PRP Records

Probable Primes Top 10000

(259919 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 ?
40016^128661+97100118Lelio R Paula10/2016
400219^78285+40100108Lelio R Paula07/2016
40036^128640+5100102Lelio R Paula11/2014
4004(14*10^100075+61)/3100076Robert Price12/2018
400528562^3189+3189^28562100072Hans Havermann05/2018
40066^128565-127100044Lelio R Paula08/2016
40072^332309-133100035Lelio R Paula02/2011
40082^332307+731100035Lelio R Paula07/2011
40092^332301+12927100033Lelio R Paula04/2013
401023406^18781+18781^23406100031Hans Havermann04/2018
40112^332277-4573100026Yves Minet03/2019
401212^92684-13100023Lelio R Paula07/2016
401378557*2^332193+55669100005Jorge Menendez04/2019
401478557*2^332192+72689100005Jorge Menendez04/2019
401510^100003+45799100004Stefano Morozzi04/2019
401610^100003+155461100004Stefano Morozzi04/2019
401710^100003+211389100004Stefano Morozzi04/2019
401810^100003+381027100004Stefano Morozzi04/2019
401910^100003+540703100004Stefano Morozzi04/2019
402010^100003+823977100004Stefano Morozzi04/2019
403210^100002+236023100003Stefano Morozzi05/2018
403310^100002+433741100003Stefano Morozzi05/2018
40212^332202+104659100003Stefano Morozzi04/2019
40222^332202+857539100003Stefano Morozzi04/2019
40232^332202+181773100003Stefano Morozzi04/2019
40242^332202+687543100003Stefano Morozzi04/2019
40252^332202+941595100003Stefano Morozzi04/2019
40262^332202+445813100003Stefano Morozzi04/2019
40272^332202+1599727100003Stefano Morozzi04/2019
40282^332202+1389567100003Stefano Morozzi04/2019
40292^332202+1206315100003Stefano Morozzi04/2019
40302^332202+1958647100003Stefano Morozzi04/2019
403110^100003-562857100003Patrick De Geest07/2019
4034(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
4035(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
403610^100002-249519100002Patrick De Geest07/2018
403710^100001+314199100002Patrick De Geest07/2018
410625206!+p(4114)100001Henri Lifchitz09/2005
410725206!-p(5447)100001Henri Lifchitz10/2005
410825206!-p(12402)100001Henri Lifchitz04/2006
410925206!-p(16290)100001Henri Lifchitz09/2006
411025206!-p(19647)100001Henri Lifchitz02/2007
41112^332194+11473100001Henri Lifchitz03/2007
410110^100000+342909100001Milton L. Brown12/2007
410210^100000+346579100001Robert Price04/2012
410310^100000+829767100001Robert Price05/2012
410410^100000+871899100001Robert Price05/2012
410510^100000+1475997100001Robert Price07/2012
409410^100000+1751769100001Robert Price08/2012
409510^100000+2155489100001Robert Price10/2012
409610^100000+2483527100001Robert Price12/2012
409710^100000+2503087100001Robert Price12/2012
409810^100000+2686179100001Robert Price12/2012
409910^100000+2688933100001Robert Price12/2012
410010^100000+3667159100001Robert Price08/2013
407810^100000+3938473100001Robert Price05/2015
407910^100000+3979761100001Robert Price05/2015
408010^100000+4293973100001Robert Price09/2015
406710^100000+4858267100001Robert Price12/2015
406810^100000+5113299100001Robert Price02/2016
406910^100000+5169411100001Robert Price02/2016
407010^100000+5354043100001Robert Price05/2016
407110^100000+5717979100001Robert Price05/2016
407210^100000+6080631100001Robert Price07/2016
407310^100000+6308469100001Robert Price07/2016
407410^100000+6512023100001Robert Price08/2016
407510^100000+6596557100001Robert Price08/2016
407610^100000+7115409100001Robert Price10/2016
407710^100000+7235803100001Robert Price10/2016
408110^100000+7867333100001Robert Price12/2016
408210^100000+8743093100001Robert Price02/2017
408310^100000+8955391100001Robert Price03/2017
408410^100000+9180019100001Robert Price03/2017
408510^100000+9225987100001Robert Price04/2017
408610^100000+9265587100001Robert Price04/2017
408710^100000+9287049100001Robert Price04/2017
408810^100000+9425053100001Robert Price05/2017
408910^100000+9450769100001Robert Price05/2017
409010^100000+9528747100001Robert Smith05/2017
409110^100000+9548071100001Robert Price06/2017
409210^100000+10064287100001Robert Price08/2017
409310^100000+10229569100001Robert Price10/2017
403810^100000+11187931100001Robert Price03/2018
403910^100000+11264721100001Robert Price04/2018
404010^100000+11477661100001Robert Price05/2018
404110^100000+11644653100001Robert Price07/2018
404210^100001-431439100001Patrick De Geest07/2018
404310^100000+11769399100001Robert Price08/2018
404410^100000+11848159100001Robert Price08/2018
404510^100000+11863467100001Robert Price08/2018
406410^100000+11992051100001Robert Price09/2018
40652^332196-1-2*29696100001Matt Stath11/2018
406610^100000+12363957100001Robert Price11/2018
40462^332196+1+2*17152100001Matt Stath12/2018
404710^100000+12778033100001Robert Price02/2019
404810^100000+13581679100001Robert Price05/2019
404910^100000+13613199100001Robert Price05/2019
405010^100000+13752327100001Robert Price05/2019
405110^100000+14139243100001Robert Price06/2019
405210^100000+14151057100001Robert Price06/2019
405310^100000+14218923100001Robert Price06/2019
405410^100000+15136771100001Robert Price09/2019
405510^100000+15219873100001Robert Price10/2019
405610^100000+15274039100001Robert Price10/2019
405710^100000+15394069100001Robert Price10/2019
405810^100000+15547119100001Robert Price10/2019
405910^100000+15932923100001Robert Price11/2019
406010^100000+16345467100001Robert Price12/2019
406110^100000+16672143100001Robert Price01/2020
406210^100000+16731939100001Robert Price02/2020
406310^100000+16907049100001Robert Price03/2020
411210^99999+309403100000Daniel Heuer01/2004
411310^100000-260199100000Patrick De Geest01/2010
411410^99999-5951199999Patrick De Geest07/2009
411510^99998+23543799999Patrick De Geest02/2020
411610^99998-28658799998Patrick De Geest02/2020
411710^99997+7229799998Patrick De Geest02/2020
411810^99997-40262799997Patrick De Geest02/2020
411910^99996+27985399997Patrick De Geest02/2020
412010^99996-9496199996Patrick De Geest02/2020
412110^99995+5463399996Patrick De Geest02/2020
412210^99995-10142999995Patrick De Geest02/2020
412310^99994+11727199995Patrick De Geest02/2020
412410^99994-45228999994Patrick De Geest02/2020
412510^99993+37131199994Patrick De Geest02/2020
412610^99993-18649199993Patrick De Geest02/2020
412710^99992+1743199993Patrick De Geest02/2020
412810^99992-2860799992Patrick De Geest02/2020
412910^99991+12539199992Patrick De Geest02/2020
413010^99991-20457399991Patrick De Geest02/2020
413110^99990+1389999991Patrick De Geest02/2020
413210^99990-811199990Patrick De Geest02/2020
41332^332141-11307399985Enzo Doria07/2014
4135(3^209561+2)/72810125599978Lelio R Paula09/2013
413423827^15702+15702^2382799978Hans Havermann04/2018
41362^332085+186589799968Enzo Doria03/2016
4137(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
41382^332023+19199949Lelio R Paula02/2011
41392^331938+7114999924Enzo Doria04/2016
41402^331932-7879599922Lelio R Paula09/2016
41412^331921+77199919Lelio R Paula01/2013
4142(3^209419-2)/513275599912Lelio R Paula09/2013
41432^331860-11498999900Enzo Doria05/2015
41442^331746-1165599866Lelio R Paula09/2016
414511^95891-2899861Lelio R Paula08/2016
4146(2^331694-5)/1199849Lelio R Paula10/2013
4147(3^209246+7)/6499834Lelio R Paula09/2013
414825062^9617+9617^2506299823Hans Havermann04/2018
414915^84866-5299811Lelio R Paula08/2016
415013^89600+3099810Lelio R Paula08/2016
415122950^22309+22309^2295099798Hans Havermann03/2018
41525^142772-3899794Lelio R Paula08/2016
4153(23*2^331459+1)/47599778Lelio R Paula11/2013
41542^331416-331416+199767Robert Price10/2014
41552^331256-5799718Lelio R Paula12/2012
415628192^3443+3443^2819299714Hans Havermann03/2018
41572^331185+73799697Lelio R Paula01/2013
4158(4*10^99693+149)/999693Robert Price03/2017
41592^331154+188052799688Enzo Doria10/2016
4161(19^77951+1)/2099679Paul Bourdelais03/2010
416024354^12385+12385^2435499679Hans Havermann03/2018
41622^331110+187045999675Enzo Doria05/2016
41635*2^331075+799665Lelio R Paula08/2014
416425776^7351+7351^2577699659Hans Havermann02/2018
4165(16*10^99656-31)/399657Robert Price03/2016
41662^330968+34599632Lelio R Paula09/2016
41682*5^142528-799624Lelio R Paula11/2014
41672^330942+7732999624Enzo Doria05/2016
416914^86914-9999615Lelio R Paula08/2016
4170(19*2^330902+1)/7799611Lelio R Paula11/2013
417122971^21692+21692^2297199610Hans Havermann03/2018
41722^330845+7168799595Enzo Doria04/2016
4173(23*2^330770+1)/399573Lelio R Paula11/2013
417424494^11613+11613^2449499567Hans Havermann03/2018
41752^330735+841599562Lelio R Paula09/2016
41762^330720+7407199557Enzo Doria04/2016
417731^66738-299531Lelio R Paula09/2013
41787*3^208567+499513Lelio R Paula08/2014
4179(13*10^99508+47)/399509Robert Price01/2017
41802^330553+77999507Lelio R Paula01/2013
418115^84606-9499505Lelio R Paula08/2016
41826^127858+4799493Lelio R Paula08/2016
41835^142337+4899490Lelio R Paula08/2016
41847^117724-2099489Lelio R Paula08/2016
4185(29*10^99474-17)/399475Erik Branger09/2014
4186(9*2^330407-1)/799463Lelio R Paula03/2014
4187(68*10^99441+7)/399443Robert Price03/2016
418810^99434-12345678999434Robert Price02/2020
418946^59791-45^5979199418Jean-Louis Charton01/2013
419023839^14802+14802^2383999417Hans Havermann02/2018
4191(2*10^99408+529)/999408Robert Price01/2017
419253^57646-299398Lelio R Paula09/2013
41932^330165+187002599390Enzo Doria05/2016
41942^330142-15599383Lelio R Paula12/2012
41952^330088-11525999367Enzo Doria06/2015
419624216^12671+12671^2421699354Hans Havermann01/2018
4197Phi(200548,10)/320876999354Makoto Kamada04/2019
4198(746*10^99303+1)/999305Robert Price02/2017
41993^208107+4099293Lelio R Paula08/2016
4200(5*2^329833-1)/36999288Lelio R Paula02/2014
42018*3^208093+599287Lelio R Paula08/2014
42025^142043+5699284Lelio R Paula08/2016
420322*10^99275+799277Robert Price04/2016
42042^329778+187618999274Enzo Doria07/2016
4205(10^99239-13)/399239Robert Price02/2017
42063^207987+6299236Lelio R Paula08/2016
42072^329638+4999231Lelio R Paula12/2012
42087^117413-1899226Lelio R Paula08/2016
42092^329586-45890399216Enzo Doria04/2015
42102^329553+10199206Lelio R Paula12/2012
42112^329551-11289799205Enzo Doria06/2014
4212(3^207925+7)/5099204Lelio R Paula09/2013
42136^127458-1799399182Enzo Doria03/2013
421427197^4428+4428^2719799166Hans Havermann10/2017
4215(46*10^99143-1)/999144Robert Price12/2014
42167*10^99133+6999134Robert Price10/2017
421718^78968-306599127Enzo Doria03/2013
421825927^6654+6654^2592799122Hans Havermann10/2017
421987915!4+1699122Robert Price09/2019
42202^329259+18999117Lelio R Paula12/2012
42218*10^99113+3999114Robert Price01/2017
42226^127364+7799109Lelio R Paula08/2016
42236^127285+1399047Lelio R Paula08/2016
4224(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
42252^329007+7328399041Enzo Doria04/2016
42265*3^207543-899024Lelio R Paula08/2014
42272^328885+14999005Lelio R Paula12/2012
422823392^17075+17075^2339299004Hans Havermann09/2017
4229(2^328879-9)/11999001Lelio R Paula10/2013
42305^141618+5498987Lelio R Paula08/2016
42318*10^98982+5198983Robert Price05/2017
4232(21*2^328809-1)/770998979Lelio R Paula03/2014
42332^328794-279760198977Enzo Doria04/2016
42346^127176+598963Lelio R Paula11/2014
423524262^11989+11989^2426298960Hans Havermann09/2017
42362^328700-10970998949Enzo Doria04/2014
423787771!4-12898944Robert Price11/2019
423846711!2-2^4671198916Robert Price09/2015
42399*7^117037+498909Lelio R Paula11/2014
4240127^47012+12698905Norbert Schneider01/2019
4241(10^98890+149)/398890Serge Batalov12/2014
424222775^21978+21978^2277598889Hans Havermann08/2017
42432^328497-21693398888Enzo Doria05/2014
42442^328487+3276998885Lelio R Paula08/2016
42453^207250-11235898884Enzo Doria06/2014
424613^88754-9098867Lelio R Paula08/2016
42472^328406+70998861Lelio R Paula02/2013
4248(17*2^328413-1)/1617398860Lelio R Paula03/2014
42497^116976+7698857Lelio R Paula08/2016
42502^328335+115598839Lelio R Paula08/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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