PRP Records

Probable Primes Top 10000

(247113 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 ?
8751(19*2^193114-1)/118675558129Lelio R Paula01/2014
87532^193091-123758127Yves Minet08/2012
87529*7^68780-258127Lelio R Paula09/2014
87542473^17130+17130^247358126Norbert Schneider10/2018
87552^193083-86968810558124Lelio R Paula10/2012
87562^193058-4558117Lelio R Paula04/2011
8757(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
875811^55795-4258105Lelio R Paula03/2013
87593^121779-1658104Lelio R Paula10/2012
8760(13*10^58103+191)/358104Robert Price08/2017
87612^192986+19558095Lelio R Paula04/2011
87627^68740+2*3^6874058093Mike Oakes07/2010
8763(85*10^58091-1)/358093Robert Price07/2017
8764(404*10^58087-53)/958089Robert Price11/2017
876512^53821+1158083Lelio R Paula02/2013
8766119^27979-11858072Norbert Schneider10/2013
8767(10223*2^192828+1)/24358049Lelio R Paula05/2014
87682^192808-112758041Yves Minet05/2013
8769(27*2^192803+1)/982758037Lelio R Paula07/2012
8771(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
87703*10^58032-2358033Robert Price11/2017
87722^192678+7294358002Enzo Doria04/2016
8773(13*10^57997-37)/357998Robert Price08/2017
87742^192657-318957996Yves Minet10/2014
87756^74525-14957992Lelio R Paula10/2012
877642^35723-4157988Norbert Schneider06/2014
8777(29*2^192625-1)/18357986Lelio R Paula01/2014
8778(3^121520-8)/384757977Lelio R Paula03/2012
8779(2^192596-5)/13957976Lelio R Paula02/2012
878010^57975+6783357976Patrick De Geest09/2013
878110^57975-4769357975Patrick De Geest09/2013
8782(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
8783(29*10^57967+673)/957968Robert Price10/2017
8784(3^121492-5)/457966Lelio R Paula03/2012
87852^192549+3557964Lelio R Paula04/2011
878628799!2+257962Robert Price10/2012
8787(7*2^192534-1)/134757957Lelio R Paula01/2014
87887001^15069-10057943Enzo Doria07/2012
8789L(277273)/1109092157940Donovan Johnson11/2005
8790(2^192469-1017)/3557938Lelio R Paula02/2012
87912^192457-1155*19245757936Henri Lifchitz02/2005
87922^192443+138557932Lelio R Paula05/2011
8793132^27317-13157928Norbert Schneider03/2015
879441522!3-5904957912Robert Price12/2015
8795(3*2^192380-1)/16957911Lelio R Paula01/2014
87962^192339-251557900Yves Minet07/2014
87972^192303+769557889Lelio R Paula10/2012
87982^192273-595557880Lelio R Paula05/2011
87992^192257+1609557876Lelio R Paula05/2011
8800109^28401-257865Lelio R Paula10/2017
88012^192218-11186157864Enzo Doria05/2014
88022^192214-394157863Yves Minet04/2017
8803(2^192212+3)/25957860Lelio R Paula02/2012
8804(3^121270+8)/15593975357853Lelio R Paula03/2012
880580^30393-7957841Norbert Schneider03/2015
880620^44455-312357838Enzo Doria03/2013
88082^192122-19557835Lelio R Paula04/2011
8807(29*10^57834+91)/357835Robert Price03/2016
88098*6^74306+557823Lelio R Paula09/2014
8810(39^36341-1)/3857820Robert Price04/2012
88112^192037-11180557809Enzo Doria05/2014
88122^192023-192023^257805Henri Lifchitz05/2005
881321^43717+257804Ray Chandler08/2011
88148*5^82687+757797Lelio R Paula09/2014
88155^82680-2457791Lelio R Paula10/2012
8816(2^191915+47)/9557771Lelio R Paula02/2012
8817(74*10^57763+133)/957764Robert Price10/2017
88186^74227-9557760Lelio R Paula10/2012
88192^191861+2983557756Lelio R Paula10/2012
88211908^17605+17605^190857755Serge Batalov05/2014
88205*10^57754+5957755Robert Price09/2016
8822(5*2^191821-1)/892406757738Lelio R Paula01/2014
88233*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
882441399!3-656157723Robert Price11/2015
8825(44*10^57721-233)/957722Robert Price10/2017
88262^191745+1757721Lelio R Paula04/2011
88272^191730-76157717Yves Minet01/2012
8828(2^191733-3)/225157715Lelio R Paula02/2012
88292^191698-11157707Lelio R Paula04/2011
8830(13*10^57691+23)/957692Robert Price02/2015
883120^44340-542357688Enzo Doria03/2013
8832(27*2^191629+1)/12557686Lelio R Paula07/2012
88334*10^57684+3*7^5768457685Mike Oakes11/2010
88342*3^120898+557684Lelio R Paula04/2014
8835(6883*2^191610-1)/734757681Lelio R Paula04/2015
88366^74117-4957675Lelio R Paula10/2012
88372^191586-11320157674Enzo Doria07/2014
88382^191580+19357672Lelio R Paula04/2011
8839(103*29^39433+10401)/457669Curtis Bright05/2015
88402^191560+25525557666Lelio R Paula05/2011
88412^191515-8557652Lelio R Paula04/2011
88422^191502-112757648Yves Minet05/2013
88432*5^82473-3^8247357647Mike Oakes08/2010
8844(13*10^57634-61)/357635Robert Price08/2017
884585^29868-29868^8557628Norbert Schneider11/2017
88462^191430+10357627Lelio R Paula04/2011
88473*2^191408+557621Lelio R Paula03/2014
88482^191382-185893157612Enzo Doria04/2016
88496*7^68163+557606Lelio R Paula09/2014
885091^29403-257602Lelio R Paula08/2013
885111^55308-795057598Enzo Doria02/2013
88522^191329+6557596Lelio R Paula04/2011
885311^55302-24057592Enzo Doria07/2012
88542^191299-103146757587Paul Bourdelais11/2012
88552^191295-11199157586Enzo Doria05/2014
88562^191279-129757581Yves Minet08/2012
88573*6^73961+557554Lelio R Paula09/2014
8858(3^120623+5)/5214457548Lelio R Paula04/2012
8859(17*10^57543-29)/357544Robert Price09/2017
886042^35445-4157537Norbert Schneider06/2014
8861(71^31079-1)/7057534Paul Bourdelais08/2017
88622^191069-72340357518Paul Bourdelais11/2012
88634*10^57506-357507Serge Batalov11/2010
886410^57501+6735957502Patrick De Geest06/2016
886510^57501-100000000157501Robert Price05/2016
886610^57501-24986157501Patrick De Geest06/2016
8867(9^60251+4^60251)/1357493Robert Price02/2013
886820^44184-600357485Enzo Doria03/2013
88692^190948+1270557482Lelio R Paula10/2012
88702^190945+2957481Henri Lifchitz06/2005
88712^190922-40157474Yves Minet01/2012
887215^48860+4657464Lelio R Paula02/2013
88733^120434+2057462Lelio R Paula10/2012
88747^67964-3857437Lelio R Paula10/2012
88752^190799-11306557437Enzo Doria07/2014
88769*5^82159+257428Lelio R Paula09/2014
8877(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8880lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8879(103*10^57414-1)/357416Serge Batalov12/2014
8878(1654*30^38869-1)/2957416Karsten Bonath05/2017
88812*10^57410+9^5741057411Mike Oakes04/2011
88822^190704-159557408Lelio R Paula05/2011
888311^55121-174057403Enzo Doria11/2012
88842^190644-18557390Lelio R Paula04/2011
888541182!3-3^4118257389Robert Price08/2015
88862^190629-11225557386Enzo Doria06/2014
8887(2*10^57384-71)/357384Robert Price01/2017
88882*6^73735+5^7373557378Mike Oakes11/2009
88892^190605+5957378Lelio R Paula04/2011
88906^73727-757371Lelio R Paula10/2012
88912^190561-11222557365Enzo Doria06/2014
889210^57358+17089957359Patrick De Geest06/2016
889310^57358-800157358Robert Price03/2016
889418^45687-1157350Lelio R Paula02/2013
889511^55069-21057349Enzo Doria07/2012
889611^55068-1257348Lelio R Paula02/2013
889719^44839+5457339Lelio R Paula02/2013
8898(7*2^190468-1)/851157334Lelio R Paula01/2014
8899(23*10^57333-59)/957334Robert Price03/2017
89002^190455-1155*19045557333Henri Lifchitz02/2005
890165^31620+2857325Lelio R Paula01/2016
89022^190403+1609557318Lelio R Paula05/2011
8903(19*10^57316+119)/357317Robert Price02/2017
8904(21*2^190393+1)/21157314Lelio R Paula07/2012
89062^190392-11202557314Enzo Doria05/2014
890513173^13912-13912^1317357314Norbert Schneider08/2018
8907(24737*2^190234+1)/957270Lelio R Paula05/2014
8908(7*2^190230+1)/2357265Lelio R Paula07/2012
8909(10223*2^190197+1)/321157256Lelio R Paula05/2014
891018^45590-9757228Lelio R Paula02/2013
8911(3*2^190105-1)/1920557224Lelio R Paula01/2014
8912(16*10^57219-31)/357220Robert Price03/2016
8913(2^190074+47)/5157217Lelio R Paula02/2012
89143^119894-14057204Lelio R Paula10/2012
8916(37^36473-1)/3657196Robert Price03/2012
89152^190000-216357196Yves Minet08/2013
89172^189987-279810757192Enzo Doria04/2016
89182^189935-11211757177Enzo Doria05/2014
89192^189909-11223157169Enzo Doria06/2014
8920132049#+14905357161Makoto Morimoto12/2015
892141032!3-2757158Robert Price09/2014
892219^44694+2257153Lelio R Paula02/2013
892312^52956-1757150Lelio R Paula02/2013
89242^189823-96757143Yves Minet01/2012
8925(25*10^57138-61)/957139Robert Price02/2015
89265^81743-4^(81743+1)57136Robert Price04/2016
89277^67593-5457123Lelio R Paula10/2012
89287*3^119712+257118Lelio R Paula03/2014
89305^81700+1657106Lelio R Paula10/2012
89292^189700+7656157106Enzo Doria05/2016
89322^189671+13157097Lelio R Paula04/2011
89314*6^73374+557097Lelio R Paula09/2014
8933(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8934(29*2^189619-1)/39357080Lelio R Paula01/2014
89353^119587+8057058Lelio R Paula10/2012
89362^189502-11345357046Enzo Doria07/2014
89372^189455+15357032Lelio R Paula04/2011
893824^41317-41317^2457027Norbert Schneider07/2016
89392^189414-1757020Lelio R Paula03/2011
894024^41311+2357018Norbert Schneider12/2013
8941norm(Mod(x,x^4+x^3-x+1)^207341-1)/256998Paul Vanderveen05/2018
8942(4*10^56989-31)/956989Erik Branger05/2011
894311^54712-162056977Enzo Doria11/2012
89442^189237-11223156967Enzo Doria06/2014
894517^46285-4856952Lelio R Paula02/2013
89462^189188+7524156952Enzo Doria04/2016
89472^189181+9439556950Henri Lifchitz01/2005
89487001^14808-10856940Enzo Doria07/2012
89492^189147-11263956939Enzo Doria06/2014
8950(19*10^56933-43)/356934Robert Price10/2017
89512^189110-356928M. Frind & P. Underwood11/2002
89522^189069+1290956916Lelio R Paula04/2011
8953(13*10^56909+191)/356910Robert Price08/2017
8954(35*10^56898-17)/956899Serge Batalov02/2009
89552^189011-595556898Lelio R Paula04/2011
89566^73119-556898Lelio R Paula10/2012
895713^51076-9056896Lelio R Paula02/2013
89582^188997+5689756894Yves Minet02/2010
89595^81388-1376656888Enzo Doria02/2013
8960(104^28201+1)/10556881Richard Fischer04/2018
8961(156^25933+1)/15756873Eric Chen12/2017
896220^43713-640356872Enzo Doria03/2013
8963(71*10^56858-287)/956859Robert Price05/2017
89642^188857-25423356852Gary Barnes09/2009
896515^48338-8856850Lelio R Paula02/2013
896610^56849+13643756850Patrick De Geest07/2017
896710^56849-70156849Robert Price06/2017
8968(2^188788+78557)/356831Lelio R Paula05/2012
89692^188771+1609556826Lelio R Paula04/2011
89707*2^188742-956818Lelio R Paula03/2014
897112^52646-6556815Lelio R Paula02/2013
89725003^15358-15856813Enzo Doria07/2012
89732^188713+57729457556809Lelio R Paula03/2013
89742^188693-11209956803Enzo Doria05/2014
8975(7^67211+4^67211)/1156799Robert Price10/2012
89762^188678-9439556798Lelio R Paula09/2011
897720^43651-850356792Enzo Doria03/2013
89792^188657-237156792Yves Minet10/2013
8978152^26029-151^2602956792Eric Chen04/2018
8980(14^49549+5^49549)/1956789Robert Price05/2013
8981(45^34351-1)/4456788Robert Price05/2014
89827*10^56785-2356786Robert Price04/2016
8983(10^56781-31)/356781Serge Batalov12/2014
89847*10^56779+356780Erik Branger11/2009
898512858^13817-13817^1285856777Norbert Schneider11/2018
898610^56765+25917956766Patrick De Geest09/2013
898710^56765-24949756765Patrick De Geest09/2013
8988t(188706)56764Robert Price04/2015
89892^188551-90432756760Paul Bourdelais11/2012
8991(64*10^56756+17)/956757Robert Price09/2015
8990131101#+14629156757Makoto Morimoto02/2016
89922^188539-11251956756Enzo Doria06/2014
89936^72927+10156749Lelio R Paula10/2012
899420^43617-160356748Enzo Doria03/2013
8995(3^118892-8)/9135892956718Lelio R Paula03/2012
899613339^13748-13748^1333956713Norbert Schneider09/2018
8997(509203*2^188338-1)/356701Lelio R Paula03/2015
899820^43567-562356682Enzo Doria03/2013
89992^188234-11318356665Enzo Doria07/2014
9000(139^26437+1)/14056653Richard Fischer03/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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