PRP Records

Probable Primes Top 10000

(212140 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 ?
850111^55302-24057592Enzo Doria07/2012
85022^191299-103146757587Paul Bourdelais11/2012
85032^191295-11199157586Enzo Doria05/2014
85042^191279-129757581Yves Minet08/2012
85053*6^73961+557554Lelio R Paula09/2014
8506(3^120623+5)/5214457548Lelio R Paula04/2012
8507(17*10^57543-29)/357544Robert Price09/2017
850842^35445-4157537Norbert Schneider06/2014
8509(71^31079-1)/7057534Paul Bourdelais08/2017
85102^191069-72340357518Paul Bourdelais11/2012
85114*10^57506-357507Serge Batalov11/2010
851210^57501+6735957502Patrick De Geest06/2016
851310^57501-100000000157501Robert Price05/2016
851410^57501-24986157501Patrick De Geest06/2016
8515(9^60251+4^60251)/1357493Robert Price02/2013
851620^44184-600357485Enzo Doria03/2013
85172^190948+1270557482Lelio R Paula10/2012
85182^190945+2957481Henri Lifchitz06/2005
85192^190922-40157474Yves Minet01/2012
852015^48860+4657464Lelio R Paula02/2013
85213^120434+2057462Lelio R Paula10/2012
85227^67964-3857437Lelio R Paula10/2012
85232^190799-11306557437Enzo Doria07/2014
85249*5^82159+257428Lelio R Paula09/2014
8525(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8528lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8526(103*10^57414-1)/357416Serge Batalov12/2014
8527(1654*30^38869-1)/2957416Karsten Bonath05/2017
85292*10^57410+9^5741057411Mike Oakes04/2011
85302^190704-159557408Lelio R Paula05/2011
853111^55121-174057403Enzo Doria11/2012
85322^190644-18557390Lelio R Paula04/2011
853341182!3-3^4118257389Robert Price08/2015
85342^190629-11225557386Enzo Doria06/2014
8535(2*10^57384-71)/357384Robert Price01/2017
85362*6^73735+5^7373557378Mike Oakes11/2009
85372^190605+5957378Lelio R Paula04/2011
85386^73727-757371Lelio R Paula10/2012
85392^190561-11222557365Enzo Doria06/2014
854010^57358+17089957359Patrick De Geest06/2016
854110^57358-800157358Robert Price03/2016
854218^45687-1157350Lelio R Paula02/2013
854311^55069-21057349Enzo Doria07/2012
854411^55068-1257348Lelio R Paula02/2013
854519^44839+5457339Lelio R Paula02/2013
8546(7*2^190468-1)/851157334Lelio R Paula01/2014
8547(23*10^57333-59)/957334Robert Price03/2017
85482^190455-1155*19045557333Henri Lifchitz02/2005
854965^31620+2857325Lelio R Paula01/2016
85502^190403+1609557318Lelio R Paula05/2011
8551(19*10^57316+119)/357317Robert Price02/2017
8553(21*2^190393+1)/21157314Lelio R Paula07/2012
85522^190392-11202557314Enzo Doria05/2014
8554(24737*2^190234+1)/957270Lelio R Paula05/2014
8555(7*2^190230+1)/2357265Lelio R Paula07/2012
8556(10223*2^190197+1)/321157256Lelio R Paula05/2014
855718^45590-9757228Lelio R Paula02/2013
8558(3*2^190105-1)/1920557224Lelio R Paula01/2014
8559(16*10^57219-31)/357220Robert Price03/2016
8560(2^190074+47)/5157217Lelio R Paula02/2012
85613^119894-14057204Lelio R Paula10/2012
8563(37^36473-1)/3657196Robert Price03/2012
85622^190000-216357196Yves Minet08/2013
85642^189987-279810757192Enzo Doria04/2016
85652^189935-11211757177Enzo Doria05/2014
85662^189909-11223157169Enzo Doria06/2014
8567132049#+14905357161Makoto Morimoto12/2015
856841032!3-2757158Robert Price09/2014
856919^44694+2257153Lelio R Paula02/2013
857012^52956-1757150Lelio R Paula02/2013
85712^189823-96757143Yves Minet01/2012
8572(25*10^57138-61)/957139Robert Price02/2015
85735^81743-4^(81743+1)57136Robert Price04/2016
85747^67593-5457123Lelio R Paula10/2012
85757*3^119712+257118Lelio R Paula03/2014
85765^81700+1657106Lelio R Paula10/2012
85772^189700+7656157106Enzo Doria05/2016
85792^189671+13157097Lelio R Paula04/2011
85784*6^73374+557097Lelio R Paula09/2014
8580(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8581(29*2^189619-1)/39357080Lelio R Paula01/2014
85823^119587+8057058Lelio R Paula10/2012
85832^189502-11345357046Enzo Doria07/2014
85842^189455+15357032Lelio R Paula04/2011
858524^41317-41317^2457027Norbert Schneider07/2016
85862^189414-1757020Lelio R Paula03/2011
858724^41311+2357018Norbert Schneider12/2013
8588norm(Mod(x,x^4+x^3-x+1)^207341-1)/256998Paul Vanderveen05/2018
8589(4*10^56989-31)/956989Erik Branger05/2011
859011^54712-162056977Enzo Doria11/2012
85912^189237-11223156967Enzo Doria06/2014
859317^46285-4856952Lelio R Paula02/2013
85922^189188+7524156952Enzo Doria04/2016
85942^189181+9439556950Henri Lifchitz01/2005
85957001^14808-10856940Enzo Doria07/2012
85962^189147-11263956939Enzo Doria06/2014
8597(19*10^56933-43)/356934Robert Price10/2017
85982^189110-356928M. Frind & P. Underwood11/2002
85992^189069+1290956916Lelio R Paula04/2011
8600(13*10^56909+191)/356910Robert Price08/2017
8601(35*10^56898-17)/956899Serge Batalov02/2009
86022^189011-595556898Lelio R Paula04/2011
86036^73119-556898Lelio R Paula10/2012
860413^51076-9056896Lelio R Paula02/2013
86052^188997+5689756894Yves Minet02/2010
86065^81388-1376656888Enzo Doria02/2013
8607(104^28201+1)/10556881Richard Fischer04/2018
8608(156^25933+1)/15756873Eric Chen12/2017
860920^43713-640356872Enzo Doria03/2013
8610(71*10^56858-287)/956859Robert Price05/2017
86112^188857-25423356852Gary Barnes09/2009
861215^48338-8856850Lelio R Paula02/2013
861310^56849+13643756850Patrick De Geest07/2017
861410^56849-70156849Robert Price06/2017
8615(2^188788+78557)/356831Lelio R Paula05/2012
86162^188771+1609556826Lelio R Paula04/2011
86177*2^188742-956818Lelio R Paula03/2014
861812^52646-6556815Lelio R Paula02/2013
86195003^15358-15856813Enzo Doria07/2012
86202^188713+57729457556809Lelio R Paula03/2013
86212^188693-11209956803Enzo Doria05/2014
8622(7^67211+4^67211)/1156799Robert Price10/2012
86232^188678-9439556798Lelio R Paula09/2011
862420^43651-850356792Enzo Doria03/2013
86262^188657-237156792Yves Minet10/2013
8625152^26029-151^2602956792Eric Chen04/2018
8627(14^49549+5^49549)/1956789Robert Price05/2013
8628(45^34351-1)/4456788Robert Price05/2014
86297*10^56785-2356786Robert Price04/2016
8630(10^56781-31)/356781Serge Batalov12/2014
86317*10^56779+356780Erik Branger11/2009
863210^56765+25917956766Patrick De Geest09/2013
863310^56765-24949756765Patrick De Geest09/2013
8634t(188706)56764Robert Price04/2015
86352^188551-90432756760Paul Bourdelais11/2012
8637(64*10^56756+17)/956757Robert Price09/2015
8636131101#+14629156757Makoto Morimoto02/2016
86382^188539-11251956756Enzo Doria06/2014
86396^72927+10156749Lelio R Paula10/2012
864020^43617-160356748Enzo Doria03/2013
8641(3^118892-8)/9135892956718Lelio R Paula03/2012
8642(509203*2^188338-1)/356701Lelio R Paula03/2015
864320^43567-562356682Enzo Doria03/2013
86442^188234-11318356665Enzo Doria07/2014
8645(139^26437+1)/14056653Richard Fischer03/2018
8646(7*2^188215-1)/149731512556651Lelio R Paula01/2014
8647(1017*2^188171-1)/3556647Lelio R Paula03/2015
8648(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
8649(2^188176-1017)/45381454356638Lelio R Paula02/2012
865033*10^56634+756636Robert Price07/2016
8651(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
865214^49413+3356634Lelio R Paula02/2013
86533^118680+11056625Lelio R Paula10/2012
8654(13*10^56624+161)/356625Robert Price04/2017
8655(3^118676-2)/751665326356613Lelio R Paula03/2012
8656(13*2^188062+1)/1756613Lelio R Paula07/2012
86572^188056-131356611Yves Minet08/2012
865820^43510-558356608Enzo Doria03/2013
86592^188032+1228556604Lelio R Paula03/2011
8660(19*10^56597-43)/356598Robert Price10/2017
8661(265*10^56588+17)/356590Robert Price05/2016
86622^187959+577556582Lelio R Paula03/2011
8663(5*2^187959+1)/5356581Lelio R Paula07/2012
86643*10^56575-1356576Robert Price11/2017
8665(11*2^187889-1)/35156559Lelio R Paula01/2014
8666(100049^11311+1)/10005056553Faysal YAtim09/2007
8667(19*10^56544-1)/956545Serge Batalov03/2009
866820^43447-892356526Enzo Doria03/2013
86692^187743-11217756517Enzo Doria06/2014
8670(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
86715^80831-2256499Lelio R Paula10/2012
86725^80828-1316656497Enzo Doria02/2013
86737*2^187590-556472Lelio R Paula03/2014
86742^187555+7547356460Enzo Doria04/2016
86752^187541-28356456Yves Minet01/2012
8676(55*10^56453-1)/956454Serge Batalov03/2009
86772^187506-145156445Yves Minet08/2012
8678189^24794-256443Lelio R Paula10/2017
86796^72522+14356434Lelio R Paula10/2012
8680(15185*2^187452-1)/94956430Lelio R Paula03/2015
86812^187390+7956411Lelio R Paula03/2011
86822^187386+1290956409Lelio R Paula03/2011
86832^187382+61356408Jason Earls04/2008
8684(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
868520^43337-956383Lelio R Paula02/2013
8686(26*10^56371-173)/356372Robert Price10/2017
8687(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
86892^187230+42756362Henri Lifchitz01/2005
868811^54121-948056362Enzo Doria02/2013
8690(21*2^187202-1)/4356354Lelio R Paula01/2014
86912^187173-9156345Lelio R Paula03/2011
8692(23*2^187174-1)/2071988356340Lelio R Paula01/2014
86932^187125-283356331Yves Minet09/2014
86949*7^66655-456331Lelio R Paula09/2014
869518^44874-9756330Lelio R Paula02/2013
869660*79^29679+1956322Serge Batalov03/2016
86975^80571+5656317Lelio R Paula10/2012
86985^80551-2256303Lelio R Paula10/2012
8699(76*10^56281+41)/956282Robert Price10/2015
8700(88*10^56271-43)/956272Robert Price11/2015
8701(5*10^56256-119)/356257Robert Price04/2016
87021508^17691+17691^150856230Serge Batalov05/2014
87033^117844-5856226Lelio R Paula10/2012
8704(19*10^56224+737)/956225Robert Price10/2017
870595^28427+256221Lelio R Paula05/2013
87062^186713+7681756207Enzo Doria05/2016
870716534^2505+2505^1653456196Hans Havermann06/2016
870814428^7849+7849^1442856195Hans Havermann06/2016
87092*10^56194-5156195Robert Price11/2017
871014898^5909+5909^1489856189Hans Havermann06/2016
871118^44758+9556184Lelio R Paula02/2013
87122^186555-74156159Lelio R Paula05/2011
8713(4*10^56156+173)/356157Robert Price01/2017
8715(3^117708+7)/44789656156Lelio R Paula03/2012
871415711^3752+3752^1571156156Hans Havermann06/2016
8716(23*2^186549-1)/242902556152Lelio R Paula01/2014
8717387^21694+21694^38756138Norbert Schneider08/2014
87182^186422+1723956119Yves Minet01/2010
87192^186418+424242956118Jason Earls10/2008
8720136^26300+13556113Norbert Schneider04/2015
87215*2^186392+956111Lelio R Paula03/2014
872214345^8152+8152^1434556108Hans Havermann07/2016
8723(5*2^186351-1)/3956097Lelio R Paula01/2014
87242^186319-54123756088Paul Bourdelais11/2012
87252*10^56083-4356084Robert Price07/2017
8726(16*10^56082-61)/956083Serge Batalov05/2009
8727(14*10^56080-143)/356081Robert Price01/2017
8728(265*10^56076+17)/356078Robert Price05/2016
87297^66346-5056069Lelio R Paula10/2012
873020^43094-3356067Lelio R Paula02/2013
873120^43090-138356062Enzo Doria03/2013
87323^117482+266056054Lelio R Paula10/2012
8733(22699*2^186193+1)/11156052Lelio R Paula05/2014
8734(68*10^56042+13)/956043Ray Chandler09/2010
87353*6^71992+5^7199256022Mike Oakes03/2010
873613691^12352+12352^1369156020Hans Havermann07/2016
8737(2^186095+7)/7556019Lelio R Paula02/2012
8738247^23412+23412^24756018Norbert Schneider08/2014
87391839^17156+17156^183956008Serge Batalov05/2014
874013736^11949+11949^1373656007Hans Havermann04/2016
8741(5*2^186036-1)/1156003Lelio R Paula01/2014
8742(299*10^55998-17)/356000Robert Price01/2017
8743p(12103)#/2-12855994Robert Price05/2017
87452^186003-17433755993Gary Barnes09/2009
8744(2^186010+78557)/12355993Lelio R Paula05/2012
874620^43037-9355993Lelio R Paula02/2013
874716375^2626+2626^1637555991Hans Havermann03/2016
874815631^3816+3816^1563155985Hans Havermann03/2016
874921^42335-255977Lelio R Paula08/2013
8750Phi(64736,139)55959Enzo Doria07/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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