PRP Records

Probable Primes Top 10000

(202622 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
75013*6^79842-562130Lelio R Paula09/2014
75027*10^62127-1762128Robert Price01/2017
75032^206373+841562125Lelio R Paula02/2013
750420^47745-958362118Enzo Doria03/2013
750541^38516-262118Lelio R Paula08/2013
75062^206332-5869562113Lelio R Paula09/2011
750711^59639-126062108Enzo Doria11/2012
75082^206232-1589362083Enzo Doria04/2013
7509(115*10^62073-1)/362075Serge Batalov12/2014
75102^206206+7579962075Enzo Doria04/2016
7511(74*10^62072+43)/962073Robert Price10/2015
75122^206194-18562071Lelio R Paula08/2011
75136^79757-10362064Lelio R Paula04/2013
7514p(13285)#/2-6462063Robert Price04/2017
7515(29*10^62030-41)/362031Robert Price07/2016
751620^47675-8162027Lelio R Paula06/2013
75173^129972+9862013Lelio R Paula04/2013
75182^205962+362001Donovan Johnson02/2006
75192^205933-205933^261993Henri Lifchitz05/2005
7520(68*10^61991+7)/361993Robert Price03/2016
752120^47641-66361983Enzo Doria03/2013
75223^129861+266061960Lelio R Paula04/2013
7523(55459*2^205800+1)/134561954Lelio R Paula06/2014
752418^49354-9761953Lelio R Paula05/2013
7525(209*10^61947-17)/361949Robert Price05/2017
752714*10^61937+108961939Jens K. Andersen11/2007
7526(11*2^205758-1)/5361939Lelio R Paula01/2014
752820^47600+6361930Lelio R Paula06/2013
7529(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
753044117!3+24361918Robert Price09/2014
7531(31*2^205677-1)/5961915Lelio R Paula01/2014
7532(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
753320^47575-8161897Lelio R Paula06/2013
7534(58695*2^205593-1)/72761892Lelio R Paula04/2015
753587^31909+8661889Norbert Schneider10/2015
75362^205568+14161883Lelio R Paula08/2011
753710^61868+5892761869Patrick De Geest12/2012
753810^61868-3961868Robert Price05/2011
75405^88505-8861863Lelio R Paula04/2013
7539(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
754113^55528-9861856Lelio R Paula05/2013
7542(55^35543-1)/5461856Paul Bourdelais08/2017
754330535!2-861844Robert Price06/2015
754411^59371-120061829Enzo Doria11/2012
75457*2^205370-561824Lelio R Paula04/2014
7546(47*10^61821+403)/961822Robert Price04/2017
75472^205275+769561794Lelio R Paula02/2013
75482^205269+1291561793Lelio R Paula02/2013
7549(47*2^205265+1)/3561792Lelio R Paula04/2015
755019^48309+4061776Lelio R Paula05/2013
7551(424*10^61770-1)/961772Robert Price11/2017
75522^205192-407961769Yves Minet06/2011
75532^205184+1609561767Lelio R Paula09/2011
755420^47472-342361763Enzo Doria03/2013
7555(17*10^61760-89)/961761Robert Price11/2017
75562^205149-179561757Lelio R Paula09/2011
75572^205110-1761745Lelio R Paula08/2011
7558(373^24007+1)/37461737Eric Chen10/2017
7559(2^205025-7)/2561718Lelio R Paula03/2012
756027^43117-26^4311761717Robert Price08/2012
75612^205016+3761716Lelio R Paula08/2011
7562gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
75631263^19898+19898^126361712Serge Batalov05/2014
7564135^28963-13461701Norbert Schneider04/2015
7565(33*2^204966+1)/23434161698Michael Porter01/2015
7566(7*10^61696+167)/361696Robert Kinser10/2017
7567(46*10^61693+17)/961694Robert Price06/2015
7568((((((((((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
75691850^18879+18879^185061681Serge Batalov05/2014
75702^204891-100561679Lelio R Paula09/2011
7571151^28306-261679Lelio R Paula10/2017
7572(3^129271-5)/4150661674Lelio R Paula03/2012
757315937^7408+7408^1593761672Hans Havermann02/2017
75745^88216-1261661Lelio R Paula04/2013
757518185^2454+2454^1818561645Hans Havermann01/2017
75772^204767-1586561642Enzo Doria04/2013
7576(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
75787*2^204751-961638Lelio R Paula04/2014
75794*10^61625+2161626Robert Price08/2016
758015369^10226+10226^1536961626Hans Havermann02/2017
75812^204702-1812561622Enzo Doria05/2013
75825*3^129146+861620Lelio R Paula04/2014
75832^204673+12961613Lelio R Paula08/2011
758418^49079+9761608Lelio R Paula05/2013
7585106^30416+10561602Norbert Schneider12/2016
75862^204590-3361588Lelio R Paula08/2011
75872^204586-11197561587Enzo Doria06/2014
75882^204580-1607761585Enzo Doria04/2013
75892^204574-1604161583Enzo Doria04/2013
759015^52358+5661578Lelio R Paula05/2013
7591(28*10^61574+11)/361575Robert Price11/2015
75922^204516-1749361566Enzo Doria05/2013
75934*5^88076-361564Lelio R Paula09/2014
759411^59110-252061557Enzo Doria12/2012
75952^204477-5869561554Lelio R Paula09/2011
759612^57026-7361542Lelio R Paula05/2013
759717^50013+9061539Lelio R Paula05/2013
759856^35201-55^3520161538Robert Price10/2013
75998*7^72810+561533Lelio R Paula09/2014
7601204^26641-203^2664161531Jean-Louis Charton08/2009
760043867!3-656161531Robert Price11/2015
760410^61525+9^(61525-1)61526Robert Price03/2016
760210^61525+6225761526Patrick De Geest12/2016
760314821^14166+14166^1482161526Hans Havermann01/2017
760612^57010-8561525Lelio R Paula05/2013
760510^61525-21357961525Patrick De Geest12/2016
76072^204332-9961511Lelio R Paula08/2011
76082^204323-222161508Yves Minet08/2013
76102^204317-19561506Lelio R Paula08/2011
76093^128910-8661506Lelio R Paula04/2013
76112^204318+7453961506Enzo Doria04/2016
7612(2^204334-3)/114133361505Lelio R Paula03/2012
76132^204297-103609361500Paul Bourdelais11/2012
76143^128880+5861492Lelio R Paula04/2013
76152^204216-11167761476Enzo Doria05/2014
7616(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
76172^204129+20412961449Henri Lifchitz04/2002
76183^128787+2^(128787-1)61448Robert Price05/2016
761911^58999-7861442Lelio R Paula05/2013
76202^204083-11196761436Enzo Doria05/2014
7621(45^37159+1)/4661431Robert Price11/2013
7622677^21702+21702^67761430Norbert Schneider06/2016
762314837^13810+13810^1483761429Hans Havermann02/2017
7624(7*2^204043+1)/3961423Lelio R Paula03/2012
762511^58976-174061418Enzo Doria11/2012
76262^204016-1608561415Enzo Doria04/2013
7627V(379967)61393Serge Batalov03/2015
762843777!3-3^4377761392Robert Price08/2015
76297^72642+8861390Lelio R Paula04/2013
76303^128656+3261385Lelio R Paula04/2013
76312^203916-1749361385Enzo Doria05/2013
76326^78880+2361381Lelio R Paula04/2013
7633(388*10^61374-1)/961376Robert Price11/2017
76342^203877-11179961374Enzo Doria05/2014
76352^203867-161561371Lelio R Paula10/2011
76364*10^61367+1961368Robert Price04/2016
7637(19*2^203854+1)/4231961363Lelio R Paula08/2012
7638L(293659)/7652812271961361Serge Batalov07/2017
76392^203825-1580561358Enzo Doria04/2013
76402^203816-1582561355Enzo Doria04/2013
76415*10^61348+5961349Robert Price09/2016
764221^46395-261345Lelio R Paula08/2013
7643(809*29^41946-165)/2861344Curtis Bright05/2015
76447*6^78826+561340Lelio R Paula09/2014
7645(3^128558+7)/8377316642969661324Lelio R Paula04/2012
76462^203706-11161322Lelio R Paula08/2011
764717567^3094+3094^1756761318Hans Havermann02/2017
76482^203689-3161317Thomas Masser10/2005
7649(11*2^203678-1)/5368961310Lelio R Paula01/2014
76502^203642+3961303Lelio R Paula08/2011
7651floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
765211^58849-604061285Enzo Doria02/2013
765343694!3-361264Robert Price10/2014
765458*(10^(3*20420)-1)/111-161260Robert Price10/2014
76552^203490+1290961257Lelio R Paula10/2011
7656(16*10^61251-31)/361252Robert Price03/2016
765720^47077-570361249Enzo Doria03/2013
76582^203434-11308161240Enzo Doria07/2014
76595^87606+461234Wojciech Florek11/2005
76602^203412-16761234Lelio R Paula08/2011
76612^203402+108961231Lelio R Paula10/2011
7662(8*10^61230+67)/361231Robert Price01/2017
7663(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
76641265^19732+19732^126561211Serge Batalov05/2014
76652^203330+14561209Lelio R Paula08/2011
76666^78647-13761200Lelio R Paula04/2013
766785^31718+8461198Norbert Schneider10/2015
766811^58763-27061196Enzo Doria07/2012
76692^203285-11232161195Enzo Doria06/2014
76702^203253-99514361186Paul Bourdelais11/2012
767115319^9862+9862^1531961184Hans Havermann07/2016
76727^72395-4461181Lelio R Paula04/2013
7673(49*10^61167-67)/961168Robert Price08/2017
76745*2^203176-761163Lelio R Paula04/2014
7675(26*10^61156-413)/961157Robert Price10/2017
76777^72358+5461150Lelio R Paula04/2013
76762^203133-11177561150Enzo Doria05/2014
7678(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
76792^203112-1800961143Enzo Doria05/2013
768043607!3+72961129Robert Price09/2014
76812^203065-11485361129Enzo Doria05/2015
76823^128111+19661125Lelio R Paula04/2013
7683128^29007+29007^12861124Serge Batalov05/2014
76844*10^61119+4961120Robert Price08/2017
768522355*2^203009-361117Donovan Johnson03/2004
76862^203018+3361115Lelio R Paula08/2011
76872^203017-161561115Lelio R Paula10/2011
768816697^4570+4570^1669761110Hans Havermann12/2016
76892^202998-1724161109Enzo Doria05/2013
769020^46964+9361102Lelio R Paula06/2013
7691(55*10^61097-1)/961098Ray Chandler02/2012
769220^46960-546361097Enzo Doria03/2013
7693(11*10^61095+49)/361096Robert Price05/2016
76942^202934-595561090Lelio R Paula10/2011
769519^47772-6861089Lelio R Paula05/2013
76962^202877-49942361073Paul Bourdelais03/2013
76972^202763-1712561038Enzo Doria05/2013
7698(23*2^202756+1)/961037Lelio R Paula03/2012
769914788^13355+13355^1478861011Hans Havermann12/2016
770016069^6258+6258^1606961005Hans Havermann12/2016
77015^87276-1433661004Enzo Doria02/2013
770250^35899-49^3589960992Robert Price12/2012
77032^202599-304960989Yves Minet10/2014
77042^202535-11157160970Enzo Doria05/2014
7705(13*10^60966+107)/360967Robert Price11/2017
770710^60959+5760960Patrick De Geest12/2008
77066*10^60959-9160960Robert Price11/2017
770910^60959-6095960959Henri Lifchitz08/2002
770810^60959-2917760959Patrick De Geest08/2008
77105^87206+4^(87206+1)60955Robert Price07/2016
77112^202476-1590960952Enzo Doria04/2013
77122^202472-1751360951Enzo Doria05/2013
771314858^12651+12651^1485860950Hans Havermann12/2016
77142^202389-5869560926Lelio R Paula09/2011
77153^127597-3460880Lelio R Paula04/2013
771615088^10831+10831^1508860876Hans Havermann12/2016
77172^202198-11326160868Enzo Doria07/2014
77182^202182+13560863Lelio R Paula08/2011
77192^202176+8560862Lelio R Paula08/2011
77205183^16384+5182^1638460860Henri Lifchitz01/2007
7721(31*2^202163+1)/360859Lelio R Paula03/2012
772214708^13707+13707^1470860847Hans Havermann12/2016
77232^202112+202112^2-160842Robert Price04/2014
7724(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
772564743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7726(19*2^202098-1)/679560836Lelio R Paula01/2014
7727(6^78175-11)/560832Paul Bourdelais11/2011
77282^202063+160560828Lelio R Paula09/2011
77292^202058+85960826Lelio R Paula09/2011
77301576^19021+19021^157660821Serge Batalov05/2014
7731(2^202009+3)/600560807Lelio R Paula03/2012
773210^60776+360777Robert Price01/2011
773310^60776-1481960776Patrick De Geest12/2012
773455*10^60772+760774Robert Price10/2017
7735(6883*2^201869-1)/3560771Lelio R Paula04/2015
7736(27*2^201841-1)/4360760Lelio R Paula01/2014
77372^201822-17760755Lelio R Paula08/2011
7738(13*10^60744+17)/360745Robert Price06/2015
7739(31*2^201754-1)/9960734Lelio R Paula01/2014
7740(26*10^60717-71)/960718Robert Price03/2015
774137^38712-260709Lelio R Paula08/2013
77422^201657-11200360705Enzo Doria05/2014
7743(10^60703+3^60703)/1360702Robert Price01/2013
77442^201622-11281760695Enzo Doria06/2014
77452^201620-1717760694Enzo Doria05/2013
7746(2^201615-3)*6-760693Gilbert Mozzo05/2016
77472^201609-4978960691Henri Lifchitz03/2005
77482^201582-1906160683Enzo Doria05/2013
774943316!3+2760679Robert Price09/2014
7750(509203*2^201564-1)/506760679Lelio R Paula04/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!