PRP Records

Probable Primes Top 10000

(172213 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
92517^58126+7249123Lelio R Paula06/2012
92527^58125+449122Lelio R Paula06/2012
9253(991537^8192+1)/249122Lelio R Paula12/2014
9254(14*10^49119-11)/349120Erik Branger05/2013
9255t(185595)49118Robert Price12/2013
9256(2*10^49117+457)/949117Robert Price01/2017
9257(988635^8192+1)/249112Lelio R Paula12/2014
9258(26*10^49106-23)/349107Robert Price08/2016
9259(986617^8192+1)/249104Lelio R Paula12/2014
926014313^2696+2696^1431349104Hans Havermann08/2015
9261(89*10^49101-53)/949102Erik Branger05/2013
92629*7^58099-449101Lelio R Paula09/2014
9263(-lucasV(1,2,326291)+2)/(5*83563*7935289)49100Mike Oakes02/2017
926423^36054-105049096Enzo Doria08/2012
9265(984325^8192+1)/13107449091Lelio R Paula12/2014
9266(3^51443-87)^2-8949090Jorge Menendez02/2017
9267928649*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9268592271*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9269580043*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9270555500*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9271512651*2*((10^49081-1)/9)+149087Danilo Nitsche01/2016
9272143358*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9273107445*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
9274117360*2*((10^49081-1)/9)+149086Danilo Nitsche01/2016
927528124*2*((10^49081-1)/9)+149085Danilo Nitsche01/2016
927618^39100-2949082Lelio R Paula11/2012
9277(10^49081-1)/949081Harvey Dubner09/1999
9278(978811^8192+1)/249076Lelio R Paula12/2014
927917200^713+713^1720049074Anatoly F. Selevich07/2006
92809*2^163006+549071Lelio R Paula02/2014
928111^47113-171049064Enzo Doria11/2012
928211^47106-141049056Enzo Doria11/2012
92832^162954-2349055Lelio R Paula08/2010
92842^162924-2863549046Lelio R Paula04/2009
928524771!2-849045Robert Price06/2015
9286(26*10^49039-77)/349040Robert Price02/2017
92875^70155-449037Theodore Burton11/2005
92883^102763-1449031Lelio R Paula06/2012
9289(21*2^162876+1)/2349031Lelio R Paula07/2012
92905^70146+5849030Lelio R Paula06/2012
92912^162864-74438949027Paul Bourdelais11/2012
92922^162860-11285949026Enzo Doria06/2014
9294(10^49025-1)/3-2*10^2451249025Patrick De Geest07/2005
92932^162856-22920949025Enzo Doria01/2013
9295(10^(2*24512+1)-6*10^24512-1)/349025Robert Price02/2016
9296(965897^8192+1)/32768249024Lelio R Paula12/2014
9297(5*2^162859-1)/5391949022Lelio R Paula01/2014
92986^62990+3149016Lelio R Paula06/2012
929946329!4+249014Robert Price03/2017
93002^162816-21920949013Enzo Doria11/2012
9301(127^23297-1)/12649011Alexander Zhirkov10/2010
9303(13^43997+12^43997)/2549009Robert Price04/2013
930210^49008+6666949009Patrick De Geest01/2016
930410^49008-503749008Robert Price09/2015
93055^70110+5249005Lelio R Paula06/2012
930610^49000+21303749001Patrick De Geest07/2012
930715^41664-9449001Lelio R Paula11/2012
93083^102699-34049000Lelio R Paula06/2012
930910^49000-62149000Patrick De Geest07/2012
931010^48999+26879149000Patrick De Geest07/2012
931110^48999-7463948999Patrick De Geest07/2012
9312(21181*2^162764+1)/6558370948994Lelio R Paula05/2014
93131033^16254+16254^103348992Serge Batalov05/2014
93148602^12451+12451^860248990Norbert Schneider07/2014
931512^45385+548979Lelio R Paula10/2012
9316(951919^8192+1)/248977Lelio R Paula12/2014
9317(12007^12007+2128)/37/1180148977Makoto Morimoto07/2016
93182^162669-179548969Lelio R Paula01/2009
93192^162668-11275748968Enzo Doria06/2014
932013527^4168+4168^1352748967Hans Havermann04/2016
9321(6883*2^162649-1)/548966Lelio R Paula03/2015
9322(944123^8192+1)/248948Lelio R Paula12/2014
9323(229*10^48944-1)/348946Robert Price12/2016
93242003^14821-10248935Enzo Doria06/2012
93257^57901+8248933Lelio R Paula06/2012
9326t(166683)48933Robert Price10/2014
932711^46985-1848930Lelio R Paula10/2012
93282^162521+9876533148924Jason Earls12/2008
9329V(380406)48914Serge Batalov03/2015
93302^162482+6583548912Lelio R Paula10/2011
933112^45317+748906Lelio R Paula10/2012
9332(4^81223+3^81223)/748901Jean-Louis Charton03/2011
9333(2^162474-5)/135309483148901Lelio R Paula01/2012
93343^102477+266048894Lelio R Paula07/2012
93352^162412+2983548891Lelio R Paula10/2011
93369*6^62820+748885Lelio R Paula09/2014
9337(169^21943+1)/17048885Richard Fischer11/2015
9338(11987^11987+3067)/2/3/5^2/11/13/285748884Makoto Morimoto07/2016
933913^43881-5048881Lelio R Paula11/2012
93408173^12492-12492^817348874Norbert Schneider05/2013
934120^37563-136348871Enzo Doria03/2013
9342(923522^8192+1)/11468948864Lelio R Paula11/2014
934313137^5242+5242^1313748864Hans Havermann04/2016
934415^41545+9248861Lelio R Paula11/2012
9345(11981^11981+632)/97/170948860Makoto Morimoto07/2016
9346(919695^8192+1)/13107448850Lelio R Paula12/2014
9347(917697^8192+1)/248847Lelio R Paula12/2014
9348(12^45259-5^45259)/748842Robert Price03/2013
93499*5^69862+848833Lelio R Paula09/2014
935012^45244-9548827Lelio R Paula10/2012
9351(29*2^162182-1)/548823Lelio R Paula01/2014
9352(2^162167-3)*6+10^48818*13803-748823Gilbert Mozzo11/2016
9353(2^162167-3)*6-748818Gilbert Mozzo03/2016
93547*10^48816-6948817Robert Price01/2017
9355(11971^11971+3180)/103/757748814Makoto Morimoto07/2016
93562^162143-5148810Lelio R Paula08/2010
93582^162136-28451948808Gary Barnes08/2009
93575^69828-1538648808Enzo Doria02/2013
93595^69826-3*4^6982648807Mike Oakes02/2010
93602^162123+7406348804Enzo Doria04/2016
936121001^11289-10448794Enzo Doria07/2012
93625^69802-3248790Lelio R Paula05/2012
9363(902939^8192+1)/248789Lelio R Paula12/2014
9364(2^162059+78557)/3548784Lelio R Paula05/2012
9365(900239^8192+1)/248778Lelio R Paula12/2014
9366138^22794-13748777Norbert Schneider10/2015
93672^162033+7675748777Enzo Doria05/2016
936818^38850-3748768Lelio R Paula11/2012
9369(898286^8192+1)/78643348765Lelio R Paula11/2014
937068^26610+6748764Norbert Schneider10/2012
93712^161987+1501548763Lelio R Paula10/2011
9372(11959^11959+6523)/2/558148762Makoto Morimoto07/2016
93733^102198-8648761Lelio R Paula06/2012
9374(13224!+1)/22149748755Donovan Johnson04/2006
937518^38838-1348753Lelio R Paula11/2012
9376161923*2^161923+161923+248749Robert Price05/2016
9377(892493^8192+1)/13107448743Lelio R Paula12/2014
9378(11953^11953+133)/2/4686148734Makoto Morimoto06/2016
93792^161881-1494148732Enzo Doria04/2013
9380(888215^8192+1)/248730Lelio R Paula12/2014
9381-lucasV(1,2,323749)-248730Mike Oakes02/2017
938210268^12147+12147^1026848728Norbert Schneider11/2013
9383(26*10^48726-11)/348727Erik Branger05/2013
93843*6^62618-748727Lelio R Paula09/2014
93862^161857-4548724Lelio R Paula08/2010
9385(889160^8192+1)/7328363315348724Lelio R Paula11/2014
93872^161837+46748718Lelio R Paula11/2007
93883^102102+1048716Lelio R Paula01/2007
93892^161806-829548709Lelio R Paula04/2009
9390(25*2^161811-1)/45748709Lelio R Paula01/2014
939113311^4558+4558^1331148702Hans Havermann05/2016
939224^35284-45748700Enzo Doria03/2013
93933^102058+868048695Lelio R Paula06/2012
939413537^3948+3948^1353748685Hans Havermann05/2016
9395(11941^11941+6414)/548684Makoto Morimoto07/2016
93962^161719-1509748683Enzo Doria04/2013
93973*10^48668-7^4866848669Mike Oakes01/2010
939813201!+13201!2+13201#-248666Joe McLean10/2007
94002*3^101994-548664Lelio R Paula03/2014
9399(11939^11939+2801)/2^2/5/19/307/221047348664Makoto Morimoto07/2016
940111933^11933+131648648Makoto Morimoto07/2016
9402(-lucasV(1,2,323096)+2)/(3*193)48629Mike Oakes02/2017
9403(lucasV(1,2,323208)-2)/(3^3*5*7*11*37*1733*2011*16603*17957*80803)48622Mike Oakes02/2017
940495^24584+9448621Norbert Schneider05/2013
9405(11927^11927+2091)/2/2273/6268348613Makoto Morimoto07/2016
9406(10^48604-31)/348604Serge Batalov12/2014
9407Phi(11923,11925)48600Henri Lifchitz11/2003
9408(11923^11923+3199)/2/4264948598Makoto Morimoto07/2016
940975^25915-248593Lelio R Paula08/2013
94103^101816-10448579Lelio R Paula07/2012
9411(852175^8192+1)/32768248578Lelio R Paula12/2014
9412132^22904+13148570Norbert Schneider03/2015
94132^161333-11487148567Enzo Doria05/2015
941413889^3138+3138^1388948566Hans Havermann05/2016
941513174^4857+4857^1317448565Hans Havermann05/2016
94172^161326+796948564Yves Minet02/2010
9416(2^161330-5)/2948564Lelio R Paula01/2012
9418(848412^8192+1)/78643348562Lelio R Paula11/2014
9419(847181^8192+1)/248562Lelio R Paula12/2014
94204*10^48548+7948549Robert Price01/2017
9422(13*10^48547+11)/348548Erik Branger05/2013
9421(9913*2^161263-1)/1748548Lelio R Paula03/2015
94232^161258+6343948544Yves Minet11/2010
94242^161238-45949148538Enzo Doria05/2015
9425(11909^11909+305)/2/15777148535Makoto Morimoto07/2016
94262^161226+6661548534Lelio R Paula12/2008
94272^161205-595548528Lelio R Paula04/2009
942810^48526+1348527Jason Earls02/2008
942910^48526-4144148526Patrick De Geest06/2009
94302^161199-1456948526Enzo Doria04/2013
94319*2^161190-748524Lelio R Paula02/2014
9432(3^101708+7)/5338448523Lelio R Paula03/2012
9433(2^161187+78557)/23615548517Lelio R Paula05/2012
9434(19*2^161174-1)/568548516Lelio R Paula01/2014
9435(835525^8192+1)/248513Lelio R Paula12/2014
943620^37287-6148512Lelio R Paula11/2012
94372^161143-1408948509Enzo Doria04/2013
9438(11903^11903+3950)/7/56348509Makoto Morimoto07/2016
9439(8*10^48507+49)/348508Robert Price03/2016
94402^161106-24658148498Gary Barnes08/2009
94412^161098+1891548496Lelio R Paula10/2011
9442(832081^8192+1)/147456248492Lelio R Paula12/2014
94438*10^48490+2148491Robert Price02/2017
94447^57369+2248483Lelio R Paula06/2012
94453^101615+266048483Lelio R Paula06/2012
9446(11897^11897+3419)/2^2/59348483Makoto Morimoto07/2016
94477337^12542-12542^733748482Norbert Schneider11/2016
9448(828754^8192+1)/63897748478Lelio R Paula11/2014
9449(265*10^48474+11)/348476Robert Price03/2017
945013260^4523+4523^1326048471Hans Havermann05/2016
94512^161003-11305948467Enzo Doria07/2014
9452(73*10^48461+53)/948462Erik Branger05/2013
9453(822278^8192+1)/6553748452Syoichiro Yamada05/2008
945410^48449+11250148450Patrick De Geest05/2007
945510^48449-4844948449Henri Lifchitz07/2002
945610^48442+5748443Robert Price01/2011
94572^160922-86968810548443Lelio R Paula10/2011
945810^48442-3353348442Patrick De Geest01/2012
94595101^13065-11048441Enzo Doria07/2012
9460(818917^8192+1)/248441Lelio R Paula12/2014
9461(11887^11887+7018)/19/31/32731948433Makoto Morimoto07/2016
94622^160883+7676348431Enzo Doria05/2016
94632^160873+1891548428Lelio R Paula10/2011
946413206^4645+4645^1320648427Hans Havermann04/2016
946510^48420+613948421Patrick De Geest05/2016
946610^48420-2*10^1592-148420Serge Batalov01/2015
946710^48420-2927348420Patrick De Geest03/2016
94692^160822-216348413Yves Minet08/2013
9468(lucasV(1,2,321685)+2)/(571*911)48413Mike Oakes02/2017
947110^48410+9^(48410-1)48411Robert Price03/2016
947010^48410+9016348411Patrick De Geest12/2016
9474(3^101473+4)/26448148410Lelio R Paula03/2012
94739*2^160811+748410Lelio R Paula02/2014
947210^48410-328748410Patrick De Geest12/2016
9475(22699*2^160806+1)/157348409Lelio R Paula05/2014
94763*7^57278-848407Lelio R Paula09/2014
94772^160789-11321548403Enzo Doria07/2014
94786900^12607-12607^690048397Norbert Schneider12/2016
94793^101404+248383Mike Oakes11/2009
94803^101395-11048378Lelio R Paula06/2012
94812^160701+19148376Lelio R Paula01/2011
94826*F(231436)+148368Gilbert Mozzo06/2015
94832^160654-1548362Lelio R Paula08/2010
948420^37167+5348356Lelio R Paula11/2012
9485(799247^8192+1)/248355Lelio R Paula12/2014
9486(238*10^48352-1)/348354Robert Price05/2016
948718661^390+390^1866148352Anatoly F. Selevich01/2007
948821^36566+248349Ray Chandler08/2011
94897^57208-9248347Lelio R Paula06/2012
94905^69165-2^6916648345Mike Oakes10/2010
9491(11867^11867+2981)/2^3/11134148345Makoto Morimoto07/2016
9492(3^101331-4)/467948344Lelio R Paula03/2012
949313^43396-2448341Lelio R Paula10/2012
9494Phi(85113,10)/170227/340453/2080331947/20239360723/57723206898508348339Serge Batalov06/2011
94957*2^160574-948339Lelio R Paula02/2014
9496lucasU(42,1,29781)+lucasU(42,1,29780)48334Mike Oakes04/2009
94973^101296-1931848331Enzo Doria02/2013
9498(lucasV(1,2,321119)+2)/(5*53)48331Mike Oakes01/2017
9499(11863^11863+2822)/3/140681/14848348322Makoto Morimoto07/2016
950017^39270+5248320Lelio R Paula11/2012


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!