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 ?
475111^81699-279085081Enzo Doria12/2012
47522^282612-9585075Lelio R Paula08/2012
47532^282609-406985074Yves Minet02/2018
475475^45366-285065Lelio R Paula08/2013
47552^282511+6985045Lelio R Paula08/2012
475669^46249+285045Lelio R Paula06/2013
47573^178226+1085036Robert Price10/2013
4758(182*10^85017+43)/985019Robert Price11/2017
4759(14*10^85010+73)/385011Robert Price04/2016
47609*2^282338-784994Lelio R Paula08/2014
4761(9913*2^282330-1)/157800384988Lelio R Paula04/2015
47622^282203+584952Lelio R Paula08/2012
47632^282184+1384946Lelio R Paula08/2012
476411^81568-240084945Enzo Doria12/2012
476511^81562-234084939Enzo Doria12/2012
4766(41*10^84927+31)/984928Robert Price05/2015
4767(2*10^84904-17)/384904Robert Price08/2014
4768(4^141017+23)/384901Robert Price02/2017
47696^109100-1865384897Enzo Doria03/2013
47702^281973+102584883Lelio R Paula09/2013
47712^281951-10965184876Enzo Doria04/2014
477211^81491-543084865Enzo Doria01/2013
4773((1+sqrt(3)+sqrt(2))^79357-1)*((1+sqrt(3)-sqrt(2))^79357-1)*((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(384849Mike Oakes04/2009
47742^281825-186148384838Enzo Doria03/2016
47752^281809-9730584833Lelio R Paula09/2013
47762^281780-11489384825Enzo Doria05/2015
47773^177719+6484794Lelio R Paula12/2015
47792^281675-19984793Lelio R Paula08/2012
47782^281673-11122384793Enzo Doria05/2014
4780(4*10^84779+149)/984779Robert Price03/2017
4781(72*10^84772-27)/984773Ray Chandler01/2011
478211^81398-63084768Enzo Doria11/2012
4783(25*2^281577-1)/2384764Lelio R Paula02/2014
47842^281500-45584740Yves Minet03/2012
478510^84725+114514191984726Marisa Kirisame03/2015
478610^84725+14204184726Patrick De Geest10/2015
478710^84725-13867784725Patrick De Geest02/2016
478876^45044+7584720Norbert Schneider02/2015
478954^48897-5384709Norbert Schneider08/2014
4790(9913*2^281377-1)/6584706Lelio R Paula04/2015
4791Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
47922^281337-11122384691Enzo Doria05/2014
47932^281308+5461584683Lelio R Paula09/2013
47947*5^121144-684677Lelio R Paula10/2014
4795(2^281252+47)/384665Lelio R Paula01/2013
479611^81297-315084663Enzo Doria12/2012
47972^281208-30384653Yves Minet02/2012
4798197^36892-284648Lelio R Paula10/2017
4799(21*2^281187+1)/248384644Lelio R Paula01/2013
480011^81247-8484611Lelio R Paula10/2015
480117^68747-6484590Lelio R Paula11/2015
48025^121018-1559684588Enzo Doria02/2013
48036^108702+784587Lelio R Paula11/2014
480410^84582+10067784583Patrick De Geest05/2016
480510^84582-800184582Robert Price03/2016
48063*5^121004-884579Lelio R Paula10/2014
48075^120996-8484573Lelio R Paula10/2015
4808(10223*2^280881+1)/6841984553Lelio R Paula06/2014
48092^280852+9768184545Yves Minet08/2004
48102^280848-120384544Lelio R Paula09/2013
48115^120946-2484538Lelio R Paula10/2015
48122^280810-211184533Yves Minet08/2013
481311^81161-516084521Enzo Doria01/2013
48142^280737-9384511Lelio R Paula08/2012
48152^280698+31584499Lelio R Paula09/2013
48163^177099-34084498Lelio R Paula12/2015
4817(5*10^84469-107)/384470Robert Price01/2017
4818(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4819(2^280500-1017)/82384436Lelio R Paula01/2013
482014^73660-584424Lelio R Paula11/2015
4821(19*10^84409-61)/384410Robert Price04/2017
48222^280388+11784406Lelio R Paula08/2012
48232^280389-56653384406Paul Bourdelais03/2013
4824(141584^16384+1)/6553784390Syoichiro Yamada06/2008
48252^280240-17384361Lelio R Paula08/2012
4826(184*10^84348-1)/384350Robert Price02/2017
48274*10^84346+9384347Robert Price01/2017
48287*2^280156-584337Lelio R Paula08/2014
48298*7^99782-384327Lelio R Paula10/2014
48312^280116+13384324Lelio R Paula08/2012
48302^280118+5461584324Lelio R Paula09/2013
4832(509203*2^280090-1)/384321Lelio R Paula04/2015
48336^108354+4784316Lelio R Paula12/2015
483410^84305+14196384306Patrick De Geest07/2013
483510^84305-5784305Robert Price05/2011
48369^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
48373^176648-11280484283Enzo Doria06/2014
48386^108310+11584282Lelio R Paula12/2015
4839(11*2^279968-1)/584280Lelio R Paula02/2014
48406^108288-1664384265Enzo Doria02/2013
48412^279917-5869584264Lelio R Paula08/2013
484265^46477+3684259Lelio R Paula01/2016
48432^279866-190784249Yves Minet05/2013
4844(3^176580-5)/2807684246Lelio R Paula12/2012
4845(p(17530)#+4)/284246Robert Price09/2017
4846(2*10^84239+1)/384239Serge Batalov07/2009
484818^67103-4184233Lelio R Paula11/2015
484720^64743-4384233Lelio R Paula01/2016
4849143^39070+39070^14384209Serge Batalov05/2014
485011^80857-540084204Enzo Doria01/2013
4851(13*10^84179+161)/384180Robert Price04/2017
48522^279634-11040584179Enzo Doria05/2014
4853(74*10^84170+313)/984171Robert Price11/2017
48542^279582-101784163Lelio R Paula08/2013
4855(22*10^84159-19)/384160Robert Price02/2017
4856p(17513)#/2+51284156Robert Price05/2017
4857(19*10^84144-43)/384145Robert Price10/2017
4858(9*2^279507-1)/13784139Lelio R Paula02/2014
485911^80792-81084137Enzo Doria11/2012
4860(97*10^84134-1)/384136Serge Batalov12/2014
4861p(17507)#/2+3284125Robert Price12/2016
486221485^8224+8224^2148584116Hans Havermann04/2017
48633^176294-34084114Lelio R Paula12/2015
4864(3^176287+4)/219184107Lelio R Paula12/2012
48652^279388-71984105Yves Minet05/2012
4866(22699*2^279378+1)/22184104Lelio R Paula06/2014
48672^279332-11044784088Enzo Doria05/2014
48682^279320+784084Lelio R Paula06/2012
4869127^39966-284081Lelio R Paula10/2017
4870(11*2^279240-1)/9584059Lelio R Paula02/2014
48712^279218-11134784053Enzo Doria05/2014
487235^54435+284052Lelio R Paula05/2013
4873(31*2^279191-1)/1251152384040Lelio R Paula02/2014
487420996^10059+10059^2099684038Hans Havermann05/2017
487597*10^84033-384035Robert Price01/2017
487621234^9067+9067^2123484033Hans Havermann05/2017
4877(134569^16384+1)/284033Richard Fischer06/2018
48782^279095-10971784016Enzo Doria04/2014
487914^73282-9983991Lelio R Paula11/2015
488021457^8200+8200^2145783979Hans Havermann06/2017
488189*10^83976-783978Robert Price03/2017
48822^278955+17383974Lelio R Paula06/2012
4883(7*2^278851+1)/3983942Lelio R Paula12/2012
4884(9913*2^278844-1)/4080383940Lelio R Paula04/2015
48855^120076-1484683930Enzo Doria02/2013
4886(85*10^83921-1)/383923Robert Price07/2017
4887(2^278770-3)/2383917Lelio R Paula12/2012
4888(10^83916+449)/983916Serge Batalov12/2014
48902^278715+9983902Lelio R Paula06/2012
4889(132109^16384+1)/283902Richard Fischer05/2018
489140235!2-2^4023583899Robert Price09/2015
48922^278698-17183897Lelio R Paula06/2012
4893(19*10^83894-43)/383895Robert Price10/2017
48946^107802+2583887Lelio R Paula12/2015
48958*10^83880+3983881Robert Price01/2017
4896(58*10^83878+23)/983879Robert Price09/2015
48977^99244-9083871Lelio R Paula10/2015
48982^278554+425783854Lelio R Paula08/2013
48992^278504-10961983839Enzo Doria04/2014
49002^278499+187043383837Enzo Doria05/2016
4901105^41475+10483829Norbert Schneider11/2016
490215^71276-6883828Lelio R Paula11/2015
49032^278464-21641383827Enzo Doria04/2013
4904(76*10^83816-211)/983817Robert Price10/2017
4905(8*10^83811-101)/383812Robert Price10/2017
49062^278400+4075583807Lelio R Paula08/2013
4907(9*2^278381-1)/783802Lelio R Paula02/2014
49083*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
490919551^19268+19268^1955183773Hans Havermann05/2017
491020625^11522+11522^2062583770Hans Havermann05/2017
4911(44*10^83768-791)/983769Robert Price10/2017
4912(87^43189+1)/8883764Paul Bourdelais08/2017
49132^278235-4983758Lelio R Paula06/2012
491423543^3610+3610^2354383755Hans Havermann05/2017
491618^66711-9183741Lelio R Paula11/2015
49154*10^83740-8983741Robert Price08/2017
4917(3*2^278172-1)/1183738Lelio R Paula02/2014
4918(15*29^57251+2561)/2883724Curtis Bright05/2015
49194*7^99059-983716Lelio R Paula10/2014
4920(2^278128-3)/12684472414983714Lelio R Paula12/2012
49212^278077+186721183710Enzo Doria03/2016
49222^278059-2783705Lelio R Paula06/2012
4923214^35917+35917^21483702Norbert Schneider12/2014
4924(23*10^83693+7)/383694Robert Price10/2015
492585^43375-283689Lelio R Paula09/2013
49265*3^175360+483669Lelio R Paula07/2014
4927(23^61441-1)/2283665Robert Price01/2012
492820091^14596+14596^2009183664Hans Havermann03/2017
49292^277907-11062983659Enzo Doria05/2014
493019522^19283+19283^1952283656Hans Havermann04/2017
49318*5^119664-383643Lelio R Paula10/2014
49328*3^175299-783640Lelio R Paula07/2014
4933(26*10^83638-413)/983639Robert Price10/2017
49343^175250+2283616Robert Price12/2013
493511^80285+3083609Lelio R Paula10/2015
493626870^1293+1293^2687083609Hans Havermann03/2017
49372^277691+187442383594Enzo Doria06/2016
493813^75022-6083571Lelio R Paula11/2015
493914^72905-5183559Lelio R Paula11/2015
4940(17*2^277565-1)/54383554Lelio R Paula02/2014
49415^119532-1283550Lelio R Paula10/2015
49426^107358-1625383541Enzo Doria02/2013
49432^277478-46021183530Enzo Doria06/2015
4944(22*10^83525-7)/383526Erik Branger09/2014
4945(30^56543+1)/3183520Robert Price07/2013
49462^277417-46078383511Paul Bourdelais04/2013
4947(22699*2^277387+1)/21983504Lelio R Paula06/2014
4948(31*2^277383-1)/24783500Lelio R Paula02/2014
494921368^8085+8085^2136883500Hans Havermann04/2017
4950(9*2^277342+1)/1383489Lelio R Paula12/2012
49515^119439-6683485Lelio R Paula10/2015
4952(14*10^83471-101)/383472Robert Price04/2017
49535*6^107263+783468Lelio R Paula10/2014
4954(64*10^83461-1)/983462Serge Batalov11/2010
495517^67796-9283420Lelio R Paula11/2015
49562^277106-11005783418Enzo Doria04/2014
49576^107200-1983418Lelio R Paula12/2015
495811^80096-183083412Enzo Doria12/2012
49593^174801+5683402Lelio R Paula12/2015
49602^277033-11197383396Enzo Doria05/2014
496120519^11572+11572^2051983378Hans Havermann03/2017
496220850^9971+9971^2085083374Hans Havermann03/2017
49636^107122-1886383358Enzo Doria03/2013
49644*10^83354-8983355Robert Price08/2017
49653^174697-3483352Robert Price11/2013
4966(9787*2^276855-1)/234583343Lelio R Paula04/2015
49672^276825+7522783333Enzo Doria04/2016
49685^119214+8483328Lelio R Paula10/2015
49692^276803-15983327Lelio R Paula06/2012
4970(3*2^276753-1)/2583311Lelio R Paula02/2014
4971114^40495+40495^11483295Norbert Schneider12/2014
497239967!2+102483282Robert Price02/2015
49732^276641+5783278Lelio R Paula06/2012
497435^53934-341483278Enzo Doria03/2013
4975(2^276655+78557)/36542583276Lelio R Paula12/2012
49762^276615-403583270Lelio R Paula08/2013
49772^276588+115583262Lelio R Paula08/2013
49792^276587-93783261Yves Minet10/2009
49782^276584-11318383261Enzo Doria07/2014
4980(2^276592-1017)/1384373983256Lelio R Paula12/2012
49812^276547-10959183249Enzo Doria04/2014
498213^74733-3283249Lelio R Paula11/2015
49832^276523-258783242Yves Minet07/2014
498418^66311-4383239Lelio R Paula11/2015
498511^79919-153083228Enzo Doria12/2012
49862^276468-10974583226Enzo Doria04/2014
49872^276462+538583224Lelio R Paula08/2013
4988(9787*2^276422-1)/383215Lelio R Paula04/2015
49892^276391-1583202Lelio R Paula06/2012
4990(4*10^83201+173)/383202Robert Price01/2017
49912^276316-10965583180Enzo Doria04/2014
49922^276305-11206383177Enzo Doria06/2014
4993(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
499474913!4-283161Robert Price07/2017
49952^276227-183720783153Enzo Doria05/2015
4996(2^276227+3)/783152Lelio R Paula12/2012
49972^276184-6338983140Paul Bourdelais02/2012
49982^276066-11160383105Enzo Doria05/2014
4999(2^276028-3)*6-783094Gilbert Mozzo09/2016
5000(2^275897+9)/115383051Lelio R Paula12/2012


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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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