PRP Records

Probable Primes Top 10000

(183432 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 ?
5012^782423+1879733235533Enzo Doria09/2016
5022^781682-2789543235310Enzo Doria12/2015
5032^780408-113453234927Enzo Doria08/2014
5042^780368-1864829234915Enzo Doria01/2016
5052^779593-1836559234681Enzo Doria05/2015
506(5^335429+1)/6234455Paul Bourdelais08/2010
5072^778395-113617234321Enzo Doria08/2014
5082^776245-2792353233674Enzo Doria02/2016
5092^776060-114029233618Enzo Doria11/2014
5102^775987-2789557233596Enzo Doria12/2015
5112^775672+1866721233501Enzo Doria03/2016
512(11^223999+1)/12233270Paul Bourdelais02/2010
5132^774118+1885789233033Enzo Doria04/2017
51421^176191-20^176191232964Jean-Louis Charton01/2015
5152^773679-113425232901Enzo Doria08/2014
51610^232599+192489232600Patrick De Geest12/2013
51710^232599-3232599Markus Tervooren10/2010
5182^772552-458879232562Enzo Doria04/2015
5192^772214+1874899232460Enzo Doria06/2016
5202^771994-1862771232394Enzo Doria12/2015
5212^771889+1876037232362Enzo Doria07/2016
5222^771660+1866511232293Enzo Doria02/2016
5235^332150-18188232163Enzo Doria06/2014
5243^485977-2^485977231870Mike Oakes09/2009
5252^770082-114161231818Enzo Doria01/2015
526(20^177967+1)/21231540Paul Bourdelais05/2013
5272^767622-9221231078Lelio R Paula01/2016
5282^767344+1880311230994Enzo Doria09/2016
529(3^483611-1)/2230741Paul Bourdelais02/2010
530(10^230706+179)/9230706Serge Batalov12/2014
5312^766309+1875257230682Enzo Doria06/2016
5322^765635+1879883230480Enzo Doria09/2016
5332^764348-113697230092Enzo Doria09/2014
5342^764131+78863230027Enzo Doria05/2016
5352^763701+60197229897Enzo Doria03/2016
5362^762841-25905229639Enzo Doria10/2013
5372^761117-113569229120Enzo Doria08/2014
5382^757985-2790013228177Enzo Doria12/2015
5392^757038-1862081227892Enzo Doria12/2015
5402^756839+95849227832Makoto Morimoto10/2013
541(2^756839+6989)/756091227826Makoto Morimoto09/2016
5422^756773-112723227812Enzo Doria07/2014
543524309#+616367227431Makoto Morimoto02/2016
5442^755097-114193227307Enzo Doria12/2014
5452^754473-2791513227120Enzo Doria01/2016
5462^751426-764321226202Enzo Doria12/2013
547(18^180181-1)/17226176Andy Steward04/2007
5482^750740-3225996Paul Bourdelais03/2012
5492^750725+60227225991Enzo Doria02/2016
5502^750525-113743225931Enzo Doria09/2014
551(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5522^749444-1861889225606Enzo Doria12/2015
553tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5542^749096+1876861225501Enzo Doria07/2016
5552^748657+79607225369Enzo Doria06/2016
5562^746653-291583224765Enzo Doria07/2015
5572^746461-114043224708Enzo Doria11/2014
5582^745098-350471224297Enzo Doria06/2015
559(154*10^224061-1)/9224063Serge Batalov12/2014
5602^744211-1845787224030Enzo Doria07/2015
561234178^9+9^234178223463Anatoly F. Selevich07/2011
5622^741651-461197223260Enzo Doria07/2015
5632^741362-1845251223173Enzo Doria07/2015
5642^740455-1863877222900Enzo Doria12/2015
5652^739636-2792219222653Enzo Doria02/2016
56611^213654-180222498Enzo Doria01/2013
5672^738957-1859743222449Enzo Doria11/2015
568(10^221654+179)/9221654Serge Batalov12/2014
5692^736281+79817221643Enzo Doria06/2016
57010^221631+247617221632Patrick De Geest10/2013
57110^221631-9221631Alexander Gramolin02/2011
5722^735970-1839821221550Enzo Doria06/2015
5732^735367+60293221368Enzo Doria03/2016
574(29^151153+1)/30221045Paul Bourdelais09/2017
5752^733264-2784089220735Enzo Doria10/2015
5762^733114-24555220690Enzo Doria09/2013
5772^731891-636259220322Enzo Doria12/2013
5782^731124-25539220091Enzo Doria09/2013
5792^730972-462029220045Enzo Doria07/2015
5802^730833+1868627220003Enzo Doria04/2016
5812^730645-2787133219947Enzo Doria11/2015
5822^730547-25581219917Enzo Doria09/2013
5832^730460+82291219891Enzo Doria09/2016
584L(1051849)219824Renaud Lifchitz03/2009
58511^210961-240219694Enzo Doria01/2013
5862^729611-113437219635Enzo Doria08/2014
587F(1049897)219416Henri Lifchitz10/2008
5882^728604+1879321219332Enzo Doria10/2016
58933^144412+2219292Robert Price04/2015
5902^727998-1862711219150Enzo Doria12/2015
5912^727729-114073219069Enzo Doria12/2014
5922^727496-1851809218999Enzo Doria08/2015
5932^726591+2793143218726Enzo Doria02/2016
5942^725534-2791931218408Enzo Doria02/2016
5952^722184+1877821217400Enzo Doria08/2016
596(109*10^217360-1)/9217362Serge Batalov12/2014
597281*499979#/46410-2702372216849Robert Smith08/2016
598281*499979#/46410+2400766216849Robert Smith08/2016
599tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
6002^718756-114107216368Enzo Doria12/2014
6012^717305+80327215931Enzo Doria07/2016
6022^717069-59773215860Enzo Doria10/2015
603277^88301-276^88301215674Jean-Louis Charton06/2012
604227^91413-40215372Enzo Doria04/2015
6052^714717+782897215152Enzo Doria11/2016
606tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
6072^713241+1879157214707Enzo Doria08/2016
60811^206081-10^206081214612Jean-Louis Charton10/2011
6092^712801-69553214575Enzo Doria01/2016
6102^712603-25357214515Enzo Doria09/2013
6112^711721-1846723214250Enzo Doria07/2015
6122^710730-396765213952Enzo Doria09/2013
6132^708468-114329213271Enzo Doria02/2015
614(163*10^212779-1)/9212781Serge Batalov12/2014
6152^706838-69041212780Enzo Doria11/2015
6162^704577-113871212099Enzo Doria10/2014
6172^704110-2792441211959Enzo Doria02/2016
6182^703943-1862947211908Enzo Doria12/2015
619(10^211610-91)/9211610Serge Batalov12/2014
620227^89797+2211565Lelio R Paula08/2012
6212^702194-3211382Paul Bourdelais03/2012
6222^702064+1874911211343Enzo Doria07/2016
6232^701968-113873211314Enzo Doria10/2014
6242^701713-113779211237Enzo Doria09/2014
6252^701449-25201211158Enzo Doria09/2013
6262^701403-2786977211144Enzo Doria11/2015
6272^701189-25423211079Enzo Doria09/2013
6282^701162-459161211071Enzo Doria05/2015
6292^700400+9385210842Lelio R Paula01/2014
6302^700131+1874693210761Enzo Doria06/2016
63111^202357-1140210734Enzo Doria12/2012
6322^698929-2788423210399Enzo Doria11/2015
633(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
6342^698316+1878601210215Enzo Doria08/2016
6352^697036+1878751209829Enzo Doria08/2016
636(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6372^696254-115151209594Enzo Doria06/2015
6382^694633+1887257209106Enzo Doria05/2017
6392^693959+180923208903Enzo Doria07/2016
6402^693462-1847561208753Enzo Doria07/2015
6412^690890-59981207979Enzo Doria11/2015
6422^690163+1877063207760Enzo Doria07/2016
6432^689286-29381207496Enzo Doria08/2015
6442^689122-114521207447Enzo Doria04/2015
6452^688373+6077207221Enzo Doria02/2016
6462^688201+1875527207170Enzo Doria07/2016
6472^687619+81563206994Enzo Doria08/2016
6482^686572-1845299206679Enzo Doria07/2015
649(21^156217-1)/20206552Paul Bourdelais04/2010
6502^685578+3206380Paul Bourdelais04/2012
6512^684836-49349206157Enzo Doria10/2015
6522^684163-2790967205954Enzo Doria12/2015
653326^81943-325^81943205941Jean-Louis Charton07/2012
654(2^684127-1)/23765203727205933Jens K. Andersen04/2009
6554^341233-3^341233205443Jean-Louis Charton01/2006
6562^681545+467205166Lelio R Paula11/2013
6572^681306+81049205094Enzo Doria07/2016
6582^680697+1877057204911Enzo Doria07/2016
6592^680415+71783204826Enzo Doria04/2016
6602^679860-459995204659Enzo Doria06/2015
6612^679593+1879547204578Enzo Doria09/2016
6622^678651+1875023204295Enzo Doria07/2016
6632^678561+678561204268Henri Lifchitz05/2006
6642^678101-114043204129Enzo Doria11/2014
6652^678028+1875631204107Enzo Doria06/2016
6662^676992-59783203795Enzo Doria10/2015
6672^676972+1866871203789Enzo Doria03/2016
6682^676761-9203726Robert Price01/2017
6692^676563-2792407203666Enzo Doria02/2016
6702^676306-114713203589Enzo Doria04/2015
671(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
6722^674627-25161203083Enzo Doria09/2013
6732^674603-69337203076Enzo Doria12/2015
6742^674459+74213203033Enzo Doria04/2016
6752^674116-458879202930Enzo Doria04/2015
6762^674076-114755202918Enzo Doria04/2015
6775^289937-4^289937202658Jean-Louis Charton03/2013
6782^672556-1835519202460Enzo Doria04/2015
6792^671446-351401202126Enzo Doria07/2015
6802^671373+77747202104Enzo Doria05/2016
6812^670726-114845201909Enzo Doria05/2015
6822^670539-25045201853Enzo Doria09/2013
6832^670213+282317201755Enzo Doria09/2016
6842^669854-113501201647Enzo Doria08/2014
6852^669718+81619201606Enzo Doria08/2016
686(145*10^201504-1)/9201506Serge Batalov12/2014
6872^668938-1839821201371Enzo Doria06/2015
6882^668492+1879303201237Enzo Doria08/2016
6896^258413-5^258413201085Jean-Louis Charton03/2013
6902^667894+1875589201057Enzo Doria06/2016
6912^667569-1836559200959Enzo Doria05/2015
692(172*10^200746-1)/9200748Serge Batalov12/2014
6932^666430+782569200616Enzo Doria10/2016
694103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
695numbpart(32235776596)200002Serge Batalov04/2017
696(10^200001+149)/3200001Serge Batalov12/2014
6972^662103-29287199313Enzo Doria08/2015
6982^660482-2891198825Yves Minet05/2016
6992^659583+1879223198555Enzo Doria08/2016
700(53*10^198529+1)/9198530Serge Batalov07/2010
7012^658828-29819198327Enzo Doria08/2015
7022^658776-2791229198312Enzo Doria01/2016
7032^658544-1854029198242Enzo Doria09/2015
704(157^90239-1)/156198154Alexander Zhirkov06/2016
7052^656462+1874419197615Enzo Doria06/2016
7062^655893-344563197444Enzo Doria07/2015
7072^655875+71333197439Enzo Doria04/2016
7082^655845-9197430Robert Price01/2017
7092^655682-1849121197380Enzo Doria08/2015
7102^655045-49603197189Enzo Doria10/2015
7112^655000-2784089197175Enzo Doria10/2015
712(18^157051-1)/17197141Paul Bourdelais03/2010
7132^654400-39719196995Enzo Doria09/2015
7142^654216-459995196939Enzo Doria06/2015
7152^653851+82295196829Enzo Doria09/2016
7162^653636-29429196765Enzo Doria08/2015
7172^653601-69673196754Enzo Doria02/2016
718(44*10^196684+1)/9196685Serge Batalov07/2010
7192^652786-1852571196509Enzo Doria08/2015
7202^652752-1325196498Yves Minet07/2015
7212^652470-1859141196414Enzo Doria10/2015
7222^652307+1877483196364Enzo Doria08/2016
7232^652293-115273196360Enzo Doria06/2015
7242^651218-1868201196037Enzo Doria04/2016
7252^651047-49687195985Enzo Doria10/2015
7262^650285-2785333195756Enzo Doria10/2015
7272^649811+1877573195613Enzo Doria08/2016
7282^649586+182839195545Enzo Doria11/2016
7292^649537-1867363195531Enzo Doria04/2016
7302^649536-1861499195530Enzo Doria12/2015
731(103*10^195478-1)/3195480Serge Batalov12/2014
7322^649102-59351195400Enzo Doria10/2015
7332^648988+1178971195365Enzo Doria06/2016
7342^648975-114319195361Enzo Doria02/2015
7352^648619-24835195254Enzo Doria09/2013
7362^648190-24737195125Enzo Doria09/2013
73711^187185-90194934Enzo Doria09/2012
7382^647068+77281194787Enzo Doria05/2016
73915^165559-14^165559194713Jean-Louis Charton03/2011
740F(931517)194676Henri Lifchitz09/2008
7412^646589+1179407194643Enzo Doria06/2016
7422^646289-114621194553Enzo Doria05/2015
7432^646236-39659194537Enzo Doria09/2015
7442^646161-59833194514Enzo Doria11/2015
7452*10^194413+3194414Robert Price07/2015
7462^645360-1848599194273Enzo Doria08/2015
747(112*10^194150-1)/3194152Serge Batalov12/2014
7482^644382+75169193979Enzo Doria04/2016
7492^644304-1861409193955Enzo Doria11/2015
7505*10^193907-9193908Robert Price05/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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