PRP Records

Probable Primes Top 10000

(174961 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 ?
77517001^15069-10057943Enzo Doria07/2012
7752L(277273)/1109092157940Donovan Johnson11/2005
7753(2^192469-1017)/3557938Lelio R Paula02/2012
77542^192457-1155*19245757936Henri Lifchitz02/2005
77552^192443+138557932Lelio R Paula05/2011
7756132^27317-13157928Norbert Schneider03/2015
775741522!3-5904957912Robert Price12/2015
7758(3*2^192380-1)/16957911Lelio R Paula01/2014
77592^192339-251557900Yves Minet07/2014
77602^192303+769557889Lelio R Paula10/2012
77612^192273-595557880Lelio R Paula05/2011
77622^192257+1609557876Lelio R Paula05/2011
77632^192218-11186157864Enzo Doria05/2014
77642^192214-394157863Yves Minet04/2017
7765(2^192212+3)/25957860Lelio R Paula02/2012
7766(3^121270+8)/15593975357853Lelio R Paula03/2012
776780^30393-7957841Norbert Schneider03/2015
776820^44455-312357838Enzo Doria03/2013
77702^192122-19557835Lelio R Paula04/2011
7769(29*10^57834+91)/357835Robert Price03/2016
77718*6^74306+557823Lelio R Paula09/2014
7772(39^36341-1)/3857820Robert Price04/2012
77732^192037-11180557809Enzo Doria05/2014
77742^192023-192023^257805Henri Lifchitz05/2005
777521^43717+257804Ray Chandler08/2011
77768*5^82687+757797Lelio R Paula09/2014
77775^82680-2457791Lelio R Paula10/2012
7778(2^191915+47)/9557771Lelio R Paula02/2012
77796^74227-9557760Lelio R Paula10/2012
77802^191861+2983557756Lelio R Paula10/2012
77821908^17605+17605^190857755Serge Batalov05/2014
77815*10^57754+5957755Robert Price09/2016
7783(5*2^191821-1)/892406757738Lelio R Paula01/2014
77843*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
778541399!3-656157723Robert Price11/2015
77862^191745+1757721Lelio R Paula04/2011
77872^191730-76157717Yves Minet01/2012
7788(2^191733-3)/225157715Lelio R Paula02/2012
77892^191698-11157707Lelio R Paula04/2011
7790(13*10^57691+23)/957692Robert Price02/2015
779120^44340-542357688Enzo Doria03/2013
7792(27*2^191629+1)/12557686Lelio R Paula07/2012
77934*10^57684+3*7^5768457685Mike Oakes11/2010
77942*3^120898+557684Lelio R Paula04/2014
7795(6883*2^191610-1)/734757681Lelio R Paula04/2015
77966^74117-4957675Lelio R Paula10/2012
77972^191586-11320157674Enzo Doria07/2014
77982^191580+19357672Lelio R Paula04/2011
7799(103*29^39433+10401)/457669Curtis Bright05/2015
78002^191560+25525557666Lelio R Paula05/2011
78012^191515-8557652Lelio R Paula04/2011
78022^191502-112757648Yves Minet05/2013
78032*5^82473-3^8247357647Mike Oakes08/2010
78042^191430+10357627Lelio R Paula04/2011
78053*2^191408+557621Lelio R Paula03/2014
78062^191382-185893157612Enzo Doria04/2016
78076*7^68163+557606Lelio R Paula09/2014
780891^29403-257602Lelio R Paula08/2013
780911^55308-795057598Enzo Doria02/2013
78102^191329+6557596Lelio R Paula04/2011
781111^55302-24057592Enzo Doria07/2012
78122^191299-103146757587Paul Bourdelais11/2012
78132^191295-11199157586Enzo Doria05/2014
78142^191279-129757581Yves Minet08/2012
78153*6^73961+557554Lelio R Paula09/2014
7816(3^120623+5)/5214457548Lelio R Paula04/2012
781742^35445-4157537Norbert Schneider06/2014
78182^191069-72340357518Paul Bourdelais11/2012
78194*10^57506-357507Serge Batalov11/2010
782010^57501+6735957502Patrick De Geest06/2016
782110^57501-100000000157501Robert Price05/2016
782210^57501-24986157501Patrick De Geest06/2016
7823(9^60251+4^60251)/1357493Robert Price02/2013
782420^44184-600357485Enzo Doria03/2013
78252^190948+1270557482Lelio R Paula10/2012
78262^190945+2957481Henri Lifchitz06/2005
78272^190922-40157474Yves Minet01/2012
782815^48860+4657464Lelio R Paula02/2013
78293^120434+2057462Lelio R Paula10/2012
78307^67964-3857437Lelio R Paula10/2012
78312^190799-11306557437Enzo Doria07/2014
78329*5^82159+257428Lelio R Paula09/2014
7833(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
7836lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
7835(103*10^57414-1)/357416Serge Batalov12/2014
7834(1654*30^38869-1)/2957416Karsten Bonath05/2017
78372*10^57410+9^5741057411Mike Oakes04/2011
78382^190704-159557408Lelio R Paula05/2011
783911^55121-174057403Enzo Doria11/2012
78402^190644-18557390Lelio R Paula04/2011
784141182!3-3^4118257389Robert Price08/2015
78422^190629-11225557386Enzo Doria06/2014
7843(2*10^57384-71)/357384Robert Price01/2017
78442*6^73735+5^7373557378Mike Oakes11/2009
78452^190605+5957378Lelio R Paula04/2011
78466^73727-757371Lelio R Paula10/2012
78472^190561-11222557365Enzo Doria06/2014
784810^57358+17089957359Patrick De Geest06/2016
784910^57358-800157358Robert Price03/2016
785018^45687-1157350Lelio R Paula02/2013
785111^55069-21057349Enzo Doria07/2012
785211^55068-1257348Lelio R Paula02/2013
785319^44839+5457339Lelio R Paula02/2013
7855(7*2^190468-1)/851157334Lelio R Paula01/2014
7854(23*10^57333-59)/957334Robert Price03/2017
78562^190455-1155*19045557333Henri Lifchitz02/2005
785765^31620+2857325Lelio R Paula01/2016
78582^190403+1609557318Lelio R Paula05/2011
7859(19*10^57316+119)/357317Robert Price02/2017
7860(21*2^190393+1)/21157314Lelio R Paula07/2012
78612^190392-11202557314Enzo Doria05/2014
7862(24737*2^190234+1)/957270Lelio R Paula05/2014
7863(7*2^190230+1)/2357265Lelio R Paula07/2012
7864(10223*2^190197+1)/321157256Lelio R Paula05/2014
786518^45590-9757228Lelio R Paula02/2013
7866(3*2^190105-1)/1920557224Lelio R Paula01/2014
7867(16*10^57219-31)/357220Robert Price03/2016
7868(2^190074+47)/5157217Lelio R Paula02/2012
78693^119894-14057204Lelio R Paula10/2012
7871(37^36473-1)/3657196Robert Price03/2012
78702^190000-216357196Yves Minet08/2013
78722^189987-279810757192Enzo Doria04/2016
78732^189935-11211757177Enzo Doria05/2014
78742^189909-11223157169Enzo Doria06/2014
7875132049#+14905357161Makoto Morimoto12/2015
787641032!3-2757158Robert Price09/2014
787719^44694+2257153Lelio R Paula02/2013
787812^52956-1757150Lelio R Paula02/2013
78792^189823-96757143Yves Minet01/2012
7880(25*10^57138-61)/957139Robert Price02/2015
78815^81743-4^(81743+1)57136Robert Price04/2016
78827^67593-5457123Lelio R Paula10/2012
78837*3^119712+257118Lelio R Paula03/2014
78845^81700+1657106Lelio R Paula10/2012
78852^189700+7656157106Enzo Doria05/2016
78872^189671+13157097Lelio R Paula04/2011
78864*6^73374+557097Lelio R Paula09/2014
7888(67607*2^189651+1)/4372757091Lelio R Paula05/2014
7889(29*2^189619-1)/39357080Lelio R Paula01/2014
78903^119587+8057058Lelio R Paula10/2012
78912^189502-11345357046Enzo Doria07/2014
78922^189455+15357032Lelio R Paula04/2011
789324^41317-41317^2457027Norbert Schneider07/2016
78942^189414-1757020Lelio R Paula03/2011
789524^41311+2357018Norbert Schneider12/2013
7896(4*10^56989-31)/956989Erik Branger05/2011
789711^54712-162056977Enzo Doria11/2012
78982^189237-11223156967Enzo Doria06/2014
790017^46285-4856952Lelio R Paula02/2013
78992^189188+7524156952Enzo Doria04/2016
79012^189181+9439556950Henri Lifchitz01/2005
79027001^14808-10856940Enzo Doria07/2012
79032^189147-11263956939Enzo Doria06/2014
79042^189110-356928M. Frind & P. Underwood11/2002
79052^189069+1290956916Lelio R Paula04/2011
7906(35*10^56898-17)/956899Serge Batalov02/2009
79072^189011-595556898Lelio R Paula04/2011
79086^73119-556898Lelio R Paula10/2012
790913^51076-9056896Lelio R Paula02/2013
79102^188997+5689756894Yves Minet02/2010
79115^81388-1376656888Enzo Doria02/2013
791220^43713-640356872Enzo Doria03/2013
7913(71*10^56858-287)/956859Robert Price05/2017
79142^188857-25423356852Gary Barnes09/2009
791515^48338-8856850Lelio R Paula02/2013
791610^56849-70156849Robert Price06/2017
7917(2^188788+78557)/356831Lelio R Paula05/2012
79182^188771+1609556826Lelio R Paula04/2011
79197*2^188742-956818Lelio R Paula03/2014
792012^52646-6556815Lelio R Paula02/2013
79215003^15358-15856813Enzo Doria07/2012
79222^188713+57729457556809Lelio R Paula03/2013
79232^188693-11209956803Enzo Doria05/2014
7924(7^67211+4^67211)/1156799Robert Price10/2012
79252^188678-9439556798Lelio R Paula09/2011
792620^43651-850356792Enzo Doria03/2013
79272^188657-237156792Yves Minet10/2013
7928(14^49549+5^49549)/1956789Robert Price05/2013
7929(45^34351-1)/4456788Robert Price05/2014
79307*10^56785-2356786Robert Price04/2016
7931(10^56781-31)/356781Serge Batalov12/2014
79327*10^56779+356780Erik Branger11/2009
793310^56765+25917956766Patrick De Geest09/2013
793410^56765-24949756765Patrick De Geest09/2013
7935t(188706)56764Robert Price04/2015
79362^188551-90432756760Paul Bourdelais11/2012
7937(64*10^56756+17)/956757Robert Price09/2015
7938131101#+14629156757Makoto Morimoto02/2016
79392^188539-11251956756Enzo Doria06/2014
79406^72927+10156749Lelio R Paula10/2012
794120^43617-160356748Enzo Doria03/2013
7942(3^118892-8)/9135892956718Lelio R Paula03/2012
7943(509203*2^188338-1)/356701Lelio R Paula03/2015
794420^43567-562356682Enzo Doria03/2013
79452^188234-11318356665Enzo Doria07/2014
7946(7*2^188215-1)/149731512556651Lelio R Paula01/2014
7947(1017*2^188171-1)/3556647Lelio R Paula03/2015
7948(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
7949(2^188176-1017)/45381454356638Lelio R Paula02/2012
795033*10^56634+756636Robert Price07/2016
7951(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
795214^49413+3356634Lelio R Paula02/2013
79533^118680+11056625Lelio R Paula10/2012
7954(13*10^56624+161)/356625Robert Price04/2017
7955(3^118676-2)/751665326356613Lelio R Paula03/2012
7956(13*2^188062+1)/1756613Lelio R Paula07/2012
79572^188056-131356611Yves Minet08/2012
795820^43510-558356608Enzo Doria03/2013
79592^188032+1228556604Lelio R Paula03/2011
7960(265*10^56588+17)/356590Robert Price05/2016
79612^187959+577556582Lelio R Paula03/2011
7962(5*2^187959+1)/5356581Lelio R Paula07/2012
7963(11*2^187889-1)/35156559Lelio R Paula01/2014
7964(100049^11311+1)/10005056553Faysal YAtim09/2007
7965(19*10^56544-1)/956545Serge Batalov03/2009
796620^43447-892356526Enzo Doria03/2013
79672^187743-11217756517Enzo Doria06/2014
7968(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
79695^80831-2256499Lelio R Paula10/2012
79705^80828-1316656497Enzo Doria02/2013
79717*2^187590-556472Lelio R Paula03/2014
79722^187555+7547356460Enzo Doria04/2016
79732^187541-28356456Yves Minet01/2012
7974(55*10^56453-1)/956454Serge Batalov03/2009
79752^187506-145156445Yves Minet08/2012
79766^72522+14356434Lelio R Paula10/2012
7977(15185*2^187452-1)/94956430Lelio R Paula03/2015
79782^187390+7956411Lelio R Paula03/2011
79792^187386+1290956409Lelio R Paula03/2011
79802^187382+61356408Jason Earls04/2008
7981(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
798220^43337-956383Lelio R Paula02/2013
7983(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
79842^187230+42756362Henri Lifchitz01/2005
798511^54121-948056362Enzo Doria02/2013
7986(21*2^187202-1)/4356354Lelio R Paula01/2014
79872^187173-9156345Lelio R Paula03/2011
7988(23*2^187174-1)/2071988356340Lelio R Paula01/2014
79892^187125-283356331Yves Minet09/2014
79909*7^66655-456331Lelio R Paula09/2014
799118^44874-9756330Lelio R Paula02/2013
799260*79^29679+1956322Serge Batalov03/2016
79935^80571+5656317Lelio R Paula10/2012
79945^80551-2256303Lelio R Paula10/2012
7995(76*10^56281+41)/956282Robert Price10/2015
7996(88*10^56271-43)/956272Robert Price11/2015
7997(5*10^56256-119)/356257Robert Price04/2016
79981508^17691+17691^150856230Serge Batalov05/2014
79993^117844-5856226Lelio R Paula10/2012
800095^28427+256221Lelio R Paula05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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