PRP Records

Probable Primes Top 10000

(174961 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 ?
7001(13*2^207264-1)/362394Lelio R Paula01/2014
7002(79*10^62387-61)/962388Robert Price10/2015
70035^89244+3*2^8924462379Mike Oakes02/2010
70046^80160-1362377Lelio R Paula04/2013
7005(1000121^10391+1)/100012262341Faysal YAtim07/2008
7006(17*10^62328-11)/362329Robert Price07/2015
70072^207023+1171562321Lelio R Paula09/2011
7008(265*10^62298+11)/362300Robert Price03/2017
70092^206947-6962298Lelio R Paula08/2011
70102^206938+2983562295Lelio R Paula02/2013
70112^206911-72687762287Paul Bourdelais03/2013
7012(6883*2^206884-1)/362282Lelio R Paula04/2015
70132^206892-11281762281Enzo Doria06/2014
70143^130523+4662276Lelio R Paula04/2013
70152^206872-11345362275Enzo Doria07/2014
70162^206840-9362266Lelio R Paula08/2011
7017(1017*2^206815-1)/63562258Lelio R Paula04/2015
701896^31406+9562256Norbert Schneider03/2016
7019(2^206824+7)/64621362255Lelio R Paula03/2012
70202^206765-94168362243Paul Bourdelais11/2012
7021(6^79987-1)/562242Paul Bourdelais11/2007
70222^206755-157962240Yves Minet03/2013
702311^59764-582062238Enzo Doria01/2013
70245*10^62233+362234Dmitry Domanov11/2010
70258*3^130421+762228Lelio R Paula04/2014
702619^48661+1062226Lelio R Paula05/2013
7028(17*2^206705+1)/562225Lelio R Paula08/2012
70272^206705-11263562225Enzo Doria06/2014
70293^130403+868062219Lelio R Paula04/2013
703011^59740-711062213Enzo Doria01/2013
70322^206596-16762192Lelio R Paula08/2011
70312^206597+1891562192Lelio R Paula02/2013
70336^79918+13762189Lelio R Paula04/2013
7034lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
70352^206574+61362185Jason Earls04/2008
70363^130328+8062183Lelio R Paula04/2013
7037(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
70382^206550+7681962178Enzo Doria05/2016
703911^59703-2462175Lelio R Paula05/2013
70402^206524+7578162170Enzo Doria04/2016
70412^206506+42762165Henri Lifchitz01/2005
70422^206465+769562153Lelio R Paula02/2013
70432^206464-164962152Yves Minet03/2013
70445^88917+5662151Lelio R Paula04/2013
70452^206444-11156962146Enzo Doria05/2014
70465^88908-4262145Lelio R Paula04/2013
704718^49495-2962130Lelio R Paula05/2013
70483*6^79842-562130Lelio R Paula09/2014
70497*10^62127-1762128Robert Price01/2017
70502^206373+841562125Lelio R Paula02/2013
705120^47745-958362118Enzo Doria03/2013
705241^38516-262118Lelio R Paula08/2013
70532^206332-5869562113Lelio R Paula09/2011
705411^59639-126062108Enzo Doria11/2012
70552^206232-1589362083Enzo Doria04/2013
7056(115*10^62073-1)/362075Serge Batalov12/2014
70572^206206+7579962075Enzo Doria04/2016
7058(74*10^62072+43)/962073Robert Price10/2015
70592^206194-18562071Lelio R Paula08/2011
70606^79757-10362064Lelio R Paula04/2013
7061p(13285)#/2-6462063Robert Price04/2017
7062(29*10^62030-41)/362031Robert Price07/2016
706320^47675-8162027Lelio R Paula06/2013
70643^129972+9862013Lelio R Paula04/2013
70652^205962+362001Donovan Johnson02/2006
70662^205933-205933^261993Henri Lifchitz05/2005
7067(68*10^61991+7)/361993Robert Price03/2016
706820^47641-66361983Enzo Doria03/2013
70693^129861+266061960Lelio R Paula04/2013
7070(55459*2^205800+1)/134561954Lelio R Paula06/2014
707118^49354-9761953Lelio R Paula05/2013
7072(209*10^61947-17)/361949Robert Price05/2017
707414*10^61937+108961939Jens K. Andersen11/2007
7073(11*2^205758-1)/5361939Lelio R Paula01/2014
707520^47600+6361930Lelio R Paula06/2013
707644117!3+24361918Robert Price09/2014
7077(31*2^205677-1)/5961915Lelio R Paula01/2014
7078(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
707920^47575-8161897Lelio R Paula06/2013
7080(58695*2^205593-1)/72761892Lelio R Paula04/2015
708187^31909+8661889Norbert Schneider10/2015
70822^205568+14161883Lelio R Paula08/2011
708310^61868+5892761869Patrick De Geest12/2012
708410^61868-3961868Robert Price05/2011
70855^88505-8861863Lelio R Paula04/2013
7086(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
708713^55528-9861856Lelio R Paula05/2013
708830535!2-861844Robert Price06/2015
708911^59371-120061829Enzo Doria11/2012
70907*2^205370-561824Lelio R Paula04/2014
7091(47*10^61821+403)/961822Robert Price04/2017
70922^205275+769561794Lelio R Paula02/2013
70932^205269+1291561793Lelio R Paula02/2013
7094(47*2^205265+1)/3561792Lelio R Paula04/2015
709519^48309+4061776Lelio R Paula05/2013
70962^205192-407961769Yves Minet06/2011
70972^205184+1609561767Lelio R Paula09/2011
709820^47472-342361763Enzo Doria03/2013
70992^205149-179561757Lelio R Paula09/2011
71002^205110-1761745Lelio R Paula08/2011
7101(2^205025-7)/2561718Lelio R Paula03/2012
710227^43117-26^4311761717Robert Price08/2012
71032^205016+3761716Lelio R Paula08/2011
7104gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
71051263^19898+19898^126361712Serge Batalov05/2014
7106135^28963-13461701Norbert Schneider04/2015
7107(33*2^204966+1)/23434161698Michael Porter01/2015
7108(46*10^61693+17)/961694Robert Price06/2015
7109((((((((((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
71101850^18879+18879^185061681Serge Batalov05/2014
71112^204891-100561679Lelio R Paula09/2011
7112(3^129271-5)/4150661674Lelio R Paula03/2012
711315937^7408+7408^1593761672Hans Havermann02/2017
71145^88216-1261661Lelio R Paula04/2013
711518185^2454+2454^1818561645Hans Havermann01/2017
71172^204767-1586561642Enzo Doria04/2013
7116(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
71187*2^204751-961638Lelio R Paula04/2014
71204*10^61625+2161626Robert Price08/2016
711915369^10226+10226^1536961626Hans Havermann02/2017
71212^204702-1812561622Enzo Doria05/2013
71225*3^129146+861620Lelio R Paula04/2014
71232^204673+12961613Lelio R Paula08/2011
712418^49079+9761608Lelio R Paula05/2013
7125106^30416+10561602Norbert Schneider12/2016
71262^204590-3361588Lelio R Paula08/2011
71272^204586-11197561587Enzo Doria06/2014
71282^204580-1607761585Enzo Doria04/2013
71292^204574-1604161583Enzo Doria04/2013
713015^52358+5661578Lelio R Paula05/2013
7131(28*10^61574+11)/361575Robert Price11/2015
71322^204516-1749361566Enzo Doria05/2013
71334*5^88076-361564Lelio R Paula09/2014
713411^59110-252061557Enzo Doria12/2012
71352^204477-5869561554Lelio R Paula09/2011
713612^57026-7361542Lelio R Paula05/2013
713717^50013+9061539Lelio R Paula05/2013
713856^35201-55^3520161538Robert Price10/2013
71398*7^72810+561533Lelio R Paula09/2014
7141204^26641-203^2664161531Jean-Louis Charton08/2009
714043867!3-656161531Robert Price11/2015
714410^61525+9^(61525-1)61526Robert Price03/2016
714210^61525+6225761526Patrick De Geest12/2016
714314821^14166+14166^1482161526Hans Havermann01/2017
714612^57010-8561525Lelio R Paula05/2013
714510^61525-21357961525Patrick De Geest12/2016
71472^204332-9961511Lelio R Paula08/2011
71482^204323-222161508Yves Minet08/2013
71502^204317-19561506Lelio R Paula08/2011
71493^128910-8661506Lelio R Paula04/2013
71512^204318+7453961506Enzo Doria04/2016
7152(2^204334-3)/114133361505Lelio R Paula03/2012
71532^204297-103609361500Paul Bourdelais11/2012
71543^128880+5861492Lelio R Paula04/2013
71552^204216-11167761476Enzo Doria05/2014
7156(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
71572^204129+20412961449Henri Lifchitz04/2002
71583^128787+2^(128787-1)61448Robert Price05/2016
715911^58999-7861442Lelio R Paula05/2013
71602^204083-11196761436Enzo Doria05/2014
7161(45^37159+1)/4661431Robert Price11/2013
7162677^21702+21702^67761430Norbert Schneider06/2016
716314837^13810+13810^1483761429Hans Havermann02/2017
7164(7*2^204043+1)/3961423Lelio R Paula03/2012
716511^58976-174061418Enzo Doria11/2012
71662^204016-1608561415Enzo Doria04/2013
7167V(379967)61393Serge Batalov03/2015
716843777!3-3^4377761392Robert Price08/2015
71697^72642+8861390Lelio R Paula04/2013
71703^128656+3261385Lelio R Paula04/2013
71712^203916-1749361385Enzo Doria05/2013
71726^78880+2361381Lelio R Paula04/2013
71732^203877-11179961374Enzo Doria05/2014
71742^203867-161561371Lelio R Paula10/2011
71754*10^61367+1961368Robert Price04/2016
7176(19*2^203854+1)/4231961363Lelio R Paula08/2012
71772^203825-1580561358Enzo Doria04/2013
71782^203816-1582561355Enzo Doria04/2013
71795*10^61348+5961349Robert Price09/2016
718021^46395-261345Lelio R Paula08/2013
7181(809*29^41946-165)/2861344Curtis Bright05/2015
71827*6^78826+561340Lelio R Paula09/2014
7183(3^128558+7)/8377316642969661324Lelio R Paula04/2012
71842^203706-11161322Lelio R Paula08/2011
718517567^3094+3094^1756761318Hans Havermann02/2017
71862^203689-3161317Thomas Masser10/2005
7187(11*2^203678-1)/5368961310Lelio R Paula01/2014
71892^203642+3961303Lelio R Paula08/2011
7188floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
719011^58849-604061285Enzo Doria02/2013
719143694!3-361264Robert Price10/2014
719258*(10^(3*20420)-1)/111-161260Robert Price10/2014
71932^203490+1290961257Lelio R Paula10/2011
7194(16*10^61251-31)/361252Robert Price03/2016
719520^47077-570361249Enzo Doria03/2013
71962^203434-11308161240Enzo Doria07/2014
71985^87606+461234Wojciech Florek11/2005
71972^203412-16761234Lelio R Paula08/2011
72002^203402+108961231Lelio R Paula10/2011
7199(8*10^61230+67)/361231Robert Price01/2017
7201(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
72021265^19732+19732^126561211Serge Batalov05/2014
72032^203330+14561209Lelio R Paula08/2011
72046^78647-13761200Lelio R Paula04/2013
720585^31718+8461198Norbert Schneider10/2015
720611^58763-27061196Enzo Doria07/2012
72072^203285-11232161195Enzo Doria06/2014
72082^203253-99514361186Paul Bourdelais11/2012
720915319^9862+9862^1531961184Hans Havermann07/2016
72107^72395-4461181Lelio R Paula04/2013
72115*2^203176-761163Lelio R Paula04/2014
72137^72358+5461150Lelio R Paula04/2013
72122^203133-11177561150Enzo Doria05/2014
7214(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
72152^203112-1800961143Enzo Doria05/2013
721643607!3+72961129Robert Price09/2014
72172^203065-11485361129Enzo Doria05/2015
72183^128111+19661125Lelio R Paula04/2013
7219128^29007+29007^12861124Serge Batalov05/2014
722022355*2^203009-361117Donovan Johnson03/2004
72212^203018+3361115Lelio R Paula08/2011
72222^203017-161561115Lelio R Paula10/2011
722316697^4570+4570^1669761110Hans Havermann12/2016
72242^202998-1724161109Enzo Doria05/2013
722520^46964+9361102Lelio R Paula06/2013
7226(55*10^61097-1)/961098Ray Chandler02/2012
722720^46960-546361097Enzo Doria03/2013
7228(11*10^61095+49)/361096Robert Price05/2016
72292^202934-595561090Lelio R Paula10/2011
723019^47772-6861089Lelio R Paula05/2013
72312^202877-49942361073Paul Bourdelais03/2013
72322^202763-1712561038Enzo Doria05/2013
7233(23*2^202756+1)/961037Lelio R Paula03/2012
723414788^13355+13355^1478861011Hans Havermann12/2016
723516069^6258+6258^1606961005Hans Havermann12/2016
72365^87276-1433661004Enzo Doria02/2013
723750^35899-49^3589960992Robert Price12/2012
72382^202599-304960989Yves Minet10/2014
72392^202535-11157160970Enzo Doria05/2014
724010^60959+5760960Patrick De Geest12/2008
724210^60959-6095960959Henri Lifchitz08/2002
724110^60959-2917760959Patrick De Geest08/2008
72435^87206+4^(87206+1)60955Robert Price07/2016
72442^202476-1590960952Enzo Doria04/2013
72452^202472-1751360951Enzo Doria05/2013
724614858^12651+12651^1485860950Hans Havermann12/2016
72472^202389-5869560926Lelio R Paula09/2011
72483^127597-3460880Lelio R Paula04/2013
724915088^10831+10831^1508860876Hans Havermann12/2016
72502^202198-11326160868Enzo Doria07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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