PRP Records

Probable Primes Top 10000

(255312 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 ?
5012^840797-3253106Paul Bourdelais06/2019
5022^840716-2969253081Yves Minet05/2016
5032^840358-462491252973Enzo Doria08/2015
5042^840310+1878379252959Enzo Doria08/2016
50511^242579-60252620Enzo Doria10/2012
50645^152659+2252378Robert Price09/2015
507(95^127583+1)/96252322Paul Bourdelais07/2019
5082^837725+1869377252181Enzo Doria05/2016
5092^837536-311039252124Enzo Doria06/2015
51021^190632-2252058Robert Price07/2015
5112^837242+1873297252035Enzo Doria06/2016
5122^836656-2787929251859Enzo Doria11/2015
5132^836380+1875541251776Enzo Doria07/2016
514(359^98327-1)/358251233Alexander Zhirkov11/2017
515tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
5162^832511-461197250611Enzo Doria07/2015
5172^832505+1881137250609Enzo Doria11/2016
5182^832363+583295250567Enzo Doria12/2016
5192^832244-403635250531Enzo Doria01/2014
5202^831157+1880657250204Enzo Doria11/2016
5212^831088-7200899250183Enzo Doria01/2015
5222^830956-1349250143Yves Minet07/2015
5232^830037+282317249867Enzo Doria09/2016
5242^829589-113653249732Enzo Doria09/2014
5252^828281-3193249338Yves Minet08/2016
5262^828064-2785619249273Enzo Doria10/2015
5272^827602+60409249134Enzo Doria03/2016
52810^249010+348861249011Patrick De Geest04/2016
52910^249010-21249010Serge Batalov12/2014
5302^826733+1882907248872Enzo Doria12/2016
5312^825682+1876549248556Enzo Doria07/2016
5322^824991-114121248348Enzo Doria12/2014
5332^824642-362727248242Enzo Doria12/2013
5342^824565-114265248219Enzo Doria01/2015
535(73*10^248145-1)/9248146Robert Price01/2015
536(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
537(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
5382^822296+76501247536Enzo Doria05/2016
5392^821590-114167247324Enzo Doria12/2014
5402^821512-2790659247300Enzo Doria12/2015
5412^820077+382847246868Enzo Doria11/2016
5422^820001+81269246845Enzo Doria07/2016
5432^819463-59197246683Enzo Doria10/2015
5442^819296+80581246633Enzo Doria07/2016
5452^817160-350369245990Enzo Doria06/2015
54688093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
5472^815111-113857245373Enzo Doria10/2014
5482^814914-4001245314Yves Minet05/2017
549846^83761-845^83761245200Jean-Louis Charton12/2012
5502^814356-2790449245146Enzo Doria12/2015
5512^814276-459029245122Enzo Doria04/2015
5522^814023+180923245046Enzo Doria07/2016
553(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
5542^811842-113675244389Enzo Doria09/2014
5552^811132-2787929244176Enzo Doria11/2015
5562^809746-2790971243758Enzo Doria01/2016
5572^808767-3295243464Yves Minet12/2016
5582^808621-113809243420Enzo Doria09/2014
5592^807724+1879621243150Enzo Doria09/2016
5602^805843-113611242583Enzo Doria08/2014
5612^805745-459763242554Enzo Doria05/2015
5622^805353+782687242436Enzo Doria11/2016
5632^804277-417933242112Enzo Doria01/2014
5642^803468-269039241868Enzo Doria10/2013
5652^803172+80851241779Enzo Doria07/2016
5663^506233-2241535Robert Price11/2013
5672^802025-25999241434Enzo Doria10/2013
568(3^505823+3^252912+1)/7241339Serge Batalov03/2014
5692^801303+1872923241217Enzo Doria05/2016
5702^800579-1862947240999Enzo Doria12/2015
5713^504206+2240568Luke W. Richards03/2018
5722^798973-26283240515Enzo Doria10/2013
5732^798671-69487240424Enzo Doria12/2015
5742^797220+79831239988Enzo Doria06/2016
5752^796910-26001239894Enzo Doria10/2013
5762^796598+653119239800Enzo Doria12/2016
5772^796432-1859729239750Enzo Doria11/2015
5782^796002-1852211239621Enzo Doria08/2015
5792^795709+75767239533Enzo Doria04/2016
5802^795708+81721239532Enzo Doria08/2016
5812^795468-2786249239460Enzo Doria10/2015
5822^795442+80779239452Enzo Doria07/2016
5832^795075-1852057239342Enzo Doria08/2015
584(86^123677+1)/87239252Paul Bourdelais01/2019
5852^794043+1875023239031Enzo Doria06/2016
5862^793347-69577238822Enzo Doria01/2016
5872^792988-344429238714Enzo Doria08/2015
5882^792700-2786369238627Enzo Doria11/2015
5892^792663-1844797238616Enzo Doria06/2015
5902^792605-291943238598Enzo Doria07/2015
591(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
5922^789373+1869377237625Enzo Doria05/2016
593((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5942^788942+1866409237496Enzo Doria02/2016
5952^788844-114329237466Enzo Doria01/2015
5962^788705-1859713237424Enzo Doria11/2015
5972^786180+1871971236664Enzo Doria05/2016
59811^227092-90236492Enzo Doria11/2012
5992^785260+1866361236387Enzo Doria02/2016
6002^785220+1880611236375Enzo Doria10/2016
60119^184650-2236122Robert Price10/2014
60210^236059+216513236060Patrick De Geest04/2016
60310^236059-20909236059Robert Price09/2015
604(87^121487-1)/86235625Paul Bourdelais12/2018
6052^782634-113981235597Enzo Doria11/2014
6062^782423+1879733235533Enzo Doria09/2016
6072^781682-2789543235310Enzo Doria12/2015
6082^780408-113453234927Enzo Doria08/2014
6092^780368-1864829234915Enzo Doria01/2016
6102^779593-1836559234681Enzo Doria05/2015
611(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
612(5^335429+1)/6234455Paul Bourdelais08/2010
6132^778395-113617234321Enzo Doria08/2014
6142^776245-2792353233674Enzo Doria02/2016
6152^776060-114029233618Enzo Doria11/2014
6162^775987-2789557233596Enzo Doria12/2015
6172^775672+1866721233501Enzo Doria03/2016
618(11^223999+1)/12233270Paul Bourdelais02/2010
6192^774118+1885789233033Enzo Doria04/2017
62021^176191-20^176191232964Jean-Louis Charton01/2015
6212^773679-113425232901Enzo Doria08/2014
62210^232599+192489232600Patrick De Geest12/2013
62310^232599-3232599Markus Tervooren10/2010
6242^772552-458879232562Enzo Doria04/2015
6252^772214+1874899232460Enzo Doria06/2016
6262^771994-1862771232394Enzo Doria12/2015
6272^771889+1876037232362Enzo Doria07/2016
6282^771660+1866511232293Enzo Doria02/2016
6295^332150-18188232163Enzo Doria06/2014
6303^485977-2^485977231870Mike Oakes09/2009
6312^770082-114161231818Enzo Doria01/2015
632(20^177967+1)/21231540Paul Bourdelais05/2013
6332^767622-9221231078Lelio R Paula01/2016
6342^767344+1880311230994Enzo Doria09/2016
635(3^483611-1)/2230741Paul Bourdelais02/2010
636(10^230706+179)/9230706Serge Batalov12/2014
6372^766309+1875257230682Enzo Doria06/2016
6382^765635+1879883230480Enzo Doria09/2016
6392^764348-113697230092Enzo Doria09/2014
6402^764131+78863230027Enzo Doria05/2016
6412^763701+60197229897Enzo Doria03/2016
6422^762841-25905229639Enzo Doria10/2013
6432^761117-113569229120Enzo Doria08/2014
644(98^114859+1)/99228709Paul Bourdelais12/2018
645(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
6462^757985-2790013228177Enzo Doria12/2015
6472^757038-1862081227892Enzo Doria12/2015
6482^756839+95849227832Makoto Morimoto10/2013
649(2^756839+6989)/756091227826Makoto Morimoto09/2016
650(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
6512^756773-112723227812Enzo Doria07/2014
652524309#+616367227431Makoto Morimoto02/2016
6532^755097-114193227307Enzo Doria12/2014
6542^754473-2791513227120Enzo Doria01/2016
6552^751426-764321226202Enzo Doria12/2013
656(18^180181-1)/17226176Andy Steward04/2007
6572^750740-3225996Paul Bourdelais03/2012
6582^750725+60227225991Enzo Doria02/2016
6592^750525-113743225931Enzo Doria09/2014
660(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
6612^749444-1861889225606Enzo Doria12/2015
662tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
6632^749096+1876861225501Enzo Doria07/2016
664(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
6652^748657+79607225369Enzo Doria06/2016
6662^746653-291583224765Enzo Doria07/2015
6672^746461-114043224708Enzo Doria11/2014
6682^745098-350471224297Enzo Doria06/2015
669(154*10^224061-1)/9224063Serge Batalov12/2014
6702^744211-1845787224030Enzo Doria07/2015
6712^743592-134579223844Hans Havermann10/2018
6722^742452+3223501Paul Bourdelais06/2019
673234178^9+9^234178223463Anatoly F. Selevich07/2011
6742^741651-461197223260Enzo Doria07/2015
6752^741362-1845251223173Enzo Doria07/2015
6762^740455-1863877222900Enzo Doria12/2015
6772^739636-2792219222653Enzo Doria02/2016
67811^213654-180222498Enzo Doria01/2013
6792^738957-1859743222449Enzo Doria11/2015
680(54^128189+1)/55222073Paul Bourdelais11/2018
681(10^221654+179)/9221654Serge Batalov12/2014
6822^736281+79817221643Enzo Doria06/2016
68310^221631+247617221632Patrick De Geest10/2013
68410^221631-9221631Alexander Gramolin02/2011
6852^735970-1839821221550Enzo Doria06/2015
6862^735367+60293221368Enzo Doria03/2016
687(29^151153+1)/30221045Paul Bourdelais09/2017
6882^733264-2784089220735Enzo Doria10/2015
6892^733114-24555220690Enzo Doria09/2013
6902^731891-636259220322Enzo Doria12/2013
6912^731124-25539220091Enzo Doria09/2013
6922^730972-462029220045Enzo Doria07/2015
6932^730833+1868627220003Enzo Doria04/2016
6942^730645-2787133219947Enzo Doria11/2015
6952^730547-25581219917Enzo Doria09/2013
6962^730460+82291219891Enzo Doria09/2016
697(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
698L(1051849)219824Renaud Lifchitz03/2009
69911^210961-240219694Enzo Doria01/2013
7002^729611-113437219635Enzo Doria08/2014
701F(1049897)219416Henri Lifchitz10/2008
7022^728604+1879321219332Enzo Doria10/2016
70333^144412+2219292Robert Price04/2015
7042^728277-183313219234Hans Havermann10/2018
7052^727998-1862711219150Enzo Doria12/2015
7062^727729-114073219069Enzo Doria12/2014
7072^727496-1851809218999Enzo Doria08/2015
7082^726591+2793143218726Enzo Doria02/2016
7092^725534-2791931218408Enzo Doria02/2016
7102^722184+1877821217400Enzo Doria08/2016
711(109*10^217360-1)/9217362Serge Batalov12/2014
712281*499979#/46410-2702372216849Robert Smith08/2016
713281*499979#/46410+2400766216849Robert Smith08/2016
714tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
7152^718756-114107216368Enzo Doria12/2014
7162^717305+80327215931Enzo Doria07/2016
7172^717069-59773215860Enzo Doria10/2015
71830^146021-29^146021215691Jean-Louis Charton09/2018
719277^88301-276^88301215674Jean-Louis Charton06/2012
720227^91413-40215372Enzo Doria04/2015
7212^714717+782897215152Enzo Doria11/2016
722tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
7232^713241+1879157214707Enzo Doria08/2016
72411^206081-10^206081214612Jean-Louis Charton10/2011
7252^712801-69553214575Enzo Doria01/2016
7262^712603-25357214515Enzo Doria09/2013
7272^711721-1846723214250Enzo Doria07/2015
7282^710730-396765213952Enzo Doria09/2013
7292^708468-114329213271Enzo Doria02/2015
730(163*10^212779-1)/9212781Serge Batalov12/2014
7312^706838-69041212780Enzo Doria11/2015
7322^704577-113871212099Enzo Doria10/2014
7332^704110-2792441211959Enzo Doria02/2016
7342^703943-1862947211908Enzo Doria12/2015
735(60^119083+1)/61211746Paul Bourdelais10/2018
736(10^211610-91)/9211610Serge Batalov12/2014
737227^89797+2211565Lelio R Paula08/2012
7382^702194-3211382Paul Bourdelais03/2012
7392^702064+1874911211343Enzo Doria07/2016
7402^701968-113873211314Enzo Doria10/2014
7412^701713-113779211237Enzo Doria09/2014
7422^701449-25201211158Enzo Doria09/2013
7432^701403-2786977211144Enzo Doria11/2015
7442^701189-25423211079Enzo Doria09/2013
7452^701162-459161211071Enzo Doria05/2015
746(24^152783-1)/23210872Paul Bourdelais04/2018
7472^700400+9385210842Lelio R Paula01/2014
7482^700131+1874693210761Enzo Doria06/2016
74911^202357-1140210734Enzo Doria12/2012
7502^698929-2788423210399Enzo Doria11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 14 2019 11:13 (Time in France)

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