PRP Records

Probable Primes Top 10000

(259919 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 (> 50000) Who ? When ?
6251(2^278428+1750)/283815Stefano Morozzi01/2020
6252(8*10^83811-101)/383812Robert Price10/2017
62532^278400+4075583807Lelio R Paula08/2013
6254(2^278394+3718)/283805Stefano Morozzi01/2020
6255(2^278388+3586)/283803Stefano Morozzi01/2020
6256(9*2^278381-1)/783802Lelio R Paula02/2014
62573*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
625819551^19268+19268^1955183773Hans Havermann05/2017
625920625^11522+11522^2062583770Hans Havermann05/2017
6260(44*10^83768-791)/983769Robert Price10/2017
6261(87^43189+1)/8883764Paul Bourdelais08/2017
62622^278235-4983758Lelio R Paula06/2012
626323543^3610+3610^2354383755Hans Havermann05/2017
626518^66711-9183741Lelio R Paula11/2015
62644*10^83740-8983741Robert Price08/2017
6266(3*2^278172-1)/1183738Lelio R Paula02/2014
6267(15*29^57251+2561)/2883724Curtis Bright05/2015
62684*7^99059-983716Lelio R Paula10/2014
6269(2^278128-3)/12684472414983714Lelio R Paula12/2012
62702^278077+186721183710Enzo Doria03/2016
62712^278059-2783705Lelio R Paula06/2012
6272214^35917+35917^21483702Norbert Schneider12/2014
6273(23*10^83693+7)/383694Robert Price10/2015
627485^43375-283689Lelio R Paula09/2013
62755*3^175360+483669Lelio R Paula07/2014
6276(23^61441-1)/2283665Robert Price01/2012
627720091^14596+14596^2009183664Hans Havermann03/2017
62782^277907-11062983659Enzo Doria05/2014
627919522^19283+19283^1952283656Hans Havermann04/2017
6280(2^277881+2570)/283651Stefano Morozzi01/2020
62818*5^119664-383643Lelio R Paula10/2014
62828*3^175299-783640Lelio R Paula07/2014
6283(26*10^83638-413)/983639Robert Price10/2017
62843^175250+2283616Robert Price12/2013
628611^80285+3083609Lelio R Paula10/2015
628526870^1293+1293^2687083609Hans Havermann03/2017
62872^277691+187442383594Enzo Doria06/2016
628813^75022-6083571Lelio R Paula11/2015
6289(2^277593+2622)/283564Stefano Morozzi01/2020
629014^72905-5183559Lelio R Paula11/2015
6291(17*2^277565-1)/54383554Lelio R Paula02/2014
62925^119532-1283550Lelio R Paula10/2015
62936^107358-1625383541Enzo Doria02/2013
62942^277478-46021183530Enzo Doria06/2015
6295(2^277474+814)/283528Stefano Morozzi01/2020
6296(22*10^83525-7)/383526Erik Branger09/2014
6297(30^56543+1)/3183520Robert Price07/2013
62982^277417-46078383511Paul Bourdelais04/2013
6299(2^277404+3582)/283507Stefano Morozzi01/2020
6300(22699*2^277387+1)/21983504Lelio R Paula06/2014
6301(31*2^277383-1)/24783500Lelio R Paula02/2014
630221368^8085+8085^2136883500Hans Havermann04/2017
6303(2^277353+3750)/283492Stefano Morozzi01/2020
6304(2^277348+3538)/283490Stefano Morozzi01/2020
6305(9*2^277342+1)/1383489Lelio R Paula12/2012
63065^119439-6683485Lelio R Paula10/2015
6307(14*10^83471-101)/383472Robert Price04/2017
63085*6^107263+783468Lelio R Paula10/2014
6309(64*10^83461-1)/983462Serge Batalov11/2010
63102^277244-17570983459Hans Havermann10/2018
6311(2^277230+1450)/283455Stefano Morozzi01/2020
6312(2^277232+3658)/283455Stefano Morozzi01/2020
631317^67796-9283420Lelio R Paula11/2015
63142^277106-11005783418Enzo Doria04/2014
63156^107200-1983418Lelio R Paula12/2015
631611^80096-183083412Enzo Doria12/2012
63173^174801+5683402Lelio R Paula12/2015
63182^277033-11197383396Enzo Doria05/2014
6319120^40105-11983386Norbert Schneider09/2018
6320(2^276992+2046)/283383Stefano Morozzi01/2020
6321(2^276990+474)/283382Stefano Morozzi01/2020
632220519^11572+11572^2051983378Hans Havermann03/2017
632320850^9971+9971^2085083374Hans Havermann03/2017
63266^107122-1886383358Enzo Doria03/2013
6324(2^276908+2322)/283358Stefano Morozzi01/2020
6325(2^276910+2734)/283358Stefano Morozzi01/2020
63274*10^83354-8983355Robert Price08/2017
63283^174697-3483352Robert Price11/2013
6330(9787*2^276855-1)/234583343Lelio R Paula04/2015
6329(2^276860+1678)/283343Stefano Morozzi01/2020
6331(2^276841+3354)/283338Stefano Morozzi01/2020
63322^276825+7522783333Enzo Doria04/2016
63335^119214+8483328Lelio R Paula10/2015
63342^276803-15983327Lelio R Paula06/2012
6335(3*2^276753-1)/2583311Lelio R Paula02/2014
6336114^40495+40495^11483295Norbert Schneider12/2014
633739967!2+102483282Robert Price02/2015
63382^276641+5783278Lelio R Paula06/2012
633935^53934-341483278Enzo Doria03/2013
6340(2^276655+78557)/36542583276Lelio R Paula12/2012
63412^276615-403583270Lelio R Paula08/2013
63422^276588+115583262Lelio R Paula08/2013
63432^276587-93783261Yves Minet10/2009
63442^276584-11318383261Enzo Doria07/2014
6345(2^276592-1017)/1384373983256Lelio R Paula12/2012
63462^276547-10959183249Enzo Doria04/2014
634713^74733-3283249Lelio R Paula11/2015
63482^276523-258783242Yves Minet07/2014
634918^66311-4383239Lelio R Paula11/2015
635011^79919-153083228Enzo Doria12/2012
63512^276468-10974583226Enzo Doria04/2014
63522^276462+538583224Lelio R Paula08/2013
6353(9787*2^276422-1)/383215Lelio R Paula04/2015
63552^276391-1583202Lelio R Paula06/2012
6354(4*10^83201+173)/383202Robert Price01/2017
6356(2^276327+534)/283183Stefano Morozzi01/2020
63572^276316-10965583180Enzo Doria04/2014
63582^276305-11206383177Enzo Doria06/2014
6359(2^276296+3406)/283174Stefano Morozzi01/2020
6360(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
6361(2^276277+3254)/283168Stefano Morozzi01/2020
636274913!4-283161Robert Price07/2017
63632^276227-183720783153Enzo Doria05/2015
6365(2^276227+3)/783152Lelio R Paula12/2012
6364(2^276229+12)/2883152Stefano Morozzi03/2020
6366(2^276205+1190)/283146Stefano Morozzi01/2020
63672^276184-6338983140Paul Bourdelais02/2012
6368(2^276165+2046)/283134Stefano Morozzi01/2020
6369(2^276105+1274)/283116Stefano Morozzi01/2020
63702^276066-11160383105Enzo Doria05/2014
6371(2^276028-3)*6-783094Gilbert Mozzo09/2016
63722^275926-469183063Yves Minet05/2019
6373(2^275919+1386)/283060Stefano Morozzi01/2020
6374(2^275897+9)/115383051Lelio R Paula12/2012
63752^275879-10980783048Enzo Doria04/2014
6377F(397379)83047Henri Lifchitz08/2003
6376U(397379)83047Serge Batalov03/2015
63783^174040-1483039Robert Price08/2013
6379(86*10^83038-221)/983039Robert Price06/2017
63802^275841-688383037Lelio R Paula07/2011
63813^174002-14083021Lelio R Paula12/2015
63826^106681+7783014Lelio R Paula12/2015
6383187^36539-283011Lelio R Paula10/2017
63841036^27529+27529^103683010Norbert Schneider03/2020
638511^79701-315083001Enzo Doria12/2012
6386(2^275721+1554)/283000Stefano Morozzi01/2020
6387(2^275704+1858)/282995Stefano Morozzi01/2020
6388(2^275696+1726)/282993Stefano Morozzi01/2020
6389(55459*2^275657+1)/2182985Lelio R Paula06/2014
6390(7*10^82960-457)/982960Robert Price09/2017
63912^275535-685582945Lelio R Paula08/2013
63923^173828-1482938Robert Price08/2013
63932^275512-10967782938Enzo Doria04/2014
6394(2^275450+1698)/282919Stefano Morozzi01/2020
63952^275446-11004582918Enzo Doria04/2014
6396(2^275473+47)/2952609744782916Lelio R Paula12/2012
63973^173755-1482903Robert Price08/2013
6398(182*10^82898+43)/982900Robert Price11/2017
63992^275363-11230982893Enzo Doria06/2014
640061^46427-6082888Norbert Schneider10/2014
64013*10^82880-7^8288082881Mike Oakes02/2010
64022^275290+9019582871Lelio R Paula07/2013
6403(35*10^82870-71)/982871Robert Price05/2015
64042^275270-185962182865Enzo Doria03/2016
64052^275259+8182862Henri Lifchitz01/2007
6406(2^275247+1590)/282858Stefano Morozzi01/2020
6407(113703^16384+1)/282834Richard Fischer04/2018
6408(2^275146+954)/282827Stefano Morozzi01/2020
64097^98003+98003^7+182823Robert Price05/2014
6410(2^275101+3566)/282814Stefano Morozzi01/2020
6411(2^275050+3150)/282798Stefano Morozzi01/2020
6412(2^275044+2482)/282797Stefano Morozzi01/2020
641310^82790+12604382791Patrick De Geest07/2013
641410^82790-4782790Robert Price05/2011
64152^274985-11266382779Enzo Doria06/2014
64162^274935+1501582764Lelio R Paula07/2013
6417(17*2^274922+1)/382761Lelio R Paula12/2012
6418[(55^5)^9511-(22434^2)^9511]/1982759Richard Fischer11/2019
6419(43*10^82752-61)/982753Robert Price06/2015
6420(3*2^274862+1)/102782740Lelio R Paula12/2012
6421(2^274851+3126)/282739Stefano Morozzi01/2020
6422(31*2^274848-1)/406582736Lelio R Paula02/2014
6423(4^137405+23)/382726Robert Price02/2017
6424(2^274798+414)/282723Stefano Morozzi01/2020
64252^274791-11049182721Enzo Doria05/2014
6426(11*2^274776-1)/9582715Lelio R Paula02/2014
6427(47*10^82706-119)/982707Robert Price09/2017
64282^274704-11139582695Enzo Doria05/2014
64292^274686-391182689Yves Minet04/2017
6430(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
6431(3^173263-5)/1449882664Lelio R Paula12/2012
6432(2^274554+894)/282649Stefano Morozzi01/2020
64342^274511-6487582637Lelio R Paula08/2013
6433(2^274512+1222)/282637Stefano Morozzi01/2020
643512^76572-8382636Lelio R Paula11/2015
64363^173191-2^17319182634Mike Oakes02/2004
6437(2^274500+2970)/282633Stefano Morozzi01/2020
6438(2^274429+3726)/282612Stefano Morozzi01/2020
643914^72072-1582604Lelio R Paula11/2015
6440(2^274374+2950)/282595Stefano Morozzi01/2020
6441(55459*2^274339+1)/382589Lelio R Paula06/2014
64422^274351+12382588Lelio R Paula06/2012
6443(1017*2^274339-1)/351582584Lelio R Paula04/2015
6444(2^274248+750)/282557Stefano Morozzi01/2020
6445(2^274240+822)/282555Stefano Morozzi01/2020
64466^106086+11382551Lelio R Paula12/2015
6447(17*10^82540-377)/982541Robert Price11/2017
64482^274093-5869582511Lelio R Paula07/2013
64497*10^82509-4782510Robert Price02/2017
64502^274081-655582507Lelio R Paula07/2013
64522^274074-274074+182505Robert Price10/2014
645314^71985+4782505Lelio R Paula11/2015
64515*10^82504+2182505Robert Price01/2017
6454(2^274062+498)/282501Stefano Morozzi01/2020
64556^106014-13982495Lelio R Paula12/2015
6456(2^274046+47)/75382494Lelio R Paula12/2012
64572^274008-183809982485Enzo Doria05/2015
64582^273981-11002982477Enzo Doria04/2014
645919^64490-3082467Lelio R Paula12/2015
6460(2^273864+3150)/282441Stefano Morozzi01/2020
64632^273785+1171582418Lelio R Paula07/2013
64628*10^82417+5182418Robert Price05/2017
6461(2^273786+2242)/282418Stefano Morozzi01/2020
646411^79133-1082409Theodore Burton11/2005
6465(2^273752+1882)/282408Stefano Morozzi01/2020
646691^42063+9082404Norbert Schneider01/2016
64682^273662-6382381Lelio R Paula06/2012
64672^273661+25582381Lelio R Paula07/2013
6469(62*10^82377-17)/982378Robert Price09/2015
64702^273608+52428782365Paul Underwood08/2018
64718*10^82360-5182361Robert Price10/2017
6472(79*10^82347-1)/382349Robert Price11/2017
6473(11*10^82323+91)/382323Robert Price02/2017
6474(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
6475(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
647615^69984+3282308Lelio R Paula11/2015
64779*6^105746+782288Lelio R Paula10/2014
647889^42211-8882286Norbert Schneider01/2016
6479gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
6480(19*10^82270-43)/382271Robert Price10/2017
64812^273282-11024182267Enzo Doria05/2014
6482(2^273277+3746)/282265Stefano Morozzi01/2020
6483(13^73849+4^73849)/1782263Robert Price05/2013
648510^82254+9^(82254+1)82255Robert Price08/2016
648410^82254+45777382255Patrick De Geest12/2016
648610^82254-9960982254Patrick De Geest12/2016
6487(754*10^82250-7)/982252Robert Price11/2017
648818^65524+1382251Lelio R Paula11/2015
64892^273206-10782244Lelio R Paula06/2012
64902^273193-45914582240Enzo Doria05/2015
64922^273126+3693782220Yves Minet06/2010
649139505!2+12882220Robert Price03/2015
6493(2^273090+2214)/282208Stefano Morozzi01/2020
64942^273053-11211182198Enzo Doria06/2014
6495(2^273052+3138)/282197Stefano Morozzi01/2020
64962^273016+118582187Lelio R Paula07/2013
6497(2^273008+3)/782183Lelio R Paula12/2012
6498(2^272992+2230)/282179Stefano Morozzi01/2020
64995^117554-1538682167Enzo Doria02/2013
6500(38*10^82161+403)/982162Robert Price11/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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