PRP Records

Probable Primes Top 10000

(173006 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 ?
70012^206506+42762165Henri Lifchitz01/2005
70022^206465+769562153Lelio R Paula02/2013
70032^206464-164962152Yves Minet03/2013
70045^88917+5662151Lelio R Paula04/2013
70052^206444-11156962146Enzo Doria05/2014
70065^88908-4262145Lelio R Paula04/2013
700718^49495-2962130Lelio R Paula05/2013
70083*6^79842-562130Lelio R Paula09/2014
70097*10^62127-1762128Robert Price01/2017
70102^206373+841562125Lelio R Paula02/2013
701120^47745-958362118Enzo Doria03/2013
701241^38516-262118Lelio R Paula08/2013
70132^206332-5869562113Lelio R Paula09/2011
701411^59639-126062108Enzo Doria11/2012
70152^206232-1589362083Enzo Doria04/2013
7016(115*10^62073-1)/362075Serge Batalov12/2014
70172^206206+7579962075Enzo Doria04/2016
7018(74*10^62072+43)/962073Robert Price10/2015
70192^206194-18562071Lelio R Paula08/2011
70206^79757-10362064Lelio R Paula04/2013
7021p(13285)#/2-6462063Robert Price04/2017
7022(29*10^62030-41)/362031Robert Price07/2016
702320^47675-8162027Lelio R Paula06/2013
70243^129972+9862013Lelio R Paula04/2013
70252^205962+362001Donovan Johnson02/2006
70262^205933-205933^261993Henri Lifchitz05/2005
7027(68*10^61991+7)/361993Robert Price03/2016
702820^47641-66361983Enzo Doria03/2013
70293^129861+266061960Lelio R Paula04/2013
7030(55459*2^205800+1)/134561954Lelio R Paula06/2014
703118^49354-9761953Lelio R Paula05/2013
7032(209*10^61947-17)/361949Robert Price05/2017
703414*10^61937+108961939Jens K. Andersen11/2007
7033(11*2^205758-1)/5361939Lelio R Paula01/2014
703520^47600+6361930Lelio R Paula06/2013
703644117!3+24361918Robert Price09/2014
7037(31*2^205677-1)/5961915Lelio R Paula01/2014
7038(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
703920^47575-8161897Lelio R Paula06/2013
7040(58695*2^205593-1)/72761892Lelio R Paula04/2015
704187^31909+8661889Norbert Schneider10/2015
70422^205568+14161883Lelio R Paula08/2011
704310^61868+5892761869Patrick De Geest12/2012
704410^61868-3961868Robert Price05/2011
70455^88505-8861863Lelio R Paula04/2013
7046(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
704713^55528-9861856Lelio R Paula05/2013
704830535!2-861844Robert Price06/2015
704911^59371-120061829Enzo Doria11/2012
70507*2^205370-561824Lelio R Paula04/2014
7051(47*10^61821+403)/961822Robert Price04/2017
70522^205275+769561794Lelio R Paula02/2013
70532^205269+1291561793Lelio R Paula02/2013
7054(47*2^205265+1)/3561792Lelio R Paula04/2015
705519^48309+4061776Lelio R Paula05/2013
70562^205192-407961769Yves Minet06/2011
70572^205184+1609561767Lelio R Paula09/2011
705820^47472-342361763Enzo Doria03/2013
70592^205149-179561757Lelio R Paula09/2011
70602^205110-1761745Lelio R Paula08/2011
7061(2^205025-7)/2561718Lelio R Paula03/2012
706227^43117-26^4311761717Robert Price08/2012
70632^205016+3761716Lelio R Paula08/2011
7064gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
70651263^19898+19898^126361712Serge Batalov05/2014
7066135^28963-13461701Norbert Schneider04/2015
7067(33*2^204966+1)/23434161698Michael Porter01/2015
7068(46*10^61693+17)/961694Robert Price06/2015
7069((((((((((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
70701850^18879+18879^185061681Serge Batalov05/2014
70712^204891-100561679Lelio R Paula09/2011
7072(3^129271-5)/4150661674Lelio R Paula03/2012
707315937^7408+7408^1593761672Hans Havermann02/2017
70745^88216-1261661Lelio R Paula04/2013
707518185^2454+2454^1818561645Hans Havermann01/2017
70772^204767-1586561642Enzo Doria04/2013
7076(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
70787*2^204751-961638Lelio R Paula04/2014
70804*10^61625+2161626Robert Price08/2016
707915369^10226+10226^1536961626Hans Havermann02/2017
70812^204702-1812561622Enzo Doria05/2013
70825*3^129146+861620Lelio R Paula04/2014
70832^204673+12961613Lelio R Paula08/2011
708418^49079+9761608Lelio R Paula05/2013
7085106^30416+10561602Norbert Schneider12/2016
70862^204590-3361588Lelio R Paula08/2011
70872^204586-11197561587Enzo Doria06/2014
70882^204580-1607761585Enzo Doria04/2013
70892^204574-1604161583Enzo Doria04/2013
709015^52358+5661578Lelio R Paula05/2013
7091(28*10^61574+11)/361575Robert Price11/2015
70922^204516-1749361566Enzo Doria05/2013
70934*5^88076-361564Lelio R Paula09/2014
709411^59110-252061557Enzo Doria12/2012
70952^204477-5869561554Lelio R Paula09/2011
709612^57026-7361542Lelio R Paula05/2013
709717^50013+9061539Lelio R Paula05/2013
709856^35201-55^3520161538Robert Price10/2013
70998*7^72810+561533Lelio R Paula09/2014
7101204^26641-203^2664161531Jean-Louis Charton08/2009
710043867!3-656161531Robert Price11/2015
710410^61525+9^(61525-1)61526Robert Price03/2016
710210^61525+6225761526Patrick De Geest12/2016
710314821^14166+14166^1482161526Hans Havermann01/2017
710612^57010-8561525Lelio R Paula05/2013
710510^61525-21357961525Patrick De Geest12/2016
71072^204332-9961511Lelio R Paula08/2011
71082^204323-222161508Yves Minet08/2013
71102^204317-19561506Lelio R Paula08/2011
71093^128910-8661506Lelio R Paula04/2013
71112^204318+7453961506Enzo Doria04/2016
7112(2^204334-3)/114133361505Lelio R Paula03/2012
71132^204297-103609361500Paul Bourdelais11/2012
71143^128880+5861492Lelio R Paula04/2013
71152^204216-11167761476Enzo Doria05/2014
7116(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
71172^204129+20412961449Henri Lifchitz04/2002
71183^128787+2^(128787-1)61448Robert Price05/2016
711911^58999-7861442Lelio R Paula05/2013
71202^204083-11196761436Enzo Doria05/2014
7121(45^37159+1)/4661431Robert Price11/2013
7122677^21702+21702^67761430Norbert Schneider06/2016
712314837^13810+13810^1483761429Hans Havermann02/2017
7124(7*2^204043+1)/3961423Lelio R Paula03/2012
712511^58976-174061418Enzo Doria11/2012
71262^204016-1608561415Enzo Doria04/2013
7127V(379967)61393Serge Batalov03/2015
712843777!3-3^4377761392Robert Price08/2015
71297^72642+8861390Lelio R Paula04/2013
71303^128656+3261385Lelio R Paula04/2013
71312^203916-1749361385Enzo Doria05/2013
71326^78880+2361381Lelio R Paula04/2013
71332^203877-11179961374Enzo Doria05/2014
71342^203867-161561371Lelio R Paula10/2011
71354*10^61367+1961368Robert Price04/2016
7136(19*2^203854+1)/4231961363Lelio R Paula08/2012
71372^203825-1580561358Enzo Doria04/2013
71382^203816-1582561355Enzo Doria04/2013
71395*10^61348+5961349Robert Price09/2016
714021^46395-261345Lelio R Paula08/2013
7141(809*29^41946-165)/2861344Curtis Bright05/2015
71427*6^78826+561340Lelio R Paula09/2014
7143(3^128558+7)/8377316642969661324Lelio R Paula04/2012
71442^203706-11161322Lelio R Paula08/2011
714517567^3094+3094^1756761318Hans Havermann02/2017
71462^203689-3161317Thomas Masser10/2005
7147(11*2^203678-1)/5368961310Lelio R Paula01/2014
71492^203642+3961303Lelio R Paula08/2011
7148floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
715011^58849-604061285Enzo Doria02/2013
715143694!3-361264Robert Price10/2014
715258*(10^(3*20420)-1)/111-161260Robert Price10/2014
71532^203490+1290961257Lelio R Paula10/2011
7154(16*10^61251-31)/361252Robert Price03/2016
715520^47077-570361249Enzo Doria03/2013
71562^203434-11308161240Enzo Doria07/2014
71575^87606+461234Wojciech Florek11/2005
71582^203412-16761234Lelio R Paula08/2011
71592^203402+108961231Lelio R Paula10/2011
7160(8*10^61230+67)/361231Robert Price01/2017
7161(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
71621265^19732+19732^126561211Serge Batalov05/2014
71632^203330+14561209Lelio R Paula08/2011
71646^78647-13761200Lelio R Paula04/2013
716585^31718+8461198Norbert Schneider10/2015
716611^58763-27061196Enzo Doria07/2012
71672^203285-11232161195Enzo Doria06/2014
71682^203253-99514361186Paul Bourdelais11/2012
716915319^9862+9862^1531961184Hans Havermann07/2016
71707^72395-4461181Lelio R Paula04/2013
71715*2^203176-761163Lelio R Paula04/2014
71737^72358+5461150Lelio R Paula04/2013
71722^203133-11177561150Enzo Doria05/2014
7174(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
71752^203112-1800961143Enzo Doria05/2013
717643607!3+72961129Robert Price09/2014
71772^203065-11485361129Enzo Doria05/2015
71783^128111+19661125Lelio R Paula04/2013
7179128^29007+29007^12861124Serge Batalov05/2014
718022355*2^203009-361117Donovan Johnson03/2004
71812^203018+3361115Lelio R Paula08/2011
71822^203017-161561115Lelio R Paula10/2011
718316697^4570+4570^1669761110Hans Havermann12/2016
71842^202998-1724161109Enzo Doria05/2013
718520^46964+9361102Lelio R Paula06/2013
7186(55*10^61097-1)/961098Ray Chandler02/2012
718720^46960-546361097Enzo Doria03/2013
7188(11*10^61095+49)/361096Robert Price05/2016
71892^202934-595561090Lelio R Paula10/2011
719019^47772-6861089Lelio R Paula05/2013
71912^202877-49942361073Paul Bourdelais03/2013
71922^202763-1712561038Enzo Doria05/2013
7193(23*2^202756+1)/961037Lelio R Paula03/2012
719414788^13355+13355^1478861011Hans Havermann12/2016
719516069^6258+6258^1606961005Hans Havermann12/2016
71965^87276-1433661004Enzo Doria02/2013
719750^35899-49^3589960992Robert Price12/2012
71982^202599-304960989Yves Minet10/2014
71992^202535-11157160970Enzo Doria05/2014
720010^60959+5760960Patrick De Geest12/2008
720210^60959-6095960959Henri Lifchitz08/2002
720110^60959-2917760959Patrick De Geest08/2008
72035^87206+4^(87206+1)60955Robert Price07/2016
72042^202476-1590960952Enzo Doria04/2013
72052^202472-1751360951Enzo Doria05/2013
720614858^12651+12651^1485860950Hans Havermann12/2016
72072^202389-5869560926Lelio R Paula09/2011
72083^127597-3460880Lelio R Paula04/2013
720915088^10831+10831^1508860876Hans Havermann12/2016
72102^202198-11326160868Enzo Doria07/2014
72112^202182+13560863Lelio R Paula08/2011
72122^202176+8560862Lelio R Paula08/2011
72135183^16384+5182^1638460860Henri Lifchitz01/2007
7214(31*2^202163+1)/360859Lelio R Paula03/2012
721514708^13707+13707^1470860847Hans Havermann12/2016
72162^202112+202112^2-160842Robert Price04/2014
7217(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
721864743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7219(19*2^202098-1)/679560836Lelio R Paula01/2014
7220(6^78175-11)/560832Paul Bourdelais11/2011
72212^202063+160560828Lelio R Paula09/2011
72222^202058+85960826Lelio R Paula09/2011
72231576^19021+19021^157660821Serge Batalov05/2014
7224(2^202009+3)/600560807Lelio R Paula03/2012
722510^60776+360777Robert Price01/2011
722610^60776-1481960776Patrick De Geest12/2012
7227(6883*2^201869-1)/3560771Lelio R Paula04/2015
7228(27*2^201841-1)/4360760Lelio R Paula01/2014
72292^201822-17760755Lelio R Paula08/2011
7230(13*10^60744+17)/360745Robert Price06/2015
7231(31*2^201754-1)/9960734Lelio R Paula01/2014
7232(26*10^60717-71)/960718Robert Price03/2015
723337^38712-260709Lelio R Paula08/2013
72342^201657-11200360705Enzo Doria05/2014
7235(10^60703+3^60703)/1360702Robert Price01/2013
72362^201622-11281760695Enzo Doria06/2014
72372^201620-1717760694Enzo Doria05/2013
7238(2^201615-3)*6-760693Gilbert Mozzo05/2016
72392^201609-4978960691Henri Lifchitz03/2005
72402^201582-1906160683Enzo Doria05/2013
724143316!3+2760679Robert Price09/2014
7242(509203*2^201564-1)/506760679Lelio R Paula04/2015
72432^201560+10560676Lelio R Paula08/2011
7244(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
72452^201545-1802160672Enzo Doria05/2013
72462^201543+1171560671Lelio R Paula09/2011
72482^201512-11175560662Enzo Doria05/2014
7247p(13013)#/2+6460662Robert Price03/2017
724911^58248+1660660Lelio R Paula05/2013
72502^201496-2760657Lelio R Paula08/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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