PRP Records

Probable Primes Top 10000

(252402 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 ?
95012^179790+3354123Donovan Johnson02/2006
950214287^6138+6138^1428754120Hans Havermann06/2016
9503(17*10^54117+1)/954118Serge Batalov05/2010
95042^179763-18954115Lelio R Paula02/2011
9505(21181*2^179770+1)/302910554115Lelio R Paula05/2014
95061828^16589+16589^182854113Serge Batalov05/2014
950820^41588-588354108Enzo Doria03/2013
950750^31847-4954108Norbert Schneider07/2014
95092^179733-685554106Lelio R Paula10/2009
951020^41584-558354103Enzo Doria03/2013
951110^54084+3*3^5408454085Mike Oakes05/2010
95122^179613-179554069Lelio R Paula10/2009
95132^179589-101152354062Paul Bourdelais11/2012
95142^179574-253154058Yves Minet07/2014
9515(41*10^54051-23)/954052Robert Price05/2015
9516117^26131-11654044Norbert Schneider10/2013
9517(10^54038-31)/354038Serge Batalov12/2014
951811^51885-8454033Lelio R Paula01/2013
951914990^4011+4011^1499054013Hans Havermann07/2016
9520(19*2^179414+1)/754010Lelio R Paula07/2012
95213^113182-1040854002Enzo Doria02/2013
952235^34970-878653997Enzo Doria03/2013
95232^179371-163758753997Enzo Doria05/2015
952419^42225-9253996Lelio R Paula01/2013
952510190^13471-13471^1019053995Norbert Schneider05/2018
9526(3^113188+7)/7391767578453994Lelio R Paula03/2012
95277*3^113162+853993Lelio R Paula03/2014
9528(10^53991+179)/953991Serge Batalov12/2014
95302^179350-214553990Lelio R Paula10/2009
9529(-lucasV(1,2,358718)-2)/(5*17*19)53990Mike Oakes04/2017
95318^59782-6^59782-3^5978253989Mike Oakes11/2009
95323*7^63861+853970Lelio R Paula09/2014
95332^179274+7138953967Enzo Doria04/2016
95342^179259-5869553963Lelio R Paula10/2009
95356^69345+6153961Lelio R Paula10/2012
9536(-lucasV(1,2,358635)+2)/(7*179317*232171*960251*1716271)53957Mike Oakes04/2017
9537(40216^11719-1)/4021553955Serge Batalov04/2015
953889*10^53951-953953Robert Price05/2017
95396703^14100-14100^670353951Norbert Schneider11/2018
954014^47067-353945Lelio R Paula01/2013
9541p(11700)#/2-51253937Robert Price07/2017
9542(2^179168-5)/5953934Lelio R Paula02/2012
95432^179128+841553923Lelio R Paula07/2012
95442^179120+253353921Henri Lifchitz09/2004
9546(2^179126+78557)/464932118753913Lelio R Paula05/2012
954574^28842+7353913Norbert Schneider11/2012
95471271^17368+17368^127153913Serge Batalov05/2014
95482^179079+5353909Lelio R Paula02/2011
954917^43807+5453903Lelio R Paula01/2013
955017^43807+3053903Lelio R Paula01/2013
95513^112951-31053892Lelio R Paula10/2012
9552Phi(7,2957!)53888Robert Price05/2015
95538275^13754-13754^827553885Norbert Schneider10/2018
9554(10223*2^178975+1)/3398553877Lelio R Paula05/2014
95552^178944-21920953868Enzo Doria11/2012
9556(10^53859+149)/353859Serge Batalov12/2014
95572^178910-19153858Lelio R Paula02/2011
955816170^2141+2141^1617053857Hans Havermann07/2016
9559(5*10^53855-107)/353856Robert Price01/2017
9560(72*10^53847-27)/9953847Patrick De Geest08/2004
95612^178841-86968810553837Lelio R Paula06/2012
95622*10^53834-2753835Robert Price02/2017
95642^178821-101152353831Paul Bourdelais11/2012
956312601^13128-13128^1260153831Norbert Schneider10/2017
95652^178819-1553830Lelio R Paula02/2011
9566(14450!-1)/22529658153829Donovan Johnson04/2006
9567(124351#+125386)/(2^5*71*883*4489103*9820259)53826Makoto Morimoto10/2017
956810530^13381-13381^1053053825Norbert Schneider03/2018
95692^178761-46553813Lelio R Paula10/2009
957018900^703+703^1890053808Anatoly F. Selevich02/2007
957113918^7343+7343^1391853806Hans Havermann08/2016
957210^53804+3174953805Patrick De Geest12/2012
957310^53804-7153804Robert Price05/2011
9574t(178994)53804Robert Price03/2015
9575(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
95762^178671-11321553786Enzo Doria07/2014
957715110^3621+3621^1511053774Hans Havermann07/2016
95782^178611+9553768Lelio R Paula02/2011
95792^178597+571153764Lelio R Paula10/2011
95802^178598+1291553764Lelio R Paula07/2012
9581(9179*2^178579-1)/30353760Lelio R Paula03/2015
958210671^13342-13342^1067153745Norbert Schneider02/2018
95835*7^63589+253740Lelio R Paula09/2014
95842^178516-11251553739Enzo Doria06/2014
958520^41302-2753736Lelio R Paula01/2013
95866^69054-3920953735Mike Oakes12/2010
958713086^12769+12769^1308653734Hans Havermann07/2016
95882^178455+7604353721Enzo Doria04/2016
9589(10^53718-7)/353718Makoto Kamada10/2004
9590(67607*2^178426+1)/353716Lelio R Paula05/2014
95919*10^53707+1153708Robert Kinser01/2017
959294601!8-253708Robert Price04/2017
959313214^11595+11595^1321453706Hans Havermann07/2016
9594Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
95952^178367-37953694Yves Minet03/2013
9596(2^178364-5)/1153692Lelio R Paula02/2012
95974339^14760-16853688Enzo Doria06/2012
959812^49746-1153685Lelio R Paula01/2013
959912950^13051-13051^1295053670Norbert Schneider08/2017
9601(9913*2^178266-1)/224753665Lelio R Paula03/2015
960013725^8128+8128^1372553665Hans Havermann07/2016
96022^178250-11326153659Enzo Doria07/2014
96032^178226+1171553652Lelio R Paula10/2009
960435^34742-197653645Enzo Doria03/2013
960520^41228-56353639Enzo Doria03/2013
9606359^20992+20992^35953637Norbert Schneider08/2014
9607(27*2^178183-1)/2906553636Lelio R Paula01/2014
9608(3^112414+7)/3738169653628Lelio R Paula03/2012
960917994^955+955^1799453623Anatoly F. Selevich10/2006
96102^178117-155153619Yves Minet08/2012
96112^178099-1128753614Enzo Doria06/2014
961210751^13298-13298^1075153611Norbert Schneider01/2018
9613(15*2^178080-1)/30907153604Lelio R Paula01/2014
96145^76672-1376653592Enzo Doria02/2013
96156^68868-13753590Lelio R Paula10/2012
9616(5*2^178021+1)/817353587Lelio R Paula07/2012
96175^76654-2653579Lelio R Paula10/2012
9618(3^112297-2)/762753576Lelio R Paula03/2012
96193*2^177948-753569Lelio R Paula03/2014
962010^53558+1854353559Patrick De Geest12/2012
962110^53558-2153558Robert Price03/2011
96222^177792-9553521Lelio R Paula02/2011
962313392^9919+9919^1339253521Hans Havermann07/2016
962413105^12132+12132^1310553520Hans Havermann07/2016
962513^48042+8253517Lelio R Paula01/2013
96262^177768+3912153514Yves Minet10/2010
962713835^7366+7366^1383553504Hans Havermann07/2016
962817^43477+8453497Lelio R Paula01/2013
96295*10^53492+953493Dmitry Domanov11/2010
96302^177683+9553488Lelio R Paula01/2011
963111057^13226-13226^1105753482Norbert Schneider12/2017
9632(2^177678+3)/51462753481Lelio R Paula02/2012
96332^177641-25546353476Gary Barnes08/2009
9634p(11608)#/2+1653469Robert Price12/2016
9635(14*10^53465+211)/953466Robert Price11/2017
963637302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
963712001^13104-13104^1200153455Norbert Schneider10/2017
96381829^16384+1828^1638453449Henri Lifchitz01/2007
963910^53442+1262153443Patrick De Geest06/2018
964010^53442-200753442Patrick De Geest06/2018
964135^34608-960253438Enzo Doria03/2013
9642(3^111992+8)/1486753430Lelio R Paula03/2012
96442^177480+186966153427Enzo Doria05/2016
964311791^13122-13122^1179153427Norbert Schneider10/2017
9645(8*10^53411+1)/953411Serge Batalov12/2008
96464*5^76410-353409Lelio R Paula09/2014
96472^177380-11304553397Enzo Doria07/2014
96495^76362-2*3^7636253375Mike Oakes11/2009
964872365!6-2453375Robert Price08/2018
96504159^14747-14053370Enzo Doria07/2012
9651(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
9652p(11586)#/2+3253357Robert Price12/2016
965315^45362-4653350Lelio R Paula01/2013
965414147^5892+5892^1414753338Hans Havermann07/2016
96557^63109+4653334Lelio R Paula10/2012
965620^40986-134353325Enzo Doria03/2013
96574*10^53324-8953325Robert Price08/2017
965820^40977-888353313Enzo Doria03/2013
96593^111711+266053300Lelio R Paula10/2012
96602^177040-1186553295Enzo Doria10/2012
9661(7*10^53287+17)/353288Erik Branger03/2014
966235^34506-1075853280Enzo Doria03/2013
9663(11*10^53274-17)/353275Erik Branger03/2014
9664(1017*2^176971-1)/33553275Lelio R Paula03/2015
96652^176961-283353271Yves Minet09/2014
96663^111642+11053267Lelio R Paula10/2012
966717^43290-9853267Lelio R Paula01/2013
96687^63028+3653265Lelio R Paula10/2012
9669(22*10^53264+71)/353265Robert Price05/2017
96707^63023-3653261Lelio R Paula10/2012
967119783^492+492^1978353256Anatoly F. Selevich02/2007
967213350^9739+9739^1335053247Hans Havermann10/2015
967314394^4993+4993^1439453235Hans Havermann10/2015
96742^176823-11280753230Enzo Doria06/2014
96751684^16495+16495^168453219Serge Batalov05/2014
967615277^3042+3042^1527753213Hans Havermann06/2016
9677(50322^11317-1)/5032153206Serge Batalov04/2015
96782^176742-159553205Lelio R Paula10/2009
9679(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
968072149!6-1253200Robert Price08/2018
9681(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9682(3*2^176696-1)/29953189Lelio R Paula01/2014
9683(7*10^53185-1)/353186Erik Branger03/2014
96842^176629+46553171Lelio R Paula07/2012
9685(3*2^176604-1)/35953162Lelio R Paula01/2014
968610955^13158-13158^1095553154Norbert Schneider11/2017
96875^76038-1436653149Enzo Doria02/2013
968815156^3209+3209^1515653143Hans Havermann06/2016
96892^176532-283753142Yves Minet09/2014
969052^30967-5153140Norbert Schneider08/2014
96919*5^76023-253139Lelio R Paula09/2014
9692(14283!+1)/46421617753135Michael Porter03/2016
96932^176461-16553121Lelio R Paula02/2011
9694(62*10^53111+1)/953112Serge Batalov05/2010
96952^176403-13953103Lelio R Paula02/2011
969655^30508-253095Lelio R Paula08/2013
9697(48591^11329-1)/4859053090Serge Batalov04/2015
96983^111254-8853082Lelio R Paula10/2012
969915^45129-5653076Lelio R Paula01/2013
9700(640^18913-1)/63953071Eric Chen09/2018
97012^176293-7353070Lelio R Paula01/2011
9702(67*10^53068+41)/953069Robert Price09/2015
970315271^2986+2986^1527153069Hans Havermann06/2016
97042^176255-66753059Yves Minet01/2012
970536471*2^176221+864753053Paul Vanderveen04/2016
9706(19*10^53049-1)/953050Serge Batalov03/2009
97079*2^176203-553044Lelio R Paula03/2014
97082^176205-9439553043Lelio R Paula08/2011
9709(19*2^176224-1)/21791691353042Lelio R Paula01/2014
97108600^13481-13481^860053041Norbert Schneider05/2018
971117^43103+1453037Lelio R Paula01/2013
9712(31*2^176188-1)/355553036Lelio R Paula01/2014
97132^176177+6094753035David Broadhurst05/2002
9714(22*10^53033-7)/353034Erik Branger09/2014
971513810^6909+6909^1381053023Hans Havermann06/2016
97162^176108+1609553014Lelio R Paula10/2009
97172^176107+1891553014Lelio R Paula07/2012
97183^111080-962852999Enzo Doria02/2013
97192^176047-155152996Yves Minet08/2012
97202^176042+7351952994Enzo Doria04/2016
9721lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
97222^175984-11225952977Enzo Doria06/2014
972311^50870+1052976Lelio R Paula01/2013
9724(11*10^52956+19)/352957Robert Price03/2016
97256773^13820-13820^677352942Norbert Schneider11/2018
9726gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9727(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9728(98*10^52931-89)/9952931Ray Chandler11/2010
972913774^6963+6963^1377452931Hans Havermann06/2016
97302^175812-136752925Yves Minet05/2013
97312^175801+1155*17580152922Henri Lifchitz01/2005
973211^50801-909052904Enzo Doria02/2013
97337803^13592-13592^780352904Norbert Schneider07/2018
973443^32374+1252882Robert Price11/2013
9735155^24138+15452871Norbert Schneider12/2018
97362^175628+1352870Lelio R Paula01/2011
97372^175615-174752866Yves Minet09/2012
9738(13*10^52861+107)/352862Robert Price11/2017
97399*2^175586-752858Lelio R Paula03/2014
974012174^12937+12937^1217452854Norbert Schneider04/2016
9741(15*2^175565+1)/835952848Lelio R Paula07/2012
9742(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
974314256^5077+5077^1425652828Hans Havermann06/2016
97442^175467+8287552821Lelio R Paula07/2012
9745(7*10^52819+167)/352820Robert Kinser10/2017
9747(67607*2^175426+1)/352813Lelio R Paula05/2014
974671671!6-3252813Robert Price08/2018
974813^47400-6052801Lelio R Paula01/2013
97494*10^52792+6352793Robert Price06/2016
975018^42055-292952791Enzo Doria03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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