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 ?
87512^182627+2842554977Lelio R Paula11/2009
87522^182597-11305354968Enzo Doria07/2014
8753(3^115213+2)/3090672554964Lelio R Paula03/2012
87542^182581-197554963Yves Minet09/2012
8755(2*10^54960-179)/354960Robert Price11/2017
875627449!!-1654959Robert Price06/2015
8757(22*10^54958-73)/354959Robert Price09/2017
87594^91283-3^9128354958Jean-Louis Charton01/2004
87582^182565+10754958Lelio R Paula11/2009
87602^182560+205354957Lelio R Paula12/2010
87612^182451-18245154924Henri Lifchitz10/2004
87622^182444+8154922Henri Lifchitz10/2005
87632^182433+7410554918Enzo Doria04/2016
876420^42206-524354912Enzo Doria03/2013
87652^182394+8554907Lelio R Paula02/2011
87662^182374-11228754901Enzo Doria06/2014
8767(47^32833-33^32833)/1454899Serge Batalov12/2016
87682^182363-11316754897Enzo Doria07/2014
87692^182359-11222154896Enzo Doria06/2014
8770(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
8771(17*2^182274+1)/146754869Lelio R Paula01/2012
877218^43698-554853Lelio R Paula02/2013
87732^182209-189354851Yves Minet09/2012
87742^182194-344354846Yves Minet12/2016
877515023^4468+4468^1502354836Hans Havermann08/2016
87762^182135+9014354829Yves Minet10/2010
87772^182119+7433354824Enzo Doria04/2016
877814289^6860+6860^1428954818Hans Havermann08/2016
87793^114892-114892^354818Norbert Schneider03/2017
87802^182070-4735554809Lelio R Paula01/2011
87813^114869+7654807Lelio R Paula10/2012
87828^60681-60681^854801Norbert Schneider12/2016
87831897^16710+16710^189754777Serge Batalov05/2014
8784Phi(61868,59)54776Enzo Doria04/2012
8785113^26679+254775Lelio R Paula05/2013
87863^114789-7454769Lelio R Paula10/2012
878715^46567+9854768Lelio R Paula02/2013
8788(2*10^54767-71)/354767Robert Price01/2017
8789(298*10^54765-7)/354767Robert Price06/2017
8790(21*2^181931-1)/16999754763Lelio R Paula01/2014
87922^181913+2954762Henri Lifchitz06/2005
8791(31*10^54761-121)/954762Robert Price06/2016
87932^181887+18954754Lelio R Paula02/2011
87942^181874+181874^2-154750Robert Price04/2014
8795(2^181865+9)/733954743Lelio R Paula02/2012
87965^78314-9254740Lelio R Paula10/2012
8797(163*10^54727-1)/954729Serge Batalov12/2014
879815^46531+7454725Lelio R Paula02/2013
8799277^22400-34854712Enzo Doria07/2012
88006^70302+10154706Lelio R Paula10/2012
88013^114622-1040854689Enzo Doria02/2013
8803(23*2^181674+1)/48954688Lelio R Paula01/2012
88022^181669-155154688Yves Minet08/2012
8804(57352^11491-1)/5735154676Serge Batalov04/2015
8805(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8806(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
880713^49073+4654665Lelio R Paula01/2013
8808(57042^11491-1)/5704154649Serge Batalov04/2015
881020^42000+7354644Lelio R Paula02/2013
8809(67607*2^181517+1)/165554644Lelio R Paula05/2014
881133*10^54634+754636Robert Price07/2016
881220^41988+6154628Lelio R Paula01/2013
881320^41988-812354628Enzo Doria03/2013
88142^181420+2118154613Yves Minet03/2011
8815(19*10^54608+161)/954609Robert Price07/2016
881619^42696-2454598Lelio R Paula02/2013
8817(44*10^54596-503)/954597Robert Price10/2017
8818(74*10^54583+61)/954584Robert Price10/2015
88192^181316-9439554582Lelio R Paula09/2011
882014751^5006+5006^1475154572Hans Havermann08/2016
882114^47609+3954567Lelio R Paula02/2013
882212696^13295-13295^1269654559Norbert Schneider01/2018
8823(2^124979+lucasV(2,-2,124979)+1)/354552Paul Vanderveen12/2017
88253^114327-7454548Lelio R Paula10/2012
8824(44*10^54547-161)/954548Robert Price11/2017
8826gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
8827(17*10^54537-47)/354538Robert Price05/2017
88282^181155-1155*18115554534Henri Lifchitz02/2005
8829Phi(61672,83)54533Enzo Doria05/2012
8830(2*10^54527-197)/354527Robert Price11/2017
88319*2^181128+754526Lelio R Paula03/2014
883289*10^54518-754520Robert Price03/2017
88332^181090-11324754514Enzo Doria07/2014
883414031^7670+7670^1403154508Hans Havermann08/2016
883514210^6849+6849^1421054505Hans Havermann08/2016
88362^181043-19954500Lelio R Paula02/2011
883712^50499+554498Lelio R Paula01/2013
883812^50491+554489Lelio R Paula01/2013
88396^70016-14554484Lelio R Paula10/2012
884011^52313-960054479Enzo Doria02/2013
88412^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
88422^180946-11104154471Enzo Doria05/2014
8843(64*10^54467+287)/954468Robert Price04/2016
8844(32*10^54458+319)/954459Robert Price10/2017
88455^77907-2*3^7790754455Mike Oakes11/2009
884620^41853-562354453Enzo Doria03/2013
884714^47506-7554448Lelio R Paula02/2013
8848(25*10^54443-67)/354444Robert Price11/2017
88492^180839-11343754438Enzo Doria08/2014
88503^114085+2854433Lelio R Paula10/2012
8851Phi(141230,10)54432Ray Chandler08/2009
88526^69946-5554429Lelio R Paula10/2012
8853p(11796)#/2-102454427Robert Price09/2017
88545*2^180796+354426Lelio R Paula03/2014
8855(23*2^180782-1)/9154421Lelio R Paula01/2014
88569*6^69928-754416Lelio R Paula09/2014
885792^27701-91^2770154399Robert Price08/2015
8858(2^180687-3)*6-754393Gilbert Mozzo04/2016
8859(5*10^54388-11)/354389Erik Branger12/2013
886020^41799-304354382Enzo Doria03/2013
886113860^8387+8387^1386054382Hans Havermann08/2016
8862(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
88637^64329-1854365Lelio R Paula10/2012
88642^180551-96754352Yves Minet01/2012
886515^46209-7454347Lelio R Paula02/2013
886610^54345+2973954346Patrick De Geest08/2013
886710^54345-14138154345Patrick De Geest09/2013
8868lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
8869177^24171-254336Lelio R Paula10/2017
88702^180496+1554335Lelio R Paula02/2011
88711845^16636+16636^184554334Serge Batalov05/2014
887211^52169-7054329Lelio R Paula01/2013
887313693^9262+9262^1369354317Hans Havermann06/2016
88742^180429-11310154315Enzo Doria07/2014
88752^180423-11205154313Enzo Doria05/2014
887616112^2349+2349^1611254312Hans Havermann06/2016
8877(79^28621-1)/7854311Paul Bourdelais08/2017
8878(13^48751+4^48751)/1754305Robert Price05/2013
88792^180370+1291554297Lelio R Paula09/2012
8880(10^54290+41)/354290Robert Price01/2017
888115108^3917+3917^1510854283Hans Havermann06/2016
88822^180317-301954281Yves Minet10/2014
88832^180314+85554280Lelio R Paula10/2009
888419^42425+9454252Lelio R Paula02/2013
88852^180180-100544954240Paul Bourdelais11/2012
88872^180173-277354238Yves Minet07/2014
888613367^11418+11418^1336754238Hans Havermann06/2016
8888427^20614+20614^42754224Norbert Schneider06/2016
88892^180124-8795954223Gary Barnes08/2009
88902^180111-11310154219Enzo Doria07/2014
88912^180101-11487154216Enzo Doria05/2015
8892(11*2^180099+1)/5161754212Lelio R Paula07/2012
88932^180070+46554207Lelio R Paula09/2012
889413683^9154+9154^1368354207Hans Havermann06/2016
8895810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
88962^180014+61354190Jason Earls04/2008
88972^180007+10154188Lelio R Paula02/2011
88982^180001+4187754186Jim Fougeron08/2002
88992^180000+13015354186Jim Fougeron09/2002
89003^113565-7454185Lelio R Paula10/2012
890150^31891-4954182Norbert Schneider07/2014
8902(5*2^179991-1)/1142754180Lelio R Paula01/2014
89033^113548+2654177Lelio R Paula10/2012
8904(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
8905181^23996-254176Lelio R Paula10/2017
89064159^14969-13854173Enzo Doria07/2012
89082^179955+577554172Lelio R Paula10/2009
89072^179953-23131354172Enzo Doria05/2014
89095^77485+654160Lelio R Paula10/2012
891018^43141+8554154Lelio R Paula02/2013
891110^54149+18764754150Patrick De Geest07/2017
89143^113489-34054149Lelio R Paula10/2012
891210^54149-80000154149Robert Price06/2017
891310^54149-3650154149Patrick De Geest07/2017
89157^64070+9054146Lelio R Paula10/2012
891612549^13210-13210^1254954143Norbert Schneider12/2017
891718^43131+7154142Lelio R Paula02/2013
89182^179826-13154134Lelio R Paula02/2011
89192^179815-11273554130Enzo Doria06/2014
89202^179806+7384954127Enzo Doria04/2016
89212^179790+3354123Donovan Johnson02/2006
892214287^6138+6138^1428754120Hans Havermann06/2016
8923(17*10^54117+1)/954118Serge Batalov05/2010
89242^179763-18954115Lelio R Paula02/2011
8925(21181*2^179770+1)/302910554115Lelio R Paula05/2014
89261828^16589+16589^182854113Serge Batalov05/2014
892820^41588-588354108Enzo Doria03/2013
892750^31847-4954108Norbert Schneider07/2014
89292^179733-685554106Lelio R Paula10/2009
893020^41584-558354103Enzo Doria03/2013
893110^54084+3*3^5408454085Mike Oakes05/2010
89322^179613-179554069Lelio R Paula10/2009
89332^179589-101152354062Paul Bourdelais11/2012
89342^179574-253154058Yves Minet07/2014
8935(41*10^54051-23)/954052Robert Price05/2015
8936117^26131-11654044Norbert Schneider10/2013
8937(10^54038-31)/354038Serge Batalov12/2014
893811^51885-8454033Lelio R Paula01/2013
893914990^4011+4011^1499054013Hans Havermann07/2016
8940(19*2^179414+1)/754010Lelio R Paula07/2012
89413^113182-1040854002Enzo Doria02/2013
894235^34970-878653997Enzo Doria03/2013
89432^179371-163758753997Enzo Doria05/2015
894419^42225-9253996Lelio R Paula01/2013
8945(3^113188+7)/7391767578453994Lelio R Paula03/2012
89467*3^113162+853993Lelio R Paula03/2014
8947(10^53991+179)/953991Serge Batalov12/2014
89492^179350-214553990Lelio R Paula10/2009
8948(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
89508^59782-6^59782-3^5978253989Mike Oakes11/2009
89513*7^63861+853970Lelio R Paula09/2014
89522^179274+7138953967Enzo Doria04/2016
89532^179259-5869553963Lelio R Paula10/2009
89546^69345+6153961Lelio R Paula10/2012
8955(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
8956(40216^11719-1)/4021553955Serge Batalov04/2015
895789*10^53951-953953Robert Price05/2017
895814^47067-353945Lelio R Paula01/2013
8959p(11700)#/2-51253937Robert Price07/2017
8960(2^179168-5)/5953934Lelio R Paula02/2012
89612^179128+841553923Lelio R Paula07/2012
89622^179120+253353921Henri Lifchitz09/2004
8964(2^179126+78557)/464932118753913Lelio R Paula05/2012
896374^28842+7353913Norbert Schneider11/2012
89651271^17368+17368^127153913Serge Batalov05/2014
89662^179079+5353909Lelio R Paula02/2011
896717^43807+5453903Lelio R Paula01/2013
896817^43807+3053903Lelio R Paula01/2013
89693^112951-31053892Lelio R Paula10/2012
8970Phi(7,2957!)53888Robert Price05/2015
8971(10223*2^178975+1)/3398553877Lelio R Paula05/2014
89722^178944-21920953868Enzo Doria11/2012
8973(10^53859+149)/353859Serge Batalov12/2014
89742^178910-19153858Lelio R Paula02/2011
897516170^2141+2141^1617053857Hans Havermann07/2016
8976(5*10^53855-107)/353856Robert Price01/2017
8977(72*10^53847-27)/9953847Patrick De Geest08/2004
89782^178841-86968810553837Lelio R Paula06/2012
89792*10^53834-2753835Robert Price02/2017
89812^178821-101152353831Paul Bourdelais11/2012
898012601^13128-13128^1260153831Norbert Schneider10/2017
89822^178819-1553830Lelio R Paula02/2011
8983(14450!-1)/22529658153829Donovan Johnson04/2006
8984(124351#+125386)/(2^5*71*883*4489103*9820259)53826Makoto Morimoto10/2017
89852^178761-46553813Lelio R Paula10/2009
898618900^703+703^1890053808Anatoly F. Selevich02/2007
898713918^7343+7343^1391853806Hans Havermann08/2016
898810^53804+3174953805Patrick De Geest12/2012
898910^53804-7153804Robert Price05/2011
8990t(178994)53804Robert Price03/2015
8991(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
89922^178671-11321553786Enzo Doria07/2014
899315110^3621+3621^1511053774Hans Havermann07/2016
89942^178611+9553768Lelio R Paula02/2011
89952^178597+571153764Lelio R Paula10/2011
89962^178598+1291553764Lelio R Paula07/2012
8997(9179*2^178579-1)/30353760Lelio R Paula03/2015
89985*7^63589+253740Lelio R Paula09/2014
89992^178516-11251553739Enzo Doria06/2014
900020^41302-2753736Lelio R Paula01/2013


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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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