PRP Records

Probable Primes Top 10000

(288949 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 ?
650110^99992-2860799992Patrick De Geest02/2020
650210^99991+12539199992Patrick De Geest02/2020
650310^99991-20457399991Patrick De Geest02/2020
650410^99990+1389999991Patrick De Geest02/2020
650510^99990-811199990Patrick De Geest02/2020
65062^332141-11307399985Enzo Doria07/2014
6508(3^209561+2)/72810125599978Lelio R Paula09/2013
650723827^15702+15702^2382799978Hans Havermann04/2018
65092^332085+186589799968Enzo Doria03/2016
6510(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
65112^332023+19199949Lelio R Paula02/2011
65127*10^99944+2799945Robert Price11/2020
65132^331938+7114999924Enzo Doria04/2016
65142^331932-7879599922Lelio R Paula09/2016
65152^331921+77199919Lelio R Paula01/2013
6516(3^209419-2)/513275599912Lelio R Paula09/2013
65172^331860-11498999900Enzo Doria05/2015
65182^331746-1165599866Lelio R Paula09/2016
651911^95891-2899861Lelio R Paula08/2016
6520(2^331694-5)/1199849Lelio R Paula10/2013
6521(3^209246+7)/6499834Lelio R Paula09/2013
652225062^9617+9617^2506299823Hans Havermann04/2018
652315^84866-5299811Lelio R Paula08/2016
652413^89600+3099810Lelio R Paula08/2016
65252^331527+10028024506599800Paul Bourdelais10/2021
652622950^22309+22309^2295099798Hans Havermann03/2018
65275^142772-3899794Lelio R Paula08/2016
6528(23*2^331459+1)/47599778Lelio R Paula11/2013
65292^331416-331416+199767Robert Price10/2014
65302^331256-5799718Lelio R Paula12/2012
653128192^3443+3443^2819299714Hans Havermann03/2018
65322^331185+73799697Lelio R Paula01/2013
6533(4*10^99693+149)/999693Robert Price03/2017
65342^331154+188052799688Enzo Doria10/2016
6536(19^77951+1)/2099679Paul Bourdelais03/2010
653524354^12385+12385^2435499679Hans Havermann03/2018
65372^331110+187045999675Enzo Doria05/2016
65385*2^331075+799665Lelio R Paula08/2014
653925776^7351+7351^2577699659Hans Havermann02/2018
6540(16*10^99656-31)/399657Robert Price03/2016
65412^330968+34599632Lelio R Paula09/2016
6542(2^330969+690)/299632Stefano Morozzi09/2020
65442*5^142528-799624Lelio R Paula11/2014
65432^330942+7732999624Enzo Doria05/2016
654514^86914-9999615Lelio R Paula08/2016
6546(19*2^330902+1)/7799611Lelio R Paula11/2013
654722971^21692+21692^2297199610Hans Havermann03/2018
65482^330845+7168799595Enzo Doria04/2016
6549(23*2^330770+1)/399573Lelio R Paula11/2013
655024494^11613+11613^2449499567Hans Havermann03/2018
65512^330735+841599562Lelio R Paula09/2016
65522^330720+7407199557Enzo Doria04/2016
655331^66738-299531Lelio R Paula09/2013
65547*3^208567+499513Lelio R Paula08/2014
6555(13*10^99508+47)/399509Robert Price01/2017
65562^330553+77999507Lelio R Paula01/2013
655715^84606-9499505Lelio R Paula08/2016
6558(10^99497+173)/399497Robert Price05/2021
65599*10^99493-4399494Robert Price09/2021
65606^127858+4799493Lelio R Paula08/2016
65615^142337+4899490Lelio R Paula08/2016
65627^117724-2099489Lelio R Paula08/2016
6563(29*10^99474-17)/399475Erik Branger09/2014
6564(185*10^99466-11)/399468Robert Price10/2020
6565(2^330410+2038)/299464Stefano Morozzi09/2020
6566(9*2^330407-1)/799463Lelio R Paula03/2014
6567(2^330373+2114)/299452Stefano Morozzi09/2020
6568(68*10^99441+7)/399443Robert Price03/2016
656910^99434+15557199435Patrick De Geest04/2020
657010^99434-12345678999434Robert Price02/2020
657110^99434-19123799434Patrick De Geest04/2020
657246^59791-45^5979199418Jean-Louis Charton01/2013
657323839^14802+14802^2383999417Hans Havermann02/2018
6574(2*10^99408+529)/999408Robert Price01/2017
6575(2^330216+3510)/299405Stefano Morozzi09/2020
657653^57646-299398Lelio R Paula09/2013
65772^330165+187002599390Enzo Doria05/2016
65787*10^99383+9799384Robert Price09/2021
65792^330142-15599383Lelio R Paula12/2012
65802^330088-11525999367Enzo Doria06/2015
658124216^12671+12671^2421699354Hans Havermann01/2018
6582Phi(200548,10)/320876999354Makoto Kamada04/2019
6583(746*10^99303+1)/999305Robert Price02/2017
65843^208107+4099293Lelio R Paula08/2016
6585(5*2^329833-1)/36999288Lelio R Paula02/2014
65868*3^208093+599287Lelio R Paula08/2014
65875^142043+5699284Lelio R Paula08/2016
6588(13*10^99282-157)/999283Robert Price05/2021
6589(10^99284+7)/53/6799281Alfred Reich06/2021
659022*10^99275+799277Robert Price04/2016
65912^329778+187618999274Enzo Doria07/2016
6592(10^99239-13)/399239Robert Price02/2017
65933^207987+6299236Lelio R Paula08/2016
6594(62*10^99235+91)/999236Robert Price07/2021
65952^329638+4999231Lelio R Paula12/2012
65967^117413-1899226Lelio R Paula08/2016
65972^329586-45890399216Enzo Doria04/2015
65982^329553+10199206Lelio R Paula12/2012
65992^329551-11289799205Enzo Doria06/2014
6600(3^207925+7)/5099204Lelio R Paula09/2013
66016^127458-1799399182Enzo Doria03/2013
660227197^4428+4428^2719799166Hans Havermann10/2017
6603(46*10^99143-1)/999144Robert Price12/2014
66047*10^99133+6999134Robert Price10/2017
660518^78968-306599127Enzo Doria03/2013
660625927^6654+6654^2592799122Hans Havermann10/2017
660787915!4+1699122Robert Price09/2019
66082^329259+18999117Lelio R Paula12/2012
66098*10^99113+3999114Robert Price01/2017
66106^127364+7799109Lelio R Paula08/2016
6611(82*10^99103+143)/999104Robert Price06/2021
6612(2^329135+1110)/299080Stefano Morozzi09/2020
6613(59*10^99069+391)/999070Robert Price03/2021
66146^127285+1399047Lelio R Paula08/2016
6615(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
66162^329007+7328399041Enzo Doria04/2016
66175*3^207543-899024Lelio R Paula08/2014
6618(2^328930+570)/299018Stefano Morozzi09/2020
66192^328885+14999005Lelio R Paula12/2012
662023392^17075+17075^2339299004Hans Havermann09/2017
6621(2^328879-9)/11999001Lelio R Paula10/2013
66225^141618+5498987Lelio R Paula08/2016
66238*10^98982+5198983Robert Price05/2017
6624(21*2^328809-1)/770998979Lelio R Paula03/2014
66252^328794-279760198977Enzo Doria04/2016
66266^127176+598963Lelio R Paula11/2014
66272*10^98961-2198962Robert Price09/2020
662824262^11989+11989^2426298960Hans Havermann09/2017
66292^328700-10970998949Enzo Doria04/2014
6630(2^328698+1810)/298948Stefano Morozzi01/2021
663187771!4-12898944Robert Price11/2019
6632(2^328658+3042)/298936Stefano Morozzi09/2020
663346711!2-2^4671198916Robert Price09/2015
66349*7^117037+498909Lelio R Paula11/2014
6635127^47012+12698905Norbert Schneider01/2019
6636(2^328525+1250)/298896Stefano Morozzi09/2020
6637(10^98890+149)/398890Serge Batalov12/2014
663822775^21978+21978^2277598889Hans Havermann08/2017
66392^328497-21693398888Enzo Doria05/2014
66402^328487+3276998885Lelio R Paula08/2016
66413^207250-11235898884Enzo Doria06/2014
664213^88754-9098867Lelio R Paula08/2016
66432^328406+70998861Lelio R Paula02/2013
66442*10^98860-2198861Robert Price09/2020
6645(17*2^328413-1)/1617398860Lelio R Paula03/2014
66467^116976+7698857Lelio R Paula08/2016
6647(2^328378+2710)/298852Stefano Morozzi09/2020
66482^328335+115598839Lelio R Paula08/2016
6650(3*2^328311+1)/598832Lelio R Paula11/2013
6649287^40210+40210^28798832Norbert Schneider11/2014
6651(2^328284+9)/132598821Lelio R Paula10/2013
6652(21*2^328258+1)/212598814Lelio R Paula11/2013
665324746^9825+9825^2474698795Hans Havermann07/2020
665426620^5143+5143^2662098793Hans Havermann07/2020
665565^54491+4898788Lelio R Paula04/2016
66563^207042+9898785Lelio R Paula08/2016
6657(2^328121+3110)/298774Stefano Morozzi09/2020
665810^98754+7338398755Patrick De Geest02/2021
66613^206977-11275698754Enzo Doria07/2014
666010^98754-4000000000198754Robert Price09/2020
665910^98754-16934398754Patrick De Geest02/2021
66627^116846-5098747Lelio R Paula08/2016
666323267^17512+17512^2326798730Hans Havermann04/2020
66642^327967-2863598728Lelio R Paula08/2016
6665707^34642+34642^70798710Norbert Schneider12/2017
66666^126850-4798709Lelio R Paula08/2016
6667(2^327886+2170)/298704Stefano Morozzi09/2020
6668(22*10^98697+47)/398698Robert Price06/2021
66698*6^126830-798694Lelio R Paula11/2014
667011^94770-27098693Enzo Doria08/2012
6671(2^327846+3250)/298692Stefano Morozzi01/2021
66722^327832+4398688Lelio R Paula12/2012
66732^327795+76198677Lelio R Paula02/2013
6674(2^327796+1522)/298677Stefano Morozzi09/2020
667510^98669+14741198670Patrick De Geest11/2016
667710^98669-9^(98669-1)98669Robert Price05/2016
667610^98669-10524998669Patrick De Geest11/2016
66782^327671-10980198639Enzo Doria04/2014
667924398^11037+11037^2439898638Hans Havermann10/2019
66805^141090-1498618Lelio R Paula08/2016
668120^75799+4798617Lelio R Paula08/2016
668228101^3226+3226^2810198597Hans Havermann07/2020
66832^327515-101798592Lelio R Paula08/2016
66846^126692+9768198586Mike Oakes04/2011
66852^327467-74198578Lelio R Paula08/2016
668622713^21800+21800^2271398540Hans Havermann05/2020
6687(2^327329+9)/1998535Lelio R Paula10/2013
66887^116577-6698519Lelio R Paula08/2016
6689(3*2^327250+1)/798512Lelio R Paula11/2013
669023220^17479+17479^2322098512Hans Havermann03/2020
6691(2^327240+3798)/298509Stefano Morozzi02/2021
6692(19*2^327192+1)/27598494Lelio R Paula11/2013
66932^327162-6694598486Lelio R Paula08/2016
669430139^1852+1852^3013998484Hans Havermann02/2020
669523182^17703+17703^2318298479Hans Havermann01/2020
66964*10^98472-398473Erik Branger11/2013
669726167^5794+5794^2616798466Hans Havermann01/2020
6698(6883*2^327047-1)/7798453Lelio R Paula05/2015
6699(71*10^98446+1)/998447Serge Batalov11/2010
670013^88363+9498432Lelio R Paula08/2016
670148^58543-47^5854398425Jean-Louis Charton11/2005
67026^126481+4198422Lelio R Paula08/2016
670378*10^98413-798415Robert Price05/2017
670422634^22263+22263^2263498404Hans Havermann07/2020
67057^116416+4698383Lelio R Paula08/2016
67067^116407-2498376Lelio R Paula07/2016
6707439^37228+37228^43998374Norbert Schneider08/2018
67082^326782-186067198372Enzo Doria03/2016
670917^79948+5898372Lelio R Paula08/2016
671022499^22602-22602^2249998368Norbert Schneider08/2020
67113^206143-9898356Lelio R Paula08/2016
67128*5^140705+798350Lelio R Paula11/2014
6713(2^326632+1662)/298326Stefano Morozzi09/2020
67142^326585+1198312Lelio R Paula12/2012
67152^326582-45916198311Enzo Doria05/2015
6717(2^326548+9)/598301Lelio R Paula10/2013
6716(2^326549+18)/1098301Stefano Morozzi03/2020
67182^326538+7165998298Enzo Doria04/2016
6719(2^326520+2082)/298293Stefano Morozzi09/2020
6720(2^326521+1002)/298293Stefano Morozzi09/2020
672115^83575-5898292Lelio R Paula08/2016
672210^98288+398289Robert Price03/2011
672310^98288-11701798288Patrick De Geest11/2011
6724(44*10^98284-719)/998285Robert Price12/2017
672523466^15419+15419^2346698277Hans Havermann02/2020
67262^326421-279757398263Enzo Doria04/2016
67272^326401+1609598257Lelio R Paula07/2016
67287^116240-116240^798235Norbert Schneider05/2017
672917^79826-7898222Lelio R Paula08/2016
67302^326268-80998217Yves Minet04/2011
673122659^21590+21590^2265998210Hans Havermann10/2019
673222268^22587-22587^2226898202Norbert Schneider08/2020
6733(418*10^98199+23)/998201Robert Price08/2017
673412*10^98198-798200Robert Price11/2017
673515^83496-7698199Lelio R Paula08/2016
6736(10223*2^326179+1)/612598190Lelio R Paula07/2014
67379*5^140471-498186Lelio R Paula11/2014
673822774^20455+20455^2277498175Hans Havermann07/2020
67392^326069-238398157Yves Minet10/2013
67402^325973+118598128Lelio R Paula07/2016
6741(25*2^325949-1)/1798121Lelio R Paula02/2014
67422^325945-184726998120Enzo Doria07/2015
67438*10^98111-6798112Robert Price10/2017
6744(2^325902+1138)/298106Stefano Morozzi09/2020
67452^325866+1598096Lelio R Paula12/2012
674622591^21952+21952^2259198079Hans Havermann02/2020
67472^325765+197430598066Enzo Doria06/2016
67482^325733-5869598056Lelio R Paula07/2016
6749(7*10^98055-529)/998055Robert Price08/2021
67502^325717-364598051Lelio R Paula07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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