PRP Records

Probable Primes Top 10000

(218736 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 ?
8501(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
8502(19*2^193114-1)/118675558129Lelio R Paula01/2014
85042^193091-123758127Yves Minet08/2012
85039*7^68780-258127Lelio R Paula09/2014
85052^193083-86968810558124Lelio R Paula10/2012
85062^193058-4558117Lelio R Paula04/2011
8507(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
850811^55795-4258105Lelio R Paula03/2013
85093^121779-1658104Lelio R Paula10/2012
8510(13*10^58103+191)/358104Robert Price08/2017
85112^192986+19558095Lelio R Paula04/2011
85127^68740+2*3^6874058093Mike Oakes07/2010
8513(85*10^58091-1)/358093Robert Price07/2017
8514(404*10^58087-53)/958089Robert Price11/2017
851512^53821+1158083Lelio R Paula02/2013
8516119^27979-11858072Norbert Schneider10/2013
8517(10223*2^192828+1)/24358049Lelio R Paula05/2014
85182^192808-112758041Yves Minet05/2013
8519(27*2^192803+1)/982758037Lelio R Paula07/2012
8521(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
85203*10^58032-2358033Robert Price11/2017
85222^192678+7294358002Enzo Doria04/2016
8523(13*10^57997-37)/357998Robert Price08/2017
85242^192657-318957996Yves Minet10/2014
85256^74525-14957992Lelio R Paula10/2012
852642^35723-4157988Norbert Schneider06/2014
8527(29*2^192625-1)/18357986Lelio R Paula01/2014
8528(3^121520-8)/384757977Lelio R Paula03/2012
8529(2^192596-5)/13957976Lelio R Paula02/2012
853010^57975+6783357976Patrick De Geest09/2013
853110^57975-4769357975Patrick De Geest09/2013
8532(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
8533(29*10^57967+673)/957968Robert Price10/2017
8534(3^121492-5)/457966Lelio R Paula03/2012
85352^192549+3557964Lelio R Paula04/2011
853628799!2+257962Robert Price10/2012
8537(7*2^192534-1)/134757957Lelio R Paula01/2014
85387001^15069-10057943Enzo Doria07/2012
8539L(277273)/1109092157940Donovan Johnson11/2005
8540(2^192469-1017)/3557938Lelio R Paula02/2012
85412^192457-1155*19245757936Henri Lifchitz02/2005
85422^192443+138557932Lelio R Paula05/2011
8543132^27317-13157928Norbert Schneider03/2015
854441522!3-5904957912Robert Price12/2015
8545(3*2^192380-1)/16957911Lelio R Paula01/2014
85462^192339-251557900Yves Minet07/2014
85472^192303+769557889Lelio R Paula10/2012
85482^192273-595557880Lelio R Paula05/2011
85492^192257+1609557876Lelio R Paula05/2011
8550109^28401-257865Lelio R Paula10/2017
85512^192218-11186157864Enzo Doria05/2014
85522^192214-394157863Yves Minet04/2017
8553(2^192212+3)/25957860Lelio R Paula02/2012
8554(3^121270+8)/15593975357853Lelio R Paula03/2012
855580^30393-7957841Norbert Schneider03/2015
855620^44455-312357838Enzo Doria03/2013
85572^192122-19557835Lelio R Paula04/2011
8558(29*10^57834+91)/357835Robert Price03/2016
85598*6^74306+557823Lelio R Paula09/2014
8560(39^36341-1)/3857820Robert Price04/2012
85612^192037-11180557809Enzo Doria05/2014
85622^192023-192023^257805Henri Lifchitz05/2005
856321^43717+257804Ray Chandler08/2011
85648*5^82687+757797Lelio R Paula09/2014
85655^82680-2457791Lelio R Paula10/2012
8566(2^191915+47)/9557771Lelio R Paula02/2012
8567(74*10^57763+133)/957764Robert Price10/2017
85686^74227-9557760Lelio R Paula10/2012
85692^191861+2983557756Lelio R Paula10/2012
85701908^17605+17605^190857755Serge Batalov05/2014
85715*10^57754+5957755Robert Price09/2016
8572(5*2^191821-1)/892406757738Lelio R Paula01/2014
85733*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
857441399!3-656157723Robert Price11/2015
8575(44*10^57721-233)/957722Robert Price10/2017
85762^191745+1757721Lelio R Paula04/2011
85772^191730-76157717Yves Minet01/2012
8578(2^191733-3)/225157715Lelio R Paula02/2012
85792^191698-11157707Lelio R Paula04/2011
8580(13*10^57691+23)/957692Robert Price02/2015
858120^44340-542357688Enzo Doria03/2013
8582(27*2^191629+1)/12557686Lelio R Paula07/2012
85834*10^57684+3*7^5768457685Mike Oakes11/2010
85842*3^120898+557684Lelio R Paula04/2014
8585(6883*2^191610-1)/734757681Lelio R Paula04/2015
85866^74117-4957675Lelio R Paula10/2012
85872^191586-11320157674Enzo Doria07/2014
85882^191580+19357672Lelio R Paula04/2011
8589(103*29^39433+10401)/457669Curtis Bright05/2015
85902^191560+25525557666Lelio R Paula05/2011
85912^191515-8557652Lelio R Paula04/2011
85922^191502-112757648Yves Minet05/2013
85932*5^82473-3^8247357647Mike Oakes08/2010
8594(13*10^57634-61)/357635Robert Price08/2017
859585^29868-29868^8557628Norbert Schneider11/2017
85962^191430+10357627Lelio R Paula04/2011
85973*2^191408+557621Lelio R Paula03/2014
85982^191382-185893157612Enzo Doria04/2016
85996*7^68163+557606Lelio R Paula09/2014
860091^29403-257602Lelio R Paula08/2013
860111^55308-795057598Enzo Doria02/2013
86022^191329+6557596Lelio R Paula04/2011
860311^55302-24057592Enzo Doria07/2012
86042^191299-103146757587Paul Bourdelais11/2012
86052^191295-11199157586Enzo Doria05/2014
86062^191279-129757581Yves Minet08/2012
86073*6^73961+557554Lelio R Paula09/2014
8608(3^120623+5)/5214457548Lelio R Paula04/2012
8609(17*10^57543-29)/357544Robert Price09/2017
861042^35445-4157537Norbert Schneider06/2014
8611(71^31079-1)/7057534Paul Bourdelais08/2017
86122^191069-72340357518Paul Bourdelais11/2012
86134*10^57506-357507Serge Batalov11/2010
861410^57501+6735957502Patrick De Geest06/2016
861510^57501-100000000157501Robert Price05/2016
861610^57501-24986157501Patrick De Geest06/2016
8617(9^60251+4^60251)/1357493Robert Price02/2013
861820^44184-600357485Enzo Doria03/2013
86192^190948+1270557482Lelio R Paula10/2012
86202^190945+2957481Henri Lifchitz06/2005
86212^190922-40157474Yves Minet01/2012
862215^48860+4657464Lelio R Paula02/2013
86233^120434+2057462Lelio R Paula10/2012
86247^67964-3857437Lelio R Paula10/2012
86252^190799-11306557437Enzo Doria07/2014
86269*5^82159+257428Lelio R Paula09/2014
8627(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8630lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8628(103*10^57414-1)/357416Serge Batalov12/2014
8629(1654*30^38869-1)/2957416Karsten Bonath05/2017
86312*10^57410+9^5741057411Mike Oakes04/2011
86322^190704-159557408Lelio R Paula05/2011
863311^55121-174057403Enzo Doria11/2012
86342^190644-18557390Lelio R Paula04/2011
863541182!3-3^4118257389Robert Price08/2015
86362^190629-11225557386Enzo Doria06/2014
8637(2*10^57384-71)/357384Robert Price01/2017
86382*6^73735+5^7373557378Mike Oakes11/2009
86392^190605+5957378Lelio R Paula04/2011
86406^73727-757371Lelio R Paula10/2012
86412^190561-11222557365Enzo Doria06/2014
864210^57358+17089957359Patrick De Geest06/2016
864310^57358-800157358Robert Price03/2016
864418^45687-1157350Lelio R Paula02/2013
864511^55069-21057349Enzo Doria07/2012
864611^55068-1257348Lelio R Paula02/2013
864719^44839+5457339Lelio R Paula02/2013
8648(7*2^190468-1)/851157334Lelio R Paula01/2014
8649(23*10^57333-59)/957334Robert Price03/2017
86502^190455-1155*19045557333Henri Lifchitz02/2005
865165^31620+2857325Lelio R Paula01/2016
86522^190403+1609557318Lelio R Paula05/2011
8653(19*10^57316+119)/357317Robert Price02/2017
8655(21*2^190393+1)/21157314Lelio R Paula07/2012
86542^190392-11202557314Enzo Doria05/2014
8656(24737*2^190234+1)/957270Lelio R Paula05/2014
8657(7*2^190230+1)/2357265Lelio R Paula07/2012
8658(10223*2^190197+1)/321157256Lelio R Paula05/2014
865918^45590-9757228Lelio R Paula02/2013
8660(3*2^190105-1)/1920557224Lelio R Paula01/2014
8661(16*10^57219-31)/357220Robert Price03/2016
8662(2^190074+47)/5157217Lelio R Paula02/2012
86633^119894-14057204Lelio R Paula10/2012
8665(37^36473-1)/3657196Robert Price03/2012
86642^190000-216357196Yves Minet08/2013
86662^189987-279810757192Enzo Doria04/2016
86672^189935-11211757177Enzo Doria05/2014
86682^189909-11223157169Enzo Doria06/2014
8669132049#+14905357161Makoto Morimoto12/2015
867041032!3-2757158Robert Price09/2014
867119^44694+2257153Lelio R Paula02/2013
867212^52956-1757150Lelio R Paula02/2013
86732^189823-96757143Yves Minet01/2012
8674(25*10^57138-61)/957139Robert Price02/2015
86755^81743-4^(81743+1)57136Robert Price04/2016
86767^67593-5457123Lelio R Paula10/2012
86777*3^119712+257118Lelio R Paula03/2014
86785^81700+1657106Lelio R Paula10/2012
86792^189700+7656157106Enzo Doria05/2016
86812^189671+13157097Lelio R Paula04/2011
86804*6^73374+557097Lelio R Paula09/2014
8682(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8683(29*2^189619-1)/39357080Lelio R Paula01/2014
86843^119587+8057058Lelio R Paula10/2012
86852^189502-11345357046Enzo Doria07/2014
86862^189455+15357032Lelio R Paula04/2011
868724^41317-41317^2457027Norbert Schneider07/2016
86882^189414-1757020Lelio R Paula03/2011
868924^41311+2357018Norbert Schneider12/2013
8690norm(Mod(x,x^4+x^3-x+1)^207341-1)/256998Paul Vanderveen05/2018
8691(4*10^56989-31)/956989Erik Branger05/2011
869211^54712-162056977Enzo Doria11/2012
86932^189237-11223156967Enzo Doria06/2014
869417^46285-4856952Lelio R Paula02/2013
86952^189188+7524156952Enzo Doria04/2016
86962^189181+9439556950Henri Lifchitz01/2005
86977001^14808-10856940Enzo Doria07/2012
86982^189147-11263956939Enzo Doria06/2014
8699(19*10^56933-43)/356934Robert Price10/2017
87002^189110-356928M. Frind & P. Underwood11/2002
87012^189069+1290956916Lelio R Paula04/2011
8702(13*10^56909+191)/356910Robert Price08/2017
8703(35*10^56898-17)/956899Serge Batalov02/2009
87052^189011-595556898Lelio R Paula04/2011
87046^73119-556898Lelio R Paula10/2012
870613^51076-9056896Lelio R Paula02/2013
87072^188997+5689756894Yves Minet02/2010
87085^81388-1376656888Enzo Doria02/2013
8709(104^28201+1)/10556881Richard Fischer04/2018
8710(156^25933+1)/15756873Eric Chen12/2017
871120^43713-640356872Enzo Doria03/2013
8712(71*10^56858-287)/956859Robert Price05/2017
87132^188857-25423356852Gary Barnes09/2009
871415^48338-8856850Lelio R Paula02/2013
871510^56849+13643756850Patrick De Geest07/2017
871610^56849-70156849Robert Price06/2017
8717(2^188788+78557)/356831Lelio R Paula05/2012
87182^188771+1609556826Lelio R Paula04/2011
87197*2^188742-956818Lelio R Paula03/2014
872012^52646-6556815Lelio R Paula02/2013
87215003^15358-15856813Enzo Doria07/2012
87222^188713+57729457556809Lelio R Paula03/2013
87232^188693-11209956803Enzo Doria05/2014
8724(7^67211+4^67211)/1156799Robert Price10/2012
87252^188678-9439556798Lelio R Paula09/2011
872620^43651-850356792Enzo Doria03/2013
87282^188657-237156792Yves Minet10/2013
8727152^26029-151^2602956792Eric Chen04/2018
8729(14^49549+5^49549)/1956789Robert Price05/2013
8730(45^34351-1)/4456788Robert Price05/2014
87317*10^56785-2356786Robert Price04/2016
8732(10^56781-31)/356781Serge Batalov12/2014
87337*10^56779+356780Erik Branger11/2009
873410^56765+25917956766Patrick De Geest09/2013
873510^56765-24949756765Patrick De Geest09/2013
8736t(188706)56764Robert Price04/2015
87372^188551-90432756760Paul Bourdelais11/2012
8739(64*10^56756+17)/956757Robert Price09/2015
8738131101#+14629156757Makoto Morimoto02/2016
87402^188539-11251956756Enzo Doria06/2014
87416^72927+10156749Lelio R Paula10/2012
874220^43617-160356748Enzo Doria03/2013
8743(3^118892-8)/9135892956718Lelio R Paula03/2012
8744(509203*2^188338-1)/356701Lelio R Paula03/2015
874520^43567-562356682Enzo Doria03/2013
87462^188234-11318356665Enzo Doria07/2014
8747(139^26437+1)/14056653Richard Fischer03/2018
8748(7*2^188215-1)/149731512556651Lelio R Paula01/2014
8749(1017*2^188171-1)/3556647Lelio R Paula03/2015
8750(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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