PRP Records

Probable Primes Top 10000

(174961 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 (> 30000) Who ? When ?
5015^332150-18188232163Enzo Doria06/2014
5023^485977-2^485977231870Mike Oakes09/2009
5032^770082-114161231818Enzo Doria01/2015
504(20^177967+1)/21231540Paul Bourdelais05/2013
5052^767622-9221231078Lelio R Paula01/2016
5062^767344+1880311230994Enzo Doria09/2016
507(3^483611-1)/2230741Paul Bourdelais02/2010
508(10^230706+179)/9230706Serge Batalov12/2014
5092^766309+1875257230682Enzo Doria06/2016
5102^765635+1879883230480Enzo Doria09/2016
5112^764348-113697230092Enzo Doria09/2014
5122^764131+78863230027Enzo Doria05/2016
5132^763701+60197229897Enzo Doria03/2016
5142^762841-25905229639Enzo Doria10/2013
5152^761117-113569229120Enzo Doria08/2014
5162^757985-2790013228177Enzo Doria12/2015
5172^757038-1862081227892Enzo Doria12/2015
5182^756839+95849227832Makoto Morimoto10/2013
519(2^756839+6989)/756091227826Makoto Morimoto09/2016
5202^756773-112723227812Enzo Doria07/2014
521524309#+616367227431Makoto Morimoto02/2016
5222^755097-114193227307Enzo Doria12/2014
5232^754473-2791513227120Enzo Doria01/2016
5242^751426-764321226202Enzo Doria12/2013
525(18^180181-1)/17226176Andy Steward04/2007
5262^750740-3225996Paul Bourdelais03/2012
5272^750725+60227225991Enzo Doria02/2016
5282^750525-113743225931Enzo Doria09/2014
529(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5302^749444-1861889225606Enzo Doria12/2015
531tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5322^749096+1876861225501Enzo Doria07/2016
5332^748657+79607225369Enzo Doria06/2016
5342^746653-291583224765Enzo Doria07/2015
5352^746461-114043224708Enzo Doria11/2014
5362^745098-350471224297Enzo Doria06/2015
537(154*10^224061-1)/9224063Serge Batalov12/2014
5382^744211-1845787224030Enzo Doria07/2015
539234178^9+9^234178223463Anatoly F. Selevich07/2011
5402^741651-461197223260Enzo Doria07/2015
5412^741362-1845251223173Enzo Doria07/2015
5422^740455-1863877222900Enzo Doria12/2015
5432^739636-2792219222653Enzo Doria02/2016
54411^213654-180222498Enzo Doria01/2013
5452^738957-1859743222449Enzo Doria11/2015
546(10^221654+179)/9221654Serge Batalov12/2014
5472^736281+79817221643Enzo Doria06/2016
54810^221631+247617221632Patrick De Geest10/2013
54910^221631-9221631Alexander Gramolin02/2011
5502^735970-1839821221550Enzo Doria06/2015
5512^735367+60293221368Enzo Doria03/2016
5522^733264-2784089220735Enzo Doria10/2015
5532^733114-24555220690Enzo Doria09/2013
5542^731891-636259220322Enzo Doria12/2013
5552^731124-25539220091Enzo Doria09/2013
5562^730972-462029220045Enzo Doria07/2015
5572^730833+1868627220003Enzo Doria04/2016
5582^730645-2787133219947Enzo Doria11/2015
5592^730547-25581219917Enzo Doria09/2013
5602^730460+82291219891Enzo Doria09/2016
561L(1051849)219824Renaud Lifchitz03/2009
56211^210961-240219694Enzo Doria01/2013
5632^729611-113437219635Enzo Doria08/2014
564F(1049897)219416Henri Lifchitz10/2008
5652^728604+1879321219332Enzo Doria10/2016
56633^144412+2219292Robert Price04/2015
5672^727998-1862711219150Enzo Doria12/2015
5682^727729-114073219069Enzo Doria12/2014
5692^727496-1851809218999Enzo Doria08/2015
5702^726591+2793143218726Enzo Doria02/2016
5712^725534-2791931218408Enzo Doria02/2016
5722^722184+1877821217400Enzo Doria08/2016
573(109*10^217360-1)/9217362Serge Batalov12/2014
574281*499979#/46410-2702372216849Robert Smith08/2016
575281*499979#/46410+2400766216849Robert Smith08/2016
576tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
5772^718756-114107216368Enzo Doria12/2014
5782^717305+80327215931Enzo Doria07/2016
5792^717069-59773215860Enzo Doria10/2015
580277^88301-276^88301215674Jean-Louis Charton06/2012
581227^91413-40215372Enzo Doria04/2015
5822^714717+782897215152Enzo Doria11/2016
583tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
5842^713241+1879157214707Enzo Doria08/2016
58511^206081-10^206081214612Jean-Louis Charton10/2011
5862^712801-69553214575Enzo Doria01/2016
5872^712603-25357214515Enzo Doria09/2013
5882^711721-1846723214250Enzo Doria07/2015
5892^710730-396765213952Enzo Doria09/2013
5902^708468-114329213271Enzo Doria02/2015
591(163*10^212779-1)/9212781Serge Batalov12/2014
5922^706838-69041212780Enzo Doria11/2015
5932^704577-113871212099Enzo Doria10/2014
5942^704110-2792441211959Enzo Doria02/2016
5952^703943-1862947211908Enzo Doria12/2015
596(10^211610-91)/9211610Serge Batalov12/2014
597227^89797+2211565Lelio R Paula08/2012
5982^702194-3211382Paul Bourdelais03/2012
5992^702064+1874911211343Enzo Doria07/2016
6002^701968-113873211314Enzo Doria10/2014
6012^701713-113779211237Enzo Doria09/2014
6022^701449-25201211158Enzo Doria09/2013
6032^701403-2786977211144Enzo Doria11/2015
6042^701189-25423211079Enzo Doria09/2013
6052^701162-459161211071Enzo Doria05/2015
6062^700400+9385210842Lelio R Paula01/2014
6072^700131+1874693210761Enzo Doria06/2016
60811^202357-1140210734Enzo Doria12/2012
6092^698929-2788423210399Enzo Doria11/2015
610(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
6112^698316+1878601210215Enzo Doria08/2016
6122^697036+1878751209829Enzo Doria08/2016
613(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6142^696254-115151209594Enzo Doria06/2015
6152^694633+1887257209106Enzo Doria05/2017
6162^693959+180923208903Enzo Doria07/2016
6172^693462-1847561208753Enzo Doria07/2015
6182^690890-59981207979Enzo Doria11/2015
6192^690163+1877063207760Enzo Doria07/2016
6202^689286-29381207496Enzo Doria08/2015
6212^689122-114521207447Enzo Doria04/2015
6222^688373+6077207221Enzo Doria02/2016
6232^688201+1875527207170Enzo Doria07/2016
6242^687619+81563206994Enzo Doria08/2016
6252^686572-1845299206679Enzo Doria07/2015
626(21^156217-1)/20206552Paul Bourdelais04/2010
6272^685578+3206380Paul Bourdelais04/2012
6282^684836-49349206157Enzo Doria10/2015
6292^684163-2790967205954Enzo Doria12/2015
630326^81943-325^81943205941Jean-Louis Charton07/2012
631(2^684127-1)/23765203727205933Jens K. Andersen04/2009
6324^341233-3^341233205443Jean-Louis Charton01/2006
6332^681545+467205166Lelio R Paula11/2013
6342^681306+81049205094Enzo Doria07/2016
6352^680697+1877057204911Enzo Doria07/2016
6362^680415+71783204826Enzo Doria04/2016
6372^679860-459995204659Enzo Doria06/2015
6382^679593+1879547204578Enzo Doria09/2016
6392^678651+1875023204295Enzo Doria07/2016
6402^678561+678561204268Henri Lifchitz05/2006
6412^678101-114043204129Enzo Doria11/2014
6422^678028+1875631204107Enzo Doria06/2016
6432^676992-59783203795Enzo Doria10/2015
6442^676972+1866871203789Enzo Doria03/2016
6452^676761-9203726Robert Price01/2017
6462^676563-2792407203666Enzo Doria02/2016
6472^676306-114713203589Enzo Doria04/2015
648(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
6492^674627-25161203083Enzo Doria09/2013
6502^674603-69337203076Enzo Doria12/2015
6512^674459+74213203033Enzo Doria04/2016
6522^674116-458879202930Enzo Doria04/2015
6532^674076-114755202918Enzo Doria04/2015
6545^289937-4^289937202658Jean-Louis Charton03/2013
6552^672556-1835519202460Enzo Doria04/2015
6562^671446-351401202126Enzo Doria07/2015
6572^671373+77747202104Enzo Doria05/2016
6582^670726-114845201909Enzo Doria05/2015
6592^670539-25045201853Enzo Doria09/2013
6602^670213+282317201755Enzo Doria09/2016
6612^669854-113501201647Enzo Doria08/2014
6622^669718+81619201606Enzo Doria08/2016
663(145*10^201504-1)/9201506Serge Batalov12/2014
6642^668938-1839821201371Enzo Doria06/2015
6652^668492+1879303201237Enzo Doria08/2016
6666^258413-5^258413201085Jean-Louis Charton03/2013
6672^667894+1875589201057Enzo Doria06/2016
6682^667569-1836559200959Enzo Doria05/2015
669(172*10^200746-1)/9200748Serge Batalov12/2014
6702^666430+782569200616Enzo Doria10/2016
671103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
672numbpart(32235776596)200002Serge Batalov04/2017
673(10^200001+149)/3200001Serge Batalov12/2014
6742^662103-29287199313Enzo Doria08/2015
6752^660482-2891198825Yves Minet05/2016
6762^659583+1879223198555Enzo Doria08/2016
677(53*10^198529+1)/9198530Serge Batalov07/2010
6782^658828-29819198327Enzo Doria08/2015
6792^658776-2791229198312Enzo Doria01/2016
6802^658544-1854029198242Enzo Doria09/2015
681(157^90239-1)/156198154Alexander Zhirkov06/2016
6822^656462+1874419197615Enzo Doria06/2016
6832^655893-344563197444Enzo Doria07/2015
6842^655875+71333197439Enzo Doria04/2016
6852^655845-9197430Robert Price01/2017
6862^655682-1849121197380Enzo Doria08/2015
6872^655045-49603197189Enzo Doria10/2015
6882^655000-2784089197175Enzo Doria10/2015
689(18^157051-1)/17197141Paul Bourdelais03/2010
6902^654400-39719196995Enzo Doria09/2015
6912^654216-459995196939Enzo Doria06/2015
6922^653851+82295196829Enzo Doria09/2016
6932^653636-29429196765Enzo Doria08/2015
6942^653601-69673196754Enzo Doria02/2016
695(44*10^196684+1)/9196685Serge Batalov07/2010
6962^652786-1852571196509Enzo Doria08/2015
6972^652752-1325196498Yves Minet07/2015
6982^652470-1859141196414Enzo Doria10/2015
6992^652307+1877483196364Enzo Doria08/2016
7002^652293-115273196360Enzo Doria06/2015
7012^651218-1868201196037Enzo Doria04/2016
7022^651047-49687195985Enzo Doria10/2015
7032^650285-2785333195756Enzo Doria10/2015
7042^649811+1877573195613Enzo Doria08/2016
7052^649586+182839195545Enzo Doria11/2016
7062^649537-1867363195531Enzo Doria04/2016
7072^649536-1861499195530Enzo Doria12/2015
708(103*10^195478-1)/3195480Serge Batalov12/2014
7092^649102-59351195400Enzo Doria10/2015
7102^648988+1178971195365Enzo Doria06/2016
7112^648975-114319195361Enzo Doria02/2015
7122^648619-24835195254Enzo Doria09/2013
7132^648190-24737195125Enzo Doria09/2013
71411^187185-90194934Enzo Doria09/2012
7152^647068+77281194787Enzo Doria05/2016
71615^165559-14^165559194713Jean-Louis Charton03/2011
717F(931517)194676Henri Lifchitz09/2008
7182^646589+1179407194643Enzo Doria06/2016
7192^646289-114621194553Enzo Doria05/2015
7202^646236-39659194537Enzo Doria09/2015
7212^646161-59833194514Enzo Doria11/2015
7222*10^194413+3194414Robert Price07/2015
7232^645360-1848599194273Enzo Doria08/2015
724(112*10^194150-1)/3194152Serge Batalov12/2014
7252^644382+75169193979Enzo Doria04/2016
7262^644304-1861409193955Enzo Doria11/2015
7275*10^193907-9193908Robert Price05/2015
7282^644043+1876703193877Enzo Doria07/2016
7292^643735+1879733193784Enzo Doria09/2016
730(5^277183+1)/6193742Paul Bourdelais07/2010
7312^643216-286565193628Enzo Doria07/2015
7322^642888-24965193529Enzo Doria09/2013
7332^642448-114825193397Enzo Doria05/2015
7342^642437-1856623193393Enzo Doria10/2015
7352^642039-59797193273Enzo Doria11/2015
7362^641692-286349193169Enzo Doria07/2015
7372^641690-24737193168Enzo Doria09/2013
7382^641514+1876549193115Enzo Doria07/2016
7392^640888-2785619192927Enzo Doria10/2015
7402^640874-2783741192923Enzo Doria09/2015
7412^640181+467192714Lelio R Paula08/2013
7422^639536-1850249192520Enzo Doria08/2015
7432^639110-2792441192392Enzo Doria02/2016
7442^638955-29827192345Enzo Doria08/2015
7452^638713-2784223192272Enzo Doria10/2015
7462^638490-113507192205Enzo Doria08/2014
7472^638189-39943192115Enzo Doria09/2015
7482^638110+1877119192091Enzo Doria07/2016
7492^638066-2785211192078Enzo Doria10/2015
7502^637475-115309191900Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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