PRP Records

Probable Primes Top 10000

(255169 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 ?
5012^840310+1878379252959Enzo Doria08/2016
50211^242579-60252620Enzo Doria10/2012
50345^152659+2252378Robert Price09/2015
504(95^127583+1)/96252322Paul Bourdelais07/2019
5052^837725+1869377252181Enzo Doria05/2016
5062^837536-311039252124Enzo Doria06/2015
50721^190632-2252058Robert Price07/2015
5082^837242+1873297252035Enzo Doria06/2016
5092^836656-2787929251859Enzo Doria11/2015
5102^836380+1875541251776Enzo Doria07/2016
511(359^98327-1)/358251233Alexander Zhirkov11/2017
512tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
5132^832511-461197250611Enzo Doria07/2015
5142^832505+1881137250609Enzo Doria11/2016
5152^832363+583295250567Enzo Doria12/2016
5162^832244-403635250531Enzo Doria01/2014
5172^831157+1880657250204Enzo Doria11/2016
5182^831088-7200899250183Enzo Doria01/2015
5192^830956-1349250143Yves Minet07/2015
5202^830037+282317249867Enzo Doria09/2016
5212^829589-113653249732Enzo Doria09/2014
5222^828281-3193249338Yves Minet08/2016
5232^828064-2785619249273Enzo Doria10/2015
5242^827602+60409249134Enzo Doria03/2016
52510^249010+348861249011Patrick De Geest04/2016
52610^249010-21249010Serge Batalov12/2014
5272^826733+1882907248872Enzo Doria12/2016
5282^825682+1876549248556Enzo Doria07/2016
5292^824991-114121248348Enzo Doria12/2014
5302^824642-362727248242Enzo Doria12/2013
5312^824565-114265248219Enzo Doria01/2015
532(73*10^248145-1)/9248146Robert Price01/2015
533(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
534(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
5352^822296+76501247536Enzo Doria05/2016
5362^821590-114167247324Enzo Doria12/2014
5372^821512-2790659247300Enzo Doria12/2015
5382^820077+382847246868Enzo Doria11/2016
5392^820001+81269246845Enzo Doria07/2016
5402^819463-59197246683Enzo Doria10/2015
5412^819296+80581246633Enzo Doria07/2016
5422^817160-350369245990Enzo Doria06/2015
54388093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
5442^815111-113857245373Enzo Doria10/2014
5452^814914-4001245314Yves Minet05/2017
546846^83761-845^83761245200Jean-Louis Charton12/2012
5472^814356-2790449245146Enzo Doria12/2015
5482^814276-459029245122Enzo Doria04/2015
5492^814023+180923245046Enzo Doria07/2016
550(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
5512^811842-113675244389Enzo Doria09/2014
5522^811132-2787929244176Enzo Doria11/2015
5532^809746-2790971243758Enzo Doria01/2016
5542^808767-3295243464Yves Minet12/2016
5552^808621-113809243420Enzo Doria09/2014
5562^807724+1879621243150Enzo Doria09/2016
5572^805843-113611242583Enzo Doria08/2014
5582^805745-459763242554Enzo Doria05/2015
5592^805353+782687242436Enzo Doria11/2016
5602^804277-417933242112Enzo Doria01/2014
5612^803468-269039241868Enzo Doria10/2013
5622^803172+80851241779Enzo Doria07/2016
5633^506233-2241535Robert Price11/2013
5642^802025-25999241434Enzo Doria10/2013
565(3^505823+3^252912+1)/7241339Serge Batalov03/2014
5662^801303+1872923241217Enzo Doria05/2016
5672^800579-1862947240999Enzo Doria12/2015
5683^504206+2240568Luke W. Richards03/2018
5692^798973-26283240515Enzo Doria10/2013
5702^798671-69487240424Enzo Doria12/2015
5712^797220+79831239988Enzo Doria06/2016
5722^796910-26001239894Enzo Doria10/2013
5732^796598+653119239800Enzo Doria12/2016
5742^796432-1859729239750Enzo Doria11/2015
5752^796002-1852211239621Enzo Doria08/2015
5762^795709+75767239533Enzo Doria04/2016
5772^795708+81721239532Enzo Doria08/2016
5782^795468-2786249239460Enzo Doria10/2015
5792^795442+80779239452Enzo Doria07/2016
5802^795075-1852057239342Enzo Doria08/2015
581(86^123677+1)/87239252Paul Bourdelais01/2019
5822^794043+1875023239031Enzo Doria06/2016
5832^793347-69577238822Enzo Doria01/2016
5842^792988-344429238714Enzo Doria08/2015
5852^792700-2786369238627Enzo Doria11/2015
5862^792663-1844797238616Enzo Doria06/2015
5872^792605-291943238598Enzo Doria07/2015
588(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
5892^789373+1869377237625Enzo Doria05/2016
590((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5912^788942+1866409237496Enzo Doria02/2016
5922^788844-114329237466Enzo Doria01/2015
5932^788705-1859713237424Enzo Doria11/2015
5942^786180+1871971236664Enzo Doria05/2016
59511^227092-90236492Enzo Doria11/2012
5962^785260+1866361236387Enzo Doria02/2016
5972^785220+1880611236375Enzo Doria10/2016
59819^184650-2236122Robert Price10/2014
59910^236059+216513236060Patrick De Geest04/2016
60010^236059-20909236059Robert Price09/2015
601(87^121487-1)/86235625Paul Bourdelais12/2018
6022^782634-113981235597Enzo Doria11/2014
6032^782423+1879733235533Enzo Doria09/2016
6042^781682-2789543235310Enzo Doria12/2015
6052^780408-113453234927Enzo Doria08/2014
6062^780368-1864829234915Enzo Doria01/2016
6072^779593-1836559234681Enzo Doria05/2015
608(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
609(5^335429+1)/6234455Paul Bourdelais08/2010
6102^778395-113617234321Enzo Doria08/2014
6112^776245-2792353233674Enzo Doria02/2016
6122^776060-114029233618Enzo Doria11/2014
6132^775987-2789557233596Enzo Doria12/2015
6142^775672+1866721233501Enzo Doria03/2016
615(11^223999+1)/12233270Paul Bourdelais02/2010
6162^774118+1885789233033Enzo Doria04/2017
61721^176191-20^176191232964Jean-Louis Charton01/2015
6182^773679-113425232901Enzo Doria08/2014
61910^232599+192489232600Patrick De Geest12/2013
62010^232599-3232599Markus Tervooren10/2010
6212^772552-458879232562Enzo Doria04/2015
6222^772214+1874899232460Enzo Doria06/2016
6232^771994-1862771232394Enzo Doria12/2015
6242^771889+1876037232362Enzo Doria07/2016
6252^771660+1866511232293Enzo Doria02/2016
6265^332150-18188232163Enzo Doria06/2014
6273^485977-2^485977231870Mike Oakes09/2009
6282^770082-114161231818Enzo Doria01/2015
629(20^177967+1)/21231540Paul Bourdelais05/2013
6302^767622-9221231078Lelio R Paula01/2016
6312^767344+1880311230994Enzo Doria09/2016
632(3^483611-1)/2230741Paul Bourdelais02/2010
633(10^230706+179)/9230706Serge Batalov12/2014
6342^766309+1875257230682Enzo Doria06/2016
6352^765635+1879883230480Enzo Doria09/2016
6362^764348-113697230092Enzo Doria09/2014
6372^764131+78863230027Enzo Doria05/2016
6382^763701+60197229897Enzo Doria03/2016
6392^762841-25905229639Enzo Doria10/2013
6402^761117-113569229120Enzo Doria08/2014
641(98^114859+1)/99228709Paul Bourdelais12/2018
642(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
6432^757985-2790013228177Enzo Doria12/2015
6442^757038-1862081227892Enzo Doria12/2015
6452^756839+95849227832Makoto Morimoto10/2013
647(2^756839+6989)/756091227826Makoto Morimoto09/2016
646(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
6482^756773-112723227812Enzo Doria07/2014
649524309#+616367227431Makoto Morimoto02/2016
6502^755097-114193227307Enzo Doria12/2014
6512^754473-2791513227120Enzo Doria01/2016
6522^751426-764321226202Enzo Doria12/2013
653(18^180181-1)/17226176Andy Steward04/2007
6542^750740-3225996Paul Bourdelais03/2012
6552^750725+60227225991Enzo Doria02/2016
6562^750525-113743225931Enzo Doria09/2014
657(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
6582^749444-1861889225606Enzo Doria12/2015
659tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
6602^749096+1876861225501Enzo Doria07/2016
661(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
6622^748657+79607225369Enzo Doria06/2016
6632^746653-291583224765Enzo Doria07/2015
6642^746461-114043224708Enzo Doria11/2014
6652^745098-350471224297Enzo Doria06/2015
666(154*10^224061-1)/9224063Serge Batalov12/2014
6672^744211-1845787224030Enzo Doria07/2015
6682^743592-134579223844Hans Havermann10/2018
6692^742452+3223501Paul Bourdelais06/2019
670234178^9+9^234178223463Anatoly F. Selevich07/2011
6712^741651-461197223260Enzo Doria07/2015
6722^741362-1845251223173Enzo Doria07/2015
6732^740455-1863877222900Enzo Doria12/2015
6742^739636-2792219222653Enzo Doria02/2016
67511^213654-180222498Enzo Doria01/2013
6762^738957-1859743222449Enzo Doria11/2015
677(54^128189+1)/55222073Paul Bourdelais11/2018
678(10^221654+179)/9221654Serge Batalov12/2014
6792^736281+79817221643Enzo Doria06/2016
68010^221631+247617221632Patrick De Geest10/2013
68110^221631-9221631Alexander Gramolin02/2011
6822^735970-1839821221550Enzo Doria06/2015
6832^735367+60293221368Enzo Doria03/2016
684(29^151153+1)/30221045Paul Bourdelais09/2017
6852^733264-2784089220735Enzo Doria10/2015
6862^733114-24555220690Enzo Doria09/2013
6872^731891-636259220322Enzo Doria12/2013
6882^731124-25539220091Enzo Doria09/2013
6892^730972-462029220045Enzo Doria07/2015
6902^730833+1868627220003Enzo Doria04/2016
6912^730645-2787133219947Enzo Doria11/2015
6922^730547-25581219917Enzo Doria09/2013
6932^730460+82291219891Enzo Doria09/2016
694(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
695L(1051849)219824Renaud Lifchitz03/2009
69611^210961-240219694Enzo Doria01/2013
6972^729611-113437219635Enzo Doria08/2014
698F(1049897)219416Henri Lifchitz10/2008
6992^728604+1879321219332Enzo Doria10/2016
70033^144412+2219292Robert Price04/2015
7012^728277-183313219234Hans Havermann10/2018
7022^727998-1862711219150Enzo Doria12/2015
7032^727729-114073219069Enzo Doria12/2014
7042^727496-1851809218999Enzo Doria08/2015
7052^726591+2793143218726Enzo Doria02/2016
7062^725534-2791931218408Enzo Doria02/2016
7072^722184+1877821217400Enzo Doria08/2016
708(109*10^217360-1)/9217362Serge Batalov12/2014
709281*499979#/46410-2702372216849Robert Smith08/2016
710281*499979#/46410+2400766216849Robert Smith08/2016
711tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
7122^718756-114107216368Enzo Doria12/2014
7132^717305+80327215931Enzo Doria07/2016
7142^717069-59773215860Enzo Doria10/2015
71530^146021-29^146021215691Jean-Louis Charton09/2018
716277^88301-276^88301215674Jean-Louis Charton06/2012
717227^91413-40215372Enzo Doria04/2015
7182^714717+782897215152Enzo Doria11/2016
719tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
7202^713241+1879157214707Enzo Doria08/2016
72111^206081-10^206081214612Jean-Louis Charton10/2011
7222^712801-69553214575Enzo Doria01/2016
7232^712603-25357214515Enzo Doria09/2013
7242^711721-1846723214250Enzo Doria07/2015
7252^710730-396765213952Enzo Doria09/2013
7262^708468-114329213271Enzo Doria02/2015
727(163*10^212779-1)/9212781Serge Batalov12/2014
7282^706838-69041212780Enzo Doria11/2015
7292^704577-113871212099Enzo Doria10/2014
7302^704110-2792441211959Enzo Doria02/2016
7312^703943-1862947211908Enzo Doria12/2015
732(60^119083+1)/61211746Paul Bourdelais10/2018
733(10^211610-91)/9211610Serge Batalov12/2014
734227^89797+2211565Lelio R Paula08/2012
7352^702194-3211382Paul Bourdelais03/2012
7362^702064+1874911211343Enzo Doria07/2016
7372^701968-113873211314Enzo Doria10/2014
7382^701713-113779211237Enzo Doria09/2014
7392^701449-25201211158Enzo Doria09/2013
7402^701403-2786977211144Enzo Doria11/2015
7412^701189-25423211079Enzo Doria09/2013
7422^701162-459161211071Enzo Doria05/2015
743(24^152783-1)/23210872Paul Bourdelais04/2018
7442^700400+9385210842Lelio R Paula01/2014
7452^700131+1874693210761Enzo Doria06/2016
74611^202357-1140210734Enzo Doria12/2012
7472^698929-2788423210399Enzo Doria11/2015
748(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
7492^698316+1878601210215Enzo Doria08/2016
7502^697036+1878751209829Enzo Doria08/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 13 2019 10:51 (Time in France)

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