PRP Records

Probable Primes Top 10000

(180278 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 ?
8251(11*10^55254+1)/355255Erik Branger03/2014
82523^115802-2655252Lelio R Paula10/2012
82532^183534-364555250Lelio R Paula01/2011
8254(15*2^183533-1)/11355249Lelio R Paula01/2014
82555^79032-1376655241Enzo Doria02/2013
82568*3^115759-755232Lelio R Paula03/2014
82576^70974-13755229Lelio R Paula10/2012
82582^183446-11307355223Enzo Doria07/2014
82592^183441+57729457555222Lelio R Paula03/2013
82605^79000-655219Lelio R Paula10/2012
82612^183413-90155213Yves Minet01/2012
826219^43168-5055202Lelio R Paula02/2013
82632^183340+1968355191Lelio R Paula02/2012
82646^70923+3555189Lelio R Paula10/2012
82652^183317-403555184Lelio R Paula01/2011
82662^183284-1555174Lelio R Paula03/2011
82672^183255+14955166Lelio R Paula02/2011
82684*10^55165+8755166Robert Price05/2016
8270(3^115574+4)/6303755139Lelio R Paula03/2012
82692^183165-11233355139Enzo Doria06/2014
82712^183142+85555132Lelio R Paula01/2011
8272(49*10^55129+383)/955130Robert Price04/2017
82732^183019+25525555095Lelio R Paula01/2011
82743*10^55077+755078Erik Branger11/2013
8275(62*10^55075-71)/955076Robert Price09/2015
827627499!2-3255070Robert Price10/2015
827715307^3958+3958^1530755067Hans Havermann08/2016
827870^29836-6955051Norbert Schneider10/2012
827918^43854-8355049Lelio R Paula02/2013
82807^65126+5855038Lelio R Paula10/2012
82812^182827-161555037Lelio R Paula11/2009
82827*10^55030-955031Dmitry Domanov11/2010
82836^70702+2355017Lelio R Paula10/2012
8284(23*2^182753+1)/15155014Lelio R Paula07/2012
82852^182743-161555012Lelio R Paula11/2009
8286(24737*2^182736+1)/39955011Lelio R Paula05/2014
82873^115280-956855003Enzo Doria02/2013
82882^182656-1284954985Enzo Doria10/2012
82899*19^42995+1654981Curtis Bright05/2015
82902^182627+2842554977Lelio R Paula11/2009
82912^182597-11305354968Enzo Doria07/2014
8292(3^115213+2)/3090672554964Lelio R Paula03/2012
82932^182581-197554963Yves Minet09/2012
829427449!!-1654959Robert Price06/2015
82964^91283-3^9128354958Jean-Louis Charton01/2004
82952^182565+10754958Lelio R Paula11/2009
82972^182560+205354957Lelio R Paula12/2010
82982^182451-18245154924Henri Lifchitz10/2004
82992^182444+8154922Henri Lifchitz10/2005
83002^182433+7410554918Enzo Doria04/2016
830120^42206-524354912Enzo Doria03/2013
83022^182394+8554907Lelio R Paula02/2011
83032^182374-11228754901Enzo Doria06/2014
8304(47^32833-33^32833)/1454899Serge Batalov12/2016
83052^182363-11316754897Enzo Doria07/2014
83062^182359-11222154896Enzo Doria06/2014
8307(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
8308(17*2^182274+1)/146754869Lelio R Paula01/2012
830918^43698-554853Lelio R Paula02/2013
83102^182209-189354851Yves Minet09/2012
83112^182194-344354846Yves Minet12/2016
831215023^4468+4468^1502354836Hans Havermann08/2016
83132^182135+9014354829Yves Minet10/2010
83142^182119+7433354824Enzo Doria04/2016
831514289^6860+6860^1428954818Hans Havermann08/2016
83163^114892-114892^354818Norbert Schneider03/2017
83172^182070-4735554809Lelio R Paula01/2011
83183^114869+7654807Lelio R Paula10/2012
83198^60681-60681^854801Norbert Schneider12/2016
83201897^16710+16710^189754777Serge Batalov05/2014
8321Phi(61868,59)54776Enzo Doria04/2012
8322113^26679+254775Lelio R Paula05/2013
83233^114789-7454769Lelio R Paula10/2012
832415^46567+9854768Lelio R Paula02/2013
8325(2*10^54767-71)/354767Robert Price01/2017
8326(298*10^54765-7)/354767Robert Price06/2017
8327(21*2^181931-1)/16999754763Lelio R Paula01/2014
83292^181913+2954762Henri Lifchitz06/2005
8328(31*10^54761-121)/954762Robert Price06/2016
83302^181887+18954754Lelio R Paula02/2011
83312^181874+181874^2-154750Robert Price04/2014
8332(2^181865+9)/733954743Lelio R Paula02/2012
83335^78314-9254740Lelio R Paula10/2012
8334(163*10^54727-1)/954729Serge Batalov12/2014
833515^46531+7454725Lelio R Paula02/2013
8336277^22400-34854712Enzo Doria07/2012
83376^70302+10154706Lelio R Paula10/2012
83383^114622-1040854689Enzo Doria02/2013
8340(23*2^181674+1)/48954688Lelio R Paula01/2012
83392^181669-155154688Yves Minet08/2012
8341(57352^11491-1)/5735154676Serge Batalov04/2015
8342(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8343(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
834413^49073+4654665Lelio R Paula01/2013
8345(57042^11491-1)/5704154649Serge Batalov04/2015
834720^42000+7354644Lelio R Paula02/2013
8346(67607*2^181517+1)/165554644Lelio R Paula05/2014
834833*10^54634+754636Robert Price07/2016
834920^41988+6154628Lelio R Paula01/2013
835020^41988-812354628Enzo Doria03/2013
83512^181420+2118154613Yves Minet03/2011
8352(19*10^54608+161)/954609Robert Price07/2016
835319^42696-2454598Lelio R Paula02/2013
8354(74*10^54583+61)/954584Robert Price10/2015
83552^181316-9439554582Lelio R Paula09/2011
835614751^5006+5006^1475154572Hans Havermann08/2016
835714^47609+3954567Lelio R Paula02/2013
83583^114327-7454548Lelio R Paula10/2012
8359gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
8360(17*10^54537-47)/354538Robert Price05/2017
83612^181155-1155*18115554534Henri Lifchitz02/2005
8362Phi(61672,83)54533Enzo Doria05/2012
83639*2^181128+754526Lelio R Paula03/2014
836489*10^54518-754520Robert Price03/2017
83652^181090-11324754514Enzo Doria07/2014
836614031^7670+7670^1403154508Hans Havermann08/2016
836714210^6849+6849^1421054505Hans Havermann08/2016
83682^181043-19954500Lelio R Paula02/2011
836912^50499+554498Lelio R Paula01/2013
837012^50491+554489Lelio R Paula01/2013
83716^70016-14554484Lelio R Paula10/2012
837211^52313-960054479Enzo Doria02/2013
83732^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
83742^180946-11104154471Enzo Doria05/2014
8375(64*10^54467+287)/954468Robert Price04/2016
83765^77907-2*3^7790754455Mike Oakes11/2009
837720^41853-562354453Enzo Doria03/2013
837814^47506-7554448Lelio R Paula02/2013
83792^180839-11343754438Enzo Doria08/2014
83803^114085+2854433Lelio R Paula10/2012
8381Phi(141230,10)54432Ray Chandler08/2009
83826^69946-5554429Lelio R Paula10/2012
83835*2^180796+354426Lelio R Paula03/2014
8384(23*2^180782-1)/9154421Lelio R Paula01/2014
83859*6^69928-754416Lelio R Paula09/2014
838692^27701-91^2770154399Robert Price08/2015
8387(2^180687-3)*6-754393Gilbert Mozzo04/2016
8388(5*10^54388-11)/354389Erik Branger12/2013
838920^41799-304354382Enzo Doria03/2013
839013860^8387+8387^1386054382Hans Havermann08/2016
8391(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
83927^64329-1854365Lelio R Paula10/2012
83932^180551-96754352Yves Minet01/2012
839415^46209-7454347Lelio R Paula02/2013
839510^54345+2973954346Patrick De Geest08/2013
839610^54345-14138154345Patrick De Geest09/2013
8397lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
83982^180496+1554335Lelio R Paula02/2011
83991845^16636+16636^184554334Serge Batalov05/2014
840011^52169-7054329Lelio R Paula01/2013
840113693^9262+9262^1369354317Hans Havermann06/2016
84022^180429-11310154315Enzo Doria07/2014
84032^180423-11205154313Enzo Doria05/2014
840416112^2349+2349^1611254312Hans Havermann06/2016
8405(13^48751+4^48751)/1754305Robert Price05/2013
84062^180370+1291554297Lelio R Paula09/2012
8407(10^54290+41)/354290Robert Price01/2017
840815108^3917+3917^1510854283Hans Havermann06/2016
84092^180317-301954281Yves Minet10/2014
84102^180314+85554280Lelio R Paula10/2009
841119^42425+9454252Lelio R Paula02/2013
84122^180180-100544954240Paul Bourdelais11/2012
84132^180173-277354238Yves Minet07/2014
841413367^11418+11418^1336754238Hans Havermann06/2016
8415427^20614+20614^42754224Norbert Schneider06/2016
84162^180124-8795954223Gary Barnes08/2009
84172^180111-11310154219Enzo Doria07/2014
84182^180101-11487154216Enzo Doria05/2015
8419(11*2^180099+1)/5161754212Lelio R Paula07/2012
84212^180070+46554207Lelio R Paula09/2012
842013683^9154+9154^1368354207Hans Havermann06/2016
8422810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
84232^180014+61354190Jason Earls04/2008
84242^180007+10154188Lelio R Paula02/2011
84252^180001+4187754186Jim Fougeron08/2002
84262^180000+13015354186Jim Fougeron09/2002
84273^113565-7454185Lelio R Paula10/2012
842850^31891-4954182Norbert Schneider07/2014
8429(5*2^179991-1)/1142754180Lelio R Paula01/2014
84303^113548+2654177Lelio R Paula10/2012
8431(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
84324159^14969-13854173Enzo Doria07/2012
84332^179955+577554172Lelio R Paula10/2009
84342^179953-23131354172Enzo Doria05/2014
84355^77485+654160Lelio R Paula10/2012
843618^43141+8554154Lelio R Paula02/2013
843710^54149+18764754150Patrick De Geest07/2017
84403^113489-34054149Lelio R Paula10/2012
843810^54149-80000154149Robert Price06/2017
843910^54149-3650154149Patrick De Geest07/2017
84417^64070+9054146Lelio R Paula10/2012
844218^43131+7154142Lelio R Paula02/2013
84432^179826-13154134Lelio R Paula02/2011
84442^179815-11273554130Enzo Doria06/2014
84452^179806+7384954127Enzo Doria04/2016
84462^179790+3354123Donovan Johnson02/2006
844714287^6138+6138^1428754120Hans Havermann06/2016
8448(17*10^54117+1)/954118Serge Batalov05/2010
84492^179763-18954115Lelio R Paula02/2011
8450(21181*2^179770+1)/302910554115Lelio R Paula05/2014
84511828^16589+16589^182854113Serge Batalov05/2014
845320^41588-588354108Enzo Doria03/2013
845250^31847-4954108Norbert Schneider07/2014
84542^179733-685554106Lelio R Paula10/2009
845520^41584-558354103Enzo Doria03/2013
845610^54084+3*3^5408454085Mike Oakes05/2010
84572^179613-179554069Lelio R Paula10/2009
84582^179589-101152354062Paul Bourdelais11/2012
84592^179574-253154058Yves Minet07/2014
8460(41*10^54051-23)/954052Robert Price05/2015
8461117^26131-11654044Norbert Schneider10/2013
8462(10^54038-31)/354038Serge Batalov12/2014
846311^51885-8454033Lelio R Paula01/2013
846414990^4011+4011^1499054013Hans Havermann07/2016
8465(19*2^179414+1)/754010Lelio R Paula07/2012
84663^113182-1040854002Enzo Doria02/2013
846735^34970-878653997Enzo Doria03/2013
84682^179371-163758753997Enzo Doria05/2015
846919^42225-9253996Lelio R Paula01/2013
8470(3^113188+7)/7391767578453994Lelio R Paula03/2012
84717*3^113162+853993Lelio R Paula03/2014
8472(10^53991+179)/953991Serge Batalov12/2014
84732^179350-214553990Lelio R Paula10/2009
8474(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
84758^59782-6^59782-3^5978253989Mike Oakes11/2009
84763*7^63861+853970Lelio R Paula09/2014
84772^179274+7138953967Enzo Doria04/2016
84782^179259-5869553963Lelio R Paula10/2009
84796^69345+6153961Lelio R Paula10/2012
8480(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
8481(40216^11719-1)/4021553955Serge Batalov04/2015
848289*10^53951-953953Robert Price05/2017
848314^47067-353945Lelio R Paula01/2013
8484p(11700)#/2-51253937Robert Price07/2017
8485(2^179168-5)/5953934Lelio R Paula02/2012
84862^179128+841553923Lelio R Paula07/2012
84872^179120+253353921Henri Lifchitz09/2004
8488(2^179126+78557)/464932118753913Lelio R Paula05/2012
848974^28842+7353913Norbert Schneider11/2012
84901271^17368+17368^127153913Serge Batalov05/2014
84912^179079+5353909Lelio R Paula02/2011
849217^43807+5453903Lelio R Paula01/2013
849317^43807+3053903Lelio R Paula01/2013
84943^112951-31053892Lelio R Paula10/2012
8495Phi(7,2957!)53888Robert Price05/2015
8496(10223*2^178975+1)/3398553877Lelio R Paula05/2014
84972^178944-21920953868Enzo Doria11/2012
8498(10^53859+149)/353859Serge Batalov12/2014
84992^178910-19153858Lelio R Paula02/2011
850016170^2141+2141^1617053857Hans Havermann07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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