PRP Records

Probable Primes Top 10000

(173006 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 ?
501(10^230706+179)/9230706Serge Batalov12/2014
5022^766309+1875257230682Enzo Doria06/2016
5032^765635+1879883230480Enzo Doria09/2016
5042^764348-113697230092Enzo Doria09/2014
5052^764131+78863230027Enzo Doria05/2016
5062^763701+60197229897Enzo Doria03/2016
5072^762841-25905229639Enzo Doria10/2013
5082^761117-113569229120Enzo Doria08/2014
5092^757985-2790013228177Enzo Doria12/2015
5102^757038-1862081227892Enzo Doria12/2015
5112^756839+95849227832Makoto Morimoto10/2013
512(2^756839+6989)/756091227826Makoto Morimoto09/2016
5132^756773-112723227812Enzo Doria07/2014
514524309#+616367227431Makoto Morimoto02/2016
5152^755097-114193227307Enzo Doria12/2014
5162^754473-2791513227120Enzo Doria01/2016
5172^751426-764321226202Enzo Doria12/2013
518(18^180181-1)/17226176Andy Steward04/2007
5192^750740-3225996Paul Bourdelais03/2012
5202^750725+60227225991Enzo Doria02/2016
5212^750525-113743225931Enzo Doria09/2014
522(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5232^749444-1861889225606Enzo Doria12/2015
524tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5252^749096+1876861225501Enzo Doria07/2016
5262^748657+79607225369Enzo Doria06/2016
5272^746653-291583224765Enzo Doria07/2015
5282^746461-114043224708Enzo Doria11/2014
5292^745098-350471224297Enzo Doria06/2015
530(154*10^224061-1)/9224063Serge Batalov12/2014
5312^744211-1845787224030Enzo Doria07/2015
532234178^9+9^234178223463Anatoly F. Selevich07/2011
5332^741651-461197223260Enzo Doria07/2015
5342^741362-1845251223173Enzo Doria07/2015
5352^740455-1863877222900Enzo Doria12/2015
5362^739636-2792219222653Enzo Doria02/2016
53711^213654-180222498Enzo Doria01/2013
5382^738957-1859743222449Enzo Doria11/2015
539(10^221654+179)/9221654Serge Batalov12/2014
5402^736281+79817221643Enzo Doria06/2016
54110^221631+247617221632Patrick De Geest10/2013
54210^221631-9221631Alexander Gramolin02/2011
5432^735970-1839821221550Enzo Doria06/2015
5442^735367+60293221368Enzo Doria03/2016
5452^733264-2784089220735Enzo Doria10/2015
5462^733114-24555220690Enzo Doria09/2013
5472^731891-636259220322Enzo Doria12/2013
5482^731124-25539220091Enzo Doria09/2013
5492^730972-462029220045Enzo Doria07/2015
5502^730833+1868627220003Enzo Doria04/2016
5512^730645-2787133219947Enzo Doria11/2015
5522^730547-25581219917Enzo Doria09/2013
5532^730460+82291219891Enzo Doria09/2016
554L(1051849)219824Renaud Lifchitz03/2009
55511^210961-240219694Enzo Doria01/2013
5562^729611-113437219635Enzo Doria08/2014
557F(1049897)219416Henri Lifchitz10/2008
5582^728604+1879321219332Enzo Doria10/2016
55933^144412+2219292Robert Price04/2015
5602^727998-1862711219150Enzo Doria12/2015
5612^727729-114073219069Enzo Doria12/2014
5622^727496-1851809218999Enzo Doria08/2015
5632^726591+2793143218726Enzo Doria02/2016
5642^725534-2791931218408Enzo Doria02/2016
5652^722184+1877821217400Enzo Doria08/2016
566(109*10^217360-1)/9217362Serge Batalov12/2014
567281*499979#/46410-2702372216849Robert Smith08/2016
568281*499979#/46410+2400766216849Robert Smith08/2016
569tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
5702^718756-114107216368Enzo Doria12/2014
5712^717305+80327215931Enzo Doria07/2016
5722^717069-59773215860Enzo Doria10/2015
573277^88301-276^88301215674Jean-Louis Charton06/2012
574227^91413-40215372Enzo Doria04/2015
5752^714717+782897215152Enzo Doria11/2016
576tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
5772^713241+1879157214707Enzo Doria08/2016
57811^206081-10^206081214612Jean-Louis Charton10/2011
5792^712801-69553214575Enzo Doria01/2016
5802^712603-25357214515Enzo Doria09/2013
5812^711721-1846723214250Enzo Doria07/2015
5822^710730-396765213952Enzo Doria09/2013
5832^708468-114329213271Enzo Doria02/2015
584(163*10^212779-1)/9212781Serge Batalov12/2014
5852^706838-69041212780Enzo Doria11/2015
5862^704577-113871212099Enzo Doria10/2014
5872^704110-2792441211959Enzo Doria02/2016
5882^703943-1862947211908Enzo Doria12/2015
589(10^211610-91)/9211610Serge Batalov12/2014
590227^89797+2211565Lelio R Paula08/2012
5912^702194-3211382Paul Bourdelais03/2012
5922^702064+1874911211343Enzo Doria07/2016
5932^701968-113873211314Enzo Doria10/2014
5942^701713-113779211237Enzo Doria09/2014
5952^701449-25201211158Enzo Doria09/2013
5962^701403-2786977211144Enzo Doria11/2015
5972^701189-25423211079Enzo Doria09/2013
5982^701162-459161211071Enzo Doria05/2015
5992^700400+9385210842Lelio R Paula01/2014
6002^700131+1874693210761Enzo Doria06/2016
60111^202357-1140210734Enzo Doria12/2012
6022^698929-2788423210399Enzo Doria11/2015
603(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
6042^698316+1878601210215Enzo Doria08/2016
6052^697036+1878751209829Enzo Doria08/2016
606(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6072^696254-115151209594Enzo Doria06/2015
6082^693959+180923208903Enzo Doria07/2016
6092^693462-1847561208753Enzo Doria07/2015
6102^690890-59981207979Enzo Doria11/2015
6112^690163+1877063207760Enzo Doria07/2016
6122^689286-29381207496Enzo Doria08/2015
6132^689122-114521207447Enzo Doria04/2015
6142^688373+6077207221Enzo Doria02/2016
6152^688201+1875527207170Enzo Doria07/2016
6162^687619+81563206994Enzo Doria08/2016
6172^686572-1845299206679Enzo Doria07/2015
618(21^156217-1)/20206552Paul Bourdelais04/2010
6192^685578+3206380Paul Bourdelais04/2012
6202^684836-49349206157Enzo Doria10/2015
6212^684163-2790967205954Enzo Doria12/2015
622326^81943-325^81943205941Jean-Louis Charton07/2012
623(2^684127-1)/23765203727205933Jens K. Andersen04/2009
6244^341233-3^341233205443Jean-Louis Charton01/2006
6252^681545+467205166Lelio R Paula11/2013
6262^681306+81049205094Enzo Doria07/2016
6272^680697+1877057204911Enzo Doria07/2016
6282^680415+71783204826Enzo Doria04/2016
6292^679860-459995204659Enzo Doria06/2015
6302^679593+1879547204578Enzo Doria09/2016
6312^678651+1875023204295Enzo Doria07/2016
6322^678561+678561204268Henri Lifchitz05/2006
6332^678101-114043204129Enzo Doria11/2014
6342^678028+1875631204107Enzo Doria06/2016
6352^676992-59783203795Enzo Doria10/2015
6362^676972+1866871203789Enzo Doria03/2016
6372^676761-9203726Robert Price01/2017
6382^676563-2792407203666Enzo Doria02/2016
6392^676306-114713203589Enzo Doria04/2015
640(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
6412^674627-25161203083Enzo Doria09/2013
6422^674603-69337203076Enzo Doria12/2015
6432^674459+74213203033Enzo Doria04/2016
6442^674116-458879202930Enzo Doria04/2015
6452^674076-114755202918Enzo Doria04/2015
6465^289937-4^289937202658Jean-Louis Charton03/2013
6472^672556-1835519202460Enzo Doria04/2015
6482^671446-351401202126Enzo Doria07/2015
6492^671373+77747202104Enzo Doria05/2016
6502^670726-114845201909Enzo Doria05/2015
6512^670539-25045201853Enzo Doria09/2013
6522^670213+282317201755Enzo Doria09/2016
6532^669854-113501201647Enzo Doria08/2014
6542^669718+81619201606Enzo Doria08/2016
655(145*10^201504-1)/9201506Serge Batalov12/2014
6562^668938-1839821201371Enzo Doria06/2015
6572^668492+1879303201237Enzo Doria08/2016
6586^258413-5^258413201085Jean-Louis Charton03/2013
6592^667894+1875589201057Enzo Doria06/2016
6602^667569-1836559200959Enzo Doria05/2015
661(172*10^200746-1)/9200748Serge Batalov12/2014
6622^666430+782569200616Enzo Doria10/2016
663103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
664numbpart(32235776596)200002Serge Batalov04/2017
665(10^200001+149)/3200001Serge Batalov12/2014
6662^662103-29287199313Enzo Doria08/2015
6672^660482-2891198825Yves Minet05/2016
6682^659583+1879223198555Enzo Doria08/2016
669(53*10^198529+1)/9198530Serge Batalov07/2010
6702^658828-29819198327Enzo Doria08/2015
6712^658776-2791229198312Enzo Doria01/2016
6722^658544-1854029198242Enzo Doria09/2015
673(157^90239-1)/156198154Alexander Zhirkov06/2016
6742^656462+1874419197615Enzo Doria06/2016
6752^655893-344563197444Enzo Doria07/2015
6762^655875+71333197439Enzo Doria04/2016
6772^655845-9197430Robert Price01/2017
6782^655682-1849121197380Enzo Doria08/2015
6792^655045-49603197189Enzo Doria10/2015
6802^655000-2784089197175Enzo Doria10/2015
681(18^157051-1)/17197141Paul Bourdelais03/2010
6822^654400-39719196995Enzo Doria09/2015
6832^654216-459995196939Enzo Doria06/2015
6842^653851+82295196829Enzo Doria09/2016
6852^653636-29429196765Enzo Doria08/2015
6862^653601-69673196754Enzo Doria02/2016
687(44*10^196684+1)/9196685Serge Batalov07/2010
6882^652786-1852571196509Enzo Doria08/2015
6892^652752-1325196498Yves Minet07/2015
6902^652470-1859141196414Enzo Doria10/2015
6912^652307+1877483196364Enzo Doria08/2016
6922^652293-115273196360Enzo Doria06/2015
6932^651218-1868201196037Enzo Doria04/2016
6942^651047-49687195985Enzo Doria10/2015
6952^650285-2785333195756Enzo Doria10/2015
6962^649811+1877573195613Enzo Doria08/2016
6972^649586+182839195545Enzo Doria11/2016
6982^649537-1867363195531Enzo Doria04/2016
6992^649536-1861499195530Enzo Doria12/2015
700(103*10^195478-1)/3195480Serge Batalov12/2014
7012^649102-59351195400Enzo Doria10/2015
7022^648988+1178971195365Enzo Doria06/2016
7032^648975-114319195361Enzo Doria02/2015
7042^648619-24835195254Enzo Doria09/2013
7052^648190-24737195125Enzo Doria09/2013
70611^187185-90194934Enzo Doria09/2012
7072^647068+77281194787Enzo Doria05/2016
70815^165559-14^165559194713Jean-Louis Charton03/2011
709F(931517)194676Henri Lifchitz09/2008
7102^646589+1179407194643Enzo Doria06/2016
7112^646289-114621194553Enzo Doria05/2015
7122^646236-39659194537Enzo Doria09/2015
7132^646161-59833194514Enzo Doria11/2015
7142*10^194413+3194414Robert Price07/2015
7152^645360-1848599194273Enzo Doria08/2015
716(112*10^194150-1)/3194152Serge Batalov12/2014
7172^644382+75169193979Enzo Doria04/2016
7182^644304-1861409193955Enzo Doria11/2015
7195*10^193907-9193908Robert Price05/2015
7202^644043+1876703193877Enzo Doria07/2016
7212^643735+1879733193784Enzo Doria09/2016
722(5^277183+1)/6193742Paul Bourdelais07/2010
7232^643216-286565193628Enzo Doria07/2015
7242^642888-24965193529Enzo Doria09/2013
7252^642448-114825193397Enzo Doria05/2015
7262^642437-1856623193393Enzo Doria10/2015
7272^642039-59797193273Enzo Doria11/2015
7282^641692-286349193169Enzo Doria07/2015
7292^641690-24737193168Enzo Doria09/2013
7302^641514+1876549193115Enzo Doria07/2016
7312^640888-2785619192927Enzo Doria10/2015
7322^640874-2783741192923Enzo Doria09/2015
7332^640181+467192714Lelio R Paula08/2013
7342^639536-1850249192520Enzo Doria08/2015
7352^639110-2792441192392Enzo Doria02/2016
7362^638955-29827192345Enzo Doria08/2015
7372^638713-2784223192272Enzo Doria10/2015
7382^638490-113507192205Enzo Doria08/2014
7392^638189-39943192115Enzo Doria09/2015
7402^638110+1877119192091Enzo Doria07/2016
7412^638066-2785211192078Enzo Doria10/2015
7422^637475-115309191900Enzo Doria07/2015
7432^636661+1876577191655Enzo Doria07/2016
7442^636177-1855123191509Enzo Doria09/2015
7452^636158-113627191503Enzo Doria08/2014
746(37*25^136966+63)/4191472Curtis Bright05/2015
7472^636035+79823191466Enzo Doria06/2016
7482^636011-1860847191459Enzo Doria11/2015
7492^635926-1860611191433Enzo Doria11/2015
7503*10^191152-7191153Robert Price08/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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