PRP Records

Probable Primes Top 10000

(181746 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 ?
97512003^14821-10248935Enzo Doria06/2012
97527^57901+8248933Lelio R Paula06/2012
9753t(166683)48933Robert Price10/2014
975411^46985-1848930Lelio R Paula10/2012
97552^162521+9876533148924Jason Earls12/2008
9756V(380406)48914Serge Batalov03/2015
97572^162482+6583548912Lelio R Paula10/2011
975812^45317+748906Lelio R Paula10/2012
9759(4^81223+3^81223)/748901Jean-Louis Charton03/2011
9760(2^162474-5)/135309483148901Lelio R Paula01/2012
97613^102477+266048894Lelio R Paula07/2012
97622^162412+2983548891Lelio R Paula10/2011
97639*6^62820+748885Lelio R Paula09/2014
9764(169^21943+1)/17048885Richard Fischer11/2015
9765(11987^11987+3067)/2/3/5^2/11/13/285748884Makoto Morimoto07/2016
976613^43881-5048881Lelio R Paula11/2012
97678173^12492-12492^817348874Norbert Schneider05/2013
976820^37563-136348871Enzo Doria03/2013
9770(923522^8192+1)/11468948864Lelio R Paula11/2014
976913137^5242+5242^1313748864Hans Havermann04/2016
977115^41545+9248861Lelio R Paula11/2012
9772(11981^11981+632)/97/170948860Makoto Morimoto07/2016
9773(919695^8192+1)/13107448850Lelio R Paula12/2014
9774(917697^8192+1)/248847Lelio R Paula12/2014
9775(12^45259-5^45259)/748842Robert Price03/2013
97769*5^69862+848833Lelio R Paula09/2014
977712^45244-9548827Lelio R Paula10/2012
9778(29*2^162182-1)/548823Lelio R Paula01/2014
9779(2^162167-3)*6+10^48818*13803-748823Gilbert Mozzo11/2016
9780(2^162167-3)*6-748818Gilbert Mozzo03/2016
97817*10^48816-6948817Robert Price01/2017
9782(11971^11971+3180)/103/757748814Makoto Morimoto07/2016
97832^162143-5148810Lelio R Paula08/2010
97842^162136-28451948808Gary Barnes08/2009
97855^69828-1538648808Enzo Doria02/2013
97865^69826-3*4^6982648807Mike Oakes02/2010
97872^162123+7406348804Enzo Doria04/2016
978821001^11289-10448794Enzo Doria07/2012
97895^69802-3248790Lelio R Paula05/2012
9790(902939^8192+1)/248789Lelio R Paula12/2014
9791(2^162059+78557)/3548784Lelio R Paula05/2012
9792(900239^8192+1)/248778Lelio R Paula12/2014
9793138^22794-13748777Norbert Schneider10/2015
97942^162033+7675748777Enzo Doria05/2016
979518^38850-3748768Lelio R Paula11/2012
9796(898286^8192+1)/78643348765Lelio R Paula11/2014
979768^26610+6748764Norbert Schneider10/2012
97982^161987+1501548763Lelio R Paula10/2011
9799(11959^11959+6523)/2/558148762Makoto Morimoto07/2016
98003^102198-8648761Lelio R Paula06/2012
9801(13224!+1)/22149748755Donovan Johnson04/2006
980218^38838-1348753Lelio R Paula11/2012
9803161923*2^161923+161923+248749Robert Price05/2016
9804(892493^8192+1)/13107448743Lelio R Paula12/2014
9805(11953^11953+133)/2/4686148734Makoto Morimoto06/2016
98062^161881-1494148732Enzo Doria04/2013
9807(888215^8192+1)/248730Lelio R Paula12/2014
9808-lucasV(1,2,323749)-248730Mike Oakes02/2017
980910268^12147+12147^1026848728Norbert Schneider11/2013
9811(26*10^48726-11)/348727Erik Branger05/2013
98103*6^62618-748727Lelio R Paula09/2014
98132^161857-4548724Lelio R Paula08/2010
9812(889160^8192+1)/7328363315348724Lelio R Paula11/2014
98142^161837+46748718Lelio R Paula11/2007
98153^102102+1048716Lelio R Paula01/2007
98162^161806-829548709Lelio R Paula04/2009
9817(25*2^161811-1)/45748709Lelio R Paula01/2014
981813311^4558+4558^1331148702Hans Havermann05/2016
981924^35284-45748700Enzo Doria03/2013
98203^102058+868048695Lelio R Paula06/2012
982113537^3948+3948^1353748685Hans Havermann05/2016
9822(11941^11941+6414)/548684Makoto Morimoto07/2016
98232^161719-1509748683Enzo Doria04/2013
9824(41*10^48678+373)/948679Robert Price04/2017
98253*10^48668-7^4866848669Mike Oakes01/2010
982613201!+13201!2+13201#-248666Joe McLean10/2007
98272*3^101994-548664Lelio R Paula03/2014
9828(11939^11939+2801)/2^2/5/19/307/221047348664Makoto Morimoto07/2016
982911933^11933+131648648Makoto Morimoto07/2016
9830(-lucasV(1,2,323096)+2)/(3*193)48629Mike Oakes02/2017
9831(lucasV(1,2,323208)-2)/(3^3*5*7*11*37*1733*2011*16603*17957*80803)48622Mike Oakes02/2017
983295^24584+9448621Norbert Schneider05/2013
9833(11927^11927+2091)/2/2273/6268348613Makoto Morimoto07/2016
9834(10^48604-31)/348604Serge Batalov12/2014
9835Phi(11923,11925)48600Henri Lifchitz11/2003
9836(11923^11923+3199)/2/4264948598Makoto Morimoto07/2016
983775^25915-248593Lelio R Paula08/2013
98383^101816-10448579Lelio R Paula07/2012
9839(852175^8192+1)/32768248578Lelio R Paula12/2014
9840numbpart(61681*61682/2)48578Serge Batalov04/2017
9841132^22904+13148570Norbert Schneider03/2015
98422^161333-11487148567Enzo Doria05/2015
984313889^3138+3138^1388948566Hans Havermann05/2016
984413174^4857+4857^1317448565Hans Havermann05/2016
98452^161326+796948564Yves Minet02/2010
9846(2^161330-5)/2948564Lelio R Paula01/2012
9847(848412^8192+1)/78643348562Lelio R Paula11/2014
9848(847181^8192+1)/248562Lelio R Paula12/2014
98494*10^48548+7948549Robert Price01/2017
9851(13*10^48547+11)/348548Erik Branger05/2013
9850(9913*2^161263-1)/1748548Lelio R Paula03/2015
98522^161258+6343948544Yves Minet11/2010
98532^161238-45949148538Enzo Doria05/2015
9854(11909^11909+305)/2/15777148535Makoto Morimoto07/2016
98552^161226+6661548534Lelio R Paula12/2008
98562^161205-595548528Lelio R Paula04/2009
985710^48526+1348527Jason Earls02/2008
985810^48526-4144148526Patrick De Geest06/2009
98592^161199-1456948526Enzo Doria04/2013
98609*2^161190-748524Lelio R Paula02/2014
9861(3^101708+7)/5338448523Lelio R Paula03/2012
9862(2^161187+78557)/23615548517Lelio R Paula05/2012
9863(19*2^161174-1)/568548516Lelio R Paula01/2014
9864(835525^8192+1)/248513Lelio R Paula12/2014
986520^37287-6148512Lelio R Paula11/2012
98662^161143-1408948509Enzo Doria04/2013
9867(11903^11903+3950)/7/56348509Makoto Morimoto07/2016
9868(8*10^48507+49)/348508Robert Price03/2016
98692^161106-24658148498Gary Barnes08/2009
98702^161098+1891548496Lelio R Paula10/2011
9871(832081^8192+1)/147456248492Lelio R Paula12/2014
98728*10^48490+2148491Robert Price02/2017
98737^57369+2248483Lelio R Paula06/2012
98743^101615+266048483Lelio R Paula06/2012
9875(11897^11897+3419)/2^2/59348483Makoto Morimoto07/2016
98767337^12542-12542^733748482Norbert Schneider11/2016
9878(828754^8192+1)/63897748478Lelio R Paula11/2014
98773*10^48477+1348478Robert Price08/2017
9879(265*10^48474+11)/348476Robert Price03/2017
988013260^4523+4523^1326048471Hans Havermann05/2016
98812^161003-11305948467Enzo Doria07/2014
9882(73*10^48461+53)/948462Erik Branger05/2013
9883(822278^8192+1)/6553748452Syoichiro Yamada05/2008
988410^48449+11250148450Patrick De Geest05/2007
988510^48449-4844948449Henri Lifchitz07/2002
988610^48442+5748443Robert Price01/2011
98872^160922-86968810548443Lelio R Paula10/2011
988810^48442-3353348442Patrick De Geest01/2012
98895101^13065-11048441Enzo Doria07/2012
9890(818917^8192+1)/248441Lelio R Paula12/2014
9891(11887^11887+7018)/19/31/32731948433Makoto Morimoto07/2016
98922^160883+7676348431Enzo Doria05/2016
98932^160873+1891548428Lelio R Paula10/2011
989413206^4645+4645^1320648427Hans Havermann04/2016
989510^48420+613948421Patrick De Geest05/2016
989710^48420-2*10^1592-148420Serge Batalov01/2015
989610^48420-2927348420Patrick De Geest03/2016
98992^160822-216348413Yves Minet08/2013
9898(lucasV(1,2,321685)+2)/(571*911)48413Mike Oakes02/2017
990110^48410+9^(48410-1)48411Robert Price03/2016
990010^48410+9016348411Patrick De Geest12/2016
9904(3^101473+4)/26448148410Lelio R Paula03/2012
99039*2^160811+748410Lelio R Paula02/2014
990210^48410-328748410Patrick De Geest12/2016
9905(22699*2^160806+1)/157348409Lelio R Paula05/2014
99063*7^57278-848407Lelio R Paula09/2014
99072^160789-11321548403Enzo Doria07/2014
99086900^12607-12607^690048397Norbert Schneider12/2016
99093^101404+248383Mike Oakes11/2009
99103^101395-11048378Lelio R Paula06/2012
99112^160701+19148376Lelio R Paula01/2011
99126*F(231436)+148368Gilbert Mozzo06/2015
99132^160654-1548362Lelio R Paula08/2010
991420^37167+5348356Lelio R Paula11/2012
9915(799247^8192+1)/248355Lelio R Paula12/2014
9916(238*10^48352-1)/348354Robert Price05/2016
991718661^390+390^1866148352Anatoly F. Selevich01/2007
991821^36566+248349Ray Chandler08/2011
99197^57208-9248347Lelio R Paula06/2012
99205^69165-2^6916648345Mike Oakes10/2010
9921(11867^11867+2981)/2^3/11134148345Makoto Morimoto07/2016
9922(3^101331-4)/467948344Lelio R Paula03/2012
992313^43396-2448341Lelio R Paula10/2012
9924Phi(85113,10)/170227/340453/2080331947/20239360723/57723206898508348339Serge Batalov06/2011
99257*2^160574-948339Lelio R Paula02/2014
9926lucasU(42,1,29781)+lucasU(42,1,29780)48334Mike Oakes04/2009
99273^101296-1931848331Enzo Doria02/2013
9928(lucasV(1,2,321119)+2)/(5*53)48331Mike Oakes01/2017
9930(11863^11863+2822)/3/140681/14848348322Makoto Morimoto07/2016
99295970^12797-12797^597048322Norbert Schneider03/2017
993117^39270+5248320Lelio R Paula11/2012
9932(791013^8192+1)/248318Lelio R Paula12/2014
993310^48314+7146948315Patrick De Geest06/2016
993611^46393-795048314Enzo Doria02/2013
993510^48314-2*10^4988-148314Serge Batalov01/2015
993410^48314-42379748314Patrick De Geest03/2016
99372^160491+8771348313Yves Minet03/2010
99388*6^62084-748312Lelio R Paula09/2014
99392^160477+7297748309Enzo Doria04/2016
99402^160471+9948307Lelio R Paula07/2009
9941(9913*2^160481-1)/419187548307Lelio R Paula03/2015
9943(43^29573+1)/4448305Robert Price11/2013
99422^160463-290748305Yves Minet09/2014
9944(68*10^48304-257)/948305Robert Price06/2017
9945Phi(77061,10)/4151276071/1520798835148301Maksym Voznyy02/2010
99465^69098-1457648298Enzo Doria02/2013
9947(2*10^48297-17)/348297Erik Branger03/2013
994810^48292+10470748293Patrick De Geest06/2016
994910^48292-2*10^392-148292Serge Batalov01/2015
995010^48292-6680348292Patrick De Geest03/2016
995145709!4+248291Robert Price03/2017
99522^160402-112748286Yves Minet05/2013
99532^160398-145148285Yves Minet08/2012
995411^46365+2648285Lelio R Paula10/2012
9955t(160462)48285Robert Price05/2015
9956(3^50599-75)^2-7748284Jorge Menendez02/2017
99572^160387-372148282Yves Minet04/2017
99583^101192+2^10119348281Mike Oakes10/2009
99595^69063-1848273Lelio R Paula05/2012
99605^69060-1541648271Enzo Doria02/2013
99612^160343-66748269Yves Minet01/2012
99622^160302-214548256Lelio R Paula04/2009
996312^44705-8548245Lelio R Paula10/2012
9964(58695*2^160249-1)/14948243Lelio R Paula03/2015
99652^160218+1270548231Lelio R Paula10/2011
9966(F(14425)^17-F(14424)^17)/F(14423)48230Wayne Halsdorf02/2010
9967(771035^8192+1)/248227Lelio R Paula12/2014
996918348^425+425^1834848226Anatoly F. Selevich12/2006
9968(29*2^160204-1)/6748226Lelio R Paula01/2014
99702^160166+577548215Lelio R Paula04/2009
997111875^11478+11478^1187548211Anatoly F. Selevich10/2009
997217^39177-4048206Lelio R Paula11/2012
9973(5*2^160135-1)/429039948200Lelio R Paula01/2014
9974(763957^8192+1)/248194Lelio R Paula12/2014
9975(11833^11833+1278)/7/89/10748193Makoto Morimoto06/2016
9976gcd(V(576505),5*F(115301)*(F(115301)+1)+1)48192Serge Batalov04/2015
99778788^12217+12217^878848183Norbert Schneider01/2014
9978(11831^11831+1584)/5/23/97/140948181Makoto Morimoto07/2016
9979(760473^8192+1)/248178Lelio R Paula12/2014
9980-lucasV(-1,2,320104)/3148178Mike Oakes01/2017
9981gcd(V(864525),5*F(172905)*(F(172905)-1)+1)48176Serge Batalov04/2015
9982(760135^8192+1)/29491448171Lelio R Paula12/2014
99844357^13236-11048169Enzo Doria06/2012
9983(11827^11827+4120)/1748169Makoto Morimoto07/2016
9985(3*2^160013-1)/242548166Lelio R Paula01/2014
998613^43238+8248165Lelio R Paula11/2012
99872^159992+65748163Lelio R Paula02/2013
99882^159984-38300948160Gary Barnes08/2009
99892^159958-5869548153Lelio R Paula03/2009
9990471^18014-18014^47148152Norbert Schneider08/2017
99916408*10^48143+11821^11821-2448147Gilbert Mozzo12/2012
9992(755045^8192+1)/22937848147Lelio R Paula12/2014
999311821^11821-2448143Henri Lifchitz10/2011
9994(33*2^159934+1)/193696948141Michael Porter10/2015
9995(11821^11821+1240)/19/1378948138Makoto Morimoto06/2016
999620^36997-5148135Lelio R Paula11/2012
9997(3^100895+7)/2432177503448129Lelio R Paula03/2012
9998(15185*2^159869-1)/182748127Lelio R Paula03/2015
99993*7^56945+848125Lelio R Paula09/2014
10000(749655^8192+1)/13107448122Lelio R Paula12/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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