PRP Records

Probable Primes Top 10000

(172142 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 ?
72512^198129-5559643Lelio R Paula04/2011
72525^85318-1463659635Enzo Doria02/2013
7253(2^198119+47)/156093559634Lelio R Paula02/2012
72542^198090-1609759632Enzo Doria04/2013
72559*10^59617+8959618Robert Price11/2016
725642625!3+8159612Robert Price09/2014
72575^85277-8459607Lelio R Paula10/2012
72582^197984-1824559600Enzo Doria05/2013
72592^197951-213759590Yves Minet06/2013
726066^32749-65^3274959589Robert Price09/2013
72615*10^59586-359587Dmitry Domanov11/2010
72622^197909-1896159577Enzo Doria05/2013
7263(3^124871+2)/4503159574Lelio R Paula04/2012
72642^197872+8159566Henri Lifchitz10/2005
72652^197873-1846959566Enzo Doria05/2013
7266(22*10^59558-31)/959559Robert Price04/2015
72682^197840-46559556Lelio R Paula05/2011
7267(31*2^197856-1)/388960559556Lelio R Paula01/2014
72692^197808-1780559547Enzo Doria05/2013
72702^197781-1790559539Enzo Doria05/2013
72712^197777-1747359537Enzo Doria05/2013
72726^76507-14959535Lelio R Paula10/2012
7274Phi(61456,109)59526Enzo Doria05/2012
727318^47420+2359526Lelio R Paula03/2013
72753^124747+9459520Lelio R Paula10/2012
727617^48370+1859517Lelio R Paula03/2013
727720^45740-152359510Enzo Doria03/2013
7278(7*2^197642-1)/305159494Lelio R Paula01/2014
727918^47390-185359488Enzo Doria03/2013
7280(2^197581-7)/191559475Lelio R Paula02/2012
7281(24737*2^197559+1)/7759474Lelio R Paula06/2014
72822^197540-245959466Yves Minet07/2014
7283(44*10^59454+1)/959455Serge Batalov11/2010
72842^197494-1780559452Enzo Doria05/2013
72852^197482-1682159449Enzo Doria05/2013
72862^197485+7576759449Enzo Doria04/2016
7287(3*2^197483+1)/2559448Lelio R Paula07/2012
72882^197466-186835159444Enzo Doria04/2016
72892^197411-1778159427Enzo Doria05/2013
7291(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
72902^197392-11462959421Enzo Doria05/2015
72922^197355-15759410Lelio R Paula04/2011
72935^84992-8459407Lelio R Paula10/2012
72942*3^124504-559404Lelio R Paula04/2014
72952^197307-1916559396Enzo Doria05/2013
72962^197303+3276959395Lelio R Paula05/2011
7297(53*10^59389+1)/959390Serge Batalov11/2010
72986^76316-3559386Lelio R Paula10/2012
72992^197259-292959381Yves Minet09/2014
7300lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
730117^48253-659373Lelio R Paula03/2013
73022^197156-1583759350Enzo Doria04/2013
73032^197149-1848159348Enzo Doria05/2013
73042^197142-1715759346Enzo Doria05/2013
7306(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
7305(8^65707-5^65707)/359339Robert Price12/2012
7307(2*14283^14283+1)/792549797559334David Broadhurst09/2010
73082^197012-11171959307Enzo Doria05/2014
73092^196975+51359296Lelio R Paula05/2011
73102^196960+9759291Lelio R Paula04/2011
73119^62116+8^(62116-1)59274Robert Price03/2016
73122^196900-9730559273Lelio R Paula09/2011
73135*6^76155+759261Lelio R Paula09/2014
731415^50385-1459258Wojciech Florek06/2006
7315(136777#-1)/882358147759254Donovan Johnson05/2006
7316(2^196744-3)*6-759227Gilbert Mozzo05/2016
7317(67607*2^196696+1)/359216Lelio R Paula05/2014
73182^196696-11296759212Enzo Doria06/2014
731920^45508-422359208Enzo Doria03/2013
7320gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
732114^51651-8159199Lelio R Paula03/2013
73222^196650-145159198Yves Minet08/2012
73232^196636-279779959194Enzo Doria04/2016
73241111*2^196610-55559189Henri Lifchitz04/2005
73253^124041+65859183Lelio R Paula10/2012
73262^196590-11179759180Enzo Doria05/2014
7327(10^59174-13)/359174Robert Price02/2017
7328(9179*2^196533-1)/78359164Lelio R Paula04/2015
7329379*10^59152+959155Arkadiusz Wesolowski10/2011
733013^53095+4059145Lelio R Paula03/2013
73312*F(282999)-159144Henri Lifchitz12/2009
73324*7^69984+359144Lelio R Paula09/2014
7333(5*10^59142+1)/359143Erik Branger12/2013
73342^196463+571159142Lelio R Paula10/2011
73352^196453-9730559139Lelio R Paula09/2011
7336(28*10^59135+53)/959136Serge Batalov11/2008
7337(28*10^59133+113)/359134Robert Price03/2016
73382^196434+759133Lelio R Paula04/2011
7339(8*10^59127-29)/359128Robert Price05/2016
73402^196414+25559127Lelio R Paula05/2011
73415^84586-9259124Lelio R Paula10/2012
73422^196388-1717759119Enzo Doria05/2013
73433^123890+2059111Lelio R Paula10/2012
73442^196355-102177759109Paul Bourdelais11/2012
734511^56754-141059104Enzo Doria11/2012
7346(7*2^196297-1)/120040759087Lelio R Paula01/2014
7347(16*10^59062-19)/359063Robert Price03/2016
734835^38249-122859060Enzo Doria03/2013
73495^84475-1859046Lelio R Paula10/2012
73502^196123-1770159039Enzo Doria05/2013
735112^54702-3159034Lelio R Paula03/2013
73522^196101-17559033Lelio R Paula04/2011
73532^196085+577559028Lelio R Paula05/2011
73542^196034+1171559013Lelio R Paula05/2011
73552^196018-1848559008Enzo Doria05/2013
73562^195984-216358998Yves Minet08/2013
73573^123645-1658994Lelio R Paula10/2012
735839^37078-3858994Norbert Schneider05/2014
73592^195958-1685358990Enzo Doria05/2013
73602^195930-307158981Yves Minet10/2014
73612^195924+51358980Lelio R Paula05/2011
73622^195863+15558961Lelio R Paula04/2011
7363(28*10^58956+113)/358957Robert Price03/2016
736411^56612-930058956Enzo Doria02/2013
73652^195833-1717358952Enzo Doria05/2013
7366(27*2^195833-1)/5358952Lelio R Paula01/2014
7367(13*2^195821-1)/12242558945Lelio R Paula01/2014
7368139^27504-13858942Norbert Schneider10/2015
73693^123495+4458923Lelio R Paula10/2012
73702^195737-1856558923Enzo Doria05/2013
737114^51407+4758920Lelio R Paula03/2013
73722^195691-9958909Lelio R Paula04/2011
73732^195667-185982758902Enzo Doria04/2016
73742^195642+7549958895Enzo Doria04/2016
73758*6^75678+558890Lelio R Paula09/2014
73762^195618+7318958887Enzo Doria04/2016
7377(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
7378t(197953)58881Robert Price12/2014
73792^195581-1610558876Enzo Doria04/2013
7380(8*10^58872+67)/358873Robert Price01/2017
73817*2^195542-558865Lelio R Paula03/2014
73822*10^58861+9^5886158862Mike Oakes04/2011
738311^56513-162058853Enzo Doria11/2012
73842^195496+16558851Lelio R Paula04/2011
73855^84187+6658845Lelio R Paula10/2012
7386(28*10^58843-43)/358844Robert Price04/2016
73872^195462-1756558840Enzo Doria05/2013
73882^195435+5927358832Yves Minet01/2011
73892^195424-1860558829Enzo Doria05/2013
73902^195385-11158817Lelio R Paula04/2011
7391(47*2^195254+1)/26882158774Lelio R Paula03/2015
73922^195207-1810958764Enzo Doria05/2013
73932^195199-156758761Yves Minet08/2012
73942^195190+7375958759Enzo Doria04/2016
73959*7^69525-458757Lelio R Paula09/2014
73962^195170-1804558753Enzo Doria05/2013
73972^195166-16558751Lelio R Paula04/2011
7398(22699*2^195140+1)/17558746Lelio R Paula05/2014
73997*3^123109-258739Lelio R Paula04/2014
740018^46790+7758735Lelio R Paula03/2013
74022^195095-33729758730Gary Barnes09/2009
7401(14*10^58729+31)/958730Robert Price02/2015
740399^29424+9858720Norbert Schneider07/2013
7404(15185*2^195039-1)/21958715Lelio R Paula04/2015
74052^195001-6958702Lelio R Paula04/2011
74062^194978-48781158695Gary Barnes09/2009
7407163^26530+26530^16358690Serge Batalov05/2014
74082^194940-194940+158683Robert Price10/2014
7409(76*10^58669+41)/958670Robert Price10/2015
741014^51186+8758666Lelio R Paula03/2013
74112^194878-9730558665Lelio R Paula09/2011
74125^83927-1813658663Enzo Doria05/2014
7413(24737*2^194865+1)/108558662Lelio R Paula06/2014
74147^69411+4058660Lelio R Paula10/2012
74156^75382-7958659Lelio R Paula10/2012
74162^194854+2758657Lelio R Paula04/2011
74172^194801+2983558641Lelio R Paula10/2012
74182^194752+19558627Lelio R Paula04/2011
74197^69371-6^6937158626Predrag Minovic08/2004
74202^194747-11251958625Enzo Doria06/2014
7421(15*2^194737+1)/5958622Lelio R Paula07/2012
7422(23*2^194700+1)/358612Lelio R Paula02/2012
74235^83836+7658599Lelio R Paula10/2012
742418^46664+3158577Lelio R Paula03/2013
7425(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
74262^194574+16558573Lelio R Paula04/2011
74292^194569-1221158572Enzo Doria06/2014
742710^58571+5^58571+2^5857158572Robert Price12/2016
742810^58571+20283758572Patrick De Geest02/2017
7430(10^58571+41)/358571Robert Price01/2017
743110^58571-34362958571Patrick De Geest02/2017
743211^56235-795058563Enzo Doria02/2013
74332^194479-11323958545Enzo Doria07/2014
74342^194455-11224958537Enzo Doria06/2014
74352^194405-11191958522Enzo Doria05/2014
7437(7^69247-4^69247)/358521Robert Price06/2012
74365*7^69246+858521Lelio R Paula09/2014
74382^194358-116758508Lelio R Paula05/2011
7439(2^194366+7)/137358507Lelio R Paula02/2012
7440(493*10^58486-7)/958488Robert Price07/2016
74413^122579-34058486Lelio R Paula10/2012
7442(11*10^58458-149)/358459Robert Price01/2017
74432^194186+8558456Lelio R Paula04/2011
74443^122506-2^(122506-1)58451Robert Price01/2016
744515^49690-2658440Lelio R Paula03/2013
744610^58437+11072158438Patrick De Geest12/2012
744710^58437-1158437Robert Price05/2011
74482^194095+6958429Lelio R Paula04/2011
7449(29*10^58417-77)/358418Robert Price01/2017
74502^194034+17758411Lelio R Paula04/2011
7451789^20158+20158^78958400Norbert Schneider06/2016
745214^50949+7558395Lelio R Paula03/2013
74532^193974-11476158392Enzo Doria05/2015
74542^193965+558390Henri Lifchitz12/2002
7455(5*10^58384-29)/358385Robert Price02/2017
74563^122360+8058381Lelio R Paula10/2012
745710103^14577-11458373Enzo Doria07/2012
7458(22699*2^193883+1)/2158368Lelio R Paula06/2014
7459(31*2^193886+1)/14076558362Lelio R Paula07/2012
746011^56041-156058361Enzo Doria11/2012
7461(2^193881+9)/1769958360Lelio R Paula02/2012
74623^122313+5858359Lelio R Paula10/2012
74636^74996-11958359Lelio R Paula10/2012
7464(11*2^193859+1)/1358358Lelio R Paula07/2012
74652^193861-11225558358Enzo Doria06/2014
7466(22699*2^193854+1)/492758357Lelio R Paula06/2014
746718^46487+3758354Lelio R Paula03/2013
746817^47419+5458347Lelio R Paula03/2013
7469(31*2^193791+1)/358338Lelio R Paula02/2012
7470(27*2^193805-1)/98224958337Lelio R Paula01/2014
74713^122219-2^12221958314Mike Oakes09/2003
74722^193674-1882558302Lelio R Paula05/2011
74735*10^58275+358276Dmitry Domanov11/2010
74742^193578-11291358273Enzo Doria06/2014
74752^193541+129958262Lelio R Paula05/2011
747610^58250+9358251Robert Price01/2011
747710^58250-17560758250Patrick De Geest12/2012
74782^193492+841558247Lelio R Paula10/2012
74792^193444+15758233Lelio R Paula04/2011
7480Phi(28754,28754)58231Henri Lifchitz08/2013
74812^193430-11188158229Enzo Doria05/2014
748210^58225+12457958226Patrick De Geest12/2012
748310^58225-9358225Robert Price05/2011
74842^193375-29558212Yves Minet05/2013
74852^193345+7726758203Enzo Doria05/2016
748621^44017-20^4401758201Robert Price05/2012
7487(17*2^193329-1)/958199Lelio R Paula01/2014
748817^47291+2058190Lelio R Paula03/2013
74892^193214-13558164Lelio R Paula04/2011
749019^45483-8058162Lelio R Paula03/2013
7491(4*10^58155+83)/358156Robert Price01/2017
749214^50739-1358154Lelio R Paula03/2013
7493(1017*2^193184-1)/482358154Lelio R Paula04/2015
7494(2*10^58151+457)/958151Robert Price01/2017
7495(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
7496(19*2^193114-1)/118675558129Lelio R Paula01/2014
74982^193091-123758127Yves Minet08/2012
74979*7^68780-258127Lelio R Paula09/2014
74992^193083-86968810558124Lelio R Paula10/2012
75002^193058-4558117Lelio R Paula04/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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