PRP Records

Probable Primes Top 10000

(252402 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 ?
8501(35*10^59584-197)/959585Robert Kinser10/2017
85022^197932-395959584Yves Minet04/2017
85032^197909-1896159577Enzo Doria05/2013
8504(3^124871+2)/4503159574Lelio R Paula04/2012
85052^197872+8159566Henri Lifchitz10/2005
85062^197873-1846959566Enzo Doria05/2013
8507(22*10^59558-31)/959559Robert Price04/2015
85092^197840-46559556Lelio R Paula05/2011
8508(31*2^197856-1)/388960559556Lelio R Paula01/2014
85102^197808-1780559547Enzo Doria05/2013
85112^197781-1790559539Enzo Doria05/2013
85122^197777-1747359537Enzo Doria05/2013
85136^76507-14959535Lelio R Paula10/2012
8515Phi(61456,109)59526Enzo Doria05/2012
851418^47420+2359526Lelio R Paula03/2013
8516(59^33613+1)/6059522Paul Bourdelais08/2017
85173^124747+9459520Lelio R Paula10/2012
851817^48370+1859517Lelio R Paula03/2013
851920^45740-152359510Enzo Doria03/2013
8520(47*10^59509+493)/959510Robert Price11/2017
8521(7*2^197642-1)/305159494Lelio R Paula01/2014
852218^47390-185359488Enzo Doria03/2013
8523(2^197581-7)/191559475Lelio R Paula02/2012
8524(24737*2^197559+1)/7759474Lelio R Paula06/2014
85252^197540-245959466Yves Minet07/2014
8526(44*10^59454+1)/959455Serge Batalov11/2010
85272^197494-1780559452Enzo Doria05/2013
85282^197482-1682159449Enzo Doria05/2013
85292^197485+7576759449Enzo Doria04/2016
8530(3*2^197483+1)/2559448Lelio R Paula07/2012
85312^197466-186835159444Enzo Doria04/2016
85322^197411-1778159427Enzo Doria05/2013
8533(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
85342^197392-11462959421Enzo Doria05/2015
85352^197355-15759410Lelio R Paula04/2011
85365^84992-8459407Lelio R Paula10/2012
85372*3^124504-559404Lelio R Paula04/2014
85382^197307-1916559396Enzo Doria05/2013
85402^197303+3276959395Lelio R Paula05/2011
85392*10^59394-6959395Robert Price07/2017
8541(53*10^59389+1)/959390Serge Batalov11/2010
85426^76316-3559386Lelio R Paula10/2012
85432^197259-292959381Yves Minet09/2014
8544lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
854517^48253-659373Lelio R Paula03/2013
85462^197156-1583759350Enzo Doria04/2013
85472^197152-429559349Yves Minet08/2018
85482^197149-1848159348Enzo Doria05/2013
85492^197142-1715759346Enzo Doria05/2013
8551(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
8550(8^65707-5^65707)/359339Robert Price12/2012
8552(2*14283^14283+1)/792549797559334David Broadhurst09/2010
85532^197012-11171959307Enzo Doria05/2014
85542^196975+51359296Lelio R Paula05/2011
8555(61*10^59294+119)/959295Robert Price09/2017
85564*10^59292+3959293Robert Price11/2017
85572^196960+9759291Lelio R Paula04/2011
85589^62116+8^(62116-1)59274Robert Price03/2016
85592^196900-9730559273Lelio R Paula09/2011
85605*6^76155+759261Lelio R Paula09/2014
856115^50385-1459258Wojciech Florek06/2006
8562(136777#-1)/882358147759254Donovan Johnson05/2006
8563(2^196744-3)*6-759227Gilbert Mozzo05/2016
8564(67607*2^196696+1)/359216Lelio R Paula05/2014
85652^196696-11296759212Enzo Doria06/2014
856620^45508-422359208Enzo Doria03/2013
8567gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
856814^51651-8159199Lelio R Paula03/2013
85692^196650-145159198Yves Minet08/2012
85702^196636-279779959194Enzo Doria04/2016
85711111*2^196610-55559189Henri Lifchitz04/2005
85723^124041+65859183Lelio R Paula10/2012
85732^196590-11179759180Enzo Doria05/2014
8574(10^59174-13)/359174Robert Price02/2017
8575(2*10^59174-113)/359174Robert Price09/2017
8576(9179*2^196533-1)/78359164Lelio R Paula04/2015
8577379*10^59152+959155Arkadiusz Wesolowski10/2011
8578(404*10^59149-53)/959151Robert Price11/2017
857913^53095+4059145Lelio R Paula03/2013
85812*F(282999)-159144Henri Lifchitz12/2009
85804*7^69984+359144Lelio R Paula09/2014
8582(5*10^59142+1)/359143Erik Branger12/2013
85832^196463+571159142Lelio R Paula10/2011
85842^196453-9730559139Lelio R Paula09/2011
8585(28*10^59135+53)/959136Serge Batalov11/2008
8586(28*10^59133+113)/359134Robert Price03/2016
85872^196434+759133Lelio R Paula04/2011
8588(8*10^59127-29)/359128Robert Price05/2016
85892^196414+25559127Lelio R Paula05/2011
85905^84586-9259124Lelio R Paula10/2012
85912^196388-1717759119Enzo Doria05/2013
859279427!6-659119Robert Price08/2018
85933^123890+2059111Lelio R Paula10/2012
85942^196355-102177759109Paul Bourdelais11/2012
859511^56754-141059104Enzo Doria11/2012
8596(7*2^196297-1)/120040759087Lelio R Paula01/2014
8597(16*10^59062-19)/359063Robert Price03/2016
859835^38249-122859060Enzo Doria03/2013
85995^84475-1859046Lelio R Paula10/2012
86002^196123-1770159039Enzo Doria05/2013
860112^54702-3159034Lelio R Paula03/2013
86022^196101-17559033Lelio R Paula04/2011
86032^196085+577559028Lelio R Paula05/2011
86042^196034+1171559013Lelio R Paula05/2011
86052^196018-1848559008Enzo Doria05/2013
86062^195984-216358998Yves Minet08/2013
86073^123645-1658994Lelio R Paula10/2012
860839^37078-3858994Norbert Schneider05/2014
86092^195958-1685358990Enzo Doria05/2013
86102^195930-307158981Yves Minet10/2014
86112^195924+51358980Lelio R Paula05/2011
86122^195863+15558961Lelio R Paula04/2011
8613(28*10^58956+113)/358957Robert Price03/2016
861411^56612-930058956Enzo Doria02/2013
86152^195833-1717358952Enzo Doria05/2013
8616(27*2^195833-1)/5358952Lelio R Paula01/2014
8617(13*2^195821-1)/12242558945Lelio R Paula01/2014
8618139^27504-13858942Norbert Schneider10/2015
8619(418*10^58923+23)/958925Robert Price08/2017
86203^123495+4458923Lelio R Paula10/2012
86212^195737-1856558923Enzo Doria05/2013
862279185!6-1658921Robert Price08/2018
862314^51407+4758920Lelio R Paula03/2013
86242^195691-9958909Lelio R Paula04/2011
86252^195667-185982758902Enzo Doria04/2016
86272^195642+7549958895Enzo Doria04/2016
8626(299*10^58893+1)/358895Robert Price11/2017
86288*6^75678+558890Lelio R Paula09/2014
86292^195618+7318958887Enzo Doria04/2016
8630(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
8631t(197953)58881Robert Price12/2014
86322^195581-1610558876Enzo Doria04/2013
8633(8*10^58872+67)/358873Robert Price01/2017
86347*2^195542-558865Lelio R Paula03/2014
86352*10^58861+9^5886158862Mike Oakes04/2011
863611^56513-162058853Enzo Doria11/2012
86372^195496+16558851Lelio R Paula04/2011
86385^84187+6658845Lelio R Paula10/2012
8639(28*10^58843-43)/358844Robert Price04/2016
86402^195462-1756558840Enzo Doria05/2013
86412^195449-417158837Yves Minet02/2018
86422^195435+5927358832Yves Minet01/2011
86432^195424-1860558829Enzo Doria05/2013
86442^195385-11158817Lelio R Paula04/2011
86457*10^58815-8358816Robert Price09/2017
86462^195357-430358809Yves Minet08/2018
8647(47*2^195254+1)/26882158774Lelio R Paula03/2015
86482^195207-1810958764Enzo Doria05/2013
86492^195199-156758761Yves Minet08/2012
86502^195190+7375958759Enzo Doria04/2016
86519*7^69525-458757Lelio R Paula09/2014
86522^195170-1804558753Enzo Doria05/2013
86532^195166-16558751Lelio R Paula04/2011
8654(754*10^58748-7)/958750Robert Price11/2017
8655(22699*2^195140+1)/17558746Lelio R Paula05/2014
86567*3^123109-258739Lelio R Paula04/2014
8657(8*10^58738-611)/958738Robert Price11/2017
865818^46790+7758735Lelio R Paula03/2013
86602^195095-33729758730Gary Barnes09/2009
8659(14*10^58729+31)/958730Robert Price02/2015
866199^29424+9858720Norbert Schneider07/2013
8662(15185*2^195039-1)/21958715Lelio R Paula04/2015
86632^195001-6958702Lelio R Paula04/2011
86642^194978-48781158695Gary Barnes09/2009
8665163^26530+26530^16358690Serge Batalov05/2014
86662^194940-194940+158683Robert Price10/2014
8667(76*10^58669+41)/958670Robert Price10/2015
866814^51186+8758666Lelio R Paula03/2013
86692^194878-9730558665Lelio R Paula09/2011
86705^83927-1813658663Enzo Doria05/2014
8671(24737*2^194865+1)/108558662Lelio R Paula06/2014
86727^69411+4058660Lelio R Paula10/2012
86736^75382-7958659Lelio R Paula10/2012
86742^194854+2758657Lelio R Paula04/2011
86752^194801+2983558641Lelio R Paula10/2012
86762^194752+19558627Lelio R Paula04/2011
86777^69371-6^6937158626Predrag Minovic08/2004
86782^194747-11251958625Enzo Doria06/2014
8679(15*2^194737+1)/5958622Lelio R Paula07/2012
8680(23*2^194700+1)/358612Lelio R Paula02/2012
868110^58608+5527358609Patrick De Geest07/2017
868210^58608-80000158608Robert Price06/2017
868310^58608-6011958608Patrick De Geest07/2017
86845^83836+7658599Lelio R Paula10/2012
868518^46664+3158577Lelio R Paula03/2013
8686(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
86872^194574+16558573Lelio R Paula04/2011
86902^194569-1221158572Enzo Doria06/2014
868810^58571+5^58571+2^5857158572Robert Price12/2016
868910^58571+20283758572Patrick De Geest02/2017
8691(10^58571+41)/358571Robert Price01/2017
869210^58571-34362958571Patrick De Geest02/2017
8693(43*10^58563-403)/958564Robert Price04/2017
869511^56235-795058563Enzo Doria02/2013
8694145^27095-14458563Norbert Schneider11/2018
8696(14*10^58550+211)/958551Robert Price11/2017
86972^194479-11323958545Enzo Doria07/2014
86982^194455-11224958537Enzo Doria06/2014
86992^194405-11191958522Enzo Doria05/2014
8700(4*10^58521-19)/358522Robert Price06/2017
8702(7^69247-4^69247)/358521Robert Price06/2012
87015*7^69246+858521Lelio R Paula09/2014
87032^194358-116758508Lelio R Paula05/2011
8704(2^194366+7)/137358507Lelio R Paula02/2012
8705(493*10^58486-7)/958488Robert Price07/2016
87063^122579-34058486Lelio R Paula10/2012
8707(11*10^58458-149)/358459Robert Price01/2017
8708(47*10^58456+133)/958457Robert Price04/2017
87092^194186+8558456Lelio R Paula04/2011
87103^122506-2^(122506-1)58451Robert Price01/2016
8711(74^31267-1)/7358444Paul Bourdelais08/2017
8712177^25998-258443Lelio R Paula10/2017
871315^49690-2658440Lelio R Paula03/2013
871410^58437+11072158438Patrick De Geest12/2012
871510^58437-1158437Robert Price05/2011
87162^194095+6958429Lelio R Paula04/2011
8717(29*10^58417-77)/358418Robert Price01/2017
87182^194034+17758411Lelio R Paula04/2011
8719789^20158+20158^78958400Norbert Schneider06/2016
872014^50949+7558395Lelio R Paula03/2013
87212^193974-11476158392Enzo Doria05/2015
87222^193965+558390Henri Lifchitz12/2002
8723(5*10^58384-29)/358385Robert Price02/2017
87243^122360+8058381Lelio R Paula10/2012
872510103^14577-11458373Enzo Doria07/2012
8726(22699*2^193883+1)/2158368Lelio R Paula06/2014
8727(31*2^193886+1)/14076558362Lelio R Paula07/2012
872811^56041-156058361Enzo Doria11/2012
8729(2^193881+9)/1769958360Lelio R Paula02/2012
87303^122313+5858359Lelio R Paula10/2012
87316^74996-11958359Lelio R Paula10/2012
8732(11*2^193859+1)/1358358Lelio R Paula07/2012
87332^193861-11225558358Enzo Doria06/2014
8734(22699*2^193854+1)/492758357Lelio R Paula06/2014
873518^46487+3758354Lelio R Paula03/2013
873617^47419+5458347Lelio R Paula03/2013
8737(31*2^193791+1)/358338Lelio R Paula02/2012
8738(27*2^193805-1)/98224958337Lelio R Paula01/2014
8739144^27025-14358330Norbert Schneider11/2018
87403^122219-2^12221958314Mike Oakes09/2003
8741(199*10^58306+11)/358308Robert Price05/2017
87422^193674-1882558302Lelio R Paula05/2011
87435*10^58275+358276Dmitry Domanov11/2010
87442^193578-11291358273Enzo Doria06/2014
87452^193541+129958262Lelio R Paula05/2011
874610^58250+9358251Robert Price01/2011
874710^58250-17560758250Patrick De Geest12/2012
8748(107^28703+1)/10858248Richard Fischer05/2018
87492^193492+841558247Lelio R Paula10/2012
87502^193444+15758233Lelio R Paula04/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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