PRP Records

Probable Primes Top 10000

(224660 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 ?
87512*10^57410+9^5741057411Mike Oakes04/2011
87522^190704-159557408Lelio R Paula05/2011
875311^55121-174057403Enzo Doria11/2012
87542^190644-18557390Lelio R Paula04/2011
875541182!3-3^4118257389Robert Price08/2015
87562^190629-11225557386Enzo Doria06/2014
8757(2*10^57384-71)/357384Robert Price01/2017
87582*6^73735+5^7373557378Mike Oakes11/2009
87592^190605+5957378Lelio R Paula04/2011
87606^73727-757371Lelio R Paula10/2012
87612^190561-11222557365Enzo Doria06/2014
876210^57358+17089957359Patrick De Geest06/2016
876310^57358-800157358Robert Price03/2016
876418^45687-1157350Lelio R Paula02/2013
876511^55069-21057349Enzo Doria07/2012
876611^55068-1257348Lelio R Paula02/2013
876719^44839+5457339Lelio R Paula02/2013
8769(7*2^190468-1)/851157334Lelio R Paula01/2014
8768(23*10^57333-59)/957334Robert Price03/2017
87702^190455-1155*19045557333Henri Lifchitz02/2005
877165^31620+2857325Lelio R Paula01/2016
87722^190403+1609557318Lelio R Paula05/2011
8773(19*10^57316+119)/357317Robert Price02/2017
8774(21*2^190393+1)/21157314Lelio R Paula07/2012
87762^190392-11202557314Enzo Doria05/2014
877513173^13912-13912^1317357314Norbert Schneider08/2018
8777(24737*2^190234+1)/957270Lelio R Paula05/2014
8778(7*2^190230+1)/2357265Lelio R Paula07/2012
8779(10223*2^190197+1)/321157256Lelio R Paula05/2014
878018^45590-9757228Lelio R Paula02/2013
8781(3*2^190105-1)/1920557224Lelio R Paula01/2014
8782(16*10^57219-31)/357220Robert Price03/2016
8783(2^190074+47)/5157217Lelio R Paula02/2012
87843^119894-14057204Lelio R Paula10/2012
8786(37^36473-1)/3657196Robert Price03/2012
87852^190000-216357196Yves Minet08/2013
87872^189987-279810757192Enzo Doria04/2016
87882^189935-11211757177Enzo Doria05/2014
87892^189909-11223157169Enzo Doria06/2014
8790132049#+14905357161Makoto Morimoto12/2015
879141032!3-2757158Robert Price09/2014
879219^44694+2257153Lelio R Paula02/2013
879312^52956-1757150Lelio R Paula02/2013
87942^189823-96757143Yves Minet01/2012
8795(25*10^57138-61)/957139Robert Price02/2015
87965^81743-4^(81743+1)57136Robert Price04/2016
87977^67593-5457123Lelio R Paula10/2012
87987*3^119712+257118Lelio R Paula03/2014
88005^81700+1657106Lelio R Paula10/2012
87992^189700+7656157106Enzo Doria05/2016
88022^189671+13157097Lelio R Paula04/2011
88014*6^73374+557097Lelio R Paula09/2014
8803(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8804(29*2^189619-1)/39357080Lelio R Paula01/2014
88053^119587+8057058Lelio R Paula10/2012
88062^189502-11345357046Enzo Doria07/2014
88072^189455+15357032Lelio R Paula04/2011
880824^41317-41317^2457027Norbert Schneider07/2016
88092^189414-1757020Lelio R Paula03/2011
881024^41311+2357018Norbert Schneider12/2013
8811norm(Mod(x,x^4+x^3-x+1)^207341-1)/256998Paul Vanderveen05/2018
8812(4*10^56989-31)/956989Erik Branger05/2011
881311^54712-162056977Enzo Doria11/2012
88142^189237-11223156967Enzo Doria06/2014
881517^46285-4856952Lelio R Paula02/2013
88162^189188+7524156952Enzo Doria04/2016
88172^189181+9439556950Henri Lifchitz01/2005
88187001^14808-10856940Enzo Doria07/2012
88192^189147-11263956939Enzo Doria06/2014
8820(19*10^56933-43)/356934Robert Price10/2017
88212^189110-356928M. Frind & P. Underwood11/2002
88222^189069+1290956916Lelio R Paula04/2011
8823(13*10^56909+191)/356910Robert Price08/2017
8824(35*10^56898-17)/956899Serge Batalov02/2009
88252^189011-595556898Lelio R Paula04/2011
88266^73119-556898Lelio R Paula10/2012
882713^51076-9056896Lelio R Paula02/2013
88282^188997+5689756894Yves Minet02/2010
88295^81388-1376656888Enzo Doria02/2013
8830(104^28201+1)/10556881Richard Fischer04/2018
8831(156^25933+1)/15756873Eric Chen12/2017
883220^43713-640356872Enzo Doria03/2013
8833(71*10^56858-287)/956859Robert Price05/2017
88342^188857-25423356852Gary Barnes09/2009
883515^48338-8856850Lelio R Paula02/2013
883610^56849+13643756850Patrick De Geest07/2017
883710^56849-70156849Robert Price06/2017
8838(2^188788+78557)/356831Lelio R Paula05/2012
88392^188771+1609556826Lelio R Paula04/2011
88407*2^188742-956818Lelio R Paula03/2014
884112^52646-6556815Lelio R Paula02/2013
88425003^15358-15856813Enzo Doria07/2012
88432^188713+57729457556809Lelio R Paula03/2013
88442^188693-11209956803Enzo Doria05/2014
8845(7^67211+4^67211)/1156799Robert Price10/2012
88462^188678-9439556798Lelio R Paula09/2011
884720^43651-850356792Enzo Doria03/2013
88492^188657-237156792Yves Minet10/2013
8848152^26029-151^2602956792Eric Chen04/2018
8850(14^49549+5^49549)/1956789Robert Price05/2013
8851(45^34351-1)/4456788Robert Price05/2014
88527*10^56785-2356786Robert Price04/2016
8853(10^56781-31)/356781Serge Batalov12/2014
88547*10^56779+356780Erik Branger11/2009
885510^56765+25917956766Patrick De Geest09/2013
885610^56765-24949756765Patrick De Geest09/2013
8857t(188706)56764Robert Price04/2015
88582^188551-90432756760Paul Bourdelais11/2012
8860(64*10^56756+17)/956757Robert Price09/2015
8859131101#+14629156757Makoto Morimoto02/2016
88612^188539-11251956756Enzo Doria06/2014
88626^72927+10156749Lelio R Paula10/2012
886320^43617-160356748Enzo Doria03/2013
8864(3^118892-8)/9135892956718Lelio R Paula03/2012
886513339^13748-13748^1333956713Norbert Schneider09/2018
8866(509203*2^188338-1)/356701Lelio R Paula03/2015
886720^43567-562356682Enzo Doria03/2013
88682^188234-11318356665Enzo Doria07/2014
8869(139^26437+1)/14056653Richard Fischer03/2018
8870(7*2^188215-1)/149731512556651Lelio R Paula01/2014
8871(1017*2^188171-1)/3556647Lelio R Paula03/2015
8872(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
8873(2^188176-1017)/45381454356638Lelio R Paula02/2012
887433*10^56634+756636Robert Price07/2016
8875(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
887614^49413+3356634Lelio R Paula02/2013
88773^118680+11056625Lelio R Paula10/2012
8878(13*10^56624+161)/356625Robert Price04/2017
8879(3^118676-2)/751665326356613Lelio R Paula03/2012
8880(13*2^188062+1)/1756613Lelio R Paula07/2012
88812^188056-131356611Yves Minet08/2012
888220^43510-558356608Enzo Doria03/2013
88832^188032+1228556604Lelio R Paula03/2011
8884(19*10^56597-43)/356598Robert Price10/2017
8885(265*10^56588+17)/356590Robert Price05/2016
88862^187959+577556582Lelio R Paula03/2011
8887(5*2^187959+1)/5356581Lelio R Paula07/2012
88883*10^56575-1356576Robert Price11/2017
8889(11*2^187889-1)/35156559Lelio R Paula01/2014
8890(100049^11311+1)/10005056553Faysal YAtim09/2007
8891(19*10^56544-1)/956545Serge Batalov03/2009
889220^43447-892356526Enzo Doria03/2013
88932^187743-11217756517Enzo Doria06/2014
8894(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
88955^80831-2256499Lelio R Paula10/2012
88965^80828-1316656497Enzo Doria02/2013
88977*2^187590-556472Lelio R Paula03/2014
88982^187555+7547356460Enzo Doria04/2016
88992^187541-28356456Yves Minet01/2012
8901(55*10^56453-1)/956454Serge Batalov03/2009
890012933^13730-13730^1293356454Norbert Schneider09/2018
89022^187506-145156445Yves Minet08/2012
8903189^24794-256443Lelio R Paula10/2017
890413600^13653-13653^1360056436Norbert Schneider08/2018
89056^72522+14356434Lelio R Paula10/2012
8906(15185*2^187452-1)/94956430Lelio R Paula03/2015
89072^187390+7956411Lelio R Paula03/2011
89082^187386+1290956409Lelio R Paula03/2011
89092^187382+61356408Jason Earls04/2008
8910(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
891120^43337-956383Lelio R Paula02/2013
8912(26*10^56371-173)/356372Robert Price10/2017
8913(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
89142^187230+42756362Henri Lifchitz01/2005
891511^54121-948056362Enzo Doria02/2013
891610758^13979-13979^1075856360Norbert Schneider09/2018
891710635^13996-13996^1063556359Norbert Schneider09/2018
8918(21*2^187202-1)/4356354Lelio R Paula01/2014
89192^187173-9156345Lelio R Paula03/2011
8920(23*2^187174-1)/2071988356340Lelio R Paula01/2014
89212^187125-283356331Yves Minet09/2014
89229*7^66655-456331Lelio R Paula09/2014
892418^44874-9756330Lelio R Paula02/2013
892313304^13659-13659^1330456330Norbert Schneider08/2018
892560*79^29679+1956322Serge Batalov03/2016
89265^80571+5656317Lelio R Paula10/2012
89275^80551-2256303Lelio R Paula10/2012
8928(76*10^56281+41)/956282Robert Price10/2015
8929(88*10^56271-43)/956272Robert Price11/2015
8930(5*10^56256-119)/356257Robert Price04/2016
89311508^17691+17691^150856230Serge Batalov05/2014
89323^117844-5856226Lelio R Paula10/2012
8933(19*10^56224+737)/956225Robert Price10/2017
893495^28427+256221Lelio R Paula05/2013
89352^186713+7681756207Enzo Doria05/2016
893616534^2505+2505^1653456196Hans Havermann06/2016
893714428^7849+7849^1442856195Hans Havermann06/2016
89382*10^56194-5156195Robert Price11/2017
893914898^5909+5909^1489856189Hans Havermann06/2016
894018^44758+9556184Lelio R Paula02/2013
89412^186555-74156159Lelio R Paula05/2011
8942(4*10^56156+173)/356157Robert Price01/2017
8943(3^117708+7)/44789656156Lelio R Paula03/2012
894415711^3752+3752^1571156156Hans Havermann06/2016
8945(23*2^186549-1)/242902556152Lelio R Paula01/2014
8946387^21694+21694^38756138Norbert Schneider08/2014
89472^186422+1723956119Yves Minet01/2010
89482^186418+424242956118Jason Earls10/2008
8949136^26300+13556113Norbert Schneider04/2015
89505*2^186392+956111Lelio R Paula03/2014
895114345^8152+8152^1434556108Hans Havermann07/2016
8952(5*2^186351-1)/3956097Lelio R Paula01/2014
89532^186319-54123756088Paul Bourdelais11/2012
89542*10^56083-4356084Robert Price07/2017
8955(16*10^56082-61)/956083Serge Batalov05/2009
8956(14*10^56080-143)/356081Robert Price01/2017
8957(265*10^56076+17)/356078Robert Price05/2016
89587^66346-5056069Lelio R Paula10/2012
895920^43094-3356067Lelio R Paula02/2013
896020^43090-138356062Enzo Doria03/2013
89613^117482+266056054Lelio R Paula10/2012
8962(22699*2^186193+1)/11156052Lelio R Paula05/2014
8963(68*10^56042+13)/956043Ray Chandler09/2010
89643*6^71992+5^7199256022Mike Oakes03/2010
896513691^12352+12352^1369156020Hans Havermann07/2016
8966(2^186095+7)/7556019Lelio R Paula02/2012
8967247^23412+23412^24756018Norbert Schneider08/2014
89681839^17156+17156^183956008Serge Batalov05/2014
896913736^11949+11949^1373656007Hans Havermann04/2016
8970(5*2^186036-1)/1156003Lelio R Paula01/2014
8971(299*10^55998-17)/356000Robert Price01/2017
8972p(12103)#/2-12855994Robert Price05/2017
89742^186003-17433755993Gary Barnes09/2009
8975(2^186010+78557)/12355993Lelio R Paula05/2012
897320^43037-9355993Lelio R Paula02/2013
897616375^2626+2626^1637555991Hans Havermann03/2016
897715631^3816+3816^1563155985Hans Havermann03/2016
897821^42335-255977Lelio R Paula08/2013
8979Phi(64736,139)55959Enzo Doria07/2012
898015215^4762+4762^1521555958Hans Havermann03/2016
898119317^788+788^1931755953Anatoly F. Selevich12/2006
898213582^13165+13165^1358255950Hans Havermann08/2016
8983(78557*2^185842+1)/18955947Lelio R Paula06/2014
898411867^13730-13730^1186755941Norbert Schneider09/2018
898515^47562-8655938Lelio R Paula02/2013
89864*10^55932+9155933Robert Price11/2017
89873^117222+455930Lelio R Paula03/2012
898824^40519-23^4051955925Robert Price07/2012
898913636^12623+12623^1363655924Hans Havermann07/2016
89902^185767-9955922Lelio R Paula03/2011
8991(19*2^185750-1)/1555917Lelio R Paula01/2014
899315^47542-5855914Lelio R Paula02/2013
899252211!4+255914Robert Price08/2017
899420^42973-558355910Enzo Doria03/2013
89954*10^55906+2155907Robert Price08/2016
89962^185713-11155906Lelio R Paula03/2011
899713^50174+8855891Lelio R Paula01/2013
899814569^6846+6846^1456955879Hans Havermann08/2016
8999Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
90003^117087-8055865Lelio R Paula10/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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