PRP Records

Probable Primes Top 10000

(172742 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 ?
77512^189935-11211757177Enzo Doria05/2014
77522^189909-11223157169Enzo Doria06/2014
7753132049#+14905357161Makoto Morimoto12/2015
775441032!3-2757158Robert Price09/2014
775519^44694+2257153Lelio R Paula02/2013
775612^52956-1757150Lelio R Paula02/2013
77572^189823-96757143Yves Minet01/2012
7758(25*10^57138-61)/957139Robert Price02/2015
77595^81743-4^(81743+1)57136Robert Price04/2016
77607^67593-5457123Lelio R Paula10/2012
77617*3^119712+257118Lelio R Paula03/2014
77635^81700+1657106Lelio R Paula10/2012
77622^189700+7656157106Enzo Doria05/2016
77652^189671+13157097Lelio R Paula04/2011
77644*6^73374+557097Lelio R Paula09/2014
7766(67607*2^189651+1)/4372757091Lelio R Paula05/2014
7767(29*2^189619-1)/39357080Lelio R Paula01/2014
77683^119587+8057058Lelio R Paula10/2012
77692^189502-11345357046Enzo Doria07/2014
77702^189455+15357032Lelio R Paula04/2011
777124^41317-41317^2457027Norbert Schneider07/2016
77722^189414-1757020Lelio R Paula03/2011
777324^41311+2357018Norbert Schneider12/2013
7774(4*10^56989-31)/956989Erik Branger05/2011
777511^54712-162056977Enzo Doria11/2012
77762^189237-11223156967Enzo Doria06/2014
777717^46285-4856952Lelio R Paula02/2013
77782^189188+7524156952Enzo Doria04/2016
77792^189181+9439556950Henri Lifchitz01/2005
77807001^14808-10856940Enzo Doria07/2012
77812^189147-11263956939Enzo Doria06/2014
77822^189110-356928M. Frind & P. Underwood11/2002
77832^189069+1290956916Lelio R Paula04/2011
7784(35*10^56898-17)/956899Serge Batalov02/2009
77852^189011-595556898Lelio R Paula04/2011
77866^73119-556898Lelio R Paula10/2012
778713^51076-9056896Lelio R Paula02/2013
77882^188997+5689756894Yves Minet02/2010
77895^81388-1376656888Enzo Doria02/2013
779020^43713-640356872Enzo Doria03/2013
77912^188857-25423356852Gary Barnes09/2009
779215^48338-8856850Lelio R Paula02/2013
7793(2^188788+78557)/356831Lelio R Paula05/2012
77942^188771+1609556826Lelio R Paula04/2011
77957*2^188742-956818Lelio R Paula03/2014
779612^52646-6556815Lelio R Paula02/2013
77975003^15358-15856813Enzo Doria07/2012
77982^188713+57729457556809Lelio R Paula03/2013
77992^188693-11209956803Enzo Doria05/2014
7800(7^67211+4^67211)/1156799Robert Price10/2012
78012^188678-9439556798Lelio R Paula09/2011
780220^43651-850356792Enzo Doria03/2013
78032^188657-237156792Yves Minet10/2013
7804(14^49549+5^49549)/1956789Robert Price05/2013
7805(45^34351-1)/4456788Robert Price05/2014
78067*10^56785-2356786Robert Price04/2016
7807(10^56781-31)/356781Serge Batalov12/2014
78087*10^56779+356780Erik Branger11/2009
780910^56765+25917956766Patrick De Geest09/2013
781010^56765-24949756765Patrick De Geest09/2013
7811t(188706)56764Robert Price04/2015
78122^188551-90432756760Paul Bourdelais11/2012
7813(64*10^56756+17)/956757Robert Price09/2015
7814131101#+14629156757Makoto Morimoto02/2016
78152^188539-11251956756Enzo Doria06/2014
78166^72927+10156749Lelio R Paula10/2012
781720^43617-160356748Enzo Doria03/2013
7818(3^118892-8)/9135892956718Lelio R Paula03/2012
7819(509203*2^188338-1)/356701Lelio R Paula03/2015
782020^43567-562356682Enzo Doria03/2013
78212^188234-11318356665Enzo Doria07/2014
7822(7*2^188215-1)/149731512556651Lelio R Paula01/2014
7823(1017*2^188171-1)/3556647Lelio R Paula03/2015
7824(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
7825(2^188176-1017)/45381454356638Lelio R Paula02/2012
782633*10^56634+756636Robert Price07/2016
7827(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
782814^49413+3356634Lelio R Paula02/2013
78293^118680+11056625Lelio R Paula10/2012
7830(13*10^56624+161)/356625Robert Price04/2017
7831(3^118676-2)/751665326356613Lelio R Paula03/2012
7832(13*2^188062+1)/1756613Lelio R Paula07/2012
78332^188056-131356611Yves Minet08/2012
783420^43510-558356608Enzo Doria03/2013
78352^188032+1228556604Lelio R Paula03/2011
7836(265*10^56588+17)/356590Robert Price05/2016
78372^187959+577556582Lelio R Paula03/2011
7838(5*2^187959+1)/5356581Lelio R Paula07/2012
7839(11*2^187889-1)/35156559Lelio R Paula01/2014
7840(100049^11311+1)/10005056553Faysal YAtim09/2007
7841(19*10^56544-1)/956545Serge Batalov03/2009
784220^43447-892356526Enzo Doria03/2013
78432^187743-11217756517Enzo Doria06/2014
7844(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
78455^80831-2256499Lelio R Paula10/2012
78465^80828-1316656497Enzo Doria02/2013
78477*2^187590-556472Lelio R Paula03/2014
78482^187555+7547356460Enzo Doria04/2016
78492^187541-28356456Yves Minet01/2012
7850(55*10^56453-1)/956454Serge Batalov03/2009
78512^187506-145156445Yves Minet08/2012
78526^72522+14356434Lelio R Paula10/2012
7853(15185*2^187452-1)/94956430Lelio R Paula03/2015
78542^187390+7956411Lelio R Paula03/2011
78552^187386+1290956409Lelio R Paula03/2011
78562^187382+61356408Jason Earls04/2008
7857(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
785820^43337-956383Lelio R Paula02/2013
7859(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
78612^187230+42756362Henri Lifchitz01/2005
786011^54121-948056362Enzo Doria02/2013
7862(21*2^187202-1)/4356354Lelio R Paula01/2014
78632^187173-9156345Lelio R Paula03/2011
7864(23*2^187174-1)/2071988356340Lelio R Paula01/2014
78652^187125-283356331Yves Minet09/2014
78669*7^66655-456331Lelio R Paula09/2014
786718^44874-9756330Lelio R Paula02/2013
786860*79^29679+1956322Serge Batalov03/2016
78695^80571+5656317Lelio R Paula10/2012
78705^80551-2256303Lelio R Paula10/2012
7871(76*10^56281+41)/956282Robert Price10/2015
7872(88*10^56271-43)/956272Robert Price11/2015
7873(5*10^56256-119)/356257Robert Price04/2016
78741508^17691+17691^150856230Serge Batalov05/2014
78753^117844-5856226Lelio R Paula10/2012
787695^28427+256221Lelio R Paula05/2013
78772^186713+7681756207Enzo Doria05/2016
787816534^2505+2505^1653456196Hans Havermann06/2016
787914428^7849+7849^1442856195Hans Havermann06/2016
788014898^5909+5909^1489856189Hans Havermann06/2016
788118^44758+9556184Lelio R Paula02/2013
78822^186555-74156159Lelio R Paula05/2011
7883(4*10^56156+173)/356157Robert Price01/2017
7885(3^117708+7)/44789656156Lelio R Paula03/2012
788415711^3752+3752^1571156156Hans Havermann06/2016
7886(23*2^186549-1)/242902556152Lelio R Paula01/2014
7887387^21694+21694^38756138Norbert Schneider08/2014
78882^186422+1723956119Yves Minet01/2010
78892^186418+424242956118Jason Earls10/2008
7890136^26300+13556113Norbert Schneider04/2015
78915*2^186392+956111Lelio R Paula03/2014
789214345^8152+8152^1434556108Hans Havermann07/2016
7893(5*2^186351-1)/3956097Lelio R Paula01/2014
78942^186319-54123756088Paul Bourdelais11/2012
7895(16*10^56082-61)/956083Serge Batalov05/2009
7896(14*10^56080-143)/356081Robert Price01/2017
7897(265*10^56076+17)/356078Robert Price05/2016
78987^66346-5056069Lelio R Paula10/2012
789920^43094-3356067Lelio R Paula02/2013
790020^43090-138356062Enzo Doria03/2013
79013^117482+266056054Lelio R Paula10/2012
7902(22699*2^186193+1)/11156052Lelio R Paula05/2014
7903(68*10^56042+13)/956043Ray Chandler09/2010
79043*6^71992+5^7199256022Mike Oakes03/2010
790513691^12352+12352^1369156020Hans Havermann07/2016
7906(2^186095+7)/7556019Lelio R Paula02/2012
7907247^23412+23412^24756018Norbert Schneider08/2014
79081839^17156+17156^183956008Serge Batalov05/2014
790913736^11949+11949^1373656007Hans Havermann04/2016
7910(5*2^186036-1)/1156003Lelio R Paula01/2014
7911(299*10^55998-17)/356000Robert Price01/2017
79142^186003-17433755993Gary Barnes09/2009
7912(2^186010+78557)/12355993Lelio R Paula05/2012
791320^43037-9355993Lelio R Paula02/2013
791516375^2626+2626^1637555991Hans Havermann03/2016
791615631^3816+3816^1563155985Hans Havermann03/2016
791721^42335-255977Lelio R Paula08/2013
7918Phi(64736,139)55959Enzo Doria07/2012
791915215^4762+4762^1521555958Hans Havermann03/2016
792019317^788+788^1931755953Anatoly F. Selevich12/2006
792113582^13165+13165^1358255950Hans Havermann08/2016
7922(78557*2^185842+1)/18955947Lelio R Paula06/2014
792315^47562-8655938Lelio R Paula02/2013
79243^117222+455930Lelio R Paula03/2012
792524^40519-23^4051955925Robert Price07/2012
792613636^12623+12623^1363655924Hans Havermann07/2016
79272^185767-9955922Lelio R Paula03/2011
7928(19*2^185750-1)/1555917Lelio R Paula01/2014
792915^47542-5855914Lelio R Paula02/2013
793020^42973-558355910Enzo Doria03/2013
79314*10^55906+2155907Robert Price08/2016
79322^185713-11155906Lelio R Paula03/2011
793313^50174+8855891Lelio R Paula01/2013
793414569^6846+6846^1456955879Hans Havermann08/2016
7935Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
79363^117087-8055865Lelio R Paula10/2012
7937(7*10^55851-43)/955851Robert Price10/2014
79382^185519-16955847Lelio R Paula03/2011
79397^66074+1055840Lelio R Paula10/2012
7940(19*10^55833-49)/355834Robert Price02/2017
794112^51732+555829Lelio R Paula01/2013
79423*2^185429+755821Lelio R Paula03/2014
7943(9787*2^185420-1)/38155819Lelio R Paula04/2015
794414427^7396+7396^1442755819Hans Havermann08/2016
794510^55811+2155812Robert Price01/2011
794610^55811-7410355811Patrick De Geest12/2012
794711^53591-153055810Enzo Doria11/2012
79482^185355-214555798Lelio R Paula03/2011
794914531^6912+6912^1453155794Hans Havermann07/2016
79502^185327-161555789Lelio R Paula03/2011
79512^185280-1277955775Enzo Doria10/2012
795215504^3955+3955^1550455771Hans Havermann07/2016
79535^79770-4455757Lelio R Paula10/2012
795418^44416-8555755Lelio R Paula02/2013
79552^185208-45999555754Enzo Doria06/2015
79562^185200+118555751Lelio R Paula03/2011
79577^65964+6^(65964-1)55747Robert Price03/2016
79582^185151-23715755737Gary Barnes09/2009
7959110017^11055-10255734Enzo Doria07/2012
796014754^5987+5987^1475455729Hans Havermann07/2016
796140090!3-955711Robert Price09/2014
79629*10^55707+8955708Robert Price11/2016
79632^185023-225755698Yves Minet06/2009
796418628^977+977^1862855696Anatoly F. Selevich01/2007
79652^185006-9355693Lelio R Paula03/2011
79662^185003-251555692Yves Minet07/2014
79676^71524-1955657Lelio R Paula10/2012
79682^184872-219555653Yves Minet08/2013
7969507^20572+20572^50755648Norbert Schneider06/2016
7970134^26151-13355626Norbert Schneider03/2015
797115340^4221+4221^1534055614Hans Havermann07/2016
797227743!2+255612Robert Price01/2013
797320^42744+8155612Lelio R Paula02/2013
797414609^6406+6406^1460955611Hans Havermann07/2016
79752^184724-11288355608Enzo Doria06/2014
797613507^13074+13074^1350755601Hans Havermann07/2016
79772^184689+12955597Lelio R Paula03/2011
7978(9179*2^184672-1)/19355594Lelio R Paula03/2015
7979(22*10^55592-19)/355593Robert Price02/2017
7980Phi(59984,89)55582Enzo Doria05/2012
798111^53368+1655578Lelio R Paula01/2013
798220^42717-192355577Enzo Doria03/2013
7983117^26870+26870^11755573Serge Batalov05/2014
798412^51488+5555565Lelio R Paula01/2013
7985(44*10^55558-17)/955559Robert Price06/2015
798610^55555+3285755556Patrick De Geest06/2010
798710^55555-13672155555Patrick De Geest06/2010
7988(11*2^184541-1)/35155551Lelio R Paula01/2014
798920^42696-204355549Enzo Doria03/2013
7990(2*10^55544+1)/355544Serge Batalov06/2009
7991(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
79925003^15013-16055537Enzo Doria07/2012
799339^34896-255522Lelio R Paula08/2013
7994(6^71345-61)/555517Lelio R Paula05/2014
79952^184407-301955513Yves Minet10/2014
7996(43*10^55512-61)/955513Robert Price06/2015
799720^42667-84355512Enzo Doria03/2013
7998133^26134-13255505Norbert Schneider03/2015
7999(31*2^184378-1)/71155502Lelio R Paula01/2014
80009*7^65667-455497Lelio R Paula09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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