PRP Records

Probable Primes Top 10000

(173006 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 ?
6751(2^212131-3)/48563856Lelio R Paula04/2012
67522^212112-45999563853Enzo Doria06/2015
675315^54290+5863850Lelio R Paula05/2013
67543*2^212097-763849Lelio R Paula04/2014
675555^36683-5463842Norbert Schneider08/2014
6756(509203*2^212056-1)/363841Lelio R Paula04/2015
6757(3^133805-7)/17263839Lelio R Paula04/2012
67582^212049+14963834Lelio R Paula08/2011
67595^91318-1863829Lelio R Paula04/2013
676018468^2857+2857^1846863824Hans Havermann03/2017
6761(2^212024-5)/111163823Lelio R Paula04/2012
67622^211961+1291563807Lelio R Paula02/2013
6763(3^133707-7)/578063791Lelio R Paula04/2012
6764747^22198+22198^74763782Norbert Schneider07/2016
67652^211800-1716963759Enzo Doria05/2013
6766(14*10^63747-11)/363748Erik Branger09/2014
676791*19^49848+663746Curtis Bright05/2015
676818855^2402+2402^1885563741Hans Havermann03/2017
6769(142*10^63734-7)/963736Robert Price02/2017
67702^211699-11163728Lelio R Paula08/2011
677111^61192-555063725Enzo Doria01/2013
6772(11*10^63718+7)/963719Serge Batalov06/2011
67736^81872-1363709Lelio R Paula04/2013
67743^133522+9863707Lelio R Paula05/2013
67762^211607-6163701Lelio R Paula08/2011
67755^91135+863701Lelio R Paula04/2013
677711^61157-27063689Enzo Doria07/2012
677910^63685+114514191963686Marisa Kirisame03/2015
677810^63685+10383763686Patrick De Geest03/2016
678010^63685-13079763685Patrick De Geest03/2016
67812^211547+1155*21154763682Henri Lifchitz02/2005
67822^211543+4563681Lelio R Paula08/2011
67832^211534+4363679Lelio R Paula08/2011
678411^61140-6063671Enzo Doria07/2012
67852^211491-11232163666Enzo Doria06/2014
678619085^2164+2164^1908563654Hans Havermann03/2017
6787(2^211430-5)/85963644Lelio R Paula04/2012
67882^211401-9163639Lelio R Paula08/2011
6789(6883*2^211378-1)/6963634Lelio R Paula04/2015
6790(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
6791(29*2^211384-1)/5012262163627Lelio R Paula01/2014
67922^211333+1501563618Lelio R Paula01/2013
679333^41889-3263610Norbert Schneider03/2014
679413^57093+1863599Lelio R Paula05/2013
6795(5*2^211219-1)/963583Lelio R Paula01/2014
6796(107*10^63576-17)/963578Robert Price02/2017
679723^46687-102063575Enzo Doria08/2012
6798(67607*2^211188+1)/523431963573Lelio R Paula06/2014
6799(3^133243+7)/1072663570Lelio R Paula04/2012
6800(7*2^211181+1)/274563570Lelio R Paula06/2012
6802(20^48859-1)/1963566Paul Bourdelais03/2010
68012*3^133227+563566Lelio R Paula04/2014
68032^211155+11363564Lelio R Paula08/2011
68042^211134+34563558Lelio R Paula09/2011
68052^211121+1638563554Lelio R Paula09/2011
680616996^5483+5483^1699663549Hans Havermann02/2017
6807(2^211079+9)/36428363536Lelio R Paula03/2012
680815852^10157+10157^1585263516Hans Havermann02/2017
68092^210948-1587363502Enzo Doria04/2013
68107^75136+663498Lelio R Paula04/2013
68112^210928+1291563496Lelio R Paula02/2013
68127*10^63493+3963494Robert Price07/2016
68132^210909+13563490Lelio R Paula08/2011
6814(3*2^210832+1)/763467Lelio R Paula07/2012
68158*7^75098-363467Lelio R Paula09/2014
681617683^3882+3882^1768363466Hans Havermann03/2017
6818Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
68172^210820-1690563464Enzo Doria05/2013
68195^90795-3663463Lelio R Paula04/2013
68202^210816-1319763462Enzo Doria10/2012
68212^210750+13363443Lelio R Paula08/2011
6822291^25742+25742^29163426Norbert Schneider09/2014
6823(3^132908+8)/27985963408Lelio R Paula04/2012
68246^81480-13963404Lelio R Paula04/2013
68252^210576-17363390Lelio R Paula08/2011
682618^50497+5563388Lelio R Paula05/2013
68272^210545+1163381Lelio R Paula08/2011
68282^210543+6363380Lelio R Paula08/2011
682983^33016+8263361Norbert Schneider04/2015
68302^210464+9876533163356Jason Earls12/2008
68317*10^63351+963352Dmitry Domanov11/2010
6832p(13534)#/2+51263348Robert Price05/2017
68331741^19546+19546^174163345Serge Batalov05/2014
683410^63336+1981963337Patrick De Geest12/2013
683510^63336-12288363336Patrick De Geest12/2013
6836(19^49523-2^49523)/1763327Robert Price09/2013
6837(2^210378+47)/9551693163323Lelio R Paula03/2012
683831191!2+25663316Robert Price01/2015
683916458^7031+7031^1645863315Hans Havermann01/2017
6840(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
6841(2^210283+7)/169114563296Lelio R Paula03/2012
68422^210217+129963282Lelio R Paula09/2011
6843(2^210221-3)/26963281Lelio R Paula04/2012
6844Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
684596^31913-9563261Norbert Schneider04/2016
68463^132572+28063253Lelio R Paula04/2013
68473^132570-2^(132570-1)63252Robert Price01/2016
684811^60734-492063248Enzo Doria01/2013
68502^210061+2163235Donovan Johnson06/2006
684918^50375+9563235Lelio R Paula05/2013
685185^32773-263233Lelio R Paula08/2013
6852(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
6853(2^210054-1017)/67163230Lelio R Paula04/2012
68543*2^210022+563224Lelio R Paula04/2014
685515^53756+3263222Lelio R Paula05/2013
685717^51380+2263221Lelio R Paula05/2013
6856(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
685843^38700+4263216Norbert Schneider06/2014
68595^90431-9663209Lelio R Paula04/2013
6860(172*10^63202-1)/963204Serge Batalov12/2014
68612^209914-1600563191Enzo Doria04/2013
68623*6^81190-563179Lelio R Paula09/2014
68632^209820+425763163Lelio R Paula10/2011
686499^31648+263158Lelio R Paula05/2013
686516976^5253+5253^1697663158Hans Havermann01/2017
68662^209790+6763154Lelio R Paula08/2011
68672^209759+9019563144Lelio R Paula02/2013
6868145823#+21150763142Arkadiusz Wesolowski03/2013
68702^209707+51363129Lelio R Paula10/2011
6869(3^132314-8)/1763129Lelio R Paula04/2012
6871(2*10^63117+7)/963117Erik Branger03/2011
68729*2^209654-763114Lelio R Paula04/2014
687311^60598-1463107Lelio R Paula05/2013
687415103^15078+15078^1510363106Hans Havermann01/2017
687515346^12941+12941^1534663103Hans Havermann01/2017
68763^132253+7663101Lelio R Paula04/2013
687717549^3936+3936^1754963090Hans Havermann01/2017
6878(55459*2^209553+1)/42363084Lelio R Paula06/2014
688020^48480+3163074Lelio R Paula06/2013
6879(26*10^63073-23)/363074Robert Price08/2016
68812^209499+7625363066Enzo Doria04/2016
688211^60546-1134063053Enzo Doria12/2012
68832^209426+5788963044Yves Minet02/2010
6884(22699*2^209405+1)/2163041Lelio R Paula06/2014
68855^90189+5463040Lelio R Paula04/2013
6886(314021^11467+1)/31402263029Faysal YAtim05/2008
6887V(301486)63007Henri Lifchitz05/2003
6888(31*2^209298+1)/9563005Lelio R Paula08/2012
6889(27*2^209245+1)/562990Lelio R Paula08/2012
68906^80946-5^(80946-1)62989Robert Price05/2016
6891467^23596+23596^46762986Norbert Schneider08/2016
6892(7*2^209212-1)/362980Lelio R Paula01/2014
6893(27*2^209206-1)/1162978Lelio R Paula01/2014
68941456^19909+19909^145662976Serge Batalov05/2014
6896(3^131964-5)/18521239662955Lelio R Paula04/2012
689535^40772-146662955Enzo Doria03/2013
68975^90064-1370662953Enzo Doria02/2013
68982^208993+10762914Lelio R Paula08/2011
68992^208993+7762914Lelio R Paula08/2011
6900(2^208948-7)/26162898Lelio R Paula03/2012
6901(151*10^62879-1)/362881Robert Price04/2017
690215^53464-8262879Lelio R Paula05/2013
69032^208843-11292162869Enzo Doria06/2014
69042^208779+8162849Henri Lifchitz01/2007
6905(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
6906(73*10^62824+17)/962825Robert Price10/2015
69073^131670-8262823Lelio R Paula04/2013
690819^49128-9062823Lelio R Paula05/2013
690911^60314-441062811Enzo Doria01/2013
6910(17*2^208614-1)/5362799Lelio R Paula01/2014
69112^208594+9362794Donovan Johnson06/2008
6912(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
6913(2^208534+7)/905962772Lelio R Paula03/2012
6914(13^56333+1)/1462751Paul Bourdelais03/2010
691510^62750+5762751Robert Price01/2011
691610^62750-26742962750Patrick De Geest01/2013
69172^208427-6962743Lelio R Paula08/2011
69182^208421-11177562741Enzo Doria05/2014
69192^208404-11207962736Enzo Doria06/2014
69202^208343-222162718Yves Minet08/2013
69212^208335+51362716Lelio R Paula10/2011
6923(2^208328+47)/362713Lelio R Paula03/2012
692211^60220-204062713Enzo Doria12/2012
69242^208292+8162703Henri Lifchitz10/2005
692515013^15012-1501262698Henri Lifchitz10/2014
69262^208271-11274762696Enzo Doria06/2014
692711^60202-438062694Enzo Doria01/2013
6928(3^131403-4)/15762693Lelio R Paula04/2012
69292^208127-12666762653Paul Bourdelais01/2012
693071^33843+262653Lelio R Paula05/2013
6931(3^131325+7)/106685062652Lelio R Paula04/2012
69322^208019+11962620Lelio R Paula08/2011
6933(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
693411^60126-1137062615Enzo Doria12/2012
69352^207976-248962608Yves Minet07/2014
6936(22699*2^207945+1)/28170962597Lelio R Paula06/2014
69374*21^47335+20562588Curtis Bright05/2015
693815^53210+862580Lelio R Paula05/2013
69392^207865+2962574Henri Lifchitz08/2005
694015^53199-3862567Lelio R Paula05/2013
6941(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
69422^207782+5890562549Lelio R Paula10/2011
6943(2^207748-3)/843762535Lelio R Paula03/2012
6944(2^207711+5)/1362527Lelio R Paula03/2012
694510^62523+6362524Robert Price01/2011
694610^62523-29237362523Patrick De Geest01/2013
69472^207691+1155*20769162522Henri Lifchitz02/2005
6948(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
69492^207626-11215762502Enzo Doria06/2014
69503^130987+5262497Lelio R Paula04/2013
69518*6^80299-762486Lelio R Paula09/2014
695211^59997-267062481Enzo Doria12/2012
695393^31740+262480Lelio R Paula05/2013
6954(10^62451+119)/362451Serge Batalov12/2014
6955(2^207443+47)/764562443Lelio R Paula03/2012
69562^207364+11562423Lelio R Paula08/2011
69573^130815-4662415Lelio R Paula04/2013
6958(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
695920^47968-948362408Enzo Doria03/2013
6960(10^62402+101)/362402Robert Price04/2016
6961(13*2^207264-1)/362394Lelio R Paula01/2014
6962(79*10^62387-61)/962388Robert Price10/2015
69635^89244+3*2^8924462379Mike Oakes02/2010
69646^80160-1362377Lelio R Paula04/2013
6965(1000121^10391+1)/100012262341Faysal YAtim07/2008
6966(17*10^62328-11)/362329Robert Price07/2015
69672^207023+1171562321Lelio R Paula09/2011
6968(265*10^62298+11)/362300Robert Price03/2017
69692^206947-6962298Lelio R Paula08/2011
69702^206938+2983562295Lelio R Paula02/2013
69712^206911-72687762287Paul Bourdelais03/2013
6972(6883*2^206884-1)/362282Lelio R Paula04/2015
69732^206892-11281762281Enzo Doria06/2014
69743^130523+4662276Lelio R Paula04/2013
69752^206872-11345362275Enzo Doria07/2014
69762^206840-9362266Lelio R Paula08/2011
6977(1017*2^206815-1)/63562258Lelio R Paula04/2015
697896^31406+9562256Norbert Schneider03/2016
6979(2^206824+7)/64621362255Lelio R Paula03/2012
69802^206765-94168362243Paul Bourdelais11/2012
6981(6^79987-1)/562242Paul Bourdelais11/2007
69822^206755-157962240Yves Minet03/2013
698311^59764-582062238Enzo Doria01/2013
69845*10^62233+362234Dmitry Domanov11/2010
69858*3^130421+762228Lelio R Paula04/2014
698619^48661+1062226Lelio R Paula05/2013
6988(17*2^206705+1)/562225Lelio R Paula08/2012
69872^206705-11263562225Enzo Doria06/2014
69893^130403+868062219Lelio R Paula04/2013
699011^59740-711062213Enzo Doria01/2013
69922^206596-16762192Lelio R Paula08/2011
69912^206597+1891562192Lelio R Paula02/2013
69936^79918+13762189Lelio R Paula04/2013
6994lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
69952^206574+61362185Jason Earls04/2008
69963^130328+8062183Lelio R Paula04/2013
6997(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
69982^206550+7681962178Enzo Doria05/2016
699911^59703-2462175Lelio R Paula05/2013
70002^206524+7578162170Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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