PRP Records

Probable Primes Top 10000

(271067 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 ?
725120091^14596+14596^2009183664Hans Havermann03/2017
72522^277907-11062983659Enzo Doria05/2014
725319522^19283+19283^1952283656Hans Havermann04/2017
7254(2^277881+2570)/283651Stefano Morozzi01/2020
72558*5^119664-383643Lelio R Paula10/2014
72568*3^175299-783640Lelio R Paula07/2014
7257(26*10^83638-413)/983639Robert Price10/2017
72583^175250+2283616Robert Price12/2013
726011^80285+3083609Lelio R Paula10/2015
725926870^1293+1293^2687083609Hans Havermann03/2017
7261(6730^21841-1)/672983604Serge Batalov08/2020
7262(2828^24223-1)/282783602Serge Batalov08/2020
72632^277691+187442383594Enzo Doria06/2016
726413^75022-6083571Lelio R Paula11/2015
7265(2^277593+2622)/283564Stefano Morozzi01/2020
726614^72905-5183559Lelio R Paula11/2015
7267(17*2^277565-1)/54383554Lelio R Paula02/2014
72685^119532-1283550Lelio R Paula10/2015
72696^107358-1625383541Enzo Doria02/2013
72702^277478-46021183530Enzo Doria06/2015
7271(2^277474+814)/283528Stefano Morozzi01/2020
7272(22*10^83525-7)/383526Erik Branger09/2014
7273(30^56543+1)/3183520Robert Price07/2013
72742^277417-46078383511Paul Bourdelais04/2013
7275(2^277404+3582)/283507Stefano Morozzi01/2020
7276(22699*2^277387+1)/21983504Lelio R Paula06/2014
7277(31*2^277383-1)/24783500Lelio R Paula02/2014
727821368^8085+8085^2136883500Hans Havermann04/2017
7279(2^277353+3750)/283492Stefano Morozzi01/2020
7280(2^277348+3538)/283490Stefano Morozzi01/2020
7281(9*2^277342+1)/1383489Lelio R Paula12/2012
72825^119439-6683485Lelio R Paula10/2015
7283(14*10^83471-101)/383472Robert Price04/2017
72845*6^107263+783468Lelio R Paula10/2014
7285(64*10^83461-1)/983462Serge Batalov11/2010
72862^277244-17570983459Hans Havermann10/2018
7287(2^277230+1450)/283455Stefano Morozzi01/2020
7288(2^277232+3658)/283455Stefano Morozzi01/2020
728917^67796-9283420Lelio R Paula11/2015
72902^277106-11005783418Enzo Doria04/2014
72916^107200-1983418Lelio R Paula12/2015
729211^80096-183083412Enzo Doria12/2012
72933^174801+5683402Lelio R Paula12/2015
72942^277033-11197383396Enzo Doria05/2014
7295120^40105-11983386Norbert Schneider09/2018
7296(2^276992+2046)/283383Stefano Morozzi01/2020
7297(2^276990+474)/283382Stefano Morozzi01/2020
729820519^11572+11572^2051983378Hans Havermann03/2017
729920850^9971+9971^2085083374Hans Havermann03/2017
73026^107122-1886383358Enzo Doria03/2013
7300(2^276908+2322)/283358Stefano Morozzi01/2020
7301(2^276910+2734)/283358Stefano Morozzi01/2020
73034*10^83354-8983355Robert Price08/2017
73043^174697-3483352Robert Price11/2013
7306(9787*2^276855-1)/234583343Lelio R Paula04/2015
7305(2^276860+1678)/283343Stefano Morozzi01/2020
7307(2^276841+3354)/283338Stefano Morozzi01/2020
73092^276825+7522783333Enzo Doria04/2016
730834*10^83331-983333Robert Price06/2020
73105^119214+8483328Lelio R Paula10/2015
73112^276803-15983327Lelio R Paula06/2012
7312(3*2^276753-1)/2583311Lelio R Paula02/2014
73137*10^83297-3983298Robert Price07/2020
7314114^40495+40495^11483295Norbert Schneider12/2014
731539967!2+102483282Robert Price02/2015
7316(1894^25411-1)/189383279Serge Batalov08/2020
73182^276641+5783278Lelio R Paula06/2012
731935^53934-341483278Enzo Doria03/2013
731721777^6670+6670^2177783278Hans Havermann06/2020
7320(2^276655+78557)/36542583276Lelio R Paula12/2012
73212^276615-403583270Lelio R Paula08/2013
73222^276588+115583262Lelio R Paula08/2013
73232^276587-93783261Yves Minet10/2009
73242^276584-11318383261Enzo Doria07/2014
7325(2^276592-1017)/1384373983256Lelio R Paula12/2012
73262^276547-10959183249Enzo Doria04/2014
732713^74733-3283249Lelio R Paula11/2015
73282^276523-258783242Yves Minet07/2014
732918^66311-4383239Lelio R Paula11/2015
733011^79919-153083228Enzo Doria12/2012
73312^276468-10974583226Enzo Doria04/2014
73322^276462+538583224Lelio R Paula08/2013
7333(9787*2^276422-1)/383215Lelio R Paula04/2015
73352^276391-1583202Lelio R Paula06/2012
7334(4*10^83201+173)/383202Robert Price01/2017
7336(2^276327+534)/283183Stefano Morozzi01/2020
73372^276316-10965583180Enzo Doria04/2014
73382^276305-11206383177Enzo Doria06/2014
7339(2^276296+3406)/283174Stefano Morozzi01/2020
7340(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
7341(2^276277+3254)/283168Stefano Morozzi01/2020
734274913!4-283161Robert Price07/2017
7343(3023^23893-1)/302283155Serge Batalov08/2020
73442^276227-183720783153Enzo Doria05/2015
7346(2^276227+3)/783152Lelio R Paula12/2012
7345(2^276229+12)/2883152Stefano Morozzi03/2020
7347(2^276205+1190)/283146Stefano Morozzi01/2020
73482^276184-6338983140Paul Bourdelais02/2012
7349(2^276165+2046)/283134Stefano Morozzi01/2020
7350(2^276105+1274)/283116Stefano Morozzi01/2020
73512^276066-11160383105Enzo Doria05/2014
735219438^18837+18837^1943883098Hans Havermann07/2020
7353(431^31543-1)/43083097Serge Batalov08/2020
7354(2^276028-3)*6-783094Gilbert Mozzo09/2016
7355(26*10^83067+79)/383068Robert Price09/2020
73562^275926-469183063Yves Minet05/2019
7357(2^275919+1386)/283060Stefano Morozzi01/2020
7358(2^275897+9)/115383051Lelio R Paula12/2012
73592^275879-10980783048Enzo Doria04/2014
7361F(397379)83047Henri Lifchitz08/2003
7360U(397379)83047Serge Batalov03/2015
73623^174040-1483039Robert Price08/2013
7363(86*10^83038-221)/983039Robert Price06/2017
736421632^6897+6897^2163283038Hans Havermann05/2020
73652^275841-688383037Lelio R Paula07/2011
736619610^17127+17127^1961083023Hans Havermann06/2020
73673^174002-14083021Lelio R Paula12/2015
73686^106681+7783014Lelio R Paula12/2015
7369187^36539-283011Lelio R Paula10/2017
73701036^27529+27529^103683010Norbert Schneider03/2020
737111^79701-315083001Enzo Doria12/2012
7372(2^275721+1554)/283000Stefano Morozzi01/2020
7373(2^275704+1858)/282995Stefano Morozzi01/2020
7374(2^275696+1726)/282993Stefano Morozzi01/2020
7375(55459*2^275657+1)/2182985Lelio R Paula06/2014
7376(7*10^82960-457)/982960Robert Price09/2017
73772^275535-685582945Lelio R Paula08/2013
73783^173828-1482938Robert Price08/2013
73792^275512-10967782938Enzo Doria04/2014
7380(2^275450+1698)/282919Stefano Morozzi01/2020
73812^275446-11004582918Enzo Doria04/2014
7382(2^275473+47)/2952609744782916Lelio R Paula12/2012
73833^173755-1482903Robert Price08/2013
7384(182*10^82898+43)/982900Robert Price11/2017
73852^275363-11230982893Enzo Doria06/2014
738661^46427-6082888Norbert Schneider10/2014
73873*10^82880-7^8288082881Mike Oakes02/2010
73882^275290+9019582871Lelio R Paula07/2013
7389(35*10^82870-71)/982871Robert Price05/2015
73902^275270-185962182865Enzo Doria03/2016
73912^275259+8182862Henri Lifchitz01/2007
739221436^7335+7335^2143682859Hans Havermann05/2020
7393(2^275247+1590)/282858Stefano Morozzi01/2020
739422515^4784+4784^2251582851Hans Havermann05/2020
73956*10^82842-3182843Robert Price07/2020
7396(10013^20707-1)/1001282836Serge Batalov08/2020
7397(113703^16384+1)/282834Richard Fischer04/2018
7398(2^275146+954)/282827Stefano Morozzi01/2020
73997^98003+98003^7+182823Robert Price05/2014
7400(2^275101+3566)/282814Stefano Morozzi01/2020
7401(2^275050+3150)/282798Stefano Morozzi01/2020
7402(2^275044+2482)/282797Stefano Morozzi01/2020
740310^82790+12604382791Patrick De Geest07/2013
740410^82790-4782790Robert Price05/2011
740520762^9711+9711^2076282784Hans Havermann05/2020
74062^274985-11266382779Enzo Doria06/2014
74072^274935+1501582764Lelio R Paula07/2013
7408(17*2^274922+1)/382761Lelio R Paula12/2012
7409[(55^5)^9511-(22434^2)^9511]/1982759Richard Fischer11/2019
7410(43*10^82752-61)/982753Robert Price06/2015
7411(3*2^274862+1)/102782740Lelio R Paula12/2012
7412(2^274851+3126)/282739Stefano Morozzi01/2020
7413(31*2^274848-1)/406582736Lelio R Paula02/2014
7414(4^137405+23)/382726Robert Price02/2017
7415(2^274798+414)/282723Stefano Morozzi01/2020
74162^274791-11049182721Enzo Doria05/2014
7417(11*2^274776-1)/9582715Lelio R Paula02/2014
7418(47*10^82706-119)/982707Robert Price09/2017
74192^274704-11139582695Enzo Doria05/2014
74202^274686-391182689Yves Minet04/2017
7421(1629^25741-1)/162882675Serge Batalov08/2020
742221474^7075+7075^2147482670Hans Havermann06/2020
7423(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
7424(3^173263-5)/1449882664Lelio R Paula12/2012
742520488^10815+10815^2048882650Hans Havermann07/2020
7426(2^274554+894)/282649Stefano Morozzi01/2020
74282^274511-6487582637Lelio R Paula08/2013
7427(2^274512+1222)/282637Stefano Morozzi01/2020
742912^76572-8382636Lelio R Paula11/2015
74303^173191-2^17319182634Mike Oakes02/2004
7431(2^274500+2970)/282633Stefano Morozzi01/2020
743220507^10698+10698^2050782629Hans Havermann07/2020
7433(2^274429+3726)/282612Stefano Morozzi01/2020
743414^72072-1582604Lelio R Paula11/2015
7435(2^274374+2950)/282595Stefano Morozzi01/2020
7436(55459*2^274339+1)/382589Lelio R Paula06/2014
74372^274351+12382588Lelio R Paula06/2012
7438(1017*2^274339-1)/351582584Lelio R Paula04/2015
743921208^7833+7833^2120882583Hans Havermann07/2020
7440(2^274248+750)/282557Stefano Morozzi01/2020
7441(2^274240+822)/282555Stefano Morozzi01/2020
74426^106086+11382551Lelio R Paula12/2015
7443(17*10^82540-377)/982541Robert Price11/2017
7444(3470^23311-1)/346982526Serge Batalov08/2020
74452^274093-5869582511Lelio R Paula07/2013
74467*10^82509-4782510Robert Price02/2017
74472^274081-655582507Lelio R Paula07/2013
74492^274074-274074+182505Robert Price10/2014
745014^71985+4782505Lelio R Paula11/2015
74485*10^82504+2182505Robert Price01/2017
7451(2^274062+498)/282501Stefano Morozzi01/2020
74526^106014-13982495Lelio R Paula12/2015
7453(2^274046+47)/75382494Lelio R Paula12/2012
74542^274008-183809982485Enzo Doria05/2015
74552^273981-11002982477Enzo Doria04/2014
745619^64490-3082467Lelio R Paula12/2015
7457(2^273864+3150)/282441Stefano Morozzi01/2020
745821328^7333+7333^2132882439Hans Havermann07/2020
745920829^9070+9070^2082982434Hans Havermann07/2020
74622^273785+1171582418Lelio R Paula07/2013
74618*10^82417+5182418Robert Price05/2017
7460(2^273786+2242)/282418Stefano Morozzi01/2020
746311^79133-1082409Theodore Burton11/2005
7464(2^273752+1882)/282408Stefano Morozzi01/2020
746591^42063+9082404Norbert Schneider01/2016
74672^273662-6382381Lelio R Paula06/2012
74662^273661+25582381Lelio R Paula07/2013
7468(62*10^82377-17)/982378Robert Price09/2015
74692^273608+52428782365Paul Underwood08/2018
74708*10^82360-5182361Robert Price10/2017
7471(79*10^82347-1)/382349Robert Price11/2017
7472(11*10^82323+91)/382323Robert Price02/2017
7473(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
7474(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
747515^69984+3282308Lelio R Paula11/2015
74769*6^105746+782288Lelio R Paula10/2014
747789^42211-8882286Norbert Schneider01/2016
7478gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
747920596^9883+9883^2059682279Hans Havermann06/2020
7480(19*10^82270-43)/382271Robert Price10/2017
74812^273282-11024182267Enzo Doria05/2014
7482(2^273277+3746)/282265Stefano Morozzi01/2020
7483(13^73849+4^73849)/1782263Robert Price05/2013
748410^82254+9^(82254+1)82255Robert Price08/2016
748510^82254+45777382255Patrick De Geest12/2016
748610^82254-9960982254Patrick De Geest12/2016
7487(754*10^82250-7)/982252Robert Price11/2017
748818^65524+1382251Lelio R Paula11/2015
74892^273206-10782244Lelio R Paula06/2012
74902^273193-45914582240Enzo Doria05/2015
74922^273126+3693782220Yves Minet06/2010
749139505!2+12882220Robert Price03/2015
7493(2^273090+2214)/282208Stefano Morozzi01/2020
74942^273053-11211182198Enzo Doria06/2014
7495(2^273052+3138)/282197Stefano Morozzi01/2020
74962^273016+118582187Lelio R Paula07/2013
7497(2^273008+3)/782183Lelio R Paula12/2012
7498(2^272992+2230)/282179Stefano Morozzi01/2020
75005^117554-1538682167Enzo Doria02/2013
749921158^7647+7647^2115882167Hans Havermann06/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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