PRP Records

Probable Primes Top 10000

(277054 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 ?
5012^898762-251511270555Enzo Doria12/2013
5022^898589+47270503Lelio R Paula03/2016
503187322*10^270343-187321270349Danilo Nitsche09/2013
50448358*10^270343-48357270348Danilo Nitsche09/2013
505(10^270343-1)/9270343Maksym Voznyy07/2007
5062^897867-3217270285Yves Minet12/2016
5072^897849-115273270280Enzo Doria07/2015
5082^896616-114179269909Enzo Doria12/2014
5092^894928+583561269401Enzo Doria04/2017
5102^894673-39343269324Enzo Doria08/2015
511F(1285607)268676Henri Lifchitz11/2008
5122^892112+187663268553Enzo Doria08/2016
513(10^268207+1)/11268206Paul Bourdelais02/2010
5142^890957-69583268205Enzo Doria12/2015
51532841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
5162^890122-351401267954Enzo Doria07/2015
517(19^209359-1)/18267718Paul Bourdelais08/2010
518(85^138647+1)/86267507Paul Bourdelais07/2019
519(485^99523-1)/484267291Michael Stocker05/2020
5202^886324+77791266811Enzo Doria06/2016
5212^884714+1880527266326Enzo Doria10/2016
52211^255426+255426^11265999Serge Batalov05/2014
5232^883462-343421265949Enzo Doria07/2015
5242^883442+1875019265943Enzo Doria06/2016
5252^883333-291583265910Enzo Doria07/2015
5262^880411+1882673265031Enzo Doria12/2016
5272^879530-2788031264765Enzo Doria12/2015
5282^878118+2793079264340Enzo Doria02/2016
529(37^168527-1)/36264283Paul Bourdelais08/2019
5302^875748-461129263627Enzo Doria07/2015
5312^875181-2789923263456Enzo Doria12/2015
5322^875101-350083263432Enzo Doria08/2015
5332^874684+1883587263307Enzo Doria01/2017
5342^874616+1872211263286Enzo Doria05/2016
5353^551491+16263129Robert Price04/2020
5362^874073+2792957263123Enzo Doria02/2016
5372^873628+1878751262989Enzo Doria08/2016
5382^873288-269262886Yves Minet01/2015
5392^871146-3173262242Yves Minet07/2016
5402^869601-163261776Yves Minet01/2015
5412^869326+282859261694Enzo Doria11/2016
5422^869035-114181261606Enzo Doria12/2014
5432^865715+80303260607Enzo Doria07/2016
5442^865048+1882411260406Enzo Doria12/2016
5452^864899-113871260361Enzo Doria10/2014
546(7*10^260198-61)/9260198Erik Branger11/2011
5472^864298-2788421260180Enzo Doria12/2015
5482^864039-2791357260102Enzo Doria01/2016
5492^863621-113833259976Enzo Doria10/2014
5502^862837+75767259740Enzo Doria05/2016
5512^862637-31259680Jorge Menendez05/2019
5522^862088+1874941259515Enzo Doria06/2016
5532^861987-134557259484Hans Havermann10/2018
5542^861516-1854029259343Enzo Doria09/2015
5552^860975-1853977259180Enzo Doria09/2015
5563^543128+16259138Robert Price04/2020
5572^860625-1858843259074Enzo Doria10/2015
5582^860110+77689258919Enzo Doria05/2016
5592^859600+1880371258766Enzo Doria10/2016
5602^859433+494711258716Makoto Morimoto10/2013
561(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
562(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
5632^859240+1875271258658Enzo Doria06/2016
564Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
565(144^119671+1)/145258292Paul Bourdelais08/2019
566(11*2^857159-13)/15258031Renaud Lifchitz08/2011
5672^857016-633113257988Enzo Doria12/2013
5682^855732-113969257602Enzo Doria10/2014
5692^853682-3911256984Enzo Doria05/2014
57011^246668-90256879Enzo Doria12/2012
5712^851904-113939256449Enzo Doria10/2014
5722^851725-851725^2256395Henri Lifchitz03/2019
57311^246167-90256357Enzo Doria12/2012
5742^850700-569049256087Enzo Doria11/2013
57521^193601-20^193601255983Jean-Louis Charton02/2015
576(37^163193+1)/38255918Paul Bourdelais07/2019
5772^849177-114025255628Enzo Doria12/2014
5782^848502-3173255425Yves Minet07/2016
5792^848178-140291255328Enzo Doria01/2014
5802^847622-2441255160Yves Minet02/2016
5812^847291+182843255061Enzo Doria11/2016
5822^847174+1879429255025Enzo Doria09/2016
58324*29^174239+13361254809Curtis Bright04/2015
5842^845610-1868591254554Enzo Doria04/2016
5852^845484+81931254517Enzo Doria08/2016
5862^845402-114761254492Enzo Doria05/2015
5872^844334-2792441254170Enzo Doria02/2016
58811^243796-90253888Enzo Doria12/2012
58930^171733-29^171733253671Jean-Louis Charton10/2018
5902^842209+1876037253531Enzo Doria07/2016
5912^842123-59197253505Enzo Doria10/2015
5922^840797-3253106Paul Bourdelais06/2019
5932^840716-2969253081Yves Minet05/2016
5942^840358-462491252973Enzo Doria08/2015
5952^840310+1878379252959Enzo Doria08/2016
59611^242579-60252620Enzo Doria10/2012
59745^152659+2252378Robert Price09/2015
598(95^127583+1)/96252322Paul Bourdelais07/2019
5992^837725+1869377252181Enzo Doria05/2016
6002^837536-311039252124Enzo Doria06/2015
60121^190632-2252058Robert Price07/2015
6022^837242+1873297252035Enzo Doria06/2016
6032^836656-2787929251859Enzo Doria11/2015
6042^836380+1875541251776Enzo Doria07/2016
605(359^98327-1)/358251233Alexander Zhirkov11/2017
606tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
6072^832511-461197250611Enzo Doria07/2015
6082^832505+1881137250609Enzo Doria11/2016
6092^832363+583295250567Enzo Doria12/2016
6102^832244-403635250531Enzo Doria01/2014
6112^831157+1880657250204Enzo Doria11/2016
6122^831088-7200899250183Enzo Doria01/2015
6132^830956-1349250143Yves Minet07/2015
6142^830037+282317249867Enzo Doria09/2016
6152^829589-113653249732Enzo Doria09/2014
6162^828281-3193249338Yves Minet08/2016
6172^828064-2785619249273Enzo Doria10/2015
6182^827602+60409249134Enzo Doria03/2016
61910^249010+348861249011Patrick De Geest04/2016
62010^249010-21249010Serge Batalov12/2014
6212^826733+1882907248872Enzo Doria12/2016
6222^825682+1876549248556Enzo Doria07/2016
6232^824991-114121248348Enzo Doria12/2014
6242^824642-362727248242Enzo Doria12/2013
6252^824565-114265248219Enzo Doria01/2015
626(73*10^248145-1)/9248146Robert Price01/2015
627(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
628(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
6292^822296+76501247536Enzo Doria05/2016
6302^821590-114167247324Enzo Doria12/2014
6312^821512-2790659247300Enzo Doria12/2015
6322^820077+382847246868Enzo Doria11/2016
6332^820001+81269246845Enzo Doria07/2016
6342^819463-59197246683Enzo Doria10/2015
6352^819296+80581246633Enzo Doria07/2016
6362^817160-350369245990Enzo Doria06/2015
63788093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
6382^815111-113857245373Enzo Doria10/2014
6392^814914-4001245314Yves Minet05/2017
640846^83761-845^83761245200Jean-Louis Charton12/2012
6412^814356-2790449245146Enzo Doria12/2015
6422^814276-459029245122Enzo Doria04/2015
6432^814023+180923245046Enzo Doria07/2016
644(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
6453^513007+16244767Robert Price04/2020
6462^811842-113675244389Enzo Doria09/2014
6472^811132-2787929244176Enzo Doria11/2015
6482^809746-2790971243758Enzo Doria01/2016
6492^808767-3295243464Yves Minet12/2016
6502^808621-113809243420Enzo Doria09/2014
6512^807724+1879621243150Enzo Doria09/2016
65220^186554-3242713Paul Bourdelais12/2020
6532^805843-113611242583Enzo Doria08/2014
6542^805745-459763242554Enzo Doria05/2015
6552^805353+782687242436Enzo Doria11/2016
6562^804277-417933242112Enzo Doria01/2014
6572^803468-269039241868Enzo Doria10/2013
6582^803172+80851241779Enzo Doria07/2016
6593^506233-2241535Robert Price11/2013
6602^802025-25999241434Enzo Doria10/2013
661(3^505823+3^252912+1)/7241339Serge Batalov03/2014
6622^801303+1872923241217Enzo Doria05/2016
6632^800579-1862947240999Enzo Doria12/2015
6643^504206+2240568Luke W. Richards03/2018
6652^798973-26283240515Enzo Doria10/2013
6662^798671-69487240424Enzo Doria12/2015
6672^797220+79831239988Enzo Doria06/2016
6682^796910-26001239894Enzo Doria10/2013
6692^796598+653119239800Enzo Doria12/2016
6702^796432-1859729239750Enzo Doria11/2015
6712^796002-1852211239621Enzo Doria08/2015
6722^795709+75767239533Enzo Doria04/2016
6732^795708+81721239532Enzo Doria08/2016
6742^795468-2786249239460Enzo Doria10/2015
6752^795442+80779239452Enzo Doria07/2016
6762^795075-1852057239342Enzo Doria08/2015
677(86^123677+1)/87239252Paul Bourdelais01/2019
6782^794043+1875023239031Enzo Doria06/2016
6792^793347-69577238822Enzo Doria01/2016
6802^792988-344429238714Enzo Doria08/2015
6812^792700-2786369238627Enzo Doria11/2015
6822^792663-1844797238616Enzo Doria06/2015
6832^792605-291943238598Enzo Doria07/2015
684(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
6852^789373+1869377237625Enzo Doria05/2016
686((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
6872^788942+1866409237496Enzo Doria02/2016
6882^788844-114329237466Enzo Doria01/2015
6892^788705-1859713237424Enzo Doria11/2015
6902^786180+1871971236664Enzo Doria05/2016
69111^227092-90236492Enzo Doria11/2012
6922^785260+1866361236387Enzo Doria02/2016
6932^785220+1880611236375Enzo Doria10/2016
69419^184650-2236122Robert Price10/2014
69510^236059+216513236060Patrick De Geest04/2016
69610^236059-20909236059Robert Price09/2015
697(87^121487-1)/86235625Paul Bourdelais12/2018
6982^782634-113981235597Enzo Doria11/2014
6992^782423+1879733235533Enzo Doria09/2016
7002^781682-2789543235310Enzo Doria12/2015
7012^780408-113453234927Enzo Doria08/2014
7022^780368-1864829234915Enzo Doria01/2016
7032^779593-1836559234681Enzo Doria05/2015
704(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
705(5^335429+1)/6234455Paul Bourdelais08/2010
7062^778395-113617234321Enzo Doria08/2014
7072^776245-2792353233674Enzo Doria02/2016
7082^776060-114029233618Enzo Doria11/2014
7092^775987-2789557233596Enzo Doria12/2015
7102^775672+1866721233501Enzo Doria03/2016
711(11^223999+1)/12233270Paul Bourdelais02/2010
7122^774118+1885789233033Enzo Doria04/2017
71321^176191-20^176191232964Jean-Louis Charton01/2015
7142^773679-113425232901Enzo Doria08/2014
71510^232599+192489232600Patrick De Geest12/2013
71610^232599-3232599Markus Tervooren10/2010
7172^772552-458879232562Enzo Doria04/2015
7182^772214+1874899232460Enzo Doria06/2016
7192^771994-1862771232394Enzo Doria12/2015
7202^771889+1876037232362Enzo Doria07/2016
7212^771660+1866511232293Enzo Doria02/2016
7225^332150-18188232163Enzo Doria06/2014
7233^485977-2^485977231870Mike Oakes09/2009
7242^770082-114161231818Enzo Doria01/2015
725(20^177967+1)/21231540Paul Bourdelais05/2013
7262^767622-9221231078Lelio R Paula01/2016
7272^767344+1880311230994Enzo Doria09/2016
728(3^483611-1)/2230741Paul Bourdelais02/2010
729(10^230706+179)/9230706Serge Batalov12/2014
7302^766309+1875257230682Enzo Doria06/2016
7312^765635+1879883230480Enzo Doria09/2016
7322^764348-113697230092Enzo Doria09/2014
7332^764131+78863230027Enzo Doria05/2016
7342^763701+60197229897Enzo Doria03/2016
7352^762841-25905229639Enzo Doria10/2013
7362^761117-113569229120Enzo Doria08/2014
737(98^114859+1)/99228709Paul Bourdelais12/2018
738(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
7392^757985-2790013228177Enzo Doria12/2015
7402^757038-1862081227892Enzo Doria12/2015
7412^756839+95849227832Makoto Morimoto10/2013
742(2^756839+6989)/756091227826Makoto Morimoto09/2016
743(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
7442^756773-112723227812Enzo Doria07/2014
745524309#+616367227431Makoto Morimoto02/2016
7462^755097-114193227307Enzo Doria12/2014
7472^754473-2791513227120Enzo Doria01/2016
7482^751426-764321226202Enzo Doria12/2013
749(18^180181-1)/17226176Andy Steward04/2007
7502^750740-3225996Paul Bourdelais03/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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