PRP Records

Probable Primes Top 10000

(224660 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 ?
775115346^12941+12941^1534663103Hans Havermann01/2017
77523^132253+7663101Lelio R Paula04/2013
7753(56*10^63100+403)/963101Robert Price10/2017
775417549^3936+3936^1754963090Hans Havermann01/2017
7755(55459*2^209553+1)/42363084Lelio R Paula06/2014
7756(331^25033-1)/33063077Eric Chen09/2017
775820^48480+3163074Lelio R Paula06/2013
7757(26*10^63073-23)/363074Robert Price08/2016
77592^209499+7625363066Enzo Doria04/2016
776011^60546-1134063053Enzo Doria12/2012
77612^209426+5788963044Yves Minet02/2010
7762(22699*2^209405+1)/2163041Lelio R Paula06/2014
77635^90189+5463040Lelio R Paula04/2013
7764(22*10^63034-73)/363035Robert Price09/2017
7765(314021^11467+1)/31402263029Faysal YAtim05/2008
7766V(301486)63007Henri Lifchitz05/2003
7767(31*2^209298+1)/9563005Lelio R Paula08/2012
7768(27*2^209245+1)/562990Lelio R Paula08/2012
77696^80946-5^(80946-1)62989Robert Price05/2016
7770467^23596+23596^46762986Norbert Schneider08/2016
7771(7*2^209212-1)/362980Lelio R Paula01/2014
7772(27*2^209206-1)/1162978Lelio R Paula01/2014
77731456^19909+19909^145662976Serge Batalov05/2014
7775(3^131964-5)/18521239662955Lelio R Paula04/2012
777435^40772-146662955Enzo Doria03/2013
77765^90064-1370662953Enzo Doria02/2013
7777(22*10^62926+257)/962927Robert Price11/2017
7778(13*10^62914+401)/962915Robert Price10/2017
77792^208993+10762914Lelio R Paula08/2011
77802^208993+7762914Lelio R Paula08/2011
7781189^27636-262913Lelio R Paula10/2017
7782(2^208948-7)/26162898Lelio R Paula03/2012
7783(151*10^62879-1)/362881Robert Price04/2017
778415^53464-8262879Lelio R Paula05/2013
77852^208843-11292162869Enzo Doria06/2014
77862^208779+8162849Henri Lifchitz01/2007
7787(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
7788(73*10^62824+17)/962825Robert Price10/2015
77893^131670-8262823Lelio R Paula04/2013
779019^49128-9062823Lelio R Paula05/2013
779111^60314-441062811Enzo Doria01/2013
7792(17*2^208614-1)/5362799Lelio R Paula01/2014
77932^208594+9362794Donovan Johnson06/2008
7794(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
7795(2^208534+7)/905962772Lelio R Paula03/2012
7797(13^56333+1)/1462751Paul Bourdelais03/2010
779610^62750+5762751Robert Price01/2011
779810^62750-26742962750Patrick De Geest01/2013
77992^208427-6962743Lelio R Paula08/2011
78002^208421-11177562741Enzo Doria05/2014
78012^208404-11207962736Enzo Doria06/2014
78022^208343-222162718Yves Minet08/2013
78032^208335+51362716Lelio R Paula10/2011
7805(2^208328+47)/362713Lelio R Paula03/2012
780411^60220-204062713Enzo Doria12/2012
78062^208292+8162703Henri Lifchitz10/2005
780715013^15012-1501262698Henri Lifchitz10/2014
78082^208271-11274762696Enzo Doria06/2014
780911^60202-438062694Enzo Doria01/2013
7810(3^131403-4)/15762693Lelio R Paula04/2012
78112^208127-12666762653Paul Bourdelais01/2012
781271^33843+262653Lelio R Paula05/2013
7813(3^131325+7)/106685062652Lelio R Paula04/2012
78142^208019+11962620Lelio R Paula08/2011
7815(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
781611^60126-1137062615Enzo Doria12/2012
78172^207976-248962608Yves Minet07/2014
7818(22699*2^207945+1)/28170962597Lelio R Paula06/2014
78194*21^47335+20562588Curtis Bright05/2015
782015^53210+862580Lelio R Paula05/2013
78212^207865+2962574Henri Lifchitz08/2005
782215^53199-3862567Lelio R Paula05/2013
7823(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
78242^207782+5890562549Lelio R Paula10/2011
7825(2^207748-3)/843762535Lelio R Paula03/2012
7826(2^207711+5)/1362527Lelio R Paula03/2012
7827(268*10^62523-1)/362525Robert Price10/2017
782810^62523+6362524Robert Price01/2011
782910^62523-29237362523Patrick De Geest01/2013
78312^207691+1155*20769162522Henri Lifchitz02/2005
7830(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
78322^207626-11215762502Enzo Doria06/2014
78333^130987+5262497Lelio R Paula04/2013
78348*6^80299-762486Lelio R Paula09/2014
783511^59997-267062481Enzo Doria12/2012
783693^31740+262480Lelio R Paula05/2013
7837(10^62451+119)/362451Serge Batalov12/2014
7838(2^207443+47)/764562443Lelio R Paula03/2012
78392^207364+11562423Lelio R Paula08/2011
78403^130815-4662415Lelio R Paula04/2013
7841(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
784220^47968-948362408Enzo Doria03/2013
7843(10^62402+101)/362402Robert Price04/2016
7844(13*2^207264-1)/362394Lelio R Paula01/2014
7845(79*10^62387-61)/962388Robert Price10/2015
78465^89244+3*2^8924462379Mike Oakes02/2010
78476^80160-1362377Lelio R Paula04/2013
7848(7*10^62362+53)/362363Robert Price10/2017
7849(1000121^10391+1)/100012262341Faysal YAtim07/2008
7850(17*10^62328-11)/362329Robert Price07/2015
78512^207023+1171562321Lelio R Paula09/2011
7852(265*10^62298+11)/362300Robert Price03/2017
78532^206947-6962298Lelio R Paula08/2011
78542^206938+2983562295Lelio R Paula02/2013
78552^206911-72687762287Paul Bourdelais03/2013
7856(6883*2^206884-1)/362282Lelio R Paula04/2015
78572^206892-11281762281Enzo Doria06/2014
7858(7*10^62278+113)/362279Robert Price10/2017
78593^130523+4662276Lelio R Paula04/2013
78602^206872-11345362275Enzo Doria07/2014
78612^206840-9362266Lelio R Paula08/2011
7862(1017*2^206815-1)/63562258Lelio R Paula04/2015
786396^31406+9562256Norbert Schneider03/2016
7864(2^206824+7)/64621362255Lelio R Paula03/2012
78652^206765-94168362243Paul Bourdelais11/2012
7866(6^79987-1)/562242Paul Bourdelais11/2007
78672^206755-157962240Yves Minet03/2013
786811^59764-582062238Enzo Doria01/2013
78695*10^62233+362234Dmitry Domanov11/2010
78708*3^130421+762228Lelio R Paula04/2014
787119^48661+1062226Lelio R Paula05/2013
7872(17*2^206705+1)/562225Lelio R Paula08/2012
78732^206705-11263562225Enzo Doria06/2014
78743^130403+868062219Lelio R Paula04/2013
787511^59740-711062213Enzo Doria01/2013
78772^206596-16762192Lelio R Paula08/2011
78762^206597+1891562192Lelio R Paula02/2013
78786^79918+13762189Lelio R Paula04/2013
7879lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
78802^206574+61362185Jason Earls04/2008
78813^130328+8062183Lelio R Paula04/2013
7882(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
78832^206550+7681962178Enzo Doria05/2016
788411^59703-2462175Lelio R Paula05/2013
78852^206524+7578162170Enzo Doria04/2016
78862^206506+42762165Henri Lifchitz01/2005
78872^206465+769562153Lelio R Paula02/2013
78882^206464-164962152Yves Minet03/2013
78895^88917+5662151Lelio R Paula04/2013
78902^206444-11156962146Enzo Doria05/2014
78915^88908-4262145Lelio R Paula04/2013
789218^49495-2962130Lelio R Paula05/2013
78933*6^79842-562130Lelio R Paula09/2014
78947*10^62127-1762128Robert Price01/2017
78952^206373+841562125Lelio R Paula02/2013
789620^47745-958362118Enzo Doria03/2013
789741^38516-262118Lelio R Paula08/2013
78982^206332-5869562113Lelio R Paula09/2011
789911^59639-126062108Enzo Doria11/2012
79002^206232-1589362083Enzo Doria04/2013
7901(115*10^62073-1)/362075Serge Batalov12/2014
79022^206206+7579962075Enzo Doria04/2016
7903(74*10^62072+43)/962073Robert Price10/2015
79042^206194-18562071Lelio R Paula08/2011
79056^79757-10362064Lelio R Paula04/2013
7906p(13285)#/2-6462063Robert Price04/2017
7907(29*10^62030-41)/362031Robert Price07/2016
790820^47675-8162027Lelio R Paula06/2013
79093^129972+9862013Lelio R Paula04/2013
79102^205962+362001Donovan Johnson02/2006
79112^205933-205933^261993Henri Lifchitz05/2005
7912(68*10^61991+7)/361993Robert Price03/2016
791320^47641-66361983Enzo Doria03/2013
79143^129861+266061960Lelio R Paula04/2013
7915(55459*2^205800+1)/134561954Lelio R Paula06/2014
791618^49354-9761953Lelio R Paula05/2013
7917(209*10^61947-17)/361949Robert Price05/2017
791914*10^61937+108961939Jens K. Andersen11/2007
7918(11*2^205758-1)/5361939Lelio R Paula01/2014
792020^47600+6361930Lelio R Paula06/2013
7921(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
792244117!3+24361918Robert Price09/2014
7923(31*2^205677-1)/5961915Lelio R Paula01/2014
7924(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
792520^47575-8161897Lelio R Paula06/2013
7926(58695*2^205593-1)/72761892Lelio R Paula04/2015
792787^31909+8661889Norbert Schneider10/2015
79282^205568+14161883Lelio R Paula08/2011
792910^61868+5892761869Patrick De Geest12/2012
793010^61868-3961868Robert Price05/2011
79315^88505-8861863Lelio R Paula04/2013
7932(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
793413^55528-9861856Lelio R Paula05/2013
7933(55^35543-1)/5461856Paul Bourdelais08/2017
793530535!2-861844Robert Price06/2015
793611^59371-120061829Enzo Doria11/2012
79377*2^205370-561824Lelio R Paula04/2014
7938(47*10^61821+403)/961822Robert Price04/2017
79392^205275+769561794Lelio R Paula02/2013
79402^205269+1291561793Lelio R Paula02/2013
7941(47*2^205265+1)/3561792Lelio R Paula04/2015
794219^48309+4061776Lelio R Paula05/2013
7943(424*10^61770-1)/961772Robert Price11/2017
79442^205192-407961769Yves Minet06/2011
79452^205184+1609561767Lelio R Paula09/2011
794620^47472-342361763Enzo Doria03/2013
7947(17*10^61760-89)/961761Robert Price11/2017
79482^205149-179561757Lelio R Paula09/2011
79492^205110-1761745Lelio R Paula08/2011
7950(373^24007+1)/37461737Eric Chen10/2017
7951(2^205025-7)/2561718Lelio R Paula03/2012
795227^43117-26^4311761717Robert Price08/2012
79532^205016+3761716Lelio R Paula08/2011
7954gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
79551263^19898+19898^126361712Serge Batalov05/2014
7956135^28963-13461701Norbert Schneider04/2015
7957(33*2^204966+1)/23434161698Michael Porter01/2015
7958(7*10^61696+167)/361696Robert Kinser10/2017
7959(46*10^61693+17)/961694Robert Price06/2015
7960((((((((((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
79611850^18879+18879^185061681Serge Batalov05/2014
79622^204891-100561679Lelio R Paula09/2011
7963151^28306-261679Lelio R Paula10/2017
7964(3^129271-5)/4150661674Lelio R Paula03/2012
796515937^7408+7408^1593761672Hans Havermann02/2017
79665^88216-1261661Lelio R Paula04/2013
796718185^2454+2454^1818561645Hans Havermann01/2017
79692^204767-1586561642Enzo Doria04/2013
7968(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
79707*2^204751-961638Lelio R Paula04/2014
79724*10^61625+2161626Robert Price08/2016
797115369^10226+10226^1536961626Hans Havermann02/2017
79732^204702-1812561622Enzo Doria05/2013
79745*3^129146+861620Lelio R Paula04/2014
79752^204673+12961613Lelio R Paula08/2011
797618^49079+9761608Lelio R Paula05/2013
7977106^30416+10561602Norbert Schneider12/2016
79782^204590-3361588Lelio R Paula08/2011
79792^204586-11197561587Enzo Doria06/2014
79802^204580-1607761585Enzo Doria04/2013
79812^204574-1604161583Enzo Doria04/2013
798215^52358+5661578Lelio R Paula05/2013
7983(28*10^61574+11)/361575Robert Price11/2015
79842^204516-1749361566Enzo Doria05/2013
79854*5^88076-361564Lelio R Paula09/2014
798611^59110-252061557Enzo Doria12/2012
79872^204477-5869561554Lelio R Paula09/2011
798812^57026-7361542Lelio R Paula05/2013
7989(257^25537+1)/25861541Richard Fischer04/2018
799017^50013+9061539Lelio R Paula05/2013
799156^35201-55^3520161538Robert Price10/2013
79928*7^72810+561533Lelio R Paula09/2014
7994204^26641-203^2664161531Jean-Louis Charton08/2009
799343867!3-656161531Robert Price11/2015
799710^61525+9^(61525-1)61526Robert Price03/2016
799510^61525+6225761526Patrick De Geest12/2016
799614821^14166+14166^1482161526Hans Havermann01/2017
799912^57010-8561525Lelio R Paula05/2013
799810^61525-21357961525Patrick De Geest12/2016
80002^204332-9961511Lelio R Paula08/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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