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 ?
8501(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
8502(17*2^182274+1)/146754869Lelio R Paula01/2012
850318^43698-554853Lelio R Paula02/2013
85042^182209-189354851Yves Minet09/2012
85052^182194-344354846Yves Minet12/2016
850615023^4468+4468^1502354836Hans Havermann08/2016
85072^182135+9014354829Yves Minet10/2010
85082^182119+7433354824Enzo Doria04/2016
850914289^6860+6860^1428954818Hans Havermann08/2016
85103^114892-114892^354818Norbert Schneider03/2017
85112^182070-4735554809Lelio R Paula01/2011
85123^114869+7654807Lelio R Paula10/2012
85138^60681-60681^854801Norbert Schneider12/2016
85141897^16710+16710^189754777Serge Batalov05/2014
8515Phi(61868,59)54776Enzo Doria04/2012
8516113^26679+254775Lelio R Paula05/2013
85173^114789-7454769Lelio R Paula10/2012
851815^46567+9854768Lelio R Paula02/2013
8519(2*10^54767-71)/354767Robert Price01/2017
8520(298*10^54765-7)/354767Robert Price06/2017
8521(21*2^181931-1)/16999754763Lelio R Paula01/2014
85232^181913+2954762Henri Lifchitz06/2005
8522(31*10^54761-121)/954762Robert Price06/2016
85242^181887+18954754Lelio R Paula02/2011
85252^181874+181874^2-154750Robert Price04/2014
8526(2^181865+9)/733954743Lelio R Paula02/2012
85275^78314-9254740Lelio R Paula10/2012
8528(163*10^54727-1)/954729Serge Batalov12/2014
852915^46531+7454725Lelio R Paula02/2013
8530277^22400-34854712Enzo Doria07/2012
85316^70302+10154706Lelio R Paula10/2012
85323^114622-1040854689Enzo Doria02/2013
8534(23*2^181674+1)/48954688Lelio R Paula01/2012
85332^181669-155154688Yves Minet08/2012
8535(57352^11491-1)/5735154676Serge Batalov04/2015
8536(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8537(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
853813^49073+4654665Lelio R Paula01/2013
8539(57042^11491-1)/5704154649Serge Batalov04/2015
854120^42000+7354644Lelio R Paula02/2013
8540(67607*2^181517+1)/165554644Lelio R Paula05/2014
854233*10^54634+754636Robert Price07/2016
854320^41988+6154628Lelio R Paula01/2013
854420^41988-812354628Enzo Doria03/2013
85452^181420+2118154613Yves Minet03/2011
8546(19*10^54608+161)/954609Robert Price07/2016
854719^42696-2454598Lelio R Paula02/2013
8548(74*10^54583+61)/954584Robert Price10/2015
85492^181316-9439554582Lelio R Paula09/2011
855014751^5006+5006^1475154572Hans Havermann08/2016
855114^47609+3954567Lelio R Paula02/2013
85523^114327-7454548Lelio R Paula10/2012
8553gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
8554(17*10^54537-47)/354538Robert Price05/2017
85552^181155-1155*18115554534Henri Lifchitz02/2005
8556Phi(61672,83)54533Enzo Doria05/2012
85579*2^181128+754526Lelio R Paula03/2014
855889*10^54518-754520Robert Price03/2017
85592^181090-11324754514Enzo Doria07/2014
856014031^7670+7670^1403154508Hans Havermann08/2016
856114210^6849+6849^1421054505Hans Havermann08/2016
85622^181043-19954500Lelio R Paula02/2011
856312^50499+554498Lelio R Paula01/2013
856412^50491+554489Lelio R Paula01/2013
85656^70016-14554484Lelio R Paula10/2012
856611^52313-960054479Enzo Doria02/2013
85672^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
85682^180946-11104154471Enzo Doria05/2014
8569(64*10^54467+287)/954468Robert Price04/2016
85705^77907-2*3^7790754455Mike Oakes11/2009
857120^41853-562354453Enzo Doria03/2013
857214^47506-7554448Lelio R Paula02/2013
85732^180839-11343754438Enzo Doria08/2014
85743^114085+2854433Lelio R Paula10/2012
8575Phi(141230,10)54432Ray Chandler08/2009
85766^69946-5554429Lelio R Paula10/2012
8577p(11796)#/2-102454427Robert Price09/2017
85785*2^180796+354426Lelio R Paula03/2014
8579(23*2^180782-1)/9154421Lelio R Paula01/2014
85809*6^69928-754416Lelio R Paula09/2014
858192^27701-91^2770154399Robert Price08/2015
8582(2^180687-3)*6-754393Gilbert Mozzo04/2016
8583(5*10^54388-11)/354389Erik Branger12/2013
858420^41799-304354382Enzo Doria03/2013
858513860^8387+8387^1386054382Hans Havermann08/2016
8586(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
85877^64329-1854365Lelio R Paula10/2012
85882^180551-96754352Yves Minet01/2012
858915^46209-7454347Lelio R Paula02/2013
859010^54345+2973954346Patrick De Geest08/2013
859110^54345-14138154345Patrick De Geest09/2013
8592lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
8593177^24171-254336Lelio R Paula10/2017
85942^180496+1554335Lelio R Paula02/2011
85951845^16636+16636^184554334Serge Batalov05/2014
859611^52169-7054329Lelio R Paula01/2013
859713693^9262+9262^1369354317Hans Havermann06/2016
85982^180429-11310154315Enzo Doria07/2014
85992^180423-11205154313Enzo Doria05/2014
860016112^2349+2349^1611254312Hans Havermann06/2016
8601(79^28621-1)/7854311Paul Bourdelais08/2017
8602(13^48751+4^48751)/1754305Robert Price05/2013
86032^180370+1291554297Lelio R Paula09/2012
8604(10^54290+41)/354290Robert Price01/2017
860515108^3917+3917^1510854283Hans Havermann06/2016
86062^180317-301954281Yves Minet10/2014
86072^180314+85554280Lelio R Paula10/2009
860819^42425+9454252Lelio R Paula02/2013
86092^180180-100544954240Paul Bourdelais11/2012
86102^180173-277354238Yves Minet07/2014
861113367^11418+11418^1336754238Hans Havermann06/2016
8612427^20614+20614^42754224Norbert Schneider06/2016
86132^180124-8795954223Gary Barnes08/2009
86142^180111-11310154219Enzo Doria07/2014
86152^180101-11487154216Enzo Doria05/2015
8616(11*2^180099+1)/5161754212Lelio R Paula07/2012
86182^180070+46554207Lelio R Paula09/2012
861713683^9154+9154^1368354207Hans Havermann06/2016
8619810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
86202^180014+61354190Jason Earls04/2008
86212^180007+10154188Lelio R Paula02/2011
86222^180001+4187754186Jim Fougeron08/2002
86232^180000+13015354186Jim Fougeron09/2002
86243^113565-7454185Lelio R Paula10/2012
862550^31891-4954182Norbert Schneider07/2014
8626(5*2^179991-1)/1142754180Lelio R Paula01/2014
86273^113548+2654177Lelio R Paula10/2012
8628(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
8629181^23996-254176Lelio R Paula10/2017
86304159^14969-13854173Enzo Doria07/2012
86322^179955+577554172Lelio R Paula10/2009
86312^179953-23131354172Enzo Doria05/2014
86335^77485+654160Lelio R Paula10/2012
863418^43141+8554154Lelio R Paula02/2013
863510^54149+18764754150Patrick De Geest07/2017
86383^113489-34054149Lelio R Paula10/2012
863610^54149-80000154149Robert Price06/2017
863710^54149-3650154149Patrick De Geest07/2017
86397^64070+9054146Lelio R Paula10/2012
864018^43131+7154142Lelio R Paula02/2013
86412^179826-13154134Lelio R Paula02/2011
86422^179815-11273554130Enzo Doria06/2014
86432^179806+7384954127Enzo Doria04/2016
86442^179790+3354123Donovan Johnson02/2006
864514287^6138+6138^1428754120Hans Havermann06/2016
8646(17*10^54117+1)/954118Serge Batalov05/2010
86472^179763-18954115Lelio R Paula02/2011
8648(21181*2^179770+1)/302910554115Lelio R Paula05/2014
86491828^16589+16589^182854113Serge Batalov05/2014
865120^41588-588354108Enzo Doria03/2013
865050^31847-4954108Norbert Schneider07/2014
86522^179733-685554106Lelio R Paula10/2009
865320^41584-558354103Enzo Doria03/2013
865410^54084+3*3^5408454085Mike Oakes05/2010
86552^179613-179554069Lelio R Paula10/2009
86562^179589-101152354062Paul Bourdelais11/2012
86572^179574-253154058Yves Minet07/2014
8658(41*10^54051-23)/954052Robert Price05/2015
8659117^26131-11654044Norbert Schneider10/2013
8660(10^54038-31)/354038Serge Batalov12/2014
866111^51885-8454033Lelio R Paula01/2013
866214990^4011+4011^1499054013Hans Havermann07/2016
8663(19*2^179414+1)/754010Lelio R Paula07/2012
86643^113182-1040854002Enzo Doria02/2013
866535^34970-878653997Enzo Doria03/2013
86662^179371-163758753997Enzo Doria05/2015
866719^42225-9253996Lelio R Paula01/2013
8668(3^113188+7)/7391767578453994Lelio R Paula03/2012
86697*3^113162+853993Lelio R Paula03/2014
8670(10^53991+179)/953991Serge Batalov12/2014
86712^179350-214553990Lelio R Paula10/2009
8672(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
86738^59782-6^59782-3^5978253989Mike Oakes11/2009
86743*7^63861+853970Lelio R Paula09/2014
86752^179274+7138953967Enzo Doria04/2016
86762^179259-5869553963Lelio R Paula10/2009
86776^69345+6153961Lelio R Paula10/2012
8678(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
8679(40216^11719-1)/4021553955Serge Batalov04/2015
868089*10^53951-953953Robert Price05/2017
868114^47067-353945Lelio R Paula01/2013
8682p(11700)#/2-51253937Robert Price07/2017
8683(2^179168-5)/5953934Lelio R Paula02/2012
86842^179128+841553923Lelio R Paula07/2012
86852^179120+253353921Henri Lifchitz09/2004
8686(2^179126+78557)/464932118753913Lelio R Paula05/2012
868774^28842+7353913Norbert Schneider11/2012
86881271^17368+17368^127153913Serge Batalov05/2014
86892^179079+5353909Lelio R Paula02/2011
869017^43807+5453903Lelio R Paula01/2013
869117^43807+3053903Lelio R Paula01/2013
86923^112951-31053892Lelio R Paula10/2012
8693Phi(7,2957!)53888Robert Price05/2015
8694(10223*2^178975+1)/3398553877Lelio R Paula05/2014
86952^178944-21920953868Enzo Doria11/2012
8696(10^53859+149)/353859Serge Batalov12/2014
86972^178910-19153858Lelio R Paula02/2011
869816170^2141+2141^1617053857Hans Havermann07/2016
8699(5*10^53855-107)/353856Robert Price01/2017
8700(72*10^53847-27)/9953847Patrick De Geest08/2004
87012^178841-86968810553837Lelio R Paula06/2012
87022*10^53834-2753835Robert Price02/2017
87032^178821-101152353831Paul Bourdelais11/2012
87042^178819-1553830Lelio R Paula02/2011
8705(14450!-1)/22529658153829Donovan Johnson04/2006
87062^178761-46553813Lelio R Paula10/2009
870718900^703+703^1890053808Anatoly F. Selevich02/2007
870813918^7343+7343^1391853806Hans Havermann08/2016
870910^53804+3174953805Patrick De Geest12/2012
871110^53804-7153804Robert Price05/2011
8710t(178994)53804Robert Price03/2015
8712(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
87132^178671-11321553786Enzo Doria07/2014
871415110^3621+3621^1511053774Hans Havermann07/2016
87152^178611+9553768Lelio R Paula02/2011
87162^178597+571153764Lelio R Paula10/2011
87172^178598+1291553764Lelio R Paula07/2012
8718(9179*2^178579-1)/30353760Lelio R Paula03/2015
87195*7^63589+253740Lelio R Paula09/2014
87202^178516-11251553739Enzo Doria06/2014
872120^41302-2753736Lelio R Paula01/2013
87226^69054-3920953735Mike Oakes12/2010
872313086^12769+12769^1308653734Hans Havermann07/2016
87242^178455+7604353721Enzo Doria04/2016
8725(10^53718-7)/353718Makoto Kamada10/2004
8726(67607*2^178426+1)/353716Lelio R Paula05/2014
87279*10^53707+1153708Robert Kinser01/2017
872894601!8-253708Robert Price04/2017
872913214^11595+11595^1321453706Hans Havermann07/2016
8730Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
87312^178367-37953694Yves Minet03/2013
8732(2^178364-5)/1153692Lelio R Paula02/2012
87334339^14760-16853688Enzo Doria06/2012
873412^49746-1153685Lelio R Paula01/2013
873512950^13051-13051^1295053670Norbert Schneider08/2017
8736(9913*2^178266-1)/224753665Lelio R Paula03/2015
873713725^8128+8128^1372553665Hans Havermann07/2016
87382^178250-11326153659Enzo Doria07/2014
87392^178226+1171553652Lelio R Paula10/2009
874035^34742-197653645Enzo Doria03/2013
874120^41228-56353639Enzo Doria03/2013
8742359^20992+20992^35953637Norbert Schneider08/2014
8743(27*2^178183-1)/2906553636Lelio R Paula01/2014
8744(3^112414+7)/3738169653628Lelio R Paula03/2012
874517994^955+955^1799453623Anatoly F. Selevich10/2006
87462^178117-155153619Yves Minet08/2012
87472^178099-1128753614Enzo Doria06/2014
8748(15*2^178080-1)/30907153604Lelio R Paula01/2014
87495^76672-1376653592Enzo Doria02/2013
87506^68868-13753590Lelio R Paula10/2012


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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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