PRP Records

Probable Primes Top 10000

(288949 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 ?
7512^829589-113653249732Enzo Doria09/2014
7522^828281-3193249338Yves Minet08/2016
7532^828064-2785619249273Enzo Doria10/2015
7542^827602+60409249134Enzo Doria03/2016
75510^249010+348861249011Patrick De Geest04/2016
75610^249010-21249010Serge Batalov12/2014
7572^826733+1882907248872Enzo Doria12/2016
7582^825682+1876549248556Enzo Doria07/2016
7592^824991-114121248348Enzo Doria12/2014
7602^824642-362727248242Enzo Doria12/2013
7612^824565-114265248219Enzo Doria01/2015
762(73*10^248145-1)/9248146Robert Price01/2015
763(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
764(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
7652^822296+76501247536Enzo Doria05/2016
7662^821590-114167247324Enzo Doria12/2014
7672^821512-2790659247300Enzo Doria12/2015
7682^820077+382847246868Enzo Doria11/2016
7692^820001+81269246845Enzo Doria07/2016
7702^819463-59197246683Enzo Doria10/2015
7712^819296+80581246633Enzo Doria07/2016
7722^817160-350369245990Enzo Doria06/2015
77388093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
7742^815111-113857245373Enzo Doria10/2014
7752^814914-4001245314Yves Minet05/2017
776846^83761-845^83761245200Jean-Louis Charton12/2012
7772^814356-2790449245146Enzo Doria12/2015
7782^814276-459029245122Enzo Doria04/2015
7792^814023+180923245046Enzo Doria07/2016
780(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
7813^513007+16244767Robert Price04/2020
7822^811842-113675244389Enzo Doria09/2014
7832^811132-2787929244176Enzo Doria11/2015
7842^809746-2790971243758Enzo Doria01/2016
7852^808767-3295243464Yves Minet12/2016
7862^808621-113809243420Enzo Doria09/2014
7872^807724+1879621243150Enzo Doria09/2016
78820^186554-3242713Paul Bourdelais12/2020
7892^805843-113611242583Enzo Doria08/2014
7902^805745-459763242554Enzo Doria05/2015
7912^805353+782687242436Enzo Doria11/2016
7926^311257+5242206Paul Bourdelais02/2021
7932^804277-417933242112Enzo Doria01/2014
7942^803468-269039241868Enzo Doria10/2013
7952^803172+80851241779Enzo Doria07/2016
7963^506233-2241535Robert Price11/2013
7972^802025-25999241434Enzo Doria10/2013
798(3^505823+3^252912+1)/7241339Serge Batalov03/2014
7992^801303+1872923241217Enzo Doria05/2016
8002^800579-1862947240999Enzo Doria12/2015
8013^504206+2240568Luke W. Richards03/2018
8022^798973-26283240515Enzo Doria10/2013
8032^798671-69487240424Enzo Doria12/2015
8042^797220+79831239988Enzo Doria06/2016
8052^796910-26001239894Enzo Doria10/2013
8062^796598+653119239800Enzo Doria12/2016
8072^796432-1859729239750Enzo Doria11/2015
8082^796002-1852211239621Enzo Doria08/2015
8092^795709+75767239533Enzo Doria04/2016
8102^795708+81721239532Enzo Doria08/2016
8112^795468-2786249239460Enzo Doria10/2015
8122^795442+80779239452Enzo Doria07/2016
8132^795075-1852057239342Enzo Doria08/2015
814(86^123677+1)/87239252Paul Bourdelais01/2019
8152^794043+1875023239031Enzo Doria06/2016
8162^793347-69577238822Enzo Doria01/2016
8172^792988-344429238714Enzo Doria08/2015
8182^792700-2786369238627Enzo Doria11/2015
8192^792663-1844797238616Enzo Doria06/2015
8202^792605-291943238598Enzo Doria07/2015
821(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
8222^789373+1869377237625Enzo Doria05/2016
823((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
8242^788942+1866409237496Enzo Doria02/2016
8252^788844-114329237466Enzo Doria01/2015
8262^788705-1859713237424Enzo Doria11/2015
8272^786180+1871971236664Enzo Doria05/2016
82811^227092-90236492Enzo Doria11/2012
8292^785260+1866361236387Enzo Doria02/2016
8302^785220+1880611236375Enzo Doria10/2016
83119^184650-2236122Robert Price10/2014
83210^236059+216513236060Patrick De Geest04/2016
83310^236059-20909236059Robert Price09/2015
834(87^121487-1)/86235625Paul Bourdelais12/2018
8352^782634-113981235597Enzo Doria11/2014
8362^782423+1879733235533Enzo Doria09/2016
8372^781682-2789543235310Enzo Doria12/2015
8382^780408-113453234927Enzo Doria08/2014
8392^780368-1864829234915Enzo Doria01/2016
8402^779593-1836559234681Enzo Doria05/2015
841(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
842(5^335429+1)/6234455Paul Bourdelais08/2010
8432^778395-113617234321Enzo Doria08/2014
8442^776245-2792353233674Enzo Doria02/2016
8452^776060-114029233618Enzo Doria11/2014
8462^775987-2789557233596Enzo Doria12/2015
8472^775672+1866721233501Enzo Doria03/2016
8482^775238+57233370Stefano Morozzi05/2021
849(11^223999+1)/12233270Paul Bourdelais02/2010
8502^774118+1885789233033Enzo Doria04/2017
85121^176191-20^176191232964Jean-Louis Charton01/2015
8522^773679-113425232901Enzo Doria08/2014
85310^232599+192489232600Patrick De Geest12/2013
85410^232599-3232599Markus Tervooren10/2010
8552^772552-458879232562Enzo Doria04/2015
8562^772214+1874899232460Enzo Doria06/2016
8572^771994-1862771232394Enzo Doria12/2015
8582^771889+1876037232362Enzo Doria07/2016
8592^771660+1866511232293Enzo Doria02/2016
8605^332150-18188232163Enzo Doria06/2014
8613^485977-2^485977231870Mike Oakes09/2009
8622^770082-114161231818Enzo Doria01/2015
863(20^177967+1)/21231540Paul Bourdelais05/2013
8642^767622-9221231078Lelio R Paula01/2016
8652^767344+1880311230994Enzo Doria09/2016
866(3^483611-1)/2230741Paul Bourdelais02/2010
867(10^230706+179)/9230706Serge Batalov12/2014
8682^766309+1875257230682Enzo Doria06/2016
8692^765635+1879883230480Enzo Doria09/2016
8702^764348-113697230092Enzo Doria09/2014
8712^764131+78863230027Enzo Doria05/2016
8722^763701+60197229897Enzo Doria03/2016
8732^762841-25905229639Enzo Doria10/2013
8742^761117-113569229120Enzo Doria08/2014
875(98^114859+1)/99228709Paul Bourdelais12/2018
876(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
8772^757985-2790013228177Enzo Doria12/2015
8782^757038-1862081227892Enzo Doria12/2015
8792^756839+95849227832Makoto Morimoto10/2013
880(2^756839+6989)/756091227826Makoto Morimoto09/2016
881(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
8822^756773-112723227812Enzo Doria07/2014
883524309#+616367227431Makoto Morimoto02/2016
8842^755097-114193227307Enzo Doria12/2014
8852^754473-2791513227120Enzo Doria01/2016
8862^754376+25227090Stefano Morozzi05/2021
8872^754038+25226989Stefano Morozzi05/2021
8882^751426-764321226202Enzo Doria12/2013
889(18^180181-1)/17226176Andy Steward04/2007
8902^750740-3225996Paul Bourdelais03/2012
8912^750725+60227225991Enzo Doria02/2016
8922^750525-113743225931Enzo Doria09/2014
893(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
8942^749444-1861889225606Enzo Doria12/2015
895tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
8962^749096+1876861225501Enzo Doria07/2016
897(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
8982^748657+79607225369Enzo Doria06/2016
8992^746653-291583224765Enzo Doria07/2015
9002^746461-114043224708Enzo Doria11/2014
9012^746302+25224660Stefano Morozzi05/2021
9022^745098-350471224297Enzo Doria06/2015
9032^745039-4897224280Yves Minet03/2021
904(154*10^224061-1)/9224063Serge Batalov12/2014
9052^744211-1845787224030Enzo Doria07/2015
9062^743592-134579223844Hans Havermann10/2018
9072^742452+3223501Paul Bourdelais06/2019
908234178^9+9^234178223463Anatoly F. Selevich07/2011
9092^741651-461197223260Enzo Doria07/2015
9102^741362-1845251223173Enzo Doria07/2015
9112^740455-1863877222900Enzo Doria12/2015
9122^739636-2792219222653Enzo Doria02/2016
91311^213654-180222498Enzo Doria01/2013
9142^738957-1859743222449Enzo Doria11/2015
9152^737825+57222108Stefano Morozzi05/2021
916(54^128189+1)/55222073Paul Bourdelais11/2018
917(10^221654+179)/9221654Serge Batalov12/2014
9182^736281+79817221643Enzo Doria06/2016
91910^221631+247617221632Patrick De Geest10/2013
92010^221631-9221631Alexander Gramolin02/2011
92110^221628+7221629Alfred Reich04/2021
9222^735970-1839821221550Enzo Doria06/2015
9232^735367+60293221368Enzo Doria03/2016
924(29^151153+1)/30221045Paul Bourdelais09/2017
9252^733264-2784089220735Enzo Doria10/2015
9262^733114-24555220690Enzo Doria09/2013
9272^731891-636259220322Enzo Doria12/2013
9282^731124-25539220091Enzo Doria09/2013
9292^730972-462029220045Enzo Doria07/2015
9302^730833+1868627220003Enzo Doria04/2016
9312^730645-2787133219947Enzo Doria11/2015
9322^730547-25581219917Enzo Doria09/2013
9332^730460+82291219891Enzo Doria09/2016
934(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
935L(1051849)219824Renaud Lifchitz03/2009
93611^210961-240219694Enzo Doria01/2013
9372^729611-113437219635Enzo Doria08/2014
9387^259710-2219481Paul Bourdelais01/2021
939F(1049897)219416Henri Lifchitz10/2008
9402^728604+1879321219332Enzo Doria10/2016
94133^144412+2219292Robert Price04/2015
9422^728277-183313219234Hans Havermann10/2018
9432^727998-1862711219150Enzo Doria12/2015
9442^727729-114073219069Enzo Doria12/2014
9452^727496-1851809218999Enzo Doria08/2015
9462^726591+2793143218726Enzo Doria02/2016
9472^725534-2791931218408Enzo Doria02/2016
948Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
9492^722184+1877821217400Enzo Doria08/2016
950(109*10^217360-1)/9217362Serge Batalov12/2014
9512^721721-4453217260Yves Minet03/2021
952281*499979#/46410-2702372216849Robert Smith08/2016
953281*499979#/46410+2400766216849Robert Smith08/2016
954tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
9552^718756-114107216368Enzo Doria12/2014
9562^717672+121216041Stefano Morozzi05/2021
9572^717305+80327215931Enzo Doria07/2016
9582^717069-59773215860Enzo Doria10/2015
95930^146021-29^146021215691Jean-Louis Charton09/2018
960277^88301-276^88301215674Jean-Louis Charton06/2012
961227^91413-40215372Enzo Doria04/2015
9622^714717+782897215152Enzo Doria11/2016
963tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
9642^713241+1879157214707Enzo Doria08/2016
96511^206081-10^206081214612Jean-Louis Charton10/2011
9662^712801-69553214575Enzo Doria01/2016
9672^712603-25357214515Enzo Doria09/2013
9682^711721-1846723214250Enzo Doria07/2015
9692^710730-396765213952Enzo Doria09/2013
9702^708468-114329213271Enzo Doria02/2015
971(163*10^212779-1)/9212781Serge Batalov12/2014
9722^706838-69041212780Enzo Doria11/2015
9732^704577-113871212099Enzo Doria10/2014
9742^704110-2792441211959Enzo Doria02/2016
9752^703943-1862947211908Enzo Doria12/2015
976(60^119083+1)/61211746Paul Bourdelais10/2018
977(10^211610-91)/9211610Serge Batalov12/2014
978227^89797+2211565Lelio R Paula08/2012
9792^702194-3211382Paul Bourdelais03/2012
9802^702064+1874911211343Enzo Doria07/2016
9812^701968-113873211314Enzo Doria10/2014
9822^701713-113779211237Enzo Doria09/2014
9832^701449-25201211158Enzo Doria09/2013
9842^701403-2786977211144Enzo Doria11/2015
9852^701189-25423211079Enzo Doria09/2013
9862^701162-459161211071Enzo Doria05/2015
987(24^152783-1)/23210872Paul Bourdelais04/2018
9882^700400+9385210842Lelio R Paula01/2014
9892^700131+1874693210761Enzo Doria06/2016
990(2^700095+225414)/2210750Stefano Morozzi04/2020
991(2^700090+278254)/2210748Stefano Morozzi04/2020
992(2^700075+303666)/2210744Stefano Morozzi04/2020
993(2^700073+75882)/2210743Stefano Morozzi04/2020
994(2^700074+328890)/2210743Stefano Morozzi04/2020
995(2^700052+79162)/2210737Stefano Morozzi04/2020
996(2^700052+304458)/2210737Stefano Morozzi04/2020
997(2^700048+376578)/2210736Stefano Morozzi04/2020
99811^202357-1140210734Enzo Doria12/2012
999(2^700021+25874)/2210728Stefano Morozzi04/2020
1000(2^700018+377518)/2210727Stefano Morozzi04/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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