PRP Records

Probable Primes Top 10000

(212140 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 (> 30000) Who ? When ?
32512^334524+145100702Lelio R Paula07/2009
3252(1017*2^334391-1)/3535100662Lelio R Paula05/2015
32532^334294-113111100633Enzo Doria07/2014
32546^129308-17723100622Enzo Doria03/2013
32556^129305+95100619Lelio R Paula10/2016
32562^334244-1167100618Lelio R Paula09/2016
3257(21*2^334050+1)/935100558Lelio R Paula12/2013
3258(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3259(35*10^100542+1)/9100543Serge Batalov11/2010
326013^90251+24100535Lelio R Paula10/2016
32612^333963+789100533Lelio R Paula08/2011
32622^333919-1840087100520Enzo Doria06/2015
32632^333911+72623100518Enzo Doria04/2016
326418^80064-67100503Lelio R Paula10/2016
32655^143742-48100472Lelio R Paula10/2016
32662^333757-112123100471Enzo Doria06/2014
32672^333603-108861100425Enzo Doria03/2014
32689*7^118818-2100414Lelio R Paula11/2014
32692^333546-17097100408Enzo Doria05/2013
327017^81597+72100401Lelio R Paula10/2016
3271p(20559)#/2+8100384Robert Price01/2017
327211^96390-24100380Lelio R Paula10/2016
32734832563059*2^333333+30029100353Donovan Johnson01/2008
32742^333354+763100350Lelio R Paula08/2011
32752^333289-109483100330Enzo Doria04/2014
32762^333240-2790209100316Enzo Doria03/2016
327723601^17798+17798^23601100314Hans Havermann05/2018
3278(2^333227-2^166614+1)/510031111/2006
32792^333225+719100311Lelio R Paula08/2011
32802^333221-2785333100310Enzo Doria10/2015
328176^53332-75100308Norbert Schneider02/2015
32826^128892-17573100298Enzo Doria03/2013
32832^333105-113215100275Enzo Doria07/2014
3284(31*2^333102+1)/2375100272Lelio R Paula11/2013
328517^81476-74100253Lelio R Paula10/2016
328623392^19207+19207^23392100199Hans Havermann06/2018
328717^81417-16100180Theodore Burton11/2005
32882^332739-113215100165Enzo Doria07/2014
32892^332730-1865621100162Enzo Doria03/2016
329091^51127-2100160Lelio R Paula09/2013
329115^85159-32100155Lelio R Paula10/2016
32926^128661+97100118Lelio R Paula10/2016
329319^78285+40100108Lelio R Paula07/2016
32946^128640+5100102Lelio R Paula11/2014
329528562^3189+3189^28562100072Hans Havermann05/2018
32966^128565-127100044Lelio R Paula08/2016
32972^332309-133100035Lelio R Paula02/2011
32982^332307+731100035Lelio R Paula07/2011
32992^332301+12927100033Lelio R Paula04/2013
330023406^18781+18781^23406100031Hans Havermann04/2018
330112^92684-13100023Lelio R Paula07/2016
330210^100002+236023100003Stefano Morozzi05/2018
330310^100002+433741100003Stefano Morozzi05/2018
3304(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
3305(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
333125206!+p(4114)100001Henri Lifchitz09/2005
333225206!-p(5447)100001Henri Lifchitz10/2005
333325206!-p(12402)100001Henri Lifchitz04/2006
333425206!-p(16290)100001Henri Lifchitz09/2006
333525206!-p(19647)100001Henri Lifchitz02/2007
33362^332194+11473100001Henri Lifchitz03/2007
331710^100000+342909100001Milton L. Brown12/2007
335010^100000+346579100001Robert Price04/2012
335110^100000+829767100001Robert Price05/2012
335210^100000+871899100001Robert Price05/2012
335310^100000+1475997100001Robert Price07/2012
333710^100000+1751769100001Robert Price08/2012
333810^100000+2155489100001Robert Price10/2012
333910^100000+2483527100001Robert Price12/2012
334010^100000+2503087100001Robert Price12/2012
334110^100000+2686179100001Robert Price12/2012
334210^100000+2688933100001Robert Price12/2012
334310^100000+3667159100001Robert Price08/2013
334710^100000+3938473100001Robert Price05/2015
334810^100000+3979761100001Robert Price05/2015
334910^100000+4293973100001Robert Price09/2015
334410^100000+4858267100001Robert Price12/2015
334510^100000+5113299100001Robert Price02/2016
334610^100000+5169411100001Robert Price02/2016
330910^100000+5354043100001Robert Price05/2016
331010^100000+5717979100001Robert Price05/2016
331110^100000+6080631100001Robert Price07/2016
331210^100000+6308469100001Robert Price07/2016
331310^100000+6512023100001Robert Price08/2016
331410^100000+6596557100001Robert Price08/2016
331510^100000+7115409100001Robert Price10/2016
331610^100000+7235803100001Robert Price10/2016
331810^100000+7867333100001Robert Price12/2016
331910^100000+8743093100001Robert Price02/2017
332010^100000+8955391100001Robert Price03/2017
332110^100000+9180019100001Robert Price03/2017
332210^100000+9225987100001Robert Price04/2017
332310^100000+9265587100001Robert Price04/2017
332410^100000+9287049100001Robert Price04/2017
332510^100000+9425053100001Robert Price05/2017
332610^100000+9450769100001Robert Price05/2017
332710^100000+9528747100001Robert Smith05/2017
332810^100000+9548071100001Robert Price06/2017
332910^100000+10064287100001Robert Price08/2017
333010^100000+10229569100001Robert Price10/2017
330610^100000+11187931100001Robert Price03/2018
330710^100000+11264721100001Robert Price04/2018
330810^100000+11477661100001Robert Price05/2018
335510^99999+309403100000Daniel Heuer01/2004
335410^100000-260199100000Patrick De Geest01/2010
335610^99999-5951199999Patrick De Geest07/2009
33572^332141-11307399985Enzo Doria07/2014
3358(3^209561+2)/72810125599978Lelio R Paula09/2013
335923827^15702+15702^2382799978Hans Havermann04/2018
33602^332085+186589799968Enzo Doria03/2016
3361(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
33622^332023+19199949Lelio R Paula02/2011
33632^331938+7114999924Enzo Doria04/2016
33642^331932-7879599922Lelio R Paula09/2016
33652^331921+77199919Lelio R Paula01/2013
3366(3^209419-2)/513275599912Lelio R Paula09/2013
33672^331860-11498999900Enzo Doria05/2015
33682^331746-1165599866Lelio R Paula09/2016
336911^95891-2899861Lelio R Paula08/2016
3370(2^331694-5)/1199849Lelio R Paula10/2013
3371(3^209246+7)/6499834Lelio R Paula09/2013
337225062^9617+9617^2506299823Hans Havermann04/2018
337315^84866-5299811Lelio R Paula08/2016
337413^89600+3099810Lelio R Paula08/2016
337522950^22309+22309^2295099798Hans Havermann03/2018
33765^142772-3899794Lelio R Paula08/2016
3377(23*2^331459+1)/47599778Lelio R Paula11/2013
33782^331416-331416+199767Robert Price10/2014
33792^331256-5799718Lelio R Paula12/2012
338028192^3443+3443^2819299714Hans Havermann03/2018
33812^331185+73799697Lelio R Paula01/2013
3382(4*10^99693+149)/999693Robert Price03/2017
33832^331154+188052799688Enzo Doria10/2016
3385(19^77951+1)/2099679Paul Bourdelais03/2010
338424354^12385+12385^2435499679Hans Havermann03/2018
33862^331110+187045999675Enzo Doria05/2016
33875*2^331075+799665Lelio R Paula08/2014
338825776^7351+7351^2577699659Hans Havermann02/2018
3389(16*10^99656-31)/399657Robert Price03/2016
33902^330968+34599632Lelio R Paula09/2016
33922*5^142528-799624Lelio R Paula11/2014
33912^330942+7732999624Enzo Doria05/2016
339314^86914-9999615Lelio R Paula08/2016
3394(19*2^330902+1)/7799611Lelio R Paula11/2013
339522971^21692+21692^2297199610Hans Havermann03/2018
33962^330845+7168799595Enzo Doria04/2016
3397(23*2^330770+1)/399573Lelio R Paula11/2013
339824494^11613+11613^2449499567Hans Havermann03/2018
33992^330735+841599562Lelio R Paula09/2016
34002^330720+7407199557Enzo Doria04/2016
340131^66738-299531Lelio R Paula09/2013
34027*3^208567+499513Lelio R Paula08/2014
3403(13*10^99508+47)/399509Robert Price01/2017
34042^330553+77999507Lelio R Paula01/2013
340515^84606-9499505Lelio R Paula08/2016
34066^127858+4799493Lelio R Paula08/2016
34075^142337+4899490Lelio R Paula08/2016
34087^117724-2099489Lelio R Paula08/2016
3409(29*10^99474-17)/399475Erik Branger09/2014
3410(9*2^330407-1)/799463Lelio R Paula03/2014
3411(68*10^99441+7)/399443Robert Price03/2016
341246^59791-45^5979199418Jean-Louis Charton01/2013
341323839^14802+14802^2383999417Hans Havermann02/2018
3414(2*10^99408+529)/999408Robert Price01/2017
341553^57646-299398Lelio R Paula09/2013
34162^330165+187002599390Enzo Doria05/2016
34172^330142-15599383Lelio R Paula12/2012
34182^330088-11525999367Enzo Doria06/2015
341924216^12671+12671^2421699354Hans Havermann01/2018
3420(746*10^99303+1)/999305Robert Price02/2017
34213^208107+4099293Lelio R Paula08/2016
3422(5*2^329833-1)/36999288Lelio R Paula02/2014
34238*3^208093+599287Lelio R Paula08/2014
34245^142043+5699284Lelio R Paula08/2016
342522*10^99275+799277Robert Price04/2016
34262^329778+187618999274Enzo Doria07/2016
3427(10^99239-13)/399239Robert Price02/2017
34283^207987+6299236Lelio R Paula08/2016
34292^329638+4999231Lelio R Paula12/2012
34307^117413-1899226Lelio R Paula08/2016
34312^329586-45890399216Enzo Doria04/2015
34322^329553+10199206Lelio R Paula12/2012
34332^329551-11289799205Enzo Doria06/2014
3434(3^207925+7)/5099204Lelio R Paula09/2013
34356^127458-1799399182Enzo Doria03/2013
343627197^4428+4428^2719799166Hans Havermann10/2017
3437(46*10^99143-1)/999144Robert Price12/2014
34387*10^99133+6999134Robert Price10/2017
343918^78968-306599127Enzo Doria03/2013
344025927^6654+6654^2592799122Hans Havermann10/2017
34412^329259+18999117Lelio R Paula12/2012
34428*10^99113+3999114Robert Price01/2017
34436^127364+7799109Lelio R Paula08/2016
34446^127285+1399047Lelio R Paula08/2016
3445(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
34462^329007+7328399041Enzo Doria04/2016
34475*3^207543-899024Lelio R Paula08/2014
34482^328885+14999005Lelio R Paula12/2012
344923392^17075+17075^2339299004Hans Havermann09/2017
3450(2^328879-9)/11999001Lelio R Paula10/2013
34515^141618+5498987Lelio R Paula08/2016
34528*10^98982+5198983Robert Price05/2017
3453(21*2^328809-1)/770998979Lelio R Paula03/2014
34542^328794-279760198977Enzo Doria04/2016
34556^127176+598963Lelio R Paula11/2014
345624262^11989+11989^2426298960Hans Havermann09/2017
34572^328700-10970998949Enzo Doria04/2014
345846711!2-2^4671198916Robert Price09/2015
34599*7^117037+498909Lelio R Paula11/2014
3460(10^98890+149)/398890Serge Batalov12/2014
346122775^21978+21978^2277598889Hans Havermann08/2017
34622^328497-21693398888Enzo Doria05/2014
34632^328487+3276998885Lelio R Paula08/2016
34643^207250-11235898884Enzo Doria06/2014
346513^88754-9098867Lelio R Paula08/2016
34662^328406+70998861Lelio R Paula02/2013
3467(17*2^328413-1)/1617398860Lelio R Paula03/2014
34687^116976+7698857Lelio R Paula08/2016
34692^328335+115598839Lelio R Paula08/2016
3470(3*2^328311+1)/598832Lelio R Paula11/2013
3471287^40210+40210^28798832Norbert Schneider11/2014
3472(2^328284+9)/132598821Lelio R Paula10/2013
3473(21*2^328258+1)/212598814Lelio R Paula11/2013
347465^54491+4898788Lelio R Paula04/2016
34753^207042+9898785Lelio R Paula08/2016
34763^206977-11275698754Enzo Doria07/2014
34777^116846-5098747Lelio R Paula08/2016
34782^327967-2863598728Lelio R Paula08/2016
3479707^34642+34642^70798710Norbert Schneider12/2017
34806^126850-4798709Lelio R Paula08/2016
34818*6^126830-798694Lelio R Paula11/2014
348211^94770-27098693Enzo Doria08/2012
34832^327832+4398688Lelio R Paula12/2012
34842^327795+76198677Lelio R Paula02/2013
348510^98669+14741198670Patrick De Geest11/2016
348710^98669-9^(98669-1)98669Robert Price05/2016
348610^98669-10524998669Patrick De Geest11/2016
34882^327671-10980198639Enzo Doria04/2014
34895^141090-1498618Lelio R Paula08/2016
349020^75799+4798617Lelio R Paula08/2016
34912^327515-101798592Lelio R Paula08/2016
34926^126692+9768198586Mike Oakes04/2011
34932^327467-74198578Lelio R Paula08/2016
3494(2^327329+9)/1998535Lelio R Paula10/2013
34957^116577-6698519Lelio R Paula08/2016
3496(3*2^327250+1)/798512Lelio R Paula11/2013
3497(19*2^327192+1)/27598494Lelio R Paula11/2013
34982^327162-6694598486Lelio R Paula08/2016
34994*10^98472-398473Erik Branger11/2013
3500(6883*2^327047-1)/7798453Lelio R Paula05/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!