PRP Records

Probable Primes Top 10000

(202622 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 ?
8251(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
8252(29*10^57967+673)/957968Robert Price10/2017
8253(3^121492-5)/457966Lelio R Paula03/2012
82542^192549+3557964Lelio R Paula04/2011
825528799!2+257962Robert Price10/2012
8256(7*2^192534-1)/134757957Lelio R Paula01/2014
82577001^15069-10057943Enzo Doria07/2012
8258L(277273)/1109092157940Donovan Johnson11/2005
8259(2^192469-1017)/3557938Lelio R Paula02/2012
82602^192457-1155*19245757936Henri Lifchitz02/2005
82612^192443+138557932Lelio R Paula05/2011
8262132^27317-13157928Norbert Schneider03/2015
826341522!3-5904957912Robert Price12/2015
8264(3*2^192380-1)/16957911Lelio R Paula01/2014
82652^192339-251557900Yves Minet07/2014
82662^192303+769557889Lelio R Paula10/2012
82672^192273-595557880Lelio R Paula05/2011
82682^192257+1609557876Lelio R Paula05/2011
8269109^28401-257865Lelio R Paula10/2017
82702^192218-11186157864Enzo Doria05/2014
82712^192214-394157863Yves Minet04/2017
8272(2^192212+3)/25957860Lelio R Paula02/2012
8273(3^121270+8)/15593975357853Lelio R Paula03/2012
827480^30393-7957841Norbert Schneider03/2015
827520^44455-312357838Enzo Doria03/2013
82762^192122-19557835Lelio R Paula04/2011
8277(29*10^57834+91)/357835Robert Price03/2016
82788*6^74306+557823Lelio R Paula09/2014
8279(39^36341-1)/3857820Robert Price04/2012
82802^192037-11180557809Enzo Doria05/2014
82812^192023-192023^257805Henri Lifchitz05/2005
828221^43717+257804Ray Chandler08/2011
82838*5^82687+757797Lelio R Paula09/2014
82845^82680-2457791Lelio R Paula10/2012
8285(2^191915+47)/9557771Lelio R Paula02/2012
8286(74*10^57763+133)/957764Robert Price10/2017
82876^74227-9557760Lelio R Paula10/2012
82882^191861+2983557756Lelio R Paula10/2012
82901908^17605+17605^190857755Serge Batalov05/2014
82895*10^57754+5957755Robert Price09/2016
8291(5*2^191821-1)/892406757738Lelio R Paula01/2014
82923*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
829341399!3-656157723Robert Price11/2015
8294(44*10^57721-233)/957722Robert Price10/2017
82952^191745+1757721Lelio R Paula04/2011
82962^191730-76157717Yves Minet01/2012
8297(2^191733-3)/225157715Lelio R Paula02/2012
82982^191698-11157707Lelio R Paula04/2011
8299(13*10^57691+23)/957692Robert Price02/2015
830020^44340-542357688Enzo Doria03/2013
8301(27*2^191629+1)/12557686Lelio R Paula07/2012
83024*10^57684+3*7^5768457685Mike Oakes11/2010
83032*3^120898+557684Lelio R Paula04/2014
8304(6883*2^191610-1)/734757681Lelio R Paula04/2015
83056^74117-4957675Lelio R Paula10/2012
83062^191586-11320157674Enzo Doria07/2014
83072^191580+19357672Lelio R Paula04/2011
8308(103*29^39433+10401)/457669Curtis Bright05/2015
83092^191560+25525557666Lelio R Paula05/2011
83102^191515-8557652Lelio R Paula04/2011
83112^191502-112757648Yves Minet05/2013
83122*5^82473-3^8247357647Mike Oakes08/2010
8313(13*10^57634-61)/357635Robert Price08/2017
831485^29868-29868^8557628Norbert Schneider11/2017
83152^191430+10357627Lelio R Paula04/2011
83163*2^191408+557621Lelio R Paula03/2014
83172^191382-185893157612Enzo Doria04/2016
83186*7^68163+557606Lelio R Paula09/2014
831991^29403-257602Lelio R Paula08/2013
832011^55308-795057598Enzo Doria02/2013
83212^191329+6557596Lelio R Paula04/2011
832211^55302-24057592Enzo Doria07/2012
83232^191299-103146757587Paul Bourdelais11/2012
83242^191295-11199157586Enzo Doria05/2014
83252^191279-129757581Yves Minet08/2012
83263*6^73961+557554Lelio R Paula09/2014
8327(3^120623+5)/5214457548Lelio R Paula04/2012
8328(17*10^57543-29)/357544Robert Price09/2017
832942^35445-4157537Norbert Schneider06/2014
8330(71^31079-1)/7057534Paul Bourdelais08/2017
83312^191069-72340357518Paul Bourdelais11/2012
83324*10^57506-357507Serge Batalov11/2010
833310^57501+6735957502Patrick De Geest06/2016
833410^57501-100000000157501Robert Price05/2016
833510^57501-24986157501Patrick De Geest06/2016
8336(9^60251+4^60251)/1357493Robert Price02/2013
833720^44184-600357485Enzo Doria03/2013
83382^190948+1270557482Lelio R Paula10/2012
83392^190945+2957481Henri Lifchitz06/2005
83402^190922-40157474Yves Minet01/2012
834115^48860+4657464Lelio R Paula02/2013
83423^120434+2057462Lelio R Paula10/2012
83437^67964-3857437Lelio R Paula10/2012
83442^190799-11306557437Enzo Doria07/2014
83459*5^82159+257428Lelio R Paula09/2014
8346(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8349lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8347(103*10^57414-1)/357416Serge Batalov12/2014
8348(1654*30^38869-1)/2957416Karsten Bonath05/2017
83502*10^57410+9^5741057411Mike Oakes04/2011
83512^190704-159557408Lelio R Paula05/2011
835211^55121-174057403Enzo Doria11/2012
83532^190644-18557390Lelio R Paula04/2011
835441182!3-3^4118257389Robert Price08/2015
83552^190629-11225557386Enzo Doria06/2014
8356(2*10^57384-71)/357384Robert Price01/2017
83572*6^73735+5^7373557378Mike Oakes11/2009
83582^190605+5957378Lelio R Paula04/2011
83596^73727-757371Lelio R Paula10/2012
83602^190561-11222557365Enzo Doria06/2014
836110^57358+17089957359Patrick De Geest06/2016
836210^57358-800157358Robert Price03/2016
836318^45687-1157350Lelio R Paula02/2013
836411^55069-21057349Enzo Doria07/2012
836511^55068-1257348Lelio R Paula02/2013
836619^44839+5457339Lelio R Paula02/2013
8367(7*2^190468-1)/851157334Lelio R Paula01/2014
8368(23*10^57333-59)/957334Robert Price03/2017
83692^190455-1155*19045557333Henri Lifchitz02/2005
837065^31620+2857325Lelio R Paula01/2016
83712^190403+1609557318Lelio R Paula05/2011
8372(19*10^57316+119)/357317Robert Price02/2017
8374(21*2^190393+1)/21157314Lelio R Paula07/2012
83732^190392-11202557314Enzo Doria05/2014
8375(24737*2^190234+1)/957270Lelio R Paula05/2014
8376(7*2^190230+1)/2357265Lelio R Paula07/2012
8377(10223*2^190197+1)/321157256Lelio R Paula05/2014
837818^45590-9757228Lelio R Paula02/2013
8379(3*2^190105-1)/1920557224Lelio R Paula01/2014
8380(16*10^57219-31)/357220Robert Price03/2016
8381(2^190074+47)/5157217Lelio R Paula02/2012
83823^119894-14057204Lelio R Paula10/2012
8384(37^36473-1)/3657196Robert Price03/2012
83832^190000-216357196Yves Minet08/2013
83852^189987-279810757192Enzo Doria04/2016
83862^189935-11211757177Enzo Doria05/2014
83872^189909-11223157169Enzo Doria06/2014
8388132049#+14905357161Makoto Morimoto12/2015
838941032!3-2757158Robert Price09/2014
839019^44694+2257153Lelio R Paula02/2013
839112^52956-1757150Lelio R Paula02/2013
83922^189823-96757143Yves Minet01/2012
8393(25*10^57138-61)/957139Robert Price02/2015
83945^81743-4^(81743+1)57136Robert Price04/2016
83957^67593-5457123Lelio R Paula10/2012
83967*3^119712+257118Lelio R Paula03/2014
83975^81700+1657106Lelio R Paula10/2012
83982^189700+7656157106Enzo Doria05/2016
84002^189671+13157097Lelio R Paula04/2011
83994*6^73374+557097Lelio R Paula09/2014
8401(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8402(29*2^189619-1)/39357080Lelio R Paula01/2014
84033^119587+8057058Lelio R Paula10/2012
84042^189502-11345357046Enzo Doria07/2014
84052^189455+15357032Lelio R Paula04/2011
840624^41317-41317^2457027Norbert Schneider07/2016
84072^189414-1757020Lelio R Paula03/2011
840824^41311+2357018Norbert Schneider12/2013
8409(4*10^56989-31)/956989Erik Branger05/2011
841011^54712-162056977Enzo Doria11/2012
84112^189237-11223156967Enzo Doria06/2014
841317^46285-4856952Lelio R Paula02/2013
84122^189188+7524156952Enzo Doria04/2016
84142^189181+9439556950Henri Lifchitz01/2005
84157001^14808-10856940Enzo Doria07/2012
84162^189147-11263956939Enzo Doria06/2014
8417(19*10^56933-43)/356934Robert Price10/2017
84182^189110-356928M. Frind & P. Underwood11/2002
84192^189069+1290956916Lelio R Paula04/2011
8420(13*10^56909+191)/356910Robert Price08/2017
8421(35*10^56898-17)/956899Serge Batalov02/2009
84222^189011-595556898Lelio R Paula04/2011
84236^73119-556898Lelio R Paula10/2012
842413^51076-9056896Lelio R Paula02/2013
84252^188997+5689756894Yves Minet02/2010
84265^81388-1376656888Enzo Doria02/2013
8427(156^25933+1)/15756873Eric Chen12/2017
842820^43713-640356872Enzo Doria03/2013
8429(71*10^56858-287)/956859Robert Price05/2017
84302^188857-25423356852Gary Barnes09/2009
843115^48338-8856850Lelio R Paula02/2013
843210^56849+13643756850Patrick De Geest07/2017
843310^56849-70156849Robert Price06/2017
8434(2^188788+78557)/356831Lelio R Paula05/2012
84352^188771+1609556826Lelio R Paula04/2011
84367*2^188742-956818Lelio R Paula03/2014
843712^52646-6556815Lelio R Paula02/2013
84385003^15358-15856813Enzo Doria07/2012
84392^188713+57729457556809Lelio R Paula03/2013
84402^188693-11209956803Enzo Doria05/2014
8441(7^67211+4^67211)/1156799Robert Price10/2012
84422^188678-9439556798Lelio R Paula09/2011
844320^43651-850356792Enzo Doria03/2013
84442^188657-237156792Yves Minet10/2013
8445(14^49549+5^49549)/1956789Robert Price05/2013
8446(45^34351-1)/4456788Robert Price05/2014
84477*10^56785-2356786Robert Price04/2016
8448(10^56781-31)/356781Serge Batalov12/2014
84497*10^56779+356780Erik Branger11/2009
845010^56765+25917956766Patrick De Geest09/2013
845110^56765-24949756765Patrick De Geest09/2013
8452t(188706)56764Robert Price04/2015
84532^188551-90432756760Paul Bourdelais11/2012
8455(64*10^56756+17)/956757Robert Price09/2015
8454131101#+14629156757Makoto Morimoto02/2016
84562^188539-11251956756Enzo Doria06/2014
84576^72927+10156749Lelio R Paula10/2012
845820^43617-160356748Enzo Doria03/2013
8459(3^118892-8)/9135892956718Lelio R Paula03/2012
8460(509203*2^188338-1)/356701Lelio R Paula03/2015
846120^43567-562356682Enzo Doria03/2013
84622^188234-11318356665Enzo Doria07/2014
8463(7*2^188215-1)/149731512556651Lelio R Paula01/2014
8464(1017*2^188171-1)/3556647Lelio R Paula03/2015
8465(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
8466(2^188176-1017)/45381454356638Lelio R Paula02/2012
846733*10^56634+756636Robert Price07/2016
8468(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
846914^49413+3356634Lelio R Paula02/2013
84703^118680+11056625Lelio R Paula10/2012
8471(13*10^56624+161)/356625Robert Price04/2017
8472(3^118676-2)/751665326356613Lelio R Paula03/2012
8473(13*2^188062+1)/1756613Lelio R Paula07/2012
84742^188056-131356611Yves Minet08/2012
847520^43510-558356608Enzo Doria03/2013
84762^188032+1228556604Lelio R Paula03/2011
8477(19*10^56597-43)/356598Robert Price10/2017
8478(265*10^56588+17)/356590Robert Price05/2016
84792^187959+577556582Lelio R Paula03/2011
8480(5*2^187959+1)/5356581Lelio R Paula07/2012
84813*10^56575-1356576Robert Price11/2017
8482(11*2^187889-1)/35156559Lelio R Paula01/2014
8483(100049^11311+1)/10005056553Faysal YAtim09/2007
8484(19*10^56544-1)/956545Serge Batalov03/2009
848520^43447-892356526Enzo Doria03/2013
84862^187743-11217756517Enzo Doria06/2014
8487(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
84885^80831-2256499Lelio R Paula10/2012
84895^80828-1316656497Enzo Doria02/2013
84907*2^187590-556472Lelio R Paula03/2014
84912^187555+7547356460Enzo Doria04/2016
84922^187541-28356456Yves Minet01/2012
8493(55*10^56453-1)/956454Serge Batalov03/2009
84942^187506-145156445Yves Minet08/2012
8495189^24794-256443Lelio R Paula10/2017
84966^72522+14356434Lelio R Paula10/2012
8497(15185*2^187452-1)/94956430Lelio R Paula03/2015
84982^187390+7956411Lelio R Paula03/2011
84992^187386+1290956409Lelio R Paula03/2011
85002^187382+61356408Jason Earls04/2008


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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