PRP Records

Probable Primes Top 10000

(218736 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 ?
8251Phi(61456,109)59526Enzo Doria05/2012
8252(59^33613+1)/6059522Paul Bourdelais08/2017
82533^124747+9459520Lelio R Paula10/2012
825417^48370+1859517Lelio R Paula03/2013
825520^45740-152359510Enzo Doria03/2013
8256(47*10^59509+493)/959510Robert Price11/2017
8257(7*2^197642-1)/305159494Lelio R Paula01/2014
825818^47390-185359488Enzo Doria03/2013
8259(2^197581-7)/191559475Lelio R Paula02/2012
8260(24737*2^197559+1)/7759474Lelio R Paula06/2014
82612^197540-245959466Yves Minet07/2014
8262(44*10^59454+1)/959455Serge Batalov11/2010
82632^197494-1780559452Enzo Doria05/2013
82642^197482-1682159449Enzo Doria05/2013
82652^197485+7576759449Enzo Doria04/2016
8266(3*2^197483+1)/2559448Lelio R Paula07/2012
82672^197466-186835159444Enzo Doria04/2016
82682^197411-1778159427Enzo Doria05/2013
8269(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
82702^197392-11462959421Enzo Doria05/2015
82712^197355-15759410Lelio R Paula04/2011
82725^84992-8459407Lelio R Paula10/2012
82732*3^124504-559404Lelio R Paula04/2014
82742^197307-1916559396Enzo Doria05/2013
82762^197303+3276959395Lelio R Paula05/2011
82752*10^59394-6959395Robert Price07/2017
8277(53*10^59389+1)/959390Serge Batalov11/2010
82786^76316-3559386Lelio R Paula10/2012
82792^197259-292959381Yves Minet09/2014
8280lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
828117^48253-659373Lelio R Paula03/2013
82822^197156-1583759350Enzo Doria04/2013
82832^197152-429559349Yves Minet08/2018
82842^197149-1848159348Enzo Doria05/2013
82852^197142-1715759346Enzo Doria05/2013
8287(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
8286(8^65707-5^65707)/359339Robert Price12/2012
8288(2*14283^14283+1)/792549797559334David Broadhurst09/2010
82892^197012-11171959307Enzo Doria05/2014
82902^196975+51359296Lelio R Paula05/2011
8291(61*10^59294+119)/959295Robert Price09/2017
82924*10^59292+3959293Robert Price11/2017
82932^196960+9759291Lelio R Paula04/2011
82949^62116+8^(62116-1)59274Robert Price03/2016
82952^196900-9730559273Lelio R Paula09/2011
82965*6^76155+759261Lelio R Paula09/2014
829715^50385-1459258Wojciech Florek06/2006
8298(136777#-1)/882358147759254Donovan Johnson05/2006
8299(2^196744-3)*6-759227Gilbert Mozzo05/2016
8300(67607*2^196696+1)/359216Lelio R Paula05/2014
83012^196696-11296759212Enzo Doria06/2014
830220^45508-422359208Enzo Doria03/2013
8303gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
830414^51651-8159199Lelio R Paula03/2013
83052^196650-145159198Yves Minet08/2012
83062^196636-279779959194Enzo Doria04/2016
83071111*2^196610-55559189Henri Lifchitz04/2005
83083^124041+65859183Lelio R Paula10/2012
83092^196590-11179759180Enzo Doria05/2014
8310(10^59174-13)/359174Robert Price02/2017
8311(2*10^59174-113)/359174Robert Price09/2017
8312(9179*2^196533-1)/78359164Lelio R Paula04/2015
8313379*10^59152+959155Arkadiusz Wesolowski10/2011
8314(404*10^59149-53)/959151Robert Price11/2017
831513^53095+4059145Lelio R Paula03/2013
83162*F(282999)-159144Henri Lifchitz12/2009
83174*7^69984+359144Lelio R Paula09/2014
8318(5*10^59142+1)/359143Erik Branger12/2013
83192^196463+571159142Lelio R Paula10/2011
83202^196453-9730559139Lelio R Paula09/2011
8321(28*10^59135+53)/959136Serge Batalov11/2008
8322(28*10^59133+113)/359134Robert Price03/2016
83232^196434+759133Lelio R Paula04/2011
8324(8*10^59127-29)/359128Robert Price05/2016
83252^196414+25559127Lelio R Paula05/2011
83265^84586-9259124Lelio R Paula10/2012
83272^196388-1717759119Enzo Doria05/2013
832879427!6-659119Robert Price08/2018
83293^123890+2059111Lelio R Paula10/2012
83302^196355-102177759109Paul Bourdelais11/2012
833111^56754-141059104Enzo Doria11/2012
8332(7*2^196297-1)/120040759087Lelio R Paula01/2014
8333(16*10^59062-19)/359063Robert Price03/2016
833435^38249-122859060Enzo Doria03/2013
83355^84475-1859046Lelio R Paula10/2012
83362^196123-1770159039Enzo Doria05/2013
833712^54702-3159034Lelio R Paula03/2013
83382^196101-17559033Lelio R Paula04/2011
83392^196085+577559028Lelio R Paula05/2011
83402^196034+1171559013Lelio R Paula05/2011
83412^196018-1848559008Enzo Doria05/2013
83422^195984-216358998Yves Minet08/2013
83433^123645-1658994Lelio R Paula10/2012
834439^37078-3858994Norbert Schneider05/2014
83452^195958-1685358990Enzo Doria05/2013
83462^195930-307158981Yves Minet10/2014
83472^195924+51358980Lelio R Paula05/2011
83482^195863+15558961Lelio R Paula04/2011
8349(28*10^58956+113)/358957Robert Price03/2016
835011^56612-930058956Enzo Doria02/2013
83512^195833-1717358952Enzo Doria05/2013
8352(27*2^195833-1)/5358952Lelio R Paula01/2014
8353(13*2^195821-1)/12242558945Lelio R Paula01/2014
8354139^27504-13858942Norbert Schneider10/2015
8355(418*10^58923+23)/958925Robert Price08/2017
83563^123495+4458923Lelio R Paula10/2012
83572^195737-1856558923Enzo Doria05/2013
835879185!6-1658921Robert Price08/2018
835914^51407+4758920Lelio R Paula03/2013
83602^195691-9958909Lelio R Paula04/2011
83612^195667-185982758902Enzo Doria04/2016
83632^195642+7549958895Enzo Doria04/2016
8362(299*10^58893+1)/358895Robert Price11/2017
83648*6^75678+558890Lelio R Paula09/2014
83652^195618+7318958887Enzo Doria04/2016
8366(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
8367t(197953)58881Robert Price12/2014
83682^195581-1610558876Enzo Doria04/2013
8369(8*10^58872+67)/358873Robert Price01/2017
83707*2^195542-558865Lelio R Paula03/2014
83712*10^58861+9^5886158862Mike Oakes04/2011
837211^56513-162058853Enzo Doria11/2012
83732^195496+16558851Lelio R Paula04/2011
83745^84187+6658845Lelio R Paula10/2012
8375(28*10^58843-43)/358844Robert Price04/2016
83762^195462-1756558840Enzo Doria05/2013
83772^195449-417158837Yves Minet02/2018
83782^195435+5927358832Yves Minet01/2011
83792^195424-1860558829Enzo Doria05/2013
83802^195385-11158817Lelio R Paula04/2011
83817*10^58815-8358816Robert Price09/2017
83822^195357-430358809Yves Minet08/2018
8383(47*2^195254+1)/26882158774Lelio R Paula03/2015
83842^195207-1810958764Enzo Doria05/2013
83852^195199-156758761Yves Minet08/2012
83862^195190+7375958759Enzo Doria04/2016
83879*7^69525-458757Lelio R Paula09/2014
83882^195170-1804558753Enzo Doria05/2013
83892^195166-16558751Lelio R Paula04/2011
8390(754*10^58748-7)/958750Robert Price11/2017
8391(22699*2^195140+1)/17558746Lelio R Paula05/2014
83927*3^123109-258739Lelio R Paula04/2014
8393(8*10^58738-611)/958738Robert Price11/2017
839418^46790+7758735Lelio R Paula03/2013
83962^195095-33729758730Gary Barnes09/2009
8395(14*10^58729+31)/958730Robert Price02/2015
839799^29424+9858720Norbert Schneider07/2013
8398(15185*2^195039-1)/21958715Lelio R Paula04/2015
83992^195001-6958702Lelio R Paula04/2011
84002^194978-48781158695Gary Barnes09/2009
8401163^26530+26530^16358690Serge Batalov05/2014
84022^194940-194940+158683Robert Price10/2014
8403(76*10^58669+41)/958670Robert Price10/2015
840414^51186+8758666Lelio R Paula03/2013
84052^194878-9730558665Lelio R Paula09/2011
84065^83927-1813658663Enzo Doria05/2014
8407(24737*2^194865+1)/108558662Lelio R Paula06/2014
84087^69411+4058660Lelio R Paula10/2012
84096^75382-7958659Lelio R Paula10/2012
84102^194854+2758657Lelio R Paula04/2011
84112^194801+2983558641Lelio R Paula10/2012
84122^194752+19558627Lelio R Paula04/2011
84137^69371-6^6937158626Predrag Minovic08/2004
84142^194747-11251958625Enzo Doria06/2014
8415(15*2^194737+1)/5958622Lelio R Paula07/2012
8416(23*2^194700+1)/358612Lelio R Paula02/2012
841710^58608+5527358609Patrick De Geest07/2017
841810^58608-80000158608Robert Price06/2017
841910^58608-6011958608Patrick De Geest07/2017
84205^83836+7658599Lelio R Paula10/2012
842118^46664+3158577Lelio R Paula03/2013
8422(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
84232^194574+16558573Lelio R Paula04/2011
84262^194569-1221158572Enzo Doria06/2014
842410^58571+5^58571+2^5857158572Robert Price12/2016
842510^58571+20283758572Patrick De Geest02/2017
8427(10^58571+41)/358571Robert Price01/2017
842810^58571-34362958571Patrick De Geest02/2017
8429(43*10^58563-403)/958564Robert Price04/2017
843011^56235-795058563Enzo Doria02/2013
8431(14*10^58550+211)/958551Robert Price11/2017
84322^194479-11323958545Enzo Doria07/2014
84332^194455-11224958537Enzo Doria06/2014
84342^194405-11191958522Enzo Doria05/2014
8435(4*10^58521-19)/358522Robert Price06/2017
8437(7^69247-4^69247)/358521Robert Price06/2012
84365*7^69246+858521Lelio R Paula09/2014
84382^194358-116758508Lelio R Paula05/2011
8439(2^194366+7)/137358507Lelio R Paula02/2012
8440(493*10^58486-7)/958488Robert Price07/2016
84413^122579-34058486Lelio R Paula10/2012
8442(11*10^58458-149)/358459Robert Price01/2017
8443(47*10^58456+133)/958457Robert Price04/2017
84442^194186+8558456Lelio R Paula04/2011
84453^122506-2^(122506-1)58451Robert Price01/2016
8446(74^31267-1)/7358444Paul Bourdelais08/2017
8447177^25998-258443Lelio R Paula10/2017
844815^49690-2658440Lelio R Paula03/2013
844910^58437+11072158438Patrick De Geest12/2012
845010^58437-1158437Robert Price05/2011
84512^194095+6958429Lelio R Paula04/2011
8452(29*10^58417-77)/358418Robert Price01/2017
84532^194034+17758411Lelio R Paula04/2011
8454789^20158+20158^78958400Norbert Schneider06/2016
845514^50949+7558395Lelio R Paula03/2013
84562^193974-11476158392Enzo Doria05/2015
84572^193965+558390Henri Lifchitz12/2002
8458(5*10^58384-29)/358385Robert Price02/2017
84593^122360+8058381Lelio R Paula10/2012
846010103^14577-11458373Enzo Doria07/2012
8461(22699*2^193883+1)/2158368Lelio R Paula06/2014
8462(31*2^193886+1)/14076558362Lelio R Paula07/2012
846311^56041-156058361Enzo Doria11/2012
8464(2^193881+9)/1769958360Lelio R Paula02/2012
84653^122313+5858359Lelio R Paula10/2012
84666^74996-11958359Lelio R Paula10/2012
8467(11*2^193859+1)/1358358Lelio R Paula07/2012
84682^193861-11225558358Enzo Doria06/2014
8469(22699*2^193854+1)/492758357Lelio R Paula06/2014
847018^46487+3758354Lelio R Paula03/2013
847117^47419+5458347Lelio R Paula03/2013
8472(31*2^193791+1)/358338Lelio R Paula02/2012
8473(27*2^193805-1)/98224958337Lelio R Paula01/2014
84743^122219-2^12221958314Mike Oakes09/2003
8475(199*10^58306+11)/358308Robert Price05/2017
84762^193674-1882558302Lelio R Paula05/2011
84775*10^58275+358276Dmitry Domanov11/2010
84782^193578-11291358273Enzo Doria06/2014
84792^193541+129958262Lelio R Paula05/2011
848010^58250+9358251Robert Price01/2011
848110^58250-17560758250Patrick De Geest12/2012
8482(107^28703+1)/10858248Richard Fischer05/2018
84832^193492+841558247Lelio R Paula10/2012
84842^193444+15758233Lelio R Paula04/2011
8485Phi(28754,28754)58231Henri Lifchitz08/2013
84862^193430-11188158229Enzo Doria05/2014
848710^58225+12457958226Patrick De Geest12/2012
848810^58225-9358225Robert Price05/2011
84892^193375-29558212Yves Minet05/2013
84902^193345+7726758203Enzo Doria05/2016
849121^44017-20^4401758201Robert Price05/2012
8492(17*2^193329-1)/958199Lelio R Paula01/2014
849317^47291+2058190Lelio R Paula03/2013
8494p(12528)#/2-12858170Robert Price05/2017
84952^193214-13558164Lelio R Paula04/2011
849619^45483-8058162Lelio R Paula03/2013
8497(4*10^58155+83)/358156Robert Price01/2017
849814^50739-1358154Lelio R Paula03/2013
8499(1017*2^193184-1)/482358154Lelio R Paula04/2015
8500(2*10^58151+457)/958151Robert Price01/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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