PRP Records

Probable Primes Top 10000

(252538 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 (> 50000) Who ? When ?
95012^181913+2954762Henri Lifchitz06/2005
95022^181887+18954754Lelio R Paula02/2011
95032^181874+181874^2-154750Robert Price04/2014
9504(2^181865+9)/733954743Lelio R Paula02/2012
95055^78314-9254740Lelio R Paula10/2012
9506(163*10^54727-1)/954729Serge Batalov12/2014
950715^46531+7454725Lelio R Paula02/2013
9508277^22400-34854712Enzo Doria07/2012
95096^70302+10154706Lelio R Paula10/2012
95103^114622-1040854689Enzo Doria02/2013
9512(23*2^181674+1)/48954688Lelio R Paula01/2012
95112^181669-155154688Yves Minet08/2012
9513(57352^11491-1)/5735154676Serge Batalov04/2015
9514(31*2^181629-1)/1073472154671Lelio R Paula01/2014
9515(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
951613^49073+4654665Lelio R Paula01/2013
9517(57042^11491-1)/5704154649Serge Batalov04/2015
951920^42000+7354644Lelio R Paula02/2013
9518(67607*2^181517+1)/165554644Lelio R Paula05/2014
952033*10^54634+754636Robert Price07/2016
952120^41988+6154628Lelio R Paula01/2013
952220^41988-812354628Enzo Doria03/2013
95242^181420+2118154613Yves Minet03/2011
95239854^13675-13675^985454613Norbert Schneider08/2018
9525(19*10^54608+161)/954609Robert Price07/2016
952619^42696-2454598Lelio R Paula02/2013
9527(44*10^54596-503)/954597Robert Price10/2017
9528(74*10^54583+61)/954584Robert Price10/2015
95292^181316-9439554582Lelio R Paula09/2011
953014751^5006+5006^1475154572Hans Havermann08/2016
953114^47609+3954567Lelio R Paula02/2013
953212696^13295-13295^1269654559Norbert Schneider01/2018
9533(2^124979+lucasV(2,-2,124979)+1)/354552Paul Vanderveen12/2017
95353^114327-7454548Lelio R Paula10/2012
9534(44*10^54547-161)/954548Robert Price11/2017
9536gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
9537(17*10^54537-47)/354538Robert Price05/2017
95382^181155-1155*18115554534Henri Lifchitz02/2005
9539Phi(61672,83)54533Enzo Doria05/2012
9540(2*10^54527-197)/354527Robert Price11/2017
95419*2^181128+754526Lelio R Paula03/2014
954289*10^54518-754520Robert Price03/2017
95432^181090-11324754514Enzo Doria07/2014
954414031^7670+7670^1403154508Hans Havermann08/2016
954514210^6849+6849^1421054505Hans Havermann08/2016
95462^181043-19954500Lelio R Paula02/2011
954712^50499+554498Lelio R Paula01/2013
954812^50491+554489Lelio R Paula01/2013
95496^70016-14554484Lelio R Paula10/2012
955011^52313-960054479Enzo Doria02/2013
95512^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
95522^180946-11104154471Enzo Doria05/2014
9553(64*10^54467+287)/954468Robert Price04/2016
9554(32*10^54458+319)/954459Robert Price10/2017
95555^77907-2*3^7790754455Mike Oakes11/2009
955620^41853-562354453Enzo Doria03/2013
955714^47506-7554448Lelio R Paula02/2013
9558(25*10^54443-67)/354444Robert Price11/2017
95592^180839-11343754438Enzo Doria08/2014
95603^114085+2854433Lelio R Paula10/2012
9561Phi(141230,10)54432Ray Chandler08/2009
95626^69946-5554429Lelio R Paula10/2012
9563p(11796)#/2-102454427Robert Price09/2017
95645*2^180796+354426Lelio R Paula03/2014
9565(23*2^180782-1)/9154421Lelio R Paula01/2014
95669*6^69928-754416Lelio R Paula09/2014
956792^27701-91^2770154399Robert Price08/2015
9568(2^180687-3)*6-754393Gilbert Mozzo04/2016
9569(5*10^54388-11)/354389Erik Branger12/2013
957120^41799-304354382Enzo Doria03/2013
957013860^8387+8387^1386054382Hans Havermann08/2016
9572(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
95737^64329-1854365Lelio R Paula10/2012
95742^180551-96754352Yves Minet01/2012
95759075^13732-13732^907554350Norbert Schneider09/2018
957615^46209-7454347Lelio R Paula02/2013
957710^54345+2973954346Patrick De Geest08/2013
957810^54345-14138154345Patrick De Geest09/2013
9579lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
9580177^24171-254336Lelio R Paula10/2017
95812^180496+1554335Lelio R Paula02/2011
95821845^16636+16636^184554334Serge Batalov05/2014
958311^52169-7054329Lelio R Paula01/2013
95842^180446-403154320Yves Minet02/2018
958513693^9262+9262^1369354317Hans Havermann06/2016
95862^180429-11310154315Enzo Doria07/2014
95872^180423-11205154313Enzo Doria05/2014
958816112^2349+2349^1611254312Hans Havermann06/2016
9589(79^28621-1)/7854311Paul Bourdelais08/2017
9590(13^48751+4^48751)/1754305Robert Price05/2013
95912^180370+1291554297Lelio R Paula09/2012
9592(10^54290+41)/354290Robert Price01/2017
959315108^3917+3917^1510854283Hans Havermann06/2016
95942^180317-301954281Yves Minet10/2014
95952^180314+85554280Lelio R Paula10/2009
959619^42425+9454252Lelio R Paula02/2013
95972^180180-100544954240Paul Bourdelais11/2012
95982^180173-277354238Yves Minet07/2014
959913367^11418+11418^1336754238Hans Havermann06/2016
9600427^20614+20614^42754224Norbert Schneider06/2016
96012^180124-8795954223Gary Barnes08/2009
96022^180111-11310154219Enzo Doria07/2014
96032^180101-11487154216Enzo Doria05/2015
9604(11*2^180099+1)/5161754212Lelio R Paula07/2012
96062^180070+46554207Lelio R Paula09/2012
960513683^9154+9154^1368354207Hans Havermann06/2016
9607810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
96082^180014+61354190Jason Earls04/2008
96092^180007+10154188Lelio R Paula02/2011
96102^180001+4187754186Jim Fougeron08/2002
96112^180000+13015354186Jim Fougeron09/2002
96123^113565-7454185Lelio R Paula10/2012
961350^31891-4954182Norbert Schneider07/2014
9614(5*2^179991-1)/1142754180Lelio R Paula01/2014
96153^113548+2654177Lelio R Paula10/2012
9616(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
9617181^23996-254176Lelio R Paula10/2017
96184159^14969-13854173Enzo Doria07/2012
96202^179955+577554172Lelio R Paula10/2009
96192^179953-23131354172Enzo Doria05/2014
96215^77485+654160Lelio R Paula10/2012
962218^43141+8554154Lelio R Paula02/2013
962310^54149+18764754150Patrick De Geest07/2017
96263^113489-34054149Lelio R Paula10/2012
962410^54149-80000154149Robert Price06/2017
962510^54149-3650154149Patrick De Geest07/2017
96277^64070+9054146Lelio R Paula10/2012
962812549^13210-13210^1254954143Norbert Schneider12/2017
962918^43131+7154142Lelio R Paula02/2013
96302^179826-13154134Lelio R Paula02/2011
96312^179815-11273554130Enzo Doria06/2014
96322^179806+7384954127Enzo Doria04/2016
96332^179790+3354123Donovan Johnson02/2006
963414287^6138+6138^1428754120Hans Havermann06/2016
9635(17*10^54117+1)/954118Serge Batalov05/2010
96362^179763-18954115Lelio R Paula02/2011
9637(21181*2^179770+1)/302910554115Lelio R Paula05/2014
96381828^16589+16589^182854113Serge Batalov05/2014
964020^41588-588354108Enzo Doria03/2013
963950^31847-4954108Norbert Schneider07/2014
96412^179733-685554106Lelio R Paula10/2009
964220^41584-558354103Enzo Doria03/2013
964310^54084+3*3^5408454085Mike Oakes05/2010
96442^179613-179554069Lelio R Paula10/2009
96452^179589-101152354062Paul Bourdelais11/2012
96462^179574-253154058Yves Minet07/2014
9647(41*10^54051-23)/954052Robert Price05/2015
9648117^26131-11654044Norbert Schneider10/2013
9649(10^54038-31)/354038Serge Batalov12/2014
965011^51885-8454033Lelio R Paula01/2013
965114990^4011+4011^1499054013Hans Havermann07/2016
9652(19*2^179414+1)/754010Lelio R Paula07/2012
96533^113182-1040854002Enzo Doria02/2013
965435^34970-878653997Enzo Doria03/2013
96552^179371-163758753997Enzo Doria05/2015
965619^42225-9253996Lelio R Paula01/2013
965710190^13471-13471^1019053995Norbert Schneider05/2018
9658(3^113188+7)/7391767578453994Lelio R Paula03/2012
96597*3^113162+853993Lelio R Paula03/2014
9660(10^53991+179)/953991Serge Batalov12/2014
96622^179350-214553990Lelio R Paula10/2009
9661(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
96638^59782-6^59782-3^5978253989Mike Oakes11/2009
96643*7^63861+853970Lelio R Paula09/2014
96652^179274+7138953967Enzo Doria04/2016
96662^179259-5869553963Lelio R Paula10/2009
96676^69345+6153961Lelio R Paula10/2012
96687674^13889-13889^767453960Norbert Schneider12/2018
9669(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
9670(40216^11719-1)/4021553955Serge Batalov04/2015
967189*10^53951-953953Robert Price05/2017
96726703^14100-14100^670353951Norbert Schneider11/2018
967314^47067-353945Lelio R Paula01/2013
9674p(11700)#/2-51253937Robert Price07/2017
9675(2^179168-5)/5953934Lelio R Paula02/2012
96762^179128+841553923Lelio R Paula07/2012
96772^179120+253353921Henri Lifchitz09/2004
9678(2^179126+78557)/464932118753913Lelio R Paula05/2012
967974^28842+7353913Norbert Schneider11/2012
96801271^17368+17368^127153913Serge Batalov05/2014
96812^179079+5353909Lelio R Paula02/2011
968217^43807+5453903Lelio R Paula01/2013
968317^43807+3053903Lelio R Paula01/2013
96843^112951-31053892Lelio R Paula10/2012
9685Phi(7,2957!)53888Robert Price05/2015
96868275^13754-13754^827553885Norbert Schneider10/2018
9687(10223*2^178975+1)/3398553877Lelio R Paula05/2014
96882^178944-21920953868Enzo Doria11/2012
9689(10^53859+149)/353859Serge Batalov12/2014
96902^178910-19153858Lelio R Paula02/2011
969116170^2141+2141^1617053857Hans Havermann07/2016
9692(5*10^53855-107)/353856Robert Price01/2017
9693(72*10^53847-27)/9953847Patrick De Geest08/2004
96942^178841-86968810553837Lelio R Paula06/2012
96952*10^53834-2753835Robert Price02/2017
96972^178821-101152353831Paul Bourdelais11/2012
969612601^13128-13128^1260153831Norbert Schneider10/2017
96982^178819-1553830Lelio R Paula02/2011
9699(14450!-1)/22529658153829Donovan Johnson04/2006
9700(124351#+125386)/(2^5*71*883*4489103*9820259)53826Makoto Morimoto10/2017
970110530^13381-13381^1053053825Norbert Schneider03/2018
97022^178761-46553813Lelio R Paula10/2009
970318900^703+703^1890053808Anatoly F. Selevich02/2007
970413918^7343+7343^1391853806Hans Havermann08/2016
970510^53804+3174953805Patrick De Geest12/2012
970610^53804-7153804Robert Price05/2011
9707t(178994)53804Robert Price03/2015
9708(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
97092^178671-11321553786Enzo Doria07/2014
971015110^3621+3621^1511053774Hans Havermann07/2016
97112^178611+9553768Lelio R Paula02/2011
97122^178597+571153764Lelio R Paula10/2011
97132^178598+1291553764Lelio R Paula07/2012
9714(9179*2^178579-1)/30353760Lelio R Paula03/2015
971510671^13342-13342^1067153745Norbert Schneider02/2018
97165*7^63589+253740Lelio R Paula09/2014
97172^178516-11251553739Enzo Doria06/2014
971820^41302-2753736Lelio R Paula01/2013
97196^69054-3920953735Mike Oakes12/2010
972013086^12769+12769^1308653734Hans Havermann07/2016
97212^178455+7604353721Enzo Doria04/2016
9722(10^53718-7)/353718Makoto Kamada10/2004
9723(67607*2^178426+1)/353716Lelio R Paula05/2014
97249*10^53707+1153708Robert Kinser01/2017
972594601!8-253708Robert Price04/2017
972613214^11595+11595^1321453706Hans Havermann07/2016
9727Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
97282^178367-37953694Yves Minet03/2013
9729(2^178364-5)/1153692Lelio R Paula02/2012
97304339^14760-16853688Enzo Doria06/2012
973112^49746-1153685Lelio R Paula01/2013
973212950^13051-13051^1295053670Norbert Schneider08/2017
9734(9913*2^178266-1)/224753665Lelio R Paula03/2015
973313725^8128+8128^1372553665Hans Havermann07/2016
97352^178250-11326153659Enzo Doria07/2014
97362^178226+1171553652Lelio R Paula10/2009
973735^34742-197653645Enzo Doria03/2013
973820^41228-56353639Enzo Doria03/2013
9739359^20992+20992^35953637Norbert Schneider08/2014
9740(27*2^178183-1)/2906553636Lelio R Paula01/2014
9741(3^112414+7)/3738169653628Lelio R Paula03/2012
974217994^955+955^1799453623Anatoly F. Selevich10/2006
97432^178117-155153619Yves Minet08/2012
97442^178099-1128753614Enzo Doria06/2014
974510751^13298-13298^1075153611Norbert Schneider01/2018
9746(15*2^178080-1)/30907153604Lelio R Paula01/2014
97475^76672-1376653592Enzo Doria02/2013
97486^68868-13753590Lelio R Paula10/2012
9749(5*2^178021+1)/817353587Lelio R Paula07/2012
97505^76654-2653579Lelio R Paula10/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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