PRP Records

Probable Primes Top 10000

(253476 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 ?
9251(2^198481-5)/2831159745Lelio R Paula02/2012
9252(5^85487-1)/(4*25133179)59745Gord Palameta07/2019
92532^198400-18959725Lelio R Paula04/2011
92542^198384-1283759720Enzo Doria10/2012
925542694!3-72959719Robert Price09/2014
92562^198320-1871759701Enzo Doria05/2013
925720^45881-118359693Enzo Doria03/2013
92582^198224-685559672Lelio R Paula05/2011
92592^198181-1910159659Enzo Doria05/2013
92605*10^59650+4159651Robert Price08/2017
92612^198149-11221359649Enzo Doria06/2014
92622^198138+7369959646Enzo Doria04/2016
92632^198129-5559643Lelio R Paula04/2011
926416029^5258+5258^1602959642Hans Havermann05/2019
92655^85318-1463659635Enzo Doria02/2013
9266(2^198119+47)/156093559634Lelio R Paula02/2012
92672^198090-1609759632Enzo Doria04/2013
92689*10^59617+8959618Robert Price11/2016
926942625!3+8159612Robert Price09/2014
92705^85277-8459607Lelio R Paula10/2012
9271(871*10^59599-7)/959601Robert Price11/2017
92722^197984-1824559600Enzo Doria05/2013
927312202^14583-14583^1220259593Norbert Schneider01/2019
92752^197951-213759590Yves Minet06/2013
9274(38*10^59589+187)/959590Robert Price11/2017
927666^32749-65^3274959589Robert Price09/2013
92775*10^59586-359587Dmitry Domanov11/2010
9278(35*10^59584-197)/959585Robert Kinser10/2017
92792^197932-395959584Yves Minet04/2017
92802^197909-1896159577Enzo Doria05/2013
9281(3^124871+2)/4503159574Lelio R Paula04/2012
92822^197872+8159566Henri Lifchitz10/2005
92832^197873-1846959566Enzo Doria05/2013
9284(22*10^59558-31)/959559Robert Price04/2015
928512003^14600-14600^1200359558Norbert Schneider02/2019
92872^197840-46559556Lelio R Paula05/2011
9286(31*2^197856-1)/388960559556Lelio R Paula01/2014
92882^197808-1780559547Enzo Doria05/2013
92892^197781-1790559539Enzo Doria05/2013
92902^197777-1747359537Enzo Doria05/2013
92916^76507-14959535Lelio R Paula10/2012
9293Phi(61456,109)59526Enzo Doria05/2012
929218^47420+2359526Lelio R Paula03/2013
9294(59^33613+1)/6059522Paul Bourdelais08/2017
92953^124747+9459520Lelio R Paula10/2012
929617^48370+1859517Lelio R Paula03/2013
929720^45740-152359510Enzo Doria03/2013
9298(47*10^59509+493)/959510Robert Price11/2017
9299(7*2^197642-1)/305159494Lelio R Paula01/2014
930018^47390-185359488Enzo Doria03/2013
9302(2^197581-7)/191559475Lelio R Paula02/2012
930110621^14772-14772^1062159475Norbert Schneider05/2019
9303(24737*2^197559+1)/7759474Lelio R Paula06/2014
93042^197540-245959466Yves Minet07/2014
9305(44*10^59454+1)/959455Serge Batalov11/2010
93062^197494-1780559452Enzo Doria05/2013
93072^197482-1682159449Enzo Doria05/2013
93082^197485+7576759449Enzo Doria04/2016
9309(3*2^197483+1)/2559448Lelio R Paula07/2012
93102^197466-186835159444Enzo Doria04/2016
93112^197411-1778159427Enzo Doria05/2013
9313(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
93122^197392-11462959421Enzo Doria05/2015
931415441^7046+7046^1544159417Hans Havermann05/2019
93152^197355-15759410Lelio R Paula04/2011
93175^84992-8459407Lelio R Paula10/2012
93169899^14868-14868^989959407Norbert Schneider07/2019
93182*3^124504-559404Lelio R Paula04/2014
93192^197307-1916559396Enzo Doria05/2013
93202^197303+3276959395Lelio R Paula05/2011
93212*10^59394-6959395Robert Price07/2017
9322(53*10^59389+1)/959390Serge Batalov11/2010
93236^76316-3559386Lelio R Paula10/2012
93242^197259-292959381Yves Minet09/2014
932515036^8893+8893^1503659378Hans Havermann05/2019
9326lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
932817^48253-659373Lelio R Paula03/2013
932714678^11091+11091^1467859373Hans Havermann05/2019
93292^197156-1583759350Enzo Doria04/2013
93302^197152-429559349Yves Minet08/2018
93312^197149-1848159348Enzo Doria05/2013
93322^197142-1715759346Enzo Doria05/2013
9334(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
9333(8^65707-5^65707)/359339Robert Price12/2012
9335(2*14283^14283+1)/792549797559334David Broadhurst09/2010
933615267^7682+7682^1526759320Hans Havermann05/2019
93372^197012-11171959307Enzo Doria05/2014
93382^196975+51359296Lelio R Paula05/2011
9339(61*10^59294+119)/959295Robert Price09/2017
93404*10^59292+3959293Robert Price11/2017
93412^196960+9759291Lelio R Paula04/2011
93429^62116+8^(62116-1)59274Robert Price03/2016
93432^196900-9730559273Lelio R Paula09/2011
934413706^14327-14327^1370659270Norbert Schneider05/2019
93455*6^76155+759261Lelio R Paula09/2014
934615^50385-1459258Wojciech Florek06/2006
9347(136777#-1)/882358147759254Donovan Johnson05/2006
9348(2^196744-3)*6-759227Gilbert Mozzo05/2016
934914694^10717+10717^1469459218Hans Havermann05/2019
9350(67607*2^196696+1)/359216Lelio R Paula05/2014
93512^196696-11296759212Enzo Doria06/2014
935220^45508-422359208Enzo Doria03/2013
9353gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
935414^51651-8159199Lelio R Paula03/2013
93552^196650-145159198Yves Minet08/2012
93562^196636-279779959194Enzo Doria04/2016
93571111*2^196610-55559189Henri Lifchitz04/2005
93583^124041+65859183Lelio R Paula10/2012
93592^196590-11179759180Enzo Doria05/2014
9360(10^59174-13)/359174Robert Price02/2017
9361(2*10^59174-113)/359174Robert Price09/2017
9362(9179*2^196533-1)/78359164Lelio R Paula04/2015
936311267^14600-14600^1126759157Norbert Schneider02/2019
9364379*10^59152+959155Arkadiusz Wesolowski10/2011
936513161^14360-14360^1316159153Norbert Schneider06/2019
9366(404*10^59149-53)/959151Robert Price11/2017
936713^53095+4059145Lelio R Paula03/2013
93682*F(282999)-159144Henri Lifchitz12/2009
93694*7^69984+359144Lelio R Paula09/2014
9370(5*10^59142+1)/359143Erik Branger12/2013
93712^196463+571159142Lelio R Paula10/2011
93722^196453-9730559139Lelio R Paula09/2011
9373(28*10^59135+53)/959136Serge Batalov11/2008
9374(28*10^59133+113)/359134Robert Price03/2016
93752^196434+759133Lelio R Paula04/2011
9376(8*10^59127-29)/359128Robert Price05/2016
93772^196414+25559127Lelio R Paula05/2011
93785^84586-9259124Lelio R Paula10/2012
93792^196388-1717759119Enzo Doria05/2013
938079427!6-659119Robert Price08/2018
93813^123890+2059111Lelio R Paula10/2012
93822^196355-102177759109Paul Bourdelais11/2012
938311^56754-141059104Enzo Doria11/2012
938410902^14635-14635^1090259089Norbert Schneider02/2019
9385(7*2^196297-1)/120040759087Lelio R Paula01/2014
9386(16*10^59062-19)/359063Robert Price03/2016
938735^38249-122859060Enzo Doria03/2013
93885^84475-1859046Lelio R Paula10/2012
93892^196123-1770159039Enzo Doria05/2013
939012^54702-3159034Lelio R Paula03/2013
93912^196101-17559033Lelio R Paula04/2011
93922^196085+577559028Lelio R Paula05/2011
93932^196034+1171559013Lelio R Paula05/2011
93942^196018-1848559008Enzo Doria05/2013
93952^195984-216358998Yves Minet08/2013
93963^123645-1658994Lelio R Paula10/2012
939739^37078-3858994Norbert Schneider05/2014
93992^195958-1685358990Enzo Doria05/2013
939812480^14401-14401^1248058990Norbert Schneider07/2019
94002^195930-307158981Yves Minet10/2014
94012^195924+51358980Lelio R Paula05/2011
94022^195863+15558961Lelio R Paula04/2011
9403(28*10^58956+113)/358957Robert Price03/2016
940411^56612-930058956Enzo Doria02/2013
94052^195833-1717358952Enzo Doria05/2013
9406(27*2^195833-1)/5358952Lelio R Paula01/2014
9407(13*2^195821-1)/12242558945Lelio R Paula01/2014
9408139^27504-13858942Norbert Schneider10/2015
9409a(222666)58929Robert Price05/2019
9410(418*10^58923+23)/958925Robert Price08/2017
94113^123495+4458923Lelio R Paula10/2012
94122^195737-1856558923Enzo Doria05/2013
941379185!6-1658921Robert Price08/2018
941414^51407+4758920Lelio R Paula03/2013
94152^195691-9958909Lelio R Paula04/2011
94162^195667-185982758902Enzo Doria04/2016
94182^195642+7549958895Enzo Doria04/2016
9417(299*10^58893+1)/358895Robert Price11/2017
94218*6^75678+558890Lelio R Paula09/2014
941914222^13827+13827^1422258890Hans Havermann05/2019
94209137^14868-14868^913758890Norbert Schneider07/2019
94222^195618+7318958887Enzo Doria04/2016
9423(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
9424t(197953)58881Robert Price12/2014
94252^195581-1610558876Enzo Doria04/2013
9426(8*10^58872+67)/358873Robert Price01/2017
94277*2^195542-558865Lelio R Paula03/2014
94282*10^58861+9^5886158862Mike Oakes04/2011
942911^56513-162058853Enzo Doria11/2012
94302^195496+16558851Lelio R Paula04/2011
94315^84187+6658845Lelio R Paula10/2012
94322^195478-499158845Yves Minet05/2019
9433(28*10^58843-43)/358844Robert Price04/2016
94342^195462-1756558840Enzo Doria05/2013
94352^195449-417158837Yves Minet02/2018
94362^195435+5927358832Yves Minet01/2011
94372^195424-1860558829Enzo Doria05/2013
943810295^14658-14658^1029558818Norbert Schneider03/2019
94392^195385-11158817Lelio R Paula04/2011
94407*10^58815-8358816Robert Price09/2017
944110130^14683-14683^1013058815Norbert Schneider03/2019
94422^195357-430358809Yves Minet08/2018
944314218^13631+13631^1421858785Hans Havermann05/2019
9444(47*2^195254+1)/26882158774Lelio R Paula03/2015
94459039^14854-14854^903958765Norbert Schneider07/2019
94462^195207-1810958764Enzo Doria05/2013
94472^195199-156758761Yves Minet08/2012
94482^195190+7375958759Enzo Doria04/2016
94499*7^69525-458757Lelio R Paula09/2014
94502^195170-1804558753Enzo Doria05/2013
94512^195166-16558751Lelio R Paula04/2011
9452(754*10^58748-7)/958750Robert Price11/2017
9453(22699*2^195140+1)/17558746Lelio R Paula05/2014
94547*3^123109-258739Lelio R Paula04/2014
9455(8*10^58738-611)/958738Robert Price11/2017
945618^46790+7758735Lelio R Paula03/2013
94582^195095-33729758730Gary Barnes09/2009
9457(14*10^58729+31)/958730Robert Price02/2015
945999^29424+9858720Norbert Schneider07/2013
9460(15185*2^195039-1)/21958715Lelio R Paula04/2015
94612^195001-6958702Lelio R Paula04/2011
94622^194978-48781158695Gary Barnes09/2009
9463163^26530+26530^16358690Serge Batalov05/2014
94642^194940-194940+158683Robert Price10/2014
9465(76*10^58669+41)/958670Robert Price10/2015
946614^51186+8758666Lelio R Paula03/2013
94672^194878-9730558665Lelio R Paula09/2011
94685^83927-1813658663Enzo Doria05/2014
9469(24737*2^194865+1)/108558662Lelio R Paula06/2014
94707^69411+4058660Lelio R Paula10/2012
94716^75382-7958659Lelio R Paula10/2012
94722^194854+2758657Lelio R Paula04/2011
94732^194801+2983558641Lelio R Paula10/2012
94742^194752+19558627Lelio R Paula04/2011
94757^69371-6^6937158626Predrag Minovic08/2004
94762^194747-11251958625Enzo Doria06/2014
9477(15*2^194737+1)/5958622Lelio R Paula07/2012
9478(23*2^194700+1)/358612Lelio R Paula02/2012
947910^58608+5527358609Patrick De Geest07/2017
948010^58608-80000158608Robert Price06/2017
948110^58608-6011958608Patrick De Geest07/2017
94825^83836+7658599Lelio R Paula10/2012
948318^46664+3158577Lelio R Paula03/2013
9484(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
94852^194574+16558573Lelio R Paula04/2011
94882^194569-1221158572Enzo Doria06/2014
948610^58571+5^58571+2^5857158572Robert Price12/2016
948710^58571+20283758572Patrick De Geest02/2017
9489(10^58571+41)/358571Robert Price01/2017
949010^58571-34362958571Patrick De Geest02/2017
9491(43*10^58563-403)/958564Robert Price04/2017
949211^56235-795058563Enzo Doria02/2013
9493145^27095-14458563Norbert Schneider11/2018
94942^194505-461558552Yves Minet05/2019
9495(14*10^58550+211)/958551Robert Price11/2017
94962^194479-11323958545Enzo Doria07/2014
94972^194455-11224958537Enzo Doria06/2014
94982^194405-11191958522Enzo Doria05/2014
9499(4*10^58521-19)/358522Robert Price06/2017
95005*7^69246+858521Lelio R Paula09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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