PRP Records

Probable Primes Top 10000

(172213 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 ?
67511456^19909+19909^145662976Serge Batalov05/2014
6752(3^131964-5)/18521239662955Lelio R Paula04/2012
675335^40772-146662955Enzo Doria03/2013
67545^90064-1370662953Enzo Doria02/2013
67552^208993+10762914Lelio R Paula08/2011
67562^208993+7762914Lelio R Paula08/2011
6757(2^208948-7)/26162898Lelio R Paula03/2012
675815^53464-8262879Lelio R Paula05/2013
67592^208843-11292162869Enzo Doria06/2014
67602^208779+8162849Henri Lifchitz01/2007
6761(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
6762(73*10^62824+17)/962825Robert Price10/2015
67633^131670-8262823Lelio R Paula04/2013
676419^49128-9062823Lelio R Paula05/2013
676511^60314-441062811Enzo Doria01/2013
6766(17*2^208614-1)/5362799Lelio R Paula01/2014
67672^208594+9362794Donovan Johnson06/2008
6768(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
6769(2^208534+7)/905962772Lelio R Paula03/2012
6770(13^56333+1)/1462751Paul Bourdelais03/2010
677110^62750+5762751Robert Price01/2011
677210^62750-26742962750Patrick De Geest01/2013
67732^208427-6962743Lelio R Paula08/2011
67742^208421-11177562741Enzo Doria05/2014
67752^208404-11207962736Enzo Doria06/2014
67762^208343-222162718Yves Minet08/2013
67772^208335+51362716Lelio R Paula10/2011
6779(2^208328+47)/362713Lelio R Paula03/2012
677811^60220-204062713Enzo Doria12/2012
67802^208292+8162703Henri Lifchitz10/2005
678115013^15012-1501262698Henri Lifchitz10/2014
67822^208271-11274762696Enzo Doria06/2014
678311^60202-438062694Enzo Doria01/2013
6784(3^131403-4)/15762693Lelio R Paula04/2012
67852^208127-12666762653Paul Bourdelais01/2012
678671^33843+262653Lelio R Paula05/2013
6787(3^131325+7)/106685062652Lelio R Paula04/2012
67882^208019+11962620Lelio R Paula08/2011
6789(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
679011^60126-1137062615Enzo Doria12/2012
67912^207976-248962608Yves Minet07/2014
6792(22699*2^207945+1)/28170962597Lelio R Paula06/2014
67934*21^47335+20562588Curtis Bright05/2015
679415^53210+862580Lelio R Paula05/2013
67952^207865+2962574Henri Lifchitz08/2005
679615^53199-3862567Lelio R Paula05/2013
6797(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
67982^207782+5890562549Lelio R Paula10/2011
6799(2^207748-3)/843762535Lelio R Paula03/2012
6800(2^207711+5)/1362527Lelio R Paula03/2012
680110^62523+6362524Robert Price01/2011
680210^62523-29237362523Patrick De Geest01/2013
68032^207691+1155*20769162522Henri Lifchitz02/2005
6804(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
68052^207626-11215762502Enzo Doria06/2014
68063^130987+5262497Lelio R Paula04/2013
68078*6^80299-762486Lelio R Paula09/2014
680811^59997-267062481Enzo Doria12/2012
680993^31740+262480Lelio R Paula05/2013
6810(10^62451+119)/362451Serge Batalov12/2014
6811(2^207443+47)/764562443Lelio R Paula03/2012
68122^207364+11562423Lelio R Paula08/2011
68133^130815-4662415Lelio R Paula04/2013
6814(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
681520^47968-948362408Enzo Doria03/2013
6816(10^62402+101)/362402Robert Price04/2016
6817(13*2^207264-1)/362394Lelio R Paula01/2014
6818(79*10^62387-61)/962388Robert Price10/2015
68195^89244+3*2^8924462379Mike Oakes02/2010
68206^80160-1362377Lelio R Paula04/2013
6821(1000121^10391+1)/100012262341Faysal YAtim07/2008
6822(17*10^62328-11)/362329Robert Price07/2015
68232^207023+1171562321Lelio R Paula09/2011
6824(265*10^62298+11)/362300Robert Price03/2017
68252^206947-6962298Lelio R Paula08/2011
68262^206938+2983562295Lelio R Paula02/2013
68272^206911-72687762287Paul Bourdelais03/2013
6828(6883*2^206884-1)/362282Lelio R Paula04/2015
68292^206892-11281762281Enzo Doria06/2014
68303^130523+4662276Lelio R Paula04/2013
68312^206872-11345362275Enzo Doria07/2014
68322^206840-9362266Lelio R Paula08/2011
6833(1017*2^206815-1)/63562258Lelio R Paula04/2015
683496^31406+9562256Norbert Schneider03/2016
6835(2^206824+7)/64621362255Lelio R Paula03/2012
68362^206765-94168362243Paul Bourdelais11/2012
6837(6^79987-1)/562242Paul Bourdelais11/2007
68382^206755-157962240Yves Minet03/2013
683911^59764-582062238Enzo Doria01/2013
68405*10^62233+362234Dmitry Domanov11/2010
68418*3^130421+762228Lelio R Paula04/2014
684219^48661+1062226Lelio R Paula05/2013
6844(17*2^206705+1)/562225Lelio R Paula08/2012
68432^206705-11263562225Enzo Doria06/2014
68453^130403+868062219Lelio R Paula04/2013
684611^59740-711062213Enzo Doria01/2013
68482^206596-16762192Lelio R Paula08/2011
68472^206597+1891562192Lelio R Paula02/2013
68496^79918+13762189Lelio R Paula04/2013
6850lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
68512^206574+61362185Jason Earls04/2008
68523^130328+8062183Lelio R Paula04/2013
6853(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
68542^206550+7681962178Enzo Doria05/2016
685511^59703-2462175Lelio R Paula05/2013
68562^206524+7578162170Enzo Doria04/2016
68572^206506+42762165Henri Lifchitz01/2005
68582^206465+769562153Lelio R Paula02/2013
68592^206464-164962152Yves Minet03/2013
68605^88917+5662151Lelio R Paula04/2013
68612^206444-11156962146Enzo Doria05/2014
68625^88908-4262145Lelio R Paula04/2013
686318^49495-2962130Lelio R Paula05/2013
68643*6^79842-562130Lelio R Paula09/2014
68657*10^62127-1762128Robert Price01/2017
68662^206373+841562125Lelio R Paula02/2013
686720^47745-958362118Enzo Doria03/2013
686841^38516-262118Lelio R Paula08/2013
68692^206332-5869562113Lelio R Paula09/2011
687011^59639-126062108Enzo Doria11/2012
68712^206232-1589362083Enzo Doria04/2013
6872(115*10^62073-1)/362075Serge Batalov12/2014
68732^206206+7579962075Enzo Doria04/2016
6874(74*10^62072+43)/962073Robert Price10/2015
68752^206194-18562071Lelio R Paula08/2011
68766^79757-10362064Lelio R Paula04/2013
6877(29*10^62030-41)/362031Robert Price07/2016
687820^47675-8162027Lelio R Paula06/2013
68793^129972+9862013Lelio R Paula04/2013
68802^205962+362001Donovan Johnson02/2006
68812^205933-205933^261993Henri Lifchitz05/2005
6882(68*10^61991+7)/361993Robert Price03/2016
688320^47641-66361983Enzo Doria03/2013
68843^129861+266061960Lelio R Paula04/2013
6885(55459*2^205800+1)/134561954Lelio R Paula06/2014
688618^49354-9761953Lelio R Paula05/2013
688814*10^61937+108961939Jens K. Andersen11/2007
6887(11*2^205758-1)/5361939Lelio R Paula01/2014
688920^47600+6361930Lelio R Paula06/2013
689044117!3+24361918Robert Price09/2014
6891(31*2^205677-1)/5961915Lelio R Paula01/2014
6892(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
689320^47575-8161897Lelio R Paula06/2013
6894(58695*2^205593-1)/72761892Lelio R Paula04/2015
689587^31909+8661889Norbert Schneider10/2015
68962^205568+14161883Lelio R Paula08/2011
689710^61868+5892761869Patrick De Geest12/2012
689810^61868-3961868Robert Price05/2011
68995^88505-8861863Lelio R Paula04/2013
6900(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
690113^55528-9861856Lelio R Paula05/2013
690230535!2-861844Robert Price06/2015
690311^59371-120061829Enzo Doria11/2012
69047*2^205370-561824Lelio R Paula04/2014
69052^205275+769561794Lelio R Paula02/2013
69062^205269+1291561793Lelio R Paula02/2013
6907(47*2^205265+1)/3561792Lelio R Paula04/2015
690819^48309+4061776Lelio R Paula05/2013
69092^205192-407961769Yves Minet06/2011
69102^205184+1609561767Lelio R Paula09/2011
691120^47472-342361763Enzo Doria03/2013
69122^205149-179561757Lelio R Paula09/2011
69132^205110-1761745Lelio R Paula08/2011
6914(2^205025-7)/2561718Lelio R Paula03/2012
691527^43117-26^4311761717Robert Price08/2012
69162^205016+3761716Lelio R Paula08/2011
6917gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
69181263^19898+19898^126361712Serge Batalov05/2014
6919135^28963-13461701Norbert Schneider04/2015
6920(33*2^204966+1)/23434161698Michael Porter01/2015
6921(46*10^61693+17)/961694Robert Price06/2015
6922((((((((((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
69231850^18879+18879^185061681Serge Batalov05/2014
69242^204891-100561679Lelio R Paula09/2011
6925(3^129271-5)/4150661674Lelio R Paula03/2012
692615937^7408+7408^1593761672Hans Havermann02/2017
69275^88216-1261661Lelio R Paula04/2013
692818185^2454+2454^1818561645Hans Havermann01/2017
69302^204767-1586561642Enzo Doria04/2013
6929(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
69317*2^204751-961638Lelio R Paula04/2014
69334*10^61625+2161626Robert Price08/2016
693215369^10226+10226^1536961626Hans Havermann02/2017
69342^204702-1812561622Enzo Doria05/2013
69355*3^129146+861620Lelio R Paula04/2014
69362^204673+12961613Lelio R Paula08/2011
693718^49079+9761608Lelio R Paula05/2013
6938106^30416+10561602Norbert Schneider12/2016
69392^204590-3361588Lelio R Paula08/2011
69402^204586-11197561587Enzo Doria06/2014
69412^204580-1607761585Enzo Doria04/2013
69422^204574-1604161583Enzo Doria04/2013
694315^52358+5661578Lelio R Paula05/2013
6944(28*10^61574+11)/361575Robert Price11/2015
69452^204516-1749361566Enzo Doria05/2013
69464*5^88076-361564Lelio R Paula09/2014
694711^59110-252061557Enzo Doria12/2012
69482^204477-5869561554Lelio R Paula09/2011
694912^57026-7361542Lelio R Paula05/2013
695017^50013+9061539Lelio R Paula05/2013
695156^35201-55^3520161538Robert Price10/2013
69528*7^72810+561533Lelio R Paula09/2014
6954204^26641-203^2664161531Jean-Louis Charton08/2009
695343867!3-656161531Robert Price11/2015
695510^61525+9^(61525-1)61526Robert Price03/2016
695610^61525+6225761526Patrick De Geest12/2016
695714821^14166+14166^1482161526Hans Havermann01/2017
695912^57010-8561525Lelio R Paula05/2013
695810^61525-21357961525Patrick De Geest12/2016
69602^204332-9961511Lelio R Paula08/2011
69612^204323-222161508Yves Minet08/2013
69632^204317-19561506Lelio R Paula08/2011
69623^128910-8661506Lelio R Paula04/2013
69642^204318+7453961506Enzo Doria04/2016
6965(2^204334-3)/114133361505Lelio R Paula03/2012
69662^204297-103609361500Paul Bourdelais11/2012
69673^128880+5861492Lelio R Paula04/2013
69682^204216-11167761476Enzo Doria05/2014
6969(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
69702^204129+20412961449Henri Lifchitz04/2002
69713^128787+2^(128787-1)61448Robert Price05/2016
697211^58999-7861442Lelio R Paula05/2013
69732^204083-11196761436Enzo Doria05/2014
6974(45^37159+1)/4661431Robert Price11/2013
6975677^21702+21702^67761430Norbert Schneider06/2016
697614837^13810+13810^1483761429Hans Havermann02/2017
6977(7*2^204043+1)/3961423Lelio R Paula03/2012
697811^58976-174061418Enzo Doria11/2012
69792^204016-1608561415Enzo Doria04/2013
6980V(379967)61393Serge Batalov03/2015
698143777!3-3^4377761392Robert Price08/2015
69827^72642+8861390Lelio R Paula04/2013
69833^128656+3261385Lelio R Paula04/2013
69842^203916-1749361385Enzo Doria05/2013
69856^78880+2361381Lelio R Paula04/2013
69862^203877-11179961374Enzo Doria05/2014
69872^203867-161561371Lelio R Paula10/2011
69884*10^61367+1961368Robert Price04/2016
6989(19*2^203854+1)/4231961363Lelio R Paula08/2012
69902^203825-1580561358Enzo Doria04/2013
69912^203816-1582561355Enzo Doria04/2013
69925*10^61348+5961349Robert Price09/2016
699321^46395-261345Lelio R Paula08/2013
6994(809*29^41946-165)/2861344Curtis Bright05/2015
69957*6^78826+561340Lelio R Paula09/2014
6996(3^128558+7)/8377316642969661324Lelio R Paula04/2012
69972^203706-11161322Lelio R Paula08/2011
699817567^3094+3094^1756761318Hans Havermann02/2017
69992^203689-3161317Thomas Masser10/2005
7000(11*2^203678-1)/5368961310Lelio R Paula01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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