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 ?
42512^281809-9730584833Lelio R Paula09/2013
42522^281780-11489384825Enzo Doria05/2015
42533^177719+6484794Lelio R Paula12/2015
42552^281675-19984793Lelio R Paula08/2012
42542^281673-11122384793Enzo Doria05/2014
4256(4*10^84779+149)/984779Robert Price03/2017
4257(72*10^84772-27)/984773Ray Chandler01/2011
425811^81398-63084768Enzo Doria11/2012
4259(25*2^281577-1)/2384764Lelio R Paula02/2014
42602^281500-45584740Yves Minet03/2012
426110^84725+114514191984726Marisa Kirisame03/2015
426210^84725+14204184726Patrick De Geest10/2015
426310^84725-13867784725Patrick De Geest02/2016
426476^45044+7584720Norbert Schneider02/2015
426554^48897-5384709Norbert Schneider08/2014
4266(9913*2^281377-1)/6584706Lelio R Paula04/2015
4267Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
42682^281337-11122384691Enzo Doria05/2014
42692^281308+5461584683Lelio R Paula09/2013
42707*5^121144-684677Lelio R Paula10/2014
4271(2^281252+47)/384665Lelio R Paula01/2013
427211^81297-315084663Enzo Doria12/2012
42732^281208-30384653Yves Minet02/2012
4274(21*2^281187+1)/248384644Lelio R Paula01/2013
427511^81247-8484611Lelio R Paula10/2015
427617^68747-6484590Lelio R Paula11/2015
42775^121018-1559684588Enzo Doria02/2013
42786^108702+784587Lelio R Paula11/2014
427910^84582+10067784583Patrick De Geest05/2016
428010^84582-800184582Robert Price03/2016
42813*5^121004-884579Lelio R Paula10/2014
42825^120996-8484573Lelio R Paula10/2015
4283(10223*2^280881+1)/6841984553Lelio R Paula06/2014
42842^280852+9768184545Yves Minet08/2004
42852^280848-120384544Lelio R Paula09/2013
42865^120946-2484538Lelio R Paula10/2015
42872^280810-211184533Yves Minet08/2013
428811^81161-516084521Enzo Doria01/2013
42892^280737-9384511Lelio R Paula08/2012
42902^280698+31584499Lelio R Paula09/2013
42913^177099-34084498Lelio R Paula12/2015
4292(5*10^84469-107)/384470Robert Price01/2017
4293(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4294(2^280500-1017)/82384436Lelio R Paula01/2013
429514^73660-584424Lelio R Paula11/2015
42962^280388+11784406Lelio R Paula08/2012
42972^280389-56653384406Paul Bourdelais03/2013
4298(141584^16384+1)/6553784390Syoichiro Yamada06/2008
42992^280240-17384361Lelio R Paula08/2012
4300(184*10^84348-1)/384350Robert Price02/2017
43014*10^84346+9384347Robert Price01/2017
43027*2^280156-584337Lelio R Paula08/2014
43038*7^99782-384327Lelio R Paula10/2014
43052^280116+13384324Lelio R Paula08/2012
43042^280118+5461584324Lelio R Paula09/2013
4306(509203*2^280090-1)/384321Lelio R Paula04/2015
43076^108354+4784316Lelio R Paula12/2015
430810^84305+14196384306Patrick De Geest07/2013
430910^84305-5784305Robert Price05/2011
43109^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
43113^176648-11280484283Enzo Doria06/2014
43126^108310+11584282Lelio R Paula12/2015
4313(11*2^279968-1)/584280Lelio R Paula02/2014
43146^108288-1664384265Enzo Doria02/2013
43152^279917-5869584264Lelio R Paula08/2013
431665^46477+3684259Lelio R Paula01/2016
43172^279866-190784249Yves Minet05/2013
4318(3^176580-5)/2807684246Lelio R Paula12/2012
4319(2*10^84239+1)/384239Serge Batalov07/2009
432118^67103-4184233Lelio R Paula11/2015
432020^64743-4384233Lelio R Paula01/2016
4322143^39070+39070^14384209Serge Batalov05/2014
432311^80857-540084204Enzo Doria01/2013
4324(13*10^84179+161)/384180Robert Price04/2017
43252^279634-11040584179Enzo Doria05/2014
43262^279582-101784163Lelio R Paula08/2013
4327(22*10^84159-19)/384160Robert Price02/2017
4328(9*2^279507-1)/13784139Lelio R Paula02/2014
432911^80792-81084137Enzo Doria11/2012
4330(97*10^84134-1)/384136Serge Batalov12/2014
4331p(17507)#/2+3284125Robert Price12/2016
43323^176294-34084114Lelio R Paula12/2015
4333(3^176287+4)/219184107Lelio R Paula12/2012
43342^279388-71984105Yves Minet05/2012
4335(22699*2^279378+1)/22184104Lelio R Paula06/2014
43362^279332-11044784088Enzo Doria05/2014
43372^279320+784084Lelio R Paula06/2012
4338(11*2^279240-1)/9584059Lelio R Paula02/2014
43392^279218-11134784053Enzo Doria05/2014
434035^54435+284052Lelio R Paula05/2013
4341(31*2^279191-1)/1251152384040Lelio R Paula02/2014
434297*10^84033-384035Robert Price01/2017
43432^279095-10971784016Enzo Doria04/2014
434414^73282-9983991Lelio R Paula11/2015
434589*10^83976-783978Robert Price03/2017
43462^278955+17383974Lelio R Paula06/2012
4347(7*2^278851+1)/3983942Lelio R Paula12/2012
4348(9913*2^278844-1)/4080383940Lelio R Paula04/2015
43495^120076-1484683930Enzo Doria02/2013
4350(2^278770-3)/2383917Lelio R Paula12/2012
4351(10^83916+449)/983916Serge Batalov12/2014
43522^278715+9983902Lelio R Paula06/2012
435340235!2-2^4023583899Robert Price09/2015
43542^278698-17183897Lelio R Paula06/2012
43556^107802+2583887Lelio R Paula12/2015
43568*10^83880+3983881Robert Price01/2017
4357(58*10^83878+23)/983879Robert Price09/2015
43587^99244-9083871Lelio R Paula10/2015
43592^278554+425783854Lelio R Paula08/2013
43602^278504-10961983839Enzo Doria04/2014
43612^278499+187043383837Enzo Doria05/2016
4362105^41475+10483829Norbert Schneider11/2016
436315^71276-6883828Lelio R Paula11/2015
43642^278464-21641383827Enzo Doria04/2013
43652^278400+4075583807Lelio R Paula08/2013
4366(9*2^278381-1)/783802Lelio R Paula02/2014
43673*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
43682^278235-4983758Lelio R Paula06/2012
436918^66711-9183741Lelio R Paula11/2015
4370(3*2^278172-1)/1183738Lelio R Paula02/2014
4371(15*29^57251+2561)/2883724Curtis Bright05/2015
43724*7^99059-983716Lelio R Paula10/2014
4373(2^278128-3)/12684472414983714Lelio R Paula12/2012
43742^278077+186721183710Enzo Doria03/2016
43752^278059-2783705Lelio R Paula06/2012
4376214^35917+35917^21483702Norbert Schneider12/2014
4377(23*10^83693+7)/383694Robert Price10/2015
437885^43375-283689Lelio R Paula09/2013
43795*3^175360+483669Lelio R Paula07/2014
4380(23^61441-1)/2283665Robert Price01/2012
438120091^14596+14596^2009183664Hans Havermann03/2017
43822^277907-11062983659Enzo Doria05/2014
438319522^19283+19283^1952283656Hans Havermann04/2017
43848*5^119664-383643Lelio R Paula10/2014
43858*3^175299-783640Lelio R Paula07/2014
43863^175250+2283616Robert Price12/2013
438811^80285+3083609Lelio R Paula10/2015
438726870^1293+1293^2687083609Hans Havermann03/2017
43892^277691+187442383594Enzo Doria06/2016
439013^75022-6083571Lelio R Paula11/2015
439114^72905-5183559Lelio R Paula11/2015
4392(17*2^277565-1)/54383554Lelio R Paula02/2014
43935^119532-1283550Lelio R Paula10/2015
43946^107358-1625383541Enzo Doria02/2013
43952^277478-46021183530Enzo Doria06/2015
4396(22*10^83525-7)/383526Erik Branger09/2014
4397(30^56543+1)/3183520Robert Price07/2013
43982^277417-46078383511Paul Bourdelais04/2013
4399(22699*2^277387+1)/21983504Lelio R Paula06/2014
4400(31*2^277383-1)/24783500Lelio R Paula02/2014
4401(9*2^277342+1)/1383489Lelio R Paula12/2012
44025^119439-6683485Lelio R Paula10/2015
4403(14*10^83471-101)/383472Robert Price04/2017
44045*6^107263+783468Lelio R Paula10/2014
4405(64*10^83461-1)/983462Serge Batalov11/2010
440617^67796-9283420Lelio R Paula11/2015
44072^277106-11005783418Enzo Doria04/2014
44086^107200-1983418Lelio R Paula12/2015
440911^80096-183083412Enzo Doria12/2012
44103^174801+5683402Lelio R Paula12/2015
44112^277033-11197383396Enzo Doria05/2014
441220519^11572+11572^2051983378Hans Havermann03/2017
441320850^9971+9971^2085083374Hans Havermann03/2017
44146^107122-1886383358Enzo Doria03/2013
44153^174697-3483352Robert Price11/2013
4416(9787*2^276855-1)/234583343Lelio R Paula04/2015
44172^276825+7522783333Enzo Doria04/2016
44185^119214+8483328Lelio R Paula10/2015
44192^276803-15983327Lelio R Paula06/2012
4420(3*2^276753-1)/2583311Lelio R Paula02/2014
4421114^40495+40495^11483295Norbert Schneider12/2014
442239967!2+102483282Robert Price02/2015
44242^276641+5783278Lelio R Paula06/2012
442335^53934-341483278Enzo Doria03/2013
4425(2^276655+78557)/36542583276Lelio R Paula12/2012
44262^276615-403583270Lelio R Paula08/2013
44272^276588+115583262Lelio R Paula08/2013
44292^276587-93783261Yves Minet10/2009
44282^276584-11318383261Enzo Doria07/2014
4430(2^276592-1017)/1384373983256Lelio R Paula12/2012
44312^276547-10959183249Enzo Doria04/2014
443213^74733-3283249Lelio R Paula11/2015
44332^276523-258783242Yves Minet07/2014
443418^66311-4383239Lelio R Paula11/2015
443511^79919-153083228Enzo Doria12/2012
44362^276468-10974583226Enzo Doria04/2014
44372^276462+538583224Lelio R Paula08/2013
4438(9787*2^276422-1)/383215Lelio R Paula04/2015
44402^276391-1583202Lelio R Paula06/2012
4439(4*10^83201+173)/383202Robert Price01/2017
44412^276316-10965583180Enzo Doria04/2014
44422^276305-11206383177Enzo Doria06/2014
44432^276227-183720783153Enzo Doria05/2015
4444(2^276227+3)/783152Lelio R Paula12/2012
44452^276184-6338983140Paul Bourdelais02/2012
44462^276066-11160383105Enzo Doria05/2014
4447(2^276028-3)*6-783094Gilbert Mozzo09/2016
4448(2^275897+9)/115383051Lelio R Paula12/2012
44492^275879-10980783048Enzo Doria04/2014
4451F(397379)83047Henri Lifchitz08/2003
4450U(397379)83047Serge Batalov03/2015
44523^174040-1483039Robert Price08/2013
44532^275841-688383037Lelio R Paula07/2011
44543^174002-14083021Lelio R Paula12/2015
44556^106681+7783014Lelio R Paula12/2015
445611^79701-315083001Enzo Doria12/2012
4457(55459*2^275657+1)/2182985Lelio R Paula06/2014
44582^275535-685582945Lelio R Paula08/2013
44603^173828-1482938Robert Price08/2013
44592^275512-10967782938Enzo Doria04/2014
44612^275446-11004582918Enzo Doria04/2014
4462(2^275473+47)/2952609744782916Lelio R Paula12/2012
44633^173755-1482903Robert Price08/2013
44642^275363-11230982893Enzo Doria06/2014
446561^46427-6082888Norbert Schneider10/2014
44663*10^82880-7^8288082881Mike Oakes02/2010
44682^275290+9019582871Lelio R Paula07/2013
4467(35*10^82870-71)/982871Robert Price05/2015
44692^275270-185962182865Enzo Doria03/2016
44702^275259+8182862Henri Lifchitz01/2007
44717^98003+98003^7+182823Robert Price05/2014
447210^82790+12604382791Patrick De Geest07/2013
447310^82790-4782790Robert Price05/2011
44742^274985-11266382779Enzo Doria06/2014
44752^274935+1501582764Lelio R Paula07/2013
4476(17*2^274922+1)/382761Lelio R Paula12/2012
4477(43*10^82752-61)/982753Robert Price06/2015
4478(3*2^274862+1)/102782740Lelio R Paula12/2012
4479(31*2^274848-1)/406582736Lelio R Paula02/2014
4480(4^137405+23)/382726Robert Price02/2017
44812^274791-11049182721Enzo Doria05/2014
4482(11*2^274776-1)/9582715Lelio R Paula02/2014
44832^274704-11139582695Enzo Doria05/2014
4484(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
4485(3^173263-5)/1449882664Lelio R Paula12/2012
44862^274511-6487582637Lelio R Paula08/2013
448712^76572-8382636Lelio R Paula11/2015
44883^173191-2^17319182634Mike Oakes02/2004
448914^72072-1582604Lelio R Paula11/2015
4490(55459*2^274339+1)/382589Lelio R Paula06/2014
44912^274351+12382588Lelio R Paula06/2012
4492(1017*2^274339-1)/351582584Lelio R Paula04/2015
44936^106086+11382551Lelio R Paula12/2015
44942^274093-5869582511Lelio R Paula07/2013
44957*10^82509-4782510Robert Price02/2017
44962^274081-655582507Lelio R Paula07/2013
44982^274074-274074+182505Robert Price10/2014
449914^71985+4782505Lelio R Paula11/2015
44975*10^82504+2182505Robert Price01/2017
45006^106014-13982495Lelio R Paula12/2015


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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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