PRP Records

Probable Primes Top 10000

(247113 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 ?
850120^45740-152359510Enzo Doria03/2013
8502(47*10^59509+493)/959510Robert Price11/2017
8503(7*2^197642-1)/305159494Lelio R Paula01/2014
850418^47390-185359488Enzo Doria03/2013
8505(2^197581-7)/191559475Lelio R Paula02/2012
8506(24737*2^197559+1)/7759474Lelio R Paula06/2014
85072^197540-245959466Yves Minet07/2014
8508(44*10^59454+1)/959455Serge Batalov11/2010
85092^197494-1780559452Enzo Doria05/2013
85102^197482-1682159449Enzo Doria05/2013
85112^197485+7576759449Enzo Doria04/2016
8512(3*2^197483+1)/2559448Lelio R Paula07/2012
85132^197466-186835159444Enzo Doria04/2016
85142^197411-1778159427Enzo Doria05/2013
8515(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
85162^197392-11462959421Enzo Doria05/2015
85172^197355-15759410Lelio R Paula04/2011
85185^84992-8459407Lelio R Paula10/2012
85192*3^124504-559404Lelio R Paula04/2014
85202^197307-1916559396Enzo Doria05/2013
85212^197303+3276959395Lelio R Paula05/2011
85222*10^59394-6959395Robert Price07/2017
8523(53*10^59389+1)/959390Serge Batalov11/2010
85246^76316-3559386Lelio R Paula10/2012
85252^197259-292959381Yves Minet09/2014
8526lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
852717^48253-659373Lelio R Paula03/2013
85282^197156-1583759350Enzo Doria04/2013
85292^197152-429559349Yves Minet08/2018
85302^197149-1848159348Enzo Doria05/2013
85312^197142-1715759346Enzo Doria05/2013
8533(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
8532(8^65707-5^65707)/359339Robert Price12/2012
8534(2*14283^14283+1)/792549797559334David Broadhurst09/2010
85352^197012-11171959307Enzo Doria05/2014
85362^196975+51359296Lelio R Paula05/2011
8537(61*10^59294+119)/959295Robert Price09/2017
85384*10^59292+3959293Robert Price11/2017
85392^196960+9759291Lelio R Paula04/2011
85409^62116+8^(62116-1)59274Robert Price03/2016
85412^196900-9730559273Lelio R Paula09/2011
85425*6^76155+759261Lelio R Paula09/2014
854315^50385-1459258Wojciech Florek06/2006
8544(136777#-1)/882358147759254Donovan Johnson05/2006
8545(2^196744-3)*6-759227Gilbert Mozzo05/2016
8546(67607*2^196696+1)/359216Lelio R Paula05/2014
85472^196696-11296759212Enzo Doria06/2014
854820^45508-422359208Enzo Doria03/2013
8549gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
855014^51651-8159199Lelio R Paula03/2013
85512^196650-145159198Yves Minet08/2012
85522^196636-279779959194Enzo Doria04/2016
85531111*2^196610-55559189Henri Lifchitz04/2005
85543^124041+65859183Lelio R Paula10/2012
85552^196590-11179759180Enzo Doria05/2014
8556(10^59174-13)/359174Robert Price02/2017
8557(2*10^59174-113)/359174Robert Price09/2017
8558(9179*2^196533-1)/78359164Lelio R Paula04/2015
8559379*10^59152+959155Arkadiusz Wesolowski10/2011
8560(404*10^59149-53)/959151Robert Price11/2017
856113^53095+4059145Lelio R Paula03/2013
85632*F(282999)-159144Henri Lifchitz12/2009
85624*7^69984+359144Lelio R Paula09/2014
8564(5*10^59142+1)/359143Erik Branger12/2013
85652^196463+571159142Lelio R Paula10/2011
85662^196453-9730559139Lelio R Paula09/2011
8567(28*10^59135+53)/959136Serge Batalov11/2008
8568(28*10^59133+113)/359134Robert Price03/2016
85692^196434+759133Lelio R Paula04/2011
8570(8*10^59127-29)/359128Robert Price05/2016
85712^196414+25559127Lelio R Paula05/2011
85725^84586-9259124Lelio R Paula10/2012
85732^196388-1717759119Enzo Doria05/2013
857479427!6-659119Robert Price08/2018
85753^123890+2059111Lelio R Paula10/2012
85762^196355-102177759109Paul Bourdelais11/2012
857711^56754-141059104Enzo Doria11/2012
8578(7*2^196297-1)/120040759087Lelio R Paula01/2014
8579(16*10^59062-19)/359063Robert Price03/2016
858035^38249-122859060Enzo Doria03/2013
85815^84475-1859046Lelio R Paula10/2012
85822^196123-1770159039Enzo Doria05/2013
858312^54702-3159034Lelio R Paula03/2013
85842^196101-17559033Lelio R Paula04/2011
85852^196085+577559028Lelio R Paula05/2011
85862^196034+1171559013Lelio R Paula05/2011
85872^196018-1848559008Enzo Doria05/2013
85882^195984-216358998Yves Minet08/2013
85893^123645-1658994Lelio R Paula10/2012
859039^37078-3858994Norbert Schneider05/2014
85912^195958-1685358990Enzo Doria05/2013
85922^195930-307158981Yves Minet10/2014
85932^195924+51358980Lelio R Paula05/2011
85942^195863+15558961Lelio R Paula04/2011
8595(28*10^58956+113)/358957Robert Price03/2016
859611^56612-930058956Enzo Doria02/2013
85972^195833-1717358952Enzo Doria05/2013
8598(27*2^195833-1)/5358952Lelio R Paula01/2014
8599(13*2^195821-1)/12242558945Lelio R Paula01/2014
8600139^27504-13858942Norbert Schneider10/2015
8601(418*10^58923+23)/958925Robert Price08/2017
86023^123495+4458923Lelio R Paula10/2012
86032^195737-1856558923Enzo Doria05/2013
860479185!6-1658921Robert Price08/2018
860514^51407+4758920Lelio R Paula03/2013
86062^195691-9958909Lelio R Paula04/2011
86072^195667-185982758902Enzo Doria04/2016
86082^195642+7549958895Enzo Doria04/2016
8609(299*10^58893+1)/358895Robert Price11/2017
86108*6^75678+558890Lelio R Paula09/2014
86122^195618+7318958887Enzo Doria04/2016
8611(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
8613t(197953)58881Robert Price12/2014
86142^195581-1610558876Enzo Doria04/2013
8615(8*10^58872+67)/358873Robert Price01/2017
86167*2^195542-558865Lelio R Paula03/2014
86172*10^58861+9^5886158862Mike Oakes04/2011
861811^56513-162058853Enzo Doria11/2012
86192^195496+16558851Lelio R Paula04/2011
86205^84187+6658845Lelio R Paula10/2012
8621(28*10^58843-43)/358844Robert Price04/2016
86222^195462-1756558840Enzo Doria05/2013
86232^195449-417158837Yves Minet02/2018
86242^195435+5927358832Yves Minet01/2011
86252^195424-1860558829Enzo Doria05/2013
86262^195385-11158817Lelio R Paula04/2011
86277*10^58815-8358816Robert Price09/2017
86282^195357-430358809Yves Minet08/2018
8629(47*2^195254+1)/26882158774Lelio R Paula03/2015
86302^195207-1810958764Enzo Doria05/2013
86312^195199-156758761Yves Minet08/2012
86322^195190+7375958759Enzo Doria04/2016
86339*7^69525-458757Lelio R Paula09/2014
86342^195170-1804558753Enzo Doria05/2013
86352^195166-16558751Lelio R Paula04/2011
8636(754*10^58748-7)/958750Robert Price11/2017
8637(22699*2^195140+1)/17558746Lelio R Paula05/2014
86387*3^123109-258739Lelio R Paula04/2014
8639(8*10^58738-611)/958738Robert Price11/2017
864018^46790+7758735Lelio R Paula03/2013
86412^195095-33729758730Gary Barnes09/2009
8642(14*10^58729+31)/958730Robert Price02/2015
864399^29424+9858720Norbert Schneider07/2013
8644(15185*2^195039-1)/21958715Lelio R Paula04/2015
86452^195001-6958702Lelio R Paula04/2011
86462^194978-48781158695Gary Barnes09/2009
8647163^26530+26530^16358690Serge Batalov05/2014
86482^194940-194940+158683Robert Price10/2014
8649(76*10^58669+41)/958670Robert Price10/2015
865014^51186+8758666Lelio R Paula03/2013
86512^194878-9730558665Lelio R Paula09/2011
86525^83927-1813658663Enzo Doria05/2014
8653(24737*2^194865+1)/108558662Lelio R Paula06/2014
86547^69411+4058660Lelio R Paula10/2012
86556^75382-7958659Lelio R Paula10/2012
86562^194854+2758657Lelio R Paula04/2011
86572^194801+2983558641Lelio R Paula10/2012
86582^194752+19558627Lelio R Paula04/2011
86597^69371-6^6937158626Predrag Minovic08/2004
86602^194747-11251958625Enzo Doria06/2014
8661(15*2^194737+1)/5958622Lelio R Paula07/2012
8662(23*2^194700+1)/358612Lelio R Paula02/2012
866310^58608+5527358609Patrick De Geest07/2017
866410^58608-80000158608Robert Price06/2017
866510^58608-6011958608Patrick De Geest07/2017
86665^83836+7658599Lelio R Paula10/2012
866718^46664+3158577Lelio R Paula03/2013
8668(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
86692^194574+16558573Lelio R Paula04/2011
86722^194569-1221158572Enzo Doria06/2014
867010^58571+5^58571+2^5857158572Robert Price12/2016
867110^58571+20283758572Patrick De Geest02/2017
8673(10^58571+41)/358571Robert Price01/2017
867410^58571-34362958571Patrick De Geest02/2017
8675(43*10^58563-403)/958564Robert Price04/2017
867711^56235-795058563Enzo Doria02/2013
8676145^27095-14458563Norbert Schneider11/2018
8678(14*10^58550+211)/958551Robert Price11/2017
86792^194479-11323958545Enzo Doria07/2014
86802^194455-11224958537Enzo Doria06/2014
86812^194405-11191958522Enzo Doria05/2014
8682(4*10^58521-19)/358522Robert Price06/2017
8684(7^69247-4^69247)/358521Robert Price06/2012
86835*7^69246+858521Lelio R Paula09/2014
86852^194358-116758508Lelio R Paula05/2011
8686(2^194366+7)/137358507Lelio R Paula02/2012
8687(493*10^58486-7)/958488Robert Price07/2016
86883^122579-34058486Lelio R Paula10/2012
8689(11*10^58458-149)/358459Robert Price01/2017
8690(47*10^58456+133)/958457Robert Price04/2017
86912^194186+8558456Lelio R Paula04/2011
86923^122506-2^(122506-1)58451Robert Price01/2016
8693(74^31267-1)/7358444Paul Bourdelais08/2017
8694177^25998-258443Lelio R Paula10/2017
869515^49690-2658440Lelio R Paula03/2013
869610^58437+11072158438Patrick De Geest12/2012
869710^58437-1158437Robert Price05/2011
86982^194095+6958429Lelio R Paula04/2011
8699(29*10^58417-77)/358418Robert Price01/2017
87002^194034+17758411Lelio R Paula04/2011
8701789^20158+20158^78958400Norbert Schneider06/2016
870214^50949+7558395Lelio R Paula03/2013
87032^193974-11476158392Enzo Doria05/2015
87042^193965+558390Henri Lifchitz12/2002
8705(5*10^58384-29)/358385Robert Price02/2017
87063^122360+8058381Lelio R Paula10/2012
870710103^14577-11458373Enzo Doria07/2012
8708(22699*2^193883+1)/2158368Lelio R Paula06/2014
8709(31*2^193886+1)/14076558362Lelio R Paula07/2012
871011^56041-156058361Enzo Doria11/2012
8711(2^193881+9)/1769958360Lelio R Paula02/2012
87123^122313+5858359Lelio R Paula10/2012
87136^74996-11958359Lelio R Paula10/2012
8714(11*2^193859+1)/1358358Lelio R Paula07/2012
87152^193861-11225558358Enzo Doria06/2014
8716(22699*2^193854+1)/492758357Lelio R Paula06/2014
871718^46487+3758354Lelio R Paula03/2013
871817^47419+5458347Lelio R Paula03/2013
8719(31*2^193791+1)/358338Lelio R Paula02/2012
8720(27*2^193805-1)/98224958337Lelio R Paula01/2014
8721144^27025-14358330Norbert Schneider11/2018
87223^122219-2^12221958314Mike Oakes09/2003
8723(199*10^58306+11)/358308Robert Price05/2017
87242^193674-1882558302Lelio R Paula05/2011
87255*10^58275+358276Dmitry Domanov11/2010
87262^193578-11291358273Enzo Doria06/2014
87272^193541+129958262Lelio R Paula05/2011
872810^58250+9358251Robert Price01/2011
872910^58250-17560758250Patrick De Geest12/2012
8730(107^28703+1)/10858248Richard Fischer05/2018
87312^193492+841558247Lelio R Paula10/2012
87322^193444+15758233Lelio R Paula04/2011
8733Phi(28754,28754)58231Henri Lifchitz08/2013
87342^193430-11188158229Enzo Doria05/2014
873510^58225+12457958226Patrick De Geest12/2012
873610^58225-9358225Robert Price05/2011
87372^193375-29558212Yves Minet05/2013
873814018^14037-14037^1401858208Norbert Schneider10/2018
87392^193345+7726758203Enzo Doria05/2016
874021^44017-20^4401758201Robert Price05/2012
8741(17*2^193329-1)/958199Lelio R Paula01/2014
874217^47291+2058190Lelio R Paula03/2013
8743p(12528)#/2-12858170Robert Price05/2017
87442^193214-13558164Lelio R Paula04/2011
874519^45483-8058162Lelio R Paula03/2013
8746(4*10^58155+83)/358156Robert Price01/2017
874714^50739-1358154Lelio R Paula03/2013
8748(1017*2^193184-1)/482358154Lelio R Paula04/2015
8749(2*10^58151+457)/958151Robert Price01/2017
8750(9179*2^193183-1)/399926787958149Lelio R Paula04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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