PRP Records

Probable Primes Top 10000

(177649 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 ?
67512^213314-45564214Yves Minet02/2012
675239^40359-3864214Norbert Schneider05/2014
67532^213292-1608564208Enzo Doria04/2013
67542^213274-7764202Lelio R Paula08/2011
675519^50203+7864198Lelio R Paula08/2013
67562^213240-11286564192Enzo Doria06/2014
67572^213190-11239164177Enzo Doria06/2014
6758(9913*2^213184-1)/965764175Lelio R Paula04/2015
675914^55991+2764173Lelio R Paula07/2013
67602^213158-11258164167Enzo Doria06/2014
67612^213148+9164164Lelio R Paula08/2011
67626^82439+12564151Lelio R Paula07/2013
67637*2^213102+964151Lelio R Paula04/2014
6764L(306854)+F(306855)64129Henri Lifchitz01/2007
6765610^23017+23017^61064110Norbert Schneider07/2016
67662^212950-6487564105Lelio R Paula10/2011
6767(266*10^64102-17)/364104Robert Price06/2016
6768p(13679)#/2+6464097Robert Price03/2017
676919^50119+9464090Lelio R Paula08/2013
67702^212880-14764084Lelio R Paula08/2011
677111^61523-459064070Enzo Doria01/2013
67725^91663+3864070Lelio R Paula05/2013
67735^91650+5264061Lelio R Paula05/2013
67742^212770+6964051Lelio R Paula08/2011
6775(3^134227+1)/464042Paul Bourdelais11/2007
6776(2*10^64041-17)/364041Robert Price08/2014
6777(15^54449+1)/1664036Paul Bourdelais03/2010
6778(29*10^64027+91)/364028Robert Price03/2016
6779(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
678016878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
67812^212663+5364018Lelio R Paula08/2011
6782(4*10^64014+197)/364015Robert Price03/2017
678310^63986+6363987Robert Price01/2011
678410^63986-3155763986Patrick De Geest05/2013
678531487!2-2^3148763982Robert Price09/2015
6786(21*2^212522-1)/141632363971Lelio R Paula01/2014
67875^91517+9863968Lelio R Paula04/2013
6788(62*10^63954-17)/963955Robert Price09/2015
67905^91493-4^9149363951Predrag Minovic04/2004
6789V(364793)63951Serge Batalov03/2015
679219^50004+5863943Lelio R Paula05/2013
67915*6^82172-763943Lelio R Paula09/2014
6793(56*10^63942+223)/963943Robert Price07/2016
679419^50000-2463938Lelio R Paula05/2013
6795(23*2^212374-1)/2701963928Lelio R Paula01/2014
6796(9*2^212355-1)/76163924Lelio R Paula01/2014
67982^212344-18363922Lelio R Paula08/2011
6797(58695*2^212336-1)/37963922Lelio R Paula04/2015
679910^63916+7963917Robert Price01/2011
680010^63916-7682363916Patrick De Geest05/2013
68012^212295-2563908Lelio R Paula08/2011
68022^212285-238363905Yves Minet10/2013
6803267^26336+26336^26763905Norbert Schneider09/2014
6804(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
680619^49962+6063890Lelio R Paula05/2013
68053^133906-11305663890Enzo Doria07/2014
6807(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
68083*6^82092+563881Lelio R Paula09/2014
680915441^13706+13706^1544163879Hans Havermann02/2017
68102^212154-77635163865Paul Bourdelais03/2013
681135^41359+263862Lelio R Paula05/2013
6812(61*10^63857-43)/963858Robert Price09/2015
6813(2^212131-3)/48563856Lelio R Paula04/2012
68142^212112-45999563853Enzo Doria06/2015
681515^54290+5863850Lelio R Paula05/2013
68163*2^212097-763849Lelio R Paula04/2014
681755^36683-5463842Norbert Schneider08/2014
6818(509203*2^212056-1)/363841Lelio R Paula04/2015
6819(3^133805-7)/17263839Lelio R Paula04/2012
68202^212049+14963834Lelio R Paula08/2011
68215^91318-1863829Lelio R Paula04/2013
682218468^2857+2857^1846863824Hans Havermann03/2017
6823(2^212024-5)/111163823Lelio R Paula04/2012
68242^211961+1291563807Lelio R Paula02/2013
6825(3^133707-7)/578063791Lelio R Paula04/2012
6826747^22198+22198^74763782Norbert Schneider07/2016
68272^211800-1716963759Enzo Doria05/2013
6828(85*10^63757-1)/363759Robert Price07/2017
6829(14*10^63747-11)/363748Erik Branger09/2014
683091*19^49848+663746Curtis Bright05/2015
683118855^2402+2402^1885563741Hans Havermann03/2017
6832(142*10^63734-7)/963736Robert Price02/2017
68332^211699-11163728Lelio R Paula08/2011
683411^61192-555063725Enzo Doria01/2013
6835(11*10^63718+7)/963719Serge Batalov06/2011
68366^81872-1363709Lelio R Paula04/2013
68373^133522+9863707Lelio R Paula05/2013
68392^211607-6163701Lelio R Paula08/2011
68385^91135+863701Lelio R Paula04/2013
684011^61157-27063689Enzo Doria07/2012
684110^63685+114514191963686Marisa Kirisame03/2015
684210^63685+10383763686Patrick De Geest03/2016
684310^63685-13079763685Patrick De Geest03/2016
68442^211547+1155*21154763682Henri Lifchitz02/2005
68452^211543+4563681Lelio R Paula08/2011
68462^211534+4363679Lelio R Paula08/2011
684711^61140-6063671Enzo Doria07/2012
68482^211491-11232163666Enzo Doria06/2014
684919085^2164+2164^1908563654Hans Havermann03/2017
6850(2^211430-5)/85963644Lelio R Paula04/2012
68512^211401-9163639Lelio R Paula08/2011
6852(6883*2^211378-1)/6963634Lelio R Paula04/2015
6853(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
6854(29*2^211384-1)/5012262163627Lelio R Paula01/2014
68552^211333+1501563618Lelio R Paula01/2013
685633^41889-3263610Norbert Schneider03/2014
685713^57093+1863599Lelio R Paula05/2013
6858(5*2^211219-1)/963583Lelio R Paula01/2014
6859(107*10^63576-17)/963578Robert Price02/2017
686023^46687-102063575Enzo Doria08/2012
6861(67607*2^211188+1)/523431963573Lelio R Paula06/2014
6862(3^133243+7)/1072663570Lelio R Paula04/2012
6863(7*2^211181+1)/274563570Lelio R Paula06/2012
6865(20^48859-1)/1963566Paul Bourdelais03/2010
68642*3^133227+563566Lelio R Paula04/2014
68662^211155+11363564Lelio R Paula08/2011
68672^211134+34563558Lelio R Paula09/2011
68682^211121+1638563554Lelio R Paula09/2011
686916996^5483+5483^1699663549Hans Havermann02/2017
6870(2^211079+9)/36428363536Lelio R Paula03/2012
687115852^10157+10157^1585263516Hans Havermann02/2017
68722^210948-1587363502Enzo Doria04/2013
68737^75136+663498Lelio R Paula04/2013
68742^210928+1291563496Lelio R Paula02/2013
68757*10^63493+3963494Robert Price07/2016
68762^210909+13563490Lelio R Paula08/2011
6877(3*2^210832+1)/763467Lelio R Paula07/2012
68788*7^75098-363467Lelio R Paula09/2014
687917683^3882+3882^1768363466Hans Havermann03/2017
6881Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
68802^210820-1690563464Enzo Doria05/2013
68825^90795-3663463Lelio R Paula04/2013
68832^210816-1319763462Enzo Doria10/2012
68842^210750+13363443Lelio R Paula08/2011
6885291^25742+25742^29163426Norbert Schneider09/2014
6886(3^132908+8)/27985963408Lelio R Paula04/2012
68876^81480-13963404Lelio R Paula04/2013
68882^210576-17363390Lelio R Paula08/2011
688918^50497+5563388Lelio R Paula05/2013
68902^210545+1163381Lelio R Paula08/2011
68912^210543+6363380Lelio R Paula08/2011
689283^33016+8263361Norbert Schneider04/2015
68932^210464+9876533163356Jason Earls12/2008
68947*10^63351+963352Dmitry Domanov11/2010
6895p(13534)#/2+51263348Robert Price05/2017
68961741^19546+19546^174163345Serge Batalov05/2014
689710^63336+1981963337Patrick De Geest12/2013
689810^63336-12288363336Patrick De Geest12/2013
6899(19^49523-2^49523)/1763327Robert Price09/2013
6900(2^210378+47)/9551693163323Lelio R Paula03/2012
690131191!2+25663316Robert Price01/2015
690216458^7031+7031^1645863315Hans Havermann01/2017
6903(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
6904(2^210283+7)/169114563296Lelio R Paula03/2012
69052^210217+129963282Lelio R Paula09/2011
6906(2^210221-3)/26963281Lelio R Paula04/2012
6907Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
690896^31913-9563261Norbert Schneider04/2016
69093^132572+28063253Lelio R Paula04/2013
69103^132570-2^(132570-1)63252Robert Price01/2016
691111^60734-492063248Enzo Doria01/2013
69132^210061+2163235Donovan Johnson06/2006
691218^50375+9563235Lelio R Paula05/2013
691485^32773-263233Lelio R Paula08/2013
6915(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
6916(2^210054-1017)/67163230Lelio R Paula04/2012
69173*2^210022+563224Lelio R Paula04/2014
691815^53756+3263222Lelio R Paula05/2013
692017^51380+2263221Lelio R Paula05/2013
6919(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
692143^38700+4263216Norbert Schneider06/2014
69225^90431-9663209Lelio R Paula04/2013
6923(172*10^63202-1)/963204Serge Batalov12/2014
69242^209914-1600563191Enzo Doria04/2013
69253*6^81190-563179Lelio R Paula09/2014
69262^209820+425763163Lelio R Paula10/2011
692899^31648+263158Lelio R Paula05/2013
692716976^5253+5253^1697663158Hans Havermann01/2017
69292^209790+6763154Lelio R Paula08/2011
69302^209759+9019563144Lelio R Paula02/2013
6931145823#+21150763142Arkadiusz Wesolowski03/2013
69322^209707+51363129Lelio R Paula10/2011
6933(3^132314-8)/1763129Lelio R Paula04/2012
6934(2*10^63117+7)/963117Erik Branger03/2011
69359*2^209654-763114Lelio R Paula04/2014
693611^60598-1463107Lelio R Paula05/2013
693715103^15078+15078^1510363106Hans Havermann01/2017
693815346^12941+12941^1534663103Hans Havermann01/2017
69393^132253+7663101Lelio R Paula04/2013
694017549^3936+3936^1754963090Hans Havermann01/2017
6941(55459*2^209553+1)/42363084Lelio R Paula06/2014
694320^48480+3163074Lelio R Paula06/2013
6942(26*10^63073-23)/363074Robert Price08/2016
69442^209499+7625363066Enzo Doria04/2016
694511^60546-1134063053Enzo Doria12/2012
69462^209426+5788963044Yves Minet02/2010
6947(22699*2^209405+1)/2163041Lelio R Paula06/2014
69485^90189+5463040Lelio R Paula04/2013
6949(314021^11467+1)/31402263029Faysal YAtim05/2008
6950V(301486)63007Henri Lifchitz05/2003
6951(31*2^209298+1)/9563005Lelio R Paula08/2012
6952(27*2^209245+1)/562990Lelio R Paula08/2012
69536^80946-5^(80946-1)62989Robert Price05/2016
6954467^23596+23596^46762986Norbert Schneider08/2016
6955(7*2^209212-1)/362980Lelio R Paula01/2014
6956(27*2^209206-1)/1162978Lelio R Paula01/2014
69571456^19909+19909^145662976Serge Batalov05/2014
6959(3^131964-5)/18521239662955Lelio R Paula04/2012
695835^40772-146662955Enzo Doria03/2013
69605^90064-1370662953Enzo Doria02/2013
69612^208993+10762914Lelio R Paula08/2011
69622^208993+7762914Lelio R Paula08/2011
6963(2^208948-7)/26162898Lelio R Paula03/2012
6964(151*10^62879-1)/362881Robert Price04/2017
696515^53464-8262879Lelio R Paula05/2013
69662^208843-11292162869Enzo Doria06/2014
69672^208779+8162849Henri Lifchitz01/2007
6968(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
6969(73*10^62824+17)/962825Robert Price10/2015
69703^131670-8262823Lelio R Paula04/2013
697119^49128-9062823Lelio R Paula05/2013
697211^60314-441062811Enzo Doria01/2013
6973(17*2^208614-1)/5362799Lelio R Paula01/2014
69742^208594+9362794Donovan Johnson06/2008
6975(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
6976(2^208534+7)/905962772Lelio R Paula03/2012
6977(13^56333+1)/1462751Paul Bourdelais03/2010
697810^62750+5762751Robert Price01/2011
697910^62750-26742962750Patrick De Geest01/2013
69802^208427-6962743Lelio R Paula08/2011
69812^208421-11177562741Enzo Doria05/2014
69822^208404-11207962736Enzo Doria06/2014
69832^208343-222162718Yves Minet08/2013
69842^208335+51362716Lelio R Paula10/2011
6986(2^208328+47)/362713Lelio R Paula03/2012
698511^60220-204062713Enzo Doria12/2012
69872^208292+8162703Henri Lifchitz10/2005
698815013^15012-1501262698Henri Lifchitz10/2014
69892^208271-11274762696Enzo Doria06/2014
699011^60202-438062694Enzo Doria01/2013
6991(3^131403-4)/15762693Lelio R Paula04/2012
69922^208127-12666762653Paul Bourdelais01/2012
699371^33843+262653Lelio R Paula05/2013
6994(3^131325+7)/106685062652Lelio R Paula04/2012
69962^208019+11962620Lelio R Paula08/2011
6995(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
699711^60126-1137062615Enzo Doria12/2012
69982^207976-248962608Yves Minet07/2014
6999(22699*2^207945+1)/28170962597Lelio R Paula06/2014
70004*21^47335+20562588Curtis Bright05/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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