PRP Records

Probable Primes Top 10000

(255244 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 (> 50000) Who ? When ?
87512^208292+8162703Henri Lifchitz10/2005
875215013^15012-1501262698Henri Lifchitz10/2014
87532^208271-11274762696Enzo Doria06/2014
875411^60202-438062694Enzo Doria01/2013
8755(3^131403-4)/15762693Lelio R Paula04/2012
875620349^1202+1202^2034962673Hans Havermann06/2019
87572^208127-12666762653Paul Bourdelais01/2012
875871^33843+262653Lelio R Paula05/2013
8759(3^131325+7)/106685062652Lelio R Paula04/2012
87602^208019+11962620Lelio R Paula08/2011
8761(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
876211^60126-1137062615Enzo Doria12/2012
87632^207976-248962608Yves Minet07/2014
8764(22699*2^207945+1)/28170962597Lelio R Paula06/2014
87654*21^47335+20562588Curtis Bright05/2015
876615^53210+862580Lelio R Paula05/2013
876716529^6106+6106^1652962575Hans Havermann06/2019
87682^207865+2962574Henri Lifchitz08/2005
876915^53199-3862567Lelio R Paula05/2013
8770(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
87712^207782+5890562549Lelio R Paula10/2011
8772(2^207748-3)/843762535Lelio R Paula03/2012
8773(2^207711+5)/1362527Lelio R Paula03/2012
8774(268*10^62523-1)/362525Robert Price10/2017
877510^62523+6362524Robert Price01/2011
877610^62523-29237362523Patrick De Geest01/2013
87772^207691+1155*20769162522Henri Lifchitz02/2005
8778(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
87792^207626-11215762502Enzo Doria06/2014
87803^130987+5262497Lelio R Paula04/2013
87818*6^80299-762486Lelio R Paula09/2014
878211^59997-267062481Enzo Doria12/2012
878393^31740+262480Lelio R Paula05/2013
8784(10^62451+119)/362451Serge Batalov12/2014
8785(2^207443+47)/764562443Lelio R Paula03/2012
878616150^7347+7347^1615062438Hans Havermann06/2019
87872^207364+11562423Lelio R Paula08/2011
87883^130815-4662415Lelio R Paula04/2013
8789(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
879020^47968-948362408Enzo Doria03/2013
8791(10^62402+101)/362402Robert Price04/2016
8792(13*2^207264-1)/362394Lelio R Paula01/2014
8793(79*10^62387-61)/962388Robert Price10/2015
87945^89244+3*2^8924462379Mike Oakes02/2010
87956^80160-1362377Lelio R Paula04/2013
8796(7*10^62362+53)/362363Robert Price10/2017
8797(1000121^10391+1)/100012262341Faysal YAtim07/2008
8798(17*10^62328-11)/362329Robert Price07/2015
87992^207023+1171562321Lelio R Paula09/2011
8800(265*10^62298+11)/362300Robert Price03/2017
88012^206947-6962298Lelio R Paula08/2011
88022^206938+2983562295Lelio R Paula02/2013
88032^206911-72687762287Paul Bourdelais03/2013
8804(6883*2^206884-1)/362282Lelio R Paula04/2015
88052^206892-11281762281Enzo Doria06/2014
8806(7*10^62278+113)/362279Robert Price10/2017
88073^130523+4662276Lelio R Paula04/2013
88082^206872-11345362275Enzo Doria07/2014
88092^206840-9362266Lelio R Paula08/2011
8810(1017*2^206815-1)/63562258Lelio R Paula04/2015
881196^31406+9562256Norbert Schneider03/2016
8812(2^206824+7)/64621362255Lelio R Paula03/2012
88132^206765-94168362243Paul Bourdelais11/2012
8814(6^79987-1)/562242Paul Bourdelais11/2007
88152^206755-157962240Yves Minet03/2013
881611^59764-582062238Enzo Doria01/2013
88175*10^62233+362234Dmitry Domanov11/2010
88188*3^130421+762228Lelio R Paula04/2014
881919^48661+1062226Lelio R Paula05/2013
8820(17*2^206705+1)/562225Lelio R Paula08/2012
88212^206705-11263562225Enzo Doria06/2014
88223^130403+868062219Lelio R Paula04/2013
882311^59740-711062213Enzo Doria01/2013
882415113^13068+13068^1511362209Hans Havermann06/2019
88262^206596-16762192Lelio R Paula08/2011
88252^206597+1891562192Lelio R Paula02/2013
88276^79918+13762189Lelio R Paula04/2013
8828lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
88292^206574+61362185Jason Earls04/2008
88303^130328+8062183Lelio R Paula04/2013
8831(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
88322^206550+7681962178Enzo Doria05/2016
883311^59703-2462175Lelio R Paula05/2013
88342^206524+7578162170Enzo Doria04/2016
88352^206506+42762165Henri Lifchitz01/2005
88362^206465+769562153Lelio R Paula02/2013
88372^206464-164962152Yves Minet03/2013
88385^88917+5662151Lelio R Paula04/2013
88392^206444-11156962146Enzo Doria05/2014
88405^88908-4262145Lelio R Paula04/2013
884118^49495-2962130Lelio R Paula05/2013
88423*6^79842-562130Lelio R Paula09/2014
88437*10^62127-1762128Robert Price01/2017
88442^206373+841562125Lelio R Paula02/2013
884520^47745-958362118Enzo Doria03/2013
884641^38516-262118Lelio R Paula08/2013
88472^206332-5869562113Lelio R Paula09/2011
884811^59639-126062108Enzo Doria11/2012
884914898^14719+14719^1489862094Hans Havermann06/2019
88502^206232-1589362083Enzo Doria04/2013
8851(115*10^62073-1)/362075Serge Batalov12/2014
88522^206206+7579962075Enzo Doria04/2016
8853(74*10^62072+43)/962073Robert Price10/2015
88542^206194-18562071Lelio R Paula08/2011
88556^79757-10362064Lelio R Paula04/2013
8856p(13285)#/2-6462063Robert Price04/2017
8857(29*10^62030-41)/362031Robert Price07/2016
885820^47675-8162027Lelio R Paula06/2013
88593^129972+9862013Lelio R Paula04/2013
88602^205962+362001Donovan Johnson02/2006
88612^205933-205933^261993Henri Lifchitz05/2005
8862(68*10^61991+7)/361993Robert Price03/2016
886320^47641-66361983Enzo Doria03/2013
886416737^5036+5036^1673761962Hans Havermann06/2019
88653^129861+266061960Lelio R Paula04/2013
8866(55459*2^205800+1)/134561954Lelio R Paula06/2014
886718^49354-9761953Lelio R Paula05/2013
8868(209*10^61947-17)/361949Robert Price05/2017
887014*10^61937+108961939Jens K. Andersen11/2007
8869(11*2^205758-1)/5361939Lelio R Paula01/2014
887120^47600+6361930Lelio R Paula06/2013
887220487^1054+1054^2048761929Hans Havermann06/2019
8873(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
887415267^11374+11374^1526761922Hans Havermann06/2019
887544117!3+24361918Robert Price09/2014
8876(31*2^205677-1)/5961915Lelio R Paula01/2014
887757269!4-51261905Robert Price11/2019
8878(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
887920^47575-8161897Lelio R Paula06/2013
8880(58695*2^205593-1)/72761892Lelio R Paula04/2015
888187^31909+8661889Norbert Schneider10/2015
88822^205568+14161883Lelio R Paula08/2011
888310^61868+5892761869Patrick De Geest12/2012
888410^61868-3961868Robert Price05/2011
88855^88505-8861863Lelio R Paula04/2013
8886(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
888813^55528-9861856Lelio R Paula05/2013
8887(55^35543-1)/5461856Paul Bourdelais08/2017
888930535!2-861844Robert Price06/2015
889011^59371-120061829Enzo Doria11/2012
88917*2^205370-561824Lelio R Paula04/2014
8892(47*10^61821+403)/961822Robert Price04/2017
88932^205275+769561794Lelio R Paula02/2013
88942^205269+1291561793Lelio R Paula02/2013
8895(47*2^205265+1)/3561792Lelio R Paula04/2015
889619^48309+4061776Lelio R Paula05/2013
8897(424*10^61770-1)/961772Robert Price11/2017
88982^205192-407961769Yves Minet06/2011
88992^205184+1609561767Lelio R Paula09/2011
890020^47472-342361763Enzo Doria03/2013
8901(17*10^61760-89)/961761Robert Price11/2017
89022^205149-179561757Lelio R Paula09/2011
89032^205110-1761745Lelio R Paula08/2011
8904(373^24007+1)/37461737Eric Chen10/2017
890514734^14811-14811^1473461737Norbert Schneider06/2019
8906(2^205025-7)/2561718Lelio R Paula03/2012
890727^43117-26^4311761717Robert Price08/2012
89082^205016+3761716Lelio R Paula08/2011
8909gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
89101263^19898+19898^126361712Serge Batalov05/2014
8911135^28963-13461701Norbert Schneider04/2015
8912(33*2^204966+1)/23434161698Michael Porter01/2015
8913(7*10^61696+167)/361696Robert Kinser10/2017
8914(46*10^61693+17)/961694Robert Price06/2015
8915((((((((((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
89161850^18879+18879^185061681Serge Batalov05/2014
89182^204891-100561679Lelio R Paula09/2011
8917151^28306-261679Lelio R Paula10/2017
8919(3^129271-5)/4150661674Lelio R Paula03/2012
892015937^7408+7408^1593761672Hans Havermann02/2017
89215^88216-1261661Lelio R Paula04/2013
892218185^2454+2454^1818561645Hans Havermann01/2017
89242^204767-1586561642Enzo Doria04/2013
8923(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
89257*2^204751-961638Lelio R Paula04/2014
89264*10^61625+2161626Robert Price08/2016
892715369^10226+10226^1536961626Hans Havermann02/2017
89282^204702-1812561622Enzo Doria05/2013
89295*3^129146+861620Lelio R Paula04/2014
89302^204673+12961613Lelio R Paula08/2011
893118^49079+9761608Lelio R Paula05/2013
8932106^30416+10561602Norbert Schneider12/2016
89332^204590-3361588Lelio R Paula08/2011
89342^204586-11197561587Enzo Doria06/2014
89352^204580-1607761585Enzo Doria04/2013
89362^204574-1604161583Enzo Doria04/2013
893715^52358+5661578Lelio R Paula05/2013
8938(28*10^61574+11)/361575Robert Price11/2015
89392^204516-1749361566Enzo Doria05/2013
89404*5^88076-361564Lelio R Paula09/2014
894111^59110-252061557Enzo Doria12/2012
89422^204477-5869561554Lelio R Paula09/2011
894312^57026-7361542Lelio R Paula05/2013
8944(257^25537+1)/25861541Richard Fischer04/2018
894517^50013+9061539Lelio R Paula05/2013
894656^35201-55^3520161538Robert Price10/2013
89478*7^72810+561533Lelio R Paula09/2014
8949204^26641-203^2664161531Jean-Louis Charton08/2009
894843867!3-656161531Robert Price11/2015
895010^61525+9^(61525-1)61526Robert Price03/2016
895110^61525+6225761526Patrick De Geest12/2016
895214821^14166+14166^1482161526Hans Havermann01/2017
895412^57010-8561525Lelio R Paula05/2013
895310^61525-21357961525Patrick De Geest12/2016
89552^204332-9961511Lelio R Paula08/2011
89562^204323-222161508Yves Minet08/2013
89582^204317-19561506Lelio R Paula08/2011
89573^128910-8661506Lelio R Paula04/2013
89592^204318+7453961506Enzo Doria04/2016
8960(2^204334-3)/114133361505Lelio R Paula03/2012
89612^204297-103609361500Paul Bourdelais11/2012
89623^128880+5861492Lelio R Paula04/2013
89632^204216-11167761476Enzo Doria05/2014
896413262^14909-14909^1326261464Norbert Schneider08/2019
8965(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
896614677^14750-14750^1467761458Norbert Schneider05/2019
89672^204129+20412961449Henri Lifchitz04/2002
89683^128787+2^(128787-1)61448Robert Price05/2016
896911^58999-7861442Lelio R Paula05/2013
89702^204083-11196761436Enzo Doria05/2014
8971(45^37159+1)/4661431Robert Price11/2013
8972677^21702+21702^67761430Norbert Schneider06/2016
897314837^13810+13810^1483761429Hans Havermann02/2017
8974(7*2^204043+1)/3961423Lelio R Paula03/2012
897511^58976-174061418Enzo Doria11/2012
89762^204016-1608561415Enzo Doria04/2013
8977V(379967)61393Serge Batalov03/2015
897843777!3-3^4377761392Robert Price08/2015
89797^72642+8861390Lelio R Paula04/2013
89803^128656+3261385Lelio R Paula04/2013
89812^203916-1749361385Enzo Doria05/2013
89826^78880+2361381Lelio R Paula04/2013
8983(388*10^61374-1)/961376Robert Price11/2017
89842^203877-11179961374Enzo Doria05/2014
89852^203867-161561371Lelio R Paula10/2011
89864*10^61367+1961368Robert Price04/2016
8987(19*2^203854+1)/4231961363Lelio R Paula08/2012
898812543^14972-14972^1254361362Norbert Schneider10/2019
8989L(293659)/7652812271961361Serge Batalov07/2017
89902^203825-1580561358Enzo Doria04/2013
89912^203816-1582561355Enzo Doria04/2013
89925*10^61348+5961349Robert Price09/2016
899321^46395-261345Lelio R Paula08/2013
8994(809*29^41946-165)/2861344Curtis Bright05/2015
89957*6^78826+561340Lelio R Paula09/2014
8996(3^128558+7)/8377316642969661324Lelio R Paula04/2012
89972^203706-11161322Lelio R Paula08/2011
899817567^3094+3094^1756761318Hans Havermann02/2017
89992^203689-3161317Thomas Masser10/2005
9000(11*2^203678-1)/5368961310Lelio R Paula01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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