PRP Records

Probable Primes Top 10000

(174961 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
82512^181874+181874^2-154750Robert Price04/2014
8252(2^181865+9)/733954743Lelio R Paula02/2012
82535^78314-9254740Lelio R Paula10/2012
8254(163*10^54727-1)/954729Serge Batalov12/2014
825515^46531+7454725Lelio R Paula02/2013
8256277^22400-34854712Enzo Doria07/2012
82576^70302+10154706Lelio R Paula10/2012
82583^114622-1040854689Enzo Doria02/2013
8260(23*2^181674+1)/48954688Lelio R Paula01/2012
82592^181669-155154688Yves Minet08/2012
8261(57352^11491-1)/5735154676Serge Batalov04/2015
8262(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8263(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
826413^49073+4654665Lelio R Paula01/2013
8265(57042^11491-1)/5704154649Serge Batalov04/2015
826720^42000+7354644Lelio R Paula02/2013
8266(67607*2^181517+1)/165554644Lelio R Paula05/2014
826833*10^54634+754636Robert Price07/2016
826920^41988+6154628Lelio R Paula01/2013
827020^41988-812354628Enzo Doria03/2013
82712^181420+2118154613Yves Minet03/2011
8272(19*10^54608+161)/954609Robert Price07/2016
827319^42696-2454598Lelio R Paula02/2013
8274(74*10^54583+61)/954584Robert Price10/2015
82752^181316-9439554582Lelio R Paula09/2011
827614751^5006+5006^1475154572Hans Havermann08/2016
827714^47609+3954567Lelio R Paula02/2013
82783^114327-7454548Lelio R Paula10/2012
8279gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
8280(17*10^54537-47)/354538Robert Price05/2017
82812^181155-1155*18115554534Henri Lifchitz02/2005
8282Phi(61672,83)54533Enzo Doria05/2012
82839*2^181128+754526Lelio R Paula03/2014
828489*10^54518-754520Robert Price03/2017
82852^181090-11324754514Enzo Doria07/2014
828614031^7670+7670^1403154508Hans Havermann08/2016
828714210^6849+6849^1421054505Hans Havermann08/2016
82882^181043-19954500Lelio R Paula02/2011
828912^50499+554498Lelio R Paula01/2013
829012^50491+554489Lelio R Paula01/2013
82916^70016-14554484Lelio R Paula10/2012
829211^52313-960054479Enzo Doria02/2013
82932^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
82942^180946-11104154471Enzo Doria05/2014
8295(64*10^54467+287)/954468Robert Price04/2016
82965^77907-2*3^7790754455Mike Oakes11/2009
829720^41853-562354453Enzo Doria03/2013
829814^47506-7554448Lelio R Paula02/2013
82992^180839-11343754438Enzo Doria08/2014
83003^114085+2854433Lelio R Paula10/2012
8301Phi(141230,10)54432Ray Chandler08/2009
83026^69946-5554429Lelio R Paula10/2012
83035*2^180796+354426Lelio R Paula03/2014
8304(23*2^180782-1)/9154421Lelio R Paula01/2014
83059*6^69928-754416Lelio R Paula09/2014
830692^27701-91^2770154399Robert Price08/2015
8307(2^180687-3)*6-754393Gilbert Mozzo04/2016
8308(5*10^54388-11)/354389Erik Branger12/2013
830920^41799-304354382Enzo Doria03/2013
831013860^8387+8387^1386054382Hans Havermann08/2016
8311(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
83127^64329-1854365Lelio R Paula10/2012
83132^180551-96754352Yves Minet01/2012
831415^46209-7454347Lelio R Paula02/2013
831510^54345+2973954346Patrick De Geest08/2013
831610^54345-14138154345Patrick De Geest09/2013
8317lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
83182^180496+1554335Lelio R Paula02/2011
83191845^16636+16636^184554334Serge Batalov05/2014
832011^52169-7054329Lelio R Paula01/2013
832113693^9262+9262^1369354317Hans Havermann06/2016
83222^180429-11310154315Enzo Doria07/2014
83232^180423-11205154313Enzo Doria05/2014
832416112^2349+2349^1611254312Hans Havermann06/2016
8325(13^48751+4^48751)/1754305Robert Price05/2013
83262^180370+1291554297Lelio R Paula09/2012
8327(10^54290+41)/354290Robert Price01/2017
832815108^3917+3917^1510854283Hans Havermann06/2016
83292^180317-301954281Yves Minet10/2014
83302^180314+85554280Lelio R Paula10/2009
833119^42425+9454252Lelio R Paula02/2013
83322^180180-100544954240Paul Bourdelais11/2012
83342^180173-277354238Yves Minet07/2014
833313367^11418+11418^1336754238Hans Havermann06/2016
8335427^20614+20614^42754224Norbert Schneider06/2016
83362^180124-8795954223Gary Barnes08/2009
83372^180111-11310154219Enzo Doria07/2014
83382^180101-11487154216Enzo Doria05/2015
8339(11*2^180099+1)/5161754212Lelio R Paula07/2012
83412^180070+46554207Lelio R Paula09/2012
834013683^9154+9154^1368354207Hans Havermann06/2016
8342810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
83432^180014+61354190Jason Earls04/2008
83442^180007+10154188Lelio R Paula02/2011
83452^180001+4187754186Jim Fougeron08/2002
83462^180000+13015354186Jim Fougeron09/2002
83473^113565-7454185Lelio R Paula10/2012
834850^31891-4954182Norbert Schneider07/2014
8349(5*2^179991-1)/1142754180Lelio R Paula01/2014
83513^113548+2654177Lelio R Paula10/2012
8350(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
83524159^14969-13854173Enzo Doria07/2012
83542^179955+577554172Lelio R Paula10/2009
83532^179953-23131354172Enzo Doria05/2014
83555^77485+654160Lelio R Paula10/2012
835618^43141+8554154Lelio R Paula02/2013
83573^113489-34054149Lelio R Paula10/2012
835810^54149-80000154149Robert Price06/2017
83597^64070+9054146Lelio R Paula10/2012
836018^43131+7154142Lelio R Paula02/2013
83612^179826-13154134Lelio R Paula02/2011
83622^179815-11273554130Enzo Doria06/2014
83632^179806+7384954127Enzo Doria04/2016
83642^179790+3354123Donovan Johnson02/2006
836514287^6138+6138^1428754120Hans Havermann06/2016
8366(17*10^54117+1)/954118Serge Batalov05/2010
83672^179763-18954115Lelio R Paula02/2011
8368(21181*2^179770+1)/302910554115Lelio R Paula05/2014
83691828^16589+16589^182854113Serge Batalov05/2014
837120^41588-588354108Enzo Doria03/2013
837050^31847-4954108Norbert Schneider07/2014
83722^179733-685554106Lelio R Paula10/2009
837320^41584-558354103Enzo Doria03/2013
837410^54084+3*3^5408454085Mike Oakes05/2010
83752^179613-179554069Lelio R Paula10/2009
83762^179589-101152354062Paul Bourdelais11/2012
83772^179574-253154058Yves Minet07/2014
8378(41*10^54051-23)/954052Robert Price05/2015
8379117^26131-11654044Norbert Schneider10/2013
8380(10^54038-31)/354038Serge Batalov12/2014
838111^51885-8454033Lelio R Paula01/2013
838214990^4011+4011^1499054013Hans Havermann07/2016
8383(19*2^179414+1)/754010Lelio R Paula07/2012
83843^113182-1040854002Enzo Doria02/2013
838535^34970-878653997Enzo Doria03/2013
83862^179371-163758753997Enzo Doria05/2015
838719^42225-9253996Lelio R Paula01/2013
8388(3^113188+7)/7391767578453994Lelio R Paula03/2012
83897*3^113162+853993Lelio R Paula03/2014
8390(10^53991+179)/953991Serge Batalov12/2014
83912^179350-214553990Lelio R Paula10/2009
8392(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
83938^59782-6^59782-3^5978253989Mike Oakes11/2009
83943*7^63861+853970Lelio R Paula09/2014
83952^179274+7138953967Enzo Doria04/2016
83962^179259-5869553963Lelio R Paula10/2009
83976^69345+6153961Lelio R Paula10/2012
8398(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
8399(40216^11719-1)/4021553955Serge Batalov04/2015
840089*10^53951-953953Robert Price05/2017
840114^47067-353945Lelio R Paula01/2013
8402(2^179168-5)/5953934Lelio R Paula02/2012
84032^179128+841553923Lelio R Paula07/2012
84042^179120+253353921Henri Lifchitz09/2004
8405(2^179126+78557)/464932118753913Lelio R Paula05/2012
840774^28842+7353913Norbert Schneider11/2012
84061271^17368+17368^127153913Serge Batalov05/2014
84082^179079+5353909Lelio R Paula02/2011
840917^43807+5453903Lelio R Paula01/2013
841017^43807+3053903Lelio R Paula01/2013
84113^112951-31053892Lelio R Paula10/2012
8412Phi(7,2957!)53888Robert Price05/2015
8413(10223*2^178975+1)/3398553877Lelio R Paula05/2014
84142^178944-21920953868Enzo Doria11/2012
8415(10^53859+149)/353859Serge Batalov12/2014
84162^178910-19153858Lelio R Paula02/2011
841716170^2141+2141^1617053857Hans Havermann07/2016
8418(5*10^53855-107)/353856Robert Price01/2017
8419(72*10^53847-27)/9953847Patrick De Geest08/2004
84202^178841-86968810553837Lelio R Paula06/2012
84212*10^53834-2753835Robert Price02/2017
84222^178821-101152353831Paul Bourdelais11/2012
84232^178819-1553830Lelio R Paula02/2011
8424(14450!-1)/22529658153829Donovan Johnson04/2006
84252^178761-46553813Lelio R Paula10/2009
842618900^703+703^1890053808Anatoly F. Selevich02/2007
842713918^7343+7343^1391853806Hans Havermann08/2016
842810^53804+3174953805Patrick De Geest12/2012
843010^53804-7153804Robert Price05/2011
8429t(178994)53804Robert Price03/2015
8431(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
84322^178671-11321553786Enzo Doria07/2014
843315110^3621+3621^1511053774Hans Havermann07/2016
84342^178611+9553768Lelio R Paula02/2011
84352^178597+571153764Lelio R Paula10/2011
84362^178598+1291553764Lelio R Paula07/2012
8437(9179*2^178579-1)/30353760Lelio R Paula03/2015
84385*7^63589+253740Lelio R Paula09/2014
84392^178516-11251553739Enzo Doria06/2014
844020^41302-2753736Lelio R Paula01/2013
84416^69054-3920953735Mike Oakes12/2010
844213086^12769+12769^1308653734Hans Havermann07/2016
84432^178455+7604353721Enzo Doria04/2016
8444(10^53718-7)/353718Makoto Kamada10/2004
8445(67607*2^178426+1)/353716Lelio R Paula05/2014
84469*10^53707+1153708Robert Kinser01/2017
844794601!8-253708Robert Price04/2017
844813214^11595+11595^1321453706Hans Havermann07/2016
8449Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
84502^178367-37953694Yves Minet03/2013
8451(2^178364-5)/1153692Lelio R Paula02/2012
84524339^14760-16853688Enzo Doria06/2012
845312^49746-1153685Lelio R Paula01/2013
8454(9913*2^178266-1)/224753665Lelio R Paula03/2015
845513725^8128+8128^1372553665Hans Havermann07/2016
84562^178250-11326153659Enzo Doria07/2014
84572^178226+1171553652Lelio R Paula10/2009
845835^34742-197653645Enzo Doria03/2013
845920^41228-56353639Enzo Doria03/2013
8460359^20992+20992^35953637Norbert Schneider08/2014
8461(27*2^178183-1)/2906553636Lelio R Paula01/2014
8462(3^112414+7)/3738169653628Lelio R Paula03/2012
846317994^955+955^1799453623Anatoly F. Selevich10/2006
84642^178117-155153619Yves Minet08/2012
84652^178099-1128753614Enzo Doria06/2014
8466(15*2^178080-1)/30907153604Lelio R Paula01/2014
84675^76672-1376653592Enzo Doria02/2013
84686^68868-13753590Lelio R Paula10/2012
8469(5*2^178021+1)/817353587Lelio R Paula07/2012
84705^76654-2653579Lelio R Paula10/2012
8471(3^112297-2)/762753576Lelio R Paula03/2012
84723*2^177948-753569Lelio R Paula03/2014
847310^53558+1854353559Patrick De Geest12/2012
847410^53558-2153558Robert Price03/2011
84752^177792-9553521Lelio R Paula02/2011
847613392^9919+9919^1339253521Hans Havermann07/2016
847713105^12132+12132^1310553520Hans Havermann07/2016
847813^48042+8253517Lelio R Paula01/2013
84792^177768+3912153514Yves Minet10/2010
848013835^7366+7366^1383553504Hans Havermann07/2016
848117^43477+8453497Lelio R Paula01/2013
84825*10^53492+953493Dmitry Domanov11/2010
84832^177683+9553488Lelio R Paula01/2011
8484(2^177678+3)/51462753481Lelio R Paula02/2012
84852^177641-25546353476Gary Barnes08/2009
8486p(11608)#/2+1653469Robert Price12/2016
848737302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
84881829^16384+1828^1638453449Henri Lifchitz01/2007
848935^34608-960253438Enzo Doria03/2013
8490(3^111992+8)/1486753430Lelio R Paula03/2012
84912^177480+186966153427Enzo Doria05/2016
8492(8*10^53411+1)/953411Serge Batalov12/2008
84934*5^76410-353409Lelio R Paula09/2014
84942^177380-11304553397Enzo Doria07/2014
84955^76362-2*3^7636253375Mike Oakes11/2009
84964159^14747-14053370Enzo Doria07/2012
8497(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
8498p(11586)#/2+3253357Robert Price12/2016
849915^45362-4653350Lelio R Paula01/2013
850014147^5892+5892^1414753338Hans Havermann07/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!