PRP Records

Probable Primes Top 10000

(193013 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 ?
5012^789373+1869377237625Enzo Doria05/2016
502((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
5032^788942+1866409237496Enzo Doria02/2016
5042^788844-114329237466Enzo Doria01/2015
5052^788705-1859713237424Enzo Doria11/2015
5062^786180+1871971236664Enzo Doria05/2016
50711^227092-90236492Enzo Doria11/2012
5082^785260+1866361236387Enzo Doria02/2016
5092^785220+1880611236375Enzo Doria10/2016
51019^184650-2236122Robert Price10/2014
51110^236059+216513236060Patrick De Geest04/2016
51210^236059-20909236059Robert Price09/2015
5132^782634-113981235597Enzo Doria11/2014
5142^782423+1879733235533Enzo Doria09/2016
5152^781682-2789543235310Enzo Doria12/2015
5162^780408-113453234927Enzo Doria08/2014
5172^780368-1864829234915Enzo Doria01/2016
5182^779593-1836559234681Enzo Doria05/2015
519(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
520(5^335429+1)/6234455Paul Bourdelais08/2010
5212^778395-113617234321Enzo Doria08/2014
5222^776245-2792353233674Enzo Doria02/2016
5232^776060-114029233618Enzo Doria11/2014
5242^775987-2789557233596Enzo Doria12/2015
5252^775672+1866721233501Enzo Doria03/2016
526(11^223999+1)/12233270Paul Bourdelais02/2010
5272^774118+1885789233033Enzo Doria04/2017
52821^176191-20^176191232964Jean-Louis Charton01/2015
5292^773679-113425232901Enzo Doria08/2014
53010^232599+192489232600Patrick De Geest12/2013
53110^232599-3232599Markus Tervooren10/2010
5322^772552-458879232562Enzo Doria04/2015
5332^772214+1874899232460Enzo Doria06/2016
5342^771994-1862771232394Enzo Doria12/2015
5352^771889+1876037232362Enzo Doria07/2016
5362^771660+1866511232293Enzo Doria02/2016
5375^332150-18188232163Enzo Doria06/2014
5383^485977-2^485977231870Mike Oakes09/2009
5392^770082-114161231818Enzo Doria01/2015
540(20^177967+1)/21231540Paul Bourdelais05/2013
5412^767622-9221231078Lelio R Paula01/2016
5422^767344+1880311230994Enzo Doria09/2016
543(3^483611-1)/2230741Paul Bourdelais02/2010
544(10^230706+179)/9230706Serge Batalov12/2014
5452^766309+1875257230682Enzo Doria06/2016
5462^765635+1879883230480Enzo Doria09/2016
5472^764348-113697230092Enzo Doria09/2014
5482^764131+78863230027Enzo Doria05/2016
5492^763701+60197229897Enzo Doria03/2016
5502^762841-25905229639Enzo Doria10/2013
5512^761117-113569229120Enzo Doria08/2014
5522^757985-2790013228177Enzo Doria12/2015
5532^757038-1862081227892Enzo Doria12/2015
5542^756839+95849227832Makoto Morimoto10/2013
555(2^756839+6989)/756091227826Makoto Morimoto09/2016
5562^756773-112723227812Enzo Doria07/2014
557524309#+616367227431Makoto Morimoto02/2016
5582^755097-114193227307Enzo Doria12/2014
5592^754473-2791513227120Enzo Doria01/2016
5602^751426-764321226202Enzo Doria12/2013
561(18^180181-1)/17226176Andy Steward04/2007
5622^750740-3225996Paul Bourdelais03/2012
5632^750725+60227225991Enzo Doria02/2016
5642^750525-113743225931Enzo Doria09/2014
565(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
5662^749444-1861889225606Enzo Doria12/2015
567tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
5682^749096+1876861225501Enzo Doria07/2016
5692^748657+79607225369Enzo Doria06/2016
5702^746653-291583224765Enzo Doria07/2015
5712^746461-114043224708Enzo Doria11/2014
5722^745098-350471224297Enzo Doria06/2015
573(154*10^224061-1)/9224063Serge Batalov12/2014
5742^744211-1845787224030Enzo Doria07/2015
575234178^9+9^234178223463Anatoly F. Selevich07/2011
5762^741651-461197223260Enzo Doria07/2015
5772^741362-1845251223173Enzo Doria07/2015
5782^740455-1863877222900Enzo Doria12/2015
5792^739636-2792219222653Enzo Doria02/2016
58011^213654-180222498Enzo Doria01/2013
5812^738957-1859743222449Enzo Doria11/2015
582(10^221654+179)/9221654Serge Batalov12/2014
5832^736281+79817221643Enzo Doria06/2016
58410^221631+247617221632Patrick De Geest10/2013
58510^221631-9221631Alexander Gramolin02/2011
5862^735970-1839821221550Enzo Doria06/2015
5872^735367+60293221368Enzo Doria03/2016
588(29^151153+1)/30221045Paul Bourdelais09/2017
5892^733264-2784089220735Enzo Doria10/2015
5902^733114-24555220690Enzo Doria09/2013
5912^731891-636259220322Enzo Doria12/2013
5922^731124-25539220091Enzo Doria09/2013
5932^730972-462029220045Enzo Doria07/2015
5942^730833+1868627220003Enzo Doria04/2016
5952^730645-2787133219947Enzo Doria11/2015
5962^730547-25581219917Enzo Doria09/2013
5972^730460+82291219891Enzo Doria09/2016
598L(1051849)219824Renaud Lifchitz03/2009
59911^210961-240219694Enzo Doria01/2013
6002^729611-113437219635Enzo Doria08/2014
601F(1049897)219416Henri Lifchitz10/2008
6022^728604+1879321219332Enzo Doria10/2016
60333^144412+2219292Robert Price04/2015
6042^727998-1862711219150Enzo Doria12/2015
6052^727729-114073219069Enzo Doria12/2014
6062^727496-1851809218999Enzo Doria08/2015
6072^726591+2793143218726Enzo Doria02/2016
6082^725534-2791931218408Enzo Doria02/2016
6092^722184+1877821217400Enzo Doria08/2016
610(109*10^217360-1)/9217362Serge Batalov12/2014
611281*499979#/46410-2702372216849Robert Smith08/2016
612281*499979#/46410+2400766216849Robert Smith08/2016
613tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
6142^718756-114107216368Enzo Doria12/2014
6152^717305+80327215931Enzo Doria07/2016
6162^717069-59773215860Enzo Doria10/2015
617277^88301-276^88301215674Jean-Louis Charton06/2012
618227^91413-40215372Enzo Doria04/2015
6192^714717+782897215152Enzo Doria11/2016
620tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
6212^713241+1879157214707Enzo Doria08/2016
62211^206081-10^206081214612Jean-Louis Charton10/2011
6232^712801-69553214575Enzo Doria01/2016
6242^712603-25357214515Enzo Doria09/2013
6252^711721-1846723214250Enzo Doria07/2015
6262^710730-396765213952Enzo Doria09/2013
6272^708468-114329213271Enzo Doria02/2015
628(163*10^212779-1)/9212781Serge Batalov12/2014
6292^706838-69041212780Enzo Doria11/2015
6302^704577-113871212099Enzo Doria10/2014
6312^704110-2792441211959Enzo Doria02/2016
6322^703943-1862947211908Enzo Doria12/2015
633(10^211610-91)/9211610Serge Batalov12/2014
634227^89797+2211565Lelio R Paula08/2012
6352^702194-3211382Paul Bourdelais03/2012
6362^702064+1874911211343Enzo Doria07/2016
6372^701968-113873211314Enzo Doria10/2014
6382^701713-113779211237Enzo Doria09/2014
6392^701449-25201211158Enzo Doria09/2013
6402^701403-2786977211144Enzo Doria11/2015
6412^701189-25423211079Enzo Doria09/2013
6422^701162-459161211071Enzo Doria05/2015
6432^700400+9385210842Lelio R Paula01/2014
6442^700131+1874693210761Enzo Doria06/2016
64511^202357-1140210734Enzo Doria12/2012
6462^698929-2788423210399Enzo Doria11/2015
647(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
6482^698316+1878601210215Enzo Doria08/2016
6492^697036+1878751209829Enzo Doria08/2016
650(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
6512^696254-115151209594Enzo Doria06/2015
6522^694633+1887257209106Enzo Doria05/2017
6532^693959+180923208903Enzo Doria07/2016
6542^693462-1847561208753Enzo Doria07/2015
6552^690890-59981207979Enzo Doria11/2015
6562^690163+1877063207760Enzo Doria07/2016
6572^689286-29381207496Enzo Doria08/2015
6582^689122-114521207447Enzo Doria04/2015
6592^688373+6077207221Enzo Doria02/2016
6602^688201+1875527207170Enzo Doria07/2016
6612^687619+81563206994Enzo Doria08/2016
6622^686572-1845299206679Enzo Doria07/2015
663(21^156217-1)/20206552Paul Bourdelais04/2010
6642^685578+3206380Paul Bourdelais04/2012
6652^684836-49349206157Enzo Doria10/2015
6662^684163-2790967205954Enzo Doria12/2015
667326^81943-325^81943205941Jean-Louis Charton07/2012
668(2^684127-1)/23765203727205933Jens K. Andersen04/2009
6694^341233-3^341233205443Jean-Louis Charton01/2006
6702^681545+467205166Lelio R Paula11/2013
6712^681306+81049205094Enzo Doria07/2016
6722^680697+1877057204911Enzo Doria07/2016
6732^680415+71783204826Enzo Doria04/2016
6742^679860-459995204659Enzo Doria06/2015
6752^679593+1879547204578Enzo Doria09/2016
6762^678651+1875023204295Enzo Doria07/2016
6772^678561+678561204268Henri Lifchitz05/2006
6782^678101-114043204129Enzo Doria11/2014
6792^678028+1875631204107Enzo Doria06/2016
6802^676992-59783203795Enzo Doria10/2015
6812^676972+1866871203789Enzo Doria03/2016
6822^676761-9203726Robert Price01/2017
6832^676563-2792407203666Enzo Doria02/2016
6842^676306-114713203589Enzo Doria04/2015
685(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
6862^674627-25161203083Enzo Doria09/2013
6872^674603-69337203076Enzo Doria12/2015
6882^674459+74213203033Enzo Doria04/2016
6892^674116-458879202930Enzo Doria04/2015
6902^674076-114755202918Enzo Doria04/2015
6915^289937-4^289937202658Jean-Louis Charton03/2013
6922^672556-1835519202460Enzo Doria04/2015
6932^671446-351401202126Enzo Doria07/2015
6942^671373+77747202104Enzo Doria05/2016
6952^670726-114845201909Enzo Doria05/2015
6962^670539-25045201853Enzo Doria09/2013
6972^670213+282317201755Enzo Doria09/2016
6982^669854-113501201647Enzo Doria08/2014
6992^669718+81619201606Enzo Doria08/2016
700(145*10^201504-1)/9201506Serge Batalov12/2014
7012^668938-1839821201371Enzo Doria06/2015
7022^668492+1879303201237Enzo Doria08/2016
7036^258413-5^258413201085Jean-Louis Charton03/2013
7042^667894+1875589201057Enzo Doria06/2016
7052^667569-1836559200959Enzo Doria05/2015
706(172*10^200746-1)/9200748Serge Batalov12/2014
7072^666430+782569200616Enzo Doria10/2016
708103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
709numbpart(32235776596)200002Serge Batalov04/2017
710(10^200001+149)/3200001Serge Batalov12/2014
7112^662103-29287199313Enzo Doria08/2015
7122^660482-2891198825Yves Minet05/2016
7132^659583+1879223198555Enzo Doria08/2016
714(53*10^198529+1)/9198530Serge Batalov07/2010
7152^658828-29819198327Enzo Doria08/2015
7162^658776-2791229198312Enzo Doria01/2016
7172^658544-1854029198242Enzo Doria09/2015
718(157^90239-1)/156198154Alexander Zhirkov06/2016
7192^656462+1874419197615Enzo Doria06/2016
720(89^101363+1)/90197595Paul Bourdelais11/2017
7212^655893-344563197444Enzo Doria07/2015
7222^655875+71333197439Enzo Doria04/2016
7232^655845-9197430Robert Price01/2017
7242^655682-1849121197380Enzo Doria08/2015
7252^655045-49603197189Enzo Doria10/2015
7262^655000-2784089197175Enzo Doria10/2015
727(18^157051-1)/17197141Paul Bourdelais03/2010
7282^654400-39719196995Enzo Doria09/2015
7292^654216-459995196939Enzo Doria06/2015
7302^653851+82295196829Enzo Doria09/2016
7312^653636-29429196765Enzo Doria08/2015
7322^653601-69673196754Enzo Doria02/2016
733(44*10^196684+1)/9196685Serge Batalov07/2010
7342^652786-1852571196509Enzo Doria08/2015
7352^652752-1325196498Yves Minet07/2015
7362^652470-1859141196414Enzo Doria10/2015
7372^652307+1877483196364Enzo Doria08/2016
7382^652293-115273196360Enzo Doria06/2015
7392^651218-1868201196037Enzo Doria04/2016
7402^651047-49687195985Enzo Doria10/2015
7412^650285-2785333195756Enzo Doria10/2015
742(69^106397-1)/68195647Paul Bourdelais10/2017
7432^649811+1877573195613Enzo Doria08/2016
7442^649586+182839195545Enzo Doria11/2016
7452^649537-1867363195531Enzo Doria04/2016
7462^649536-1861499195530Enzo Doria12/2015
747(103*10^195478-1)/3195480Serge Batalov12/2014
7482^649102-59351195400Enzo Doria10/2015
7492^648988+1178971195365Enzo Doria06/2016
7502^648975-114319195361Enzo Doria02/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

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