PRP Records

Probable Primes Top 10000

(205869 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 (> 30000) Who ? When ?
5012^796432-1859729239750Enzo Doria11/2015
5022^796002-1852211239621Enzo Doria08/2015
5032^795709+75767239533Enzo Doria04/2016
5042^795708+81721239532Enzo Doria08/2016
5052^795468-2786249239460Enzo Doria10/2015
5062^795442+80779239452Enzo Doria07/2016
5072^795075-1852057239342Enzo Doria08/2015
5082^794043+1875023239031Enzo Doria06/2016
5092^793347-69577238822Enzo Doria01/2016
5102^792988-344429238714Enzo Doria08/2015
5112^792700-2786369238627Enzo Doria11/2015
5122^792663-1844797238616Enzo Doria06/2015
5132^792605-291943238598Enzo Doria07/2015
514(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
5152^789373+1869377237625Enzo Doria05/2016
516((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5172^788942+1866409237496Enzo Doria02/2016
5182^788844-114329237466Enzo Doria01/2015
5192^788705-1859713237424Enzo Doria11/2015
5202^786180+1871971236664Enzo Doria05/2016
52111^227092-90236492Enzo Doria11/2012
5222^785260+1866361236387Enzo Doria02/2016
5232^785220+1880611236375Enzo Doria10/2016
52419^184650-2236122Robert Price10/2014
52510^236059+216513236060Patrick De Geest04/2016
52610^236059-20909236059Robert Price09/2015
5272^782634-113981235597Enzo Doria11/2014
5282^782423+1879733235533Enzo Doria09/2016
5292^781682-2789543235310Enzo Doria12/2015
5302^780408-113453234927Enzo Doria08/2014
5312^780368-1864829234915Enzo Doria01/2016
5322^779593-1836559234681Enzo Doria05/2015
533(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
534(5^335429+1)/6234455Paul Bourdelais08/2010
5352^778395-113617234321Enzo Doria08/2014
5362^776245-2792353233674Enzo Doria02/2016
5372^776060-114029233618Enzo Doria11/2014
5382^775987-2789557233596Enzo Doria12/2015
5392^775672+1866721233501Enzo Doria03/2016
540(11^223999+1)/12233270Paul Bourdelais02/2010
5412^774118+1885789233033Enzo Doria04/2017
54221^176191-20^176191232964Jean-Louis Charton01/2015
5432^773679-113425232901Enzo Doria08/2014
54410^232599+192489232600Patrick De Geest12/2013
54510^232599-3232599Markus Tervooren10/2010
5462^772552-458879232562Enzo Doria04/2015
5472^772214+1874899232460Enzo Doria06/2016
5482^771994-1862771232394Enzo Doria12/2015
5492^771889+1876037232362Enzo Doria07/2016
5502^771660+1866511232293Enzo Doria02/2016
5515^332150-18188232163Enzo Doria06/2014
5523^485977-2^485977231870Mike Oakes09/2009
5532^770082-114161231818Enzo Doria01/2015
554(20^177967+1)/21231540Paul Bourdelais05/2013
5552^767622-9221231078Lelio R Paula01/2016
5562^767344+1880311230994Enzo Doria09/2016
557(3^483611-1)/2230741Paul Bourdelais02/2010
558(10^230706+179)/9230706Serge Batalov12/2014
5592^766309+1875257230682Enzo Doria06/2016
5602^765635+1879883230480Enzo Doria09/2016
5612^764348-113697230092Enzo Doria09/2014
5622^764131+78863230027Enzo Doria05/2016
5632^763701+60197229897Enzo Doria03/2016
5642^762841-25905229639Enzo Doria10/2013
5652^761117-113569229120Enzo Doria08/2014
5662^757985-2790013228177Enzo Doria12/2015
5672^757038-1862081227892Enzo Doria12/2015
5682^756839+95849227832Makoto Morimoto10/2013
569(2^756839+6989)/756091227826Makoto Morimoto09/2016
5702^756773-112723227812Enzo Doria07/2014
571524309#+616367227431Makoto Morimoto02/2016
5722^755097-114193227307Enzo Doria12/2014
5732^754473-2791513227120Enzo Doria01/2016
5742^751426-764321226202Enzo Doria12/2013
575(18^180181-1)/17226176Andy Steward04/2007
5762^750740-3225996Paul Bourdelais03/2012
5772^750725+60227225991Enzo Doria02/2016
5782^750525-113743225931Enzo Doria09/2014
579(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5802^749444-1861889225606Enzo Doria12/2015
581tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5822^749096+1876861225501Enzo Doria07/2016
5832^748657+79607225369Enzo Doria06/2016
5842^746653-291583224765Enzo Doria07/2015
5852^746461-114043224708Enzo Doria11/2014
5862^745098-350471224297Enzo Doria06/2015
587(154*10^224061-1)/9224063Serge Batalov12/2014
5882^744211-1845787224030Enzo Doria07/2015
589234178^9+9^234178223463Anatoly F. Selevich07/2011
5902^741651-461197223260Enzo Doria07/2015
5912^741362-1845251223173Enzo Doria07/2015
5922^740455-1863877222900Enzo Doria12/2015
5932^739636-2792219222653Enzo Doria02/2016
59411^213654-180222498Enzo Doria01/2013
5952^738957-1859743222449Enzo Doria11/2015
596(10^221654+179)/9221654Serge Batalov12/2014
5972^736281+79817221643Enzo Doria06/2016
59810^221631+247617221632Patrick De Geest10/2013
59910^221631-9221631Alexander Gramolin02/2011
6002^735970-1839821221550Enzo Doria06/2015
6012^735367+60293221368Enzo Doria03/2016
602(29^151153+1)/30221045Paul Bourdelais09/2017
6032^733264-2784089220735Enzo Doria10/2015
6042^733114-24555220690Enzo Doria09/2013
6052^731891-636259220322Enzo Doria12/2013
6062^731124-25539220091Enzo Doria09/2013
6072^730972-462029220045Enzo Doria07/2015
6082^730833+1868627220003Enzo Doria04/2016
6092^730645-2787133219947Enzo Doria11/2015
6102^730547-25581219917Enzo Doria09/2013
6112^730460+82291219891Enzo Doria09/2016
612L(1051849)219824Renaud Lifchitz03/2009
61311^210961-240219694Enzo Doria01/2013
6142^729611-113437219635Enzo Doria08/2014
615F(1049897)219416Henri Lifchitz10/2008
6162^728604+1879321219332Enzo Doria10/2016
61733^144412+2219292Robert Price04/2015
6182^727998-1862711219150Enzo Doria12/2015
6192^727729-114073219069Enzo Doria12/2014
6202^727496-1851809218999Enzo Doria08/2015
6212^726591+2793143218726Enzo Doria02/2016
6222^725534-2791931218408Enzo Doria02/2016
6232^722184+1877821217400Enzo Doria08/2016
624(109*10^217360-1)/9217362Serge Batalov12/2014
625281*499979#/46410-2702372216849Robert Smith08/2016
626281*499979#/46410+2400766216849Robert Smith08/2016
627tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
6282^718756-114107216368Enzo Doria12/2014
6292^717305+80327215931Enzo Doria07/2016
6302^717069-59773215860Enzo Doria10/2015
631277^88301-276^88301215674Jean-Louis Charton06/2012
632227^91413-40215372Enzo Doria04/2015
6332^714717+782897215152Enzo Doria11/2016
634tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
6352^713241+1879157214707Enzo Doria08/2016
63611^206081-10^206081214612Jean-Louis Charton10/2011
6372^712801-69553214575Enzo Doria01/2016
6382^712603-25357214515Enzo Doria09/2013
6392^711721-1846723214250Enzo Doria07/2015
6402^710730-396765213952Enzo Doria09/2013
6412^708468-114329213271Enzo Doria02/2015
642(163*10^212779-1)/9212781Serge Batalov12/2014
6432^706838-69041212780Enzo Doria11/2015
6442^704577-113871212099Enzo Doria10/2014
6452^704110-2792441211959Enzo Doria02/2016
6462^703943-1862947211908Enzo Doria12/2015
647(10^211610-91)/9211610Serge Batalov12/2014
648227^89797+2211565Lelio R Paula08/2012
6492^702194-3211382Paul Bourdelais03/2012
6502^702064+1874911211343Enzo Doria07/2016
6512^701968-113873211314Enzo Doria10/2014
6522^701713-113779211237Enzo Doria09/2014
6532^701449-25201211158Enzo Doria09/2013
6542^701403-2786977211144Enzo Doria11/2015
6552^701189-25423211079Enzo Doria09/2013
6562^701162-459161211071Enzo Doria05/2015
657(24^152783-1)/23210872Paul Bourdelais04/2018
6582^700400+9385210842Lelio R Paula01/2014
6592^700131+1874693210761Enzo Doria06/2016
66011^202357-1140210734Enzo Doria12/2012
6612^698929-2788423210399Enzo Doria11/2015
662(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
6632^698316+1878601210215Enzo Doria08/2016
6642^697036+1878751209829Enzo Doria08/2016
665(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6662^696254-115151209594Enzo Doria06/2015
6672^694633+1887257209106Enzo Doria05/2017
6682^693959+180923208903Enzo Doria07/2016
6692^693462-1847561208753Enzo Doria07/2015
6702^690890-59981207979Enzo Doria11/2015
6712^690163+1877063207760Enzo Doria07/2016
6722^689286-29381207496Enzo Doria08/2015
6732^689122-114521207447Enzo Doria04/2015
6742^688373+6077207221Enzo Doria02/2016
6752^688201+1875527207170Enzo Doria07/2016
6762^687619+81563206994Enzo Doria08/2016
6772^686572-1845299206679Enzo Doria07/2015
678(21^156217-1)/20206552Paul Bourdelais04/2010
6792^685578+3206380Paul Bourdelais04/2012
6802^684836-49349206157Enzo Doria10/2015
6812^684163-2790967205954Enzo Doria12/2015
682326^81943-325^81943205941Jean-Louis Charton07/2012
683(2^684127-1)/23765203727205933Jens K. Andersen04/2009
6844^341233-3^341233205443Jean-Louis Charton01/2006
6852^681545+467205166Lelio R Paula11/2013
6862^681306+81049205094Enzo Doria07/2016
6872^680697+1877057204911Enzo Doria07/2016
6882^680415+71783204826Enzo Doria04/2016
6892^679860-459995204659Enzo Doria06/2015
6902^679593+1879547204578Enzo Doria09/2016
6912^678651+1875023204295Enzo Doria07/2016
6922^678561+678561204268Henri Lifchitz05/2006
6932^678101-114043204129Enzo Doria11/2014
6942^678028+1875631204107Enzo Doria06/2016
6952^676992-59783203795Enzo Doria10/2015
6962^676972+1866871203789Enzo Doria03/2016
6972^676761-9203726Robert Price01/2017
6982^676563-2792407203666Enzo Doria02/2016
6992^676306-114713203589Enzo Doria04/2015
700(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
7012^674627-25161203083Enzo Doria09/2013
7022^674603-69337203076Enzo Doria12/2015
7032^674459+74213203033Enzo Doria04/2016
7042^674116-458879202930Enzo Doria04/2015
7052^674076-114755202918Enzo Doria04/2015
7065^289937-4^289937202658Jean-Louis Charton03/2013
7072^672556-1835519202460Enzo Doria04/2015
7082^671446-351401202126Enzo Doria07/2015
7092^671373+77747202104Enzo Doria05/2016
7102^670726-114845201909Enzo Doria05/2015
7112^670539-25045201853Enzo Doria09/2013
7122^670213+282317201755Enzo Doria09/2016
7132^669854-113501201647Enzo Doria08/2014
7142^669718+81619201606Enzo Doria08/2016
715(145*10^201504-1)/9201506Serge Batalov12/2014
7162^668938-1839821201371Enzo Doria06/2015
7172^668492+1879303201237Enzo Doria08/2016
7186^258413-5^258413201085Jean-Louis Charton03/2013
7192^667894+1875589201057Enzo Doria06/2016
7202^667569-1836559200959Enzo Doria05/2015
721(172*10^200746-1)/9200748Serge Batalov12/2014
7222^666430+782569200616Enzo Doria10/2016
723103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
724103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
725numbpart(32235776596)200002Serge Batalov04/2017
726(10^200001+149)/3200001Serge Batalov12/2014
7272^662103-29287199313Enzo Doria08/2015
728(2*10^199283+457)/9199283Robert Price01/2018
729(10^199248-19)/9199248Robert Price01/2018
7302^660482-2891198825Yves Minet05/2016
7312^659583+1879223198555Enzo Doria08/2016
732(53*10^198529+1)/9198530Serge Batalov07/2010
7332^658828-29819198327Enzo Doria08/2015
7342^658776-2791229198312Enzo Doria01/2016
735(4*10^198268+137)/3198269Robert Price03/2018
7362^658544-1854029198242Enzo Doria09/2015
737(157^90239-1)/156198154Alexander Zhirkov06/2016
738(4*10^197778+173)/3197779Robert Price02/2018
7392^656462+1874419197615Enzo Doria06/2016
740(89^101363+1)/90197595Paul Bourdelais11/2017
7412^655893-344563197444Enzo Doria07/2015
7422^655875+71333197439Enzo Doria04/2016
7432^655845-9197430Robert Price01/2017
7442^655682-1849121197380Enzo Doria08/2015
7452^655045-49603197189Enzo Doria10/2015
7462^655000-2784089197175Enzo Doria10/2015
747(18^157051-1)/17197141Paul Bourdelais03/2010
7482^654400-39719196995Enzo Doria09/2015
749(14*10^196965-221)/9196966Robert Price04/2018
7502^654216-459995196939Enzo Doria06/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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