PRP Records

Probable Primes Top 10000

(252402 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 (> 50000) Who ? When ?
8751Phi(28754,28754)58231Henri Lifchitz08/2013
87522^193430-11188158229Enzo Doria05/2014
875310^58225+12457958226Patrick De Geest12/2012
875410^58225-9358225Robert Price05/2011
87552^193375-29558212Yves Minet05/2013
875614018^14037-14037^1401858208Norbert Schneider10/2018
87572^193345+7726758203Enzo Doria05/2016
875821^44017-20^4401758201Robert Price05/2012
8759(17*2^193329-1)/958199Lelio R Paula01/2014
876017^47291+2058190Lelio R Paula03/2013
8761p(12528)#/2-12858170Robert Price05/2017
87622^193214-13558164Lelio R Paula04/2011
876319^45483-8058162Lelio R Paula03/2013
8764(4*10^58155+83)/358156Robert Price01/2017
876614^50739-1358154Lelio R Paula03/2013
8765(1017*2^193184-1)/482358154Lelio R Paula04/2015
8767(2*10^58151+457)/958151Robert Price01/2017
8768(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
8769(19*2^193114-1)/118675558129Lelio R Paula01/2014
87712^193091-123758127Yves Minet08/2012
87709*7^68780-258127Lelio R Paula09/2014
87722473^17130+17130^247358126Norbert Schneider10/2018
87732^193083-86968810558124Lelio R Paula10/2012
87742^193058-4558117Lelio R Paula04/2011
8775(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
877611^55795-4258105Lelio R Paula03/2013
87773^121779-1658104Lelio R Paula10/2012
8778(13*10^58103+191)/358104Robert Price08/2017
87792^192986+19558095Lelio R Paula04/2011
87807^68740+2*3^6874058093Mike Oakes07/2010
8781(85*10^58091-1)/358093Robert Price07/2017
8782(404*10^58087-53)/958089Robert Price11/2017
878312^53821+1158083Lelio R Paula02/2013
8784119^27979-11858072Norbert Schneider10/2013
8785(10223*2^192828+1)/24358049Lelio R Paula05/2014
87862^192808-112758041Yves Minet05/2013
8787(27*2^192803+1)/982758037Lelio R Paula07/2012
8789(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
87883*10^58032-2358033Robert Price11/2017
87902^192678+7294358002Enzo Doria04/2016
8791(13*10^57997-37)/357998Robert Price08/2017
87922^192657-318957996Yves Minet10/2014
87936^74525-14957992Lelio R Paula10/2012
879442^35723-4157988Norbert Schneider06/2014
8795(29*2^192625-1)/18357986Lelio R Paula01/2014
8796(3^121520-8)/384757977Lelio R Paula03/2012
8797(2^192596-5)/13957976Lelio R Paula02/2012
879810^57975+6783357976Patrick De Geest09/2013
879910^57975-4769357975Patrick De Geest09/2013
8800(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
8801(29*10^57967+673)/957968Robert Price10/2017
8802(3^121492-5)/457966Lelio R Paula03/2012
88032^192549+3557964Lelio R Paula04/2011
880428799!2+257962Robert Price10/2012
8805(7*2^192534-1)/134757957Lelio R Paula01/2014
88067001^15069-10057943Enzo Doria07/2012
8807L(277273)/1109092157940Donovan Johnson11/2005
8808(2^192469-1017)/3557938Lelio R Paula02/2012
88092^192457-1155*19245757936Henri Lifchitz02/2005
88102^192443+138557932Lelio R Paula05/2011
8811132^27317-13157928Norbert Schneider03/2015
881241522!3-5904957912Robert Price12/2015
8813(3*2^192380-1)/16957911Lelio R Paula01/2014
88142^192339-251557900Yves Minet07/2014
88152^192303+769557889Lelio R Paula10/2012
88162^192273-595557880Lelio R Paula05/2011
88172^192257+1609557876Lelio R Paula05/2011
8818109^28401-257865Lelio R Paula10/2017
88192^192218-11186157864Enzo Doria05/2014
88202^192214-394157863Yves Minet04/2017
8821(2^192212+3)/25957860Lelio R Paula02/2012
8822(3^121270+8)/15593975357853Lelio R Paula03/2012
882380^30393-7957841Norbert Schneider03/2015
882420^44455-312357838Enzo Doria03/2013
88262^192122-19557835Lelio R Paula04/2011
8825(29*10^57834+91)/357835Robert Price03/2016
88278*6^74306+557823Lelio R Paula09/2014
8828(39^36341-1)/3857820Robert Price04/2012
88292^192037-11180557809Enzo Doria05/2014
88302^192023-192023^257805Henri Lifchitz05/2005
883121^43717+257804Ray Chandler08/2011
88328*5^82687+757797Lelio R Paula09/2014
88335^82680-2457791Lelio R Paula10/2012
8834(2^191915+47)/9557771Lelio R Paula02/2012
8835(74*10^57763+133)/957764Robert Price10/2017
88366^74227-9557760Lelio R Paula10/2012
88372^191861+2983557756Lelio R Paula10/2012
88381908^17605+17605^190857755Serge Batalov05/2014
88395*10^57754+5957755Robert Price09/2016
8840(5*2^191821-1)/892406757738Lelio R Paula01/2014
88413*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
884241399!3-656157723Robert Price11/2015
8843(44*10^57721-233)/957722Robert Price10/2017
88442^191745+1757721Lelio R Paula04/2011
88452^191730-76157717Yves Minet01/2012
8846(2^191733-3)/225157715Lelio R Paula02/2012
88472^191698-11157707Lelio R Paula04/2011
8848(13*10^57691+23)/957692Robert Price02/2015
884920^44340-542357688Enzo Doria03/2013
8850(27*2^191629+1)/12557686Lelio R Paula07/2012
88514*10^57684+3*7^5768457685Mike Oakes11/2010
88522*3^120898+557684Lelio R Paula04/2014
8853(6883*2^191610-1)/734757681Lelio R Paula04/2015
88546^74117-4957675Lelio R Paula10/2012
88552^191586-11320157674Enzo Doria07/2014
88562^191580+19357672Lelio R Paula04/2011
8857(103*29^39433+10401)/457669Curtis Bright05/2015
88582^191560+25525557666Lelio R Paula05/2011
88592^191515-8557652Lelio R Paula04/2011
88602^191502-112757648Yves Minet05/2013
88612*5^82473-3^8247357647Mike Oakes08/2010
8862(13*10^57634-61)/357635Robert Price08/2017
886385^29868-29868^8557628Norbert Schneider11/2017
88642^191430+10357627Lelio R Paula04/2011
88653*2^191408+557621Lelio R Paula03/2014
88662^191382-185893157612Enzo Doria04/2016
88676*7^68163+557606Lelio R Paula09/2014
886891^29403-257602Lelio R Paula08/2013
886911^55308-795057598Enzo Doria02/2013
88702^191329+6557596Lelio R Paula04/2011
887111^55302-24057592Enzo Doria07/2012
88722^191299-103146757587Paul Bourdelais11/2012
88732^191295-11199157586Enzo Doria05/2014
88742^191279-129757581Yves Minet08/2012
88753*6^73961+557554Lelio R Paula09/2014
8876(3^120623+5)/5214457548Lelio R Paula04/2012
8877(17*10^57543-29)/357544Robert Price09/2017
887842^35445-4157537Norbert Schneider06/2014
8879(71^31079-1)/7057534Paul Bourdelais08/2017
88802^191069-72340357518Paul Bourdelais11/2012
88814*10^57506-357507Serge Batalov11/2010
888210^57501+6735957502Patrick De Geest06/2016
888310^57501-100000000157501Robert Price05/2016
888410^57501-24986157501Patrick De Geest06/2016
8885(9^60251+4^60251)/1357493Robert Price02/2013
888620^44184-600357485Enzo Doria03/2013
88872^190948+1270557482Lelio R Paula10/2012
88882^190945+2957481Henri Lifchitz06/2005
88892^190922-40157474Yves Minet01/2012
889015^48860+4657464Lelio R Paula02/2013
88913^120434+2057462Lelio R Paula10/2012
88927^67964-3857437Lelio R Paula10/2012
88932^190799-11306557437Enzo Doria07/2014
88949*5^82159+257428Lelio R Paula09/2014
8895(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8898lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8896(103*10^57414-1)/357416Serge Batalov12/2014
8897(1654*30^38869-1)/2957416Karsten Bonath05/2017
88992*10^57410+9^5741057411Mike Oakes04/2011
89002^190704-159557408Lelio R Paula05/2011
890111^55121-174057403Enzo Doria11/2012
89022^190644-18557390Lelio R Paula04/2011
890341182!3-3^4118257389Robert Price08/2015
89042^190629-11225557386Enzo Doria06/2014
8905(2*10^57384-71)/357384Robert Price01/2017
89072*6^73735+5^7373557378Mike Oakes11/2009
89062^190605+5957378Lelio R Paula04/2011
89086^73727-757371Lelio R Paula10/2012
89092^190561-11222557365Enzo Doria06/2014
891010^57358+17089957359Patrick De Geest06/2016
891110^57358-800157358Robert Price03/2016
891218^45687-1157350Lelio R Paula02/2013
891311^55069-21057349Enzo Doria07/2012
891411^55068-1257348Lelio R Paula02/2013
891519^44839+5457339Lelio R Paula02/2013
8917(7*2^190468-1)/851157334Lelio R Paula01/2014
8916(23*10^57333-59)/957334Robert Price03/2017
89182^190455-1155*19045557333Henri Lifchitz02/2005
891965^31620+2857325Lelio R Paula01/2016
89202^190403+1609557318Lelio R Paula05/2011
8921(19*10^57316+119)/357317Robert Price02/2017
8922(21*2^190393+1)/21157314Lelio R Paula07/2012
89232^190392-11202557314Enzo Doria05/2014
892413173^13912-13912^1317357314Norbert Schneider08/2018
8925(24737*2^190234+1)/957270Lelio R Paula05/2014
8926(7*2^190230+1)/2357265Lelio R Paula07/2012
8927(10223*2^190197+1)/321157256Lelio R Paula05/2014
892818^45590-9757228Lelio R Paula02/2013
8929(3*2^190105-1)/1920557224Lelio R Paula01/2014
8930(16*10^57219-31)/357220Robert Price03/2016
8931(2^190074+47)/5157217Lelio R Paula02/2012
89323^119894-14057204Lelio R Paula10/2012
8934(37^36473-1)/3657196Robert Price03/2012
89332^190000-216357196Yves Minet08/2013
89352^189987-279810757192Enzo Doria04/2016
89362^189935-11211757177Enzo Doria05/2014
89372^189909-11223157169Enzo Doria06/2014
8938132049#+14905357161Makoto Morimoto12/2015
893941032!3-2757158Robert Price09/2014
894019^44694+2257153Lelio R Paula02/2013
894112^52956-1757150Lelio R Paula02/2013
89422^189823-96757143Yves Minet01/2012
8943(25*10^57138-61)/957139Robert Price02/2015
89445^81743-4^(81743+1)57136Robert Price04/2016
89457^67593-5457123Lelio R Paula10/2012
89467*3^119712+257118Lelio R Paula03/2014
89475^81700+1657106Lelio R Paula10/2012
89482^189700+7656157106Enzo Doria05/2016
89492^189671+13157097Lelio R Paula04/2011
89504*6^73374+557097Lelio R Paula09/2014
8951(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8952(29*2^189619-1)/39357080Lelio R Paula01/2014
89533^119587+8057058Lelio R Paula10/2012
89542^189502-11345357046Enzo Doria07/2014
89552^189455+15357032Lelio R Paula04/2011
895624^41317-41317^2457027Norbert Schneider07/2016
89572^189414-1757020Lelio R Paula03/2011
895824^41311+2357018Norbert Schneider12/2013
8959norm(Mod(x,x^4+x^3-x+1)^207341-1)/256998Paul Vanderveen05/2018
8960(4*10^56989-31)/956989Erik Branger05/2011
896111^54712-162056977Enzo Doria11/2012
89622^189237-11223156967Enzo Doria06/2014
896317^46285-4856952Lelio R Paula02/2013
89642^189188+7524156952Enzo Doria04/2016
89652^189181+9439556950Henri Lifchitz01/2005
89667001^14808-10856940Enzo Doria07/2012
89672^189147-11263956939Enzo Doria06/2014
8968(19*10^56933-43)/356934Robert Price10/2017
89692^189110-356928M. Frind & P. Underwood11/2002
89702^189069+1290956916Lelio R Paula04/2011
8971(13*10^56909+191)/356910Robert Price08/2017
8972(35*10^56898-17)/956899Serge Batalov02/2009
89732^189011-595556898Lelio R Paula04/2011
89746^73119-556898Lelio R Paula10/2012
897513^51076-9056896Lelio R Paula02/2013
89762^188997+5689756894Yves Minet02/2010
89775^81388-1376656888Enzo Doria02/2013
8978(104^28201+1)/10556881Richard Fischer04/2018
8979(156^25933+1)/15756873Eric Chen12/2017
898020^43713-640356872Enzo Doria03/2013
8981(71*10^56858-287)/956859Robert Price05/2017
89822^188857-25423356852Gary Barnes09/2009
898415^48338-8856850Lelio R Paula02/2013
898310^56849+13643756850Patrick De Geest07/2017
898510^56849-70156849Robert Price06/2017
8986(2^188788+78557)/356831Lelio R Paula05/2012
89872^188771+1609556826Lelio R Paula04/2011
89887*2^188742-956818Lelio R Paula03/2014
898912^52646-6556815Lelio R Paula02/2013
89905003^15358-15856813Enzo Doria07/2012
89912^188713+57729457556809Lelio R Paula03/2013
89922^188693-11209956803Enzo Doria05/2014
8993(7^67211+4^67211)/1156799Robert Price10/2012
89942^188678-9439556798Lelio R Paula09/2011
899520^43651-850356792Enzo Doria03/2013
89972^188657-237156792Yves Minet10/2013
8996152^26029-151^2602956792Eric Chen04/2018
8998(14^49549+5^49549)/1956789Robert Price05/2013
8999(45^34351-1)/4456788Robert Price05/2014
90007*10^56785-2356786Robert Price04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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