PRP Records

Probable Primes Top 10000

(172751 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 ?
5012^762841-25905229639Enzo Doria10/2013
5022^761117-113569229120Enzo Doria08/2014
5032^757985-2790013228177Enzo Doria12/2015
5042^757038-1862081227892Enzo Doria12/2015
5052^756839+95849227832Makoto Morimoto10/2013
506(2^756839+6989)/756091227826Makoto Morimoto09/2016
5072^756773-112723227812Enzo Doria07/2014
508524309#+616367227431Makoto Morimoto02/2016
5092^755097-114193227307Enzo Doria12/2014
5102^754473-2791513227120Enzo Doria01/2016
5112^751426-764321226202Enzo Doria12/2013
512(18^180181-1)/17226176Andy Steward04/2007
5132^750740-3225996Paul Bourdelais03/2012
5142^750725+60227225991Enzo Doria02/2016
5152^750525-113743225931Enzo Doria09/2014
516(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5172^749444-1861889225606Enzo Doria12/2015
518tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5192^749096+1876861225501Enzo Doria07/2016
5202^748657+79607225369Enzo Doria06/2016
5212^746653-291583224765Enzo Doria07/2015
5222^746461-114043224708Enzo Doria11/2014
5232^745098-350471224297Enzo Doria06/2015
524(154*10^224061-1)/9224063Serge Batalov12/2014
5252^744211-1845787224030Enzo Doria07/2015
526234178^9+9^234178223463Anatoly F. Selevich07/2011
5272^741651-461197223260Enzo Doria07/2015
5282^741362-1845251223173Enzo Doria07/2015
5292^740455-1863877222900Enzo Doria12/2015
5302^739636-2792219222653Enzo Doria02/2016
53111^213654-180222498Enzo Doria01/2013
5322^738957-1859743222449Enzo Doria11/2015
533(10^221654+179)/9221654Serge Batalov12/2014
5342^736281+79817221643Enzo Doria06/2016
53510^221631+247617221632Patrick De Geest10/2013
53610^221631-9221631Alexander Gramolin02/2011
5372^735970-1839821221550Enzo Doria06/2015
5382^735367+60293221368Enzo Doria03/2016
5392^733264-2784089220735Enzo Doria10/2015
5402^733114-24555220690Enzo Doria09/2013
5412^731891-636259220322Enzo Doria12/2013
5422^731124-25539220091Enzo Doria09/2013
5432^730972-462029220045Enzo Doria07/2015
5442^730833+1868627220003Enzo Doria04/2016
5452^730645-2787133219947Enzo Doria11/2015
5462^730547-25581219917Enzo Doria09/2013
5472^730460+82291219891Enzo Doria09/2016
548L(1051849)219824Renaud Lifchitz03/2009
54911^210961-240219694Enzo Doria01/2013
5502^729611-113437219635Enzo Doria08/2014
551F(1049897)219416Henri Lifchitz10/2008
5522^728604+1879321219332Enzo Doria10/2016
55333^144412+2219292Robert Price04/2015
5542^727998-1862711219150Enzo Doria12/2015
5552^727729-114073219069Enzo Doria12/2014
5562^727496-1851809218999Enzo Doria08/2015
5572^726591+2793143218726Enzo Doria02/2016
5582^725534-2791931218408Enzo Doria02/2016
5592^722184+1877821217400Enzo Doria08/2016
560(109*10^217360-1)/9217362Serge Batalov12/2014
561281*499979#/46410-2702372216849Robert Smith08/2016
562281*499979#/46410+2400766216849Robert Smith08/2016
563tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
5642^718756-114107216368Enzo Doria12/2014
5652^717305+80327215931Enzo Doria07/2016
5662^717069-59773215860Enzo Doria10/2015
567277^88301-276^88301215674Jean-Louis Charton06/2012
568227^91413-40215372Enzo Doria04/2015
5692^714717+782897215152Enzo Doria11/2016
570tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
5712^713241+1879157214707Enzo Doria08/2016
57211^206081-10^206081214612Jean-Louis Charton10/2011
5732^712801-69553214575Enzo Doria01/2016
5742^712603-25357214515Enzo Doria09/2013
5752^711721-1846723214250Enzo Doria07/2015
5762^710730-396765213952Enzo Doria09/2013
5772^708468-114329213271Enzo Doria02/2015
578(163*10^212779-1)/9212781Serge Batalov12/2014
5792^706838-69041212780Enzo Doria11/2015
5802^704577-113871212099Enzo Doria10/2014
5812^704110-2792441211959Enzo Doria02/2016
5822^703943-1862947211908Enzo Doria12/2015
583(10^211610-91)/9211610Serge Batalov12/2014
584227^89797+2211565Lelio R Paula08/2012
5852^702194-3211382Paul Bourdelais03/2012
5862^702064+1874911211343Enzo Doria07/2016
5872^701968-113873211314Enzo Doria10/2014
5882^701713-113779211237Enzo Doria09/2014
5892^701449-25201211158Enzo Doria09/2013
5902^701403-2786977211144Enzo Doria11/2015
5912^701189-25423211079Enzo Doria09/2013
5922^701162-459161211071Enzo Doria05/2015
5932^700400+9385210842Lelio R Paula01/2014
5942^700131+1874693210761Enzo Doria06/2016
59511^202357-1140210734Enzo Doria12/2012
5962^698929-2788423210399Enzo Doria11/2015
597(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
5982^698316+1878601210215Enzo Doria08/2016
5992^697036+1878751209829Enzo Doria08/2016
600(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6012^696254-115151209594Enzo Doria06/2015
6022^693959+180923208903Enzo Doria07/2016
6032^693462-1847561208753Enzo Doria07/2015
6042^690890-59981207979Enzo Doria11/2015
6052^690163+1877063207760Enzo Doria07/2016
6062^689286-29381207496Enzo Doria08/2015
6072^689122-114521207447Enzo Doria04/2015
6082^688373+6077207221Enzo Doria02/2016
6092^688201+1875527207170Enzo Doria07/2016
6102^687619+81563206994Enzo Doria08/2016
6112^686572-1845299206679Enzo Doria07/2015
612(21^156217-1)/20206552Paul Bourdelais04/2010
6132^685578+3206380Paul Bourdelais04/2012
6142^684836-49349206157Enzo Doria10/2015
6152^684163-2790967205954Enzo Doria12/2015
616326^81943-325^81943205941Jean-Louis Charton07/2012
617(2^684127-1)/23765203727205933Jens K. Andersen04/2009
6184^341233-3^341233205443Jean-Louis Charton01/2006
6192^681545+467205166Lelio R Paula11/2013
6202^681306+81049205094Enzo Doria07/2016
6212^680697+1877057204911Enzo Doria07/2016
6222^680415+71783204826Enzo Doria04/2016
6232^679860-459995204659Enzo Doria06/2015
6242^679593+1879547204578Enzo Doria09/2016
6252^678651+1875023204295Enzo Doria07/2016
6262^678561+678561204268Henri Lifchitz05/2006
6272^678101-114043204129Enzo Doria11/2014
6282^678028+1875631204107Enzo Doria06/2016
6292^676992-59783203795Enzo Doria10/2015
6302^676972+1866871203789Enzo Doria03/2016
6312^676761-9203726Robert Price01/2017
6322^676563-2792407203666Enzo Doria02/2016
6332^676306-114713203589Enzo Doria04/2015
634(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
6352^674627-25161203083Enzo Doria09/2013
6362^674603-69337203076Enzo Doria12/2015
6372^674459+74213203033Enzo Doria04/2016
6382^674116-458879202930Enzo Doria04/2015
6392^674076-114755202918Enzo Doria04/2015
6405^289937-4^289937202658Jean-Louis Charton03/2013
6412^672556-1835519202460Enzo Doria04/2015
6422^671446-351401202126Enzo Doria07/2015
6432^671373+77747202104Enzo Doria05/2016
6442^670726-114845201909Enzo Doria05/2015
6452^670539-25045201853Enzo Doria09/2013
6462^670213+282317201755Enzo Doria09/2016
6472^669854-113501201647Enzo Doria08/2014
6482^669718+81619201606Enzo Doria08/2016
649(145*10^201504-1)/9201506Serge Batalov12/2014
6502^668938-1839821201371Enzo Doria06/2015
6512^668492+1879303201237Enzo Doria08/2016
6526^258413-5^258413201085Jean-Louis Charton03/2013
6532^667894+1875589201057Enzo Doria06/2016
6542^667569-1836559200959Enzo Doria05/2015
655(172*10^200746-1)/9200748Serge Batalov12/2014
6562^666430+782569200616Enzo Doria10/2016
657(10^200001+149)/3200001Serge Batalov12/2014
6582^662103-29287199313Enzo Doria08/2015
6592^660482-2891198825Yves Minet05/2016
6602^659583+1879223198555Enzo Doria08/2016
661(53*10^198529+1)/9198530Serge Batalov07/2010
6622^658828-29819198327Enzo Doria08/2015
6632^658776-2791229198312Enzo Doria01/2016
6642^658544-1854029198242Enzo Doria09/2015
665(157^90239-1)/156198154Alexander Zhirkov06/2016
6662^656462+1874419197615Enzo Doria06/2016
6672^655893-344563197444Enzo Doria07/2015
6682^655875+71333197439Enzo Doria04/2016
6692^655845-9197430Robert Price01/2017
6702^655682-1849121197380Enzo Doria08/2015
6712^655045-49603197189Enzo Doria10/2015
6722^655000-2784089197175Enzo Doria10/2015
673(18^157051-1)/17197141Paul Bourdelais03/2010
6742^654400-39719196995Enzo Doria09/2015
6752^654216-459995196939Enzo Doria06/2015
6762^653851+82295196829Enzo Doria09/2016
6772^653636-29429196765Enzo Doria08/2015
6782^653601-69673196754Enzo Doria02/2016
679(44*10^196684+1)/9196685Serge Batalov07/2010
6802^652786-1852571196509Enzo Doria08/2015
6812^652752-1325196498Yves Minet07/2015
6822^652470-1859141196414Enzo Doria10/2015
6832^652307+1877483196364Enzo Doria08/2016
6842^652293-115273196360Enzo Doria06/2015
6852^651218-1868201196037Enzo Doria04/2016
6862^651047-49687195985Enzo Doria10/2015
6872^650285-2785333195756Enzo Doria10/2015
6882^649811+1877573195613Enzo Doria08/2016
6892^649586+182839195545Enzo Doria11/2016
6902^649537-1867363195531Enzo Doria04/2016
6912^649536-1861499195530Enzo Doria12/2015
692(103*10^195478-1)/3195480Serge Batalov12/2014
6932^649102-59351195400Enzo Doria10/2015
6942^648988+1178971195365Enzo Doria06/2016
6952^648975-114319195361Enzo Doria02/2015
6962^648619-24835195254Enzo Doria09/2013
6972^648190-24737195125Enzo Doria09/2013
69811^187185-90194934Enzo Doria09/2012
6992^647068+77281194787Enzo Doria05/2016
70015^165559-14^165559194713Jean-Louis Charton03/2011
701F(931517)194676Henri Lifchitz09/2008
7022^646589+1179407194643Enzo Doria06/2016
7032^646289-114621194553Enzo Doria05/2015
7042^646236-39659194537Enzo Doria09/2015
7052^646161-59833194514Enzo Doria11/2015
7062*10^194413+3194414Robert Price07/2015
7072^645360-1848599194273Enzo Doria08/2015
708(112*10^194150-1)/3194152Serge Batalov12/2014
7092^644382+75169193979Enzo Doria04/2016
7102^644304-1861409193955Enzo Doria11/2015
7115*10^193907-9193908Robert Price05/2015
7122^644043+1876703193877Enzo Doria07/2016
7132^643735+1879733193784Enzo Doria09/2016
714(5^277183+1)/6193742Paul Bourdelais07/2010
7152^643216-286565193628Enzo Doria07/2015
7162^642888-24965193529Enzo Doria09/2013
7172^642448-114825193397Enzo Doria05/2015
7182^642437-1856623193393Enzo Doria10/2015
7192^642039-59797193273Enzo Doria11/2015
7202^641692-286349193169Enzo Doria07/2015
7212^641690-24737193168Enzo Doria09/2013
7222^641514+1876549193115Enzo Doria07/2016
7232^640888-2785619192927Enzo Doria10/2015
7242^640874-2783741192923Enzo Doria09/2015
7252^640181+467192714Lelio R Paula08/2013
7262^639536-1850249192520Enzo Doria08/2015
7272^639110-2792441192392Enzo Doria02/2016
7282^638955-29827192345Enzo Doria08/2015
7292^638713-2784223192272Enzo Doria10/2015
7302^638490-113507192205Enzo Doria08/2014
7312^638189-39943192115Enzo Doria09/2015
7322^638110+1877119192091Enzo Doria07/2016
7332^638066-2785211192078Enzo Doria10/2015
7342^637475-115309191900Enzo Doria07/2015
7352^636661+1876577191655Enzo Doria07/2016
7362^636177-1855123191509Enzo Doria09/2015
7372^636158-113627191503Enzo Doria08/2014
738(37*25^136966+63)/4191472Curtis Bright05/2015
7392^636035+79823191466Enzo Doria06/2016
7402^636011-1860847191459Enzo Doria11/2015
7412^635926-1860611191433Enzo Doria11/2015
7423*10^191152-7191153Robert Price08/2015
7432^634883-1865677191119Enzo Doria02/2016
7442^634801+1871957191095Enzo Doria05/2016
745(35*10^191073+1)/9191074Serge Batalov07/2010
7462^634470-59861190995Enzo Doria11/2015
7472^634368-29519190964Enzo Doria08/2015
7482^634188-350609190910Enzo Doria06/2015
7492^633088-113879190579Enzo Doria10/2014
7502^633064+1874911190572Enzo Doria06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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