PRP Records

Probable Primes Top 10000

(202622 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 ?
80012^197303+3276959395Lelio R Paula05/2011
8002(53*10^59389+1)/959390Serge Batalov11/2010
80036^76316-3559386Lelio R Paula10/2012
80042^197259-292959381Yves Minet09/2014
8005lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
800617^48253-659373Lelio R Paula03/2013
80072^197156-1583759350Enzo Doria04/2013
80082^197149-1848159348Enzo Doria05/2013
80092^197142-1715759346Enzo Doria05/2013
8011(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
8010(8^65707-5^65707)/359339Robert Price12/2012
8012(2*14283^14283+1)/792549797559334David Broadhurst09/2010
80132^197012-11171959307Enzo Doria05/2014
80142^196975+51359296Lelio R Paula05/2011
8015(61*10^59294+119)/959295Robert Price09/2017
80164*10^59292+3959293Robert Price11/2017
80172^196960+9759291Lelio R Paula04/2011
80189^62116+8^(62116-1)59274Robert Price03/2016
80192^196900-9730559273Lelio R Paula09/2011
80205*6^76155+759261Lelio R Paula09/2014
802115^50385-1459258Wojciech Florek06/2006
8022(136777#-1)/882358147759254Donovan Johnson05/2006
8023(2^196744-3)*6-759227Gilbert Mozzo05/2016
8024(67607*2^196696+1)/359216Lelio R Paula05/2014
80252^196696-11296759212Enzo Doria06/2014
802620^45508-422359208Enzo Doria03/2013
8027gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
802814^51651-8159199Lelio R Paula03/2013
80292^196650-145159198Yves Minet08/2012
80302^196636-279779959194Enzo Doria04/2016
80311111*2^196610-55559189Henri Lifchitz04/2005
80323^124041+65859183Lelio R Paula10/2012
80332^196590-11179759180Enzo Doria05/2014
8034(10^59174-13)/359174Robert Price02/2017
8035(2*10^59174-113)/359174Robert Price09/2017
8036(9179*2^196533-1)/78359164Lelio R Paula04/2015
8037379*10^59152+959155Arkadiusz Wesolowski10/2011
8038(404*10^59149-53)/959151Robert Price11/2017
803913^53095+4059145Lelio R Paula03/2013
80412*F(282999)-159144Henri Lifchitz12/2009
80404*7^69984+359144Lelio R Paula09/2014
8042(5*10^59142+1)/359143Erik Branger12/2013
80432^196463+571159142Lelio R Paula10/2011
80442^196453-9730559139Lelio R Paula09/2011
8045(28*10^59135+53)/959136Serge Batalov11/2008
8046(28*10^59133+113)/359134Robert Price03/2016
80472^196434+759133Lelio R Paula04/2011
8048(8*10^59127-29)/359128Robert Price05/2016
80492^196414+25559127Lelio R Paula05/2011
80505^84586-9259124Lelio R Paula10/2012
80512^196388-1717759119Enzo Doria05/2013
80523^123890+2059111Lelio R Paula10/2012
80532^196355-102177759109Paul Bourdelais11/2012
805411^56754-141059104Enzo Doria11/2012
8055(7*2^196297-1)/120040759087Lelio R Paula01/2014
8056(16*10^59062-19)/359063Robert Price03/2016
805735^38249-122859060Enzo Doria03/2013
80585^84475-1859046Lelio R Paula10/2012
80592^196123-1770159039Enzo Doria05/2013
806012^54702-3159034Lelio R Paula03/2013
80612^196101-17559033Lelio R Paula04/2011
80622^196085+577559028Lelio R Paula05/2011
80632^196034+1171559013Lelio R Paula05/2011
80642^196018-1848559008Enzo Doria05/2013
80652^195984-216358998Yves Minet08/2013
80663^123645-1658994Lelio R Paula10/2012
806739^37078-3858994Norbert Schneider05/2014
80682^195958-1685358990Enzo Doria05/2013
80692^195930-307158981Yves Minet10/2014
80702^195924+51358980Lelio R Paula05/2011
80712^195863+15558961Lelio R Paula04/2011
8072(28*10^58956+113)/358957Robert Price03/2016
807311^56612-930058956Enzo Doria02/2013
80742^195833-1717358952Enzo Doria05/2013
8075(27*2^195833-1)/5358952Lelio R Paula01/2014
8076(13*2^195821-1)/12242558945Lelio R Paula01/2014
8077139^27504-13858942Norbert Schneider10/2015
8078(418*10^58923+23)/958925Robert Price08/2017
80793^123495+4458923Lelio R Paula10/2012
80802^195737-1856558923Enzo Doria05/2013
808114^51407+4758920Lelio R Paula03/2013
80822^195691-9958909Lelio R Paula04/2011
80832^195667-185982758902Enzo Doria04/2016
80842^195642+7549958895Enzo Doria04/2016
8085(299*10^58893+1)/358895Robert Price11/2017
80868*6^75678+558890Lelio R Paula09/2014
80882^195618+7318958887Enzo Doria04/2016
8087(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
8089t(197953)58881Robert Price12/2014
80902^195581-1610558876Enzo Doria04/2013
8091(8*10^58872+67)/358873Robert Price01/2017
80927*2^195542-558865Lelio R Paula03/2014
80932*10^58861+9^5886158862Mike Oakes04/2011
809411^56513-162058853Enzo Doria11/2012
80952^195496+16558851Lelio R Paula04/2011
80965^84187+6658845Lelio R Paula10/2012
8097(28*10^58843-43)/358844Robert Price04/2016
80982^195462-1756558840Enzo Doria05/2013
80992^195435+5927358832Yves Minet01/2011
81002^195424-1860558829Enzo Doria05/2013
81012^195385-11158817Lelio R Paula04/2011
81027*10^58815-8358816Robert Price09/2017
8103(47*2^195254+1)/26882158774Lelio R Paula03/2015
81042^195207-1810958764Enzo Doria05/2013
81052^195199-156758761Yves Minet08/2012
81062^195190+7375958759Enzo Doria04/2016
81079*7^69525-458757Lelio R Paula09/2014
81082^195170-1804558753Enzo Doria05/2013
81092^195166-16558751Lelio R Paula04/2011
8110(754*10^58748-7)/958750Robert Price11/2017
8111(22699*2^195140+1)/17558746Lelio R Paula05/2014
81127*3^123109-258739Lelio R Paula04/2014
8113(8*10^58738-611)/958738Robert Price11/2017
811418^46790+7758735Lelio R Paula03/2013
81152^195095-33729758730Gary Barnes09/2009
8116(14*10^58729+31)/958730Robert Price02/2015
811799^29424+9858720Norbert Schneider07/2013
8118(15185*2^195039-1)/21958715Lelio R Paula04/2015
81192^195001-6958702Lelio R Paula04/2011
81202^194978-48781158695Gary Barnes09/2009
8121163^26530+26530^16358690Serge Batalov05/2014
81222^194940-194940+158683Robert Price10/2014
8123(76*10^58669+41)/958670Robert Price10/2015
812414^51186+8758666Lelio R Paula03/2013
81252^194878-9730558665Lelio R Paula09/2011
81265^83927-1813658663Enzo Doria05/2014
8127(24737*2^194865+1)/108558662Lelio R Paula06/2014
81287^69411+4058660Lelio R Paula10/2012
81296^75382-7958659Lelio R Paula10/2012
81302^194854+2758657Lelio R Paula04/2011
81312^194801+2983558641Lelio R Paula10/2012
81322^194752+19558627Lelio R Paula04/2011
81337^69371-6^6937158626Predrag Minovic08/2004
81342^194747-11251958625Enzo Doria06/2014
8135(15*2^194737+1)/5958622Lelio R Paula07/2012
8136(23*2^194700+1)/358612Lelio R Paula02/2012
813710^58608+5527358609Patrick De Geest07/2017
813810^58608-80000158608Robert Price06/2017
813910^58608-6011958608Patrick De Geest07/2017
81405^83836+7658599Lelio R Paula10/2012
814118^46664+3158577Lelio R Paula03/2013
8142(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
81432^194574+16558573Lelio R Paula04/2011
81462^194569-1221158572Enzo Doria06/2014
814410^58571+5^58571+2^5857158572Robert Price12/2016
814510^58571+20283758572Patrick De Geest02/2017
8147(10^58571+41)/358571Robert Price01/2017
814810^58571-34362958571Patrick De Geest02/2017
8149(43*10^58563-403)/958564Robert Price04/2017
815011^56235-795058563Enzo Doria02/2013
8151(14*10^58550+211)/958551Robert Price11/2017
81522^194479-11323958545Enzo Doria07/2014
81532^194455-11224958537Enzo Doria06/2014
81542^194405-11191958522Enzo Doria05/2014
8155(4*10^58521-19)/358522Robert Price06/2017
8156(7^69247-4^69247)/358521Robert Price06/2012
81575*7^69246+858521Lelio R Paula09/2014
81582^194358-116758508Lelio R Paula05/2011
8159(2^194366+7)/137358507Lelio R Paula02/2012
8160(493*10^58486-7)/958488Robert Price07/2016
81613^122579-34058486Lelio R Paula10/2012
8162(11*10^58458-149)/358459Robert Price01/2017
8163(47*10^58456+133)/958457Robert Price04/2017
81642^194186+8558456Lelio R Paula04/2011
81653^122506-2^(122506-1)58451Robert Price01/2016
8166(74^31267-1)/7358444Paul Bourdelais08/2017
8167177^25998-258443Lelio R Paula10/2017
816815^49690-2658440Lelio R Paula03/2013
816910^58437+11072158438Patrick De Geest12/2012
817010^58437-1158437Robert Price05/2011
81712^194095+6958429Lelio R Paula04/2011
8172(29*10^58417-77)/358418Robert Price01/2017
81732^194034+17758411Lelio R Paula04/2011
8174789^20158+20158^78958400Norbert Schneider06/2016
817514^50949+7558395Lelio R Paula03/2013
81762^193974-11476158392Enzo Doria05/2015
81772^193965+558390Henri Lifchitz12/2002
8178(5*10^58384-29)/358385Robert Price02/2017
81793^122360+8058381Lelio R Paula10/2012
818010103^14577-11458373Enzo Doria07/2012
8181(22699*2^193883+1)/2158368Lelio R Paula06/2014
8182(31*2^193886+1)/14076558362Lelio R Paula07/2012
818311^56041-156058361Enzo Doria11/2012
8184(2^193881+9)/1769958360Lelio R Paula02/2012
81853^122313+5858359Lelio R Paula10/2012
81866^74996-11958359Lelio R Paula10/2012
8187(11*2^193859+1)/1358358Lelio R Paula07/2012
81882^193861-11225558358Enzo Doria06/2014
8189(22699*2^193854+1)/492758357Lelio R Paula06/2014
819018^46487+3758354Lelio R Paula03/2013
819117^47419+5458347Lelio R Paula03/2013
8192(31*2^193791+1)/358338Lelio R Paula02/2012
8193(27*2^193805-1)/98224958337Lelio R Paula01/2014
81943^122219-2^12221958314Mike Oakes09/2003
8195(199*10^58306+11)/358308Robert Price05/2017
81962^193674-1882558302Lelio R Paula05/2011
81975*10^58275+358276Dmitry Domanov11/2010
81982^193578-11291358273Enzo Doria06/2014
81992^193541+129958262Lelio R Paula05/2011
820010^58250+9358251Robert Price01/2011
820110^58250-17560758250Patrick De Geest12/2012
82022^193492+841558247Lelio R Paula10/2012
82032^193444+15758233Lelio R Paula04/2011
8204Phi(28754,28754)58231Henri Lifchitz08/2013
82052^193430-11188158229Enzo Doria05/2014
820610^58225+12457958226Patrick De Geest12/2012
820710^58225-9358225Robert Price05/2011
82082^193375-29558212Yves Minet05/2013
82092^193345+7726758203Enzo Doria05/2016
821021^44017-20^4401758201Robert Price05/2012
8211(17*2^193329-1)/958199Lelio R Paula01/2014
821217^47291+2058190Lelio R Paula03/2013
8213p(12528)#/2-12858170Robert Price05/2017
82142^193214-13558164Lelio R Paula04/2011
821519^45483-8058162Lelio R Paula03/2013
8216(4*10^58155+83)/358156Robert Price01/2017
821714^50739-1358154Lelio R Paula03/2013
8218(1017*2^193184-1)/482358154Lelio R Paula04/2015
8219(2*10^58151+457)/958151Robert Price01/2017
8220(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
8221(19*2^193114-1)/118675558129Lelio R Paula01/2014
82232^193091-123758127Yves Minet08/2012
82229*7^68780-258127Lelio R Paula09/2014
82242^193083-86968810558124Lelio R Paula10/2012
82252^193058-4558117Lelio R Paula04/2011
8226(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
822711^55795-4258105Lelio R Paula03/2013
82283^121779-1658104Lelio R Paula10/2012
8229(13*10^58103+191)/358104Robert Price08/2017
82302^192986+19558095Lelio R Paula04/2011
82317^68740+2*3^6874058093Mike Oakes07/2010
8232(85*10^58091-1)/358093Robert Price07/2017
8233(404*10^58087-53)/958089Robert Price11/2017
823412^53821+1158083Lelio R Paula02/2013
8235119^27979-11858072Norbert Schneider10/2013
8236(10223*2^192828+1)/24358049Lelio R Paula05/2014
82372^192808-112758041Yves Minet05/2013
8238(27*2^192803+1)/982758037Lelio R Paula07/2012
8240(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
82393*10^58032-2358033Robert Price11/2017
82412^192678+7294358002Enzo Doria04/2016
8242(13*10^57997-37)/357998Robert Price08/2017
82432^192657-318957996Yves Minet10/2014
82446^74525-14957992Lelio R Paula10/2012
824542^35723-4157988Norbert Schneider06/2014
8246(29*2^192625-1)/18357986Lelio R Paula01/2014
8247(3^121520-8)/384757977Lelio R Paula03/2012
8248(2^192596-5)/13957976Lelio R Paula02/2012
824910^57975+6783357976Patrick De Geest09/2013
825010^57975-4769357975Patrick De Geest09/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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