PRP Records

Probable Primes Top 10000

(205869 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 ?
90012^180000+13015354186Jim Fougeron09/2002
90023^113565-7454185Lelio R Paula10/2012
900350^31891-4954182Norbert Schneider07/2014
9004(5*2^179991-1)/1142754180Lelio R Paula01/2014
90053^113548+2654177Lelio R Paula10/2012
9006(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
9007181^23996-254176Lelio R Paula10/2017
90084159^14969-13854173Enzo Doria07/2012
90102^179955+577554172Lelio R Paula10/2009
90092^179953-23131354172Enzo Doria05/2014
90115^77485+654160Lelio R Paula10/2012
901218^43141+8554154Lelio R Paula02/2013
901310^54149+18764754150Patrick De Geest07/2017
90163^113489-34054149Lelio R Paula10/2012
901410^54149-80000154149Robert Price06/2017
901510^54149-3650154149Patrick De Geest07/2017
90177^64070+9054146Lelio R Paula10/2012
901812549^13210-13210^1254954143Norbert Schneider12/2017
901918^43131+7154142Lelio R Paula02/2013
90202^179826-13154134Lelio R Paula02/2011
90212^179815-11273554130Enzo Doria06/2014
90222^179806+7384954127Enzo Doria04/2016
90232^179790+3354123Donovan Johnson02/2006
902414287^6138+6138^1428754120Hans Havermann06/2016
9025(17*10^54117+1)/954118Serge Batalov05/2010
90262^179763-18954115Lelio R Paula02/2011
9027(21181*2^179770+1)/302910554115Lelio R Paula05/2014
90281828^16589+16589^182854113Serge Batalov05/2014
903020^41588-588354108Enzo Doria03/2013
902950^31847-4954108Norbert Schneider07/2014
90312^179733-685554106Lelio R Paula10/2009
903220^41584-558354103Enzo Doria03/2013
903310^54084+3*3^5408454085Mike Oakes05/2010
90342^179613-179554069Lelio R Paula10/2009
90352^179589-101152354062Paul Bourdelais11/2012
90362^179574-253154058Yves Minet07/2014
9037(41*10^54051-23)/954052Robert Price05/2015
9038117^26131-11654044Norbert Schneider10/2013
9039(10^54038-31)/354038Serge Batalov12/2014
904011^51885-8454033Lelio R Paula01/2013
904114990^4011+4011^1499054013Hans Havermann07/2016
9042(19*2^179414+1)/754010Lelio R Paula07/2012
90433^113182-1040854002Enzo Doria02/2013
904435^34970-878653997Enzo Doria03/2013
90452^179371-163758753997Enzo Doria05/2015
904619^42225-9253996Lelio R Paula01/2013
9047(3^113188+7)/7391767578453994Lelio R Paula03/2012
90487*3^113162+853993Lelio R Paula03/2014
9049(10^53991+179)/953991Serge Batalov12/2014
90502^179350-214553990Lelio R Paula10/2009
9051(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
90528^59782-6^59782-3^5978253989Mike Oakes11/2009
90533*7^63861+853970Lelio R Paula09/2014
90542^179274+7138953967Enzo Doria04/2016
90552^179259-5869553963Lelio R Paula10/2009
90566^69345+6153961Lelio R Paula10/2012
9057(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
9058(40216^11719-1)/4021553955Serge Batalov04/2015
905989*10^53951-953953Robert Price05/2017
906014^47067-353945Lelio R Paula01/2013
9061p(11700)#/2-51253937Robert Price07/2017
9062(2^179168-5)/5953934Lelio R Paula02/2012
90632^179128+841553923Lelio R Paula07/2012
90642^179120+253353921Henri Lifchitz09/2004
9066(2^179126+78557)/464932118753913Lelio R Paula05/2012
906574^28842+7353913Norbert Schneider11/2012
90671271^17368+17368^127153913Serge Batalov05/2014
90682^179079+5353909Lelio R Paula02/2011
906917^43807+5453903Lelio R Paula01/2013
907017^43807+3053903Lelio R Paula01/2013
90713^112951-31053892Lelio R Paula10/2012
9072Phi(7,2957!)53888Robert Price05/2015
9073(10223*2^178975+1)/3398553877Lelio R Paula05/2014
90742^178944-21920953868Enzo Doria11/2012
9075(10^53859+149)/353859Serge Batalov12/2014
90762^178910-19153858Lelio R Paula02/2011
907716170^2141+2141^1617053857Hans Havermann07/2016
9078(5*10^53855-107)/353856Robert Price01/2017
9079(72*10^53847-27)/9953847Patrick De Geest08/2004
90802^178841-86968810553837Lelio R Paula06/2012
90812*10^53834-2753835Robert Price02/2017
90832^178821-101152353831Paul Bourdelais11/2012
908212601^13128-13128^1260153831Norbert Schneider10/2017
90842^178819-1553830Lelio R Paula02/2011
9085(14450!-1)/22529658153829Donovan Johnson04/2006
9086(124351#+125386)/(2^5*71*883*4489103*9820259)53826Makoto Morimoto10/2017
908710530^13381-13381^1053053825Norbert Schneider03/2018
90882^178761-46553813Lelio R Paula10/2009
908918900^703+703^1890053808Anatoly F. Selevich02/2007
909013918^7343+7343^1391853806Hans Havermann08/2016
909110^53804+3174953805Patrick De Geest12/2012
909210^53804-7153804Robert Price05/2011
9093t(178994)53804Robert Price03/2015
9094(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
90952^178671-11321553786Enzo Doria07/2014
909615110^3621+3621^1511053774Hans Havermann07/2016
90972^178611+9553768Lelio R Paula02/2011
90982^178597+571153764Lelio R Paula10/2011
90992^178598+1291553764Lelio R Paula07/2012
9100(9179*2^178579-1)/30353760Lelio R Paula03/2015
910110671^13342-13342^1067153745Norbert Schneider02/2018
91025*7^63589+253740Lelio R Paula09/2014
91032^178516-11251553739Enzo Doria06/2014
910420^41302-2753736Lelio R Paula01/2013
91056^69054-3920953735Mike Oakes12/2010
910613086^12769+12769^1308653734Hans Havermann07/2016
91072^178455+7604353721Enzo Doria04/2016
9108(10^53718-7)/353718Makoto Kamada10/2004
9109(67607*2^178426+1)/353716Lelio R Paula05/2014
91109*10^53707+1153708Robert Kinser01/2017
911194601!8-253708Robert Price04/2017
911213214^11595+11595^1321453706Hans Havermann07/2016
9113Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
91142^178367-37953694Yves Minet03/2013
9115(2^178364-5)/1153692Lelio R Paula02/2012
91164339^14760-16853688Enzo Doria06/2012
911712^49746-1153685Lelio R Paula01/2013
911812950^13051-13051^1295053670Norbert Schneider08/2017
9119(9913*2^178266-1)/224753665Lelio R Paula03/2015
912013725^8128+8128^1372553665Hans Havermann07/2016
91212^178250-11326153659Enzo Doria07/2014
91222^178226+1171553652Lelio R Paula10/2009
912335^34742-197653645Enzo Doria03/2013
912420^41228-56353639Enzo Doria03/2013
9125359^20992+20992^35953637Norbert Schneider08/2014
9126(27*2^178183-1)/2906553636Lelio R Paula01/2014
9127(3^112414+7)/3738169653628Lelio R Paula03/2012
912817994^955+955^1799453623Anatoly F. Selevich10/2006
91292^178117-155153619Yves Minet08/2012
91302^178099-1128753614Enzo Doria06/2014
913110751^13298-13298^1075153611Norbert Schneider01/2018
9132(15*2^178080-1)/30907153604Lelio R Paula01/2014
91335^76672-1376653592Enzo Doria02/2013
91346^68868-13753590Lelio R Paula10/2012
9135(5*2^178021+1)/817353587Lelio R Paula07/2012
91365^76654-2653579Lelio R Paula10/2012
9137(3^112297-2)/762753576Lelio R Paula03/2012
91383*2^177948-753569Lelio R Paula03/2014
913910^53558+1854353559Patrick De Geest12/2012
914010^53558-2153558Robert Price03/2011
91412^177792-9553521Lelio R Paula02/2011
914213392^9919+9919^1339253521Hans Havermann07/2016
914313105^12132+12132^1310553520Hans Havermann07/2016
914413^48042+8253517Lelio R Paula01/2013
91452^177768+3912153514Yves Minet10/2010
914613835^7366+7366^1383553504Hans Havermann07/2016
914717^43477+8453497Lelio R Paula01/2013
91485*10^53492+953493Dmitry Domanov11/2010
91492^177683+9553488Lelio R Paula01/2011
915011057^13226-13226^1105753482Norbert Schneider12/2017
9151(2^177678+3)/51462753481Lelio R Paula02/2012
91522^177641-25546353476Gary Barnes08/2009
9153p(11608)#/2+1653469Robert Price12/2016
9154(14*10^53465+211)/953466Robert Price11/2017
915537302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
915612001^13104-13104^1200153455Norbert Schneider10/2017
91571829^16384+1828^1638453449Henri Lifchitz01/2007
915835^34608-960253438Enzo Doria03/2013
9159(3^111992+8)/1486753430Lelio R Paula03/2012
91612^177480+186966153427Enzo Doria05/2016
916011791^13122-13122^1179153427Norbert Schneider10/2017
9162(8*10^53411+1)/953411Serge Batalov12/2008
91634*5^76410-353409Lelio R Paula09/2014
91642^177380-11304553397Enzo Doria07/2014
91655^76362-2*3^7636253375Mike Oakes11/2009
91664159^14747-14053370Enzo Doria07/2012
9167(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
9168p(11586)#/2+3253357Robert Price12/2016
916915^45362-4653350Lelio R Paula01/2013
917014147^5892+5892^1414753338Hans Havermann07/2016
91717^63109+4653334Lelio R Paula10/2012
917220^40986-134353325Enzo Doria03/2013
91734*10^53324-8953325Robert Price08/2017
917420^40977-888353313Enzo Doria03/2013
91753^111711+266053300Lelio R Paula10/2012
91762^177040-1186553295Enzo Doria10/2012
9177(7*10^53287+17)/353288Erik Branger03/2014
917835^34506-1075853280Enzo Doria03/2013
9179(11*10^53274-17)/353275Erik Branger03/2014
9180(1017*2^176971-1)/33553275Lelio R Paula03/2015
91812^176961-283353271Yves Minet09/2014
91823^111642+11053267Lelio R Paula10/2012
918317^43290-9853267Lelio R Paula01/2013
91847^63028+3653265Lelio R Paula10/2012
9185(22*10^53264+71)/353265Robert Price05/2017
91867^63023-3653261Lelio R Paula10/2012
918719783^492+492^1978353256Anatoly F. Selevich02/2007
918813350^9739+9739^1335053247Hans Havermann10/2015
918914394^4993+4993^1439453235Hans Havermann10/2015
91902^176823-11280753230Enzo Doria06/2014
91911684^16495+16495^168453219Serge Batalov05/2014
919215277^3042+3042^1527753213Hans Havermann06/2016
9193(50322^11317-1)/5032153206Serge Batalov04/2015
91942^176742-159553205Lelio R Paula10/2009
9195(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
9196(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9197(3*2^176696-1)/29953189Lelio R Paula01/2014
9198(7*10^53185-1)/353186Erik Branger03/2014
91992^176629+46553171Lelio R Paula07/2012
9200(3*2^176604-1)/35953162Lelio R Paula01/2014
920110955^13158-13158^1095553154Norbert Schneider11/2017
92025^76038-1436653149Enzo Doria02/2013
920315156^3209+3209^1515653143Hans Havermann06/2016
92042^176532-283753142Yves Minet09/2014
920552^30967-5153140Norbert Schneider08/2014
92069*5^76023-253139Lelio R Paula09/2014
9207(14283!+1)/46421617753135Michael Porter03/2016
92082^176461-16553121Lelio R Paula02/2011
9209(62*10^53111+1)/953112Serge Batalov05/2010
92102^176403-13953103Lelio R Paula02/2011
921155^30508-253095Lelio R Paula08/2013
9212(48591^11329-1)/4859053090Serge Batalov04/2015
92133^111254-8853082Lelio R Paula10/2012
921415^45129-5653076Lelio R Paula01/2013
92152^176293-7353070Lelio R Paula01/2011
9216(67*10^53068+41)/953069Robert Price09/2015
921715271^2986+2986^1527153069Hans Havermann06/2016
92182^176255-66753059Yves Minet01/2012
921936471*2^176221+864753053Paul Vanderveen04/2016
9220(19*10^53049-1)/953050Serge Batalov03/2009
92219*2^176203-553044Lelio R Paula03/2014
92222^176205-9439553043Lelio R Paula08/2011
9223(19*2^176224-1)/21791691353042Lelio R Paula01/2014
922417^43103+1453037Lelio R Paula01/2013
9225(31*2^176188-1)/355553036Lelio R Paula01/2014
92262^176177+6094753035David Broadhurst05/2002
9227(22*10^53033-7)/353034Erik Branger09/2014
922813810^6909+6909^1381053023Hans Havermann06/2016
92292^176108+1609553014Lelio R Paula10/2009
92302^176107+1891553014Lelio R Paula07/2012
92313^111080-962852999Enzo Doria02/2013
92322^176047-155152996Yves Minet08/2012
92332^176042+7351952994Enzo Doria04/2016
9234lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
92352^175984-11225952977Enzo Doria06/2014
923611^50870+1052976Lelio R Paula01/2013
9237(11*10^52956+19)/352957Robert Price03/2016
9238gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9239(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9241(98*10^52931-89)/9952931Ray Chandler11/2010
924013774^6963+6963^1377452931Hans Havermann06/2016
92422^175812-136752925Yves Minet05/2013
92432^175801+1155*17580152922Henri Lifchitz01/2005
924411^50801-909052904Enzo Doria02/2013
924543^32374+1252882Robert Price11/2013
92462^175628+1352870Lelio R Paula01/2011
92472^175615-174752866Yves Minet09/2012
9248(13*10^52861+107)/352862Robert Price11/2017
92499*2^175586-752858Lelio R Paula03/2014
925012174^12937+12937^1217452854Norbert Schneider04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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