PRP Records

Probable Primes Top 10000

(172751 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 ?
75012^195385-11158817Lelio R Paula04/2011
7502(47*2^195254+1)/26882158774Lelio R Paula03/2015
75032^195207-1810958764Enzo Doria05/2013
75042^195199-156758761Yves Minet08/2012
75052^195190+7375958759Enzo Doria04/2016
75069*7^69525-458757Lelio R Paula09/2014
75072^195170-1804558753Enzo Doria05/2013
75082^195166-16558751Lelio R Paula04/2011
7509(22699*2^195140+1)/17558746Lelio R Paula05/2014
75107*3^123109-258739Lelio R Paula04/2014
751118^46790+7758735Lelio R Paula03/2013
75132^195095-33729758730Gary Barnes09/2009
7512(14*10^58729+31)/958730Robert Price02/2015
751499^29424+9858720Norbert Schneider07/2013
7515(15185*2^195039-1)/21958715Lelio R Paula04/2015
75162^195001-6958702Lelio R Paula04/2011
75172^194978-48781158695Gary Barnes09/2009
7518163^26530+26530^16358690Serge Batalov05/2014
75192^194940-194940+158683Robert Price10/2014
7520(76*10^58669+41)/958670Robert Price10/2015
752114^51186+8758666Lelio R Paula03/2013
75222^194878-9730558665Lelio R Paula09/2011
75235^83927-1813658663Enzo Doria05/2014
7524(24737*2^194865+1)/108558662Lelio R Paula06/2014
75257^69411+4058660Lelio R Paula10/2012
75266^75382-7958659Lelio R Paula10/2012
75272^194854+2758657Lelio R Paula04/2011
75282^194801+2983558641Lelio R Paula10/2012
75292^194752+19558627Lelio R Paula04/2011
75307^69371-6^6937158626Predrag Minovic08/2004
75312^194747-11251958625Enzo Doria06/2014
7532(15*2^194737+1)/5958622Lelio R Paula07/2012
7533(23*2^194700+1)/358612Lelio R Paula02/2012
75345^83836+7658599Lelio R Paula10/2012
753518^46664+3158577Lelio R Paula03/2013
7536(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
75372^194574+16558573Lelio R Paula04/2011
75382^194569-1221158572Enzo Doria06/2014
753910^58571+5^58571+2^5857158572Robert Price12/2016
754010^58571+20283758572Patrick De Geest02/2017
7541(10^58571+41)/358571Robert Price01/2017
754210^58571-34362958571Patrick De Geest02/2017
754311^56235-795058563Enzo Doria02/2013
75442^194479-11323958545Enzo Doria07/2014
75452^194455-11224958537Enzo Doria06/2014
75462^194405-11191958522Enzo Doria05/2014
7548(7^69247-4^69247)/358521Robert Price06/2012
75475*7^69246+858521Lelio R Paula09/2014
75492^194358-116758508Lelio R Paula05/2011
7550(2^194366+7)/137358507Lelio R Paula02/2012
7551(493*10^58486-7)/958488Robert Price07/2016
75523^122579-34058486Lelio R Paula10/2012
7553(11*10^58458-149)/358459Robert Price01/2017
7554(47*10^58456+133)/958457Robert Price04/2017
75552^194186+8558456Lelio R Paula04/2011
75563^122506-2^(122506-1)58451Robert Price01/2016
755715^49690-2658440Lelio R Paula03/2013
755810^58437+11072158438Patrick De Geest12/2012
755910^58437-1158437Robert Price05/2011
75602^194095+6958429Lelio R Paula04/2011
7561(29*10^58417-77)/358418Robert Price01/2017
75622^194034+17758411Lelio R Paula04/2011
7563789^20158+20158^78958400Norbert Schneider06/2016
756414^50949+7558395Lelio R Paula03/2013
75652^193974-11476158392Enzo Doria05/2015
75662^193965+558390Henri Lifchitz12/2002
7567(5*10^58384-29)/358385Robert Price02/2017
75683^122360+8058381Lelio R Paula10/2012
756910103^14577-11458373Enzo Doria07/2012
7570(22699*2^193883+1)/2158368Lelio R Paula06/2014
7571(31*2^193886+1)/14076558362Lelio R Paula07/2012
757211^56041-156058361Enzo Doria11/2012
7573(2^193881+9)/1769958360Lelio R Paula02/2012
75743^122313+5858359Lelio R Paula10/2012
75756^74996-11958359Lelio R Paula10/2012
7576(11*2^193859+1)/1358358Lelio R Paula07/2012
75772^193861-11225558358Enzo Doria06/2014
7578(22699*2^193854+1)/492758357Lelio R Paula06/2014
757918^46487+3758354Lelio R Paula03/2013
758017^47419+5458347Lelio R Paula03/2013
7581(31*2^193791+1)/358338Lelio R Paula02/2012
7582(27*2^193805-1)/98224958337Lelio R Paula01/2014
75833^122219-2^12221958314Mike Oakes09/2003
75842^193674-1882558302Lelio R Paula05/2011
75855*10^58275+358276Dmitry Domanov11/2010
75862^193578-11291358273Enzo Doria06/2014
75872^193541+129958262Lelio R Paula05/2011
758810^58250+9358251Robert Price01/2011
758910^58250-17560758250Patrick De Geest12/2012
75902^193492+841558247Lelio R Paula10/2012
75912^193444+15758233Lelio R Paula04/2011
7592Phi(28754,28754)58231Henri Lifchitz08/2013
75932^193430-11188158229Enzo Doria05/2014
759410^58225+12457958226Patrick De Geest12/2012
759510^58225-9358225Robert Price05/2011
75962^193375-29558212Yves Minet05/2013
75972^193345+7726758203Enzo Doria05/2016
759821^44017-20^4401758201Robert Price05/2012
7599(17*2^193329-1)/958199Lelio R Paula01/2014
760017^47291+2058190Lelio R Paula03/2013
76012^193214-13558164Lelio R Paula04/2011
760219^45483-8058162Lelio R Paula03/2013
7603(4*10^58155+83)/358156Robert Price01/2017
760414^50739-1358154Lelio R Paula03/2013
7605(1017*2^193184-1)/482358154Lelio R Paula04/2015
7606(2*10^58151+457)/958151Robert Price01/2017
7607(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
7608(19*2^193114-1)/118675558129Lelio R Paula01/2014
76102^193091-123758127Yves Minet08/2012
76099*7^68780-258127Lelio R Paula09/2014
76112^193083-86968810558124Lelio R Paula10/2012
76122^193058-4558117Lelio R Paula04/2011
7613(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
761411^55795-4258105Lelio R Paula03/2013
76153^121779-1658104Lelio R Paula10/2012
76162^192986+19558095Lelio R Paula04/2011
76177^68740+2*3^6874058093Mike Oakes07/2010
761812^53821+1158083Lelio R Paula02/2013
7619119^27979-11858072Norbert Schneider10/2013
7620(10223*2^192828+1)/24358049Lelio R Paula05/2014
76212^192808-112758041Yves Minet05/2013
7622(27*2^192803+1)/982758037Lelio R Paula07/2012
7623(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
76242^192678+7294358002Enzo Doria04/2016
76252^192657-318957996Yves Minet10/2014
76266^74525-14957992Lelio R Paula10/2012
762742^35723-4157988Norbert Schneider06/2014
7628(29*2^192625-1)/18357986Lelio R Paula01/2014
7629(3^121520-8)/384757977Lelio R Paula03/2012
7630(2^192596-5)/13957976Lelio R Paula02/2012
763110^57975+6783357976Patrick De Geest09/2013
763210^57975-4769357975Patrick De Geest09/2013
7633(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
7634(3^121492-5)/457966Lelio R Paula03/2012
76352^192549+3557964Lelio R Paula04/2011
763628799!2+257962Robert Price10/2012
7637(7*2^192534-1)/134757957Lelio R Paula01/2014
76387001^15069-10057943Enzo Doria07/2012
7639L(277273)/1109092157940Donovan Johnson11/2005
7640(2^192469-1017)/3557938Lelio R Paula02/2012
76412^192457-1155*19245757936Henri Lifchitz02/2005
76422^192443+138557932Lelio R Paula05/2011
7643132^27317-13157928Norbert Schneider03/2015
764441522!3-5904957912Robert Price12/2015
7645(3*2^192380-1)/16957911Lelio R Paula01/2014
76462^192339-251557900Yves Minet07/2014
76472^192303+769557889Lelio R Paula10/2012
76482^192273-595557880Lelio R Paula05/2011
76492^192257+1609557876Lelio R Paula05/2011
76502^192218-11186157864Enzo Doria05/2014
7651(2^192212+3)/25957860Lelio R Paula02/2012
7652(3^121270+8)/15593975357853Lelio R Paula03/2012
765380^30393-7957841Norbert Schneider03/2015
765420^44455-312357838Enzo Doria03/2013
76552^192122-19557835Lelio R Paula04/2011
7656(29*10^57834+91)/357835Robert Price03/2016
76578*6^74306+557823Lelio R Paula09/2014
7658(39^36341-1)/3857820Robert Price04/2012
76592^192037-11180557809Enzo Doria05/2014
76602^192023-192023^257805Henri Lifchitz05/2005
766121^43717+257804Ray Chandler08/2011
76628*5^82687+757797Lelio R Paula09/2014
76635^82680-2457791Lelio R Paula10/2012
7664(2^191915+47)/9557771Lelio R Paula02/2012
76656^74227-9557760Lelio R Paula10/2012
76662^191861+2983557756Lelio R Paula10/2012
76671908^17605+17605^190857755Serge Batalov05/2014
76685*10^57754+5957755Robert Price09/2016
7669(5*2^191821-1)/892406757738Lelio R Paula01/2014
76703*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
767141399!3-656157723Robert Price11/2015
76722^191745+1757721Lelio R Paula04/2011
76732^191730-76157717Yves Minet01/2012
7674(2^191733-3)/225157715Lelio R Paula02/2012
76752^191698-11157707Lelio R Paula04/2011
7676(13*10^57691+23)/957692Robert Price02/2015
767720^44340-542357688Enzo Doria03/2013
7678(27*2^191629+1)/12557686Lelio R Paula07/2012
76794*10^57684+3*7^5768457685Mike Oakes11/2010
76802*3^120898+557684Lelio R Paula04/2014
7681(6883*2^191610-1)/734757681Lelio R Paula04/2015
76826^74117-4957675Lelio R Paula10/2012
76832^191586-11320157674Enzo Doria07/2014
76842^191580+19357672Lelio R Paula04/2011
7685(103*29^39433+10401)/457669Curtis Bright05/2015
76862^191560+25525557666Lelio R Paula05/2011
76872^191515-8557652Lelio R Paula04/2011
76882^191502-112757648Yves Minet05/2013
76892*5^82473-3^8247357647Mike Oakes08/2010
76902^191430+10357627Lelio R Paula04/2011
76913*2^191408+557621Lelio R Paula03/2014
76922^191382-185893157612Enzo Doria04/2016
76936*7^68163+557606Lelio R Paula09/2014
769491^29403-257602Lelio R Paula08/2013
769511^55308-795057598Enzo Doria02/2013
76962^191329+6557596Lelio R Paula04/2011
769711^55302-24057592Enzo Doria07/2012
76982^191299-103146757587Paul Bourdelais11/2012
76992^191295-11199157586Enzo Doria05/2014
77002^191279-129757581Yves Minet08/2012
77013*6^73961+557554Lelio R Paula09/2014
7702(3^120623+5)/5214457548Lelio R Paula04/2012
770342^35445-4157537Norbert Schneider06/2014
77042^191069-72340357518Paul Bourdelais11/2012
77054*10^57506-357507Serge Batalov11/2010
770610^57501+6735957502Patrick De Geest06/2016
770710^57501-100000000157501Robert Price05/2016
770810^57501-24986157501Patrick De Geest06/2016
7709(9^60251+4^60251)/1357493Robert Price02/2013
771020^44184-600357485Enzo Doria03/2013
77112^190948+1270557482Lelio R Paula10/2012
77122^190945+2957481Henri Lifchitz06/2005
77132^190922-40157474Yves Minet01/2012
771415^48860+4657464Lelio R Paula02/2013
77153^120434+2057462Lelio R Paula10/2012
77167^67964-3857437Lelio R Paula10/2012
77172^190799-11306557437Enzo Doria07/2014
77189*5^82159+257428Lelio R Paula09/2014
7719(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
7721lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
7720(103*10^57414-1)/357416Serge Batalov12/2014
77222*10^57410+9^5741057411Mike Oakes04/2011
77232^190704-159557408Lelio R Paula05/2011
772411^55121-174057403Enzo Doria11/2012
77252^190644-18557390Lelio R Paula04/2011
772641182!3-3^4118257389Robert Price08/2015
77272^190629-11225557386Enzo Doria06/2014
7728(2*10^57384-71)/357384Robert Price01/2017
77292*6^73735+5^7373557378Mike Oakes11/2009
77302^190605+5957378Lelio R Paula04/2011
77316^73727-757371Lelio R Paula10/2012
77322^190561-11222557365Enzo Doria06/2014
773310^57358+17089957359Patrick De Geest06/2016
773410^57358-800157358Robert Price03/2016
773518^45687-1157350Lelio R Paula02/2013
773611^55069-21057349Enzo Doria07/2012
773711^55068-1257348Lelio R Paula02/2013
773819^44839+5457339Lelio R Paula02/2013
7740(7*2^190468-1)/851157334Lelio R Paula01/2014
7739(23*10^57333-59)/957334Robert Price03/2017
77412^190455-1155*19045557333Henri Lifchitz02/2005
774265^31620+2857325Lelio R Paula01/2016
77432^190403+1609557318Lelio R Paula05/2011
7744(19*10^57316+119)/357317Robert Price02/2017
7746(21*2^190393+1)/21157314Lelio R Paula07/2012
77452^190392-11202557314Enzo Doria05/2014
7747(24737*2^190234+1)/957270Lelio R Paula05/2014
7748(7*2^190230+1)/2357265Lelio R Paula07/2012
7749(10223*2^190197+1)/321157256Lelio R Paula05/2014
775018^45590-9757228Lelio R Paula02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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