PRP Records

Probable Primes Top 10000

(218736 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 ?
75012^212112-45999563853Enzo Doria06/2015
750215^54290+5863850Lelio R Paula05/2013
75033*2^212097-763849Lelio R Paula04/2014
750455^36683-5463842Norbert Schneider08/2014
7505(509203*2^212056-1)/363841Lelio R Paula04/2015
7506(3^133805-7)/17263839Lelio R Paula04/2012
75072^212049+14963834Lelio R Paula08/2011
75085^91318-1863829Lelio R Paula04/2013
750918468^2857+2857^1846863824Hans Havermann03/2017
7510(2^212024-5)/111163823Lelio R Paula04/2012
75112^211961+1291563807Lelio R Paula02/2013
7513(3^133707-7)/578063791Lelio R Paula04/2012
7512(44*10^63790-161)/963791Robert Price11/2017
7514747^22198+22198^74763782Norbert Schneider07/2016
75152^211800-1716963759Enzo Doria05/2013
7516(85*10^63757-1)/363759Robert Price07/2017
751785089!6-863757Robert Price08/2018
7518(14*10^63747-11)/363748Erik Branger09/2014
751991*19^49848+663746Curtis Bright05/2015
752018855^2402+2402^1885563741Hans Havermann03/2017
7521(142*10^63734-7)/963736Robert Price02/2017
75222^211699-11163728Lelio R Paula08/2011
752311^61192-555063725Enzo Doria01/2013
7524(11*10^63718+7)/963719Serge Batalov06/2011
75256^81872-1363709Lelio R Paula04/2013
75263^133522+9863707Lelio R Paula05/2013
75282^211607-6163701Lelio R Paula08/2011
75275^91135+863701Lelio R Paula04/2013
752911^61157-27063689Enzo Doria07/2012
753110^63685+114514191963686Marisa Kirisame03/2015
753010^63685+10383763686Patrick De Geest03/2016
753210^63685-13079763685Patrick De Geest03/2016
75332^211547+1155*21154763682Henri Lifchitz02/2005
75342^211543+4563681Lelio R Paula08/2011
75352^211534+4363679Lelio R Paula08/2011
753611^61140-6063671Enzo Doria07/2012
75372^211491-11232163666Enzo Doria06/2014
753819085^2164+2164^1908563654Hans Havermann03/2017
7539(2^211430-5)/85963644Lelio R Paula04/2012
75402^211401-9163639Lelio R Paula08/2011
7541(6883*2^211378-1)/6963634Lelio R Paula04/2015
7542(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
7543(29*2^211384-1)/5012262163627Lelio R Paula01/2014
75442^211333+1501563618Lelio R Paula01/2013
754533^41889-3263610Norbert Schneider03/2014
754613^57093+1863599Lelio R Paula05/2013
7547(5*2^211219-1)/963583Lelio R Paula01/2014
7548(107*10^63576-17)/963578Robert Price02/2017
754923^46687-102063575Enzo Doria08/2012
7550(67607*2^211188+1)/523431963573Lelio R Paula06/2014
7551(3^133243+7)/1072663570Lelio R Paula04/2012
7552(7*2^211181+1)/274563570Lelio R Paula06/2012
7554(20^48859-1)/1963566Paul Bourdelais03/2010
75532*3^133227+563566Lelio R Paula04/2014
75552^211155+11363564Lelio R Paula08/2011
75562^211134+34563558Lelio R Paula09/2011
75572^211121+1638563554Lelio R Paula09/2011
755816996^5483+5483^1699663549Hans Havermann02/2017
7559(2^211079+9)/36428363536Lelio R Paula03/2012
75603*10^63522+1363523Robert Price08/2017
756115852^10157+10157^1585263516Hans Havermann02/2017
75622^210948-1587363502Enzo Doria04/2013
75637^75136+663498Lelio R Paula04/2013
75642^210928+1291563496Lelio R Paula02/2013
75657*10^63493+3963494Robert Price07/2016
75662^210909+13563490Lelio R Paula08/2011
7567(3*2^210832+1)/763467Lelio R Paula07/2012
75688*7^75098-363467Lelio R Paula09/2014
756917683^3882+3882^1768363466Hans Havermann03/2017
7571Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
75702^210820-1690563464Enzo Doria05/2013
75725^90795-3663463Lelio R Paula04/2013
757384731!6-4863463Robert Price08/2018
75742^210816-1319763462Enzo Doria10/2012
75752^210750+13363443Lelio R Paula08/2011
7576291^25742+25742^29163426Norbert Schneider09/2014
7577(3^132908+8)/27985963408Lelio R Paula04/2012
75786^81480-13963404Lelio R Paula04/2013
75792^210576-17363390Lelio R Paula08/2011
758018^50497+5563388Lelio R Paula05/2013
75812^210545+1163381Lelio R Paula08/2011
75822^210543+6363380Lelio R Paula08/2011
758383^33016+8263361Norbert Schneider04/2015
75842^210464+9876533163356Jason Earls12/2008
75857*10^63351+963352Dmitry Domanov11/2010
7586p(13534)#/2+51263348Robert Price05/2017
75871741^19546+19546^174163345Serge Batalov05/2014
758810^63336+1981963337Patrick De Geest12/2013
758910^63336-12288363336Patrick De Geest12/2013
7590(19^49523-2^49523)/1763327Robert Price09/2013
7591(2^210378+47)/9551693163323Lelio R Paula03/2012
759231191!2+25663316Robert Price01/2015
759316458^7031+7031^1645863315Hans Havermann01/2017
7594(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
7595(2^210283+7)/169114563296Lelio R Paula03/2012
75962^210217+129963282Lelio R Paula09/2011
7597(2^210221-3)/26963281Lelio R Paula04/2012
7598Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
759996^31913-9563261Norbert Schneider04/2016
76003^132572+28063253Lelio R Paula04/2013
76013^132570-2^(132570-1)63252Robert Price01/2016
760211^60734-492063248Enzo Doria01/2013
76042^210061+2163235Donovan Johnson06/2006
760318^50375+9563235Lelio R Paula05/2013
760585^32773-263233Lelio R Paula08/2013
7606(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
7607(2^210054-1017)/67163230Lelio R Paula04/2012
76083*2^210022+563224Lelio R Paula04/2014
760915^53756+3263222Lelio R Paula05/2013
761017^51380+2263221Lelio R Paula05/2013
7611(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
761243^38700+4263216Norbert Schneider06/2014
76135^90431-9663209Lelio R Paula04/2013
7614(172*10^63202-1)/963204Serge Batalov12/2014
7615(43*10^63200+83)/963201Robert Price08/2017
76162^209914-1600563191Enzo Doria04/2013
76173*6^81190-563179Lelio R Paula09/2014
76182^209820+425763163Lelio R Paula10/2011
761999^31648+263158Lelio R Paula05/2013
762016976^5253+5253^1697663158Hans Havermann01/2017
76212^209790+6763154Lelio R Paula08/2011
76222^209759+9019563144Lelio R Paula02/2013
7623145823#+21150763142Arkadiusz Wesolowski03/2013
76242^209707+51363129Lelio R Paula10/2011
7625(3^132314-8)/1763129Lelio R Paula04/2012
7626(2*10^63117+7)/963117Erik Branger03/2011
76279*2^209654-763114Lelio R Paula04/2014
762884304!6-963112Robert Price08/2018
762911^60598-1463107Lelio R Paula05/2013
763015103^15078+15078^1510363106Hans Havermann01/2017
763115346^12941+12941^1534663103Hans Havermann01/2017
76323^132253+7663101Lelio R Paula04/2013
7633(56*10^63100+403)/963101Robert Price10/2017
763417549^3936+3936^1754963090Hans Havermann01/2017
7635(55459*2^209553+1)/42363084Lelio R Paula06/2014
7636(331^25033-1)/33063077Eric Chen09/2017
763720^48480+3163074Lelio R Paula06/2013
7638(26*10^63073-23)/363074Robert Price08/2016
76392^209499+7625363066Enzo Doria04/2016
764011^60546-1134063053Enzo Doria12/2012
76412^209426+5788963044Yves Minet02/2010
7642(22699*2^209405+1)/2163041Lelio R Paula06/2014
76435^90189+5463040Lelio R Paula04/2013
7644(22*10^63034-73)/363035Robert Price09/2017
7645(314021^11467+1)/31402263029Faysal YAtim05/2008
7646V(301486)63007Henri Lifchitz05/2003
7647(31*2^209298+1)/9563005Lelio R Paula08/2012
7648(27*2^209245+1)/562990Lelio R Paula08/2012
76496^80946-5^(80946-1)62989Robert Price05/2016
7650467^23596+23596^46762986Norbert Schneider08/2016
7651(7*2^209212-1)/362980Lelio R Paula01/2014
7652(27*2^209206-1)/1162978Lelio R Paula01/2014
76531456^19909+19909^145662976Serge Batalov05/2014
7654(3^131964-5)/18521239662955Lelio R Paula04/2012
765535^40772-146662955Enzo Doria03/2013
76565^90064-1370662953Enzo Doria02/2013
7657(22*10^62926+257)/962927Robert Price11/2017
7658(13*10^62914+401)/962915Robert Price10/2017
76592^208993+10762914Lelio R Paula08/2011
76602^208993+7762914Lelio R Paula08/2011
7661189^27636-262913Lelio R Paula10/2017
7662(2^208948-7)/26162898Lelio R Paula03/2012
7663(151*10^62879-1)/362881Robert Price04/2017
766415^53464-8262879Lelio R Paula05/2013
76652^208843-11292162869Enzo Doria06/2014
76662^208779+8162849Henri Lifchitz01/2007
7667(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
7668(73*10^62824+17)/962825Robert Price10/2015
76693^131670-8262823Lelio R Paula04/2013
767019^49128-9062823Lelio R Paula05/2013
767111^60314-441062811Enzo Doria01/2013
7672(17*2^208614-1)/5362799Lelio R Paula01/2014
76732^208594+9362794Donovan Johnson06/2008
7674(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
7675(2^208534+7)/905962772Lelio R Paula03/2012
7677(13^56333+1)/1462751Paul Bourdelais03/2010
767610^62750+5762751Robert Price01/2011
767810^62750-26742962750Patrick De Geest01/2013
76792^208427-6962743Lelio R Paula08/2011
76802^208421-11177562741Enzo Doria05/2014
76812^208404-11207962736Enzo Doria06/2014
76822^208343-222162718Yves Minet08/2013
76832^208335+51362716Lelio R Paula10/2011
7685(2^208328+47)/362713Lelio R Paula03/2012
768411^60220-204062713Enzo Doria12/2012
76862^208292+8162703Henri Lifchitz10/2005
768715013^15012-1501262698Henri Lifchitz10/2014
76882^208271-11274762696Enzo Doria06/2014
768911^60202-438062694Enzo Doria01/2013
7690(3^131403-4)/15762693Lelio R Paula04/2012
76912^208127-12666762653Paul Bourdelais01/2012
769271^33843+262653Lelio R Paula05/2013
7693(3^131325+7)/106685062652Lelio R Paula04/2012
76952^208019+11962620Lelio R Paula08/2011
7694(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
769611^60126-1137062615Enzo Doria12/2012
76972^207976-248962608Yves Minet07/2014
7698(22699*2^207945+1)/28170962597Lelio R Paula06/2014
76994*21^47335+20562588Curtis Bright05/2015
770015^53210+862580Lelio R Paula05/2013
77012^207865+2962574Henri Lifchitz08/2005
770215^53199-3862567Lelio R Paula05/2013
7703(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
77042^207782+5890562549Lelio R Paula10/2011
7705(2^207748-3)/843762535Lelio R Paula03/2012
7706(2^207711+5)/1362527Lelio R Paula03/2012
7707(268*10^62523-1)/362525Robert Price10/2017
770810^62523+6362524Robert Price01/2011
770910^62523-29237362523Patrick De Geest01/2013
77112^207691+1155*20769162522Henri Lifchitz02/2005
7710(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
77122^207626-11215762502Enzo Doria06/2014
77133^130987+5262497Lelio R Paula04/2013
77148*6^80299-762486Lelio R Paula09/2014
771511^59997-267062481Enzo Doria12/2012
771693^31740+262480Lelio R Paula05/2013
7717(10^62451+119)/362451Serge Batalov12/2014
7718(2^207443+47)/764562443Lelio R Paula03/2012
77192^207364+11562423Lelio R Paula08/2011
77203^130815-4662415Lelio R Paula04/2013
7721(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
772220^47968-948362408Enzo Doria03/2013
7723(10^62402+101)/362402Robert Price04/2016
7724(13*2^207264-1)/362394Lelio R Paula01/2014
7725(79*10^62387-61)/962388Robert Price10/2015
77265^89244+3*2^8924462379Mike Oakes02/2010
77276^80160-1362377Lelio R Paula04/2013
7728(7*10^62362+53)/362363Robert Price10/2017
7729(1000121^10391+1)/100012262341Faysal YAtim07/2008
7730(17*10^62328-11)/362329Robert Price07/2015
77312^207023+1171562321Lelio R Paula09/2011
7732(265*10^62298+11)/362300Robert Price03/2017
77332^206947-6962298Lelio R Paula08/2011
77342^206938+2983562295Lelio R Paula02/2013
77352^206911-72687762287Paul Bourdelais03/2013
7736(6883*2^206884-1)/362282Lelio R Paula04/2015
77372^206892-11281762281Enzo Doria06/2014
7738(7*10^62278+113)/362279Robert Price10/2017
77393^130523+4662276Lelio R Paula04/2013
77402^206872-11345362275Enzo Doria07/2014
77412^206840-9362266Lelio R Paula08/2011
7742(1017*2^206815-1)/63562258Lelio R Paula04/2015
774396^31406+9562256Norbert Schneider03/2016
7744(2^206824+7)/64621362255Lelio R Paula03/2012
77452^206765-94168362243Paul Bourdelais11/2012
7746(6^79987-1)/562242Paul Bourdelais11/2007
77472^206755-157962240Yves Minet03/2013
774811^59764-582062238Enzo Doria01/2013
77495*10^62233+362234Dmitry Domanov11/2010
77508*3^130421+762228Lelio R Paula04/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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