PRP Records

Probable Primes Top 10000

(218736 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 ?
775119^48661+1062226Lelio R Paula05/2013
7752(17*2^206705+1)/562225Lelio R Paula08/2012
77532^206705-11263562225Enzo Doria06/2014
77543^130403+868062219Lelio R Paula04/2013
775511^59740-711062213Enzo Doria01/2013
77572^206596-16762192Lelio R Paula08/2011
77562^206597+1891562192Lelio R Paula02/2013
77586^79918+13762189Lelio R Paula04/2013
7759lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
77602^206574+61362185Jason Earls04/2008
77613^130328+8062183Lelio R Paula04/2013
7762(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
77632^206550+7681962178Enzo Doria05/2016
776411^59703-2462175Lelio R Paula05/2013
77652^206524+7578162170Enzo Doria04/2016
77662^206506+42762165Henri Lifchitz01/2005
77672^206465+769562153Lelio R Paula02/2013
77682^206464-164962152Yves Minet03/2013
77695^88917+5662151Lelio R Paula04/2013
77702^206444-11156962146Enzo Doria05/2014
77715^88908-4262145Lelio R Paula04/2013
777218^49495-2962130Lelio R Paula05/2013
77733*6^79842-562130Lelio R Paula09/2014
77747*10^62127-1762128Robert Price01/2017
77752^206373+841562125Lelio R Paula02/2013
777620^47745-958362118Enzo Doria03/2013
777741^38516-262118Lelio R Paula08/2013
77782^206332-5869562113Lelio R Paula09/2011
777911^59639-126062108Enzo Doria11/2012
77802^206232-1589362083Enzo Doria04/2013
7781(115*10^62073-1)/362075Serge Batalov12/2014
77822^206206+7579962075Enzo Doria04/2016
7783(74*10^62072+43)/962073Robert Price10/2015
77842^206194-18562071Lelio R Paula08/2011
77856^79757-10362064Lelio R Paula04/2013
7786p(13285)#/2-6462063Robert Price04/2017
7787(29*10^62030-41)/362031Robert Price07/2016
778820^47675-8162027Lelio R Paula06/2013
77893^129972+9862013Lelio R Paula04/2013
77902^205962+362001Donovan Johnson02/2006
77912^205933-205933^261993Henri Lifchitz05/2005
7792(68*10^61991+7)/361993Robert Price03/2016
779320^47641-66361983Enzo Doria03/2013
77943^129861+266061960Lelio R Paula04/2013
7795(55459*2^205800+1)/134561954Lelio R Paula06/2014
779618^49354-9761953Lelio R Paula05/2013
7797(209*10^61947-17)/361949Robert Price05/2017
779814*10^61937+108961939Jens K. Andersen11/2007
7799(11*2^205758-1)/5361939Lelio R Paula01/2014
780020^47600+6361930Lelio R Paula06/2013
7801(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
780244117!3+24361918Robert Price09/2014
7803(31*2^205677-1)/5961915Lelio R Paula01/2014
7804(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
780520^47575-8161897Lelio R Paula06/2013
7806(58695*2^205593-1)/72761892Lelio R Paula04/2015
780787^31909+8661889Norbert Schneider10/2015
78082^205568+14161883Lelio R Paula08/2011
780910^61868+5892761869Patrick De Geest12/2012
781010^61868-3961868Robert Price05/2011
78125^88505-8861863Lelio R Paula04/2013
7811(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
781313^55528-9861856Lelio R Paula05/2013
7814(55^35543-1)/5461856Paul Bourdelais08/2017
781530535!2-861844Robert Price06/2015
781611^59371-120061829Enzo Doria11/2012
78177*2^205370-561824Lelio R Paula04/2014
7818(47*10^61821+403)/961822Robert Price04/2017
78192^205275+769561794Lelio R Paula02/2013
78202^205269+1291561793Lelio R Paula02/2013
7821(47*2^205265+1)/3561792Lelio R Paula04/2015
782219^48309+4061776Lelio R Paula05/2013
7823(424*10^61770-1)/961772Robert Price11/2017
78242^205192-407961769Yves Minet06/2011
78252^205184+1609561767Lelio R Paula09/2011
782620^47472-342361763Enzo Doria03/2013
7827(17*10^61760-89)/961761Robert Price11/2017
78282^205149-179561757Lelio R Paula09/2011
78292^205110-1761745Lelio R Paula08/2011
7830(373^24007+1)/37461737Eric Chen10/2017
7831(2^205025-7)/2561718Lelio R Paula03/2012
783227^43117-26^4311761717Robert Price08/2012
78332^205016+3761716Lelio R Paula08/2011
7834gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
78351263^19898+19898^126361712Serge Batalov05/2014
7836135^28963-13461701Norbert Schneider04/2015
7837(33*2^204966+1)/23434161698Michael Porter01/2015
7838(7*10^61696+167)/361696Robert Kinser10/2017
7839(46*10^61693+17)/961694Robert Price06/2015
7840((((((((((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
78411850^18879+18879^185061681Serge Batalov05/2014
78422^204891-100561679Lelio R Paula09/2011
7843151^28306-261679Lelio R Paula10/2017
7844(3^129271-5)/4150661674Lelio R Paula03/2012
784515937^7408+7408^1593761672Hans Havermann02/2017
78465^88216-1261661Lelio R Paula04/2013
784718185^2454+2454^1818561645Hans Havermann01/2017
78492^204767-1586561642Enzo Doria04/2013
7848(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
78507*2^204751-961638Lelio R Paula04/2014
78514*10^61625+2161626Robert Price08/2016
785215369^10226+10226^1536961626Hans Havermann02/2017
78532^204702-1812561622Enzo Doria05/2013
78545*3^129146+861620Lelio R Paula04/2014
78552^204673+12961613Lelio R Paula08/2011
785618^49079+9761608Lelio R Paula05/2013
7857106^30416+10561602Norbert Schneider12/2016
78582^204590-3361588Lelio R Paula08/2011
78592^204586-11197561587Enzo Doria06/2014
78602^204580-1607761585Enzo Doria04/2013
78612^204574-1604161583Enzo Doria04/2013
786215^52358+5661578Lelio R Paula05/2013
7863(28*10^61574+11)/361575Robert Price11/2015
78642^204516-1749361566Enzo Doria05/2013
78654*5^88076-361564Lelio R Paula09/2014
786611^59110-252061557Enzo Doria12/2012
78672^204477-5869561554Lelio R Paula09/2011
786812^57026-7361542Lelio R Paula05/2013
7869(257^25537+1)/25861541Richard Fischer04/2018
787017^50013+9061539Lelio R Paula05/2013
787156^35201-55^3520161538Robert Price10/2013
78728*7^72810+561533Lelio R Paula09/2014
7874204^26641-203^2664161531Jean-Louis Charton08/2009
787343867!3-656161531Robert Price11/2015
787510^61525+9^(61525-1)61526Robert Price03/2016
787610^61525+6225761526Patrick De Geest12/2016
787714821^14166+14166^1482161526Hans Havermann01/2017
787912^57010-8561525Lelio R Paula05/2013
787810^61525-21357961525Patrick De Geest12/2016
78802^204332-9961511Lelio R Paula08/2011
78812^204323-222161508Yves Minet08/2013
78832^204317-19561506Lelio R Paula08/2011
78823^128910-8661506Lelio R Paula04/2013
78842^204318+7453961506Enzo Doria04/2016
7885(2^204334-3)/114133361505Lelio R Paula03/2012
78862^204297-103609361500Paul Bourdelais11/2012
78873^128880+5861492Lelio R Paula04/2013
78882^204216-11167761476Enzo Doria05/2014
7889(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
78902^204129+20412961449Henri Lifchitz04/2002
78913^128787+2^(128787-1)61448Robert Price05/2016
789211^58999-7861442Lelio R Paula05/2013
78932^204083-11196761436Enzo Doria05/2014
7894(45^37159+1)/4661431Robert Price11/2013
7895677^21702+21702^67761430Norbert Schneider06/2016
789614837^13810+13810^1483761429Hans Havermann02/2017
7897(7*2^204043+1)/3961423Lelio R Paula03/2012
789811^58976-174061418Enzo Doria11/2012
78992^204016-1608561415Enzo Doria04/2013
7900V(379967)61393Serge Batalov03/2015
790143777!3-3^4377761392Robert Price08/2015
79027^72642+8861390Lelio R Paula04/2013
79033^128656+3261385Lelio R Paula04/2013
79042^203916-1749361385Enzo Doria05/2013
79056^78880+2361381Lelio R Paula04/2013
7906(388*10^61374-1)/961376Robert Price11/2017
79072^203877-11179961374Enzo Doria05/2014
79082^203867-161561371Lelio R Paula10/2011
79094*10^61367+1961368Robert Price04/2016
7910(19*2^203854+1)/4231961363Lelio R Paula08/2012
7911L(293659)/7652812271961361Serge Batalov07/2017
79122^203825-1580561358Enzo Doria04/2013
79132^203816-1582561355Enzo Doria04/2013
79145*10^61348+5961349Robert Price09/2016
791521^46395-261345Lelio R Paula08/2013
7916(809*29^41946-165)/2861344Curtis Bright05/2015
79177*6^78826+561340Lelio R Paula09/2014
7918(3^128558+7)/8377316642969661324Lelio R Paula04/2012
79192^203706-11161322Lelio R Paula08/2011
792017567^3094+3094^1756761318Hans Havermann02/2017
79212^203689-3161317Thomas Masser10/2005
7922(11*2^203678-1)/5368961310Lelio R Paula01/2014
79232^203642+3961303Lelio R Paula08/2011
7924floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
792511^58849-604061285Enzo Doria02/2013
792643694!3-361264Robert Price10/2014
792758*(10^(3*20420)-1)/111-161260Robert Price10/2014
79282^203490+1290961257Lelio R Paula10/2011
7929(16*10^61251-31)/361252Robert Price03/2016
793020^47077-570361249Enzo Doria03/2013
79312^203434-11308161240Enzo Doria07/2014
79335^87606+461234Wojciech Florek11/2005
79322^203412-16761234Lelio R Paula08/2011
79352^203402+108961231Lelio R Paula10/2011
7934(8*10^61230+67)/361231Robert Price01/2017
7936(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
79371265^19732+19732^126561211Serge Batalov05/2014
79382^203330+14561209Lelio R Paula08/2011
79396^78647-13761200Lelio R Paula04/2013
794085^31718+8461198Norbert Schneider10/2015
794111^58763-27061196Enzo Doria07/2012
79422^203285-11232161195Enzo Doria06/2014
79432^203253-99514361186Paul Bourdelais11/2012
794415319^9862+9862^1531961184Hans Havermann07/2016
79457^72395-4461181Lelio R Paula04/2013
7946(49*10^61167-67)/961168Robert Price08/2017
79475*2^203176-761163Lelio R Paula04/2014
7948(26*10^61156-413)/961157Robert Price10/2017
79507^72358+5461150Lelio R Paula04/2013
79492^203133-11177561150Enzo Doria05/2014
7951(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
79522^203112-1800961143Enzo Doria05/2013
795343607!3+72961129Robert Price09/2014
79542^203065-11485361129Enzo Doria05/2015
79553^128111+19661125Lelio R Paula04/2013
7956128^29007+29007^12861124Serge Batalov05/2014
79574*10^61119+4961120Robert Price08/2017
795822355*2^203009-361117Donovan Johnson03/2004
79592^203018+3361115Lelio R Paula08/2011
79602^203017-161561115Lelio R Paula10/2011
796116697^4570+4570^1669761110Hans Havermann12/2016
79622^202998-1724161109Enzo Doria05/2013
796320^46964+9361102Lelio R Paula06/2013
7964(55*10^61097-1)/961098Ray Chandler02/2012
796520^46960-546361097Enzo Doria03/2013
7966(11*10^61095+49)/361096Robert Price05/2016
79672^202934-595561090Lelio R Paula10/2011
796819^47772-6861089Lelio R Paula05/2013
79692^202877-49942361073Paul Bourdelais03/2013
79702^202763-1712561038Enzo Doria05/2013
7971(23*2^202756+1)/961037Lelio R Paula03/2012
797214788^13355+13355^1478861011Hans Havermann12/2016
797316069^6258+6258^1606961005Hans Havermann12/2016
79745^87276-1433661004Enzo Doria02/2013
797550^35899-49^3589960992Robert Price12/2012
79762^202599-304960989Yves Minet10/2014
79772^202535-11157160970Enzo Doria05/2014
7978(13*10^60966+107)/360967Robert Price11/2017
798010^60959+5760960Patrick De Geest12/2008
79796*10^60959-9160960Robert Price11/2017
798210^60959-6095960959Henri Lifchitz08/2002
798110^60959-2917760959Patrick De Geest08/2008
79835^87206+4^(87206+1)60955Robert Price07/2016
79842^202476-1590960952Enzo Doria04/2013
79852^202472-1751360951Enzo Doria05/2013
798614858^12651+12651^1485860950Hans Havermann12/2016
79872^202389-5869560926Lelio R Paula09/2011
79883^127597-3460880Lelio R Paula04/2013
798915088^10831+10831^1508860876Hans Havermann12/2016
79902^202198-11326160868Enzo Doria07/2014
79912^202182+13560863Lelio R Paula08/2011
79922^202176+8560862Lelio R Paula08/2011
79935183^16384+5182^1638460860Henri Lifchitz01/2007
7994(31*2^202163+1)/360859Lelio R Paula03/2012
799514708^13707+13707^1470860847Hans Havermann12/2016
79962^202112+202112^2-160842Robert Price04/2014
7997(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
799864743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7999(19*2^202098-1)/679560836Lelio R Paula01/2014
8000(6^78175-11)/560832Paul Bourdelais11/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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