PRP Records

Probable Primes Top 10000

(202632 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 ?
75012^206444-11156962146Enzo Doria05/2014
75025^88908-4262145Lelio R Paula04/2013
750318^49495-2962130Lelio R Paula05/2013
75043*6^79842-562130Lelio R Paula09/2014
75057*10^62127-1762128Robert Price01/2017
75062^206373+841562125Lelio R Paula02/2013
750720^47745-958362118Enzo Doria03/2013
750841^38516-262118Lelio R Paula08/2013
75092^206332-5869562113Lelio R Paula09/2011
751011^59639-126062108Enzo Doria11/2012
75112^206232-1589362083Enzo Doria04/2013
7512(115*10^62073-1)/362075Serge Batalov12/2014
75132^206206+7579962075Enzo Doria04/2016
7514(74*10^62072+43)/962073Robert Price10/2015
75152^206194-18562071Lelio R Paula08/2011
75166^79757-10362064Lelio R Paula04/2013
7517p(13285)#/2-6462063Robert Price04/2017
7518(29*10^62030-41)/362031Robert Price07/2016
751920^47675-8162027Lelio R Paula06/2013
75203^129972+9862013Lelio R Paula04/2013
75212^205962+362001Donovan Johnson02/2006
75222^205933-205933^261993Henri Lifchitz05/2005
7523(68*10^61991+7)/361993Robert Price03/2016
752420^47641-66361983Enzo Doria03/2013
75253^129861+266061960Lelio R Paula04/2013
7526(55459*2^205800+1)/134561954Lelio R Paula06/2014
752718^49354-9761953Lelio R Paula05/2013
7528(209*10^61947-17)/361949Robert Price05/2017
753014*10^61937+108961939Jens K. Andersen11/2007
7529(11*2^205758-1)/5361939Lelio R Paula01/2014
753120^47600+6361930Lelio R Paula06/2013
7532(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
753344117!3+24361918Robert Price09/2014
7534(31*2^205677-1)/5961915Lelio R Paula01/2014
7535(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
753620^47575-8161897Lelio R Paula06/2013
7537(58695*2^205593-1)/72761892Lelio R Paula04/2015
753887^31909+8661889Norbert Schneider10/2015
75392^205568+14161883Lelio R Paula08/2011
754010^61868+5892761869Patrick De Geest12/2012
754110^61868-3961868Robert Price05/2011
75425^88505-8861863Lelio R Paula04/2013
7543(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
754513^55528-9861856Lelio R Paula05/2013
7544(55^35543-1)/5461856Paul Bourdelais08/2017
754630535!2-861844Robert Price06/2015
754711^59371-120061829Enzo Doria11/2012
75487*2^205370-561824Lelio R Paula04/2014
7549(47*10^61821+403)/961822Robert Price04/2017
75502^205275+769561794Lelio R Paula02/2013
75512^205269+1291561793Lelio R Paula02/2013
7552(47*2^205265+1)/3561792Lelio R Paula04/2015
755319^48309+4061776Lelio R Paula05/2013
7554(424*10^61770-1)/961772Robert Price11/2017
75552^205192-407961769Yves Minet06/2011
75562^205184+1609561767Lelio R Paula09/2011
755720^47472-342361763Enzo Doria03/2013
7558(17*10^61760-89)/961761Robert Price11/2017
75592^205149-179561757Lelio R Paula09/2011
75602^205110-1761745Lelio R Paula08/2011
7561(373^24007+1)/37461737Eric Chen10/2017
7562(2^205025-7)/2561718Lelio R Paula03/2012
756327^43117-26^4311761717Robert Price08/2012
75642^205016+3761716Lelio R Paula08/2011
7565gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
75661263^19898+19898^126361712Serge Batalov05/2014
7567135^28963-13461701Norbert Schneider04/2015
7568(33*2^204966+1)/23434161698Michael Porter01/2015
7569(7*10^61696+167)/361696Robert Kinser10/2017
7570(46*10^61693+17)/961694Robert Price06/2015
7571((((((((((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
75721850^18879+18879^185061681Serge Batalov05/2014
75742^204891-100561679Lelio R Paula09/2011
7573151^28306-261679Lelio R Paula10/2017
7575(3^129271-5)/4150661674Lelio R Paula03/2012
757615937^7408+7408^1593761672Hans Havermann02/2017
75775^88216-1261661Lelio R Paula04/2013
757818185^2454+2454^1818561645Hans Havermann01/2017
75802^204767-1586561642Enzo Doria04/2013
7579(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
75817*2^204751-961638Lelio R Paula04/2014
75834*10^61625+2161626Robert Price08/2016
758215369^10226+10226^1536961626Hans Havermann02/2017
75842^204702-1812561622Enzo Doria05/2013
75855*3^129146+861620Lelio R Paula04/2014
75862^204673+12961613Lelio R Paula08/2011
758718^49079+9761608Lelio R Paula05/2013
7588106^30416+10561602Norbert Schneider12/2016
75892^204590-3361588Lelio R Paula08/2011
75902^204586-11197561587Enzo Doria06/2014
75912^204580-1607761585Enzo Doria04/2013
75922^204574-1604161583Enzo Doria04/2013
759315^52358+5661578Lelio R Paula05/2013
7594(28*10^61574+11)/361575Robert Price11/2015
75952^204516-1749361566Enzo Doria05/2013
75964*5^88076-361564Lelio R Paula09/2014
759711^59110-252061557Enzo Doria12/2012
75982^204477-5869561554Lelio R Paula09/2011
759912^57026-7361542Lelio R Paula05/2013
760017^50013+9061539Lelio R Paula05/2013
760156^35201-55^3520161538Robert Price10/2013
76028*7^72810+561533Lelio R Paula09/2014
7604204^26641-203^2664161531Jean-Louis Charton08/2009
760343867!3-656161531Robert Price11/2015
760710^61525+9^(61525-1)61526Robert Price03/2016
760510^61525+6225761526Patrick De Geest12/2016
760614821^14166+14166^1482161526Hans Havermann01/2017
760912^57010-8561525Lelio R Paula05/2013
760810^61525-21357961525Patrick De Geest12/2016
76102^204332-9961511Lelio R Paula08/2011
76112^204323-222161508Yves Minet08/2013
76142^204317-19561506Lelio R Paula08/2011
76123^128910-8661506Lelio R Paula04/2013
76132^204318+7453961506Enzo Doria04/2016
7615(2^204334-3)/114133361505Lelio R Paula03/2012
76162^204297-103609361500Paul Bourdelais11/2012
76173^128880+5861492Lelio R Paula04/2013
76182^204216-11167761476Enzo Doria05/2014
7619(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
76202^204129+20412961449Henri Lifchitz04/2002
76213^128787+2^(128787-1)61448Robert Price05/2016
762211^58999-7861442Lelio R Paula05/2013
76232^204083-11196761436Enzo Doria05/2014
7624(45^37159+1)/4661431Robert Price11/2013
7625677^21702+21702^67761430Norbert Schneider06/2016
762614837^13810+13810^1483761429Hans Havermann02/2017
7627(7*2^204043+1)/3961423Lelio R Paula03/2012
762811^58976-174061418Enzo Doria11/2012
76292^204016-1608561415Enzo Doria04/2013
7630V(379967)61393Serge Batalov03/2015
763143777!3-3^4377761392Robert Price08/2015
76327^72642+8861390Lelio R Paula04/2013
76333^128656+3261385Lelio R Paula04/2013
76342^203916-1749361385Enzo Doria05/2013
76356^78880+2361381Lelio R Paula04/2013
7636(388*10^61374-1)/961376Robert Price11/2017
76372^203877-11179961374Enzo Doria05/2014
76382^203867-161561371Lelio R Paula10/2011
76394*10^61367+1961368Robert Price04/2016
7640(19*2^203854+1)/4231961363Lelio R Paula08/2012
7641L(293659)/7652812271961361Serge Batalov07/2017
76422^203825-1580561358Enzo Doria04/2013
76432^203816-1582561355Enzo Doria04/2013
76445*10^61348+5961349Robert Price09/2016
764521^46395-261345Lelio R Paula08/2013
7646(809*29^41946-165)/2861344Curtis Bright05/2015
76477*6^78826+561340Lelio R Paula09/2014
7648(3^128558+7)/8377316642969661324Lelio R Paula04/2012
76492^203706-11161322Lelio R Paula08/2011
765017567^3094+3094^1756761318Hans Havermann02/2017
76512^203689-3161317Thomas Masser10/2005
7652(11*2^203678-1)/5368961310Lelio R Paula01/2014
76532^203642+3961303Lelio R Paula08/2011
7654floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
765511^58849-604061285Enzo Doria02/2013
765643694!3-361264Robert Price10/2014
765758*(10^(3*20420)-1)/111-161260Robert Price10/2014
76582^203490+1290961257Lelio R Paula10/2011
7659(16*10^61251-31)/361252Robert Price03/2016
766020^47077-570361249Enzo Doria03/2013
76612^203434-11308161240Enzo Doria07/2014
76625^87606+461234Wojciech Florek11/2005
76632^203412-16761234Lelio R Paula08/2011
76642^203402+108961231Lelio R Paula10/2011
7665(8*10^61230+67)/361231Robert Price01/2017
7666(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
76671265^19732+19732^126561211Serge Batalov05/2014
76682^203330+14561209Lelio R Paula08/2011
76696^78647-13761200Lelio R Paula04/2013
767085^31718+8461198Norbert Schneider10/2015
767111^58763-27061196Enzo Doria07/2012
76722^203285-11232161195Enzo Doria06/2014
76732^203253-99514361186Paul Bourdelais11/2012
767415319^9862+9862^1531961184Hans Havermann07/2016
76757^72395-4461181Lelio R Paula04/2013
7676(49*10^61167-67)/961168Robert Price08/2017
76775*2^203176-761163Lelio R Paula04/2014
7678(26*10^61156-413)/961157Robert Price10/2017
76797^72358+5461150Lelio R Paula04/2013
76802^203133-11177561150Enzo Doria05/2014
7681(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
76822^203112-1800961143Enzo Doria05/2013
768343607!3+72961129Robert Price09/2014
76842^203065-11485361129Enzo Doria05/2015
76853^128111+19661125Lelio R Paula04/2013
7686128^29007+29007^12861124Serge Batalov05/2014
76874*10^61119+4961120Robert Price08/2017
768822355*2^203009-361117Donovan Johnson03/2004
76892^203018+3361115Lelio R Paula08/2011
76902^203017-161561115Lelio R Paula10/2011
769116697^4570+4570^1669761110Hans Havermann12/2016
76922^202998-1724161109Enzo Doria05/2013
769320^46964+9361102Lelio R Paula06/2013
7694(55*10^61097-1)/961098Ray Chandler02/2012
769520^46960-546361097Enzo Doria03/2013
7696(11*10^61095+49)/361096Robert Price05/2016
76972^202934-595561090Lelio R Paula10/2011
769819^47772-6861089Lelio R Paula05/2013
76992^202877-49942361073Paul Bourdelais03/2013
77002^202763-1712561038Enzo Doria05/2013
7701(23*2^202756+1)/961037Lelio R Paula03/2012
770214788^13355+13355^1478861011Hans Havermann12/2016
770316069^6258+6258^1606961005Hans Havermann12/2016
77045^87276-1433661004Enzo Doria02/2013
770550^35899-49^3589960992Robert Price12/2012
77062^202599-304960989Yves Minet10/2014
77072^202535-11157160970Enzo Doria05/2014
7708(13*10^60966+107)/360967Robert Price11/2017
771010^60959+5760960Patrick De Geest12/2008
77096*10^60959-9160960Robert Price11/2017
771210^60959-6095960959Henri Lifchitz08/2002
771110^60959-2917760959Patrick De Geest08/2008
77135^87206+4^(87206+1)60955Robert Price07/2016
77142^202476-1590960952Enzo Doria04/2013
77152^202472-1751360951Enzo Doria05/2013
771614858^12651+12651^1485860950Hans Havermann12/2016
77172^202389-5869560926Lelio R Paula09/2011
77183^127597-3460880Lelio R Paula04/2013
771915088^10831+10831^1508860876Hans Havermann12/2016
77202^202198-11326160868Enzo Doria07/2014
77212^202182+13560863Lelio R Paula08/2011
77222^202176+8560862Lelio R Paula08/2011
77235183^16384+5182^1638460860Henri Lifchitz01/2007
7724(31*2^202163+1)/360859Lelio R Paula03/2012
772514708^13707+13707^1470860847Hans Havermann12/2016
77262^202112+202112^2-160842Robert Price04/2014
7727(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
772864743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7729(19*2^202098-1)/679560836Lelio R Paula01/2014
7730(6^78175-11)/560832Paul Bourdelais11/2011
77312^202063+160560828Lelio R Paula09/2011
77322^202058+85960826Lelio R Paula09/2011
77331576^19021+19021^157660821Serge Batalov05/2014
7734(2^202009+3)/600560807Lelio R Paula03/2012
773510^60776+360777Robert Price01/2011
773610^60776-1481960776Patrick De Geest12/2012
773755*10^60772+760774Robert Price10/2017
7738(6883*2^201869-1)/3560771Lelio R Paula04/2015
7739(27*2^201841-1)/4360760Lelio R Paula01/2014
77402^201822-17760755Lelio R Paula08/2011
7741(13*10^60744+17)/360745Robert Price06/2015
7742(31*2^201754-1)/9960734Lelio R Paula01/2014
7743(26*10^60717-71)/960718Robert Price03/2015
774437^38712-260709Lelio R Paula08/2013
77452^201657-11200360705Enzo Doria05/2014
7746(10^60703+3^60703)/1360702Robert Price01/2013
77472^201622-11281760695Enzo Doria06/2014
77482^201620-1717760694Enzo Doria05/2013
7749(2^201615-3)*6-760693Gilbert Mozzo05/2016
77502^201609-4978960691Henri Lifchitz03/2005


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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