PRP Records

Probable Primes Top 10000

(180278 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 ?
775110103^14577-11458373Enzo Doria07/2012
7752(22699*2^193883+1)/2158368Lelio R Paula06/2014
7753(31*2^193886+1)/14076558362Lelio R Paula07/2012
775411^56041-156058361Enzo Doria11/2012
7755(2^193881+9)/1769958360Lelio R Paula02/2012
77563^122313+5858359Lelio R Paula10/2012
77576^74996-11958359Lelio R Paula10/2012
7758(11*2^193859+1)/1358358Lelio R Paula07/2012
77592^193861-11225558358Enzo Doria06/2014
7760(22699*2^193854+1)/492758357Lelio R Paula06/2014
776118^46487+3758354Lelio R Paula03/2013
776217^47419+5458347Lelio R Paula03/2013
7763(31*2^193791+1)/358338Lelio R Paula02/2012
7764(27*2^193805-1)/98224958337Lelio R Paula01/2014
77653^122219-2^12221958314Mike Oakes09/2003
7766(199*10^58306+11)/358308Robert Price05/2017
77672^193674-1882558302Lelio R Paula05/2011
77685*10^58275+358276Dmitry Domanov11/2010
77692^193578-11291358273Enzo Doria06/2014
77702^193541+129958262Lelio R Paula05/2011
777110^58250+9358251Robert Price01/2011
777210^58250-17560758250Patrick De Geest12/2012
77732^193492+841558247Lelio R Paula10/2012
77742^193444+15758233Lelio R Paula04/2011
7775Phi(28754,28754)58231Henri Lifchitz08/2013
77762^193430-11188158229Enzo Doria05/2014
777710^58225+12457958226Patrick De Geest12/2012
777810^58225-9358225Robert Price05/2011
77792^193375-29558212Yves Minet05/2013
77802^193345+7726758203Enzo Doria05/2016
778121^44017-20^4401758201Robert Price05/2012
7782(17*2^193329-1)/958199Lelio R Paula01/2014
778317^47291+2058190Lelio R Paula03/2013
7784p(12528)#/2-12858170Robert Price05/2017
77852^193214-13558164Lelio R Paula04/2011
778619^45483-8058162Lelio R Paula03/2013
7787(4*10^58155+83)/358156Robert Price01/2017
778814^50739-1358154Lelio R Paula03/2013
7789(1017*2^193184-1)/482358154Lelio R Paula04/2015
7790(2*10^58151+457)/958151Robert Price01/2017
7791(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
7792(19*2^193114-1)/118675558129Lelio R Paula01/2014
77942^193091-123758127Yves Minet08/2012
77939*7^68780-258127Lelio R Paula09/2014
77952^193083-86968810558124Lelio R Paula10/2012
77962^193058-4558117Lelio R Paula04/2011
7797(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
779811^55795-4258105Lelio R Paula03/2013
77993^121779-1658104Lelio R Paula10/2012
7800(13*10^58103+191)/358104Robert Price08/2017
78012^192986+19558095Lelio R Paula04/2011
78027^68740+2*3^6874058093Mike Oakes07/2010
7803(85*10^58091-1)/358093Robert Price07/2017
780412^53821+1158083Lelio R Paula02/2013
7805119^27979-11858072Norbert Schneider10/2013
7806(10223*2^192828+1)/24358049Lelio R Paula05/2014
78072^192808-112758041Yves Minet05/2013
7808(27*2^192803+1)/982758037Lelio R Paula07/2012
7809(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
78102^192678+7294358002Enzo Doria04/2016
7811(13*10^57997-37)/357998Robert Price08/2017
78122^192657-318957996Yves Minet10/2014
78136^74525-14957992Lelio R Paula10/2012
781442^35723-4157988Norbert Schneider06/2014
7815(29*2^192625-1)/18357986Lelio R Paula01/2014
7816(3^121520-8)/384757977Lelio R Paula03/2012
7817(2^192596-5)/13957976Lelio R Paula02/2012
781810^57975+6783357976Patrick De Geest09/2013
781910^57975-4769357975Patrick De Geest09/2013
7820(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
7821(3^121492-5)/457966Lelio R Paula03/2012
78222^192549+3557964Lelio R Paula04/2011
782328799!2+257962Robert Price10/2012
7824(7*2^192534-1)/134757957Lelio R Paula01/2014
78257001^15069-10057943Enzo Doria07/2012
7826L(277273)/1109092157940Donovan Johnson11/2005
7827(2^192469-1017)/3557938Lelio R Paula02/2012
78282^192457-1155*19245757936Henri Lifchitz02/2005
78292^192443+138557932Lelio R Paula05/2011
7830132^27317-13157928Norbert Schneider03/2015
783141522!3-5904957912Robert Price12/2015
7832(3*2^192380-1)/16957911Lelio R Paula01/2014
78332^192339-251557900Yves Minet07/2014
78342^192303+769557889Lelio R Paula10/2012
78352^192273-595557880Lelio R Paula05/2011
78362^192257+1609557876Lelio R Paula05/2011
78372^192218-11186157864Enzo Doria05/2014
78382^192214-394157863Yves Minet04/2017
7839(2^192212+3)/25957860Lelio R Paula02/2012
7840(3^121270+8)/15593975357853Lelio R Paula03/2012
784180^30393-7957841Norbert Schneider03/2015
784220^44455-312357838Enzo Doria03/2013
78432^192122-19557835Lelio R Paula04/2011
7844(29*10^57834+91)/357835Robert Price03/2016
78458*6^74306+557823Lelio R Paula09/2014
7846(39^36341-1)/3857820Robert Price04/2012
78472^192037-11180557809Enzo Doria05/2014
78482^192023-192023^257805Henri Lifchitz05/2005
784921^43717+257804Ray Chandler08/2011
78508*5^82687+757797Lelio R Paula09/2014
78515^82680-2457791Lelio R Paula10/2012
7852(2^191915+47)/9557771Lelio R Paula02/2012
78536^74227-9557760Lelio R Paula10/2012
78542^191861+2983557756Lelio R Paula10/2012
78551908^17605+17605^190857755Serge Batalov05/2014
78565*10^57754+5957755Robert Price09/2016
7857(5*2^191821-1)/892406757738Lelio R Paula01/2014
78583*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
785941399!3-656157723Robert Price11/2015
78602^191745+1757721Lelio R Paula04/2011
78612^191730-76157717Yves Minet01/2012
7862(2^191733-3)/225157715Lelio R Paula02/2012
78632^191698-11157707Lelio R Paula04/2011
7864(13*10^57691+23)/957692Robert Price02/2015
786520^44340-542357688Enzo Doria03/2013
7866(27*2^191629+1)/12557686Lelio R Paula07/2012
78674*10^57684+3*7^5768457685Mike Oakes11/2010
78682*3^120898+557684Lelio R Paula04/2014
7869(6883*2^191610-1)/734757681Lelio R Paula04/2015
78706^74117-4957675Lelio R Paula10/2012
78712^191586-11320157674Enzo Doria07/2014
78722^191580+19357672Lelio R Paula04/2011
7873(103*29^39433+10401)/457669Curtis Bright05/2015
78742^191560+25525557666Lelio R Paula05/2011
78752^191515-8557652Lelio R Paula04/2011
78762^191502-112757648Yves Minet05/2013
78772*5^82473-3^8247357647Mike Oakes08/2010
78782^191430+10357627Lelio R Paula04/2011
78793*2^191408+557621Lelio R Paula03/2014
78802^191382-185893157612Enzo Doria04/2016
78816*7^68163+557606Lelio R Paula09/2014
788291^29403-257602Lelio R Paula08/2013
788311^55308-795057598Enzo Doria02/2013
78842^191329+6557596Lelio R Paula04/2011
788511^55302-24057592Enzo Doria07/2012
78862^191299-103146757587Paul Bourdelais11/2012
78872^191295-11199157586Enzo Doria05/2014
78882^191279-129757581Yves Minet08/2012
78893*6^73961+557554Lelio R Paula09/2014
7890(3^120623+5)/5214457548Lelio R Paula04/2012
789142^35445-4157537Norbert Schneider06/2014
78922^191069-72340357518Paul Bourdelais11/2012
78934*10^57506-357507Serge Batalov11/2010
789410^57501+6735957502Patrick De Geest06/2016
789510^57501-100000000157501Robert Price05/2016
789610^57501-24986157501Patrick De Geest06/2016
7897(9^60251+4^60251)/1357493Robert Price02/2013
789820^44184-600357485Enzo Doria03/2013
78992^190948+1270557482Lelio R Paula10/2012
79002^190945+2957481Henri Lifchitz06/2005
79012^190922-40157474Yves Minet01/2012
790215^48860+4657464Lelio R Paula02/2013
79033^120434+2057462Lelio R Paula10/2012
79047^67964-3857437Lelio R Paula10/2012
79052^190799-11306557437Enzo Doria07/2014
79069*5^82159+257428Lelio R Paula09/2014
7907(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
7910lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
7908(103*10^57414-1)/357416Serge Batalov12/2014
7909(1654*30^38869-1)/2957416Karsten Bonath05/2017
79112*10^57410+9^5741057411Mike Oakes04/2011
79122^190704-159557408Lelio R Paula05/2011
791311^55121-174057403Enzo Doria11/2012
79142^190644-18557390Lelio R Paula04/2011
791541182!3-3^4118257389Robert Price08/2015
79162^190629-11225557386Enzo Doria06/2014
7917(2*10^57384-71)/357384Robert Price01/2017
79192*6^73735+5^7373557378Mike Oakes11/2009
79182^190605+5957378Lelio R Paula04/2011
79206^73727-757371Lelio R Paula10/2012
79212^190561-11222557365Enzo Doria06/2014
792210^57358+17089957359Patrick De Geest06/2016
792310^57358-800157358Robert Price03/2016
792418^45687-1157350Lelio R Paula02/2013
792511^55069-21057349Enzo Doria07/2012
792611^55068-1257348Lelio R Paula02/2013
792719^44839+5457339Lelio R Paula02/2013
7929(7*2^190468-1)/851157334Lelio R Paula01/2014
7928(23*10^57333-59)/957334Robert Price03/2017
79302^190455-1155*19045557333Henri Lifchitz02/2005
793165^31620+2857325Lelio R Paula01/2016
79322^190403+1609557318Lelio R Paula05/2011
7933(19*10^57316+119)/357317Robert Price02/2017
7935(21*2^190393+1)/21157314Lelio R Paula07/2012
79342^190392-11202557314Enzo Doria05/2014
7936(24737*2^190234+1)/957270Lelio R Paula05/2014
7937(7*2^190230+1)/2357265Lelio R Paula07/2012
7938(10223*2^190197+1)/321157256Lelio R Paula05/2014
793918^45590-9757228Lelio R Paula02/2013
7940(3*2^190105-1)/1920557224Lelio R Paula01/2014
7941(16*10^57219-31)/357220Robert Price03/2016
7942(2^190074+47)/5157217Lelio R Paula02/2012
79433^119894-14057204Lelio R Paula10/2012
7945(37^36473-1)/3657196Robert Price03/2012
79442^190000-216357196Yves Minet08/2013
79462^189987-279810757192Enzo Doria04/2016
79472^189935-11211757177Enzo Doria05/2014
79482^189909-11223157169Enzo Doria06/2014
7949132049#+14905357161Makoto Morimoto12/2015
795041032!3-2757158Robert Price09/2014
795119^44694+2257153Lelio R Paula02/2013
795212^52956-1757150Lelio R Paula02/2013
79532^189823-96757143Yves Minet01/2012
7954(25*10^57138-61)/957139Robert Price02/2015
79555^81743-4^(81743+1)57136Robert Price04/2016
79567^67593-5457123Lelio R Paula10/2012
79577*3^119712+257118Lelio R Paula03/2014
79595^81700+1657106Lelio R Paula10/2012
79582^189700+7656157106Enzo Doria05/2016
79612^189671+13157097Lelio R Paula04/2011
79604*6^73374+557097Lelio R Paula09/2014
7962(67607*2^189651+1)/4372757091Lelio R Paula05/2014
7963(29*2^189619-1)/39357080Lelio R Paula01/2014
79643^119587+8057058Lelio R Paula10/2012
79652^189502-11345357046Enzo Doria07/2014
79662^189455+15357032Lelio R Paula04/2011
796724^41317-41317^2457027Norbert Schneider07/2016
79682^189414-1757020Lelio R Paula03/2011
796924^41311+2357018Norbert Schneider12/2013
7970(4*10^56989-31)/956989Erik Branger05/2011
797111^54712-162056977Enzo Doria11/2012
79722^189237-11223156967Enzo Doria06/2014
797317^46285-4856952Lelio R Paula02/2013
79742^189188+7524156952Enzo Doria04/2016
79752^189181+9439556950Henri Lifchitz01/2005
79767001^14808-10856940Enzo Doria07/2012
79772^189147-11263956939Enzo Doria06/2014
79782^189110-356928M. Frind & P. Underwood11/2002
79792^189069+1290956916Lelio R Paula04/2011
7980(13*10^56909+191)/356910Robert Price08/2017
7981(35*10^56898-17)/956899Serge Batalov02/2009
79822^189011-595556898Lelio R Paula04/2011
79836^73119-556898Lelio R Paula10/2012
798413^51076-9056896Lelio R Paula02/2013
79852^188997+5689756894Yves Minet02/2010
79865^81388-1376656888Enzo Doria02/2013
798720^43713-640356872Enzo Doria03/2013
7988(71*10^56858-287)/956859Robert Price05/2017
79892^188857-25423356852Gary Barnes09/2009
799015^48338-8856850Lelio R Paula02/2013
799110^56849+13643756850Patrick De Geest07/2017
799210^56849-70156849Robert Price06/2017
7993(2^188788+78557)/356831Lelio R Paula05/2012
79942^188771+1609556826Lelio R Paula04/2011
79957*2^188742-956818Lelio R Paula03/2014
799612^52646-6556815Lelio R Paula02/2013
79975003^15358-15856813Enzo Doria07/2012
79982^188713+57729457556809Lelio R Paula03/2013
79992^188693-11209956803Enzo Doria05/2014
8000(7^67211+4^67211)/1156799Robert Price10/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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