Robert Price10/2014
50802^331256-5799718Lelio R Paula12/2012
508128192^3443+3443^2819299714Hans Havermann03/2018
50822^331185+73799697Lelio R Paula01/2013
5083(4*10^99693+149)/999693Robert Price03/2017
50842^331154+188052799688Enzo Doria10/2016
5086(19^77951+1)/2099679Paul Bourdelais03/2010
508524354^12385+12385^2435499679Hans Havermann03/2018
50872^331110+187045999675Enzo Doria05/2016
50885*2^331075+799665Lelio R Paula08/2014
508925776^7351+7351^2577699659Hans Havermann02/2018
5090(16*10^99656-31)/399657Robert Price03/2016
50912^330968+34599632Lelio R Paula09/2016
5092(2^330969+690)/299632Stefano Morozzi09/2020
50932*5^142528-799624Lelio R Paula11/2014
50942^330942+7732999624Enzo Doria05/2016
509514^86914-9999615Lelio R Paula08/2016
5096(19*2^330902+1)/7799611Lelio R Paula11/2013
509722971^21692+21692^2297199610Hans Havermann03/2018
50982^330845+7168799595Enzo Doria04/2016
5099(23*2^330770+1)/399573Lelio R Paula11/2013
510024494^11613+11613^2449499567Hans Havermann03/2018
51012^330735+841599562Lelio R Paula09/2016
51022^330720+7407199557Enzo Doria04/2016
510331^66738-299531Lelio R Paula09/2013
51047*3^208567+499513Lelio R Paula08/2014
5105(13*10^99508+47)/399509Robert Price01/2017
51062^330553+77999507Lelio R Paula01/2013
510715^84606-9499505Lelio R Paula08/2016
51086^127858+4799493Lelio R Paula08/2016
51095^142337+4899490Lelio R Paula08/2016
51107^117724-2099489Lelio R Paula08/2016
5111(29*10^99474-17)/399475Erik Branger09/2014
5112(185*10^99466-11)/399468Robert Price10/2020
5113(2^330410+2038)/299464Stefano Morozzi09/2020
5114(9*2^330407-1)/799463Lelio R Paula03/2014
5115(2^330373+2114)/299452Stefano Morozzi09/2020
5116(68*10^99441+7)/399443Robert Price03/2016
511710^99434+15557199435Patrick De Geest04/2020
511810^99434-12345678999434Robert Price02/2020
511910^99434-19123799434Patrick De Geest04/2020
512046^59791-45^5979199418Jean-Louis Charton01/2013
512123839^14802+14802^2383999417Hans Havermann02/2018
5122(2*10^99408+529)/999408Robert Price01/2017
5123(2^330216+3510)/299405Stefano Morozzi09/2020
512453^57646-299398Lelio R Paula09/2013
51252^330165+187002599390Enzo Doria05/2016
51262^330142-15599383Lelio R Paula12/2012
51272^330088-11525999367Enzo Doria06/2015
512824216^12671+12671^2421699354Hans Havermann01/2018
5129Phi(200548,10)/320876999354Makoto Kamada04/2019
5130(746*10^99303+1)/999305Robert Price02/2017
51313^208107+4099293Lelio R Paula08/2016
5132(5*2^329833-1)/36999288Lelio R Paula02/2014
51338*3^208093+599287Lelio R Paula08/2014
51345^142043+5699284Lelio R Paula08/2016
513522*10^99275+799277Robert Price04/2016
51362^329778+187618999274Enzo Doria07/2016
5137(10^99239-13)/399239Robert Price02/2017
51383^207987+6299236Lelio R Paula08/2016
51392^329638+4999231Lelio R Paula12/2012
51407^117413-1899226Lelio R Paula08/2016
51412^329586-45890399216Enzo Doria04/2015
51422^329553+10199206Lelio R Paula12/2012
51432^329551-11289799205Enzo Doria06/2014
5144(3^207925+7)/5099204Lelio R Paula09/2013
51456^127458-1799399182Enzo Doria03/2013
514627197^4428+4428^2719799166Hans Havermann10/2017
5147(46*10^99143-1)/999144Robert Price12/2014
51487*10^99133+6999134Robert Price10/2017
514918^78968-306599127Enzo Doria03/2013
515125927^6654+6654^2592799122Hans Havermann10/2017
515087915!4+1699122Robert Price09/2019
51522^329259+18999117Lelio R Paula12/2012
51538*10^99113+3999114Robert Price01/2017
51546^127364+7799109Lelio R Paula08/2016
5155(2^329135+1110)/299080Stefano Morozzi09/2020
51566^127285+1399047Lelio R Paula08/2016
5157(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
51582^329007+7328399041Enzo Doria04/2016
51595*3^207543-899024Lelio R Paula08/2014
5160(2^328930+570)/299018Stefano Morozzi09/2020
51612^328885+14999005Lelio R Paula12/2012
516223392^17075+17075^2339299004Hans Havermann09/2017
5163(2^328879-9)/11999001Lelio R Paula10/2013
51645^141618+5498987Lelio R Paula08/2016
51658*10^98982+5198983Robert Price05/2017
5166(21*2^328809-1)/770998979Lelio R Paula03/2014
51672^328794-279760198977Enzo Doria04/2016
51686^127176+598963Lelio R Paula11/2014
51692*10^98961-2198962Robert Price09/2020
517024262^11989+11989^2426298960Hans Havermann09/2017
51712^328700-10970998949Enzo Doria04/2014
5172(2^328698+1810)/298948Stefano Morozzi01/2021
517387771!4-12898944Robert Price11/2019
5174(2^328658+3042)/298936Stefano Morozzi09/2020
517546711!2-2^4671198916Robert Price09/2015
51769*7^117037+498909Lelio R Paula11/2014
5177127^47012+12698905Norbert Schneider01/2019
5178(2^328525+1250)/298896Stefano Morozzi09/2020
5179(10^98890+149)/398890Serge Batalov12/2014
518022775^21978+21978^2277598889Hans Havermann08/2017
51812^328497-21693398888Enzo Doria05/2014
51822^328487+3276998885Lelio R Paula08/2016
51833^207250-11235898884Enzo Doria06/2014
518413^88754-9098867Lelio R Paula08/2016
51862^328406+70998861Lelio R Paula02/2013
51852*10^98860-2198861Robert Price09/2020
5187(17*2^328413-1)/1617398860Lelio R Paula03/2014
51887^116976+7698857Lelio R Paula08/2016
5189(2^328378+2710)/298852Stefano Morozzi09/2020
51902^328335+115598839Lelio R Paula08/2016
5192(3*2^328311+1)/598832Lelio R Paula11/2013
5191287^40210+40210^28798832Norbert Schneider11/2014
5193(2^328284+9)/132598821Lelio R Paula10/2013
5194(21*2^328258+1)/212598814Lelio R Paula11/2013
519524746^9825+9825^2474698795Hans Havermann07/2020
519626620^5143+5143^2662098793Hans Havermann07/2020
519765^54491+4898788Lelio R Paula04/2016
51983^207042+9898785Lelio R Paula08/2016
5199(2^328121+3110)/298774Stefano Morozzi09/2020
52013^206977-11275698754Enzo Doria07/2014
520010^98754-4000000000198754Robert Price09/2020
52027^116846-5098747Lelio R Paula08/2016
520323267^17512+17512^2326798730Hans Havermann04/2020
52042^327967-2863598728Lelio R Paula08/2016
5205707^34642+34642^70798710Norbert Schneider12/2017
52066^126850-4798709Lelio R Paula08/2016
5207(2^327886+2170)/298704Stefano Morozzi09/2020
52088*6^126830-798694Lelio R Paula11/2014
520911^94770-27098693Enzo Doria08/2012
5210(2^327846+3250)/298692Stefano Morozzi01/2021
52112^327832+4398688Lelio R Paula12/2012
52122^327795+76198677Lelio R Paula02/2013
5213(2^327796+1522)/298677Stefano Morozzi09/2020
521410^98669+14741198670Patrick De Geest11/2016
521610^98669-9^(98669-1)98669Robert Price05/2016
521510^98669-10524998669Patrick De Geest11/2016
52172^327671-10980198639Enzo Doria04/2014
521824398^11037+11037^2439898638Hans Havermann10/2019
52195^141090-1498618Lelio R Paula08/2016
522020^75799+4798617Lelio R Paula08/2016
522128101^3226+3226^2810198597Hans Havermann07/2020
52222^327515-101798592Lelio R Paula08/2016
52236^126692+9768198586Mike Oakes04/2011
52242^327467-74198578Lelio R Paula08/2016
522522713^21800+21800^2271398540Hans Havermann05/2020
5226(2^327329+9)/1998535Lelio R Paula10/2013
52277^116577-6698519Lelio R Paula08/2016
5229(3*2^327250+1)/798512Lelio R Paula11/2013
522823220^17479+17479^2322098512Hans Havermann03/2020
5230(19*2^327192+1)/27598494Lelio R Paula11/2013
52312^327162-6694598486Lelio R Paula08/2016
523230139^1852+1852^3013998484Hans Havermann02/2020
523323182^17703+17703^2318298479Hans Havermann01/2020
52344*10^98472-398473Erik Branger11/2013
523526167^5794+5794^2616798466Hans Havermann01/2020
5236(6883*2^327047-1)/7798453Lelio R Paula05/2015
5237(71*10^98446+1)/998447Serge Batalov11/2010
523813^88363+9498432Lelio R Paula08/2016
523948^58543-47^5854398425Jean-Louis Charton11/2005
52406^126481+4198422Lelio R Paula08/2016
524178*10^98413-798415Robert Price05/2017
524222634^22263+22263^2263498404Hans Havermann07/2020
52437^116416+4698383Lelio R Paula08/2016
52447^116407-2498376Lelio R Paula07/2016
5245439^37228+37228^43998374Norbert Schneider08/2018
52472^326782-186067198372Enzo Doria03/2016
524617^79948+5898372Lelio R Paula08/2016
524822499^22602-22602^2249998368Norbert Schneider08/2020
52493^206143-9898356Lelio R Paula08/2016
52508*5^140705+798350Lelio R Paula11/2014


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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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