PRP Records

Probable Primes Top 10000

(225451 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 ?
50016^108702+784587Lelio R Paula11/2014
500210^84582+10067784583Patrick De Geest05/2016
500310^84582-800184582Robert Price03/2016
50043*5^121004-884579Lelio R Paula10/2014
50055^120996-8484573Lelio R Paula10/2015
5006(10223*2^280881+1)/6841984553Lelio R Paula06/2014
50072^280852+9768184545Yves Minet08/2004
50082^280848-120384544Lelio R Paula09/2013
50095^120946-2484538Lelio R Paula10/2015
50102^280810-211184533Yves Minet08/2013
501111^81161-516084521Enzo Doria01/2013
50122^280737-9384511Lelio R Paula08/2012
50132^280698+31584499Lelio R Paula09/2013
50143^177099-34084498Lelio R Paula12/2015
5015(5*10^84469-107)/384470Robert Price01/2017
5016(3^177002+7)/669602227216174484436Lelio R Paula12/2012
5017(2^280500-1017)/82384436Lelio R Paula01/2013
501814^73660-584424Lelio R Paula11/2015
5019(19*10^84409-61)/384410Robert Price04/2017
50202^280388+11784406Lelio R Paula08/2012
50212^280389-56653384406Paul Bourdelais03/2013
5022(141584^16384+1)/6553784390Syoichiro Yamada06/2008
5023119^40652+11884376Norbert Schneider09/2018
50242^280240-17384361Lelio R Paula08/2012
5025(184*10^84348-1)/384350Robert Price02/2017
50264*10^84346+9384347Robert Price01/2017
50277*2^280156-584337Lelio R Paula08/2014
50288*7^99782-384327Lelio R Paula10/2014
50302^280116+13384324Lelio R Paula08/2012
50292^280118+5461584324Lelio R Paula09/2013
5031(509203*2^280090-1)/384321Lelio R Paula04/2015
50326^108354+4784316Lelio R Paula12/2015
503310^84305+14196384306Patrick De Geest07/2013
503410^84305-5784305Robert Price05/2011
50359^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
50363^176648-11280484283Enzo Doria06/2014
50376^108310+11584282Lelio R Paula12/2015
5038(11*2^279968-1)/584280Lelio R Paula02/2014
50396^108288-1664384265Enzo Doria02/2013
50402^279917-5869584264Lelio R Paula08/2013
504165^46477+3684259Lelio R Paula01/2016
50422^279866-190784249Yves Minet05/2013
5043(3^176580-5)/2807684246Lelio R Paula12/2012
5044(p(17530)#+4)/284246Robert Price09/2017
5045(2*10^84239+1)/384239Serge Batalov07/2009
504718^67103-4184233Lelio R Paula11/2015
504620^64743-4384233Lelio R Paula01/2016
5048143^39070+39070^14384209Serge Batalov05/2014
504911^80857-540084204Enzo Doria01/2013
5050(13*10^84179+161)/384180Robert Price04/2017
50512^279634-11040584179Enzo Doria05/2014
5052(74*10^84170+313)/984171Robert Price11/2017
50532^279582-101784163Lelio R Paula08/2013
5054(22*10^84159-19)/384160Robert Price02/2017
5055p(17513)#/2+51284156Robert Price05/2017
5056(19*10^84144-43)/384145Robert Price10/2017
5057(9*2^279507-1)/13784139Lelio R Paula02/2014
505811^80792-81084137Enzo Doria11/2012
5059(97*10^84134-1)/384136Serge Batalov12/2014
5060p(17507)#/2+3284125Robert Price12/2016
506121485^8224+8224^2148584116Hans Havermann04/2017
50623^176294-34084114Lelio R Paula12/2015
5063(3^176287+4)/219184107Lelio R Paula12/2012
50642^279388-71984105Yves Minet05/2012
5065(22699*2^279378+1)/22184104Lelio R Paula06/2014
50662^279332-11044784088Enzo Doria05/2014
50672^279320+784084Lelio R Paula06/2012
5068127^39966-284081Lelio R Paula10/2017
5069(11*2^279240-1)/9584059Lelio R Paula02/2014
50702^279218-11134784053Enzo Doria05/2014
507135^54435+284052Lelio R Paula05/2013
5072(31*2^279191-1)/1251152384040Lelio R Paula02/2014
507320996^10059+10059^2099684038Hans Havermann05/2017
507497*10^84033-384035Robert Price01/2017
507521234^9067+9067^2123484033Hans Havermann05/2017
5076(134569^16384+1)/284033Richard Fischer06/2018
50772^279095-10971784016Enzo Doria04/2014
507814^73282-9983991Lelio R Paula11/2015
507921457^8200+8200^2145783979Hans Havermann06/2017
508089*10^83976-783978Robert Price03/2017
50812^278955+17383974Lelio R Paula06/2012
5082(7*2^278851+1)/3983942Lelio R Paula12/2012
5083(9913*2^278844-1)/4080383940Lelio R Paula04/2015
50845^120076-1484683930Enzo Doria02/2013
5085(85*10^83921-1)/383923Robert Price07/2017
5086(2^278770-3)/2383917Lelio R Paula12/2012
5087(10^83916+449)/983916Serge Batalov12/2014
50882^278715+9983902Lelio R Paula06/2012
5089(132109^16384+1)/283902Richard Fischer05/2018
509040235!2-2^4023583899Robert Price09/2015
50912^278698-17183897Lelio R Paula06/2012
5092(19*10^83894-43)/383895Robert Price10/2017
50936^107802+2583887Lelio R Paula12/2015
50948*10^83880+3983881Robert Price01/2017
5095(58*10^83878+23)/983879Robert Price09/2015
50967^99244-9083871Lelio R Paula10/2015
50972^278554+425783854Lelio R Paula08/2013
50982^278504-10961983839Enzo Doria04/2014
50992^278499+187043383837Enzo Doria05/2016
5100105^41475+10483829Norbert Schneider11/2016
510115^71276-6883828Lelio R Paula11/2015
51022^278464-21641383827Enzo Doria04/2013
5103(76*10^83816-211)/983817Robert Price10/2017
5104(8*10^83811-101)/383812Robert Price10/2017
51052^278400+4075583807Lelio R Paula08/2013
5106(9*2^278381-1)/783802Lelio R Paula02/2014
51073*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
510819551^19268+19268^1955183773Hans Havermann05/2017
510920625^11522+11522^2062583770Hans Havermann05/2017
5110(44*10^83768-791)/983769Robert Price10/2017
5111(87^43189+1)/8883764Paul Bourdelais08/2017
51122^278235-4983758Lelio R Paula06/2012
511323543^3610+3610^2354383755Hans Havermann05/2017
511518^66711-9183741Lelio R Paula11/2015
51144*10^83740-8983741Robert Price08/2017
5116(3*2^278172-1)/1183738Lelio R Paula02/2014
5117(15*29^57251+2561)/2883724Curtis Bright05/2015
51184*7^99059-983716Lelio R Paula10/2014
5119(2^278128-3)/12684472414983714Lelio R Paula12/2012
51202^278077+186721183710Enzo Doria03/2016
51212^278059-2783705Lelio R Paula06/2012
5122214^35917+35917^21483702Norbert Schneider12/2014
5123(23*10^83693+7)/383694Robert Price10/2015
512485^43375-283689Lelio R Paula09/2013
51255*3^175360+483669Lelio R Paula07/2014
5126(23^61441-1)/2283665Robert Price01/2012
512720091^14596+14596^2009183664Hans Havermann03/2017
51282^277907-11062983659Enzo Doria05/2014
512919522^19283+19283^1952283656Hans Havermann04/2017
51308*5^119664-383643Lelio R Paula10/2014
51318*3^175299-783640Lelio R Paula07/2014
5132(26*10^83638-413)/983639Robert Price10/2017
51333^175250+2283616Robert Price12/2013
513511^80285+3083609Lelio R Paula10/2015
513426870^1293+1293^2687083609Hans Havermann03/2017
51362^277691+187442383594Enzo Doria06/2016
513713^75022-6083571Lelio R Paula11/2015
513814^72905-5183559Lelio R Paula11/2015
5139(17*2^277565-1)/54383554Lelio R Paula02/2014
51405^119532-1283550Lelio R Paula10/2015
51416^107358-1625383541Enzo Doria02/2013
51422^277478-46021183530Enzo Doria06/2015
5143(22*10^83525-7)/383526Erik Branger09/2014
5144(30^56543+1)/3183520Robert Price07/2013
51452^277417-46078383511Paul Bourdelais04/2013
5146(22699*2^277387+1)/21983504Lelio R Paula06/2014
5147(31*2^277383-1)/24783500Lelio R Paula02/2014
514821368^8085+8085^2136883500Hans Havermann04/2017
5149(9*2^277342+1)/1383489Lelio R Paula12/2012
51505^119439-6683485Lelio R Paula10/2015
5151(14*10^83471-101)/383472Robert Price04/2017
51525*6^107263+783468Lelio R Paula10/2014
5153(64*10^83461-1)/983462Serge Batalov11/2010
51542^277244-17570983459Hans Havermann10/2018
515517^67796-9283420Lelio R Paula11/2015
51562^277106-11005783418Enzo Doria04/2014
51576^107200-1983418Lelio R Paula12/2015
515811^80096-183083412Enzo Doria12/2012
51593^174801+5683402Lelio R Paula12/2015
51602^277033-11197383396Enzo Doria05/2014
5161120^40105-11983386Norbert Schneider09/2018
516220519^11572+11572^2051983378Hans Havermann03/2017
516320850^9971+9971^2085083374Hans Havermann03/2017
51646^107122-1886383358Enzo Doria03/2013
51654*10^83354-8983355Robert Price08/2017
51663^174697-3483352Robert Price11/2013
5167(9787*2^276855-1)/234583343Lelio R Paula04/2015
51682^276825+7522783333Enzo Doria04/2016
51695^119214+8483328Lelio R Paula10/2015
51702^276803-15983327Lelio R Paula06/2012
5171(3*2^276753-1)/2583311Lelio R Paula02/2014
5172114^40495+40495^11483295Norbert Schneider12/2014
517339967!2+102483282Robert Price02/2015
51752^276641+5783278Lelio R Paula06/2012
517435^53934-341483278Enzo Doria03/2013
5176(2^276655+78557)/36542583276Lelio R Paula12/2012
51772^276615-403583270Lelio R Paula08/2013
51782^276588+115583262Lelio R Paula08/2013
51802^276587-93783261Yves Minet10/2009
51792^276584-11318383261Enzo Doria07/2014
5181(2^276592-1017)/1384373983256Lelio R Paula12/2012
51822^276547-10959183249Enzo Doria04/2014
518313^74733-3283249Lelio R Paula11/2015
51842^276523-258783242Yves Minet07/2014
518518^66311-4383239Lelio R Paula11/2015
518611^79919-153083228Enzo Doria12/2012
51872^276468-10974583226Enzo Doria04/2014
51882^276462+538583224Lelio R Paula08/2013
5189(9787*2^276422-1)/383215Lelio R Paula04/2015
51902^276391-1583202Lelio R Paula06/2012
5191(4*10^83201+173)/383202Robert Price01/2017
51922^276316-10965583180Enzo Doria04/2014
51932^276305-11206383177Enzo Doria06/2014
5194(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
519574913!4-283161Robert Price07/2017
51962^276227-183720783153Enzo Doria05/2015
5197(2^276227+3)/783152Lelio R Paula12/2012
51982^276184-6338983140Paul Bourdelais02/2012
51992^276066-11160383105Enzo Doria05/2014
5200(2^276028-3)*6-783094Gilbert Mozzo09/2016
5201(2^275897+9)/115383051Lelio R Paula12/2012
52022^275879-10980783048Enzo Doria04/2014
5204F(397379)83047Henri Lifchitz08/2003
5203U(397379)83047Serge Batalov03/2015
52053^174040-1483039Robert Price08/2013
5206(86*10^83038-221)/983039Robert Price06/2017
52072^275841-688383037Lelio R Paula07/2011
52083^174002-14083021Lelio R Paula12/2015
52096^106681+7783014Lelio R Paula12/2015
5210187^36539-283011Lelio R Paula10/2017
521111^79701-315083001Enzo Doria12/2012
5212(55459*2^275657+1)/2182985Lelio R Paula06/2014
5213(7*10^82960-457)/982960Robert Price09/2017
52142^275535-685582945Lelio R Paula08/2013
52163^173828-1482938Robert Price08/2013
52152^275512-10967782938Enzo Doria04/2014
52172^275446-11004582918Enzo Doria04/2014
5218(2^275473+47)/2952609744782916Lelio R Paula12/2012
52193^173755-1482903Robert Price08/2013
5220(182*10^82898+43)/982900Robert Price11/2017
52212^275363-11230982893Enzo Doria06/2014
522261^46427-6082888Norbert Schneider10/2014
52233*10^82880-7^8288082881Mike Oakes02/2010
52252^275290+9019582871Lelio R Paula07/2013
5224(35*10^82870-71)/982871Robert Price05/2015
52262^275270-185962182865Enzo Doria03/2016
52272^275259+8182862Henri Lifchitz01/2007
5228(113703^16384+1)/282834Richard Fischer04/2018
52297^98003+98003^7+182823Robert Price05/2014
523010^82790+12604382791Patrick De Geest07/2013
523110^82790-4782790Robert Price05/2011
52322^274985-11266382779Enzo Doria06/2014
52332^274935+1501582764Lelio R Paula07/2013
5234(17*2^274922+1)/382761Lelio R Paula12/2012
5235(43*10^82752-61)/982753Robert Price06/2015
5236(3*2^274862+1)/102782740Lelio R Paula12/2012
5237(31*2^274848-1)/406582736Lelio R Paula02/2014
5238(4^137405+23)/382726Robert Price02/2017
52392^274791-11049182721Enzo Doria05/2014
5240(11*2^274776-1)/9582715Lelio R Paula02/2014
5241(47*10^82706-119)/982707Robert Price09/2017
52422^274704-11139582695Enzo Doria05/2014
52432^274686-391182689Yves Minet04/2017
5244(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
5245(3^173263-5)/1449882664Lelio R Paula12/2012
52462^274511-6487582637Lelio R Paula08/2013
524712^76572-8382636Lelio R Paula11/2015
52483^173191-2^17319182634Mike Oakes02/2004
524914^72072-1582604Lelio R Paula11/2015
5250(55459*2^274339+1)/382589Lelio R Paula06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 20 2018 23:15 (Time in France)

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