PRP Records

Probable Primes Top 10000

(212140 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 ?
7501Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
750296^31913-9563261Norbert Schneider04/2016
75033^132572+28063253Lelio R Paula04/2013
75043^132570-2^(132570-1)63252Robert Price01/2016
750511^60734-492063248Enzo Doria01/2013
75072^210061+2163235Donovan Johnson06/2006
750618^50375+9563235Lelio R Paula05/2013
750885^32773-263233Lelio R Paula08/2013
7509(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
7510(2^210054-1017)/67163230Lelio R Paula04/2012
75113*2^210022+563224Lelio R Paula04/2014
751215^53756+3263222Lelio R Paula05/2013
751317^51380+2263221Lelio R Paula05/2013
7514(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
751543^38700+4263216Norbert Schneider06/2014
75165^90431-9663209Lelio R Paula04/2013
7517(172*10^63202-1)/963204Serge Batalov12/2014
7518(43*10^63200+83)/963201Robert Price08/2017
75192^209914-1600563191Enzo Doria04/2013
75203*6^81190-563179Lelio R Paula09/2014
75212^209820+425763163Lelio R Paula10/2011
752299^31648+263158Lelio R Paula05/2013
752316976^5253+5253^1697663158Hans Havermann01/2017
75242^209790+6763154Lelio R Paula08/2011
75252^209759+9019563144Lelio R Paula02/2013
7526145823#+21150763142Arkadiusz Wesolowski03/2013
75282^209707+51363129Lelio R Paula10/2011
7527(3^132314-8)/1763129Lelio R Paula04/2012
7529(2*10^63117+7)/963117Erik Branger03/2011
75309*2^209654-763114Lelio R Paula04/2014
753111^60598-1463107Lelio R Paula05/2013
753215103^15078+15078^1510363106Hans Havermann01/2017
753315346^12941+12941^1534663103Hans Havermann01/2017
75353^132253+7663101Lelio R Paula04/2013
7534(56*10^63100+403)/963101Robert Price10/2017
753617549^3936+3936^1754963090Hans Havermann01/2017
7537(55459*2^209553+1)/42363084Lelio R Paula06/2014
7538(331^25033-1)/33063077Eric Chen09/2017
753920^48480+3163074Lelio R Paula06/2013
7540(26*10^63073-23)/363074Robert Price08/2016
75412^209499+7625363066Enzo Doria04/2016
754211^60546-1134063053Enzo Doria12/2012
75432^209426+5788963044Yves Minet02/2010
7544(22699*2^209405+1)/2163041Lelio R Paula06/2014
75455^90189+5463040Lelio R Paula04/2013
7546(22*10^63034-73)/363035Robert Price09/2017
7547(314021^11467+1)/31402263029Faysal YAtim05/2008
7548V(301486)63007Henri Lifchitz05/2003
7549(31*2^209298+1)/9563005Lelio R Paula08/2012
7550(27*2^209245+1)/562990Lelio R Paula08/2012
75516^80946-5^(80946-1)62989Robert Price05/2016
7552467^23596+23596^46762986Norbert Schneider08/2016
7553(7*2^209212-1)/362980Lelio R Paula01/2014
7554(27*2^209206-1)/1162978Lelio R Paula01/2014
75551456^19909+19909^145662976Serge Batalov05/2014
7557(3^131964-5)/18521239662955Lelio R Paula04/2012
755635^40772-146662955Enzo Doria03/2013
75585^90064-1370662953Enzo Doria02/2013
7559(22*10^62926+257)/962927Robert Price11/2017
7560(13*10^62914+401)/962915Robert Price10/2017
75612^208993+10762914Lelio R Paula08/2011
75622^208993+7762914Lelio R Paula08/2011
7563189^27636-262913Lelio R Paula10/2017
7564(2^208948-7)/26162898Lelio R Paula03/2012
7565(151*10^62879-1)/362881Robert Price04/2017
756615^53464-8262879Lelio R Paula05/2013
75672^208843-11292162869Enzo Doria06/2014
75682^208779+8162849Henri Lifchitz01/2007
7569(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
7570(73*10^62824+17)/962825Robert Price10/2015
75713^131670-8262823Lelio R Paula04/2013
757219^49128-9062823Lelio R Paula05/2013
757311^60314-441062811Enzo Doria01/2013
7574(17*2^208614-1)/5362799Lelio R Paula01/2014
75752^208594+9362794Donovan Johnson06/2008
7576(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
7577(2^208534+7)/905962772Lelio R Paula03/2012
7578(13^56333+1)/1462751Paul Bourdelais03/2010
757910^62750+5762751Robert Price01/2011
758010^62750-26742962750Patrick De Geest01/2013
75812^208427-6962743Lelio R Paula08/2011
75822^208421-11177562741Enzo Doria05/2014
75832^208404-11207962736Enzo Doria06/2014
75842^208343-222162718Yves Minet08/2013
75852^208335+51362716Lelio R Paula10/2011
7587(2^208328+47)/362713Lelio R Paula03/2012
758611^60220-204062713Enzo Doria12/2012
75882^208292+8162703Henri Lifchitz10/2005
758915013^15012-1501262698Henri Lifchitz10/2014
75902^208271-11274762696Enzo Doria06/2014
759111^60202-438062694Enzo Doria01/2013
7592(3^131403-4)/15762693Lelio R Paula04/2012
75932^208127-12666762653Paul Bourdelais01/2012
759471^33843+262653Lelio R Paula05/2013
7595(3^131325+7)/106685062652Lelio R Paula04/2012
75962^208019+11962620Lelio R Paula08/2011
7597(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
759811^60126-1137062615Enzo Doria12/2012
75992^207976-248962608Yves Minet07/2014
7600(22699*2^207945+1)/28170962597Lelio R Paula06/2014
76014*21^47335+20562588Curtis Bright05/2015
760215^53210+862580Lelio R Paula05/2013
76032^207865+2962574Henri Lifchitz08/2005
760415^53199-3862567Lelio R Paula05/2013
7605(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
76062^207782+5890562549Lelio R Paula10/2011
7607(2^207748-3)/843762535Lelio R Paula03/2012
7608(2^207711+5)/1362527Lelio R Paula03/2012
7609(268*10^62523-1)/362525Robert Price10/2017
761010^62523+6362524Robert Price01/2011
761110^62523-29237362523Patrick De Geest01/2013
76122^207691+1155*20769162522Henri Lifchitz02/2005
7613(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
76142^207626-11215762502Enzo Doria06/2014
76153^130987+5262497Lelio R Paula04/2013
76168*6^80299-762486Lelio R Paula09/2014
761711^59997-267062481Enzo Doria12/2012
761893^31740+262480Lelio R Paula05/2013
7619(10^62451+119)/362451Serge Batalov12/2014
7620(2^207443+47)/764562443Lelio R Paula03/2012
76212^207364+11562423Lelio R Paula08/2011
76223^130815-4662415Lelio R Paula04/2013
7623(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
762420^47968-948362408Enzo Doria03/2013
7625(10^62402+101)/362402Robert Price04/2016
7626(13*2^207264-1)/362394Lelio R Paula01/2014
7627(79*10^62387-61)/962388Robert Price10/2015
76285^89244+3*2^8924462379Mike Oakes02/2010
76296^80160-1362377Lelio R Paula04/2013
7630(7*10^62362+53)/362363Robert Price10/2017
7631(1000121^10391+1)/100012262341Faysal YAtim07/2008
7632(17*10^62328-11)/362329Robert Price07/2015
76332^207023+1171562321Lelio R Paula09/2011
7634(265*10^62298+11)/362300Robert Price03/2017
76352^206947-6962298Lelio R Paula08/2011
76362^206938+2983562295Lelio R Paula02/2013
76372^206911-72687762287Paul Bourdelais03/2013
7638(6883*2^206884-1)/362282Lelio R Paula04/2015
76392^206892-11281762281Enzo Doria06/2014
7640(7*10^62278+113)/362279Robert Price10/2017
76413^130523+4662276Lelio R Paula04/2013
76422^206872-11345362275Enzo Doria07/2014
76432^206840-9362266Lelio R Paula08/2011
7644(1017*2^206815-1)/63562258Lelio R Paula04/2015
764596^31406+9562256Norbert Schneider03/2016
7646(2^206824+7)/64621362255Lelio R Paula03/2012
76472^206765-94168362243Paul Bourdelais11/2012
7648(6^79987-1)/562242Paul Bourdelais11/2007
76492^206755-157962240Yves Minet03/2013
765011^59764-582062238Enzo Doria01/2013
76515*10^62233+362234Dmitry Domanov11/2010
76528*3^130421+762228Lelio R Paula04/2014
765319^48661+1062226Lelio R Paula05/2013
7655(17*2^206705+1)/562225Lelio R Paula08/2012
76542^206705-11263562225Enzo Doria06/2014
76563^130403+868062219Lelio R Paula04/2013
765711^59740-711062213Enzo Doria01/2013
76592^206596-16762192Lelio R Paula08/2011
76582^206597+1891562192Lelio R Paula02/2013
76606^79918+13762189Lelio R Paula04/2013
7661lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
76622^206574+61362185Jason Earls04/2008
76633^130328+8062183Lelio R Paula04/2013
7664(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
76652^206550+7681962178Enzo Doria05/2016
766611^59703-2462175Lelio R Paula05/2013
76672^206524+7578162170Enzo Doria04/2016
76682^206506+42762165Henri Lifchitz01/2005
76692^206465+769562153Lelio R Paula02/2013
76702^206464-164962152Yves Minet03/2013
76715^88917+5662151Lelio R Paula04/2013
76722^206444-11156962146Enzo Doria05/2014
76735^88908-4262145Lelio R Paula04/2013
767418^49495-2962130Lelio R Paula05/2013
76753*6^79842-562130Lelio R Paula09/2014
76767*10^62127-1762128Robert Price01/2017
76772^206373+841562125Lelio R Paula02/2013
767820^47745-958362118Enzo Doria03/2013
767941^38516-262118Lelio R Paula08/2013
76802^206332-5869562113Lelio R Paula09/2011
768111^59639-126062108Enzo Doria11/2012
76822^206232-1589362083Enzo Doria04/2013
7683(115*10^62073-1)/362075Serge Batalov12/2014
76842^206206+7579962075Enzo Doria04/2016
7685(74*10^62072+43)/962073Robert Price10/2015
76862^206194-18562071Lelio R Paula08/2011
76876^79757-10362064Lelio R Paula04/2013
7688p(13285)#/2-6462063Robert Price04/2017
7689(29*10^62030-41)/362031Robert Price07/2016
769020^47675-8162027Lelio R Paula06/2013
76913^129972+9862013Lelio R Paula04/2013
76922^205962+362001Donovan Johnson02/2006
76932^205933-205933^261993Henri Lifchitz05/2005
7694(68*10^61991+7)/361993Robert Price03/2016
769520^47641-66361983Enzo Doria03/2013
76963^129861+266061960Lelio R Paula04/2013
7697(55459*2^205800+1)/134561954Lelio R Paula06/2014
769818^49354-9761953Lelio R Paula05/2013
7699(209*10^61947-17)/361949Robert Price05/2017
770114*10^61937+108961939Jens K. Andersen11/2007
7700(11*2^205758-1)/5361939Lelio R Paula01/2014
770220^47600+6361930Lelio R Paula06/2013
7703(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
770444117!3+24361918Robert Price09/2014
7705(31*2^205677-1)/5961915Lelio R Paula01/2014
7706(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
770720^47575-8161897Lelio R Paula06/2013
7708(58695*2^205593-1)/72761892Lelio R Paula04/2015
770987^31909+8661889Norbert Schneider10/2015
77102^205568+14161883Lelio R Paula08/2011
771110^61868+5892761869Patrick De Geest12/2012
771210^61868-3961868Robert Price05/2011
77145^88505-8861863Lelio R Paula04/2013
7713(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
771513^55528-9861856Lelio R Paula05/2013
7716(55^35543-1)/5461856Paul Bourdelais08/2017
771730535!2-861844Robert Price06/2015
771811^59371-120061829Enzo Doria11/2012
77197*2^205370-561824Lelio R Paula04/2014
7720(47*10^61821+403)/961822Robert Price04/2017
77212^205275+769561794Lelio R Paula02/2013
77222^205269+1291561793Lelio R Paula02/2013
7723(47*2^205265+1)/3561792Lelio R Paula04/2015
772419^48309+4061776Lelio R Paula05/2013
7725(424*10^61770-1)/961772Robert Price11/2017
77262^205192-407961769Yves Minet06/2011
77272^205184+1609561767Lelio R Paula09/2011
772820^47472-342361763Enzo Doria03/2013
7729(17*10^61760-89)/961761Robert Price11/2017
77302^205149-179561757Lelio R Paula09/2011
77312^205110-1761745Lelio R Paula08/2011
7732(373^24007+1)/37461737Eric Chen10/2017
7733(2^205025-7)/2561718Lelio R Paula03/2012
773427^43117-26^4311761717Robert Price08/2012
77352^205016+3761716Lelio R Paula08/2011
7736gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
77371263^19898+19898^126361712Serge Batalov05/2014
7738135^28963-13461701Norbert Schneider04/2015
7739(33*2^204966+1)/23434161698Michael Porter01/2015
7740(7*10^61696+167)/361696Robert Kinser10/2017
7741(46*10^61693+17)/961694Robert Price06/2015
7742((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+6676861684Phil Carmody09/2004
77431850^18879+18879^185061681Serge Batalov05/2014
77452^204891-100561679Lelio R Paula09/2011
7744151^28306-261679Lelio R Paula10/2017
7746(3^129271-5)/4150661674Lelio R Paula03/2012
774715937^7408+7408^1593761672Hans Havermann02/2017
77485^88216-1261661Lelio R Paula04/2013
774918185^2454+2454^1818561645Hans Havermann01/2017
7750(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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