PRP Records

Probable Primes Top 10000

(205869 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 ?
47512^280388+11784406Lelio R Paula08/2012
47522^280389-56653384406Paul Bourdelais03/2013
4753(141584^16384+1)/6553784390Syoichiro Yamada06/2008
47542^280240-17384361Lelio R Paula08/2012
4755(184*10^84348-1)/384350Robert Price02/2017
47564*10^84346+9384347Robert Price01/2017
47577*2^280156-584337Lelio R Paula08/2014
47588*7^99782-384327Lelio R Paula10/2014
47602^280116+13384324Lelio R Paula08/2012
47592^280118+5461584324Lelio R Paula09/2013
4761(509203*2^280090-1)/384321Lelio R Paula04/2015
47626^108354+4784316Lelio R Paula12/2015
476310^84305+14196384306Patrick De Geest07/2013
476410^84305-5784305Robert Price05/2011
47659^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
47663^176648-11280484283Enzo Doria06/2014
47676^108310+11584282Lelio R Paula12/2015
4768(11*2^279968-1)/584280Lelio R Paula02/2014
47696^108288-1664384265Enzo Doria02/2013
47702^279917-5869584264Lelio R Paula08/2013
477165^46477+3684259Lelio R Paula01/2016
47722^279866-190784249Yves Minet05/2013
4773(3^176580-5)/2807684246Lelio R Paula12/2012
4774(p(17530)#+4)/284246Robert Price09/2017
4775(2*10^84239+1)/384239Serge Batalov07/2009
477718^67103-4184233Lelio R Paula11/2015
477620^64743-4384233Lelio R Paula01/2016
4778143^39070+39070^14384209Serge Batalov05/2014
477911^80857-540084204Enzo Doria01/2013
4780(13*10^84179+161)/384180Robert Price04/2017
47812^279634-11040584179Enzo Doria05/2014
4782(74*10^84170+313)/984171Robert Price11/2017
47832^279582-101784163Lelio R Paula08/2013
4784(22*10^84159-19)/384160Robert Price02/2017
4785p(17513)#/2+51284156Robert Price05/2017
4786(19*10^84144-43)/384145Robert Price10/2017
4787(9*2^279507-1)/13784139Lelio R Paula02/2014
478811^80792-81084137Enzo Doria11/2012
4789(97*10^84134-1)/384136Serge Batalov12/2014
4790p(17507)#/2+3284125Robert Price12/2016
479121485^8224+8224^2148584116Hans Havermann04/2017
47923^176294-34084114Lelio R Paula12/2015
4793(3^176287+4)/219184107Lelio R Paula12/2012
47942^279388-71984105Yves Minet05/2012
4795(22699*2^279378+1)/22184104Lelio R Paula06/2014
47962^279332-11044784088Enzo Doria05/2014
47972^279320+784084Lelio R Paula06/2012
4798127^39966-284081Lelio R Paula10/2017
4799(11*2^279240-1)/9584059Lelio R Paula02/2014
48002^279218-11134784053Enzo Doria05/2014
480135^54435+284052Lelio R Paula05/2013
4802(31*2^279191-1)/1251152384040Lelio R Paula02/2014
480320996^10059+10059^2099684038Hans Havermann05/2017
480497*10^84033-384035Robert Price01/2017
480521234^9067+9067^2123484033Hans Havermann05/2017
48062^279095-10971784016Enzo Doria04/2014
480714^73282-9983991Lelio R Paula11/2015
480821457^8200+8200^2145783979Hans Havermann06/2017
480989*10^83976-783978Robert Price03/2017
48102^278955+17383974Lelio R Paula06/2012
4811(7*2^278851+1)/3983942Lelio R Paula12/2012
4812(9913*2^278844-1)/4080383940Lelio R Paula04/2015
48135^120076-1484683930Enzo Doria02/2013
4814(85*10^83921-1)/383923Robert Price07/2017
4815(2^278770-3)/2383917Lelio R Paula12/2012
4816(10^83916+449)/983916Serge Batalov12/2014
48172^278715+9983902Lelio R Paula06/2012
481840235!2-2^4023583899Robert Price09/2015
48192^278698-17183897Lelio R Paula06/2012
4820(19*10^83894-43)/383895Robert Price10/2017
48216^107802+2583887Lelio R Paula12/2015
48228*10^83880+3983881Robert Price01/2017
4823(58*10^83878+23)/983879Robert Price09/2015
48247^99244-9083871Lelio R Paula10/2015
48252^278554+425783854Lelio R Paula08/2013
48262^278504-10961983839Enzo Doria04/2014
48272^278499+187043383837Enzo Doria05/2016
4828105^41475+10483829Norbert Schneider11/2016
482915^71276-6883828Lelio R Paula11/2015
48302^278464-21641383827Enzo Doria04/2013
4831(76*10^83816-211)/983817Robert Price10/2017
4832(8*10^83811-101)/383812Robert Price10/2017
48332^278400+4075583807Lelio R Paula08/2013
4834(9*2^278381-1)/783802Lelio R Paula02/2014
48353*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
483619551^19268+19268^1955183773Hans Havermann05/2017
483720625^11522+11522^2062583770Hans Havermann05/2017
4838(44*10^83768-791)/983769Robert Price10/2017
4839(87^43189+1)/8883764Paul Bourdelais08/2017
48402^278235-4983758Lelio R Paula06/2012
484123543^3610+3610^2354383755Hans Havermann05/2017
484318^66711-9183741Lelio R Paula11/2015
48424*10^83740-8983741Robert Price08/2017
4844(3*2^278172-1)/1183738Lelio R Paula02/2014
4845(15*29^57251+2561)/2883724Curtis Bright05/2015
48464*7^99059-983716Lelio R Paula10/2014
4847(2^278128-3)/12684472414983714Lelio R Paula12/2012
48482^278077+186721183710Enzo Doria03/2016
48492^278059-2783705Lelio R Paula06/2012
4850214^35917+35917^21483702Norbert Schneider12/2014
4851(23*10^83693+7)/383694Robert Price10/2015
485285^43375-283689Lelio R Paula09/2013
48535*3^175360+483669Lelio R Paula07/2014
4854(23^61441-1)/2283665Robert Price01/2012
485520091^14596+14596^2009183664Hans Havermann03/2017
48562^277907-11062983659Enzo Doria05/2014
485719522^19283+19283^1952283656Hans Havermann04/2017
48588*5^119664-383643Lelio R Paula10/2014
48598*3^175299-783640Lelio R Paula07/2014
4860(26*10^83638-413)/983639Robert Price10/2017
48613^175250+2283616Robert Price12/2013
486211^80285+3083609Lelio R Paula10/2015
486326870^1293+1293^2687083609Hans Havermann03/2017
48642^277691+187442383594Enzo Doria06/2016
486513^75022-6083571Lelio R Paula11/2015
486614^72905-5183559Lelio R Paula11/2015
4867(17*2^277565-1)/54383554Lelio R Paula02/2014
48685^119532-1283550Lelio R Paula10/2015
48696^107358-1625383541Enzo Doria02/2013
48702^277478-46021183530Enzo Doria06/2015
4871(22*10^83525-7)/383526Erik Branger09/2014
4872(30^56543+1)/3183520Robert Price07/2013
48732^277417-46078383511Paul Bourdelais04/2013
4874(22699*2^277387+1)/21983504Lelio R Paula06/2014
4875(31*2^277383-1)/24783500Lelio R Paula02/2014
487621368^8085+8085^2136883500Hans Havermann04/2017
4877(9*2^277342+1)/1383489Lelio R Paula12/2012
48785^119439-6683485Lelio R Paula10/2015
4879(14*10^83471-101)/383472Robert Price04/2017
48805*6^107263+783468Lelio R Paula10/2014
4881(64*10^83461-1)/983462Serge Batalov11/2010
488217^67796-9283420Lelio R Paula11/2015
48832^277106-11005783418Enzo Doria04/2014
48846^107200-1983418Lelio R Paula12/2015
488511^80096-183083412Enzo Doria12/2012
48863^174801+5683402Lelio R Paula12/2015
48872^277033-11197383396Enzo Doria05/2014
488820519^11572+11572^2051983378Hans Havermann03/2017
488920850^9971+9971^2085083374Hans Havermann03/2017
48906^107122-1886383358Enzo Doria03/2013
48914*10^83354-8983355Robert Price08/2017
48923^174697-3483352Robert Price11/2013
4893(9787*2^276855-1)/234583343Lelio R Paula04/2015
48942^276825+7522783333Enzo Doria04/2016
48955^119214+8483328Lelio R Paula10/2015
48962^276803-15983327Lelio R Paula06/2012
4897(3*2^276753-1)/2583311Lelio R Paula02/2014
4898114^40495+40495^11483295Norbert Schneider12/2014
489939967!2+102483282Robert Price02/2015
49012^276641+5783278Lelio R Paula06/2012
490035^53934-341483278Enzo Doria03/2013
4902(2^276655+78557)/36542583276Lelio R Paula12/2012
49032^276615-403583270Lelio R Paula08/2013
49042^276588+115583262Lelio R Paula08/2013
49062^276587-93783261Yves Minet10/2009
49052^276584-11318383261Enzo Doria07/2014
4907(2^276592-1017)/1384373983256Lelio R Paula12/2012
49082^276547-10959183249Enzo Doria04/2014
490913^74733-3283249Lelio R Paula11/2015
49102^276523-258783242Yves Minet07/2014
491118^66311-4383239Lelio R Paula11/2015
491211^79919-153083228Enzo Doria12/2012
49132^276468-10974583226Enzo Doria04/2014
49142^276462+538583224Lelio R Paula08/2013
4915(9787*2^276422-1)/383215Lelio R Paula04/2015
49172^276391-1583202Lelio R Paula06/2012
4916(4*10^83201+173)/383202Robert Price01/2017
49182^276316-10965583180Enzo Doria04/2014
49192^276305-11206383177Enzo Doria06/2014
4920(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
492174913!4-283161Robert Price07/2017
49222^276227-183720783153Enzo Doria05/2015
4923(2^276227+3)/783152Lelio R Paula12/2012
49242^276184-6338983140Paul Bourdelais02/2012
49252^276066-11160383105Enzo Doria05/2014
4926(2^276028-3)*6-783094Gilbert Mozzo09/2016
4927(2^275897+9)/115383051Lelio R Paula12/2012
49282^275879-10980783048Enzo Doria04/2014
4930F(397379)83047Henri Lifchitz08/2003
4929U(397379)83047Serge Batalov03/2015
49323^174040-1483039Robert Price08/2013
4931(86*10^83038-221)/983039Robert Price06/2017
49332^275841-688383037Lelio R Paula07/2011
49343^174002-14083021Lelio R Paula12/2015
49356^106681+7783014Lelio R Paula12/2015
4936187^36539-283011Lelio R Paula10/2017
493711^79701-315083001Enzo Doria12/2012
4938(55459*2^275657+1)/2182985Lelio R Paula06/2014
4939(7*10^82960-457)/982960Robert Price09/2017
49402^275535-685582945Lelio R Paula08/2013
49413^173828-1482938Robert Price08/2013
49422^275512-10967782938Enzo Doria04/2014
49432^275446-11004582918Enzo Doria04/2014
4944(2^275473+47)/2952609744782916Lelio R Paula12/2012
49453^173755-1482903Robert Price08/2013
4946(182*10^82898+43)/982900Robert Price11/2017
49472^275363-11230982893Enzo Doria06/2014
494861^46427-6082888Norbert Schneider10/2014
49493*10^82880-7^8288082881Mike Oakes02/2010
49512^275290+9019582871Lelio R Paula07/2013
4950(35*10^82870-71)/982871Robert Price05/2015
49522^275270-185962182865Enzo Doria03/2016
49532^275259+8182862Henri Lifchitz01/2007
4954(113703^16384+1)/282834Richard Fischer04/2018
49557^98003+98003^7+182823Robert Price05/2014
495610^82790+12604382791Patrick De Geest07/2013
495710^82790-4782790Robert Price05/2011
49582^274985-11266382779Enzo Doria06/2014
49592^274935+1501582764Lelio R Paula07/2013
4960(17*2^274922+1)/382761Lelio R Paula12/2012
4961(43*10^82752-61)/982753Robert Price06/2015
4962(3*2^274862+1)/102782740Lelio R Paula12/2012
4963(31*2^274848-1)/406582736Lelio R Paula02/2014
4964(4^137405+23)/382726Robert Price02/2017
49652^274791-11049182721Enzo Doria05/2014
4966(11*2^274776-1)/9582715Lelio R Paula02/2014
4967(47*10^82706-119)/982707Robert Price09/2017
49682^274704-11139582695Enzo Doria05/2014
49692^274686-391182689Yves Minet04/2017
4970(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
4971(3^173263-5)/1449882664Lelio R Paula12/2012
49722^274511-6487582637Lelio R Paula08/2013
497312^76572-8382636Lelio R Paula11/2015
49743^173191-2^17319182634Mike Oakes02/2004
497514^72072-1582604Lelio R Paula11/2015
4976(55459*2^274339+1)/382589Lelio R Paula06/2014
49772^274351+12382588Lelio R Paula06/2012
4978(1017*2^274339-1)/351582584Lelio R Paula04/2015
49796^106086+11382551Lelio R Paula12/2015
4980(17*10^82540-377)/982541Robert Price11/2017
49812^274093-5869582511Lelio R Paula07/2013
49827*10^82509-4782510Robert Price02/2017
49832^274081-655582507Lelio R Paula07/2013
49852^274074-274074+182505Robert Price10/2014
498614^71985+4782505Lelio R Paula11/2015
49845*10^82504+2182505Robert Price01/2017
49876^106014-13982495Lelio R Paula12/2015
4988(2^274046+47)/75382494Lelio R Paula12/2012
49892^274008-183809982485Enzo Doria05/2015
49902^273981-11002982477Enzo Doria04/2014
499119^64490-3082467Lelio R Paula12/2015
49922^273785+1171582418Lelio R Paula07/2013
49938*10^82417+5182418Robert Price05/2017
499411^79133-1082409Theodore Burton11/2005
499591^42063+9082404Norbert Schneider01/2016
49962^273662-6382381Lelio R Paula06/2012
49972^273661+25582381Lelio R Paula07/2013
4998(62*10^82377-17)/982378Robert Price09/2015
49998*10^82360-5182361Robert Price10/2017
5000(79*10^82347-1)/382349Robert Price11/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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