PRP Records

Probable Primes Top 10000

(172742 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 ?
950175^25915-248593Lelio R Paula08/2013
95023^101816-10448579Lelio R Paula07/2012
9504(852175^8192+1)/32768248578Lelio R Paula12/2014
9503numbpart(61681*61682/2)48578Serge Batalov04/2017
9505132^22904+13148570Norbert Schneider03/2015
95062^161333-11487148567Enzo Doria05/2015
950713889^3138+3138^1388948566Hans Havermann05/2016
950813174^4857+4857^1317448565Hans Havermann05/2016
95092^161326+796948564Yves Minet02/2010
9510(2^161330-5)/2948564Lelio R Paula01/2012
9511(848412^8192+1)/78643348562Lelio R Paula11/2014
9512(847181^8192+1)/248562Lelio R Paula12/2014
95134*10^48548+7948549Robert Price01/2017
9515(13*10^48547+11)/348548Erik Branger05/2013
9514(9913*2^161263-1)/1748548Lelio R Paula03/2015
95162^161258+6343948544Yves Minet11/2010
95172^161238-45949148538Enzo Doria05/2015
9518(11909^11909+305)/2/15777148535Makoto Morimoto07/2016
95192^161226+6661548534Lelio R Paula12/2008
95202^161205-595548528Lelio R Paula04/2009
952110^48526+1348527Jason Earls02/2008
952210^48526-4144148526Patrick De Geest06/2009
95232^161199-1456948526Enzo Doria04/2013
95249*2^161190-748524Lelio R Paula02/2014
9525(3^101708+7)/5338448523Lelio R Paula03/2012
9526(2^161187+78557)/23615548517Lelio R Paula05/2012
9527(19*2^161174-1)/568548516Lelio R Paula01/2014
9528(835525^8192+1)/248513Lelio R Paula12/2014
952920^37287-6148512Lelio R Paula11/2012
95302^161143-1408948509Enzo Doria04/2013
9531(11903^11903+3950)/7/56348509Makoto Morimoto07/2016
9532(8*10^48507+49)/348508Robert Price03/2016
95332^161106-24658148498Gary Barnes08/2009
95342^161098+1891548496Lelio R Paula10/2011
9535(832081^8192+1)/147456248492Lelio R Paula12/2014
95368*10^48490+2148491Robert Price02/2017
95377^57369+2248483Lelio R Paula06/2012
95383^101615+266048483Lelio R Paula06/2012
9539(11897^11897+3419)/2^2/59348483Makoto Morimoto07/2016
95407337^12542-12542^733748482Norbert Schneider11/2016
9541(828754^8192+1)/63897748478Lelio R Paula11/2014
9542(265*10^48474+11)/348476Robert Price03/2017
954313260^4523+4523^1326048471Hans Havermann05/2016
95442^161003-11305948467Enzo Doria07/2014
9545(73*10^48461+53)/948462Erik Branger05/2013
9546(822278^8192+1)/6553748452Syoichiro Yamada05/2008
954710^48449+11250148450Patrick De Geest05/2007
954810^48449-4844948449Henri Lifchitz07/2002
954910^48442+5748443Robert Price01/2011
95502^160922-86968810548443Lelio R Paula10/2011
955110^48442-3353348442Patrick De Geest01/2012
95525101^13065-11048441Enzo Doria07/2012
9553(818917^8192+1)/248441Lelio R Paula12/2014
9554(11887^11887+7018)/19/31/32731948433Makoto Morimoto07/2016
95552^160883+7676348431Enzo Doria05/2016
95562^160873+1891548428Lelio R Paula10/2011
955713206^4645+4645^1320648427Hans Havermann04/2016
955810^48420+613948421Patrick De Geest05/2016
955910^48420-2*10^1592-148420Serge Batalov01/2015
956010^48420-2927348420Patrick De Geest03/2016
95622^160822-216348413Yves Minet08/2013
9561(lucasV(1,2,321685)+2)/(571*911)48413Mike Oakes02/2017
956410^48410+9^(48410-1)48411Robert Price03/2016
956310^48410+9016348411Patrick De Geest12/2016
9567(3^101473+4)/26448148410Lelio R Paula03/2012
95669*2^160811+748410Lelio R Paula02/2014
956510^48410-328748410Patrick De Geest12/2016
9568(22699*2^160806+1)/157348409Lelio R Paula05/2014
95693*7^57278-848407Lelio R Paula09/2014
95702^160789-11321548403Enzo Doria07/2014
95716900^12607-12607^690048397Norbert Schneider12/2016
95723^101404+248383Mike Oakes11/2009
95733^101395-11048378Lelio R Paula06/2012
95742^160701+19148376Lelio R Paula01/2011
95756*F(231436)+148368Gilbert Mozzo06/2015
95762^160654-1548362Lelio R Paula08/2010
957720^37167+5348356Lelio R Paula11/2012
9578(799247^8192+1)/248355Lelio R Paula12/2014
9579(238*10^48352-1)/348354Robert Price05/2016
958018661^390+390^1866148352Anatoly F. Selevich01/2007
958121^36566+248349Ray Chandler08/2011
95827^57208-9248347Lelio R Paula06/2012
95845^69165-2^6916648345Mike Oakes10/2010
9583(11867^11867+2981)/2^3/11134148345Makoto Morimoto07/2016
9585(3^101331-4)/467948344Lelio R Paula03/2012
958613^43396-2448341Lelio R Paula10/2012
9587Phi(85113,10)/170227/340453/2080331947/20239360723/57723206898508348339Serge Batalov06/2011
95887*2^160574-948339Lelio R Paula02/2014
9589lucasU(42,1,29781)+lucasU(42,1,29780)48334Mike Oakes04/2009
95913^101296-1931848331Enzo Doria02/2013
9590(lucasV(1,2,321119)+2)/(5*53)48331Mike Oakes01/2017
9593(11863^11863+2822)/3/140681/14848348322Makoto Morimoto07/2016
95925970^12797-12797^597048322Norbert Schneider03/2017
959417^39270+5248320Lelio R Paula11/2012
9595(791013^8192+1)/248318Lelio R Paula12/2014
959610^48314+7146948315Patrick De Geest06/2016
959911^46393-795048314Enzo Doria02/2013
959710^48314-2*10^4988-148314Serge Batalov01/2015
959810^48314-42379748314Patrick De Geest03/2016
96002^160491+8771348313Yves Minet03/2010
96018*6^62084-748312Lelio R Paula09/2014
96022^160477+7297748309Enzo Doria04/2016
96032^160471+9948307Lelio R Paula07/2009
9604(9913*2^160481-1)/419187548307Lelio R Paula03/2015
9606(43^29573+1)/4448305Robert Price11/2013
96052^160463-290748305Yves Minet09/2014
9607Phi(77061,10)/4151276071/1520798835148301Maksym Voznyy02/2010
96085^69098-1457648298Enzo Doria02/2013
9609(2*10^48297-17)/348297Erik Branger03/2013
961010^48292+10470748293Patrick De Geest06/2016
961210^48292-2*10^392-148292Serge Batalov01/2015
961110^48292-6680348292Patrick De Geest03/2016
961345709!4+248291Robert Price03/2017
96142^160402-112748286Yves Minet05/2013
96152^160398-145148285Yves Minet08/2012
961611^46365+2648285Lelio R Paula10/2012
9617t(160462)48285Robert Price05/2015
9618(3^50599-75)^2-7748284Jorge Menendez02/2017
96193^101192+2^10119348281Mike Oakes10/2009
96205^69063-1848273Lelio R Paula05/2012
96215^69060-1541648271Enzo Doria02/2013
96222^160343-66748269Yves Minet01/2012
96232^160302-214548256Lelio R Paula04/2009
962412^44705-8548245Lelio R Paula10/2012
9625(58695*2^160249-1)/14948243Lelio R Paula03/2015
96262^160218+1270548231Lelio R Paula10/2011
9627(F(14425)^17-F(14424)^17)/F(14423)48230Wayne Halsdorf02/2010
9628(771035^8192+1)/248227Lelio R Paula12/2014
963018348^425+425^1834848226Anatoly F. Selevich12/2006
9629(29*2^160204-1)/6748226Lelio R Paula01/2014
96312^160166+577548215Lelio R Paula04/2009
963211875^11478+11478^1187548211Anatoly F. Selevich10/2009
963317^39177-4048206Lelio R Paula11/2012
9634(5*2^160135-1)/429039948200Lelio R Paula01/2014
9635(763957^8192+1)/248194Lelio R Paula12/2014
9636(11833^11833+1278)/7/89/10748193Makoto Morimoto06/2016
9637gcd(V(576505),5*F(115301)*(F(115301)+1)+1)48192Serge Batalov04/2015
96388788^12217+12217^878848183Norbert Schneider01/2014
9639(11831^11831+1584)/5/23/97/140948181Makoto Morimoto07/2016
9640(760473^8192+1)/248178Lelio R Paula12/2014
9641-lucasV(-1,2,320104)/3148178Mike Oakes01/2017
9642gcd(V(864525),5*F(172905)*(F(172905)-1)+1)48176Serge Batalov04/2015
9643(760135^8192+1)/29491448171Lelio R Paula12/2014
96454357^13236-11048169Enzo Doria06/2012
9644(11827^11827+4120)/1748169Makoto Morimoto07/2016
9646(3*2^160013-1)/242548166Lelio R Paula01/2014
964713^43238+8248165Lelio R Paula11/2012
96482^159992+65748163Lelio R Paula02/2013
96492^159984-38300948160Gary Barnes08/2009
96502^159958-5869548153Lelio R Paula03/2009
96516408*10^48143+11821^11821-2448147Gilbert Mozzo12/2012
9652(755045^8192+1)/22937848147Lelio R Paula12/2014
965311821^11821-2448143Henri Lifchitz10/2011
9654(33*2^159934+1)/193696948141Michael Porter10/2015
9655(11821^11821+1240)/19/1378948138Makoto Morimoto06/2016
965620^36997-5148135Lelio R Paula11/2012
9657(3^100895+7)/2432177503448129Lelio R Paula03/2012
9658(15185*2^159869-1)/182748127Lelio R Paula03/2015
96593*7^56945+848125Lelio R Paula09/2014
9660(749655^8192+1)/13107448122Lelio R Paula12/2014
96614*5^68835+948115Lelio R Paula09/2014
9662(148^22171+1)/14948115Richard Fischer12/2016
9663(2^159841+78557)/92348114Lelio R Paula05/2012
9664(3^50420+59)^2+6148113Jorge Menendez02/2017
966510^48109+948110Jason Earls12/2007
966610^48108+3953148109Patrick De Geest01/2009
966710^48109-10459148109Patrick De Geest07/2009
967010^48107-4810748108Henri Lifchitz07/2002
966810^48107+12622948108Patrick De Geest04/2007
966910^48108-6134348108Patrick De Geest07/2009
967123^35328+2248108Norbert Schneider12/2013
96726213^12682+12682^621348107Norbert Schneider01/2016
9673(64*10^48106+287)/948107Robert Price04/2016
967418^38321-9748104Lelio R Paula11/2012
9675(11813^11813+748)/3/67980748101Makoto Morimoto06/2016
9676(743679^8192+1)/248099Lelio R Paula12/2014
96772^159777-133348098Yves Minet05/2013
96782^159765+71748095Lelio R Paula02/2013
967935^31143-395848087Enzo Doria03/2013
96808*10^48081-948082Dmitry Domanov11/2010
968112^44553-5948081Lelio R Paula10/2012
968235086!3+218748080Robert Price12/2015
9683(11807^11807+9647)/2/548079Makoto Morimoto07/2016
96841338^15377+15377^133848076Serge Batalov05/2014
96852^159692-125948073Yves Minet08/2012
9686(lucasV(1,2,319367)+2)/(5*11)48068Mike Oakes01/2017
96872^159669+94148066Lelio R Paula02/2013
96882^159660-287948063Yves Minet09/2014
96892^159647+57348059Lelio R Paula02/2013
969019^37581+9448057Lelio R Paula11/2012
96912^159633-57706348055Paul Bourdelais11/2012
9692(11801^11801+8503)/2^4/3/17/13748048Makoto Morimoto07/2016
9693(23*2^159599+1)/2548045Lelio R Paula07/2012
96942^159597+130748044Lelio R Paula07/2008
96953^100693-3448043Lelio R Paula06/2012
9696(349*10^48036-7)/948038Robert Price03/2017
9697(68*10^48032+7)/348034Robert Price03/2016
969824^34797-120748028Enzo Doria03/2013
9699(106*10^48026-1)/348028Serge Batalov12/2014
97002^159522+67948021Lelio R Paula02/2013
9701(726998^8192+1)/14745748013Lelio R Paula11/2014
9702(725753^8192+1)/13107448007Lelio R Paula12/2014
970310^48003+2148004Robert Price01/2011
970510^48003-3652148003Patrick De Geest01/2012
970420^36896-404348003Enzo Doria03/2013
970610^48000+7390948001Patrick De Geest05/2012
970710^48000-8240748000Patrick De Geest05/2012
970810^47999+7809348000Patrick De Geest05/2012
970910^47999-122747999Patrick De Geest05/2012
97102^159440-1260947997Enzo Doria10/2012
9711(11789^11789+297)/2/17/2347996Makoto Morimoto06/2016
9712(40^29959+1)/4147995Robert Price09/2013
9715(49*10^47989+41)/947990Erik Branger05/2013
971410^47989+2*47989-147990Robert Price03/2015
971310^47989+3028347990Patrick De Geest01/2016
971610^47989-1046347989Patrick De Geest01/2016
9717(11*2^159409-1)/2147987Lelio R Paula01/2014
97185^68644+9447981Lelio R Paula05/2012
97192^159386-214547980Lelio R Paula03/2009
9720Linear(0,1,1,-1,318751)47977Henri Lifchitz04/2007
9721(720710^8192+1)/966388940947977Lelio R Paula11/2014
9722(2^159392+5)/11779866947974Lelio R Paula01/2012
97236576^12565-12565^657647973Norbert Schneider11/2016
972410^47969+58504347970Robert Price03/2015
972510^47969+15329147970Patrick De Geest01/2016
972610^47969-15140747969Patrick De Geest01/2016
9727(9*2^159332+1)/547964Lelio R Paula07/2012
9728(11783^11783+65)/2^3/89/268603747963Makoto Morimoto06/2016
972920^36864+3147962Lelio R Paula11/2012
9730(2^159324+78557)/240947958Lelio R Paula05/2012
97312^159293-105147952Yves Minet05/2009
9732(355*29^32789-61)/1447952Curtis Bright05/2015
9733lucasU(1856,1,14670)-lucasU(1856,1,14669)47947Mike Oakes05/2009
9734(11779^11779+1425)/2^2/11/545679147946Makoto Morimoto07/2016
97353^100482-31047943Lelio R Paula06/2012
9736(11777^11777+5123)/2^2/5/13/225147939Makoto Morimoto07/2016
973717^38959+847938Lelio R Paula11/2012
97387*10^47936-6947937Robert Price01/2017
9739(708709^8192+1)/247927Lelio R Paula12/2014
9740(709609^8192+1)/29491447927Lelio R Paula12/2014
9741Phi(104749,3)47923Lelio R Paula02/2012
974224^34721-169147923Enzo Doria03/2013
97437*5^68554+647919Lelio R Paula09/2014
9744(16*10^47918-19)/347919Robert Price03/2016
974511836^11179+11179^1183647917Anatoly F. Selevich07/2009
9746Phi(65680,67)47917Enzo Doria04/2012
97473^100418-5247912Lelio R Paula06/2012
97482^159145-11281347908Enzo Doria06/2014
97496*F(229213)+147904Gilbert Mozzo06/2015
97506750^12509-12509^675047901Norbert Schneider10/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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