PRP Records

Probable Primes Top 10000

(183432 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 ?
72513^130403+868062219Lelio R Paula04/2013
725211^59740-711062213Enzo Doria01/2013
72542^206596-16762192Lelio R Paula08/2011
72532^206597+1891562192Lelio R Paula02/2013
72556^79918+13762189Lelio R Paula04/2013
7256lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
72572^206574+61362185Jason Earls04/2008
72583^130328+8062183Lelio R Paula04/2013
7259(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
72602^206550+7681962178Enzo Doria05/2016
726111^59703-2462175Lelio R Paula05/2013
72622^206524+7578162170Enzo Doria04/2016
72632^206506+42762165Henri Lifchitz01/2005
72642^206465+769562153Lelio R Paula02/2013
72652^206464-164962152Yves Minet03/2013
72665^88917+5662151Lelio R Paula04/2013
72672^206444-11156962146Enzo Doria05/2014
72685^88908-4262145Lelio R Paula04/2013
726918^49495-2962130Lelio R Paula05/2013
72703*6^79842-562130Lelio R Paula09/2014
72717*10^62127-1762128Robert Price01/2017
72722^206373+841562125Lelio R Paula02/2013
727320^47745-958362118Enzo Doria03/2013
727441^38516-262118Lelio R Paula08/2013
72752^206332-5869562113Lelio R Paula09/2011
727611^59639-126062108Enzo Doria11/2012
72772^206232-1589362083Enzo Doria04/2013
7278(115*10^62073-1)/362075Serge Batalov12/2014
72792^206206+7579962075Enzo Doria04/2016
7280(74*10^62072+43)/962073Robert Price10/2015
72812^206194-18562071Lelio R Paula08/2011
72826^79757-10362064Lelio R Paula04/2013
7283p(13285)#/2-6462063Robert Price04/2017
7284(29*10^62030-41)/362031Robert Price07/2016
728520^47675-8162027Lelio R Paula06/2013
72863^129972+9862013Lelio R Paula04/2013
72872^205962+362001Donovan Johnson02/2006
72882^205933-205933^261993Henri Lifchitz05/2005
7289(68*10^61991+7)/361993Robert Price03/2016
729020^47641-66361983Enzo Doria03/2013
72913^129861+266061960Lelio R Paula04/2013
7292(55459*2^205800+1)/134561954Lelio R Paula06/2014
729318^49354-9761953Lelio R Paula05/2013
7294(209*10^61947-17)/361949Robert Price05/2017
729514*10^61937+108961939Jens K. Andersen11/2007
7296(11*2^205758-1)/5361939Lelio R Paula01/2014
729720^47600+6361930Lelio R Paula06/2013
7298(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
729944117!3+24361918Robert Price09/2014
7300(31*2^205677-1)/5961915Lelio R Paula01/2014
7301(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
730220^47575-8161897Lelio R Paula06/2013
7303(58695*2^205593-1)/72761892Lelio R Paula04/2015
730487^31909+8661889Norbert Schneider10/2015
73052^205568+14161883Lelio R Paula08/2011
730610^61868+5892761869Patrick De Geest12/2012
730710^61868-3961868Robert Price05/2011
73095^88505-8861863Lelio R Paula04/2013
7308(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
731013^55528-9861856Lelio R Paula05/2013
7311(55^35543-1)/5461856Paul Bourdelais08/2017
731230535!2-861844Robert Price06/2015
731311^59371-120061829Enzo Doria11/2012
73147*2^205370-561824Lelio R Paula04/2014
7315(47*10^61821+403)/961822Robert Price04/2017
73162^205275+769561794Lelio R Paula02/2013
73172^205269+1291561793Lelio R Paula02/2013
7318(47*2^205265+1)/3561792Lelio R Paula04/2015
731919^48309+4061776Lelio R Paula05/2013
73202^205192-407961769Yves Minet06/2011
73212^205184+1609561767Lelio R Paula09/2011
732220^47472-342361763Enzo Doria03/2013
73232^205149-179561757Lelio R Paula09/2011
73242^205110-1761745Lelio R Paula08/2011
7325(373^24007+1)/37461737Eric Chen10/2017
7326(2^205025-7)/2561718Lelio R Paula03/2012
732727^43117-26^4311761717Robert Price08/2012
73282^205016+3761716Lelio R Paula08/2011
7329gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
73301263^19898+19898^126361712Serge Batalov05/2014
7331135^28963-13461701Norbert Schneider04/2015
7332(33*2^204966+1)/23434161698Michael Porter01/2015
7333(7*10^61696+167)/361696Robert Kinser10/2017
7334(46*10^61693+17)/961694Robert Price06/2015
7335((((((((((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
73361850^18879+18879^185061681Serge Batalov05/2014
73382^204891-100561679Lelio R Paula09/2011
7337151^28306-261679Lelio R Paula10/2017
7339(3^129271-5)/4150661674Lelio R Paula03/2012
734015937^7408+7408^1593761672Hans Havermann02/2017
73415^88216-1261661Lelio R Paula04/2013
734218185^2454+2454^1818561645Hans Havermann01/2017
73442^204767-1586561642Enzo Doria04/2013
7343(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
73457*2^204751-961638Lelio R Paula04/2014
73464*10^61625+2161626Robert Price08/2016
734715369^10226+10226^1536961626Hans Havermann02/2017
73482^204702-1812561622Enzo Doria05/2013
73495*3^129146+861620Lelio R Paula04/2014
73502^204673+12961613Lelio R Paula08/2011
735118^49079+9761608Lelio R Paula05/2013
7352106^30416+10561602Norbert Schneider12/2016
73532^204590-3361588Lelio R Paula08/2011
73542^204586-11197561587Enzo Doria06/2014
73552^204580-1607761585Enzo Doria04/2013
73562^204574-1604161583Enzo Doria04/2013
735715^52358+5661578Lelio R Paula05/2013
7358(28*10^61574+11)/361575Robert Price11/2015
73592^204516-1749361566Enzo Doria05/2013
73604*5^88076-361564Lelio R Paula09/2014
736111^59110-252061557Enzo Doria12/2012
73622^204477-5869561554Lelio R Paula09/2011
736312^57026-7361542Lelio R Paula05/2013
736417^50013+9061539Lelio R Paula05/2013
736556^35201-55^3520161538Robert Price10/2013
73668*7^72810+561533Lelio R Paula09/2014
7368204^26641-203^2664161531Jean-Louis Charton08/2009
736743867!3-656161531Robert Price11/2015
736910^61525+9^(61525-1)61526Robert Price03/2016
737010^61525+6225761526Patrick De Geest12/2016
737114821^14166+14166^1482161526Hans Havermann01/2017
737312^57010-8561525Lelio R Paula05/2013
737210^61525-21357961525Patrick De Geest12/2016
73742^204332-9961511Lelio R Paula08/2011
73752^204323-222161508Yves Minet08/2013
73772^204317-19561506Lelio R Paula08/2011
73763^128910-8661506Lelio R Paula04/2013
73782^204318+7453961506Enzo Doria04/2016
7379(2^204334-3)/114133361505Lelio R Paula03/2012
73802^204297-103609361500Paul Bourdelais11/2012
73813^128880+5861492Lelio R Paula04/2013
73822^204216-11167761476Enzo Doria05/2014
7383(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
73842^204129+20412961449Henri Lifchitz04/2002
73853^128787+2^(128787-1)61448Robert Price05/2016
738611^58999-7861442Lelio R Paula05/2013
73872^204083-11196761436Enzo Doria05/2014
7388(45^37159+1)/4661431Robert Price11/2013
7389677^21702+21702^67761430Norbert Schneider06/2016
739014837^13810+13810^1483761429Hans Havermann02/2017
7391(7*2^204043+1)/3961423Lelio R Paula03/2012
739211^58976-174061418Enzo Doria11/2012
73932^204016-1608561415Enzo Doria04/2013
7394V(379967)61393Serge Batalov03/2015
739543777!3-3^4377761392Robert Price08/2015
73967^72642+8861390Lelio R Paula04/2013
73973^128656+3261385Lelio R Paula04/2013
73982^203916-1749361385Enzo Doria05/2013
73996^78880+2361381Lelio R Paula04/2013
74002^203877-11179961374Enzo Doria05/2014
74012^203867-161561371Lelio R Paula10/2011
74024*10^61367+1961368Robert Price04/2016
7403(19*2^203854+1)/4231961363Lelio R Paula08/2012
7404L(293659)/7652812271961361Serge Batalov07/2017
74052^203825-1580561358Enzo Doria04/2013
74062^203816-1582561355Enzo Doria04/2013
74075*10^61348+5961349Robert Price09/2016
740821^46395-261345Lelio R Paula08/2013
7409(809*29^41946-165)/2861344Curtis Bright05/2015
74107*6^78826+561340Lelio R Paula09/2014
7411(3^128558+7)/8377316642969661324Lelio R Paula04/2012
74122^203706-11161322Lelio R Paula08/2011
741317567^3094+3094^1756761318Hans Havermann02/2017
74142^203689-3161317Thomas Masser10/2005
7415(11*2^203678-1)/5368961310Lelio R Paula01/2014
74172^203642+3961303Lelio R Paula08/2011
7416floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
741811^58849-604061285Enzo Doria02/2013
741943694!3-361264Robert Price10/2014
742058*(10^(3*20420)-1)/111-161260Robert Price10/2014
74212^203490+1290961257Lelio R Paula10/2011
7422(16*10^61251-31)/361252Robert Price03/2016
742320^47077-570361249Enzo Doria03/2013
74242^203434-11308161240Enzo Doria07/2014
74255^87606+461234Wojciech Florek11/2005
74262^203412-16761234Lelio R Paula08/2011
74272^203402+108961231Lelio R Paula10/2011
7428(8*10^61230+67)/361231Robert Price01/2017
7429(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
74301265^19732+19732^126561211Serge Batalov05/2014
74312^203330+14561209Lelio R Paula08/2011
74326^78647-13761200Lelio R Paula04/2013
743385^31718+8461198Norbert Schneider10/2015
743411^58763-27061196Enzo Doria07/2012
74352^203285-11232161195Enzo Doria06/2014
74362^203253-99514361186Paul Bourdelais11/2012
743715319^9862+9862^1531961184Hans Havermann07/2016
74387^72395-4461181Lelio R Paula04/2013
7439(49*10^61167-67)/961168Robert Price08/2017
74405*2^203176-761163Lelio R Paula04/2014
7441(26*10^61156-413)/961157Robert Price10/2017
74427^72358+5461150Lelio R Paula04/2013
74432^203133-11177561150Enzo Doria05/2014
7444(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
74452^203112-1800961143Enzo Doria05/2013
744643607!3+72961129Robert Price09/2014
74472^203065-11485361129Enzo Doria05/2015
74483^128111+19661125Lelio R Paula04/2013
7449128^29007+29007^12861124Serge Batalov05/2014
74504*10^61119+4961120Robert Price08/2017
745122355*2^203009-361117Donovan Johnson03/2004
74522^203018+3361115Lelio R Paula08/2011
74532^203017-161561115Lelio R Paula10/2011
745416697^4570+4570^1669761110Hans Havermann12/2016
74552^202998-1724161109Enzo Doria05/2013
745620^46964+9361102Lelio R Paula06/2013
7457(55*10^61097-1)/961098Ray Chandler02/2012
745820^46960-546361097Enzo Doria03/2013
7459(11*10^61095+49)/361096Robert Price05/2016
74602^202934-595561090Lelio R Paula10/2011
746119^47772-6861089Lelio R Paula05/2013
74622^202877-49942361073Paul Bourdelais03/2013
74632^202763-1712561038Enzo Doria05/2013
7464(23*2^202756+1)/961037Lelio R Paula03/2012
746514788^13355+13355^1478861011Hans Havermann12/2016
746616069^6258+6258^1606961005Hans Havermann12/2016
74675^87276-1433661004Enzo Doria02/2013
746850^35899-49^3589960992Robert Price12/2012
74692^202599-304960989Yves Minet10/2014
74702^202535-11157160970Enzo Doria05/2014
747110^60959+5760960Patrick De Geest12/2008
747310^60959-6095960959Henri Lifchitz08/2002
747210^60959-2917760959Patrick De Geest08/2008
74745^87206+4^(87206+1)60955Robert Price07/2016
74752^202476-1590960952Enzo Doria04/2013
74762^202472-1751360951Enzo Doria05/2013
747714858^12651+12651^1485860950Hans Havermann12/2016
74782^202389-5869560926Lelio R Paula09/2011
74793^127597-3460880Lelio R Paula04/2013
748015088^10831+10831^1508860876Hans Havermann12/2016
74812^202198-11326160868Enzo Doria07/2014
74822^202182+13560863Lelio R Paula08/2011
74832^202176+8560862Lelio R Paula08/2011
74845183^16384+5182^1638460860Henri Lifchitz01/2007
7485(31*2^202163+1)/360859Lelio R Paula03/2012
748614708^13707+13707^1470860847Hans Havermann12/2016
74872^202112+202112^2-160842Robert Price04/2014
7488(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
748964743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7490(19*2^202098-1)/679560836Lelio R Paula01/2014
7491(6^78175-11)/560832Paul Bourdelais11/2011
74922^202063+160560828Lelio R Paula09/2011
74932^202058+85960826Lelio R Paula09/2011
74941576^19021+19021^157660821Serge Batalov05/2014
7495(2^202009+3)/600560807Lelio R Paula03/2012
749610^60776+360777Robert Price01/2011
749710^60776-1481960776Patrick De Geest12/2012
7498(6883*2^201869-1)/3560771Lelio R Paula04/2015
7499(27*2^201841-1)/4360760Lelio R Paula01/2014
75002^201822-17760755Lelio R Paula08/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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