PRP Records

Probable Primes Top 10000

(259919 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 ?
5012^847291+182843255061Enzo Doria11/2016
5022^847174+1879429255025Enzo Doria09/2016
50324*29^174239+13361254809Curtis Bright04/2015
5042^845610-1868591254554Enzo Doria04/2016
5052^845484+81931254517Enzo Doria08/2016
5062^845402-114761254492Enzo Doria05/2015
5072^844334-2792441254170Enzo Doria02/2016
50811^243796-90253888Enzo Doria12/2012
50930^171733-29^171733253671Jean-Louis Charton10/2018
5102^842209+1876037253531Enzo Doria07/2016
5112^842123-59197253505Enzo Doria10/2015
5122^840797-3253106Paul Bourdelais06/2019
5132^840716-2969253081Yves Minet05/2016
5142^840358-462491252973Enzo Doria08/2015
5152^840310+1878379252959Enzo Doria08/2016
51611^242579-60252620Enzo Doria10/2012
51745^152659+2252378Robert Price09/2015
518(95^127583+1)/96252322Paul Bourdelais07/2019
5192^837725+1869377252181Enzo Doria05/2016
5202^837536-311039252124Enzo Doria06/2015
52121^190632-2252058Robert Price07/2015
5222^837242+1873297252035Enzo Doria06/2016
5232^836656-2787929251859Enzo Doria11/2015
5242^836380+1875541251776Enzo Doria07/2016
525(359^98327-1)/358251233Alexander Zhirkov11/2017
526tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
5272^832511-461197250611Enzo Doria07/2015
5282^832505+1881137250609Enzo Doria11/2016
5292^832363+583295250567Enzo Doria12/2016
5302^832244-403635250531Enzo Doria01/2014
5312^831157+1880657250204Enzo Doria11/2016
5322^831088-7200899250183Enzo Doria01/2015
5332^830956-1349250143Yves Minet07/2015
5342^830037+282317249867Enzo Doria09/2016
5352^829589-113653249732Enzo Doria09/2014
5362^828281-3193249338Yves Minet08/2016
5372^828064-2785619249273Enzo Doria10/2015
5382^827602+60409249134Enzo Doria03/2016
53910^249010+348861249011Patrick De Geest04/2016
54010^249010-21249010Serge Batalov12/2014
5412^826733+1882907248872Enzo Doria12/2016
5422^825682+1876549248556Enzo Doria07/2016
5432^824991-114121248348Enzo Doria12/2014
5442^824642-362727248242Enzo Doria12/2013
5452^824565-114265248219Enzo Doria01/2015
546(73*10^248145-1)/9248146Robert Price01/2015
547(2^823337+1)/(3*362268281)247841Gord Palameta08/2018
548(2^822971-1)/6583769/28211445881/21255852651726486149207247700Robert Kinser09/2016
5492^822296+76501247536Enzo Doria05/2016
5502^821590-114167247324Enzo Doria12/2014
5512^821512-2790659247300Enzo Doria12/2015
5522^820077+382847246868Enzo Doria11/2016
5532^820001+81269246845Enzo Doria07/2016
5542^819463-59197246683Enzo Doria10/2015
5552^819296+80581246633Enzo Doria07/2016
5562^817160-350369245990Enzo Doria06/2015
55788093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
5582^815111-113857245373Enzo Doria10/2014
5592^814914-4001245314Yves Minet05/2017
560846^83761-845^83761245200Jean-Louis Charton12/2012
5612^814356-2790449245146Enzo Doria12/2015
5622^814276-459029245122Enzo Doria04/2015
5632^814023+180923245046Enzo Doria07/2016
564(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
5652^811842-113675244389Enzo Doria09/2014
5662^811132-2787929244176Enzo Doria11/2015
5672^809746-2790971243758Enzo Doria01/2016
5682^808767-3295243464Yves Minet12/2016
5692^808621-113809243420Enzo Doria09/2014
5702^807724+1879621243150Enzo Doria09/2016
5712^805843-113611242583Enzo Doria08/2014
5722^805745-459763242554Enzo Doria05/2015
5732^805353+782687242436Enzo Doria11/2016
5742^804277-417933242112Enzo Doria01/2014
5752^803468-269039241868Enzo Doria10/2013
5762^803172+80851241779Enzo Doria07/2016
5773^506233-2241535Robert Price11/2013
5782^802025-25999241434Enzo Doria10/2013
579(3^505823+3^252912+1)/7241339Serge Batalov03/2014
5802^801303+1872923241217Enzo Doria05/2016
5812^800579-1862947240999Enzo Doria12/2015
5823^504206+2240568Luke W. Richards03/2018
5832^798973-26283240515Enzo Doria10/2013
5842^798671-69487240424Enzo Doria12/2015
5852^797220+79831239988Enzo Doria06/2016
5862^796910-26001239894Enzo Doria10/2013
5872^796598+653119239800Enzo Doria12/2016
5882^796432-1859729239750Enzo Doria11/2015
5892^796002-1852211239621Enzo Doria08/2015
5902^795709+75767239533Enzo Doria04/2016
5912^795708+81721239532Enzo Doria08/2016
5922^795468-2786249239460Enzo Doria10/2015
5932^795442+80779239452Enzo Doria07/2016
5942^795075-1852057239342Enzo Doria08/2015
595(86^123677+1)/87239252Paul Bourdelais01/2019
5962^794043+1875023239031Enzo Doria06/2016
5972^793347-69577238822Enzo Doria01/2016
5982^792988-344429238714Enzo Doria08/2015
5992^792700-2786369238627Enzo Doria11/2015
6002^792663-1844797238616Enzo Doria06/2015
6012^792605-291943238598Enzo Doria07/2015
602(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
6032^789373+1869377237625Enzo Doria05/2016
604((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
6052^788942+1866409237496Enzo Doria02/2016
6062^788844-114329237466Enzo Doria01/2015
6072^788705-1859713237424Enzo Doria11/2015
6082^786180+1871971236664Enzo Doria05/2016
60911^227092-90236492Enzo Doria11/2012
6102^785260+1866361236387Enzo Doria02/2016
6112^785220+1880611236375Enzo Doria10/2016
61219^184650-2236122Robert Price10/2014
61310^236059+216513236060Patrick De Geest04/2016
61410^236059-20909236059Robert Price09/2015
615(87^121487-1)/86235625Paul Bourdelais12/2018
6162^782634-113981235597Enzo Doria11/2014
6172^782423+1879733235533Enzo Doria09/2016
6182^781682-2789543235310Enzo Doria12/2015
6192^780408-113453234927Enzo Doria08/2014
6202^780368-1864829234915Enzo Doria01/2016
6212^779593-1836559234681Enzo Doria05/2015
622(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
623(5^335429+1)/6234455Paul Bourdelais08/2010
6242^778395-113617234321Enzo Doria08/2014
6252^776245-2792353233674Enzo Doria02/2016
6262^776060-114029233618Enzo Doria11/2014
6272^775987-2789557233596Enzo Doria12/2015
6282^775672+1866721233501Enzo Doria03/2016
629(11^223999+1)/12233270Paul Bourdelais02/2010
6302^774118+1885789233033Enzo Doria04/2017
63121^176191-20^176191232964Jean-Louis Charton01/2015
6322^773679-113425232901Enzo Doria08/2014
63310^232599+192489232600Patrick De Geest12/2013
63410^232599-3232599Markus Tervooren10/2010
6352^772552-458879232562Enzo Doria04/2015
6362^772214+1874899232460Enzo Doria06/2016
6372^771994-1862771232394Enzo Doria12/2015
6382^771889+1876037232362Enzo Doria07/2016
6392^771660+1866511232293Enzo Doria02/2016
6405^332150-18188232163Enzo Doria06/2014
6413^485977-2^485977231870Mike Oakes09/2009
6422^770082-114161231818Enzo Doria01/2015
643(20^177967+1)/21231540Paul Bourdelais05/2013
6442^767622-9221231078Lelio R Paula01/2016
6452^767344+1880311230994Enzo Doria09/2016
646(3^483611-1)/2230741Paul Bourdelais02/2010
647(10^230706+179)/9230706Serge Batalov12/2014
6482^766309+1875257230682Enzo Doria06/2016
6492^765635+1879883230480Enzo Doria09/2016
6502^764348-113697230092Enzo Doria09/2014
6512^764131+78863230027Enzo Doria05/2016
6522^763701+60197229897Enzo Doria03/2016
6532^762841-25905229639Enzo Doria10/2013
6542^761117-113569229120Enzo Doria08/2014
655(98^114859+1)/99228709Paul Bourdelais12/2018
656(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
6572^757985-2790013228177Enzo Doria12/2015
6582^757038-1862081227892Enzo Doria12/2015
6592^756839+95849227832Makoto Morimoto10/2013
660(2^756839+6989)/756091227826Makoto Morimoto09/2016
661(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
6622^756773-112723227812Enzo Doria07/2014
663524309#+616367227431Makoto Morimoto02/2016
6642^755097-114193227307Enzo Doria12/2014
6652^754473-2791513227120Enzo Doria01/2016
6662^751426-764321226202Enzo Doria12/2013
667(18^180181-1)/17226176Andy Steward04/2007
6682^750740-3225996Paul Bourdelais03/2012
6692^750725+60227225991Enzo Doria02/2016
6702^750525-113743225931Enzo Doria09/2014
671(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
6722^749444-1861889225606Enzo Doria12/2015
673tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
6742^749096+1876861225501Enzo Doria07/2016
675(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
6762^748657+79607225369Enzo Doria06/2016
6772^746653-291583224765Enzo Doria07/2015
6782^746461-114043224708Enzo Doria11/2014
6792^745098-350471224297Enzo Doria06/2015
680(154*10^224061-1)/9224063Serge Batalov12/2014
6812^744211-1845787224030Enzo Doria07/2015
6822^743592-134579223844Hans Havermann10/2018
6832^742452+3223501Paul Bourdelais06/2019
684234178^9+9^234178223463Anatoly F. Selevich07/2011
6852^741651-461197223260Enzo Doria07/2015
6862^741362-1845251223173Enzo Doria07/2015
6872^740455-1863877222900Enzo Doria12/2015
6882^739636-2792219222653Enzo Doria02/2016
68911^213654-180222498Enzo Doria01/2013
6902^738957-1859743222449Enzo Doria11/2015
691(54^128189+1)/55222073Paul Bourdelais11/2018
692(10^221654+179)/9221654Serge Batalov12/2014
6932^736281+79817221643Enzo Doria06/2016
69410^221631+247617221632Patrick De Geest10/2013
69510^221631-9221631Alexander Gramolin02/2011
6962^735970-1839821221550Enzo Doria06/2015
6972^735367+60293221368Enzo Doria03/2016
698(29^151153+1)/30221045Paul Bourdelais09/2017
6992^733264-2784089220735Enzo Doria10/2015
7002^733114-24555220690Enzo Doria09/2013
7012^731891-636259220322Enzo Doria12/2013
7022^731124-25539220091Enzo Doria09/2013
7032^730972-462029220045Enzo Doria07/2015
7042^730833+1868627220003Enzo Doria04/2016
7052^730645-2787133219947Enzo Doria11/2015
7062^730547-25581219917Enzo Doria09/2013
7072^730460+82291219891Enzo Doria09/2016
708(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
709L(1051849)219824Renaud Lifchitz03/2009
71011^210961-240219694Enzo Doria01/2013
7112^729611-113437219635Enzo Doria08/2014
712F(1049897)219416Henri Lifchitz10/2008
7132^728604+1879321219332Enzo Doria10/2016
71433^144412+2219292Robert Price04/2015
7152^728277-183313219234Hans Havermann10/2018
7162^727998-1862711219150Enzo Doria12/2015
7172^727729-114073219069Enzo Doria12/2014
7182^727496-1851809218999Enzo Doria08/2015
7192^726591+2793143218726Enzo Doria02/2016
7202^725534-2791931218408Enzo Doria02/2016
7212^722184+1877821217400Enzo Doria08/2016
722(109*10^217360-1)/9217362Serge Batalov12/2014
723281*499979#/46410-2702372216849Robert Smith08/2016
724281*499979#/46410+2400766216849Robert Smith08/2016
725tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
7262^718756-114107216368Enzo Doria12/2014
7272^717305+80327215931Enzo Doria07/2016
7282^717069-59773215860Enzo Doria10/2015
72930^146021-29^146021215691Jean-Louis Charton09/2018
730277^88301-276^88301215674Jean-Louis Charton06/2012
731227^91413-40215372Enzo Doria04/2015
7322^714717+782897215152Enzo Doria11/2016
733tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
7342^713241+1879157214707Enzo Doria08/2016
73511^206081-10^206081214612Jean-Louis Charton10/2011
7362^712801-69553214575Enzo Doria01/2016
7372^712603-25357214515Enzo Doria09/2013
7382^711721-1846723214250Enzo Doria07/2015
7392^710730-396765213952Enzo Doria09/2013
7402^708468-114329213271Enzo Doria02/2015
741(163*10^212779-1)/9212781Serge Batalov12/2014
7422^706838-69041212780Enzo Doria11/2015
7432^704577-113871212099Enzo Doria10/2014
7442^704110-2792441211959Enzo Doria02/2016
7452^703943-1862947211908Enzo Doria12/2015
746(60^119083+1)/61211746Paul Bourdelais10/2018
747(10^211610-91)/9211610Serge Batalov12/2014
748227^89797+2211565Lelio R Paula08/2012
7492^702194-3211382Paul Bourdelais03/2012
7502^702064+1874911211343Enzo Doria07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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