PRP Records

Probable Primes Top 10000

(252538 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 ?
35012^334984-112757100841Enzo Doria06/2014
350229451^2648+2648^29451100809Hans Havermann09/2018
350325583^8716+8716^25583100806Hans Havermann08/2018
35052^334857+48527100803Lelio R Paula08/2011
350412^93406+29100803Lelio R Paula10/2016
350628780^3179+3179^28780100796Hans Havermann09/2018
3507(5*2^334825+1)/47100792Lelio R Paula12/2013
35082^334809-13100788Lelio R Paula04/2011
3509(82*10^100780-1)/9100781Robert Price12/2014
351031395^1622+1622^31395100780Hans Havermann09/2018
3511(2^334779+47)/5100778Lelio R Paula12/2013
35122^334751+2049100771Lelio R Paula09/2016
351313^90443-98100749Lelio R Paula10/2016
3514(7*10^100737+71)/3100738Robert Price05/2018
3515(24737*2^334628+1)/3100737Lelio R Paula07/2014
351615^85639-28100720Lelio R Paula10/2016
351727068^5259+5259^27068100718Hans Havermann08/2018
35182^334562+577294575100711Lelio R Paula09/2016
35194*3^211077-5100710Lelio R Paula08/2014
35202^334524+145100702Lelio R Paula07/2009
352127648^4375+4375^27648100666Hans Havermann09/2018
3522(1017*2^334391-1)/3535100662Lelio R Paula05/2015
35232^334294-113111100633Enzo Doria07/2014
352425581^8582+8582^25581100626Hans Havermann08/2018
35256^129308-17723100622Enzo Doria03/2013
35266^129305+95100619Lelio R Paula10/2016
35272^334244-1167100618Lelio R Paula09/2016
3528(21*2^334050+1)/935100558Lelio R Paula12/2013
352924885^10984+10984^24885100555Hans Havermann07/2018
3530(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3531(35*10^100542+1)/9100543Serge Batalov11/2010
353223578^18367+18367^23578100538Hans Havermann07/2018
353313^90251+24100535Lelio R Paula10/2016
35342^333963+789100533Lelio R Paula08/2011
35352^333919-1840087100520Enzo Doria06/2015
35362^333911+72623100518Enzo Doria04/2016
353724605^12168+12168^24605100517Hans Havermann08/2018
353818^80064-67100503Lelio R Paula10/2016
35395^143742-48100472Lelio R Paula10/2016
354024095^14784+14784^24095100472Hans Havermann08/2018
35412^333757-112123100471Enzo Doria06/2014
354227358^4693+4693^27358100444Hans Havermann07/2018
35432^333603-108861100425Enzo Doria03/2014
35449*7^118818-2100414Lelio R Paula11/2014
35452^333546-17097100408Enzo Doria05/2013
354617^81597+72100401Lelio R Paula10/2016
3547p(20559)#/2+8100384Robert Price01/2017
354811^96390-24100380Lelio R Paula10/2016
35494832563059*2^333333+30029100353Donovan Johnson01/2008
355023565^18136+18136^23565100353Hans Havermann07/2018
35512^333354+763100350Lelio R Paula08/2011
35522^333289-109483100330Enzo Doria04/2014
35532^333240-2790209100316Enzo Doria03/2016
355423601^17798+17798^23601100314Hans Havermann05/2018
3556(2^333227-2^166614+1)/510031111/2006
35552^333225+719100311Lelio R Paula08/2011
35572^333221-2785333100310Enzo Doria10/2015
355876^53332-75100308Norbert Schneider02/2015
35596^128892-17573100298Enzo Doria03/2013
35602^333105-113215100275Enzo Doria07/2014
3561(31*2^333102+1)/2375100272Lelio R Paula11/2013
35624*10^100257-83100258Robert Price10/2018
356317^81476-74100253Lelio R Paula10/2016
356423392^19207+19207^23392100199Hans Havermann06/2018
356517^81417-16100180Theodore Burton11/2005
35662^332739-113215100165Enzo Doria07/2014
35672^332730-1865621100162Enzo Doria03/2016
356891^51127-2100160Lelio R Paula09/2013
356915^85159-32100155Lelio R Paula10/2016
35706^128661+97100118Lelio R Paula10/2016
357119^78285+40100108Lelio R Paula07/2016
35726^128640+5100102Lelio R Paula11/2014
3573(14*10^100075+61)/3100076Robert Price12/2018
357428562^3189+3189^28562100072Hans Havermann05/2018
35756^128565-127100044Lelio R Paula08/2016
35762^332309-133100035Lelio R Paula02/2011
35772^332307+731100035Lelio R Paula07/2011
35782^332301+12927100033Lelio R Paula04/2013
357923406^18781+18781^23406100031Hans Havermann04/2018
358012^92684-13100023Lelio R Paula07/2016
358110^100002+236023100003Stefano Morozzi05/2018
358210^100002+433741100003Stefano Morozzi05/2018
3583(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
3584(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
358510^100002-249519100002Patrick De Geest07/2018
358610^100001+314199100002Patrick De Geest07/2018
362625206!+p(4114)100001Henri Lifchitz09/2005
362725206!-p(5447)100001Henri Lifchitz10/2005
362825206!-p(12402)100001Henri Lifchitz04/2006
362925206!-p(16290)100001Henri Lifchitz09/2006
363025206!-p(19647)100001Henri Lifchitz02/2007
36312^332194+11473100001Henri Lifchitz03/2007
361910^100000+342909100001Milton L. Brown12/2007
362010^100000+346579100001Robert Price04/2012
362110^100000+829767100001Robert Price05/2012
362210^100000+871899100001Robert Price05/2012
362310^100000+1475997100001Robert Price07/2012
359510^100000+1751769100001Robert Price08/2012
359610^100000+2155489100001Robert Price10/2012
359710^100000+2483527100001Robert Price12/2012
359810^100000+2503087100001Robert Price12/2012
359910^100000+2686179100001Robert Price12/2012
360010^100000+2688933100001Robert Price12/2012
360110^100000+3667159100001Robert Price08/2013
360210^100000+3938473100001Robert Price05/2015
360310^100000+3979761100001Robert Price05/2015
360410^100000+4293973100001Robert Price09/2015
361610^100000+4858267100001Robert Price12/2015
361710^100000+5113299100001Robert Price02/2016
361810^100000+5169411100001Robert Price02/2016
360810^100000+5354043100001Robert Price05/2016
360910^100000+5717979100001Robert Price05/2016
361010^100000+6080631100001Robert Price07/2016
361110^100000+6308469100001Robert Price07/2016
361210^100000+6512023100001Robert Price08/2016
361310^100000+6596557100001Robert Price08/2016
361410^100000+7115409100001Robert Price10/2016
361510^100000+7235803100001Robert Price10/2016
363210^100000+7867333100001Robert Price12/2016
363310^100000+8743093100001Robert Price02/2017
363410^100000+8955391100001Robert Price03/2017
363510^100000+9180019100001Robert Price03/2017
363610^100000+9225987100001Robert Price04/2017
363710^100000+9265587100001Robert Price04/2017
363810^100000+9287049100001Robert Price04/2017
363910^100000+9425053100001Robert Price05/2017
364010^100000+9450769100001Robert Price05/2017
364110^100000+9528747100001Robert Smith05/2017
364210^100000+9548071100001Robert Price06/2017
364310^100000+10064287100001Robert Price08/2017
364410^100000+10229569100001Robert Price10/2017
358710^100000+11187931100001Robert Price03/2018
358810^100000+11264721100001Robert Price04/2018
358910^100000+11477661100001Robert Price05/2018
359010^100000+11644653100001Robert Price07/2018
359110^100001-431439100001Patrick De Geest07/2018
359210^100000+11769399100001Robert Price08/2018
359310^100000+11848159100001Robert Price08/2018
359410^100000+11863467100001Robert Price08/2018
360510^100000+11992051100001Robert Price09/2018
36062^332196-1-2*29696100001Matt Stath11/2018
360710^100000+12363957100001Robert Price11/2018
36242^332196+1+2*17152100001Matt Stath12/2018
362510^100000+12778033100001Robert Price02/2019
364610^99999+309403100000Daniel Heuer01/2004
364510^100000-260199100000Patrick De Geest01/2010
364710^99999-5951199999Patrick De Geest07/2009
36482^332141-11307399985Enzo Doria07/2014
3650(3^209561+2)/72810125599978Lelio R Paula09/2013
364923827^15702+15702^2382799978Hans Havermann04/2018
36512^332085+186589799968Enzo Doria03/2016
3652(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
36532^332023+19199949Lelio R Paula02/2011
36542^331938+7114999924Enzo Doria04/2016
36552^331932-7879599922Lelio R Paula09/2016
36562^331921+77199919Lelio R Paula01/2013
3657(3^209419-2)/513275599912Lelio R Paula09/2013
36582^331860-11498999900Enzo Doria05/2015
36592^331746-1165599866Lelio R Paula09/2016
366011^95891-2899861Lelio R Paula08/2016
3661(2^331694-5)/1199849Lelio R Paula10/2013
3662(3^209246+7)/6499834Lelio R Paula09/2013
366325062^9617+9617^2506299823Hans Havermann04/2018
366415^84866-5299811Lelio R Paula08/2016
366513^89600+3099810Lelio R Paula08/2016
366622950^22309+22309^2295099798Hans Havermann03/2018
36675^142772-3899794Lelio R Paula08/2016
3668(23*2^331459+1)/47599778Lelio R Paula11/2013
36692^331416-331416+199767Robert Price10/2014
36702^331256-5799718Lelio R Paula12/2012
367128192^3443+3443^2819299714Hans Havermann03/2018
36722^331185+73799697Lelio R Paula01/2013
3673(4*10^99693+149)/999693Robert Price03/2017
36742^331154+188052799688Enzo Doria10/2016
3676(19^77951+1)/2099679Paul Bourdelais03/2010
367524354^12385+12385^2435499679Hans Havermann03/2018
36772^331110+187045999675Enzo Doria05/2016
36785*2^331075+799665Lelio R Paula08/2014
367925776^7351+7351^2577699659Hans Havermann02/2018
3680(16*10^99656-31)/399657Robert Price03/2016
36812^330968+34599632Lelio R Paula09/2016
36832*5^142528-799624Lelio R Paula11/2014
36822^330942+7732999624Enzo Doria05/2016
368414^86914-9999615Lelio R Paula08/2016
3685(19*2^330902+1)/7799611Lelio R Paula11/2013
368622971^21692+21692^2297199610Hans Havermann03/2018
36872^330845+7168799595Enzo Doria04/2016
3688(23*2^330770+1)/399573Lelio R Paula11/2013
368924494^11613+11613^2449499567Hans Havermann03/2018
36902^330735+841599562Lelio R Paula09/2016
36912^330720+7407199557Enzo Doria04/2016
369231^66738-299531Lelio R Paula09/2013
36937*3^208567+499513Lelio R Paula08/2014
3694(13*10^99508+47)/399509Robert Price01/2017
36952^330553+77999507Lelio R Paula01/2013
369615^84606-9499505Lelio R Paula08/2016
36976^127858+4799493Lelio R Paula08/2016
36985^142337+4899490Lelio R Paula08/2016
36997^117724-2099489Lelio R Paula08/2016
3700(29*10^99474-17)/399475Erik Branger09/2014
3701(9*2^330407-1)/799463Lelio R Paula03/2014
3702(68*10^99441+7)/399443Robert Price03/2016
370346^59791-45^5979199418Jean-Louis Charton01/2013
370423839^14802+14802^2383999417Hans Havermann02/2018
3705(2*10^99408+529)/999408Robert Price01/2017
370653^57646-299398Lelio R Paula09/2013
37072^330165+187002599390Enzo Doria05/2016
37082^330142-15599383Lelio R Paula12/2012
37092^330088-11525999367Enzo Doria06/2015
371024216^12671+12671^2421699354Hans Havermann01/2018
3711(746*10^99303+1)/999305Robert Price02/2017
37123^208107+4099293Lelio R Paula08/2016
3713(5*2^329833-1)/36999288Lelio R Paula02/2014
37148*3^208093+599287Lelio R Paula08/2014
37155^142043+5699284Lelio R Paula08/2016
371622*10^99275+799277Robert Price04/2016
37172^329778+187618999274Enzo Doria07/2016
3718(10^99239-13)/399239Robert Price02/2017
37193^207987+6299236Lelio R Paula08/2016
37202^329638+4999231Lelio R Paula12/2012
37217^117413-1899226Lelio R Paula08/2016
37222^329586-45890399216Enzo Doria04/2015
37232^329553+10199206Lelio R Paula12/2012
37242^329551-11289799205Enzo Doria06/2014
3725(3^207925+7)/5099204Lelio R Paula09/2013
37266^127458-1799399182Enzo Doria03/2013
372727197^4428+4428^2719799166Hans Havermann10/2017
3728(46*10^99143-1)/999144Robert Price12/2014
37297*10^99133+6999134Robert Price10/2017
373018^78968-306599127Enzo Doria03/2013
373125927^6654+6654^2592799122Hans Havermann10/2017
37322^329259+18999117Lelio R Paula12/2012
37338*10^99113+3999114Robert Price01/2017
37346^127364+7799109Lelio R Paula08/2016
37356^127285+1399047Lelio R Paula08/2016
3736(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
37372^329007+7328399041Enzo Doria04/2016
37385*3^207543-899024Lelio R Paula08/2014
37392^328885+14999005Lelio R Paula12/2012
374023392^17075+17075^2339299004Hans Havermann09/2017
3741(2^328879-9)/11999001Lelio R Paula10/2013
37425^141618+5498987Lelio R Paula08/2016
37438*10^98982+5198983Robert Price05/2017
3744(21*2^328809-1)/770998979Lelio R Paula03/2014
37452^328794-279760198977Enzo Doria04/2016
37466^127176+598963Lelio R Paula11/2014
374724262^11989+11989^2426298960Hans Havermann09/2017
37482^328700-10970998949Enzo Doria04/2014
374946711!2-2^4671198916Robert Price09/2015
37509*7^117037+498909Lelio R Paula11/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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