PRP Records

Probable Primes Top 10000

(252538 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 ?
67512^238199-11181771706Enzo Doria05/2014
6752lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
67532^238144+9876533171689Jason Earls01/2009
675418^57102-426571679Enzo Doria03/2013
6755(73*10^71670-1)/971671Robert Price01/2015
67562^238081+1155*23808171670Henri Lifchitz02/2005
67572^238067-11192571666Enzo Doria05/2014
675836^46030+3571637Norbert Schneider04/2014
6759(74*10^71621+313)/971622Robert Price11/2017
67602^237905-9171617Lelio R Paula02/2012
6761(31*2^237902-1)/12371616Lelio R Paula01/2014
6762(15185*2^237866-1)/4396771605Lelio R Paula04/2015
6763(24737*2^237841+1)/2571601Lelio R Paula06/2014
67642^237846+129971599Lelio R Paula05/2012
67656^92004+19980171594Mike Oakes02/2011
6766159^32516+271581Lelio R Paula05/2013
67672^237781+85571580Lelio R Paula05/2012
67682^237720-407971561Yves Minet06/2011
67692^237698-11094571555Enzo Doria05/2014
67702^237695-11323971554Enzo Doria07/2014
67718*5^102362-971549Lelio R Paula10/2014
6772(4*10^71546-31)/971546Erik Branger05/2011
67732^237650+3771540Lelio R Paula02/2012
677418^56977-439171522Enzo Doria03/2013
6775(22699*2^237565+1)/413663771512Lelio R Paula06/2014
6776((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
6777(26*10^71503+7)/371504Erik Branger11/2013
6778(4*10^71498+173)/371499Robert Price01/2017
67793^149848+11071496Lelio R Paula11/2014
67802^237498+51371495Lelio R Paula05/2012
67812^237485+10771491Lelio R Paula02/2012
6782(2^237465+9)/241971481Lelio R Paula05/2012
67832^237439-11223771477Enzo Doria06/2014
67842^237407-978771467Lelio R Paula11/2009
67852^237383+7295371460Enzo Doria04/2016
678682^37337-81^3733771457Robert Price01/2015
6787(1017*2^237313-1)/1971441Lelio R Paula04/2015
67882^237311+19171438Lelio R Paula02/2012
67892^237280-5971429Lelio R Paula02/2012
679011^68564-9871403Lelio R Paula01/2015
67912^237173+7480171397Enzo Doria04/2016
679215^60697+5671386Lelio R Paula01/2015
67932^237118+17771380Lelio R Paula02/2012
67942^237110+6971378Lelio R Paula02/2012
679515^60690-5871377Lelio R Paula01/2015
6796(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6797(3^149567+2)/53971359Lelio R Paula06/2012
6798(5*10^71357-143)/371358Robert Price04/2016
67992^237039-11462171356Enzo Doria05/2015
680012^66116-3771352Lelio R Paula02/2015
6801(3^149497+2^149497)/571328Jean-Louis Charton10/2010
68022^236941-6694571327Lelio R Paula05/2012
68032^236911-114771318Yves Minet10/2009
680465^39337+4271315Lelio R Paula01/2016
68056*10^71299+771300Dmitry Domanov11/2010
6806(25*2^236843+1)/375371295Lelio R Paula06/2012
680710^71291+1518771292Patrick De Geest03/2016
680910^71291-558730911971291Robert Price03/2015
680810^71291-27358171291Patrick De Geest03/2016
6810-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
681115105^17054+17054^1510571271Norbert Schneider08/2018
6812(2^236738+9)/1371265Lelio R Paula05/2012
68135^101949+4271260Lelio R Paula07/2014
68145*10^71237+971238Dmitry Domanov11/2010
68152^236634-1602571234Enzo Doria04/2013
681671^38478+7071233Norbert Schneider12/2014
68179*7^84280+871226Lelio R Paula10/2014
6818(10^71223+59)/371223Serge Batalov12/2014
6819(15185*2^236569-1)/45371216Lelio R Paula04/2015
682051829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
68212^236528-17371203Lelio R Paula02/2012
68223*2^236511-571198Lelio R Paula04/2014
68232^236477-9971187Lelio R Paula02/2012
682411^68356-213071186Enzo Doria12/2012
682515128^17031+17031^1512871186Norbert Schneider08/2018
682611^68355-312071185Enzo Doria12/2012
682736^45737-35^4573771181Robert Price10/2012
6828(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
68292^236432+2571174Lelio R Paula02/2012
68305^101818-1280671168Enzo Doria02/2013
6831(7*10^71166-457)/971166Robert Price09/2017
683265^39253+6271163Lelio R Paula01/2016
683339^44718+3871150Norbert Schneider05/2014
68342^236296-40771133Yves Minet02/2012
68352^236286-11771130Lelio R Paula02/2012
68362^236257-11119371121Enzo Doria05/2014
68377^84149-3671115Lelio R Paula08/2014
6838164176#-p(164176)71108Henri Lifchitz12/2018
68392^236209-11212371106Enzo Doria06/2014
684018^56644-498571104Enzo Doria03/2013
6841(46*10^71077+521)/971078Robert Price08/2017
684221^53753+271074Ray Chandler08/2011
6843(86*10^71068-311)/971069Robert Price10/2017
68442^236081-11092371068Enzo Doria05/2014
6845(293*27^49642-1736)/1371058Curtis Bright05/2015
684665^39192+2271052Lelio R Paula01/2016
6847(439#+1)^397-439#^39771038Mike Oakes11/2010
68487^84050-271031Lelio R Paula09/2013
684920^54558-2370982Lelio R Paula01/2015
68502^235793-11255570981Enzo Doria06/2014
685149936!3-3^4993670981Robert Price08/2015
68522^235787-7879570979Lelio R Paula05/2012
6853Perrin(581132)70970Eric W. Weisstein02/2011
685414^61913-9770961Lelio R Paula01/2015
68562^235720+1632170959Yves Minet03/2010
68552^235718+1609570959Lelio R Paula05/2012
6857163841#+34993370957Nicolas PALAU11/2016
68582^235710+770956Lelio R Paula02/2012
6859(175^31627+1)/17670939Eric Chen10/2017
68602^235635-11208770934Enzo Doria06/2014
6861153^32467+15270931Norbert Schneider11/2018
68632^235575-196570916Lelio R Paula05/2012
68626^91133+10170916Lelio R Paula01/2015
6864(21181*2^235505+1)/370898Lelio R Paula06/2014
6865(14*10^70896+211)/970897Robert Price11/2017
68665^101425+8470894Lelio R Paula07/2014
6867177^31536+270893Lelio R Paula05/2013
686843*71^38292+470891Serge Batalov03/2016
6869(29*2^235506-1)/11202978570888Lelio R Paula01/2014
687011^68045-153070862Enzo Doria12/2012
68715*10^70858+2170859Robert Price01/2017
68732^235326+370841Donovan Johnson02/2006
687234523!2+470841Robert Price02/2015
6874(31*2^235307+1)/370836Lelio R Paula06/2012
68752^235308+13570835Lelio R Paula02/2012
6876r(35414,90)*1000+91170831Patrick De Geest07/2004
68772^235274+15970825Lelio R Paula02/2012
68783^148409+7070810Lelio R Paula11/2014
6879(19*10^70794+17)/970795Robert Price03/2015
68802^235108-23270970775Paul Bourdelais03/2013
6881(2^235099-2^117550+1)/57077211/2006
688219^55325-670748Lelio R Paula08/2014
6883257^29356+29356^25770746Norbert Schneider10/2014
688422*10^70729+370731Robert Price10/2017
68852^234956+1171570729Lelio R Paula05/2012
6886(7*10^70727-43)/970727Robert Price10/2014
68872^234890-3034170709Enzo Doria11/2012
688817^57461+1470703Lelio R Paula01/2015
6889(9179*2^234834-1)/570696Lelio R Paula04/2015
68902*10^70688+5170689Robert Price10/2017
6891123^33822-12270685Norbert Schneider01/2015
68927*10^70680-9970681Robert Price11/2017
6893(21*2^234772-1)/209570672Lelio R Paula01/2014
6894(29*2^234686-1)/2114570645Lelio R Paula01/2014
6895(15*2^234688-1)/527814170643Lelio R Paula01/2014
68972^234655-6770639Lelio R Paula02/2012
6896(79*10^70638-61)/970639Robert Price10/2015
68982^234652-17370638Lelio R Paula02/2012
68992^234618-364570628Lelio R Paula05/2012
6900(2^234610-5)/1970624Lelio R Paula05/2012
69014*5^101038+970624Lelio R Paula10/2014
69022^234603+7196370623Enzo Doria04/2016
69032^234600-11312970622Enzo Doria07/2014
69052^234586+970618Lelio R Paula02/2012
69043^148008+2670618Robert Price11/2013
6906(7*10^70616-151)/970616Robert Price09/2017
690765^38947+3270608Lelio R Paula01/2016
6908(2^234488-3)/1170587Lelio R Paula05/2012
6909(3*2^234451+1)/3570576Lelio R Paula08/2012
6910Phi(159495,10)70560Maksym Voznyy09/2015
69112^234383-403570557Lelio R Paula05/2012
69122^234315-11124170536Enzo Doria05/2014
691314^61526+9770517Lelio R Paula01/2015
6914(3*2^234170+1)/1370492Lelio R Paula08/2012
691551^41281-50^4128170491Robert Price02/2013
69162^234141-11212370484Enzo Doria06/2014
69172^234139+1228570483Lelio R Paula04/2012
69182^234133-316370482Yves Minet04/2009
69192^234115+8370476Lelio R Paula02/2012
69202^234114-159570476Lelio R Paula05/2012
692124^51061-23^5106170475Robert Price07/2012
692219471^16428-270467Faysal YAtim09/2005
69237^83381+1270466Robert Price01/2014
69242^234067-11142770462Enzo Doria05/2014
6925(266*10^70457+1)/370459Robert Price02/2016
6926(31*2^234041-1)/9770453Lelio R Paula01/2014
69272^234026+1290970449Lelio R Paula04/2012
69282^233965-1970431Lelio R Paula02/2012
6929(5*2^233932-1)/17970419Lelio R Paula01/2014
69302^233908-1710970414Enzo Doria05/2013
6931695^24772+24772^69570402Norbert Schneider09/2016
69323*5^100719-270401Lelio R Paula10/2014
69332^233829-11135570390Enzo Doria05/2014
6934(19775^16384+1)/270388Henri Lifchitz03/2007
69357*3^147519+870386Lelio R Paula04/2014
6936141^32749-270385Lelio R Paula10/2017
69375*7^83265+270368Lelio R Paula10/2014
6938(23*10^70363+97)/370364Robert Price02/2017
6939(23*2^233749-1)/3532570363Lelio R Paula01/2014
69405^100652-1391670353Enzo Doria02/2013
694145^42555-270353Lelio R Paula08/2013
69422^233661-6170339Lelio R Paula02/2012
69432^233523-11224970298Enzo Doria06/2014
69445*3^147324-870293Lelio R Paula04/2014
69452^233488-1306570287Enzo Doria11/2012
6946(3^147322+8)/4285170286Lelio R Paula06/2012
6947(22*10^70259+161)/370260Robert Price02/2017
69482^233388+46570257Lelio R Paula11/2012
694914^61299+5970257Lelio R Paula01/2015
69502^233383+9406570256Lelio R Paula04/2012
695149471!3-656170253Robert Price11/2015
69527^83121+6^(83121-1)70246Robert Price03/2016
6953(197*10^70241-11)/370243Robert Price10/2017
695423*10^70240-770242Robert Price03/2016
6955(71*10^70227-53)/970228Robert Price10/2015
6956(2^233247-9)/1770214Lelio R Paula05/2012
6957(11^67421-2^67421)/970211Robert Price01/2013
6958(23*10^70209-41)/970210Robert Price03/2015
6959(29*10^70194-11)/970195Robert Price04/2015
69603^147109+19670189Lelio R Paula05/2014
6961(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
69629^73538+8^(73538+1)70174Robert Price06/2016
69632*5^100391+770171Lelio R Paula10/2014
696499^35156-270159Lelio R Paula08/2013
6965(68*10^70148+7)/370150Robert Price03/2016
696611^67360-603070149Enzo Doria01/2013
6967(35*10^70130-377)/970131Robert Price12/2017
696849391!3+3^4939170128Robert Price09/2015
6969(229*10^70122-1)/370124Robert Price12/2016
69707^82975-9270123Lelio R Paula07/2014
697165^38670+5870106Lelio R Paula01/2016
6972105^34684+34684^10570103Serge Batalov05/2014
6973134^32955-13370099Norbert Schneider03/2015
69742^232836-22790370091Enzo Doria12/2012
69752^232837-185917370091Enzo Doria03/2016
69763*2^232820+570087Lelio R Paula04/2014
69782^232799+9019570080Lelio R Paula02/2013
69772^232799-11223770080Enzo Doria06/2014
69792^232759+26214570068Lelio R Paula04/2012
69803*2^232750+770066Lelio R Paula04/2014
698112^64918-1170059Lelio R Paula01/2015
69827^82899-1270058Lelio R Paula09/2013
6983(22*10^70051-13)/970052Robert Price03/2015
6984(2^232685-7)/251462570039Lelio R Paula04/2012
698518^55786-536370027Enzo Doria03/2013
6986(2^(77537*3+1)+243)/770023Kevin Acres11/2013
69872^232602+16970021Lelio R Paula02/2012
6988(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
69892^232580+7213370014Enzo Doria04/2016
69904*6^89958-770002Lelio R Paula09/2014
699110^70000+8048770001Milton L. Brown05/2006
699210^69999+13485770000Patrick De Geest02/2007
699610^70000-927370000Patrick De Geest08/2009
6997(79*10^69999-7)/970000Robert Price01/2015
6993((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6994(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6995(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
699810^69999-8825169999Patrick De Geest08/2009
69992^232507+108969992Lelio R Paula04/2012
7000(17*2^232445+1)/569974Lelio R Paula08/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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