PRP Records

Probable Primes Top 10000

(172142 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(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5022^749444-1861889225606Enzo Doria12/2015
503tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5042^749096+1876861225501Enzo Doria07/2016
5052^748657+79607225369Enzo Doria06/2016
5062^746653-291583224765Enzo Doria07/2015
5072^746461-114043224708Enzo Doria11/2014
5082^745098-350471224297Enzo Doria06/2015
509(154*10^224061-1)/9224063Serge Batalov12/2014
5102^744211-1845787224030Enzo Doria07/2015
511234178^9+9^234178223463Anatoly F. Selevich07/2011
5122^741651-461197223260Enzo Doria07/2015
5132^741362-1845251223173Enzo Doria07/2015
5142^740455-1863877222900Enzo Doria12/2015
5152^739636-2792219222653Enzo Doria02/2016
51611^213654-180222498Enzo Doria01/2013
5172^738957-1859743222449Enzo Doria11/2015
518(10^221654+179)/9221654Serge Batalov12/2014
5192^736281+79817221643Enzo Doria06/2016
52010^221631+247617221632Patrick De Geest10/2013
52110^221631-9221631Alexander Gramolin02/2011
5222^735970-1839821221550Enzo Doria06/2015
5232^735367+60293221368Enzo Doria03/2016
5242^733264-2784089220735Enzo Doria10/2015
5252^733114-24555220690Enzo Doria09/2013
5262^731891-636259220322Enzo Doria12/2013
5272^731124-25539220091Enzo Doria09/2013
5282^730972-462029220045Enzo Doria07/2015
5292^730833+1868627220003Enzo Doria04/2016
5302^730645-2787133219947Enzo Doria11/2015
5312^730547-25581219917Enzo Doria09/2013
5322^730460+82291219891Enzo Doria09/2016
533L(1051849)219824Renaud Lifchitz03/2009
53411^210961-240219694Enzo Doria01/2013
5352^729611-113437219635Enzo Doria08/2014
536F(1049897)219416Henri Lifchitz10/2008
5372^728604+1879321219332Enzo Doria10/2016
53833^144412+2219292Robert Price04/2015
5392^727998-1862711219150Enzo Doria12/2015
5402^727729-114073219069Enzo Doria12/2014
5412^727496-1851809218999Enzo Doria08/2015
5422^726591+2793143218726Enzo Doria02/2016
5432^725534-2791931218408Enzo Doria02/2016
5442^722184+1877821217400Enzo Doria08/2016
545(109*10^217360-1)/9217362Serge Batalov12/2014
546281*499979#/46410-2702372216849Robert Smith08/2016
547281*499979#/46410+2400766216849Robert Smith08/2016
548tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
5492^718756-114107216368Enzo Doria12/2014
5502^717305+80327215931Enzo Doria07/2016
5512^717069-59773215860Enzo Doria10/2015
552277^88301-276^88301215674Jean-Louis Charton06/2012
553227^91413-40215372Enzo Doria04/2015
5542^714717+782897215152Enzo Doria11/2016
555tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
5562^713241+1879157214707Enzo Doria08/2016
55711^206081-10^206081214612Jean-Louis Charton10/2011
5582^712801-69553214575Enzo Doria01/2016
5592^712603-25357214515Enzo Doria09/2013
5602^711721-1846723214250Enzo Doria07/2015
5612^710730-396765213952Enzo Doria09/2013
5622^708468-114329213271Enzo Doria02/2015
563(163*10^212779-1)/9212781Serge Batalov12/2014
5642^706838-69041212780Enzo Doria11/2015
5652^704577-113871212099Enzo Doria10/2014
5662^704110-2792441211959Enzo Doria02/2016
5672^703943-1862947211908Enzo Doria12/2015
568(10^211610-91)/9211610Serge Batalov12/2014
569227^89797+2211565Lelio R Paula08/2012
5702^702194-3211382Paul Bourdelais03/2012
5712^702064+1874911211343Enzo Doria07/2016
5722^701968-113873211314Enzo Doria10/2014
5732^701713-113779211237Enzo Doria09/2014
5742^701449-25201211158Enzo Doria09/2013
5752^701403-2786977211144Enzo Doria11/2015
5762^701189-25423211079Enzo Doria09/2013
5772^701162-459161211071Enzo Doria05/2015
5782^700400+9385210842Lelio R Paula01/2014
5792^700131+1874693210761Enzo Doria06/2016
58011^202357-1140210734Enzo Doria12/2012
5812^698929-2788423210399Enzo Doria11/2015
582(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
5832^698316+1878601210215Enzo Doria08/2016
5842^697036+1878751209829Enzo Doria08/2016
585(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
5862^696254-115151209594Enzo Doria06/2015
5872^693959+180923208903Enzo Doria07/2016
5882^693462-1847561208753Enzo Doria07/2015
5892^690890-59981207979Enzo Doria11/2015
5902^690163+1877063207760Enzo Doria07/2016
5912^689286-29381207496Enzo Doria08/2015
5922^689122-114521207447Enzo Doria04/2015
5932^688373+6077207221Enzo Doria02/2016
5942^688201+1875527207170Enzo Doria07/2016
5952^687619+81563206994Enzo Doria08/2016
5962^686572-1845299206679Enzo Doria07/2015
597(21^156217-1)/20206552Paul Bourdelais04/2010
5982^685578+3206380Paul Bourdelais04/2012
5992^684836-49349206157Enzo Doria10/2015
6002^684163-2790967205954Enzo Doria12/2015
601326^81943-325^81943205941Jean-Louis Charton07/2012
602(2^684127-1)/23765203727205933Jens K. Andersen04/2009
6034^341233-3^341233205443Jean-Louis Charton01/2006
6042^681545+467205166Lelio R Paula11/2013
6052^681306+81049205094Enzo Doria07/2016
6062^680697+1877057204911Enzo Doria07/2016
6072^680415+71783204826Enzo Doria04/2016
6082^679860-459995204659Enzo Doria06/2015
6092^679593+1879547204578Enzo Doria09/2016
6102^678651+1875023204295Enzo Doria07/2016
6112^678561+678561204268Henri Lifchitz05/2006
6122^678101-114043204129Enzo Doria11/2014
6132^678028+1875631204107Enzo Doria06/2016
6142^676992-59783203795Enzo Doria10/2015
6152^676972+1866871203789Enzo Doria03/2016
6162^676761-9203726Robert Price01/2017
6172^676563-2792407203666Enzo Doria02/2016
6182^676306-114713203589Enzo Doria04/2015
619(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
6202^674627-25161203083Enzo Doria09/2013
6212^674603-69337203076Enzo Doria12/2015
6222^674459+74213203033Enzo Doria04/2016
6232^674116-458879202930Enzo Doria04/2015
6242^674076-114755202918Enzo Doria04/2015
6255^289937-4^289937202658Jean-Louis Charton03/2013
6262^672556-1835519202460Enzo Doria04/2015
6272^671446-351401202126Enzo Doria07/2015
6282^671373+77747202104Enzo Doria05/2016
6292^670726-114845201909Enzo Doria05/2015
6302^670539-25045201853Enzo Doria09/2013
6312^670213+282317201755Enzo Doria09/2016
6322^669854-113501201647Enzo Doria08/2014
6332^669718+81619201606Enzo Doria08/2016
634(145*10^201504-1)/9201506Serge Batalov12/2014
6352^668938-1839821201371Enzo Doria06/2015
6362^668492+1879303201237Enzo Doria08/2016
6376^258413-5^258413201085Jean-Louis Charton03/2013
6382^667894+1875589201057Enzo Doria06/2016
6392^667569-1836559200959Enzo Doria05/2015
640(172*10^200746-1)/9200748Serge Batalov12/2014
6412^666430+782569200616Enzo Doria10/2016
642(10^200001+149)/3200001Serge Batalov12/2014
6432^662103-29287199313Enzo Doria08/2015
6442^660482-2891198825Yves Minet05/2016
6452^659583+1879223198555Enzo Doria08/2016
646(53*10^198529+1)/9198530Serge Batalov07/2010
6472^658828-29819198327Enzo Doria08/2015
6482^658776-2791229198312Enzo Doria01/2016
6492^658544-1854029198242Enzo Doria09/2015
650(157^90239-1)/156198154Alexander Zhirkov06/2016
6512^656462+1874419197615Enzo Doria06/2016
6522^655893-344563197444Enzo Doria07/2015
6532^655875+71333197439Enzo Doria04/2016
6542^655845-9197430Robert Price01/2017
6552^655682-1849121197380Enzo Doria08/2015
6562^655045-49603197189Enzo Doria10/2015
6572^655000-2784089197175Enzo Doria10/2015
658(18^157051-1)/17197141Paul Bourdelais03/2010
6592^654400-39719196995Enzo Doria09/2015
6602^654216-459995196939Enzo Doria06/2015
6612^653851+82295196829Enzo Doria09/2016
6622^653636-29429196765Enzo Doria08/2015
6632^653601-69673196754Enzo Doria02/2016
664(44*10^196684+1)/9196685Serge Batalov07/2010
6652^652786-1852571196509Enzo Doria08/2015
6662^652752-1325196498Yves Minet07/2015
6672^652470-1859141196414Enzo Doria10/2015
6682^652307+1877483196364Enzo Doria08/2016
6692^652293-115273196360Enzo Doria06/2015
6702^651218-1868201196037Enzo Doria04/2016
6712^651047-49687195985Enzo Doria10/2015
6722^650285-2785333195756Enzo Doria10/2015
6732^649811+1877573195613Enzo Doria08/2016
6742^649586+182839195545Enzo Doria11/2016
6752^649537-1867363195531Enzo Doria04/2016
6762^649536-1861499195530Enzo Doria12/2015
677(103*10^195478-1)/3195480Serge Batalov12/2014
6782^649102-59351195400Enzo Doria10/2015
6792^648988+1178971195365Enzo Doria06/2016
6802^648975-114319195361Enzo Doria02/2015
6812^648619-24835195254Enzo Doria09/2013
6822^648190-24737195125Enzo Doria09/2013
68311^187185-90194934Enzo Doria09/2012
6842^647068+77281194787Enzo Doria05/2016
68515^165559-14^165559194713Jean-Louis Charton03/2011
686F(931517)194676Henri Lifchitz09/2008
6872^646589+1179407194643Enzo Doria06/2016
6882^646289-114621194553Enzo Doria05/2015
6892^646236-39659194537Enzo Doria09/2015
6902^646161-59833194514Enzo Doria11/2015
6912*10^194413+3194414Robert Price07/2015
6922^645360-1848599194273Enzo Doria08/2015
693(112*10^194150-1)/3194152Serge Batalov12/2014
6942^644382+75169193979Enzo Doria04/2016
6952^644304-1861409193955Enzo Doria11/2015
6965*10^193907-9193908Robert Price05/2015
6972^644043+1876703193877Enzo Doria07/2016
6982^643735+1879733193784Enzo Doria09/2016
699(5^277183+1)/6193742Paul Bourdelais07/2010
7002^643216-286565193628Enzo Doria07/2015
7012^642888-24965193529Enzo Doria09/2013
7022^642448-114825193397Enzo Doria05/2015
7032^642437-1856623193393Enzo Doria10/2015
7042^642039-59797193273Enzo Doria11/2015
7052^641692-286349193169Enzo Doria07/2015
7062^641690-24737193168Enzo Doria09/2013
7072^641514+1876549193115Enzo Doria07/2016
7082^640888-2785619192927Enzo Doria10/2015
7092^640874-2783741192923Enzo Doria09/2015
7102^640181+467192714Lelio R Paula08/2013
7112^639536-1850249192520Enzo Doria08/2015
7122^639110-2792441192392Enzo Doria02/2016
7132^638955-29827192345Enzo Doria08/2015
7142^638713-2784223192272Enzo Doria10/2015
7152^638490-113507192205Enzo Doria08/2014
7162^638189-39943192115Enzo Doria09/2015
7172^638110+1877119192091Enzo Doria07/2016
7182^638066-2785211192078Enzo Doria10/2015
7192^637475-115309191900Enzo Doria07/2015
7202^636661+1876577191655Enzo Doria07/2016
7212^636177-1855123191509Enzo Doria09/2015
7222^636158-113627191503Enzo Doria08/2014
723(37*25^136966+63)/4191472Curtis Bright05/2015
7242^636035+79823191466Enzo Doria06/2016
7252^636011-1860847191459Enzo Doria11/2015
7262^635926-1860611191433Enzo Doria11/2015
7273*10^191152-7191153Robert Price08/2015
7282^634883-1865677191119Enzo Doria02/2016
7292^634801+1871957191095Enzo Doria05/2016
730(35*10^191073+1)/9191074Serge Batalov07/2010
7312^634470-59861190995Enzo Doria11/2015
7322^634368-29519190964Enzo Doria08/2015
7332^634188-350609190910Enzo Doria06/2015
7342^633088-113879190579Enzo Doria10/2014
7352^633064+1874911190572Enzo Doria06/2016
7362^632795-351205190491Enzo Doria06/2015
7372^632156+78391190298Enzo Doria06/2016
7382^632082-1851971190276Enzo Doria08/2015
7392^632020+1880311190257Enzo Doria09/2016
7402^631637-462373190142Enzo Doria08/2015
7412^631122-39251189987Enzo Doria08/2015
7422^630359+1788953189757Enzo Doria05/2016
7432^630228+1871971189718Enzo Doria05/2016
7442^630108+781189682Lelio R Paula08/2013
7452^629870-1867811189610Enzo Doria04/2016
7462^629326+2792929189447Enzo Doria02/2016
747(10^189385-61)/3189385Serge Batalov12/2014
7482^629036+1874011189359Enzo Doria06/2016
7492^628930+80779189327Enzo Doria07/2016
7502^628582+1179439189223Enzo Doria06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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