PRP Records

Probable Primes Top 10000

(290751 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 ?
75121^193601-20^193601255983Jean-Louis Charton02/2015
752(37^163193+1)/38255918Paul Bourdelais07/2019
7532^849177-114025255628Enzo Doria12/2014
7542^848502-3173255425Yves Minet07/2016
7552^848178-140291255328Enzo Doria01/2014
7562^847622-2441255160Yves Minet02/2016
7572^847291+182843255061Enzo Doria11/2016
7582^847174+1879429255025Enzo Doria09/2016
75924*29^174239+13361254809Curtis Bright04/2015
7602^845633-933075254561Paul Bourdelais11/2021
7612^845610-1868591254554Enzo Doria04/2016
7622^845484+81931254517Enzo Doria08/2016
7632^845402-114761254492Enzo Doria05/2015
7642^844334-2792441254170Enzo Doria02/2016
76511^243796-90253888Enzo Doria12/2012
766(10^253891+7)/44777/79843/16940711253875Alfred Reich10/2021
76730^171733-29^171733253671Jean-Louis Charton10/2018
7682^842209+1876037253531Enzo Doria07/2016
7692^842123-59197253505Enzo Doria10/2015
7702^840797-3253106Paul Bourdelais06/2019
7712^840716-2969253081Yves Minet05/2016
7722^840358-462491252973Enzo Doria08/2015
7732^840310+1878379252959Enzo Doria08/2016
77411^242579-60252620Enzo Doria10/2012
77545^152659+2252378Robert Price09/2015
776(95^127583+1)/96252322Paul Bourdelais07/2019
7772^837725+1869377252181Enzo Doria05/2016
7782^837536-311039252124Enzo Doria06/2015
77921^190632-2252058Robert Price07/2015
7802^837242+1873297252035Enzo Doria06/2016
7812^836656-2787929251859Enzo Doria11/2015
7822^836380+1875541251776Enzo Doria07/2016
783(359^98327-1)/358251233Alexander Zhirkov11/2017
784tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
7852^832511-461197250611Enzo Doria07/2015
7862^832505+1881137250609Enzo Doria11/2016
7872^832363+583295250567Enzo Doria12/2016
7882^832244-403635250531Enzo Doria01/2014
7892^831157+1880657250204Enzo Doria11/2016
7902^831088-7200899250183Enzo Doria01/2015
7912^830956-1349250143Yves Minet07/2015
7922^830037+282317249867Enzo Doria09/2016
7932^829589-113653249732Enzo Doria09/2014
7942^828281-3193249338Yves Minet08/2016
7952^828064-2785619249273Enzo Doria10/2015
7962^827602+60409249134Enzo Doria03/2016
79710^249010+348861249011Patrick De Geest04/2016
79810^249010-21249010Serge Batalov12/2014
7992^826733+1882907248872Enzo Doria12/2016
8002^825682+1876549248556Enzo Doria07/2016
8012^824991-114121248348Enzo Doria12/2014
8022^824642-362727248242Enzo Doria12/2013
8032^824565-114265248219Enzo Doria01/2015
804(73*10^248145-1)/9248146Robert Price01/2015
805(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
806(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
8072^822296+76501247536Enzo Doria05/2016
8082^821590-114167247324Enzo Doria12/2014
8092^821512-2790659247300Enzo Doria12/2015
8102^820077+382847246868Enzo Doria11/2016
8112^820001+81269246845Enzo Doria07/2016
8122^819463-59197246683Enzo Doria10/2015
8132^819296+80581246633Enzo Doria07/2016
8142^817160-350369245990Enzo Doria06/2015
81588093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
8162^815111-113857245373Enzo Doria10/2014
8172^814914-4001245314Yves Minet05/2017
818846^83761-845^83761245200Jean-Louis Charton12/2012
8192^814356-2790449245146Enzo Doria12/2015
8202^814276-459029245122Enzo Doria04/2015
8212^814023+180923245046Enzo Doria07/2016
822(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
8233^513007+16244767Robert Price04/2020
8242^811842-113675244389Enzo Doria09/2014
8252^811132-2787929244176Enzo Doria11/2015
8262^809746-2790971243758Enzo Doria01/2016
8272^808767-3295243464Yves Minet12/2016
8282^808621-113809243420Enzo Doria09/2014
8292^807724+1879621243150Enzo Doria09/2016
83020^186554-3242713Paul Bourdelais12/2020
8312^805843-113611242583Enzo Doria08/2014
8322^805745-459763242554Enzo Doria05/2015
8332^805353+782687242436Enzo Doria11/2016
8346^311257+5242206Paul Bourdelais02/2021
8352^804277-417933242112Enzo Doria01/2014
8362^803468-269039241868Enzo Doria10/2013
8372^803172+80851241779Enzo Doria07/2016
8383^506233-2241535Robert Price11/2013
8392^802025-25999241434Enzo Doria10/2013
840(3^505823+3^252912+1)/7241339Serge Batalov03/2014
8412^801303+1872923241217Enzo Doria05/2016
8422^800579-1862947240999Enzo Doria12/2015
8433^504206+2240568Luke W. Richards03/2018
8442^798973-26283240515Enzo Doria10/2013
8452^798671-69487240424Enzo Doria12/2015
8462^797220+79831239988Enzo Doria06/2016
8472^796910-26001239894Enzo Doria10/2013
8482^796598+653119239800Enzo Doria12/2016
8492^796432-1859729239750Enzo Doria11/2015
8502^796002-1852211239621Enzo Doria08/2015
8512^795709+75767239533Enzo Doria04/2016
8522^795708+81721239532Enzo Doria08/2016
8532^795468-2786249239460Enzo Doria10/2015
8542^795442+80779239452Enzo Doria07/2016
8552^795075-1852057239342Enzo Doria08/2015
856(86^123677+1)/87239252Paul Bourdelais01/2019
8572^794043+1875023239031Enzo Doria06/2016
8582^793347-69577238822Enzo Doria01/2016
8592^792988-344429238714Enzo Doria08/2015
8602^792700-2786369238627Enzo Doria11/2015
8612^792663-1844797238616Enzo Doria06/2015
8622^792605-291943238598Enzo Doria07/2015
863(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
8642^789373+1869377237625Enzo Doria05/2016
865((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
8662^788942+1866409237496Enzo Doria02/2016
8672^788844-114329237466Enzo Doria01/2015
8682^788705-1859713237424Enzo Doria11/2015
8692^786180+1871971236664Enzo Doria05/2016
87011^227092-90236492Enzo Doria11/2012
8712^785260+1866361236387Enzo Doria02/2016
8722^785220+1880611236375Enzo Doria10/2016
87319^184650-2236122Robert Price10/2014
87410^236059+216513236060Patrick De Geest04/2016
87510^236059-20909236059Robert Price09/2015
876(87^121487-1)/86235625Paul Bourdelais12/2018
8772^782634-113981235597Enzo Doria11/2014
8782^782423+1879733235533Enzo Doria09/2016
8792^781682-2789543235310Enzo Doria12/2015
8802^780408-113453234927Enzo Doria08/2014
8812^780368-1864829234915Enzo Doria01/2016
8822^779593-1836559234681Enzo Doria05/2015
883(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
884(5^335429+1)/6234455Paul Bourdelais08/2010
8852^778395-113617234321Enzo Doria08/2014
8862^776245-2792353233674Enzo Doria02/2016
8872^776060-114029233618Enzo Doria11/2014
8882^775987-2789557233596Enzo Doria12/2015
8892^775672+1866721233501Enzo Doria03/2016
8902^775238+57233370Stefano Morozzi05/2021
891(11^223999+1)/12233270Paul Bourdelais02/2010
8922^774118+1885789233033Enzo Doria04/2017
89321^176191-20^176191232964Jean-Louis Charton01/2015
8942^773679-113425232901Enzo Doria08/2014
89510^232599+192489232600Patrick De Geest12/2013
89610^232599-3232599Markus Tervooren10/2010
8972^772552-458879232562Enzo Doria04/2015
8982^772214+1874899232460Enzo Doria06/2016
8992^771994-1862771232394Enzo Doria12/2015
9002^771889+1876037232362Enzo Doria07/2016
9012^771660+1866511232293Enzo Doria02/2016
9025^332150-18188232163Enzo Doria06/2014
9033^485977-2^485977231870Mike Oakes09/2009
9042^770082-114161231818Enzo Doria01/2015
905(20^177967+1)/21231540Paul Bourdelais05/2013
9062^767622-9221231078Lelio R Paula01/2016
9072^767344+1880311230994Enzo Doria09/2016
908(3^483611-1)/2230741Paul Bourdelais02/2010
909(10^230706+179)/9230706Serge Batalov12/2014
9102^766309+1875257230682Enzo Doria06/2016
9112^765635+1879883230480Enzo Doria09/2016
9122^764348-113697230092Enzo Doria09/2014
9132^764131+78863230027Enzo Doria05/2016
9142^763701+60197229897Enzo Doria03/2016
9152^762841-25905229639Enzo Doria10/2013
9162^761117-113569229120Enzo Doria08/2014
917(98^114859+1)/99228709Paul Bourdelais12/2018
918(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
9192^757985-2790013228177Enzo Doria12/2015
9202^757038-1862081227892Enzo Doria12/2015
9212^756839+95849227832Makoto Morimoto10/2013
923(2^756839+6989)/756091227826Makoto Morimoto09/2016
922(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
9242^756773-112723227812Enzo Doria07/2014
925524309#+616367227431Makoto Morimoto02/2016
9262^755097-114193227307Enzo Doria12/2014
9272^754473-2791513227120Enzo Doria01/2016
9282^754376+25227090Stefano Morozzi05/2021
9292^754038+25226989Stefano Morozzi05/2021
9302^751426-764321226202Enzo Doria12/2013
931(18^180181-1)/17226176Andy Steward04/2007
9322^750740-3225996Paul Bourdelais03/2012
9332^750725+60227225991Enzo Doria02/2016
9342^750525-113743225931Enzo Doria09/2014
935(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
9362^749444-1861889225606Enzo Doria12/2015
937tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
9382^749096+1876861225501Enzo Doria07/2016
939(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
9402^748657+79607225369Enzo Doria06/2016
9412^746653-291583224765Enzo Doria07/2015
9422^746461-114043224708Enzo Doria11/2014
9432^746302+25224660Stefano Morozzi05/2021
9442^745098-350471224297Enzo Doria06/2015
9452^745039-4897224280Yves Minet03/2021
946(154*10^224061-1)/9224063Serge Batalov12/2014
9472^744211-1845787224030Enzo Doria07/2015
9482^743592-134579223844Hans Havermann10/2018
9492^742452+3223501Paul Bourdelais06/2019
950234178^9+9^234178223463Anatoly F. Selevich07/2011
9512^741651-461197223260Enzo Doria07/2015
9522^741362-1845251223173Enzo Doria07/2015
9532^740455-1863877222900Enzo Doria12/2015
9542^739636-2792219222653Enzo Doria02/2016
95511^213654-180222498Enzo Doria01/2013
9562^738957-1859743222449Enzo Doria11/2015
9572^737825+57222108Stefano Morozzi05/2021
958(54^128189+1)/55222073Paul Bourdelais11/2018
959(10^221654+179)/9221654Serge Batalov12/2014
9602^736281+79817221643Enzo Doria06/2016
96110^221631+247617221632Patrick De Geest10/2013
96210^221631-9221631Alexander Gramolin02/2011
96310^221628+7221629Alfred Reich04/2021
9642^735970-1839821221550Enzo Doria06/2015
9652^735367+60293221368Enzo Doria03/2016
966(29^151153+1)/30221045Paul Bourdelais09/2017
9672^733264-2784089220735Enzo Doria10/2015
9682^733114-24555220690Enzo Doria09/2013
9692^731891-636259220322Enzo Doria12/2013
9702^731124-25539220091Enzo Doria09/2013
9712^730972-462029220045Enzo Doria07/2015
9722^730833+1868627220003Enzo Doria04/2016
9732^730645-2787133219947Enzo Doria11/2015
9742^730547-25581219917Enzo Doria09/2013
9752^730460+82291219891Enzo Doria09/2016
976(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
977L(1051849)219824Renaud Lifchitz03/2009
97811^210961-240219694Enzo Doria01/2013
9792^729611-113437219635Enzo Doria08/2014
9807^259710-2219481Paul Bourdelais01/2021
981F(1049897)219416Henri Lifchitz10/2008
9822^728604+1879321219332Enzo Doria10/2016
98333^144412+2219292Robert Price04/2015
9842^728277-183313219234Hans Havermann10/2018
9852^727998-1862711219150Enzo Doria12/2015
9862^727729-114073219069Enzo Doria12/2014
9872^727496-1851809218999Enzo Doria08/2015
9882^726591+2793143218726Enzo Doria02/2016
9892^725534-2791931218408Enzo Doria02/2016
990Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
9912^722184+1877821217400Enzo Doria08/2016
992(109*10^217360-1)/9217362Serge Batalov12/2014
9932^721721-4453217260Yves Minet03/2021
994281*499979#/46410-2702372216849Robert Smith08/2016
995281*499979#/46410+2400766216849Robert Smith08/2016
996tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
9972^718756-114107216368Enzo Doria12/2014
9982^717672+121216041Stefano Morozzi05/2021
9992^717305+80327215931Enzo Doria07/2016
10002^717069-59773215860Enzo Doria10/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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