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) !!!


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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 ?
95017^58126+7249123Lelio R Paula06/2012
95027^58125+449122Lelio R Paula06/2012
9503(991537^8192+1)/249122Lelio R Paula12/2014
9504(14*10^49119-11)/349120Erik Branger05/2013
9505t(185595)49118Robert Price12/2013
9506(2*10^49117+457)/949117Robert Price01/2017
9507(988635^8192+1)/249112Lelio R Paula12/2014
9508(26*10^49106-23)/349107Robert Price08/2016
9509(986617^8192+1)/249104Lelio R Paula12/2014
951014313^2696+2696^1431349104Hans Havermann08/2015
9511(89*10^49101-53)/949102Erik Branger05/2013
95129*7^58099-449101Lelio R Paula09/2014
9513(-lucasV(1,2,326291)+2)/(5*83563*7935289)49100Mike Oakes02/2017
951423^36054-105049096Enzo Doria08/2012
9515(984325^8192+1)/13107449091Lelio R Paula12/2014
9516(3^51443-87)^2-8949090Jorge Menendez02/2017
9517928649*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9518592271*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9519580043*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9520555500*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9521512651*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9522143358*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9523107445*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9524117360*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
952528124*2*((10^49081-1)/9)+149085Danilo Nitsche01/2016
952618^39100-2949082Lelio R Paula11/2012
9527(10^49081-1)/949081Harvey Dubner09/1999
9528(978811^8192+1)/249076Lelio R Paula12/2014
952917200^713+713^1720049074Anatoly F. Selevich07/2006
95309*2^163006+549071Lelio R Paula02/2014
953111^47113-171049064Enzo Doria11/2012
953211^47106-141049056Enzo Doria11/2012
95332^162954-2349055Lelio R Paula08/2010
95342^162924-2863549046Lelio R Paula04/2009
953524771!2-849045Robert Price06/2015
9536(26*10^49039-77)/349040Robert Price02/2017
95375^70155-449037Theodore Burton11/2005
95383^102763-1449031Lelio R Paula06/2012
9539(21*2^162876+1)/2349031Lelio R Paula07/2012
95405^70146+5849030Lelio R Paula06/2012
95412^162864-74438949027Paul Bourdelais11/2012
95422^162860-11285949026Enzo Doria06/2014
9543(10^49025-1)/3-2*10^2451249025Patrick De Geest07/2005
95442^162856-22920949025Enzo Doria01/2013
9545(10^(2*24512+1)-6*10^24512-1)/349025Robert Price02/2016
9546(965897^8192+1)/32768249024Lelio R Paula12/2014
9547(5*2^162859-1)/5391949022Lelio R Paula01/2014
95486^62990+3149016Lelio R Paula06/2012
954946329!4+249014Robert Price03/2017
95502^162816-21920949013Enzo Doria11/2012
9551(127^23297-1)/12649011Alexander Zhirkov10/2010
9552(13^43997+12^43997)/2549009Robert Price04/2013
955310^49008+6666949009Patrick De Geest01/2016
955410^49008-503749008Robert Price09/2015
95555^70110+5249005Lelio R Paula06/2012
955610^49000+21303749001Patrick De Geest07/2012
955715^41664-9449001Lelio R Paula11/2012
95583^102699-34049000Lelio R Paula06/2012
955910^49000-62149000Patrick De Geest07/2012
956010^48999+26879149000Patrick De Geest07/2012
956110^48999-7463948999Patrick De Geest07/2012
9562(21181*2^162764+1)/6558370948994Lelio R Paula05/2014
95631033^16254+16254^103348992Serge Batalov05/2014
95648602^12451+12451^860248990Norbert Schneider07/2014
956512^45385+548979Lelio R Paula10/2012
9566(951919^8192+1)/248977Lelio R Paula12/2014
9567(12007^12007+2128)/37/1180148977Makoto Morimoto07/2016
95682^162669-179548969Lelio R Paula01/2009
95692^162668-11275748968Enzo Doria06/2014
957013527^4168+4168^1352748967Hans Havermann04/2016
9571(6883*2^162649-1)/548966Lelio R Paula03/2015
9572(944123^8192+1)/248948Lelio R Paula12/2014
9573(229*10^48944-1)/348946Robert Price12/2016
95742003^14821-10248935Enzo Doria06/2012
95757^57901+8248933Lelio R Paula06/2012
9576t(166683)48933Robert Price10/2014
957711^46985-1848930Lelio R Paula10/2012
95782^162521+9876533148924Jason Earls12/2008
9579V(380406)48914Serge Batalov03/2015
95802^162482+6583548912Lelio R Paula10/2011
958112^45317+748906Lelio R Paula10/2012
9582(4^81223+3^81223)/748901Jean-Louis Charton03/2011
9583(2^162474-5)/135309483148901Lelio R Paula01/2012
95843^102477+266048894Lelio R Paula07/2012
95852^162412+2983548891Lelio R Paula10/2011
95869*6^62820+748885Lelio R Paula09/2014
9587(169^21943+1)/17048885Richard Fischer11/2015
9588(11987^11987+3067)/2/3/5^2/11/13/285748884Makoto Morimoto07/2016
958913^43881-5048881Lelio R Paula11/2012
95908173^12492-12492^817348874Norbert Schneider05/2013
959120^37563-136348871Enzo Doria03/2013
9593(923522^8192+1)/11468948864Lelio R Paula11/2014
959213137^5242+5242^1313748864Hans Havermann04/2016
959415^41545+9248861Lelio R Paula11/2012
9595(11981^11981+632)/97/170948860Makoto Morimoto07/2016
9596(919695^8192+1)/13107448850Lelio R Paula12/2014
9597(917697^8192+1)/248847Lelio R Paula12/2014
9598(12^45259-5^45259)/748842Robert Price03/2013
95999*5^69862+848833Lelio R Paula09/2014
960012^45244-9548827Lelio R Paula10/2012
9601(29*2^162182-1)/548823Lelio R Paula01/2014
9602(2^162167-3)*6+10^48818*13803-748823Gilbert Mozzo11/2016
9603(2^162167-3)*6-748818Gilbert Mozzo03/2016
96047*10^48816-6948817Robert Price01/2017
9605(11971^11971+3180)/103/757748814Makoto Morimoto07/2016
96062^162143-5148810Lelio R Paula08/2010
96072^162136-28451948808Gary Barnes08/2009
96085^69828-1538648808Enzo Doria02/2013
96095^69826-3*4^6982648807Mike Oakes02/2010
96102^162123+7406348804Enzo Doria04/2016
961121001^11289-10448794Enzo Doria07/2012
96125^69802-3248790Lelio R Paula05/2012
9613(902939^8192+1)/248789Lelio R Paula12/2014
9614(2^162059+78557)/3548784Lelio R Paula05/2012
9615(900239^8192+1)/248778Lelio R Paula12/2014
9616138^22794-13748777Norbert Schneider10/2015
96172^162033+7675748777Enzo Doria05/2016
961818^38850-3748768Lelio R Paula11/2012
9619(898286^8192+1)/78643348765Lelio R Paula11/2014
962068^26610+6748764Norbert Schneider10/2012
96212^161987+1501548763Lelio R Paula10/2011
9622(11959^11959+6523)/2/558148762Makoto Morimoto07/2016
96233^102198-8648761Lelio R Paula06/2012
9624(13224!+1)/22149748755Donovan Johnson04/2006
962518^38838-1348753Lelio R Paula11/2012
9626161923*2^161923+161923+248749Robert Price05/2016
9627(892493^8192+1)/13107448743Lelio R Paula12/2014
9628(11953^11953+133)/2/4686148734Makoto Morimoto06/2016
96292^161881-1494148732Enzo Doria04/2013
9631(888215^8192+1)/248730Lelio R Paula12/2014
9630-lucasV(1,2,323749)-248730Mike Oakes02/2017
963210268^12147+12147^1026848728Norbert Schneider11/2013
9634(26*10^48726-11)/348727Erik Branger05/2013
96333*6^62618-748727Lelio R Paula09/2014
96362^161857-4548724Lelio R Paula08/2010
9635(889160^8192+1)/7328363315348724Lelio R Paula11/2014
96372^161837+46748718Lelio R Paula11/2007
96383^102102+1048716Lelio R Paula01/2007
96392^161806-829548709Lelio R Paula04/2009
9640(25*2^161811-1)/45748709Lelio R Paula01/2014
964113311^4558+4558^1331148702Hans Havermann05/2016
964224^35284-45748700Enzo Doria03/2013
96433^102058+868048695Lelio R Paula06/2012
964413537^3948+3948^1353748685Hans Havermann05/2016
9645(11941^11941+6414)/548684Makoto Morimoto07/2016
96462^161719-1509748683Enzo Doria04/2013
9647(41*10^48678+373)/948679Robert Price04/2017
96483*10^48668-7^4866848669Mike Oakes01/2010
964913201!+13201!2+13201#-248666Joe McLean10/2007
96502*3^101994-548664Lelio R Paula03/2014
9651(11939^11939+2801)/2^2/5/19/307/221047348664Makoto Morimoto07/2016
965211933^11933+131648648Makoto Morimoto07/2016
9653(-lucasV(1,2,323096)+2)/(3*193)48629Mike Oakes02/2017
9654(lucasV(1,2,323208)-2)/(3^3*5*7*11*37*1733*2011*16603*17957*80803)48622Mike Oakes02/2017
965595^24584+9448621Norbert Schneider05/2013
9656(11927^11927+2091)/2/2273/6268348613Makoto Morimoto07/2016
9657(10^48604-31)/348604Serge Batalov12/2014
9658Phi(11923,11925)48600Henri Lifchitz11/2003
9659(11923^11923+3199)/2/4264948598Makoto Morimoto07/2016
966075^25915-248593Lelio R Paula08/2013
96613^101816-10448579Lelio R Paula07/2012
9663(852175^8192+1)/32768248578Lelio R Paula12/2014
9662numbpart(61681*61682/2)48578Serge Batalov04/2017
9664132^22904+13148570Norbert Schneider03/2015
96652^161333-11487148567Enzo Doria05/2015
966613889^3138+3138^1388948566Hans Havermann05/2016
966713174^4857+4857^1317448565Hans Havermann05/2016
96692^161326+796948564Yves Minet02/2010
9668(2^161330-5)/2948564Lelio R Paula01/2012
9670(848412^8192+1)/78643348562Lelio R Paula11/2014
9671(847181^8192+1)/248562Lelio R Paula12/2014
96724*10^48548+7948549Robert Price01/2017
9674(13*10^48547+11)/348548Erik Branger05/2013
9673(9913*2^161263-1)/1748548Lelio R Paula03/2015
96752^161258+6343948544Yves Minet11/2010
96762^161238-45949148538Enzo Doria05/2015
9677(11909^11909+305)/2/15777148535Makoto Morimoto07/2016
96782^161226+6661548534Lelio R Paula12/2008
96792^161205-595548528Lelio R Paula04/2009
968010^48526+1348527Jason Earls02/2008
968110^48526-4144148526Patrick De Geest06/2009
96822^161199-1456948526Enzo Doria04/2013
96839*2^161190-748524Lelio R Paula02/2014
9684(3^101708+7)/5338448523Lelio R Paula03/2012
9685(2^161187+78557)/23615548517Lelio R Paula05/2012
9686(19*2^161174-1)/568548516Lelio R Paula01/2014
9687(835525^8192+1)/248513Lelio R Paula12/2014
968820^37287-6148512Lelio R Paula11/2012
96892^161143-1408948509Enzo Doria04/2013
9690(11903^11903+3950)/7/56348509Makoto Morimoto07/2016
9691(8*10^48507+49)/348508Robert Price03/2016
96922^161106-24658148498Gary Barnes08/2009
96932^161098+1891548496Lelio R Paula10/2011
9694(832081^8192+1)/147456248492Lelio R Paula12/2014
96958*10^48490+2148491Robert Price02/2017
96967^57369+2248483Lelio R Paula06/2012
96973^101615+266048483Lelio R Paula06/2012
9698(11897^11897+3419)/2^2/59348483Makoto Morimoto07/2016
96997337^12542-12542^733748482Norbert Schneider11/2016
9700(828754^8192+1)/63897748478Lelio R Paula11/2014
9701(265*10^48474+11)/348476Robert Price03/2017
970213260^4523+4523^1326048471Hans Havermann05/2016
97032^161003-11305948467Enzo Doria07/2014
9704(73*10^48461+53)/948462Erik Branger05/2013
9705(822278^8192+1)/6553748452Syoichiro Yamada05/2008
970610^48449+11250148450Patrick De Geest05/2007
970710^48449-4844948449Henri Lifchitz07/2002
970810^48442+5748443Robert Price01/2011
97092^160922-86968810548443Lelio R Paula10/2011
971010^48442-3353348442Patrick De Geest01/2012
97115101^13065-11048441Enzo Doria07/2012
9712(818917^8192+1)/248441Lelio R Paula12/2014
9713(11887^11887+7018)/19/31/32731948433Makoto Morimoto07/2016
97142^160883+7676348431Enzo Doria05/2016
97152^160873+1891548428Lelio R Paula10/2011
971613206^4645+4645^1320648427Hans Havermann04/2016
971710^48420+613948421Patrick De Geest05/2016
971810^48420-2*10^1592-148420Serge Batalov01/2015
971910^48420-2927348420Patrick De Geest03/2016
97212^160822-216348413Yves Minet08/2013
9720(lucasV(1,2,321685)+2)/(571*911)48413Mike Oakes02/2017
972310^48410+9^(48410-1)48411Robert Price03/2016
972210^48410+9016348411Patrick De Geest12/2016
9725(3^101473+4)/26448148410Lelio R Paula03/2012
97269*2^160811+748410Lelio R Paula02/2014
972410^48410-328748410Patrick De Geest12/2016
9727(22699*2^160806+1)/157348409Lelio R Paula05/2014
97283*7^57278-848407Lelio R Paula09/2014
97292^160789-11321548403Enzo Doria07/2014
97306900^12607-12607^690048397Norbert Schneider12/2016
97313^101404+248383Mike Oakes11/2009
97323^101395-11048378Lelio R Paula06/2012
97332^160701+19148376Lelio R Paula01/2011
97346*F(231436)+148368Gilbert Mozzo06/2015
97352^160654-1548362Lelio R Paula08/2010
973620^37167+5348356Lelio R Paula11/2012
9737(799247^8192+1)/248355Lelio R Paula12/2014
9738(238*10^48352-1)/348354Robert Price05/2016
973918661^390+390^1866148352Anatoly F. Selevich01/2007
974021^36566+248349Ray Chandler08/2011
97417^57208-9248347Lelio R Paula06/2012
97435^69165-2^6916648345Mike Oakes10/2010
9742(11867^11867+2981)/2^3/11134148345Makoto Morimoto07/2016
9744(3^101331-4)/467948344Lelio R Paula03/2012
974513^43396-2448341Lelio R Paula10/2012
9747Phi(85113,10)/170227/340453/2080331947/20239360723/57723206898508348339Serge Batalov06/2011
97467*2^160574-948339Lelio R Paula02/2014
9748lucasU(42,1,29781)+lucasU(42,1,29780)48334Mike Oakes04/2009
97493^101296-1931848331Enzo Doria02/2013
9750(lucasV(1,2,321119)+2)/(5*53)48331Mike Oakes01/2017


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

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