PRP Records

Probable Primes Top 10000

(253466 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 (> 50000) Who ? When ?
50121^190632-2252058Robert Price07/2015
5022^837242+1873297252035Enzo Doria06/2016
5032^836656-2787929251859Enzo Doria11/2015
5042^836380+1875541251776Enzo Doria07/2016
505(359^98327-1)/358251233Alexander Zhirkov11/2017
506tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
5072^832511-461197250611Enzo Doria07/2015
5082^832505+1881137250609Enzo Doria11/2016
5092^832363+583295250567Enzo Doria12/2016
5102^832244-403635250531Enzo Doria01/2014
5112^831157+1880657250204Enzo Doria11/2016
5122^831088-7200899250183Enzo Doria01/2015
5132^830956-1349250143Yves Minet07/2015
5142^830037+282317249867Enzo Doria09/2016
5152^829589-113653249732Enzo Doria09/2014
5162^828281-3193249338Yves Minet08/2016
5172^828064-2785619249273Enzo Doria10/2015
5182^827602+60409249134Enzo Doria03/2016
51910^249010+348861249011Patrick De Geest04/2016
52010^249010-21249010Serge Batalov12/2014
5212^826733+1882907248872Enzo Doria12/2016
5222^825682+1876549248556Enzo Doria07/2016
5232^824991-114121248348Enzo Doria12/2014
5242^824642-362727248242Enzo Doria12/2013
5252^824565-114265248219Enzo Doria01/2015
526(73*10^248145-1)/9248146Robert Price01/2015
527(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
528(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
5292^822296+76501247536Enzo Doria05/2016
5302^821590-114167247324Enzo Doria12/2014
5312^821512-2790659247300Enzo Doria12/2015
5322^820077+382847246868Enzo Doria11/2016
5332^820001+81269246845Enzo Doria07/2016
5342^819463-59197246683Enzo Doria10/2015
5352^819296+80581246633Enzo Doria07/2016
5362^817160-350369245990Enzo Doria06/2015
53788093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
5382^815111-113857245373Enzo Doria10/2014
5392^814914-4001245314Yves Minet05/2017
540846^83761-845^83761245200Jean-Louis Charton12/2012
5412^814356-2790449245146Enzo Doria12/2015
5422^814276-459029245122Enzo Doria04/2015
5432^814023+180923245046Enzo Doria07/2016
544(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
5452^811842-113675244389Enzo Doria09/2014
5462^811132-2787929244176Enzo Doria11/2015
5472^809746-2790971243758Enzo Doria01/2016
5482^808767-3295243464Yves Minet12/2016
5492^808621-113809243420Enzo Doria09/2014
5502^807724+1879621243150Enzo Doria09/2016
5512^805843-113611242583Enzo Doria08/2014
5522^805745-459763242554Enzo Doria05/2015
5532^805353+782687242436Enzo Doria11/2016
5542^804277-417933242112Enzo Doria01/2014
5552^803468-269039241868Enzo Doria10/2013
5562^803172+80851241779Enzo Doria07/2016
5573^506233-2241535Robert Price11/2013
5582^802025-25999241434Enzo Doria10/2013
559(3^505823+3^252912+1)/7241339Serge Batalov03/2014
5602^801303+1872923241217Enzo Doria05/2016
5612^800579-1862947240999Enzo Doria12/2015
5623^504206+2240568Luke W. Richards03/2018
5632^798973-26283240515Enzo Doria10/2013
5642^798671-69487240424Enzo Doria12/2015
5652^797220+79831239988Enzo Doria06/2016
5662^796910-26001239894Enzo Doria10/2013
5672^796598+653119239800Enzo Doria12/2016
5682^796432-1859729239750Enzo Doria11/2015
5692^796002-1852211239621Enzo Doria08/2015
5702^795709+75767239533Enzo Doria04/2016
5712^795708+81721239532Enzo Doria08/2016
5722^795468-2786249239460Enzo Doria10/2015
5732^795442+80779239452Enzo Doria07/2016
5742^795075-1852057239342Enzo Doria08/2015
575(86^123677+1)/87239252Paul Bourdelais01/2019
5762^794043+1875023239031Enzo Doria06/2016
5772^793347-69577238822Enzo Doria01/2016
5782^792988-344429238714Enzo Doria08/2015
5792^792700-2786369238627Enzo Doria11/2015
5802^792663-1844797238616Enzo Doria06/2015
5812^792605-291943238598Enzo Doria07/2015
582(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
5832^789373+1869377237625Enzo Doria05/2016
584((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5852^788942+1866409237496Enzo Doria02/2016
5862^788844-114329237466Enzo Doria01/2015
5872^788705-1859713237424Enzo Doria11/2015
5882^786180+1871971236664Enzo Doria05/2016
58911^227092-90236492Enzo Doria11/2012
5902^785260+1866361236387Enzo Doria02/2016
5912^785220+1880611236375Enzo Doria10/2016
59219^184650-2236122Robert Price10/2014
59310^236059+216513236060Patrick De Geest04/2016
59410^236059-20909236059Robert Price09/2015
595(87^121487-1)/86235625Paul Bourdelais12/2018
5962^782634-113981235597Enzo Doria11/2014
5972^782423+1879733235533Enzo Doria09/2016
5982^781682-2789543235310Enzo Doria12/2015
5992^780408-113453234927Enzo Doria08/2014
6002^780368-1864829234915Enzo Doria01/2016
6012^779593-1836559234681Enzo Doria05/2015
602(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
603(5^335429+1)/6234455Paul Bourdelais08/2010
6042^778395-113617234321Enzo Doria08/2014
6052^776245-2792353233674Enzo Doria02/2016
6062^776060-114029233618Enzo Doria11/2014
6072^775987-2789557233596Enzo Doria12/2015
6082^775672+1866721233501Enzo Doria03/2016
609(11^223999+1)/12233270Paul Bourdelais02/2010
6102^774118+1885789233033Enzo Doria04/2017
61121^176191-20^176191232964Jean-Louis Charton01/2015
6122^773679-113425232901Enzo Doria08/2014
61310^232599+192489232600Patrick De Geest12/2013
61410^232599-3232599Markus Tervooren10/2010
6152^772552-458879232562Enzo Doria04/2015
6162^772214+1874899232460Enzo Doria06/2016
6172^771994-1862771232394Enzo Doria12/2015
6182^771889+1876037232362Enzo Doria07/2016
6192^771660+1866511232293Enzo Doria02/2016
6205^332150-18188232163Enzo Doria06/2014
6213^485977-2^485977231870Mike Oakes09/2009
6222^770082-114161231818Enzo Doria01/2015
623(20^177967+1)/21231540Paul Bourdelais05/2013
6242^767622-9221231078Lelio R Paula01/2016
6252^767344+1880311230994Enzo Doria09/2016
626(3^483611-1)/2230741Paul Bourdelais02/2010
627(10^230706+179)/9230706Serge Batalov12/2014
6282^766309+1875257230682Enzo Doria06/2016
6292^765635+1879883230480Enzo Doria09/2016
6302^764348-113697230092Enzo Doria09/2014
6312^764131+78863230027Enzo Doria05/2016
6322^763701+60197229897Enzo Doria03/2016
6332^762841-25905229639Enzo Doria10/2013
6342^761117-113569229120Enzo Doria08/2014
635(98^114859+1)/99228709Paul Bourdelais12/2018
636(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
6372^757985-2790013228177Enzo Doria12/2015
6382^757038-1862081227892Enzo Doria12/2015
6392^756839+95849227832Makoto Morimoto10/2013
640(2^756839+6989)/756091227826Makoto Morimoto09/2016
6412^756773-112723227812Enzo Doria07/2014
642524309#+616367227431Makoto Morimoto02/2016
6432^755097-114193227307Enzo Doria12/2014
6442^754473-2791513227120Enzo Doria01/2016
6452^751426-764321226202Enzo Doria12/2013
646(18^180181-1)/17226176Andy Steward04/2007
6472^750740-3225996Paul Bourdelais03/2012
6482^750725+60227225991Enzo Doria02/2016
6492^750525-113743225931Enzo Doria09/2014
650(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
6512^749444-1861889225606Enzo Doria12/2015
652tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
6532^749096+1876861225501Enzo Doria07/2016
654(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
6552^748657+79607225369Enzo Doria06/2016
6562^746653-291583224765Enzo Doria07/2015
6572^746461-114043224708Enzo Doria11/2014
6582^745098-350471224297Enzo Doria06/2015
659(154*10^224061-1)/9224063Serge Batalov12/2014
6602^744211-1845787224030Enzo Doria07/2015
6612^743592-134579223844Hans Havermann10/2018
6622^742452+3223501Paul Bourdelais06/2019
663234178^9+9^234178223463Anatoly F. Selevich07/2011
6642^741651-461197223260Enzo Doria07/2015
6652^741362-1845251223173Enzo Doria07/2015
6662^740455-1863877222900Enzo Doria12/2015
6672^739636-2792219222653Enzo Doria02/2016
66811^213654-180222498Enzo Doria01/2013
6692^738957-1859743222449Enzo Doria11/2015
670(54^128189+1)/55222073Paul Bourdelais11/2018
671(10^221654+179)/9221654Serge Batalov12/2014
6722^736281+79817221643Enzo Doria06/2016
67310^221631+247617221632Patrick De Geest10/2013
67410^221631-9221631Alexander Gramolin02/2011
6752^735970-1839821221550Enzo Doria06/2015
6762^735367+60293221368Enzo Doria03/2016
677(29^151153+1)/30221045Paul Bourdelais09/2017
6782^733264-2784089220735Enzo Doria10/2015
6792^733114-24555220690Enzo Doria09/2013
6802^731891-636259220322Enzo Doria12/2013
6812^731124-25539220091Enzo Doria09/2013
6822^730972-462029220045Enzo Doria07/2015
6832^730833+1868627220003Enzo Doria04/2016
6842^730645-2787133219947Enzo Doria11/2015
6852^730547-25581219917Enzo Doria09/2013
6862^730460+82291219891Enzo Doria09/2016
687(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
688L(1051849)219824Renaud Lifchitz03/2009
68911^210961-240219694Enzo Doria01/2013
6902^729611-113437219635Enzo Doria08/2014
691F(1049897)219416Henri Lifchitz10/2008
6922^728604+1879321219332Enzo Doria10/2016
69333^144412+2219292Robert Price04/2015
6942^728277-183313219234Hans Havermann10/2018
6952^727998-1862711219150Enzo Doria12/2015
6962^727729-114073219069Enzo Doria12/2014
6972^727496-1851809218999Enzo Doria08/2015
6982^726591+2793143218726Enzo Doria02/2016
6992^725534-2791931218408Enzo Doria02/2016
7002^722184+1877821217400Enzo Doria08/2016
701(109*10^217360-1)/9217362Serge Batalov12/2014
702281*499979#/46410-2702372216849Robert Smith08/2016
703281*499979#/46410+2400766216849Robert Smith08/2016
704tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
7052^718756-114107216368Enzo Doria12/2014
7062^717305+80327215931Enzo Doria07/2016
7072^717069-59773215860Enzo Doria10/2015
70830^146021-29^146021215691Jean-Louis Charton09/2018
709277^88301-276^88301215674Jean-Louis Charton06/2012
710227^91413-40215372Enzo Doria04/2015
7112^714717+782897215152Enzo Doria11/2016
712tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
7132^713241+1879157214707Enzo Doria08/2016
71411^206081-10^206081214612Jean-Louis Charton10/2011
7152^712801-69553214575Enzo Doria01/2016
7162^712603-25357214515Enzo Doria09/2013
7172^711721-1846723214250Enzo Doria07/2015
7182^710730-396765213952Enzo Doria09/2013
7192^708468-114329213271Enzo Doria02/2015
720(163*10^212779-1)/9212781Serge Batalov12/2014
7212^706838-69041212780Enzo Doria11/2015
7222^704577-113871212099Enzo Doria10/2014
7232^704110-2792441211959Enzo Doria02/2016
7242^703943-1862947211908Enzo Doria12/2015
725(60^119083+1)/61211746Paul Bourdelais10/2018
726(10^211610-91)/9211610Serge Batalov12/2014
727227^89797+2211565Lelio R Paula08/2012
7282^702194-3211382Paul Bourdelais03/2012
7292^702064+1874911211343Enzo Doria07/2016
7302^701968-113873211314Enzo Doria10/2014
7312^701713-113779211237Enzo Doria09/2014
7322^701449-25201211158Enzo Doria09/2013
7332^701403-2786977211144Enzo Doria11/2015
7342^701189-25423211079Enzo Doria09/2013
7352^701162-459161211071Enzo Doria05/2015
736(24^152783-1)/23210872Paul Bourdelais04/2018
7372^700400+9385210842Lelio R Paula01/2014
7382^700131+1874693210761Enzo Doria06/2016
73911^202357-1140210734Enzo Doria12/2012
7402^698929-2788423210399Enzo Doria11/2015
741(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
7422^698316+1878601210215Enzo Doria08/2016
7432^697036+1878751209829Enzo Doria08/2016
744(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
7452^696254-115151209594Enzo Doria06/2015
746(35^135623+1)/36209410Paul Bourdelais07/2018
7472^694633+1887257209106Enzo Doria05/2017
7482^693959+180923208903Enzo Doria07/2016
7492^693462-1847561208753Enzo Doria07/2015
7502^690890-59981207979Enzo Doria11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

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