PRP Records

Probable Primes Top 10000

(247113 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 ?
7751(509203*2^212056-1)/363841Lelio R Paula04/2015
7752(3^133805-7)/17263839Lelio R Paula04/2012
77532^212049+14963834Lelio R Paula08/2011
77545^91318-1863829Lelio R Paula04/2013
775518468^2857+2857^1846863824Hans Havermann03/2017
7756(2^212024-5)/111163823Lelio R Paula04/2012
77572^211961+1291563807Lelio R Paula02/2013
7759(3^133707-7)/578063791Lelio R Paula04/2012
7758(44*10^63790-161)/963791Robert Price11/2017
7760747^22198+22198^74763782Norbert Schneider07/2016
77612^211800-1716963759Enzo Doria05/2013
7762(85*10^63757-1)/363759Robert Price07/2017
776385089!6-863757Robert Price08/2018
7764(14*10^63747-11)/363748Erik Branger09/2014
776591*19^49848+663746Curtis Bright05/2015
776618855^2402+2402^1885563741Hans Havermann03/2017
7767(142*10^63734-7)/963736Robert Price02/2017
77682^211699-11163728Lelio R Paula08/2011
776911^61192-555063725Enzo Doria01/2013
7770(11*10^63718+7)/963719Serge Batalov06/2011
77716^81872-1363709Lelio R Paula04/2013
77723^133522+9863707Lelio R Paula05/2013
77742^211607-6163701Lelio R Paula08/2011
77735^91135+863701Lelio R Paula04/2013
777511^61157-27063689Enzo Doria07/2012
777710^63685+114514191963686Marisa Kirisame03/2015
777610^63685+10383763686Patrick De Geest03/2016
777810^63685-13079763685Patrick De Geest03/2016
77792^211547+1155*21154763682Henri Lifchitz02/2005
77802^211543+4563681Lelio R Paula08/2011
77812^211534+4363679Lelio R Paula08/2011
778211^61140-6063671Enzo Doria07/2012
77832^211491-11232163666Enzo Doria06/2014
778419085^2164+2164^1908563654Hans Havermann03/2017
7785(2^211430-5)/85963644Lelio R Paula04/2012
77862^211401-9163639Lelio R Paula08/2011
7787(6883*2^211378-1)/6963634Lelio R Paula04/2015
7788(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
7789(29*2^211384-1)/5012262163627Lelio R Paula01/2014
77902^211333+1501563618Lelio R Paula01/2013
779133^41889-3263610Norbert Schneider03/2014
779213^57093+1863599Lelio R Paula05/2013
7793(5*2^211219-1)/963583Lelio R Paula01/2014
7794(107*10^63576-17)/963578Robert Price02/2017
779523^46687-102063575Enzo Doria08/2012
7796(67607*2^211188+1)/523431963573Lelio R Paula06/2014
7797(3^133243+7)/1072663570Lelio R Paula04/2012
7798(7*2^211181+1)/274563570Lelio R Paula06/2012
7800(20^48859-1)/1963566Paul Bourdelais03/2010
77992*3^133227+563566Lelio R Paula04/2014
78012^211155+11363564Lelio R Paula08/2011
78022^211134+34563558Lelio R Paula09/2011
78032^211121+1638563554Lelio R Paula09/2011
780416996^5483+5483^1699663549Hans Havermann02/2017
7805(2^211079+9)/36428363536Lelio R Paula03/2012
78063*10^63522+1363523Robert Price08/2017
780715852^10157+10157^1585263516Hans Havermann02/2017
78082^210948-1587363502Enzo Doria04/2013
78097^75136+663498Lelio R Paula04/2013
78102^210928+1291563496Lelio R Paula02/2013
78117*10^63493+3963494Robert Price07/2016
78122^210909+13563490Lelio R Paula08/2011
7813(3*2^210832+1)/763467Lelio R Paula07/2012
78148*7^75098-363467Lelio R Paula09/2014
781517683^3882+3882^1768363466Hans Havermann03/2017
7816Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
78172^210820-1690563464Enzo Doria05/2013
78185^90795-3663463Lelio R Paula04/2013
781984731!6-4863463Robert Price08/2018
78202^210816-1319763462Enzo Doria10/2012
78212^210750+13363443Lelio R Paula08/2011
7822291^25742+25742^29163426Norbert Schneider09/2014
7823(3^132908+8)/27985963408Lelio R Paula04/2012
78246^81480-13963404Lelio R Paula04/2013
78252^210576-17363390Lelio R Paula08/2011
782618^50497+5563388Lelio R Paula05/2013
78272^210545+1163381Lelio R Paula08/2011
78282^210543+6363380Lelio R Paula08/2011
782983^33016+8263361Norbert Schneider04/2015
78302^210464+9876533163356Jason Earls12/2008
78317*10^63351+963352Dmitry Domanov11/2010
7832p(13534)#/2+51263348Robert Price05/2017
78331741^19546+19546^174163345Serge Batalov05/2014
783410^63336+1981963337Patrick De Geest12/2013
783510^63336-12288363336Patrick De Geest12/2013
7836(19^49523-2^49523)/1763327Robert Price09/2013
7837(2^210378+47)/9551693163323Lelio R Paula03/2012
783831191!2+25663316Robert Price01/2015
783916458^7031+7031^1645863315Hans Havermann01/2017
7840(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
7841(2^210283+7)/169114563296Lelio R Paula03/2012
78422^210217+129963282Lelio R Paula09/2011
7843(2^210221-3)/26963281Lelio R Paula04/2012
7844Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
784596^31913-9563261Norbert Schneider04/2016
78463^132572+28063253Lelio R Paula04/2013
78473^132570-2^(132570-1)63252Robert Price01/2016
784811^60734-492063248Enzo Doria01/2013
78502^210061+2163235Donovan Johnson06/2006
784918^50375+9563235Lelio R Paula05/2013
785185^32773-263233Lelio R Paula08/2013
7852(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
7853(2^210054-1017)/67163230Lelio R Paula04/2012
78543*2^210022+563224Lelio R Paula04/2014
785515^53756+3263222Lelio R Paula05/2013
785617^51380+2263221Lelio R Paula05/2013
7857(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
785843^38700+4263216Norbert Schneider06/2014
78595^90431-9663209Lelio R Paula04/2013
7860(172*10^63202-1)/963204Serge Batalov12/2014
7861(43*10^63200+83)/963201Robert Price08/2017
78622^209914-1600563191Enzo Doria04/2013
78633*6^81190-563179Lelio R Paula09/2014
78642^209820+425763163Lelio R Paula10/2011
786699^31648+263158Lelio R Paula05/2013
786516976^5253+5253^1697663158Hans Havermann01/2017
78672^209790+6763154Lelio R Paula08/2011
78682^209759+9019563144Lelio R Paula02/2013
7869145823#+21150763142Arkadiusz Wesolowski03/2013
78702^209707+51363129Lelio R Paula10/2011
7871(3^132314-8)/1763129Lelio R Paula04/2012
7872(2*10^63117+7)/963117Erik Branger03/2011
78739*2^209654-763114Lelio R Paula04/2014
787484304!6-963112Robert Price08/2018
787511^60598-1463107Lelio R Paula05/2013
787615103^15078+15078^1510363106Hans Havermann01/2017
787715346^12941+12941^1534663103Hans Havermann01/2017
78783^132253+7663101Lelio R Paula04/2013
7879(56*10^63100+403)/963101Robert Price10/2017
788017549^3936+3936^1754963090Hans Havermann01/2017
7881(55459*2^209553+1)/42363084Lelio R Paula06/2014
7882(331^25033-1)/33063077Eric Chen09/2017
788420^48480+3163074Lelio R Paula06/2013
7883(26*10^63073-23)/363074Robert Price08/2016
78852^209499+7625363066Enzo Doria04/2016
788611^60546-1134063053Enzo Doria12/2012
78872^209426+5788963044Yves Minet02/2010
7888(22699*2^209405+1)/2163041Lelio R Paula06/2014
78895^90189+5463040Lelio R Paula04/2013
7890(22*10^63034-73)/363035Robert Price09/2017
7891(314021^11467+1)/31402263029Faysal YAtim05/2008
7892V(301486)63007Henri Lifchitz05/2003
7893(31*2^209298+1)/9563005Lelio R Paula08/2012
7894(27*2^209245+1)/562990Lelio R Paula08/2012
78956^80946-5^(80946-1)62989Robert Price05/2016
7896467^23596+23596^46762986Norbert Schneider08/2016
7897(7*2^209212-1)/362980Lelio R Paula01/2014
7898(27*2^209206-1)/1162978Lelio R Paula01/2014
78991456^19909+19909^145662976Serge Batalov05/2014
7900(3^131964-5)/18521239662955Lelio R Paula04/2012
790135^40772-146662955Enzo Doria03/2013
79025^90064-1370662953Enzo Doria02/2013
7903(22*10^62926+257)/962927Robert Price11/2017
7904(13*10^62914+401)/962915Robert Price10/2017
79052^208993+10762914Lelio R Paula08/2011
79062^208993+7762914Lelio R Paula08/2011
7907189^27636-262913Lelio R Paula10/2017
7908(2^208948-7)/26162898Lelio R Paula03/2012
7909(151*10^62879-1)/362881Robert Price04/2017
791015^53464-8262879Lelio R Paula05/2013
79112^208843-11292162869Enzo Doria06/2014
79122^208779+8162849Henri Lifchitz01/2007
7913(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
7914(73*10^62824+17)/962825Robert Price10/2015
79153^131670-8262823Lelio R Paula04/2013
791619^49128-9062823Lelio R Paula05/2013
791711^60314-441062811Enzo Doria01/2013
7918(17*2^208614-1)/5362799Lelio R Paula01/2014
79192^208594+9362794Donovan Johnson06/2008
7920(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
7921(2^208534+7)/905962772Lelio R Paula03/2012
7923(13^56333+1)/1462751Paul Bourdelais03/2010
792210^62750+5762751Robert Price01/2011
792410^62750-26742962750Patrick De Geest01/2013
79252^208427-6962743Lelio R Paula08/2011
79262^208421-11177562741Enzo Doria05/2014
79272^208404-11207962736Enzo Doria06/2014
79282^208343-222162718Yves Minet08/2013
79292^208335+51362716Lelio R Paula10/2011
7931(2^208328+47)/362713Lelio R Paula03/2012
793011^60220-204062713Enzo Doria12/2012
79322^208292+8162703Henri Lifchitz10/2005
793315013^15012-1501262698Henri Lifchitz10/2014
79342^208271-11274762696Enzo Doria06/2014
793511^60202-438062694Enzo Doria01/2013
7936(3^131403-4)/15762693Lelio R Paula04/2012
79372^208127-12666762653Paul Bourdelais01/2012
793871^33843+262653Lelio R Paula05/2013
7939(3^131325+7)/106685062652Lelio R Paula04/2012
79402^208019+11962620Lelio R Paula08/2011
7941(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
794211^60126-1137062615Enzo Doria12/2012
79432^207976-248962608Yves Minet07/2014
7944(22699*2^207945+1)/28170962597Lelio R Paula06/2014
79454*21^47335+20562588Curtis Bright05/2015
794615^53210+862580Lelio R Paula05/2013
79472^207865+2962574Henri Lifchitz08/2005
794815^53199-3862567Lelio R Paula05/2013
7949(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
79502^207782+5890562549Lelio R Paula10/2011
7951(2^207748-3)/843762535Lelio R Paula03/2012
7952(2^207711+5)/1362527Lelio R Paula03/2012
7953(268*10^62523-1)/362525Robert Price10/2017
795410^62523+6362524Robert Price01/2011
795510^62523-29237362523Patrick De Geest01/2013
79572^207691+1155*20769162522Henri Lifchitz02/2005
7956(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
79582^207626-11215762502Enzo Doria06/2014
79593^130987+5262497Lelio R Paula04/2013
79608*6^80299-762486Lelio R Paula09/2014
796111^59997-267062481Enzo Doria12/2012
796293^31740+262480Lelio R Paula05/2013
7963(10^62451+119)/362451Serge Batalov12/2014
7964(2^207443+47)/764562443Lelio R Paula03/2012
79652^207364+11562423Lelio R Paula08/2011
79663^130815-4662415Lelio R Paula04/2013
7967(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
796820^47968-948362408Enzo Doria03/2013
7969(10^62402+101)/362402Robert Price04/2016
7970(13*2^207264-1)/362394Lelio R Paula01/2014
7971(79*10^62387-61)/962388Robert Price10/2015
79725^89244+3*2^8924462379Mike Oakes02/2010
79736^80160-1362377Lelio R Paula04/2013
7974(7*10^62362+53)/362363Robert Price10/2017
7975(1000121^10391+1)/100012262341Faysal YAtim07/2008
7976(17*10^62328-11)/362329Robert Price07/2015
79772^207023+1171562321Lelio R Paula09/2011
7978(265*10^62298+11)/362300Robert Price03/2017
79792^206947-6962298Lelio R Paula08/2011
79802^206938+2983562295Lelio R Paula02/2013
79812^206911-72687762287Paul Bourdelais03/2013
7982(6883*2^206884-1)/362282Lelio R Paula04/2015
79832^206892-11281762281Enzo Doria06/2014
7984(7*10^62278+113)/362279Robert Price10/2017
79853^130523+4662276Lelio R Paula04/2013
79862^206872-11345362275Enzo Doria07/2014
79872^206840-9362266Lelio R Paula08/2011
7988(1017*2^206815-1)/63562258Lelio R Paula04/2015
798996^31406+9562256Norbert Schneider03/2016
7990(2^206824+7)/64621362255Lelio R Paula03/2012
79912^206765-94168362243Paul Bourdelais11/2012
7992(6^79987-1)/562242Paul Bourdelais11/2007
79932^206755-157962240Yves Minet03/2013
799411^59764-582062238Enzo Doria01/2013
79955*10^62233+362234Dmitry Domanov11/2010
79968*3^130421+762228Lelio R Paula04/2014
799719^48661+1062226Lelio R Paula05/2013
7998(17*2^206705+1)/562225Lelio R Paula08/2012
79992^206705-11263562225Enzo Doria06/2014
80003^130403+868062219Lelio R Paula04/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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