PRP Records

Probable Primes Top 10000

(177649 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 ?
75015^85277-8459607Lelio R Paula10/2012
75022^197984-1824559600Enzo Doria05/2013
75032^197951-213759590Yves Minet06/2013
750466^32749-65^3274959589Robert Price09/2013
75055*10^59586-359587Dmitry Domanov11/2010
75062^197932-395959584Yves Minet04/2017
75072^197909-1896159577Enzo Doria05/2013
7508(3^124871+2)/4503159574Lelio R Paula04/2012
75092^197872+8159566Henri Lifchitz10/2005
75102^197873-1846959566Enzo Doria05/2013
7511(22*10^59558-31)/959559Robert Price04/2015
75132^197840-46559556Lelio R Paula05/2011
7512(31*2^197856-1)/388960559556Lelio R Paula01/2014
75142^197808-1780559547Enzo Doria05/2013
75152^197781-1790559539Enzo Doria05/2013
75162^197777-1747359537Enzo Doria05/2013
75176^76507-14959535Lelio R Paula10/2012
7519Phi(61456,109)59526Enzo Doria05/2012
751818^47420+2359526Lelio R Paula03/2013
75203^124747+9459520Lelio R Paula10/2012
752117^48370+1859517Lelio R Paula03/2013
752220^45740-152359510Enzo Doria03/2013
7523(7*2^197642-1)/305159494Lelio R Paula01/2014
752418^47390-185359488Enzo Doria03/2013
7525(2^197581-7)/191559475Lelio R Paula02/2012
7526(24737*2^197559+1)/7759474Lelio R Paula06/2014
75272^197540-245959466Yves Minet07/2014
7528(44*10^59454+1)/959455Serge Batalov11/2010
75292^197494-1780559452Enzo Doria05/2013
75302^197482-1682159449Enzo Doria05/2013
75312^197485+7576759449Enzo Doria04/2016
7532(3*2^197483+1)/2559448Lelio R Paula07/2012
75332^197466-186835159444Enzo Doria04/2016
75342^197411-1778159427Enzo Doria05/2013
7535(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
75362^197392-11462959421Enzo Doria05/2015
75372^197355-15759410Lelio R Paula04/2011
75385^84992-8459407Lelio R Paula10/2012
75392*3^124504-559404Lelio R Paula04/2014
75402^197307-1916559396Enzo Doria05/2013
75412^197303+3276959395Lelio R Paula05/2011
75422*10^59394-6959395Robert Price07/2017
7543(53*10^59389+1)/959390Serge Batalov11/2010
75446^76316-3559386Lelio R Paula10/2012
75452^197259-292959381Yves Minet09/2014
7546lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
754717^48253-659373Lelio R Paula03/2013
75482^197156-1583759350Enzo Doria04/2013
75492^197149-1848159348Enzo Doria05/2013
75502^197142-1715759346Enzo Doria05/2013
7552(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
7551(8^65707-5^65707)/359339Robert Price12/2012
7553(2*14283^14283+1)/792549797559334David Broadhurst09/2010
75542^197012-11171959307Enzo Doria05/2014
75552^196975+51359296Lelio R Paula05/2011
75562^196960+9759291Lelio R Paula04/2011
75579^62116+8^(62116-1)59274Robert Price03/2016
75582^196900-9730559273Lelio R Paula09/2011
75595*6^76155+759261Lelio R Paula09/2014
756015^50385-1459258Wojciech Florek06/2006
7561(136777#-1)/882358147759254Donovan Johnson05/2006
7562(2^196744-3)*6-759227Gilbert Mozzo05/2016
7563(67607*2^196696+1)/359216Lelio R Paula05/2014
75642^196696-11296759212Enzo Doria06/2014
756520^45508-422359208Enzo Doria03/2013
7566gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
756714^51651-8159199Lelio R Paula03/2013
75682^196650-145159198Yves Minet08/2012
75692^196636-279779959194Enzo Doria04/2016
75701111*2^196610-55559189Henri Lifchitz04/2005
75713^124041+65859183Lelio R Paula10/2012
75722^196590-11179759180Enzo Doria05/2014
7573(10^59174-13)/359174Robert Price02/2017
7574(9179*2^196533-1)/78359164Lelio R Paula04/2015
7575379*10^59152+959155Arkadiusz Wesolowski10/2011
757613^53095+4059145Lelio R Paula03/2013
75772*F(282999)-159144Henri Lifchitz12/2009
75784*7^69984+359144Lelio R Paula09/2014
7579(5*10^59142+1)/359143Erik Branger12/2013
75802^196463+571159142Lelio R Paula10/2011
75812^196453-9730559139Lelio R Paula09/2011
7582(28*10^59135+53)/959136Serge Batalov11/2008
7583(28*10^59133+113)/359134Robert Price03/2016
75842^196434+759133Lelio R Paula04/2011
7585(8*10^59127-29)/359128Robert Price05/2016
75862^196414+25559127Lelio R Paula05/2011
75875^84586-9259124Lelio R Paula10/2012
75882^196388-1717759119Enzo Doria05/2013
75893^123890+2059111Lelio R Paula10/2012
75902^196355-102177759109Paul Bourdelais11/2012
759111^56754-141059104Enzo Doria11/2012
7592(7*2^196297-1)/120040759087Lelio R Paula01/2014
7593(16*10^59062-19)/359063Robert Price03/2016
759435^38249-122859060Enzo Doria03/2013
75955^84475-1859046Lelio R Paula10/2012
75962^196123-1770159039Enzo Doria05/2013
759712^54702-3159034Lelio R Paula03/2013
75982^196101-17559033Lelio R Paula04/2011
75992^196085+577559028Lelio R Paula05/2011
76002^196034+1171559013Lelio R Paula05/2011
76012^196018-1848559008Enzo Doria05/2013
76022^195984-216358998Yves Minet08/2013
76033^123645-1658994Lelio R Paula10/2012
760439^37078-3858994Norbert Schneider05/2014
76052^195958-1685358990Enzo Doria05/2013
76062^195930-307158981Yves Minet10/2014
76072^195924+51358980Lelio R Paula05/2011
76082^195863+15558961Lelio R Paula04/2011
7609(28*10^58956+113)/358957Robert Price03/2016
761011^56612-930058956Enzo Doria02/2013
76112^195833-1717358952Enzo Doria05/2013
7612(27*2^195833-1)/5358952Lelio R Paula01/2014
7613(13*2^195821-1)/12242558945Lelio R Paula01/2014
7614139^27504-13858942Norbert Schneider10/2015
76153^123495+4458923Lelio R Paula10/2012
76162^195737-1856558923Enzo Doria05/2013
761714^51407+4758920Lelio R Paula03/2013
76182^195691-9958909Lelio R Paula04/2011
76192^195667-185982758902Enzo Doria04/2016
76202^195642+7549958895Enzo Doria04/2016
76218*6^75678+558890Lelio R Paula09/2014
76222^195618+7318958887Enzo Doria04/2016
7623(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
7624t(197953)58881Robert Price12/2014
76252^195581-1610558876Enzo Doria04/2013
7626(8*10^58872+67)/358873Robert Price01/2017
76277*2^195542-558865Lelio R Paula03/2014
76282*10^58861+9^5886158862Mike Oakes04/2011
762911^56513-162058853Enzo Doria11/2012
76302^195496+16558851Lelio R Paula04/2011
76315^84187+6658845Lelio R Paula10/2012
7632(28*10^58843-43)/358844Robert Price04/2016
76332^195462-1756558840Enzo Doria05/2013
76342^195435+5927358832Yves Minet01/2011
76352^195424-1860558829Enzo Doria05/2013
76362^195385-11158817Lelio R Paula04/2011
7637(47*2^195254+1)/26882158774Lelio R Paula03/2015
76382^195207-1810958764Enzo Doria05/2013
76392^195199-156758761Yves Minet08/2012
76402^195190+7375958759Enzo Doria04/2016
76419*7^69525-458757Lelio R Paula09/2014
76422^195170-1804558753Enzo Doria05/2013
76432^195166-16558751Lelio R Paula04/2011
7644(22699*2^195140+1)/17558746Lelio R Paula05/2014
76457*3^123109-258739Lelio R Paula04/2014
764618^46790+7758735Lelio R Paula03/2013
76482^195095-33729758730Gary Barnes09/2009
7647(14*10^58729+31)/958730Robert Price02/2015
764999^29424+9858720Norbert Schneider07/2013
7650(15185*2^195039-1)/21958715Lelio R Paula04/2015
76512^195001-6958702Lelio R Paula04/2011
76522^194978-48781158695Gary Barnes09/2009
7653163^26530+26530^16358690Serge Batalov05/2014
76542^194940-194940+158683Robert Price10/2014
7655(76*10^58669+41)/958670Robert Price10/2015
765614^51186+8758666Lelio R Paula03/2013
76572^194878-9730558665Lelio R Paula09/2011
76585^83927-1813658663Enzo Doria05/2014
7659(24737*2^194865+1)/108558662Lelio R Paula06/2014
76607^69411+4058660Lelio R Paula10/2012
76616^75382-7958659Lelio R Paula10/2012
76622^194854+2758657Lelio R Paula04/2011
76632^194801+2983558641Lelio R Paula10/2012
76642^194752+19558627Lelio R Paula04/2011
76657^69371-6^6937158626Predrag Minovic08/2004
76662^194747-11251958625Enzo Doria06/2014
7667(15*2^194737+1)/5958622Lelio R Paula07/2012
7668(23*2^194700+1)/358612Lelio R Paula02/2012
766910^58608-80000158608Robert Price06/2017
76705^83836+7658599Lelio R Paula10/2012
767118^46664+3158577Lelio R Paula03/2013
7672(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
76732^194574+16558573Lelio R Paula04/2011
76742^194569-1221158572Enzo Doria06/2014
767510^58571+5^58571+2^5857158572Robert Price12/2016
767610^58571+20283758572Patrick De Geest02/2017
7677(10^58571+41)/358571Robert Price01/2017
767810^58571-34362958571Patrick De Geest02/2017
7679(43*10^58563-403)/958564Robert Price04/2017
768011^56235-795058563Enzo Doria02/2013
76812^194479-11323958545Enzo Doria07/2014
76822^194455-11224958537Enzo Doria06/2014
76832^194405-11191958522Enzo Doria05/2014
7684(4*10^58521-19)/358522Robert Price06/2017
7686(7^69247-4^69247)/358521Robert Price06/2012
76855*7^69246+858521Lelio R Paula09/2014
76872^194358-116758508Lelio R Paula05/2011
7688(2^194366+7)/137358507Lelio R Paula02/2012
7689(493*10^58486-7)/958488Robert Price07/2016
76903^122579-34058486Lelio R Paula10/2012
7691(11*10^58458-149)/358459Robert Price01/2017
7692(47*10^58456+133)/958457Robert Price04/2017
76932^194186+8558456Lelio R Paula04/2011
76943^122506-2^(122506-1)58451Robert Price01/2016
769515^49690-2658440Lelio R Paula03/2013
769610^58437+11072158438Patrick De Geest12/2012
769710^58437-1158437Robert Price05/2011
76982^194095+6958429Lelio R Paula04/2011
7699(29*10^58417-77)/358418Robert Price01/2017
77002^194034+17758411Lelio R Paula04/2011
7701789^20158+20158^78958400Norbert Schneider06/2016
770214^50949+7558395Lelio R Paula03/2013
77032^193974-11476158392Enzo Doria05/2015
77042^193965+558390Henri Lifchitz12/2002
7705(5*10^58384-29)/358385Robert Price02/2017
77063^122360+8058381Lelio R Paula10/2012
770710103^14577-11458373Enzo Doria07/2012
7708(22699*2^193883+1)/2158368Lelio R Paula06/2014
7709(31*2^193886+1)/14076558362Lelio R Paula07/2012
771011^56041-156058361Enzo Doria11/2012
7711(2^193881+9)/1769958360Lelio R Paula02/2012
77123^122313+5858359Lelio R Paula10/2012
77136^74996-11958359Lelio R Paula10/2012
7714(11*2^193859+1)/1358358Lelio R Paula07/2012
77152^193861-11225558358Enzo Doria06/2014
7716(22699*2^193854+1)/492758357Lelio R Paula06/2014
771718^46487+3758354Lelio R Paula03/2013
771817^47419+5458347Lelio R Paula03/2013
7719(31*2^193791+1)/358338Lelio R Paula02/2012
7720(27*2^193805-1)/98224958337Lelio R Paula01/2014
77213^122219-2^12221958314Mike Oakes09/2003
7722(199*10^58306+11)/358308Robert Price05/2017
77232^193674-1882558302Lelio R Paula05/2011
77245*10^58275+358276Dmitry Domanov11/2010
77252^193578-11291358273Enzo Doria06/2014
77262^193541+129958262Lelio R Paula05/2011
772710^58250+9358251Robert Price01/2011
772810^58250-17560758250Patrick De Geest12/2012
77292^193492+841558247Lelio R Paula10/2012
77302^193444+15758233Lelio R Paula04/2011
7731Phi(28754,28754)58231Henri Lifchitz08/2013
77322^193430-11188158229Enzo Doria05/2014
773310^58225+12457958226Patrick De Geest12/2012
773410^58225-9358225Robert Price05/2011
77352^193375-29558212Yves Minet05/2013
77362^193345+7726758203Enzo Doria05/2016
773721^44017-20^4401758201Robert Price05/2012
7738(17*2^193329-1)/958199Lelio R Paula01/2014
773917^47291+2058190Lelio R Paula03/2013
7740p(12528)#/2-12858170Robert Price05/2017
77412^193214-13558164Lelio R Paula04/2011
774219^45483-8058162Lelio R Paula03/2013
7743(4*10^58155+83)/358156Robert Price01/2017
774414^50739-1358154Lelio R Paula03/2013
7745(1017*2^193184-1)/482358154Lelio R Paula04/2015
7746(2*10^58151+457)/958151Robert Price01/2017
7747(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
7748(19*2^193114-1)/118675558129Lelio R Paula01/2014
77502^193091-123758127Yves Minet08/2012
77499*7^68780-258127Lelio R Paula09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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