PRP Records

Probable Primes Top 10000

(173006 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 ?
7751(27*2^191629+1)/12557686Lelio R Paula07/2012
77524*10^57684+3*7^5768457685Mike Oakes11/2010
77532*3^120898+557684Lelio R Paula04/2014
7754(6883*2^191610-1)/734757681Lelio R Paula04/2015
77556^74117-4957675Lelio R Paula10/2012
77562^191586-11320157674Enzo Doria07/2014
77572^191580+19357672Lelio R Paula04/2011
7758(103*29^39433+10401)/457669Curtis Bright05/2015
77592^191560+25525557666Lelio R Paula05/2011
77602^191515-8557652Lelio R Paula04/2011
77612^191502-112757648Yves Minet05/2013
77622*5^82473-3^8247357647Mike Oakes08/2010
77632^191430+10357627Lelio R Paula04/2011
77643*2^191408+557621Lelio R Paula03/2014
77652^191382-185893157612Enzo Doria04/2016
77666*7^68163+557606Lelio R Paula09/2014
776791^29403-257602Lelio R Paula08/2013
776811^55308-795057598Enzo Doria02/2013
77692^191329+6557596Lelio R Paula04/2011
777011^55302-24057592Enzo Doria07/2012
77712^191299-103146757587Paul Bourdelais11/2012
77722^191295-11199157586Enzo Doria05/2014
77732^191279-129757581Yves Minet08/2012
77743*6^73961+557554Lelio R Paula09/2014
7775(3^120623+5)/5214457548Lelio R Paula04/2012
777642^35445-4157537Norbert Schneider06/2014
77772^191069-72340357518Paul Bourdelais11/2012
77784*10^57506-357507Serge Batalov11/2010
777910^57501+6735957502Patrick De Geest06/2016
778010^57501-100000000157501Robert Price05/2016
778110^57501-24986157501Patrick De Geest06/2016
7782(9^60251+4^60251)/1357493Robert Price02/2013
778320^44184-600357485Enzo Doria03/2013
77842^190948+1270557482Lelio R Paula10/2012
77852^190945+2957481Henri Lifchitz06/2005
77862^190922-40157474Yves Minet01/2012
778715^48860+4657464Lelio R Paula02/2013
77883^120434+2057462Lelio R Paula10/2012
77897^67964-3857437Lelio R Paula10/2012
77902^190799-11306557437Enzo Doria07/2014
77919*5^82159+257428Lelio R Paula09/2014
7792(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
7794lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
7793(103*10^57414-1)/357416Serge Batalov12/2014
7795(1654*30^38869-1)/2957416Karsten Bonath05/2017
77962*10^57410+9^5741057411Mike Oakes04/2011
77972^190704-159557408Lelio R Paula05/2011
779811^55121-174057403Enzo Doria11/2012
77992^190644-18557390Lelio R Paula04/2011
780041182!3-3^4118257389Robert Price08/2015
78012^190629-11225557386Enzo Doria06/2014
7802(2*10^57384-71)/357384Robert Price01/2017
78042*6^73735+5^7373557378Mike Oakes11/2009
78032^190605+5957378Lelio R Paula04/2011
78056^73727-757371Lelio R Paula10/2012
78062^190561-11222557365Enzo Doria06/2014
780710^57358+17089957359Patrick De Geest06/2016
780810^57358-800157358Robert Price03/2016
780918^45687-1157350Lelio R Paula02/2013
781011^55069-21057349Enzo Doria07/2012
781111^55068-1257348Lelio R Paula02/2013
781219^44839+5457339Lelio R Paula02/2013
7813(7*2^190468-1)/851157334Lelio R Paula01/2014
7814(23*10^57333-59)/957334Robert Price03/2017
78152^190455-1155*19045557333Henri Lifchitz02/2005
781665^31620+2857325Lelio R Paula01/2016
78172^190403+1609557318Lelio R Paula05/2011
7818(19*10^57316+119)/357317Robert Price02/2017
7820(21*2^190393+1)/21157314Lelio R Paula07/2012
78192^190392-11202557314Enzo Doria05/2014
7821(24737*2^190234+1)/957270Lelio R Paula05/2014
7822(7*2^190230+1)/2357265Lelio R Paula07/2012
7823(10223*2^190197+1)/321157256Lelio R Paula05/2014
782418^45590-9757228Lelio R Paula02/2013
7825(3*2^190105-1)/1920557224Lelio R Paula01/2014
7826(16*10^57219-31)/357220Robert Price03/2016
7827(2^190074+47)/5157217Lelio R Paula02/2012
78283^119894-14057204Lelio R Paula10/2012
7830(37^36473-1)/3657196Robert Price03/2012
78292^190000-216357196Yves Minet08/2013
78312^189987-279810757192Enzo Doria04/2016
78322^189935-11211757177Enzo Doria05/2014
78332^189909-11223157169Enzo Doria06/2014
7834132049#+14905357161Makoto Morimoto12/2015
783541032!3-2757158Robert Price09/2014
783619^44694+2257153Lelio R Paula02/2013
783712^52956-1757150Lelio R Paula02/2013
78382^189823-96757143Yves Minet01/2012
7839(25*10^57138-61)/957139Robert Price02/2015
78405^81743-4^(81743+1)57136Robert Price04/2016
78417^67593-5457123Lelio R Paula10/2012
78427*3^119712+257118Lelio R Paula03/2014
78445^81700+1657106Lelio R Paula10/2012
78432^189700+7656157106Enzo Doria05/2016
78462^189671+13157097Lelio R Paula04/2011
78454*6^73374+557097Lelio R Paula09/2014
7847(67607*2^189651+1)/4372757091Lelio R Paula05/2014
7848(29*2^189619-1)/39357080Lelio R Paula01/2014
78493^119587+8057058Lelio R Paula10/2012
78502^189502-11345357046Enzo Doria07/2014
78512^189455+15357032Lelio R Paula04/2011
785224^41317-41317^2457027Norbert Schneider07/2016
78532^189414-1757020Lelio R Paula03/2011
785424^41311+2357018Norbert Schneider12/2013
7855(4*10^56989-31)/956989Erik Branger05/2011
785611^54712-162056977Enzo Doria11/2012
78572^189237-11223156967Enzo Doria06/2014
785817^46285-4856952Lelio R Paula02/2013
78592^189188+7524156952Enzo Doria04/2016
78602^189181+9439556950Henri Lifchitz01/2005
78617001^14808-10856940Enzo Doria07/2012
78622^189147-11263956939Enzo Doria06/2014
78632^189110-356928M. Frind & P. Underwood11/2002
78642^189069+1290956916Lelio R Paula04/2011
7865(35*10^56898-17)/956899Serge Batalov02/2009
78662^189011-595556898Lelio R Paula04/2011
78676^73119-556898Lelio R Paula10/2012
786813^51076-9056896Lelio R Paula02/2013
78692^188997+5689756894Yves Minet02/2010
78705^81388-1376656888Enzo Doria02/2013
787120^43713-640356872Enzo Doria03/2013
7872(71*10^56858-287)/956859Robert Price05/2017
78732^188857-25423356852Gary Barnes09/2009
787415^48338-8856850Lelio R Paula02/2013
7875(2^188788+78557)/356831Lelio R Paula05/2012
78762^188771+1609556826Lelio R Paula04/2011
78777*2^188742-956818Lelio R Paula03/2014
787812^52646-6556815Lelio R Paula02/2013
78795003^15358-15856813Enzo Doria07/2012
78802^188713+57729457556809Lelio R Paula03/2013
78812^188693-11209956803Enzo Doria05/2014
7882(7^67211+4^67211)/1156799Robert Price10/2012
78832^188678-9439556798Lelio R Paula09/2011
788420^43651-850356792Enzo Doria03/2013
78852^188657-237156792Yves Minet10/2013
7886(14^49549+5^49549)/1956789Robert Price05/2013
7887(45^34351-1)/4456788Robert Price05/2014
78887*10^56785-2356786Robert Price04/2016
7889(10^56781-31)/356781Serge Batalov12/2014
78907*10^56779+356780Erik Branger11/2009
789110^56765+25917956766Patrick De Geest09/2013
789210^56765-24949756765Patrick De Geest09/2013
7893t(188706)56764Robert Price04/2015
78942^188551-90432756760Paul Bourdelais11/2012
7895(64*10^56756+17)/956757Robert Price09/2015
7896131101#+14629156757Makoto Morimoto02/2016
78972^188539-11251956756Enzo Doria06/2014
78986^72927+10156749Lelio R Paula10/2012
789920^43617-160356748Enzo Doria03/2013
7900(3^118892-8)/9135892956718Lelio R Paula03/2012
7901(509203*2^188338-1)/356701Lelio R Paula03/2015
790220^43567-562356682Enzo Doria03/2013
79032^188234-11318356665Enzo Doria07/2014
7904(7*2^188215-1)/149731512556651Lelio R Paula01/2014
7905(1017*2^188171-1)/3556647Lelio R Paula03/2015
7906(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
7907(2^188176-1017)/45381454356638Lelio R Paula02/2012
790833*10^56634+756636Robert Price07/2016
7909(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
791014^49413+3356634Lelio R Paula02/2013
79113^118680+11056625Lelio R Paula10/2012
7912(13*10^56624+161)/356625Robert Price04/2017
7913(3^118676-2)/751665326356613Lelio R Paula03/2012
7914(13*2^188062+1)/1756613Lelio R Paula07/2012
79152^188056-131356611Yves Minet08/2012
791620^43510-558356608Enzo Doria03/2013
79172^188032+1228556604Lelio R Paula03/2011
7918(265*10^56588+17)/356590Robert Price05/2016
79192^187959+577556582Lelio R Paula03/2011
7920(5*2^187959+1)/5356581Lelio R Paula07/2012
7921(11*2^187889-1)/35156559Lelio R Paula01/2014
7922(100049^11311+1)/10005056553Faysal YAtim09/2007
7923(19*10^56544-1)/956545Serge Batalov03/2009
792420^43447-892356526Enzo Doria03/2013
79252^187743-11217756517Enzo Doria06/2014
7926(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
79275^80831-2256499Lelio R Paula10/2012
79285^80828-1316656497Enzo Doria02/2013
79297*2^187590-556472Lelio R Paula03/2014
79302^187555+7547356460Enzo Doria04/2016
79312^187541-28356456Yves Minet01/2012
7932(55*10^56453-1)/956454Serge Batalov03/2009
79332^187506-145156445Yves Minet08/2012
79346^72522+14356434Lelio R Paula10/2012
7935(15185*2^187452-1)/94956430Lelio R Paula03/2015
79362^187390+7956411Lelio R Paula03/2011
79372^187386+1290956409Lelio R Paula03/2011
79382^187382+61356408Jason Earls04/2008
7939(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
794020^43337-956383Lelio R Paula02/2013
7941(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
79422^187230+42756362Henri Lifchitz01/2005
794311^54121-948056362Enzo Doria02/2013
7944(21*2^187202-1)/4356354Lelio R Paula01/2014
79452^187173-9156345Lelio R Paula03/2011
7946(23*2^187174-1)/2071988356340Lelio R Paula01/2014
79472^187125-283356331Yves Minet09/2014
79489*7^66655-456331Lelio R Paula09/2014
794918^44874-9756330Lelio R Paula02/2013
795060*79^29679+1956322Serge Batalov03/2016
79515^80571+5656317Lelio R Paula10/2012
79525^80551-2256303Lelio R Paula10/2012
7953(76*10^56281+41)/956282Robert Price10/2015
7954(88*10^56271-43)/956272Robert Price11/2015
7955(5*10^56256-119)/356257Robert Price04/2016
79561508^17691+17691^150856230Serge Batalov05/2014
79573^117844-5856226Lelio R Paula10/2012
795895^28427+256221Lelio R Paula05/2013
79592^186713+7681756207Enzo Doria05/2016
796016534^2505+2505^1653456196Hans Havermann06/2016
796114428^7849+7849^1442856195Hans Havermann06/2016
796214898^5909+5909^1489856189Hans Havermann06/2016
796318^44758+9556184Lelio R Paula02/2013
79642^186555-74156159Lelio R Paula05/2011
7965(4*10^56156+173)/356157Robert Price01/2017
7967(3^117708+7)/44789656156Lelio R Paula03/2012
796615711^3752+3752^1571156156Hans Havermann06/2016
7968(23*2^186549-1)/242902556152Lelio R Paula01/2014
7969387^21694+21694^38756138Norbert Schneider08/2014
79702^186422+1723956119Yves Minet01/2010
79712^186418+424242956118Jason Earls10/2008
7972136^26300+13556113Norbert Schneider04/2015
79735*2^186392+956111Lelio R Paula03/2014
797414345^8152+8152^1434556108Hans Havermann07/2016
7975(5*2^186351-1)/3956097Lelio R Paula01/2014
79762^186319-54123756088Paul Bourdelais11/2012
7977(16*10^56082-61)/956083Serge Batalov05/2009
7978(14*10^56080-143)/356081Robert Price01/2017
7979(265*10^56076+17)/356078Robert Price05/2016
79807^66346-5056069Lelio R Paula10/2012
798120^43094-3356067Lelio R Paula02/2013
798220^43090-138356062Enzo Doria03/2013
79833^117482+266056054Lelio R Paula10/2012
7984(22699*2^186193+1)/11156052Lelio R Paula05/2014
7985(68*10^56042+13)/956043Ray Chandler09/2010
79863*6^71992+5^7199256022Mike Oakes03/2010
798713691^12352+12352^1369156020Hans Havermann07/2016
7988(2^186095+7)/7556019Lelio R Paula02/2012
7989247^23412+23412^24756018Norbert Schneider08/2014
79901839^17156+17156^183956008Serge Batalov05/2014
799113736^11949+11949^1373656007Hans Havermann04/2016
7992(5*2^186036-1)/1156003Lelio R Paula01/2014
7993(299*10^55998-17)/356000Robert Price01/2017
7994p(12103)#/2-12855994Robert Price05/2017
79962^186003-17433755993Gary Barnes09/2009
7995(2^186010+78557)/12355993Lelio R Paula05/2012
799720^43037-9355993Lelio R Paula02/2013
799816375^2626+2626^1637555991Hans Havermann03/2016
799915631^3816+3816^1563155985Hans Havermann03/2016
800021^42335-255977Lelio R Paula08/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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