PRP Records

Probable Primes Top 10000

(173006 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 ?
82512^180946-11104154471Enzo Doria05/2014
8252(64*10^54467+287)/954468Robert Price04/2016
82535^77907-2*3^7790754455Mike Oakes11/2009
825420^41853-562354453Enzo Doria03/2013
825514^47506-7554448Lelio R Paula02/2013
82562^180839-11343754438Enzo Doria08/2014
82573^114085+2854433Lelio R Paula10/2012
8258Phi(141230,10)54432Ray Chandler08/2009
82596^69946-5554429Lelio R Paula10/2012
82605*2^180796+354426Lelio R Paula03/2014
8261(23*2^180782-1)/9154421Lelio R Paula01/2014
82629*6^69928-754416Lelio R Paula09/2014
826392^27701-91^2770154399Robert Price08/2015
8264(2^180687-3)*6-754393Gilbert Mozzo04/2016
8265(5*10^54388-11)/354389Erik Branger12/2013
826620^41799-304354382Enzo Doria03/2013
826713860^8387+8387^1386054382Hans Havermann08/2016
8268(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
82697^64329-1854365Lelio R Paula10/2012
82702^180551-96754352Yves Minet01/2012
827115^46209-7454347Lelio R Paula02/2013
827210^54345+2973954346Patrick De Geest08/2013
827310^54345-14138154345Patrick De Geest09/2013
8274lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
82752^180496+1554335Lelio R Paula02/2011
82761845^16636+16636^184554334Serge Batalov05/2014
827711^52169-7054329Lelio R Paula01/2013
827813693^9262+9262^1369354317Hans Havermann06/2016
82792^180429-11310154315Enzo Doria07/2014
82802^180423-11205154313Enzo Doria05/2014
828116112^2349+2349^1611254312Hans Havermann06/2016
8282(13^48751+4^48751)/1754305Robert Price05/2013
82832^180370+1291554297Lelio R Paula09/2012
8284(10^54290+41)/354290Robert Price01/2017
828515108^3917+3917^1510854283Hans Havermann06/2016
82862^180317-301954281Yves Minet10/2014
82872^180314+85554280Lelio R Paula10/2009
828819^42425+9454252Lelio R Paula02/2013
82892^180180-100544954240Paul Bourdelais11/2012
82912^180173-277354238Yves Minet07/2014
829013367^11418+11418^1336754238Hans Havermann06/2016
8292427^20614+20614^42754224Norbert Schneider06/2016
82932^180124-8795954223Gary Barnes08/2009
82942^180111-11310154219Enzo Doria07/2014
82952^180101-11487154216Enzo Doria05/2015
8296(11*2^180099+1)/5161754212Lelio R Paula07/2012
82982^180070+46554207Lelio R Paula09/2012
829713683^9154+9154^1368354207Hans Havermann06/2016
8299810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
83002^180014+61354190Jason Earls04/2008
83012^180007+10154188Lelio R Paula02/2011
83022^180001+4187754186Jim Fougeron08/2002
83032^180000+13015354186Jim Fougeron09/2002
83043^113565-7454185Lelio R Paula10/2012
830550^31891-4954182Norbert Schneider07/2014
8306(5*2^179991-1)/1142754180Lelio R Paula01/2014
83073^113548+2654177Lelio R Paula10/2012
8308(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
83094159^14969-13854173Enzo Doria07/2012
83112^179955+577554172Lelio R Paula10/2009
83102^179953-23131354172Enzo Doria05/2014
83125^77485+654160Lelio R Paula10/2012
831318^43141+8554154Lelio R Paula02/2013
83143^113489-34054149Lelio R Paula10/2012
83157^64070+9054146Lelio R Paula10/2012
831618^43131+7154142Lelio R Paula02/2013
83172^179826-13154134Lelio R Paula02/2011
83182^179815-11273554130Enzo Doria06/2014
83192^179806+7384954127Enzo Doria04/2016
83202^179790+3354123Donovan Johnson02/2006
832114287^6138+6138^1428754120Hans Havermann06/2016
8322(17*10^54117+1)/954118Serge Batalov05/2010
83232^179763-18954115Lelio R Paula02/2011
8324(21181*2^179770+1)/302910554115Lelio R Paula05/2014
83251828^16589+16589^182854113Serge Batalov05/2014
832720^41588-588354108Enzo Doria03/2013
832650^31847-4954108Norbert Schneider07/2014
83282^179733-685554106Lelio R Paula10/2009
832920^41584-558354103Enzo Doria03/2013
833010^54084+3*3^5408454085Mike Oakes05/2010
83312^179613-179554069Lelio R Paula10/2009
83322^179589-101152354062Paul Bourdelais11/2012
83332^179574-253154058Yves Minet07/2014
8334(41*10^54051-23)/954052Robert Price05/2015
8335117^26131-11654044Norbert Schneider10/2013
8336(10^54038-31)/354038Serge Batalov12/2014
833711^51885-8454033Lelio R Paula01/2013
833814990^4011+4011^1499054013Hans Havermann07/2016
8339(19*2^179414+1)/754010Lelio R Paula07/2012
83403^113182-1040854002Enzo Doria02/2013
834135^34970-878653997Enzo Doria03/2013
83422^179371-163758753997Enzo Doria05/2015
834319^42225-9253996Lelio R Paula01/2013
8344(3^113188+7)/7391767578453994Lelio R Paula03/2012
83457*3^113162+853993Lelio R Paula03/2014
8346(10^53991+179)/953991Serge Batalov12/2014
83472^179350-214553990Lelio R Paula10/2009
8348(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
83498^59782-6^59782-3^5978253989Mike Oakes11/2009
83503*7^63861+853970Lelio R Paula09/2014
83512^179274+7138953967Enzo Doria04/2016
83522^179259-5869553963Lelio R Paula10/2009
83536^69345+6153961Lelio R Paula10/2012
8354(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
8355(40216^11719-1)/4021553955Serge Batalov04/2015
835614^47067-353945Lelio R Paula01/2013
8357(2^179168-5)/5953934Lelio R Paula02/2012
83582^179128+841553923Lelio R Paula07/2012
83592^179120+253353921Henri Lifchitz09/2004
8360(2^179126+78557)/464932118753913Lelio R Paula05/2012
836274^28842+7353913Norbert Schneider11/2012
83611271^17368+17368^127153913Serge Batalov05/2014
83632^179079+5353909Lelio R Paula02/2011
836417^43807+5453903Lelio R Paula01/2013
836517^43807+3053903Lelio R Paula01/2013
83663^112951-31053892Lelio R Paula10/2012
8367Phi(7,2957!)53888Robert Price05/2015
8368(10223*2^178975+1)/3398553877Lelio R Paula05/2014
83692^178944-21920953868Enzo Doria11/2012
8370(10^53859+149)/353859Serge Batalov12/2014
83712^178910-19153858Lelio R Paula02/2011
837216170^2141+2141^1617053857Hans Havermann07/2016
8373(5*10^53855-107)/353856Robert Price01/2017
8374(72*10^53847-27)/9953847Patrick De Geest08/2004
83752^178841-86968810553837Lelio R Paula06/2012
83762*10^53834-2753835Robert Price02/2017
83772^178821-101152353831Paul Bourdelais11/2012
83782^178819-1553830Lelio R Paula02/2011
8379(14450!-1)/22529658153829Donovan Johnson04/2006
83802^178761-46553813Lelio R Paula10/2009
838118900^703+703^1890053808Anatoly F. Selevich02/2007
838213918^7343+7343^1391853806Hans Havermann08/2016
838310^53804+3174953805Patrick De Geest12/2012
838410^53804-7153804Robert Price05/2011
8385t(178994)53804Robert Price03/2015
8386(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
83872^178671-11321553786Enzo Doria07/2014
838815110^3621+3621^1511053774Hans Havermann07/2016
83892^178611+9553768Lelio R Paula02/2011
83902^178597+571153764Lelio R Paula10/2011
83912^178598+1291553764Lelio R Paula07/2012
8392(9179*2^178579-1)/30353760Lelio R Paula03/2015
83935*7^63589+253740Lelio R Paula09/2014
83942^178516-11251553739Enzo Doria06/2014
839520^41302-2753736Lelio R Paula01/2013
83966^69054-3920953735Mike Oakes12/2010
839713086^12769+12769^1308653734Hans Havermann07/2016
83982^178455+7604353721Enzo Doria04/2016
8399(10^53718-7)/353718Makoto Kamada10/2004
8400(67607*2^178426+1)/353716Lelio R Paula05/2014
84019*10^53707+1153708Robert Kinser01/2017
840294601!8-253708Robert Price04/2017
840313214^11595+11595^1321453706Hans Havermann07/2016
8404Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
84052^178367-37953694Yves Minet03/2013
8406(2^178364-5)/1153692Lelio R Paula02/2012
84074339^14760-16853688Enzo Doria06/2012
840812^49746-1153685Lelio R Paula01/2013
8410(9913*2^178266-1)/224753665Lelio R Paula03/2015
840913725^8128+8128^1372553665Hans Havermann07/2016
84112^178250-11326153659Enzo Doria07/2014
84122^178226+1171553652Lelio R Paula10/2009
841335^34742-197653645Enzo Doria03/2013
841420^41228-56353639Enzo Doria03/2013
8415359^20992+20992^35953637Norbert Schneider08/2014
8416(27*2^178183-1)/2906553636Lelio R Paula01/2014
8417(3^112414+7)/3738169653628Lelio R Paula03/2012
841817994^955+955^1799453623Anatoly F. Selevich10/2006
84192^178117-155153619Yves Minet08/2012
84202^178099-1128753614Enzo Doria06/2014
8421(15*2^178080-1)/30907153604Lelio R Paula01/2014
84225^76672-1376653592Enzo Doria02/2013
84236^68868-13753590Lelio R Paula10/2012
8424(5*2^178021+1)/817353587Lelio R Paula07/2012
84255^76654-2653579Lelio R Paula10/2012
8426(3^112297-2)/762753576Lelio R Paula03/2012
84273*2^177948-753569Lelio R Paula03/2014
842810^53558+1854353559Patrick De Geest12/2012
842910^53558-2153558Robert Price03/2011
84302^177792-9553521Lelio R Paula02/2011
843113392^9919+9919^1339253521Hans Havermann07/2016
843213105^12132+12132^1310553520Hans Havermann07/2016
843313^48042+8253517Lelio R Paula01/2013
84342^177768+3912153514Yves Minet10/2010
843513835^7366+7366^1383553504Hans Havermann07/2016
843617^43477+8453497Lelio R Paula01/2013
84375*10^53492+953493Dmitry Domanov11/2010
84382^177683+9553488Lelio R Paula01/2011
8439(2^177678+3)/51462753481Lelio R Paula02/2012
84402^177641-25546353476Gary Barnes08/2009
8441p(11608)#/2+1653469Robert Price12/2016
844237302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
84431829^16384+1828^1638453449Henri Lifchitz01/2007
844435^34608-960253438Enzo Doria03/2013
8445(3^111992+8)/1486753430Lelio R Paula03/2012
84462^177480+186966153427Enzo Doria05/2016
8447(8*10^53411+1)/953411Serge Batalov12/2008
84484*5^76410-353409Lelio R Paula09/2014
84492^177380-11304553397Enzo Doria07/2014
84505^76362-2*3^7636253375Mike Oakes11/2009
84514159^14747-14053370Enzo Doria07/2012
8452(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
8453p(11586)#/2+3253357Robert Price12/2016
845415^45362-4653350Lelio R Paula01/2013
845514147^5892+5892^1414753338Hans Havermann07/2016
84567^63109+4653334Lelio R Paula10/2012
845720^40986-134353325Enzo Doria03/2013
845820^40977-888353313Enzo Doria03/2013
84593^111711+266053300Lelio R Paula10/2012
84602^177040-1186553295Enzo Doria10/2012
8461(7*10^53287+17)/353288Erik Branger03/2014
846235^34506-1075853280Enzo Doria03/2013
8463(11*10^53274-17)/353275Erik Branger03/2014
8464(1017*2^176971-1)/33553275Lelio R Paula03/2015
84652^176961-283353271Yves Minet09/2014
84663^111642+11053267Lelio R Paula10/2012
846717^43290-9853267Lelio R Paula01/2013
84687^63028+3653265Lelio R Paula10/2012
8469(22*10^53264+71)/353265Robert Price05/2017
84707^63023-3653261Lelio R Paula10/2012
847119783^492+492^1978353256Anatoly F. Selevich02/2007
847213350^9739+9739^1335053247Hans Havermann10/2015
847314394^4993+4993^1439453235Hans Havermann10/2015
84742^176823-11280753230Enzo Doria06/2014
84751684^16495+16495^168453219Serge Batalov05/2014
847615277^3042+3042^1527753213Hans Havermann06/2016
8477(50322^11317-1)/5032153206Serge Batalov04/2015
84782^176742-159553205Lelio R Paula10/2009
8479(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
8480(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
8481(3*2^176696-1)/29953189Lelio R Paula01/2014
8482(7*10^53185-1)/353186Erik Branger03/2014
84832^176629+46553171Lelio R Paula07/2012
8484(3*2^176604-1)/35953162Lelio R Paula01/2014
84855^76038-1436653149Enzo Doria02/2013
848615156^3209+3209^1515653143Hans Havermann06/2016
84872^176532-283753142Yves Minet09/2014
848852^30967-5153140Norbert Schneider08/2014
84899*5^76023-253139Lelio R Paula09/2014
8490(14283!+1)/46421617753135Michael Porter03/2016
84912^176461-16553121Lelio R Paula02/2011
8492(62*10^53111+1)/953112Serge Batalov05/2010
84932^176403-13953103Lelio R Paula02/2011
849455^30508-253095Lelio R Paula08/2013
8495(48591^11329-1)/4859053090Serge Batalov04/2015
84963^111254-8853082Lelio R Paula10/2012
849715^45129-5653076Lelio R Paula01/2013
84982^176293-7353070Lelio R Paula01/2011
8500(67*10^53068+41)/953069Robert Price09/2015
849915271^2986+2986^1527153069Hans Havermann06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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