PRP Records

Probable Primes Top 10000

(205869 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 ?
825111^56235-795058563Enzo Doria02/2013
8252(14*10^58550+211)/958551Robert Price11/2017
82532^194479-11323958545Enzo Doria07/2014
82542^194455-11224958537Enzo Doria06/2014
82552^194405-11191958522Enzo Doria05/2014
8256(4*10^58521-19)/358522Robert Price06/2017
8258(7^69247-4^69247)/358521Robert Price06/2012
82575*7^69246+858521Lelio R Paula09/2014
82592^194358-116758508Lelio R Paula05/2011
8260(2^194366+7)/137358507Lelio R Paula02/2012
8261(493*10^58486-7)/958488Robert Price07/2016
82623^122579-34058486Lelio R Paula10/2012
8263(11*10^58458-149)/358459Robert Price01/2017
8264(47*10^58456+133)/958457Robert Price04/2017
82652^194186+8558456Lelio R Paula04/2011
82663^122506-2^(122506-1)58451Robert Price01/2016
8267(74^31267-1)/7358444Paul Bourdelais08/2017
8268177^25998-258443Lelio R Paula10/2017
826915^49690-2658440Lelio R Paula03/2013
827010^58437+11072158438Patrick De Geest12/2012
827110^58437-1158437Robert Price05/2011
82722^194095+6958429Lelio R Paula04/2011
8273(29*10^58417-77)/358418Robert Price01/2017
82742^194034+17758411Lelio R Paula04/2011
8275789^20158+20158^78958400Norbert Schneider06/2016
827614^50949+7558395Lelio R Paula03/2013
82772^193974-11476158392Enzo Doria05/2015
82782^193965+558390Henri Lifchitz12/2002
8279(5*10^58384-29)/358385Robert Price02/2017
82803^122360+8058381Lelio R Paula10/2012
828110103^14577-11458373Enzo Doria07/2012
8282(22699*2^193883+1)/2158368Lelio R Paula06/2014
8283(31*2^193886+1)/14076558362Lelio R Paula07/2012
828411^56041-156058361Enzo Doria11/2012
8285(2^193881+9)/1769958360Lelio R Paula02/2012
82863^122313+5858359Lelio R Paula10/2012
82876^74996-11958359Lelio R Paula10/2012
8288(11*2^193859+1)/1358358Lelio R Paula07/2012
82892^193861-11225558358Enzo Doria06/2014
8290(22699*2^193854+1)/492758357Lelio R Paula06/2014
829118^46487+3758354Lelio R Paula03/2013
829217^47419+5458347Lelio R Paula03/2013
8293(31*2^193791+1)/358338Lelio R Paula02/2012
8294(27*2^193805-1)/98224958337Lelio R Paula01/2014
82953^122219-2^12221958314Mike Oakes09/2003
8296(199*10^58306+11)/358308Robert Price05/2017
82972^193674-1882558302Lelio R Paula05/2011
82985*10^58275+358276Dmitry Domanov11/2010
82992^193578-11291358273Enzo Doria06/2014
83002^193541+129958262Lelio R Paula05/2011
830110^58250+9358251Robert Price01/2011
830210^58250-17560758250Patrick De Geest12/2012
83032^193492+841558247Lelio R Paula10/2012
83042^193444+15758233Lelio R Paula04/2011
8305Phi(28754,28754)58231Henri Lifchitz08/2013
83062^193430-11188158229Enzo Doria05/2014
830710^58225+12457958226Patrick De Geest12/2012
830810^58225-9358225Robert Price05/2011
83092^193375-29558212Yves Minet05/2013
83102^193345+7726758203Enzo Doria05/2016
831121^44017-20^4401758201Robert Price05/2012
8312(17*2^193329-1)/958199Lelio R Paula01/2014
831317^47291+2058190Lelio R Paula03/2013
8314p(12528)#/2-12858170Robert Price05/2017
83152^193214-13558164Lelio R Paula04/2011
831619^45483-8058162Lelio R Paula03/2013
8317(4*10^58155+83)/358156Robert Price01/2017
831814^50739-1358154Lelio R Paula03/2013
8319(1017*2^193184-1)/482358154Lelio R Paula04/2015
8320(2*10^58151+457)/958151Robert Price01/2017
8321(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
8322(19*2^193114-1)/118675558129Lelio R Paula01/2014
83242^193091-123758127Yves Minet08/2012
83239*7^68780-258127Lelio R Paula09/2014
83252^193083-86968810558124Lelio R Paula10/2012
83262^193058-4558117Lelio R Paula04/2011
8327(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
832811^55795-4258105Lelio R Paula03/2013
83293^121779-1658104Lelio R Paula10/2012
8330(13*10^58103+191)/358104Robert Price08/2017
83312^192986+19558095Lelio R Paula04/2011
83327^68740+2*3^6874058093Mike Oakes07/2010
8333(85*10^58091-1)/358093Robert Price07/2017
8334(404*10^58087-53)/958089Robert Price11/2017
833512^53821+1158083Lelio R Paula02/2013
8336119^27979-11858072Norbert Schneider10/2013
8337(10223*2^192828+1)/24358049Lelio R Paula05/2014
83382^192808-112758041Yves Minet05/2013
8339(27*2^192803+1)/982758037Lelio R Paula07/2012
8341(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
83403*10^58032-2358033Robert Price11/2017
83422^192678+7294358002Enzo Doria04/2016
8343(13*10^57997-37)/357998Robert Price08/2017
83442^192657-318957996Yves Minet10/2014
83456^74525-14957992Lelio R Paula10/2012
834642^35723-4157988Norbert Schneider06/2014
8347(29*2^192625-1)/18357986Lelio R Paula01/2014
8348(3^121520-8)/384757977Lelio R Paula03/2012
8349(2^192596-5)/13957976Lelio R Paula02/2012
835010^57975+6783357976Patrick De Geest09/2013
835110^57975-4769357975Patrick De Geest09/2013
8352(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
8353(29*10^57967+673)/957968Robert Price10/2017
8354(3^121492-5)/457966Lelio R Paula03/2012
83552^192549+3557964Lelio R Paula04/2011
835628799!2+257962Robert Price10/2012
8357(7*2^192534-1)/134757957Lelio R Paula01/2014
83587001^15069-10057943Enzo Doria07/2012
8359L(277273)/1109092157940Donovan Johnson11/2005
8360(2^192469-1017)/3557938Lelio R Paula02/2012
83612^192457-1155*19245757936Henri Lifchitz02/2005
83622^192443+138557932Lelio R Paula05/2011
8363132^27317-13157928Norbert Schneider03/2015
836441522!3-5904957912Robert Price12/2015
8365(3*2^192380-1)/16957911Lelio R Paula01/2014
83662^192339-251557900Yves Minet07/2014
83672^192303+769557889Lelio R Paula10/2012
83682^192273-595557880Lelio R Paula05/2011
83692^192257+1609557876Lelio R Paula05/2011
8370109^28401-257865Lelio R Paula10/2017
83712^192218-11186157864Enzo Doria05/2014
83722^192214-394157863Yves Minet04/2017
8373(2^192212+3)/25957860Lelio R Paula02/2012
8374(3^121270+8)/15593975357853Lelio R Paula03/2012
837580^30393-7957841Norbert Schneider03/2015
837620^44455-312357838Enzo Doria03/2013
83772^192122-19557835Lelio R Paula04/2011
8378(29*10^57834+91)/357835Robert Price03/2016
83798*6^74306+557823Lelio R Paula09/2014
8380(39^36341-1)/3857820Robert Price04/2012
83812^192037-11180557809Enzo Doria05/2014
83822^192023-192023^257805Henri Lifchitz05/2005
838321^43717+257804Ray Chandler08/2011
83848*5^82687+757797Lelio R Paula09/2014
83855^82680-2457791Lelio R Paula10/2012
8386(2^191915+47)/9557771Lelio R Paula02/2012
8387(74*10^57763+133)/957764Robert Price10/2017
83886^74227-9557760Lelio R Paula10/2012
83892^191861+2983557756Lelio R Paula10/2012
83911908^17605+17605^190857755Serge Batalov05/2014
83905*10^57754+5957755Robert Price09/2016
8392(5*2^191821-1)/892406757738Lelio R Paula01/2014
83933*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
839441399!3-656157723Robert Price11/2015
8395(44*10^57721-233)/957722Robert Price10/2017
83962^191745+1757721Lelio R Paula04/2011
83972^191730-76157717Yves Minet01/2012
8398(2^191733-3)/225157715Lelio R Paula02/2012
83992^191698-11157707Lelio R Paula04/2011
8400(13*10^57691+23)/957692Robert Price02/2015
840120^44340-542357688Enzo Doria03/2013
8402(27*2^191629+1)/12557686Lelio R Paula07/2012
84034*10^57684+3*7^5768457685Mike Oakes11/2010
84042*3^120898+557684Lelio R Paula04/2014
8405(6883*2^191610-1)/734757681Lelio R Paula04/2015
84066^74117-4957675Lelio R Paula10/2012
84072^191586-11320157674Enzo Doria07/2014
84082^191580+19357672Lelio R Paula04/2011
8409(103*29^39433+10401)/457669Curtis Bright05/2015
84102^191560+25525557666Lelio R Paula05/2011
84112^191515-8557652Lelio R Paula04/2011
84122^191502-112757648Yves Minet05/2013
84132*5^82473-3^8247357647Mike Oakes08/2010
8414(13*10^57634-61)/357635Robert Price08/2017
841585^29868-29868^8557628Norbert Schneider11/2017
84162^191430+10357627Lelio R Paula04/2011
84173*2^191408+557621Lelio R Paula03/2014
84182^191382-185893157612Enzo Doria04/2016
84196*7^68163+557606Lelio R Paula09/2014
842091^29403-257602Lelio R Paula08/2013
842111^55308-795057598Enzo Doria02/2013
84222^191329+6557596Lelio R Paula04/2011
842311^55302-24057592Enzo Doria07/2012
84242^191299-103146757587Paul Bourdelais11/2012
84252^191295-11199157586Enzo Doria05/2014
84262^191279-129757581Yves Minet08/2012
84273*6^73961+557554Lelio R Paula09/2014
8428(3^120623+5)/5214457548Lelio R Paula04/2012
8429(17*10^57543-29)/357544Robert Price09/2017
843042^35445-4157537Norbert Schneider06/2014
8431(71^31079-1)/7057534Paul Bourdelais08/2017
84322^191069-72340357518Paul Bourdelais11/2012
84334*10^57506-357507Serge Batalov11/2010
843410^57501+6735957502Patrick De Geest06/2016
843510^57501-100000000157501Robert Price05/2016
843610^57501-24986157501Patrick De Geest06/2016
8437(9^60251+4^60251)/1357493Robert Price02/2013
843820^44184-600357485Enzo Doria03/2013
84392^190948+1270557482Lelio R Paula10/2012
84402^190945+2957481Henri Lifchitz06/2005
84412^190922-40157474Yves Minet01/2012
844215^48860+4657464Lelio R Paula02/2013
84433^120434+2057462Lelio R Paula10/2012
84447^67964-3857437Lelio R Paula10/2012
84452^190799-11306557437Enzo Doria07/2014
84469*5^82159+257428Lelio R Paula09/2014
8447(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8450lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8448(103*10^57414-1)/357416Serge Batalov12/2014
8449(1654*30^38869-1)/2957416Karsten Bonath05/2017
84512*10^57410+9^5741057411Mike Oakes04/2011
84522^190704-159557408Lelio R Paula05/2011
845311^55121-174057403Enzo Doria11/2012
84542^190644-18557390Lelio R Paula04/2011
845541182!3-3^4118257389Robert Price08/2015
84562^190629-11225557386Enzo Doria06/2014
8457(2*10^57384-71)/357384Robert Price01/2017
84582*6^73735+5^7373557378Mike Oakes11/2009
84592^190605+5957378Lelio R Paula04/2011
84606^73727-757371Lelio R Paula10/2012
84612^190561-11222557365Enzo Doria06/2014
846210^57358+17089957359Patrick De Geest06/2016
846310^57358-800157358Robert Price03/2016
846418^45687-1157350Lelio R Paula02/2013
846511^55069-21057349Enzo Doria07/2012
846611^55068-1257348Lelio R Paula02/2013
846719^44839+5457339Lelio R Paula02/2013
8468(7*2^190468-1)/851157334Lelio R Paula01/2014
8469(23*10^57333-59)/957334Robert Price03/2017
84702^190455-1155*19045557333Henri Lifchitz02/2005
847165^31620+2857325Lelio R Paula01/2016
84722^190403+1609557318Lelio R Paula05/2011
8473(19*10^57316+119)/357317Robert Price02/2017
8475(21*2^190393+1)/21157314Lelio R Paula07/2012
84742^190392-11202557314Enzo Doria05/2014
8476(24737*2^190234+1)/957270Lelio R Paula05/2014
8477(7*2^190230+1)/2357265Lelio R Paula07/2012
8478(10223*2^190197+1)/321157256Lelio R Paula05/2014
847918^45590-9757228Lelio R Paula02/2013
8480(3*2^190105-1)/1920557224Lelio R Paula01/2014
8481(16*10^57219-31)/357220Robert Price03/2016
8482(2^190074+47)/5157217Lelio R Paula02/2012
84833^119894-14057204Lelio R Paula10/2012
8485(37^36473-1)/3657196Robert Price03/2012
84842^190000-216357196Yves Minet08/2013
84862^189987-279810757192Enzo Doria04/2016
84872^189935-11211757177Enzo Doria05/2014
84882^189909-11223157169Enzo Doria06/2014
8489132049#+14905357161Makoto Morimoto12/2015
849041032!3-2757158Robert Price09/2014
849119^44694+2257153Lelio R Paula02/2013
849212^52956-1757150Lelio R Paula02/2013
84932^189823-96757143Yves Minet01/2012
8494(25*10^57138-61)/957139Robert Price02/2015
84955^81743-4^(81743+1)57136Robert Price04/2016
84967^67593-5457123Lelio R Paula10/2012
84977*3^119712+257118Lelio R Paula03/2014
84985^81700+1657106Lelio R Paula10/2012
84992^189700+7656157106Enzo Doria05/2016
85004*6^73374+557097Lelio R Paula09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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