PRP Records

Probable Primes Top 10000

(205869 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 ?
7501(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
7502(2^208534+7)/905962772Lelio R Paula03/2012
7503(13^56333+1)/1462751Paul Bourdelais03/2010
750410^62750+5762751Robert Price01/2011
750510^62750-26742962750Patrick De Geest01/2013
75062^208427-6962743Lelio R Paula08/2011
75072^208421-11177562741Enzo Doria05/2014
75082^208404-11207962736Enzo Doria06/2014
75092^208343-222162718Yves Minet08/2013
75102^208335+51362716Lelio R Paula10/2011
7512(2^208328+47)/362713Lelio R Paula03/2012
751111^60220-204062713Enzo Doria12/2012
75132^208292+8162703Henri Lifchitz10/2005
751415013^15012-1501262698Henri Lifchitz10/2014
75152^208271-11274762696Enzo Doria06/2014
751611^60202-438062694Enzo Doria01/2013
7517(3^131403-4)/15762693Lelio R Paula04/2012
75182^208127-12666762653Paul Bourdelais01/2012
751971^33843+262653Lelio R Paula05/2013
7520(3^131325+7)/106685062652Lelio R Paula04/2012
75212^208019+11962620Lelio R Paula08/2011
7522(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
752311^60126-1137062615Enzo Doria12/2012
75242^207976-248962608Yves Minet07/2014
7525(22699*2^207945+1)/28170962597Lelio R Paula06/2014
75264*21^47335+20562588Curtis Bright05/2015
752715^53210+862580Lelio R Paula05/2013
75282^207865+2962574Henri Lifchitz08/2005
752915^53199-3862567Lelio R Paula05/2013
7530(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
75312^207782+5890562549Lelio R Paula10/2011
7532(2^207748-3)/843762535Lelio R Paula03/2012
7533(2^207711+5)/1362527Lelio R Paula03/2012
7534(268*10^62523-1)/362525Robert Price10/2017
753510^62523+6362524Robert Price01/2011
753610^62523-29237362523Patrick De Geest01/2013
75372^207691+1155*20769162522Henri Lifchitz02/2005
7538(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
75392^207626-11215762502Enzo Doria06/2014
75403^130987+5262497Lelio R Paula04/2013
75418*6^80299-762486Lelio R Paula09/2014
754211^59997-267062481Enzo Doria12/2012
754393^31740+262480Lelio R Paula05/2013
7544(10^62451+119)/362451Serge Batalov12/2014
7545(2^207443+47)/764562443Lelio R Paula03/2012
75462^207364+11562423Lelio R Paula08/2011
75473^130815-4662415Lelio R Paula04/2013
7548(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
754920^47968-948362408Enzo Doria03/2013
7550(10^62402+101)/362402Robert Price04/2016
7551(13*2^207264-1)/362394Lelio R Paula01/2014
7552(79*10^62387-61)/962388Robert Price10/2015
75535^89244+3*2^8924462379Mike Oakes02/2010
75546^80160-1362377Lelio R Paula04/2013
7555(7*10^62362+53)/362363Robert Price10/2017
7556(1000121^10391+1)/100012262341Faysal YAtim07/2008
7557(17*10^62328-11)/362329Robert Price07/2015
75582^207023+1171562321Lelio R Paula09/2011
7559(265*10^62298+11)/362300Robert Price03/2017
75602^206947-6962298Lelio R Paula08/2011
75612^206938+2983562295Lelio R Paula02/2013
75622^206911-72687762287Paul Bourdelais03/2013
7563(6883*2^206884-1)/362282Lelio R Paula04/2015
75642^206892-11281762281Enzo Doria06/2014
7565(7*10^62278+113)/362279Robert Price10/2017
75663^130523+4662276Lelio R Paula04/2013
75672^206872-11345362275Enzo Doria07/2014
75682^206840-9362266Lelio R Paula08/2011
7569(1017*2^206815-1)/63562258Lelio R Paula04/2015
757096^31406+9562256Norbert Schneider03/2016
7571(2^206824+7)/64621362255Lelio R Paula03/2012
75722^206765-94168362243Paul Bourdelais11/2012
7573(6^79987-1)/562242Paul Bourdelais11/2007
75742^206755-157962240Yves Minet03/2013
757511^59764-582062238Enzo Doria01/2013
75765*10^62233+362234Dmitry Domanov11/2010
75778*3^130421+762228Lelio R Paula04/2014
757819^48661+1062226Lelio R Paula05/2013
7580(17*2^206705+1)/562225Lelio R Paula08/2012
75792^206705-11263562225Enzo Doria06/2014
75813^130403+868062219Lelio R Paula04/2013
758211^59740-711062213Enzo Doria01/2013
75842^206596-16762192Lelio R Paula08/2011
75832^206597+1891562192Lelio R Paula02/2013
75856^79918+13762189Lelio R Paula04/2013
7586lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
75872^206574+61362185Jason Earls04/2008
75883^130328+8062183Lelio R Paula04/2013
7589(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
75902^206550+7681962178Enzo Doria05/2016
759111^59703-2462175Lelio R Paula05/2013
75922^206524+7578162170Enzo Doria04/2016
75932^206506+42762165Henri Lifchitz01/2005
75942^206465+769562153Lelio R Paula02/2013
75952^206464-164962152Yves Minet03/2013
75965^88917+5662151Lelio R Paula04/2013
75972^206444-11156962146Enzo Doria05/2014
75985^88908-4262145Lelio R Paula04/2013
759918^49495-2962130Lelio R Paula05/2013
76003*6^79842-562130Lelio R Paula09/2014
76017*10^62127-1762128Robert Price01/2017
76022^206373+841562125Lelio R Paula02/2013
760320^47745-958362118Enzo Doria03/2013
760441^38516-262118Lelio R Paula08/2013
76052^206332-5869562113Lelio R Paula09/2011
760611^59639-126062108Enzo Doria11/2012
76072^206232-1589362083Enzo Doria04/2013
7608(115*10^62073-1)/362075Serge Batalov12/2014
76092^206206+7579962075Enzo Doria04/2016
7610(74*10^62072+43)/962073Robert Price10/2015
76112^206194-18562071Lelio R Paula08/2011
76126^79757-10362064Lelio R Paula04/2013
7613p(13285)#/2-6462063Robert Price04/2017
7614(29*10^62030-41)/362031Robert Price07/2016
761520^47675-8162027Lelio R Paula06/2013
76163^129972+9862013Lelio R Paula04/2013
76172^205962+362001Donovan Johnson02/2006
76182^205933-205933^261993Henri Lifchitz05/2005
7619(68*10^61991+7)/361993Robert Price03/2016
762020^47641-66361983Enzo Doria03/2013
76213^129861+266061960Lelio R Paula04/2013
7622(55459*2^205800+1)/134561954Lelio R Paula06/2014
762318^49354-9761953Lelio R Paula05/2013
7624(209*10^61947-17)/361949Robert Price05/2017
762614*10^61937+108961939Jens K. Andersen11/2007
7625(11*2^205758-1)/5361939Lelio R Paula01/2014
762720^47600+6361930Lelio R Paula06/2013
7628(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
762944117!3+24361918Robert Price09/2014
7630(31*2^205677-1)/5961915Lelio R Paula01/2014
7631(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
763220^47575-8161897Lelio R Paula06/2013
7633(58695*2^205593-1)/72761892Lelio R Paula04/2015
763487^31909+8661889Norbert Schneider10/2015
76352^205568+14161883Lelio R Paula08/2011
763610^61868+5892761869Patrick De Geest12/2012
763710^61868-3961868Robert Price05/2011
76395^88505-8861863Lelio R Paula04/2013
7638(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
764013^55528-9861856Lelio R Paula05/2013
7641(55^35543-1)/5461856Paul Bourdelais08/2017
764230535!2-861844Robert Price06/2015
764311^59371-120061829Enzo Doria11/2012
76447*2^205370-561824Lelio R Paula04/2014
7645(47*10^61821+403)/961822Robert Price04/2017
76462^205275+769561794Lelio R Paula02/2013
76472^205269+1291561793Lelio R Paula02/2013
7648(47*2^205265+1)/3561792Lelio R Paula04/2015
764919^48309+4061776Lelio R Paula05/2013
7650(424*10^61770-1)/961772Robert Price11/2017
76512^205192-407961769Yves Minet06/2011
76522^205184+1609561767Lelio R Paula09/2011
765320^47472-342361763Enzo Doria03/2013
7654(17*10^61760-89)/961761Robert Price11/2017
76552^205149-179561757Lelio R Paula09/2011
76562^205110-1761745Lelio R Paula08/2011
7657(373^24007+1)/37461737Eric Chen10/2017
7658(2^205025-7)/2561718Lelio R Paula03/2012
765927^43117-26^4311761717Robert Price08/2012
76602^205016+3761716Lelio R Paula08/2011
7661gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
76621263^19898+19898^126361712Serge Batalov05/2014
7663135^28963-13461701Norbert Schneider04/2015
7664(33*2^204966+1)/23434161698Michael Porter01/2015
7665(7*10^61696+167)/361696Robert Kinser10/2017
7666(46*10^61693+17)/961694Robert Price06/2015
7667((((((((((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
76681850^18879+18879^185061681Serge Batalov05/2014
76702^204891-100561679Lelio R Paula09/2011
7669151^28306-261679Lelio R Paula10/2017
7671(3^129271-5)/4150661674Lelio R Paula03/2012
767215937^7408+7408^1593761672Hans Havermann02/2017
76735^88216-1261661Lelio R Paula04/2013
767418185^2454+2454^1818561645Hans Havermann01/2017
76762^204767-1586561642Enzo Doria04/2013
7675(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
76777*2^204751-961638Lelio R Paula04/2014
76784*10^61625+2161626Robert Price08/2016
767915369^10226+10226^1536961626Hans Havermann02/2017
76802^204702-1812561622Enzo Doria05/2013
76815*3^129146+861620Lelio R Paula04/2014
76822^204673+12961613Lelio R Paula08/2011
768318^49079+9761608Lelio R Paula05/2013
7684106^30416+10561602Norbert Schneider12/2016
76852^204590-3361588Lelio R Paula08/2011
76862^204586-11197561587Enzo Doria06/2014
76872^204580-1607761585Enzo Doria04/2013
76882^204574-1604161583Enzo Doria04/2013
768915^52358+5661578Lelio R Paula05/2013
7690(28*10^61574+11)/361575Robert Price11/2015
76912^204516-1749361566Enzo Doria05/2013
76924*5^88076-361564Lelio R Paula09/2014
769311^59110-252061557Enzo Doria12/2012
76942^204477-5869561554Lelio R Paula09/2011
769512^57026-7361542Lelio R Paula05/2013
769617^50013+9061539Lelio R Paula05/2013
769756^35201-55^3520161538Robert Price10/2013
76988*7^72810+561533Lelio R Paula09/2014
7700204^26641-203^2664161531Jean-Louis Charton08/2009
769943867!3-656161531Robert Price11/2015
770110^61525+9^(61525-1)61526Robert Price03/2016
770210^61525+6225761526Patrick De Geest12/2016
770314821^14166+14166^1482161526Hans Havermann01/2017
770512^57010-8561525Lelio R Paula05/2013
770410^61525-21357961525Patrick De Geest12/2016
77062^204332-9961511Lelio R Paula08/2011
77072^204323-222161508Yves Minet08/2013
77092^204317-19561506Lelio R Paula08/2011
77083^128910-8661506Lelio R Paula04/2013
77102^204318+7453961506Enzo Doria04/2016
7711(2^204334-3)/114133361505Lelio R Paula03/2012
77122^204297-103609361500Paul Bourdelais11/2012
77133^128880+5861492Lelio R Paula04/2013
77142^204216-11167761476Enzo Doria05/2014
7715(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
77162^204129+20412961449Henri Lifchitz04/2002
77173^128787+2^(128787-1)61448Robert Price05/2016
771811^58999-7861442Lelio R Paula05/2013
77192^204083-11196761436Enzo Doria05/2014
7720(45^37159+1)/4661431Robert Price11/2013
7721677^21702+21702^67761430Norbert Schneider06/2016
772214837^13810+13810^1483761429Hans Havermann02/2017
7723(7*2^204043+1)/3961423Lelio R Paula03/2012
772411^58976-174061418Enzo Doria11/2012
77252^204016-1608561415Enzo Doria04/2013
7726V(379967)61393Serge Batalov03/2015
772743777!3-3^4377761392Robert Price08/2015
77287^72642+8861390Lelio R Paula04/2013
77293^128656+3261385Lelio R Paula04/2013
77302^203916-1749361385Enzo Doria05/2013
77316^78880+2361381Lelio R Paula04/2013
7732(388*10^61374-1)/961376Robert Price11/2017
77332^203877-11179961374Enzo Doria05/2014
77342^203867-161561371Lelio R Paula10/2011
77354*10^61367+1961368Robert Price04/2016
7736(19*2^203854+1)/4231961363Lelio R Paula08/2012
7737L(293659)/7652812271961361Serge Batalov07/2017
77382^203825-1580561358Enzo Doria04/2013
77392^203816-1582561355Enzo Doria04/2013
77405*10^61348+5961349Robert Price09/2016
774121^46395-261345Lelio R Paula08/2013
7742(809*29^41946-165)/2861344Curtis Bright05/2015
77437*6^78826+561340Lelio R Paula09/2014
7744(3^128558+7)/8377316642969661324Lelio R Paula04/2012
77452^203706-11161322Lelio R Paula08/2011
774617567^3094+3094^1756761318Hans Havermann02/2017
77472^203689-3161317Thomas Masser10/2005
7748(11*2^203678-1)/5368961310Lelio R Paula01/2014
77502^203642+3961303Lelio R Paula08/2011
7749floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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