PRP Records

Probable Primes Top 10000

(280932 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 ?
551025206!+p(4114)100001Henri Lifchitz09/2005
551125206!-p(5447)100001Henri Lifchitz10/2005
551225206!-p(12402)100001Henri Lifchitz04/2006
551325206!-p(16290)100001Henri Lifchitz09/2006
551425206!-p(19647)100001Henri Lifchitz02/2007
55152^332194+11473100001Henri Lifchitz03/2007
550510^100000+342909100001Milton L. Brown12/2007
550610^100000+346579100001Robert Price04/2012
550710^100000+829767100001Robert Price05/2012
550810^100000+871899100001Robert Price05/2012
550910^100000+1475997100001Robert Price07/2012
550110^100000+2503087100001Robert Price12/2012
550210^100000+2686179100001Robert Price12/2012
550310^100000+2688933100001Robert Price12/2012
550410^100000+3667159100001Robert Price08/2013
551610^99999+309403100000Daniel Heuer01/2004
551710^100000-260199100000Patrick De Geest01/2010
551810^99999-5951199999Patrick De Geest07/2009
551910^99998+23543799999Patrick De Geest02/2020
552010^99998-28658799998Patrick De Geest02/2020
552110^99997+7229799998Patrick De Geest02/2020
552210^99997-40262799997Patrick De Geest02/2020
552310^99996+27985399997Patrick De Geest02/2020
552410^99997-50000000199997Robert Price12/2020
552510^99996-9496199996Patrick De Geest02/2020
552610^99995+5463399996Patrick De Geest02/2020
552710^99995-10142999995Patrick De Geest02/2020
552810^99994+11727199995Patrick De Geest02/2020
552910^99994-45228999994Patrick De Geest02/2020
553010^99993+37131199994Patrick De Geest02/2020
553110^99993-18649199993Patrick De Geest02/2020
553210^99992+1743199993Patrick De Geest02/2020
553310^99992-2860799992Patrick De Geest02/2020
553410^99991+12539199992Patrick De Geest02/2020
553510^99991-20457399991Patrick De Geest02/2020
553610^99990+1389999991Patrick De Geest02/2020
553710^99990-811199990Patrick De Geest02/2020
55382^332141-11307399985Enzo Doria07/2014
5540(3^209561+2)/72810125599978Lelio R Paula09/2013
553923827^15702+15702^2382799978Hans Havermann04/2018
55412^332085+186589799968Enzo Doria03/2016
5542(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
55432^332023+19199949Lelio R Paula02/2011
55447*10^99944+2799945Robert Price11/2020
55452^331938+7114999924Enzo Doria04/2016
55462^331932-7879599922Lelio R Paula09/2016
55472^331921+77199919Lelio R Paula01/2013
5548(3^209419-2)/513275599912Lelio R Paula09/2013
55492^331860-11498999900Enzo Doria05/2015
55502^331746-1165599866Lelio R Paula09/2016
555111^95891-2899861Lelio R Paula08/2016
5552(2^331694-5)/1199849Lelio R Paula10/2013
5553(3^209246+7)/6499834Lelio R Paula09/2013
555425062^9617+9617^2506299823Hans Havermann04/2018
555515^84866-5299811Lelio R Paula08/2016
555613^89600+3099810Lelio R Paula08/2016
555722950^22309+22309^2295099798Hans Havermann03/2018
55585^142772-3899794Lelio R Paula08/2016
5559(23*2^331459+1)/47599778Lelio R Paula11/2013
55602^331416-331416+199767Robert Price10/2014
55612^331256-5799718Lelio R Paula12/2012
556228192^3443+3443^2819299714Hans Havermann03/2018
55632^331185+73799697Lelio R Paula01/2013
5564(4*10^99693+149)/999693Robert Price03/2017
55652^331154+188052799688Enzo Doria10/2016
5567(19^77951+1)/2099679Paul Bourdelais03/2010
556624354^12385+12385^2435499679Hans Havermann03/2018
55682^331110+187045999675Enzo Doria05/2016
55695*2^331075+799665Lelio R Paula08/2014
557025776^7351+7351^2577699659Hans Havermann02/2018
5571(16*10^99656-31)/399657Robert Price03/2016
55732^330968+34599632Lelio R Paula09/2016
5572(2^330969+690)/299632Stefano Morozzi09/2020
55752*5^142528-799624Lelio R Paula11/2014
55742^330942+7732999624Enzo Doria05/2016
557614^86914-9999615Lelio R Paula08/2016
5577(19*2^330902+1)/7799611Lelio R Paula11/2013
557822971^21692+21692^2297199610Hans Havermann03/2018
55792^330845+7168799595Enzo Doria04/2016
5580(23*2^330770+1)/399573Lelio R Paula11/2013
558124494^11613+11613^2449499567Hans Havermann03/2018
55822^330735+841599562Lelio R Paula09/2016
55832^330720+7407199557Enzo Doria04/2016
558431^66738-299531Lelio R Paula09/2013
55857*3^208567+499513Lelio R Paula08/2014
5586(13*10^99508+47)/399509Robert Price01/2017
55872^330553+77999507Lelio R Paula01/2013
558815^84606-9499505Lelio R Paula08/2016
55896^127858+4799493Lelio R Paula08/2016
55905^142337+4899490Lelio R Paula08/2016
55917^117724-2099489Lelio R Paula08/2016
5592(29*10^99474-17)/399475Erik Branger09/2014
5593(185*10^99466-11)/399468Robert Price10/2020
5594(2^330410+2038)/299464Stefano Morozzi09/2020
5595(9*2^330407-1)/799463Lelio R Paula03/2014
5596(2^330373+2114)/299452Stefano Morozzi09/2020
5597(68*10^99441+7)/399443Robert Price03/2016
559810^99434+15557199435Patrick De Geest04/2020
559910^99434-12345678999434Robert Price02/2020
560010^99434-19123799434Patrick De Geest04/2020
560146^59791-45^5979199418Jean-Louis Charton01/2013
560223839^14802+14802^2383999417Hans Havermann02/2018
5603(2*10^99408+529)/999408Robert Price01/2017
5604(2^330216+3510)/299405Stefano Morozzi09/2020
560553^57646-299398Lelio R Paula09/2013
56062^330165+187002599390Enzo Doria05/2016
56072^330142-15599383Lelio R Paula12/2012
56082^330088-11525999367Enzo Doria06/2015
561024216^12671+12671^2421699354Hans Havermann01/2018
5609Phi(200548,10)/320876999354Makoto Kamada04/2019
5611(746*10^99303+1)/999305Robert Price02/2017
56123^208107+4099293Lelio R Paula08/2016
5613(5*2^329833-1)/36999288Lelio R Paula02/2014
56148*3^208093+599287Lelio R Paula08/2014
56155^142043+5699284Lelio R Paula08/2016
561622*10^99275+799277Robert Price04/2016
56172^329778+187618999274Enzo Doria07/2016
5618(10^99239-13)/399239Robert Price02/2017
56193^207987+6299236Lelio R Paula08/2016
56202^329638+4999231Lelio R Paula12/2012
56217^117413-1899226Lelio R Paula08/2016
56222^329586-45890399216Enzo Doria04/2015
56232^329553+10199206Lelio R Paula12/2012
56242^329551-11289799205Enzo Doria06/2014
5625(3^207925+7)/5099204Lelio R Paula09/2013
56266^127458-1799399182Enzo Doria03/2013
562727197^4428+4428^2719799166Hans Havermann10/2017
5628(46*10^99143-1)/999144Robert Price12/2014
56297*10^99133+6999134Robert Price10/2017
563018^78968-306599127Enzo Doria03/2013
563125927^6654+6654^2592799122Hans Havermann10/2017
563287915!4+1699122Robert Price09/2019
56332^329259+18999117Lelio R Paula12/2012
56348*10^99113+3999114Robert Price01/2017
56356^127364+7799109Lelio R Paula08/2016
5636(2^329135+1110)/299080Stefano Morozzi09/2020
5637(59*10^99069+391)/999070Robert Price03/2021
56386^127285+1399047Lelio R Paula08/2016
5639(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
56402^329007+7328399041Enzo Doria04/2016
56415*3^207543-899024Lelio R Paula08/2014
5642(2^328930+570)/299018Stefano Morozzi09/2020
56432^328885+14999005Lelio R Paula12/2012
564423392^17075+17075^2339299004Hans Havermann09/2017
5645(2^328879-9)/11999001Lelio R Paula10/2013
56465^141618+5498987Lelio R Paula08/2016
56478*10^98982+5198983Robert Price05/2017
5648(21*2^328809-1)/770998979Lelio R Paula03/2014
56492^328794-279760198977Enzo Doria04/2016
56506^127176+598963Lelio R Paula11/2014
56512*10^98961-2198962Robert Price09/2020
565224262^11989+11989^2426298960Hans Havermann09/2017
56532^328700-10970998949Enzo Doria04/2014
5654(2^328698+1810)/298948Stefano Morozzi01/2021
565587771!4-12898944Robert Price11/2019
5656(2^328658+3042)/298936Stefano Morozzi09/2020
565746711!2-2^4671198916Robert Price09/2015
56589*7^117037+498909Lelio R Paula11/2014
5659127^47012+12698905Norbert Schneider01/2019
5660(2^328525+1250)/298896Stefano Morozzi09/2020
5661(10^98890+149)/398890Serge Batalov12/2014
566222775^21978+21978^2277598889Hans Havermann08/2017
56632^328497-21693398888Enzo Doria05/2014
56642^328487+3276998885Lelio R Paula08/2016
56653^207250-11235898884Enzo Doria06/2014
566613^88754-9098867Lelio R Paula08/2016
56682^328406+70998861Lelio R Paula02/2013
56672*10^98860-2198861Robert Price09/2020
5669(17*2^328413-1)/1617398860Lelio R Paula03/2014
56707^116976+7698857Lelio R Paula08/2016
5671(2^328378+2710)/298852Stefano Morozzi09/2020
56722^328335+115598839Lelio R Paula08/2016
5674(3*2^328311+1)/598832Lelio R Paula11/2013
5673287^40210+40210^28798832Norbert Schneider11/2014
5675(2^328284+9)/132598821Lelio R Paula10/2013
5676(21*2^328258+1)/212598814Lelio R Paula11/2013
567724746^9825+9825^2474698795Hans Havermann07/2020
567826620^5143+5143^2662098793Hans Havermann07/2020
567965^54491+4898788Lelio R Paula04/2016
56803^207042+9898785Lelio R Paula08/2016
5681(2^328121+3110)/298774Stefano Morozzi09/2020
568210^98754+7338398755Patrick De Geest02/2021
56843^206977-11275698754Enzo Doria07/2014
568510^98754-4000000000198754Robert Price09/2020
568310^98754-16934398754Patrick De Geest02/2021
56867^116846-5098747Lelio R Paula08/2016
568723267^17512+17512^2326798730Hans Havermann04/2020
56882^327967-2863598728Lelio R Paula08/2016
5689707^34642+34642^70798710Norbert Schneider12/2017
56906^126850-4798709Lelio R Paula08/2016
5691(2^327886+2170)/298704Stefano Morozzi09/2020
56928*6^126830-798694Lelio R Paula11/2014
569311^94770-27098693Enzo Doria08/2012
5694(2^327846+3250)/298692Stefano Morozzi01/2021
56952^327832+4398688Lelio R Paula12/2012
56962^327795+76198677Lelio R Paula02/2013
5697(2^327796+1522)/298677Stefano Morozzi09/2020
569810^98669+14741198670Patrick De Geest11/2016
570010^98669-9^(98669-1)98669Robert Price05/2016
569910^98669-10524998669Patrick De Geest11/2016
57012^327671-10980198639Enzo Doria04/2014
570224398^11037+11037^2439898638Hans Havermann10/2019
57035^141090-1498618Lelio R Paula08/2016
570420^75799+4798617Lelio R Paula08/2016
570528101^3226+3226^2810198597Hans Havermann07/2020
57062^327515-101798592Lelio R Paula08/2016
57076^126692+9768198586Mike Oakes04/2011
57082^327467-74198578Lelio R Paula08/2016
570922713^21800+21800^2271398540Hans Havermann05/2020
5710(2^327329+9)/1998535Lelio R Paula10/2013
57117^116577-6698519Lelio R Paula08/2016
5713(3*2^327250+1)/798512Lelio R Paula11/2013
571223220^17479+17479^2322098512Hans Havermann03/2020
5714(2^327240+3798)/298509Stefano Morozzi02/2021
5715(19*2^327192+1)/27598494Lelio R Paula11/2013
57162^327162-6694598486Lelio R Paula08/2016
571730139^1852+1852^3013998484Hans Havermann02/2020
571823182^17703+17703^2318298479Hans Havermann01/2020
57194*10^98472-398473Erik Branger11/2013
572026167^5794+5794^2616798466Hans Havermann01/2020
5721(6883*2^327047-1)/7798453Lelio R Paula05/2015
5722(71*10^98446+1)/998447Serge Batalov11/2010
572313^88363+9498432Lelio R Paula08/2016
572448^58543-47^5854398425Jean-Louis Charton11/2005
57256^126481+4198422Lelio R Paula08/2016
572678*10^98413-798415Robert Price05/2017
572722634^22263+22263^2263498404Hans Havermann07/2020
57287^116416+4698383Lelio R Paula08/2016
57297^116407-2498376Lelio R Paula07/2016
5730439^37228+37228^43998374Norbert Schneider08/2018
57322^326782-186067198372Enzo Doria03/2016
573117^79948+5898372Lelio R Paula08/2016
573322499^22602-22602^2249998368Norbert Schneider08/2020
57343^206143-9898356Lelio R Paula08/2016
57358*5^140705+798350Lelio R Paula11/2014
5736(2^326632+1662)/298326Stefano Morozzi09/2020
57372^326585+1198312Lelio R Paula12/2012
57382^326582-45916198311Enzo Doria05/2015
5740(2^326548+9)/598301Lelio R Paula10/2013
5739(2^326549+18)/1098301Stefano Morozzi03/2020
57412^326538+7165998298Enzo Doria04/2016
5742(2^326520+2082)/298293Stefano Morozzi09/2020
5743(2^326521+1002)/298293Stefano Morozzi09/2020
574415^83575-5898292Lelio R Paula08/2016
574510^98288+398289Robert Price03/2011
574610^98288-11701798288Patrick De Geest11/2011
5747(44*10^98284-719)/998285Robert Price12/2017
574823466^15419+15419^2346698277Hans Havermann02/2020
57492^326421-279757398263Enzo Doria04/2016
57502^326401+1609598257Lelio R Paula07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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