PRP Records

Probable Primes Top 10000

(172213 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 ?
42512^280388+11784406Lelio R Paula08/2012
42522^280389-56653384406Paul Bourdelais03/2013
4253(141584^16384+1)/6553784390Syoichiro Yamada06/2008
42542^280240-17384361Lelio R Paula08/2012
4255(184*10^84348-1)/384350Robert Price02/2017
42564*10^84346+9384347Robert Price01/2017
42577*2^280156-584337Lelio R Paula08/2014
42588*7^99782-384327Lelio R Paula10/2014
42592^280116+13384324Lelio R Paula08/2012
42602^280118+5461584324Lelio R Paula09/2013
4261(509203*2^280090-1)/384321Lelio R Paula04/2015
42626^108354+4784316Lelio R Paula12/2015
426310^84305+14196384306Patrick De Geest07/2013
426410^84305-5784305Robert Price05/2011
42659^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
42663^176648-11280484283Enzo Doria06/2014
42676^108310+11584282Lelio R Paula12/2015
4268(11*2^279968-1)/584280Lelio R Paula02/2014
42696^108288-1664384265Enzo Doria02/2013
42702^279917-5869584264Lelio R Paula08/2013
427165^46477+3684259Lelio R Paula01/2016
42722^279866-190784249Yves Minet05/2013
4273(3^176580-5)/2807684246Lelio R Paula12/2012
4274(2*10^84239+1)/384239Serge Batalov07/2009
427618^67103-4184233Lelio R Paula11/2015
427520^64743-4384233Lelio R Paula01/2016
4277143^39070+39070^14384209Serge Batalov05/2014
427811^80857-540084204Enzo Doria01/2013
42792^279634-11040584179Enzo Doria05/2014
42802^279582-101784163Lelio R Paula08/2013
4281(22*10^84159-19)/384160Robert Price02/2017
4282(9*2^279507-1)/13784139Lelio R Paula02/2014
428311^80792-81084137Enzo Doria11/2012
4284(97*10^84134-1)/384136Serge Batalov12/2014
4285p(17507)#/2+3284125Robert Price12/2016
42863^176294-34084114Lelio R Paula12/2015
4287(3^176287+4)/219184107Lelio R Paula12/2012
42882^279388-71984105Yves Minet05/2012
4289(22699*2^279378+1)/22184104Lelio R Paula06/2014
42902^279332-11044784088Enzo Doria05/2014
42912^279320+784084Lelio R Paula06/2012
4292(11*2^279240-1)/9584059Lelio R Paula02/2014
42932^279218-11134784053Enzo Doria05/2014
429435^54435+284052Lelio R Paula05/2013
4295(31*2^279191-1)/1251152384040Lelio R Paula02/2014
429697*10^84033-384035Robert Price01/2017
42972^279095-10971784016Enzo Doria04/2014
429814^73282-9983991Lelio R Paula11/2015
429989*10^83976-783978Robert Price03/2017
43002^278955+17383974Lelio R Paula06/2012
4301(7*2^278851+1)/3983942Lelio R Paula12/2012
4302(9913*2^278844-1)/4080383940Lelio R Paula04/2015
43035^120076-1484683930Enzo Doria02/2013
4304(2^278770-3)/2383917Lelio R Paula12/2012
4305(10^83916+449)/983916Serge Batalov12/2014
43062^278715+9983902Lelio R Paula06/2012
430740235!2-2^4023583899Robert Price09/2015
43082^278698-17183897Lelio R Paula06/2012
43096^107802+2583887Lelio R Paula12/2015
43108*10^83880+3983881Robert Price01/2017
4311(58*10^83878+23)/983879Robert Price09/2015
43127^99244-9083871Lelio R Paula10/2015
43132^278554+425783854Lelio R Paula08/2013
43142^278504-10961983839Enzo Doria04/2014
43152^278499+187043383837Enzo Doria05/2016
4316105^41475+10483829Norbert Schneider11/2016
431715^71276-6883828Lelio R Paula11/2015
43182^278464-21641383827Enzo Doria04/2013
43192^278400+4075583807Lelio R Paula08/2013
4320(9*2^278381-1)/783802Lelio R Paula02/2014
43213*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
43222^278235-4983758Lelio R Paula06/2012
432318^66711-9183741Lelio R Paula11/2015
4324(3*2^278172-1)/1183738Lelio R Paula02/2014
4325(15*29^57251+2561)/2883724Curtis Bright05/2015
43264*7^99059-983716Lelio R Paula10/2014
4327(2^278128-3)/12684472414983714Lelio R Paula12/2012
43282^278077+186721183710Enzo Doria03/2016
43292^278059-2783705Lelio R Paula06/2012
4330214^35917+35917^21483702Norbert Schneider12/2014
4331(23*10^83693+7)/383694Robert Price10/2015
433285^43375-283689Lelio R Paula09/2013
43335*3^175360+483669Lelio R Paula07/2014
4334(23^61441-1)/2283665Robert Price01/2012
433520091^14596+14596^2009183664Hans Havermann03/2017
43362^277907-11062983659Enzo Doria05/2014
43378*5^119664-383643Lelio R Paula10/2014
43388*3^175299-783640Lelio R Paula07/2014
43393^175250+2283616Robert Price12/2013
434011^80285+3083609Lelio R Paula10/2015
43412^277691+187442383594Enzo Doria06/2016
434213^75022-6083571Lelio R Paula11/2015
434314^72905-5183559Lelio R Paula11/2015
4344(17*2^277565-1)/54383554Lelio R Paula02/2014
43455^119532-1283550Lelio R Paula10/2015
43466^107358-1625383541Enzo Doria02/2013
43472^277478-46021183530Enzo Doria06/2015
4348(22*10^83525-7)/383526Erik Branger09/2014
4349(30^56543+1)/3183520Robert Price07/2013
43502^277417-46078383511Paul Bourdelais04/2013
4351(22699*2^277387+1)/21983504Lelio R Paula06/2014
4352(31*2^277383-1)/24783500Lelio R Paula02/2014
4353(9*2^277342+1)/1383489Lelio R Paula12/2012
43545^119439-6683485Lelio R Paula10/2015
43555*6^107263+783468Lelio R Paula10/2014
4356(64*10^83461-1)/983462Serge Batalov11/2010
435717^67796-9283420Lelio R Paula11/2015
43582^277106-11005783418Enzo Doria04/2014
43596^107200-1983418Lelio R Paula12/2015
436011^80096-183083412Enzo Doria12/2012
43613^174801+5683402Lelio R Paula12/2015
43622^277033-11197383396Enzo Doria05/2014
436320519^11572+11572^2051983378Hans Havermann03/2017
436420850^9971+9971^2085083374Hans Havermann03/2017
43656^107122-1886383358Enzo Doria03/2013
43663^174697-3483352Robert Price11/2013
4367(9787*2^276855-1)/234583343Lelio R Paula04/2015
43682^276825+7522783333Enzo Doria04/2016
43695^119214+8483328Lelio R Paula10/2015
43702^276803-15983327Lelio R Paula06/2012
4371(3*2^276753-1)/2583311Lelio R Paula02/2014
4372114^40495+40495^11483295Norbert Schneider12/2014
437339967!2+102483282Robert Price02/2015
43742^276641+5783278Lelio R Paula06/2012
437535^53934-341483278Enzo Doria03/2013
4376(2^276655+78557)/36542583276Lelio R Paula12/2012
43772^276615-403583270Lelio R Paula08/2013
43782^276588+115583262Lelio R Paula08/2013
43802^276587-93783261Yves Minet10/2009
43792^276584-11318383261Enzo Doria07/2014
4381(2^276592-1017)/1384373983256Lelio R Paula12/2012
43822^276547-10959183249Enzo Doria04/2014
438313^74733-3283249Lelio R Paula11/2015
43842^276523-258783242Yves Minet07/2014
438518^66311-4383239Lelio R Paula11/2015
438611^79919-153083228Enzo Doria12/2012
43872^276468-10974583226Enzo Doria04/2014
43882^276462+538583224Lelio R Paula08/2013
4389(9787*2^276422-1)/383215Lelio R Paula04/2015
43902^276391-1583202Lelio R Paula06/2012
4391(4*10^83201+173)/383202Robert Price01/2017
43922^276316-10965583180Enzo Doria04/2014
43932^276305-11206383177Enzo Doria06/2014
43942^276227-183720783153Enzo Doria05/2015
4395(2^276227+3)/783152Lelio R Paula12/2012
43962^276184-6338983140Paul Bourdelais02/2012
43972^276066-11160383105Enzo Doria05/2014
4398(2^276028-3)*6-783094Gilbert Mozzo09/2016
4399(2^275897+9)/115383051Lelio R Paula12/2012
44002^275879-10980783048Enzo Doria04/2014
4402F(397379)83047Henri Lifchitz08/2003
4401U(397379)83047Serge Batalov03/2015
44033^174040-1483039Robert Price08/2013
44042^275841-688383037Lelio R Paula07/2011
44053^174002-14083021Lelio R Paula12/2015
44066^106681+7783014Lelio R Paula12/2015
440711^79701-315083001Enzo Doria12/2012
4408(55459*2^275657+1)/2182985Lelio R Paula06/2014
44092^275535-685582945Lelio R Paula08/2013
44103^173828-1482938Robert Price08/2013
44112^275512-10967782938Enzo Doria04/2014
44122^275446-11004582918Enzo Doria04/2014
4413(2^275473+47)/2952609744782916Lelio R Paula12/2012
44143^173755-1482903Robert Price08/2013
44152^275363-11230982893Enzo Doria06/2014
441661^46427-6082888Norbert Schneider10/2014
44173*10^82880-7^8288082881Mike Oakes02/2010
44192^275290+9019582871Lelio R Paula07/2013
4418(35*10^82870-71)/982871Robert Price05/2015
44202^275270-185962182865Enzo Doria03/2016
44212^275259+8182862Henri Lifchitz01/2007
44227^98003+98003^7+182823Robert Price05/2014
442310^82790+12604382791Patrick De Geest07/2013
442410^82790-4782790Robert Price05/2011
44252^274985-11266382779Enzo Doria06/2014
44262^274935+1501582764Lelio R Paula07/2013
4427(17*2^274922+1)/382761Lelio R Paula12/2012
4428(43*10^82752-61)/982753Robert Price06/2015
4429(3*2^274862+1)/102782740Lelio R Paula12/2012
4430(31*2^274848-1)/406582736Lelio R Paula02/2014
4431(4^137405+23)/382726Robert Price02/2017
44322^274791-11049182721Enzo Doria05/2014
4433(11*2^274776-1)/9582715Lelio R Paula02/2014
44342^274704-11139582695Enzo Doria05/2014
4435(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
4436(3^173263-5)/1449882664Lelio R Paula12/2012
44372^274511-6487582637Lelio R Paula08/2013
443812^76572-8382636Lelio R Paula11/2015
44393^173191-2^17319182634Mike Oakes02/2004
444014^72072-1582604Lelio R Paula11/2015
4441(55459*2^274339+1)/382589Lelio R Paula06/2014
44422^274351+12382588Lelio R Paula06/2012
4443(1017*2^274339-1)/351582584Lelio R Paula04/2015
44446^106086+11382551Lelio R Paula12/2015
44452^274093-5869582511Lelio R Paula07/2013
44467*10^82509-4782510Robert Price02/2017
44472^274081-655582507Lelio R Paula07/2013
44492^274074-274074+182505Robert Price10/2014
445014^71985+4782505Lelio R Paula11/2015
44485*10^82504+2182505Robert Price01/2017
44516^106014-13982495Lelio R Paula12/2015
4452(2^274046+47)/75382494Lelio R Paula12/2012
44532^274008-183809982485Enzo Doria05/2015
44542^273981-11002982477Enzo Doria04/2014
445519^64490-3082467Lelio R Paula12/2015
44562^273785+1171582418Lelio R Paula07/2013
445711^79133-1082409Theodore Burton11/2005
445891^42063+9082404Norbert Schneider01/2016
44602^273662-6382381Lelio R Paula06/2012
44592^273661+25582381Lelio R Paula07/2013
4461(62*10^82377-17)/982378Robert Price09/2015
4462(11*10^82323+91)/382323Robert Price02/2017
446315^69984+3282308Lelio R Paula11/2015
44649*6^105746+782288Lelio R Paula10/2014
446589^42211-8882286Norbert Schneider01/2016
4466gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
44672^273282-11024182267Enzo Doria05/2014
4468(13^73849+4^73849)/1782263Robert Price05/2013
447010^82254+9^(82254+1)82255Robert Price08/2016
446910^82254+45777382255Patrick De Geest12/2016
447110^82254-9960982254Patrick De Geest12/2016
447218^65524+1382251Lelio R Paula11/2015
44732^273206-10782244Lelio R Paula06/2012
44742^273193-45914582240Enzo Doria05/2015
44762^273126+3693782220Yves Minet06/2010
447539505!2+12882220Robert Price03/2015
44772^273053-11211182198Enzo Doria06/2014
44782^273016+118582187Lelio R Paula07/2013
4479(2^273008+3)/782183Lelio R Paula12/2012
44805^117554-1538682167Enzo Doria02/2013
44812^272907-11143982154Enzo Doria05/2014
4482(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
44832^272875-6982144Lelio R Paula06/2012
44847^97197+482141Robert Price01/2014
4485(4*6^105554+1)/582137Serge Batalov10/2014
44866^105531-10982120Lelio R Paula12/2015
44872^272766-6582111Lelio R Paula06/2012
448819^64205-7882103Lelio R Paula12/2015
44892^272702+186997982092Enzo Doria05/2016
4490(29*2^272687-1)/982088Lelio R Paula02/2014
4491(5*10^82085-119)/382086Robert Price04/2016
44922^272660-11004982079Enzo Doria04/2014
44936^105474+6782075Lelio R Paula12/2015
44942^272637+8287582072Lelio R Paula07/2013
44952^272587-3182057Lelio R Paula06/2012
44968*5^117368+982038Lelio R Paula10/2014
4497(101525^16384+1)/13107482023Lelio R Paula11/2011
44984*5^117343-782020Lelio R Paula10/2014
4499(265*10^81990+17)/381992Robert Price05/2016
45003^171843+1081990Robert Price10/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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