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 ?
6251(4*10^71498+173)/371499Robert Price01/2017
62523^149848+11071496Lelio R Paula11/2014
62532^237498+51371495Lelio R Paula05/2012
62542^237485+10771491Lelio R Paula02/2012
6255(2^237465+9)/241971481Lelio R Paula05/2012
62562^237439-11223771477Enzo Doria06/2014
62572^237407-978771467Lelio R Paula11/2009
62582^237383+7295371460Enzo Doria04/2016
625982^37337-81^3733771457Robert Price01/2015
6260(1017*2^237313-1)/1971441Lelio R Paula04/2015
62612^237311+19171438Lelio R Paula02/2012
62622^237280-5971429Lelio R Paula02/2012
626311^68564-9871403Lelio R Paula01/2015
62642^237173+7480171397Enzo Doria04/2016
626515^60697+5671386Lelio R Paula01/2015
62662^237118+17771380Lelio R Paula02/2012
62672^237110+6971378Lelio R Paula02/2012
626815^60690-5871377Lelio R Paula01/2015
6269(5*2^237125-1)/59985119171374Lelio R Paula01/2014
6270(3^149567+2)/53971359Lelio R Paula06/2012
6271(5*10^71357-143)/371358Robert Price04/2016
62722^237039-11462171356Enzo Doria05/2015
627312^66116-3771352Lelio R Paula02/2015
6274(3^149497+2^149497)/571328Jean-Louis Charton10/2010
62752^236941-6694571327Lelio R Paula05/2012
62762^236911-114771318Yves Minet10/2009
627765^39337+4271315Lelio R Paula01/2016
62786*10^71299+771300Dmitry Domanov11/2010
6279(25*2^236843+1)/375371295Lelio R Paula06/2012
628010^71291+1518771292Patrick De Geest03/2016
628210^71291-558730911971291Robert Price03/2015
628110^71291-27358171291Patrick De Geest03/2016
6283-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
6284(2^236738+9)/1371265Lelio R Paula05/2012
62855^101949+4271260Lelio R Paula07/2014
62865*10^71237+971238Dmitry Domanov11/2010
62872^236634-1602571234Enzo Doria04/2013
628871^38478+7071233Norbert Schneider12/2014
62899*7^84280+871226Lelio R Paula10/2014
6290(10^71223+59)/371223Serge Batalov12/2014
6291(15185*2^236569-1)/45371216Lelio R Paula04/2015
629251829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
62932^236528-17371203Lelio R Paula02/2012
62943*2^236511-571198Lelio R Paula04/2014
62952^236477-9971187Lelio R Paula02/2012
629611^68356-213071186Enzo Doria12/2012
629711^68355-312071185Enzo Doria12/2012
629836^45737-35^4573771181Robert Price10/2012
6299(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
63002^236432+2571174Lelio R Paula02/2012
63015^101818-1280671168Enzo Doria02/2013
6302(7*10^71166-457)/971166Robert Price09/2017
630365^39253+6271163Lelio R Paula01/2016
630439^44718+3871150Norbert Schneider05/2014
63052^236296-40771133Yves Minet02/2012
63062^236286-11771130Lelio R Paula02/2012
63072^236257-11119371121Enzo Doria05/2014
63087^84149-3671115Lelio R Paula08/2014
63092^236209-11212371106Enzo Doria06/2014
631018^56644-498571104Enzo Doria03/2013
6311(46*10^71077+521)/971078Robert Price08/2017
631221^53753+271074Ray Chandler08/2011
6313(86*10^71068-311)/971069Robert Price10/2017
63142^236081-11092371068Enzo Doria05/2014
6315(293*27^49642-1736)/1371058Curtis Bright05/2015
631665^39192+2271052Lelio R Paula01/2016
6317(439#+1)^397-439#^39771038Mike Oakes11/2010
63187^84050-271031Lelio R Paula09/2013
631920^54558-2370982Lelio R Paula01/2015
63202^235793-11255570981Enzo Doria06/2014
632149936!3-3^4993670981Robert Price08/2015
63222^235787-7879570979Lelio R Paula05/2012
6323Perrin(581132)70970Eric W. Weisstein02/2011
632414^61913-9770961Lelio R Paula01/2015
63252^235720+1632170959Yves Minet03/2010
63262^235718+1609570959Lelio R Paula05/2012
6327163841#+34993370957Nicolas PALAU11/2016
63282^235710+770956Lelio R Paula02/2012
6329(175^31627+1)/17670939Eric Chen10/2017
63302^235635-11208770934Enzo Doria06/2014
63322^235575-196570916Lelio R Paula05/2012
63316^91133+10170916Lelio R Paula01/2015
6333(21181*2^235505+1)/370898Lelio R Paula06/2014
6334(14*10^70896+211)/970897Robert Price11/2017
63355^101425+8470894Lelio R Paula07/2014
6336177^31536+270893Lelio R Paula05/2013
633743*71^38292+470891Serge Batalov03/2016
6338(29*2^235506-1)/11202978570888Lelio R Paula01/2014
633911^68045-153070862Enzo Doria12/2012
63405*10^70858+2170859Robert Price01/2017
63422^235326+370841Donovan Johnson02/2006
634134523!2+470841Robert Price02/2015
6343(31*2^235307+1)/370836Lelio R Paula06/2012
63442^235308+13570835Lelio R Paula02/2012
6345r(35414,90)*1000+91170831Patrick De Geest07/2004
63462^235274+15970825Lelio R Paula02/2012
63473^148409+7070810Lelio R Paula11/2014
6348(19*10^70794+17)/970795Robert Price03/2015
63492^235108-23270970775Paul Bourdelais03/2013
6350(2^235099-2^117550+1)/57077211/2006
635119^55325-670748Lelio R Paula08/2014
6352257^29356+29356^25770746Norbert Schneider10/2014
635322*10^70729+370731Robert Price10/2017
63542^234956+1171570729Lelio R Paula05/2012
6355(7*10^70727-43)/970727Robert Price10/2014
63562^234890-3034170709Enzo Doria11/2012
635717^57461+1470703Lelio R Paula01/2015
6358(9179*2^234834-1)/570696Lelio R Paula04/2015
63592*10^70688+5170689Robert Price10/2017
6360123^33822-12270685Norbert Schneider01/2015
63617*10^70680-9970681Robert Price11/2017
6362(21*2^234772-1)/209570672Lelio R Paula01/2014
6363(29*2^234686-1)/2114570645Lelio R Paula01/2014
6364(15*2^234688-1)/527814170643Lelio R Paula01/2014
63662^234655-6770639Lelio R Paula02/2012
6365(79*10^70638-61)/970639Robert Price10/2015
63672^234652-17370638Lelio R Paula02/2012
63682^234618-364570628Lelio R Paula05/2012
6369(2^234610-5)/1970624Lelio R Paula05/2012
63704*5^101038+970624Lelio R Paula10/2014
63712^234603+7196370623Enzo Doria04/2016
63722^234600-11312970622Enzo Doria07/2014
63732^234586+970618Lelio R Paula02/2012
63743^148008+2670618Robert Price11/2013
6375(7*10^70616-151)/970616Robert Price09/2017
637665^38947+3270608Lelio R Paula01/2016
6377(2^234488-3)/1170587Lelio R Paula05/2012
6378(3*2^234451+1)/3570576Lelio R Paula08/2012
6379Phi(159495,10)70560Maksym Voznyy09/2015
63802^234383-403570557Lelio R Paula05/2012
63812^234315-11124170536Enzo Doria05/2014
638214^61526+9770517Lelio R Paula01/2015
6383(3*2^234170+1)/1370492Lelio R Paula08/2012
638451^41281-50^4128170491Robert Price02/2013
63852^234141-11212370484Enzo Doria06/2014
63862^234139+1228570483Lelio R Paula04/2012
63872^234133-316370482Yves Minet04/2009
63882^234115+8370476Lelio R Paula02/2012
63892^234114-159570476Lelio R Paula05/2012
639024^51061-23^5106170475Robert Price07/2012
639119471^16428-270467Faysal YAtim09/2005
63927^83381+1270466Robert Price01/2014
63932^234067-11142770462Enzo Doria05/2014
6394(266*10^70457+1)/370459Robert Price02/2016
6395(31*2^234041-1)/9770453Lelio R Paula01/2014
63962^234026+1290970449Lelio R Paula04/2012
63972^233965-1970431Lelio R Paula02/2012
6398(5*2^233932-1)/17970419Lelio R Paula01/2014
63992^233908-1710970414Enzo Doria05/2013
6400695^24772+24772^69570402Norbert Schneider09/2016
64013*5^100719-270401Lelio R Paula10/2014
64022^233829-11135570390Enzo Doria05/2014
6403(19775^16384+1)/270388Henri Lifchitz03/2007
64047*3^147519+870386Lelio R Paula04/2014
6405141^32749-270385Lelio R Paula10/2017
64065*7^83265+270368Lelio R Paula10/2014
6407(23*10^70363+97)/370364Robert Price02/2017
6408(23*2^233749-1)/3532570363Lelio R Paula01/2014
64095^100652-1391670353Enzo Doria02/2013
641045^42555-270353Lelio R Paula08/2013
64112^233661-6170339Lelio R Paula02/2012
64122^233523-11224970298Enzo Doria06/2014
64135*3^147324-870293Lelio R Paula04/2014
64142^233488-1306570287Enzo Doria11/2012
6415(3^147322+8)/4285170286Lelio R Paula06/2012
6416(22*10^70259+161)/370260Robert Price02/2017
64172^233388+46570257Lelio R Paula11/2012
641814^61299+5970257Lelio R Paula01/2015
64192^233383+9406570256Lelio R Paula04/2012
642049471!3-656170253Robert Price11/2015
64217^83121+6^(83121-1)70246Robert Price03/2016
6422(197*10^70241-11)/370243Robert Price10/2017
642323*10^70240-770242Robert Price03/2016
6424(71*10^70227-53)/970228Robert Price10/2015
6425(2^233247-9)/1770214Lelio R Paula05/2012
6426(11^67421-2^67421)/970211Robert Price01/2013
6427(23*10^70209-41)/970210Robert Price03/2015
6428(29*10^70194-11)/970195Robert Price04/2015
64293^147109+19670189Lelio R Paula05/2014
6430(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
64319^73538+8^(73538+1)70174Robert Price06/2016
64322*5^100391+770171Lelio R Paula10/2014
643399^35156-270159Lelio R Paula08/2013
6434(68*10^70148+7)/370150Robert Price03/2016
643511^67360-603070149Enzo Doria01/2013
6436(35*10^70130-377)/970131Robert Price12/2017
643749391!3+3^4939170128Robert Price09/2015
6438(229*10^70122-1)/370124Robert Price12/2016
64397^82975-9270123Lelio R Paula07/2014
644065^38670+5870106Lelio R Paula01/2016
6441105^34684+34684^10570103Serge Batalov05/2014
6442134^32955-13370099Norbert Schneider03/2015
64442^232836-22790370091Enzo Doria12/2012
64432^232837-185917370091Enzo Doria03/2016
64453*2^232820+570087Lelio R Paula04/2014
64472^232799+9019570080Lelio R Paula02/2013
64462^232799-11223770080Enzo Doria06/2014
64482^232759+26214570068Lelio R Paula04/2012
64493*2^232750+770066Lelio R Paula04/2014
645012^64918-1170059Lelio R Paula01/2015
64517^82899-1270058Lelio R Paula09/2013
6452(22*10^70051-13)/970052Robert Price03/2015
6453(2^232685-7)/251462570039Lelio R Paula04/2012
645418^55786-536370027Enzo Doria03/2013
6455(2^(77537*3+1)+243)/770023Kevin Acres11/2013
64562^232602+16970021Lelio R Paula02/2012
6457(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
64582^232580+7213370014Enzo Doria04/2016
64594*6^89958-770002Lelio R Paula09/2014
646010^70000+8048770001Milton L. Brown05/2006
646110^69999+13485770000Patrick De Geest02/2007
646610^70000-927370000Patrick De Geest08/2009
6462(79*10^69999-7)/970000Robert Price01/2015
6463((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6464(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6465(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
646710^69999-8825169999Patrick De Geest08/2009
64682^232507+108969992Lelio R Paula04/2012
6469(17*2^232445+1)/569974Lelio R Paula08/2012
6470(529^25693+1)/53069972Richard Fischer12/2017
64717^82778+4869956Lelio R Paula09/2013
64727*2^232381+369955Lelio R Paula04/2014
64732^232362-11054169948Enzo Doria05/2014
64742^232326-11239169938Enzo Doria06/2014
64753^146575+23669935Lelio R Paula09/2013
647630^47341-2969929Norbert Schneider02/2014
64775^100040-6869925Lelio R Paula09/2013
6478(35*10^69866-593)/969867Robert Price08/2017
64792^232045-1729569853Lelio R Paula04/2012
6480(2^231987+78557)/9569834Lelio R Paula05/2012
64812^231955+7424369826Yves Minet03/2011
64822^231946-1587369823Enzo Doria04/2013
648318^55618+9569816Lelio R Paula09/2013
64846^89712+5^(89712-1)69810Robert Price02/2016
64852^231870+13569800Lelio R Paula02/2012
6486(23*2^231827-1)/417969785Lelio R Paula01/2014
64872^231778+5461569773Lelio R Paula04/2012
6488(19*2^231780+1)/23569772Lelio R Paula08/2012
648914^60866+2769761Lelio R Paula09/2013
649013^62619-4469755Lelio R Paula09/2013
6491(2^231715-509203)/3569752Lelio R Paula05/2012
64922^231711-11046769752Enzo Doria05/2014
6493(19^54547+18^54547)/3769751Robert Price08/2013
6494(23*2^231697-1)/4569748Lelio R Paula01/2014
64952^231696-186149969748Enzo Doria03/2016
64962^231684-14769744Lelio R Paula02/2012
6497(23*2^231686-1)/118369743Lelio R Paula01/2014
64982^231591-47739769716Paul Bourdelais03/2013
649911^66916-42069686Enzo Doria08/2012
65005^99680-1370669674Enzo Doria02/2013


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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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