PRP Records

Probable Primes Top 10000

(271023 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 ?
5012^874073+2792957263123Enzo Doria02/2016
5022^873628+1878751262989Enzo Doria08/2016
5032^873288-269262886Yves Minet01/2015
5042^871146-3173262242Yves Minet07/2016
5052^869601-163261776Yves Minet01/2015
5062^869326+282859261694Enzo Doria11/2016
5072^869035-114181261606Enzo Doria12/2014
5082^865715+80303260607Enzo Doria07/2016
5092^865048+1882411260406Enzo Doria12/2016
5102^864899-113871260361Enzo Doria10/2014
511(7*10^260198-61)/9260198Erik Branger11/2011
5122^864298-2788421260180Enzo Doria12/2015
5132^864039-2791357260102Enzo Doria01/2016
5142^863621-113833259976Enzo Doria10/2014
5152^862837+75767259740Enzo Doria05/2016
5162^862637-31259680Jorge Menendez05/2019
5172^862088+1874941259515Enzo Doria06/2016
5182^861987-134557259484Hans Havermann10/2018
5192^861516-1854029259343Enzo Doria09/2015
5202^860975-1853977259180Enzo Doria09/2015
5213^543128+16259138Robert Price04/2020
5222^860625-1858843259074Enzo Doria10/2015
5232^860110+77689258919Enzo Doria05/2016
5242^859600+1880371258766Enzo Doria10/2016
5252^859433+494711258716Makoto Morimoto10/2013
526(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
527(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
5282^859240+1875271258658Enzo Doria06/2016
529Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
530(144^119671+1)/145258292Paul Bourdelais08/2019
531(11*2^857159-13)/15258031Renaud Lifchitz08/2011
5322^857016-633113257988Enzo Doria12/2013
5332^855732-113969257602Enzo Doria10/2014
5342^853682-3911256984Enzo Doria05/2014
53511^246668-90256879Enzo Doria12/2012
5362^851904-113939256449Enzo Doria10/2014
5372^851725-851725^2256395Henri Lifchitz03/2019
53811^246167-90256357Enzo Doria12/2012
5392^850700-569049256087Enzo Doria11/2013
54021^193601-20^193601255983Jean-Louis Charton02/2015
541(37^163193+1)/38255918Paul Bourdelais07/2019
5422^849177-114025255628Enzo Doria12/2014
5432^848502-3173255425Yves Minet07/2016
5442^848178-140291255328Enzo Doria01/2014
5452^847622-2441255160Yves Minet02/2016
5462^847291+182843255061Enzo Doria11/2016
5472^847174+1879429255025Enzo Doria09/2016
54824*29^174239+13361254809Curtis Bright04/2015
5492^845610-1868591254554Enzo Doria04/2016
5502^845484+81931254517Enzo Doria08/2016
5512^845402-114761254492Enzo Doria05/2015
5522^844334-2792441254170Enzo Doria02/2016
55311^243796-90253888Enzo Doria12/2012
55430^171733-29^171733253671Jean-Louis Charton10/2018
5552^842209+1876037253531Enzo Doria07/2016
5562^842123-59197253505Enzo Doria10/2015
5572^840797-3253106Paul Bourdelais06/2019
5582^840716-2969253081Yves Minet05/2016
5592^840358-462491252973Enzo Doria08/2015
5602^840310+1878379252959Enzo Doria08/2016
56111^242579-60252620Enzo Doria10/2012
56245^152659+2252378Robert Price09/2015
563(95^127583+1)/96252322Paul Bourdelais07/2019
5642^837725+1869377252181Enzo Doria05/2016
5652^837536-311039252124Enzo Doria06/2015
56621^190632-2252058Robert Price07/2015
5672^837242+1873297252035Enzo Doria06/2016
5682^836656-2787929251859Enzo Doria11/2015
5692^836380+1875541251776Enzo Doria07/2016
570(359^98327-1)/358251233Alexander Zhirkov11/2017
571tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
5722^832511-461197250611Enzo Doria07/2015
5732^832505+1881137250609Enzo Doria11/2016
5742^832363+583295250567Enzo Doria12/2016
5752^832244-403635250531Enzo Doria01/2014
5762^831157+1880657250204Enzo Doria11/2016
5772^831088-7200899250183Enzo Doria01/2015
5782^830956-1349250143Yves Minet07/2015
5792^830037+282317249867Enzo Doria09/2016
5802^829589-113653249732Enzo Doria09/2014
5812^828281-3193249338Yves Minet08/2016
5822^828064-2785619249273Enzo Doria10/2015
5832^827602+60409249134Enzo Doria03/2016
58410^249010+348861249011Patrick De Geest04/2016
58510^249010-21249010Serge Batalov12/2014
5862^826733+1882907248872Enzo Doria12/2016
5872^825682+1876549248556Enzo Doria07/2016
5882^824991-114121248348Enzo Doria12/2014
5892^824642-362727248242Enzo Doria12/2013
5902^824565-114265248219Enzo Doria01/2015
591(73*10^248145-1)/9248146Robert Price01/2015
592(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
593(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
5942^822296+76501247536Enzo Doria05/2016
5952^821590-114167247324Enzo Doria12/2014
5962^821512-2790659247300Enzo Doria12/2015
5972^820077+382847246868Enzo Doria11/2016
5982^820001+81269246845Enzo Doria07/2016
5992^819463-59197246683Enzo Doria10/2015
6002^819296+80581246633Enzo Doria07/2016
6012^817160-350369245990Enzo Doria06/2015
60288093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
6032^815111-113857245373Enzo Doria10/2014
6042^814914-4001245314Yves Minet05/2017
605846^83761-845^83761245200Jean-Louis Charton12/2012
6062^814356-2790449245146Enzo Doria12/2015
6072^814276-459029245122Enzo Doria04/2015
6082^814023+180923245046Enzo Doria07/2016
609(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
6103^513007+16244767Robert Price04/2020
6112^811842-113675244389Enzo Doria09/2014
6122^811132-2787929244176Enzo Doria11/2015
6132^809746-2790971243758Enzo Doria01/2016
6142^808767-3295243464Yves Minet12/2016
6152^808621-113809243420Enzo Doria09/2014
6162^807724+1879621243150Enzo Doria09/2016
6172^805843-113611242583Enzo Doria08/2014
6182^805745-459763242554Enzo Doria05/2015
6192^805353+782687242436Enzo Doria11/2016
6202^804277-417933242112Enzo Doria01/2014
6212^803468-269039241868Enzo Doria10/2013
6222^803172+80851241779Enzo Doria07/2016
6233^506233-2241535Robert Price11/2013
6242^802025-25999241434Enzo Doria10/2013
625(3^505823+3^252912+1)/7241339Serge Batalov03/2014
6262^801303+1872923241217Enzo Doria05/2016
6272^800579-1862947240999Enzo Doria12/2015
6283^504206+2240568Luke W. Richards03/2018
6292^798973-26283240515Enzo Doria10/2013
6302^798671-69487240424Enzo Doria12/2015
6312^797220+79831239988Enzo Doria06/2016
6322^796910-26001239894Enzo Doria10/2013
6332^796598+653119239800Enzo Doria12/2016
6342^796432-1859729239750Enzo Doria11/2015
6352^796002-1852211239621Enzo Doria08/2015
6362^795709+75767239533Enzo Doria04/2016
6372^795708+81721239532Enzo Doria08/2016
6382^795468-2786249239460Enzo Doria10/2015
6392^795442+80779239452Enzo Doria07/2016
6402^795075-1852057239342Enzo Doria08/2015
641(86^123677+1)/87239252Paul Bourdelais01/2019
6422^794043+1875023239031Enzo Doria06/2016
6432^793347-69577238822Enzo Doria01/2016
6442^792988-344429238714Enzo Doria08/2015
6452^792700-2786369238627Enzo Doria11/2015
6462^792663-1844797238616Enzo Doria06/2015
6472^792605-291943238598Enzo Doria07/2015
648(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
6492^789373+1869377237625Enzo Doria05/2016
650((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
6512^788942+1866409237496Enzo Doria02/2016
6522^788844-114329237466Enzo Doria01/2015
6532^788705-1859713237424Enzo Doria11/2015
6542^786180+1871971236664Enzo Doria05/2016
65511^227092-90236492Enzo Doria11/2012
6562^785260+1866361236387Enzo Doria02/2016
6572^785220+1880611236375Enzo Doria10/2016
65819^184650-2236122Robert Price10/2014
65910^236059+216513236060Patrick De Geest04/2016
66010^236059-20909236059Robert Price09/2015
661(87^121487-1)/86235625Paul Bourdelais12/2018
6622^782634-113981235597Enzo Doria11/2014
6632^782423+1879733235533Enzo Doria09/2016
6642^781682-2789543235310Enzo Doria12/2015
6652^780408-113453234927Enzo Doria08/2014
6662^780368-1864829234915Enzo Doria01/2016
6672^779593-1836559234681Enzo Doria05/2015
668(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
669(5^335429+1)/6234455Paul Bourdelais08/2010
6702^778395-113617234321Enzo Doria08/2014
6712^776245-2792353233674Enzo Doria02/2016
6722^776060-114029233618Enzo Doria11/2014
6732^775987-2789557233596Enzo Doria12/2015
6742^775672+1866721233501Enzo Doria03/2016
675(11^223999+1)/12233270Paul Bourdelais02/2010
6762^774118+1885789233033Enzo Doria04/2017
67721^176191-20^176191232964Jean-Louis Charton01/2015
6782^773679-113425232901Enzo Doria08/2014
67910^232599+192489232600Patrick De Geest12/2013
68010^232599-3232599Markus Tervooren10/2010
6812^772552-458879232562Enzo Doria04/2015
6822^772214+1874899232460Enzo Doria06/2016
6832^771994-1862771232394Enzo Doria12/2015
6842^771889+1876037232362Enzo Doria07/2016
6852^771660+1866511232293Enzo Doria02/2016
6865^332150-18188232163Enzo Doria06/2014
6873^485977-2^485977231870Mike Oakes09/2009
6882^770082-114161231818Enzo Doria01/2015
689(20^177967+1)/21231540Paul Bourdelais05/2013
6902^767622-9221231078Lelio R Paula01/2016
6912^767344+1880311230994Enzo Doria09/2016
692(3^483611-1)/2230741Paul Bourdelais02/2010
693(10^230706+179)/9230706Serge Batalov12/2014
6942^766309+1875257230682Enzo Doria06/2016
6952^765635+1879883230480Enzo Doria09/2016
6962^764348-113697230092Enzo Doria09/2014
6972^764131+78863230027Enzo Doria05/2016
6982^763701+60197229897Enzo Doria03/2016
6992^762841-25905229639Enzo Doria10/2013
7002^761117-113569229120Enzo Doria08/2014
701(98^114859+1)/99228709Paul Bourdelais12/2018
702(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
7032^757985-2790013228177Enzo Doria12/2015
7042^757038-1862081227892Enzo Doria12/2015
7052^756839+95849227832Makoto Morimoto10/2013
706(2^756839+6989)/756091227826Makoto Morimoto09/2016
707(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
7082^756773-112723227812Enzo Doria07/2014
709524309#+616367227431Makoto Morimoto02/2016
7102^755097-114193227307Enzo Doria12/2014
7112^754473-2791513227120Enzo Doria01/2016
7122^751426-764321226202Enzo Doria12/2013
713(18^180181-1)/17226176Andy Steward04/2007
7142^750740-3225996Paul Bourdelais03/2012
7152^750725+60227225991Enzo Doria02/2016
7162^750525-113743225931Enzo Doria09/2014
717(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
7182^749444-1861889225606Enzo Doria12/2015
719tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
7202^749096+1876861225501Enzo Doria07/2016
721(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
7222^748657+79607225369Enzo Doria06/2016
7232^746653-291583224765Enzo Doria07/2015
7242^746461-114043224708Enzo Doria11/2014
7252^745098-350471224297Enzo Doria06/2015
726(154*10^224061-1)/9224063Serge Batalov12/2014
7272^744211-1845787224030Enzo Doria07/2015
7282^743592-134579223844Hans Havermann10/2018
7292^742452+3223501Paul Bourdelais06/2019
730234178^9+9^234178223463Anatoly F. Selevich07/2011
7312^741651-461197223260Enzo Doria07/2015
7322^741362-1845251223173Enzo Doria07/2015
7332^740455-1863877222900Enzo Doria12/2015
7342^739636-2792219222653Enzo Doria02/2016
73511^213654-180222498Enzo Doria01/2013
7362^738957-1859743222449Enzo Doria11/2015
737(54^128189+1)/55222073Paul Bourdelais11/2018
738(10^221654+179)/9221654Serge Batalov12/2014
7392^736281+79817221643Enzo Doria06/2016
74010^221631+247617221632Patrick De Geest10/2013
74110^221631-9221631Alexander Gramolin02/2011
7422^735970-1839821221550Enzo Doria06/2015
7432^735367+60293221368Enzo Doria03/2016
744(29^151153+1)/30221045Paul Bourdelais09/2017
7452^733264-2784089220735Enzo Doria10/2015
7462^733114-24555220690Enzo Doria09/2013
7472^731891-636259220322Enzo Doria12/2013
7482^731124-25539220091Enzo Doria09/2013
7492^730972-462029220045Enzo Doria07/2015
7502^730833+1868627220003Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

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