PRP Records

Probable Primes Top 10000

(202632 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 ?
7251(14*10^63747-11)/363748Erik Branger09/2014
725291*19^49848+663746Curtis Bright05/2015
725318855^2402+2402^1885563741Hans Havermann03/2017
7254(142*10^63734-7)/963736Robert Price02/2017
72552^211699-11163728Lelio R Paula08/2011
725611^61192-555063725Enzo Doria01/2013
7257(11*10^63718+7)/963719Serge Batalov06/2011
72586^81872-1363709Lelio R Paula04/2013
72593^133522+9863707Lelio R Paula05/2013
72612^211607-6163701Lelio R Paula08/2011
72605^91135+863701Lelio R Paula04/2013
726211^61157-27063689Enzo Doria07/2012
726410^63685+114514191963686Marisa Kirisame03/2015
726310^63685+10383763686Patrick De Geest03/2016
726510^63685-13079763685Patrick De Geest03/2016
72662^211547+1155*21154763682Henri Lifchitz02/2005
72672^211543+4563681Lelio R Paula08/2011
72682^211534+4363679Lelio R Paula08/2011
726911^61140-6063671Enzo Doria07/2012
72702^211491-11232163666Enzo Doria06/2014
727119085^2164+2164^1908563654Hans Havermann03/2017
7272(2^211430-5)/85963644Lelio R Paula04/2012
72732^211401-9163639Lelio R Paula08/2011
7274(6883*2^211378-1)/6963634Lelio R Paula04/2015
7275(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
7276(29*2^211384-1)/5012262163627Lelio R Paula01/2014
72772^211333+1501563618Lelio R Paula01/2013
727833^41889-3263610Norbert Schneider03/2014
727913^57093+1863599Lelio R Paula05/2013
7280(5*2^211219-1)/963583Lelio R Paula01/2014
7281(107*10^63576-17)/963578Robert Price02/2017
728223^46687-102063575Enzo Doria08/2012
7283(67607*2^211188+1)/523431963573Lelio R Paula06/2014
7284(3^133243+7)/1072663570Lelio R Paula04/2012
7285(7*2^211181+1)/274563570Lelio R Paula06/2012
7287(20^48859-1)/1963566Paul Bourdelais03/2010
72862*3^133227+563566Lelio R Paula04/2014
72882^211155+11363564Lelio R Paula08/2011
72892^211134+34563558Lelio R Paula09/2011
72902^211121+1638563554Lelio R Paula09/2011
729116996^5483+5483^1699663549Hans Havermann02/2017
7292(2^211079+9)/36428363536Lelio R Paula03/2012
72933*10^63522+1363523Robert Price08/2017
729415852^10157+10157^1585263516Hans Havermann02/2017
72952^210948-1587363502Enzo Doria04/2013
72967^75136+663498Lelio R Paula04/2013
72972^210928+1291563496Lelio R Paula02/2013
72987*10^63493+3963494Robert Price07/2016
72992^210909+13563490Lelio R Paula08/2011
7300(3*2^210832+1)/763467Lelio R Paula07/2012
73018*7^75098-363467Lelio R Paula09/2014
730217683^3882+3882^1768363466Hans Havermann03/2017
7304Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
73032^210820-1690563464Enzo Doria05/2013
73055^90795-3663463Lelio R Paula04/2013
73062^210816-1319763462Enzo Doria10/2012
73072^210750+13363443Lelio R Paula08/2011
7308291^25742+25742^29163426Norbert Schneider09/2014
7309(3^132908+8)/27985963408Lelio R Paula04/2012
73106^81480-13963404Lelio R Paula04/2013
73112^210576-17363390Lelio R Paula08/2011
731218^50497+5563388Lelio R Paula05/2013
73132^210545+1163381Lelio R Paula08/2011
73142^210543+6363380Lelio R Paula08/2011
731583^33016+8263361Norbert Schneider04/2015
73162^210464+9876533163356Jason Earls12/2008
73177*10^63351+963352Dmitry Domanov11/2010
7318p(13534)#/2+51263348Robert Price05/2017
73191741^19546+19546^174163345Serge Batalov05/2014
732010^63336+1981963337Patrick De Geest12/2013
732110^63336-12288363336Patrick De Geest12/2013
7322(19^49523-2^49523)/1763327Robert Price09/2013
7323(2^210378+47)/9551693163323Lelio R Paula03/2012
732431191!2+25663316Robert Price01/2015
732516458^7031+7031^1645863315Hans Havermann01/2017
7326(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
7327(2^210283+7)/169114563296Lelio R Paula03/2012
73282^210217+129963282Lelio R Paula09/2011
7329(2^210221-3)/26963281Lelio R Paula04/2012
7330Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
733196^31913-9563261Norbert Schneider04/2016
73323^132572+28063253Lelio R Paula04/2013
73333^132570-2^(132570-1)63252Robert Price01/2016
733411^60734-492063248Enzo Doria01/2013
73362^210061+2163235Donovan Johnson06/2006
733518^50375+9563235Lelio R Paula05/2013
733785^32773-263233Lelio R Paula08/2013
7338(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
7339(2^210054-1017)/67163230Lelio R Paula04/2012
73403*2^210022+563224Lelio R Paula04/2014
734115^53756+3263222Lelio R Paula05/2013
734217^51380+2263221Lelio R Paula05/2013
7343(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
734443^38700+4263216Norbert Schneider06/2014
73455^90431-9663209Lelio R Paula04/2013
7346(172*10^63202-1)/963204Serge Batalov12/2014
7347(43*10^63200+83)/963201Robert Price08/2017
73482^209914-1600563191Enzo Doria04/2013
73493*6^81190-563179Lelio R Paula09/2014
73502^209820+425763163Lelio R Paula10/2011
735199^31648+263158Lelio R Paula05/2013
735216976^5253+5253^1697663158Hans Havermann01/2017
73532^209790+6763154Lelio R Paula08/2011
73542^209759+9019563144Lelio R Paula02/2013
7355145823#+21150763142Arkadiusz Wesolowski03/2013
73562^209707+51363129Lelio R Paula10/2011
7357(3^132314-8)/1763129Lelio R Paula04/2012
7358(2*10^63117+7)/963117Erik Branger03/2011
73599*2^209654-763114Lelio R Paula04/2014
736011^60598-1463107Lelio R Paula05/2013
736115103^15078+15078^1510363106Hans Havermann01/2017
736215346^12941+12941^1534663103Hans Havermann01/2017
73633^132253+7663101Lelio R Paula04/2013
7364(56*10^63100+403)/963101Robert Price10/2017
736517549^3936+3936^1754963090Hans Havermann01/2017
7366(55459*2^209553+1)/42363084Lelio R Paula06/2014
7367(331^25033-1)/33063077Eric Chen09/2017
736920^48480+3163074Lelio R Paula06/2013
7368(26*10^63073-23)/363074Robert Price08/2016
73702^209499+7625363066Enzo Doria04/2016
737111^60546-1134063053Enzo Doria12/2012
73722^209426+5788963044Yves Minet02/2010
7373(22699*2^209405+1)/2163041Lelio R Paula06/2014
73745^90189+5463040Lelio R Paula04/2013
7375(22*10^63034-73)/363035Robert Price09/2017
7376(314021^11467+1)/31402263029Faysal YAtim05/2008
7377V(301486)63007Henri Lifchitz05/2003
7378(31*2^209298+1)/9563005Lelio R Paula08/2012
7379(27*2^209245+1)/562990Lelio R Paula08/2012
73806^80946-5^(80946-1)62989Robert Price05/2016
7381467^23596+23596^46762986Norbert Schneider08/2016
7382(7*2^209212-1)/362980Lelio R Paula01/2014
7383(27*2^209206-1)/1162978Lelio R Paula01/2014
73841456^19909+19909^145662976Serge Batalov05/2014
7386(3^131964-5)/18521239662955Lelio R Paula04/2012
738535^40772-146662955Enzo Doria03/2013
73875^90064-1370662953Enzo Doria02/2013
7388(22*10^62926+257)/962927Robert Price11/2017
7389(13*10^62914+401)/962915Robert Price10/2017
73902^208993+10762914Lelio R Paula08/2011
73912^208993+7762914Lelio R Paula08/2011
7392189^27636-262913Lelio R Paula10/2017
7393(2^208948-7)/26162898Lelio R Paula03/2012
7394(151*10^62879-1)/362881Robert Price04/2017
739515^53464-8262879Lelio R Paula05/2013
73962^208843-11292162869Enzo Doria06/2014
73972^208779+8162849Henri Lifchitz01/2007
7398(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
7399(73*10^62824+17)/962825Robert Price10/2015
74003^131670-8262823Lelio R Paula04/2013
740119^49128-9062823Lelio R Paula05/2013
740211^60314-441062811Enzo Doria01/2013
7403(17*2^208614-1)/5362799Lelio R Paula01/2014
74042^208594+9362794Donovan Johnson06/2008
7405(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
7406(2^208534+7)/905962772Lelio R Paula03/2012
7407(13^56333+1)/1462751Paul Bourdelais03/2010
740810^62750+5762751Robert Price01/2011
740910^62750-26742962750Patrick De Geest01/2013
74102^208427-6962743Lelio R Paula08/2011
74112^208421-11177562741Enzo Doria05/2014
74122^208404-11207962736Enzo Doria06/2014
74132^208343-222162718Yves Minet08/2013
74142^208335+51362716Lelio R Paula10/2011
7416(2^208328+47)/362713Lelio R Paula03/2012
741511^60220-204062713Enzo Doria12/2012
74172^208292+8162703Henri Lifchitz10/2005
741815013^15012-1501262698Henri Lifchitz10/2014
74192^208271-11274762696Enzo Doria06/2014
742011^60202-438062694Enzo Doria01/2013
7421(3^131403-4)/15762693Lelio R Paula04/2012
74222^208127-12666762653Paul Bourdelais01/2012
742371^33843+262653Lelio R Paula05/2013
7424(3^131325+7)/106685062652Lelio R Paula04/2012
74252^208019+11962620Lelio R Paula08/2011
7426(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
742711^60126-1137062615Enzo Doria12/2012
74282^207976-248962608Yves Minet07/2014
7429(22699*2^207945+1)/28170962597Lelio R Paula06/2014
74304*21^47335+20562588Curtis Bright05/2015
743115^53210+862580Lelio R Paula05/2013
74322^207865+2962574Henri Lifchitz08/2005
743315^53199-3862567Lelio R Paula05/2013
7434(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
74352^207782+5890562549Lelio R Paula10/2011
7436(2^207748-3)/843762535Lelio R Paula03/2012
7437(2^207711+5)/1362527Lelio R Paula03/2012
7438(268*10^62523-1)/362525Robert Price10/2017
743910^62523+6362524Robert Price01/2011
744010^62523-29237362523Patrick De Geest01/2013
74412^207691+1155*20769162522Henri Lifchitz02/2005
7442(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
74432^207626-11215762502Enzo Doria06/2014
74443^130987+5262497Lelio R Paula04/2013
74458*6^80299-762486Lelio R Paula09/2014
744611^59997-267062481Enzo Doria12/2012
744793^31740+262480Lelio R Paula05/2013
7448(10^62451+119)/362451Serge Batalov12/2014
7449(2^207443+47)/764562443Lelio R Paula03/2012
74502^207364+11562423Lelio R Paula08/2011
74513^130815-4662415Lelio R Paula04/2013
7452(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
745320^47968-948362408Enzo Doria03/2013
7454(10^62402+101)/362402Robert Price04/2016
7455(13*2^207264-1)/362394Lelio R Paula01/2014
7456(79*10^62387-61)/962388Robert Price10/2015
74575^89244+3*2^8924462379Mike Oakes02/2010
74586^80160-1362377Lelio R Paula04/2013
7459(7*10^62362+53)/362363Robert Price10/2017
7460(1000121^10391+1)/100012262341Faysal YAtim07/2008
7461(17*10^62328-11)/362329Robert Price07/2015
74622^207023+1171562321Lelio R Paula09/2011
7463(265*10^62298+11)/362300Robert Price03/2017
74642^206947-6962298Lelio R Paula08/2011
74652^206938+2983562295Lelio R Paula02/2013
74662^206911-72687762287Paul Bourdelais03/2013
7467(6883*2^206884-1)/362282Lelio R Paula04/2015
74682^206892-11281762281Enzo Doria06/2014
7469(7*10^62278+113)/362279Robert Price10/2017
74703^130523+4662276Lelio R Paula04/2013
74712^206872-11345362275Enzo Doria07/2014
74722^206840-9362266Lelio R Paula08/2011
7473(1017*2^206815-1)/63562258Lelio R Paula04/2015
747496^31406+9562256Norbert Schneider03/2016
7475(2^206824+7)/64621362255Lelio R Paula03/2012
74762^206765-94168362243Paul Bourdelais11/2012
7477(6^79987-1)/562242Paul Bourdelais11/2007
74782^206755-157962240Yves Minet03/2013
747911^59764-582062238Enzo Doria01/2013
74805*10^62233+362234Dmitry Domanov11/2010
74818*3^130421+762228Lelio R Paula04/2014
748219^48661+1062226Lelio R Paula05/2013
7484(17*2^206705+1)/562225Lelio R Paula08/2012
74832^206705-11263562225Enzo Doria06/2014
74853^130403+868062219Lelio R Paula04/2013
748611^59740-711062213Enzo Doria01/2013
74882^206596-16762192Lelio R Paula08/2011
74872^206597+1891562192Lelio R Paula02/2013
74896^79918+13762189Lelio R Paula04/2013
7490lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
74912^206574+61362185Jason Earls04/2008
74923^130328+8062183Lelio R Paula04/2013
7493(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
74942^206550+7681962178Enzo Doria05/2016
749511^59703-2462175Lelio R Paula05/2013
74962^206524+7578162170Enzo Doria04/2016
74972^206506+42762165Henri Lifchitz01/2005
74982^206465+769562153Lelio R Paula02/2013
74992^206464-164962152Yves Minet03/2013
75005^88917+5662151Lelio R Paula04/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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