PRP Records

Probable Primes Top 10000

(191107 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 ?
875110^54345+2973954346Patrick De Geest08/2013
875210^54345-14138154345Patrick De Geest09/2013
8753lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
8754177^24171-254336Lelio R Paula10/2017
87552^180496+1554335Lelio R Paula02/2011
87561845^16636+16636^184554334Serge Batalov05/2014
875711^52169-7054329Lelio R Paula01/2013
875813693^9262+9262^1369354317Hans Havermann06/2016
87592^180429-11310154315Enzo Doria07/2014
87602^180423-11205154313Enzo Doria05/2014
876116112^2349+2349^1611254312Hans Havermann06/2016
8762(79^28621-1)/7854311Paul Bourdelais08/2017
8763(13^48751+4^48751)/1754305Robert Price05/2013
87642^180370+1291554297Lelio R Paula09/2012
8765(10^54290+41)/354290Robert Price01/2017
876615108^3917+3917^1510854283Hans Havermann06/2016
87672^180317-301954281Yves Minet10/2014
87682^180314+85554280Lelio R Paula10/2009
876919^42425+9454252Lelio R Paula02/2013
87702^180180-100544954240Paul Bourdelais11/2012
87722^180173-277354238Yves Minet07/2014
877113367^11418+11418^1336754238Hans Havermann06/2016
8773427^20614+20614^42754224Norbert Schneider06/2016
87742^180124-8795954223Gary Barnes08/2009
87752^180111-11310154219Enzo Doria07/2014
87762^180101-11487154216Enzo Doria05/2015
8777(11*2^180099+1)/5161754212Lelio R Paula07/2012
87782^180070+46554207Lelio R Paula09/2012
877913683^9154+9154^1368354207Hans Havermann06/2016
8780810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
87812^180014+61354190Jason Earls04/2008
87822^180007+10154188Lelio R Paula02/2011
87832^180001+4187754186Jim Fougeron08/2002
87842^180000+13015354186Jim Fougeron09/2002
87853^113565-7454185Lelio R Paula10/2012
878650^31891-4954182Norbert Schneider07/2014
8787(5*2^179991-1)/1142754180Lelio R Paula01/2014
87883^113548+2654177Lelio R Paula10/2012
8789(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
8790181^23996-254176Lelio R Paula10/2017
87914159^14969-13854173Enzo Doria07/2012
87932^179955+577554172Lelio R Paula10/2009
87922^179953-23131354172Enzo Doria05/2014
87945^77485+654160Lelio R Paula10/2012
879518^43141+8554154Lelio R Paula02/2013
879610^54149+18764754150Patrick De Geest07/2017
87993^113489-34054149Lelio R Paula10/2012
879710^54149-80000154149Robert Price06/2017
879810^54149-3650154149Patrick De Geest07/2017
88007^64070+9054146Lelio R Paula10/2012
880118^43131+7154142Lelio R Paula02/2013
88022^179826-13154134Lelio R Paula02/2011
88032^179815-11273554130Enzo Doria06/2014
88042^179806+7384954127Enzo Doria04/2016
88052^179790+3354123Donovan Johnson02/2006
880614287^6138+6138^1428754120Hans Havermann06/2016
8807(17*10^54117+1)/954118Serge Batalov05/2010
88082^179763-18954115Lelio R Paula02/2011
8809(21181*2^179770+1)/302910554115Lelio R Paula05/2014
88101828^16589+16589^182854113Serge Batalov05/2014
881220^41588-588354108Enzo Doria03/2013
881150^31847-4954108Norbert Schneider07/2014
88132^179733-685554106Lelio R Paula10/2009
881420^41584-558354103Enzo Doria03/2013
881510^54084+3*3^5408454085Mike Oakes05/2010
88162^179613-179554069Lelio R Paula10/2009
88172^179589-101152354062Paul Bourdelais11/2012
88182^179574-253154058Yves Minet07/2014
8819(41*10^54051-23)/954052Robert Price05/2015
8820117^26131-11654044Norbert Schneider10/2013
8821(10^54038-31)/354038Serge Batalov12/2014
882211^51885-8454033Lelio R Paula01/2013
882314990^4011+4011^1499054013Hans Havermann07/2016
8824(19*2^179414+1)/754010Lelio R Paula07/2012
88253^113182-1040854002Enzo Doria02/2013
882635^34970-878653997Enzo Doria03/2013
88272^179371-163758753997Enzo Doria05/2015
882819^42225-9253996Lelio R Paula01/2013
8829(3^113188+7)/7391767578453994Lelio R Paula03/2012
88307*3^113162+853993Lelio R Paula03/2014
8831(10^53991+179)/953991Serge Batalov12/2014
88332^179350-214553990Lelio R Paula10/2009
8832(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
88348^59782-6^59782-3^5978253989Mike Oakes11/2009
88353*7^63861+853970Lelio R Paula09/2014
88362^179274+7138953967Enzo Doria04/2016
88372^179259-5869553963Lelio R Paula10/2009
88386^69345+6153961Lelio R Paula10/2012
8839(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
8840(40216^11719-1)/4021553955Serge Batalov04/2015
884189*10^53951-953953Robert Price05/2017
884214^47067-353945Lelio R Paula01/2013
8843p(11700)#/2-51253937Robert Price07/2017
8844(2^179168-5)/5953934Lelio R Paula02/2012
88452^179128+841553923Lelio R Paula07/2012
88462^179120+253353921Henri Lifchitz09/2004
8847(2^179126+78557)/464932118753913Lelio R Paula05/2012
884874^28842+7353913Norbert Schneider11/2012
88491271^17368+17368^127153913Serge Batalov05/2014
88502^179079+5353909Lelio R Paula02/2011
885117^43807+5453903Lelio R Paula01/2013
885217^43807+3053903Lelio R Paula01/2013
88533^112951-31053892Lelio R Paula10/2012
8854Phi(7,2957!)53888Robert Price05/2015
8855(10223*2^178975+1)/3398553877Lelio R Paula05/2014
88562^178944-21920953868Enzo Doria11/2012
8857(10^53859+149)/353859Serge Batalov12/2014
88582^178910-19153858Lelio R Paula02/2011
885916170^2141+2141^1617053857Hans Havermann07/2016
8860(5*10^53855-107)/353856Robert Price01/2017
8861(72*10^53847-27)/9953847Patrick De Geest08/2004
88622^178841-86968810553837Lelio R Paula06/2012
88632*10^53834-2753835Robert Price02/2017
88652^178821-101152353831Paul Bourdelais11/2012
886412601^13128-13128^1260153831Norbert Schneider10/2017
88662^178819-1553830Lelio R Paula02/2011
8867(14450!-1)/22529658153829Donovan Johnson04/2006
8868(124351#+125386)/(2^5*71*883*4489103*9820259)53826Makoto Morimoto10/2017
88692^178761-46553813Lelio R Paula10/2009
887018900^703+703^1890053808Anatoly F. Selevich02/2007
887113918^7343+7343^1391853806Hans Havermann08/2016
887210^53804+3174953805Patrick De Geest12/2012
887310^53804-7153804Robert Price05/2011
8874t(178994)53804Robert Price03/2015
8875(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
88762^178671-11321553786Enzo Doria07/2014
887715110^3621+3621^1511053774Hans Havermann07/2016
88782^178611+9553768Lelio R Paula02/2011
88792^178597+571153764Lelio R Paula10/2011
88802^178598+1291553764Lelio R Paula07/2012
8881(9179*2^178579-1)/30353760Lelio R Paula03/2015
88825*7^63589+253740Lelio R Paula09/2014
88832^178516-11251553739Enzo Doria06/2014
888420^41302-2753736Lelio R Paula01/2013
88856^69054-3920953735Mike Oakes12/2010
888613086^12769+12769^1308653734Hans Havermann07/2016
88872^178455+7604353721Enzo Doria04/2016
8888(10^53718-7)/353718Makoto Kamada10/2004
8889(67607*2^178426+1)/353716Lelio R Paula05/2014
88909*10^53707+1153708Robert Kinser01/2017
889194601!8-253708Robert Price04/2017
889213214^11595+11595^1321453706Hans Havermann07/2016
8893Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
88942^178367-37953694Yves Minet03/2013
8895(2^178364-5)/1153692Lelio R Paula02/2012
88964339^14760-16853688Enzo Doria06/2012
889712^49746-1153685Lelio R Paula01/2013
889812950^13051-13051^1295053670Norbert Schneider08/2017
8900(9913*2^178266-1)/224753665Lelio R Paula03/2015
889913725^8128+8128^1372553665Hans Havermann07/2016
89012^178250-11326153659Enzo Doria07/2014
89022^178226+1171553652Lelio R Paula10/2009
890335^34742-197653645Enzo Doria03/2013
890420^41228-56353639Enzo Doria03/2013
8905359^20992+20992^35953637Norbert Schneider08/2014
8906(27*2^178183-1)/2906553636Lelio R Paula01/2014
8907(3^112414+7)/3738169653628Lelio R Paula03/2012
890817994^955+955^1799453623Anatoly F. Selevich10/2006
89092^178117-155153619Yves Minet08/2012
89102^178099-1128753614Enzo Doria06/2014
8911(15*2^178080-1)/30907153604Lelio R Paula01/2014
89125^76672-1376653592Enzo Doria02/2013
89136^68868-13753590Lelio R Paula10/2012
8914(5*2^178021+1)/817353587Lelio R Paula07/2012
89155^76654-2653579Lelio R Paula10/2012
8916(3^112297-2)/762753576Lelio R Paula03/2012
89173*2^177948-753569Lelio R Paula03/2014
891810^53558+1854353559Patrick De Geest12/2012
891910^53558-2153558Robert Price03/2011
89202^177792-9553521Lelio R Paula02/2011
892113392^9919+9919^1339253521Hans Havermann07/2016
892213105^12132+12132^1310553520Hans Havermann07/2016
892313^48042+8253517Lelio R Paula01/2013
89242^177768+3912153514Yves Minet10/2010
892513835^7366+7366^1383553504Hans Havermann07/2016
892617^43477+8453497Lelio R Paula01/2013
89275*10^53492+953493Dmitry Domanov11/2010
89282^177683+9553488Lelio R Paula01/2011
8929(2^177678+3)/51462753481Lelio R Paula02/2012
89302^177641-25546353476Gary Barnes08/2009
8931p(11608)#/2+1653469Robert Price12/2016
8932(14*10^53465+211)/953466Robert Price11/2017
893337302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
893412001^13104-13104^1200153455Norbert Schneider10/2017
89351829^16384+1828^1638453449Henri Lifchitz01/2007
893635^34608-960253438Enzo Doria03/2013
8937(3^111992+8)/1486753430Lelio R Paula03/2012
89392^177480+186966153427Enzo Doria05/2016
893811791^13122-13122^1179153427Norbert Schneider10/2017
8940(8*10^53411+1)/953411Serge Batalov12/2008
89414*5^76410-353409Lelio R Paula09/2014
89422^177380-11304553397Enzo Doria07/2014
89435^76362-2*3^7636253375Mike Oakes11/2009
89444159^14747-14053370Enzo Doria07/2012
8945(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
8946p(11586)#/2+3253357Robert Price12/2016
894715^45362-4653350Lelio R Paula01/2013
894814147^5892+5892^1414753338Hans Havermann07/2016
89497^63109+4653334Lelio R Paula10/2012
895020^40986-134353325Enzo Doria03/2013
89514*10^53324-8953325Robert Price08/2017
895220^40977-888353313Enzo Doria03/2013
89533^111711+266053300Lelio R Paula10/2012
89542^177040-1186553295Enzo Doria10/2012
8955(7*10^53287+17)/353288Erik Branger03/2014
895635^34506-1075853280Enzo Doria03/2013
8957(11*10^53274-17)/353275Erik Branger03/2014
8958(1017*2^176971-1)/33553275Lelio R Paula03/2015
89592^176961-283353271Yves Minet09/2014
89603^111642+11053267Lelio R Paula10/2012
896117^43290-9853267Lelio R Paula01/2013
89627^63028+3653265Lelio R Paula10/2012
8963(22*10^53264+71)/353265Robert Price05/2017
89647^63023-3653261Lelio R Paula10/2012
896519783^492+492^1978353256Anatoly F. Selevich02/2007
896613350^9739+9739^1335053247Hans Havermann10/2015
896714394^4993+4993^1439453235Hans Havermann10/2015
89682^176823-11280753230Enzo Doria06/2014
89691684^16495+16495^168453219Serge Batalov05/2014
897015277^3042+3042^1527753213Hans Havermann06/2016
8971(50322^11317-1)/5032153206Serge Batalov04/2015
89722^176742-159553205Lelio R Paula10/2009
8973(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
8974(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
8975(3*2^176696-1)/29953189Lelio R Paula01/2014
8976(7*10^53185-1)/353186Erik Branger03/2014
89772^176629+46553171Lelio R Paula07/2012
8978(3*2^176604-1)/35953162Lelio R Paula01/2014
89795^76038-1436653149Enzo Doria02/2013
898015156^3209+3209^1515653143Hans Havermann06/2016
89812^176532-283753142Yves Minet09/2014
898252^30967-5153140Norbert Schneider08/2014
89839*5^76023-253139Lelio R Paula09/2014
8984(14283!+1)/46421617753135Michael Porter03/2016
89852^176461-16553121Lelio R Paula02/2011
8986(62*10^53111+1)/953112Serge Batalov05/2010
89872^176403-13953103Lelio R Paula02/2011
898855^30508-253095Lelio R Paula08/2013
8989(48591^11329-1)/4859053090Serge Batalov04/2015
89903^111254-8853082Lelio R Paula10/2012
899115^45129-5653076Lelio R Paula01/2013
89922^176293-7353070Lelio R Paula01/2011
8993(67*10^53068+41)/953069Robert Price09/2015
899415271^2986+2986^1527153069Hans Havermann06/2016
89952^176255-66753059Yves Minet01/2012
899636471*2^176221+864753053Paul Vanderveen04/2016
8997(19*10^53049-1)/953050Serge Batalov03/2009
89989*2^176203-553044Lelio R Paula03/2014
89992^176205-9439553043Lelio R Paula08/2011
9000(19*2^176224-1)/21791691353042Lelio R Paula01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

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