PRP Records

Probable Primes Top 10000

(252932 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 ?
5501(134569^16384+1)/284033Richard Fischer06/2018
55022^279095-10971784016Enzo Doria04/2014
550314^73282-9983991Lelio R Paula11/2015
550421457^8200+8200^2145783979Hans Havermann06/2017
550589*10^83976-783978Robert Price03/2017
55062^278955+17383974Lelio R Paula06/2012
5507(7*2^278851+1)/3983942Lelio R Paula12/2012
5508(9913*2^278844-1)/4080383940Lelio R Paula04/2015
55095^120076-1484683930Enzo Doria02/2013
5510(85*10^83921-1)/383923Robert Price07/2017
5511(2^278770-3)/2383917Lelio R Paula12/2012
5512(10^83916+449)/983916Serge Batalov12/2014
55132^278715+9983902Lelio R Paula06/2012
5514(132109^16384+1)/283902Richard Fischer05/2018
551540235!2-2^4023583899Robert Price09/2015
55162^278698-17183897Lelio R Paula06/2012
5517(19*10^83894-43)/383895Robert Price10/2017
55186^107802+2583887Lelio R Paula12/2015
55198*10^83880+3983881Robert Price01/2017
5520(58*10^83878+23)/983879Robert Price09/2015
55217^99244-9083871Lelio R Paula10/2015
55222^278554+425783854Lelio R Paula08/2013
55232^278504-10961983839Enzo Doria04/2014
55242^278499+187043383837Enzo Doria05/2016
5525105^41475+10483829Norbert Schneider11/2016
552615^71276-6883828Lelio R Paula11/2015
55272^278464-21641383827Enzo Doria04/2013
5528(76*10^83816-211)/983817Robert Price10/2017
5529(8*10^83811-101)/383812Robert Price10/2017
55302^278400+4075583807Lelio R Paula08/2013
5531(9*2^278381-1)/783802Lelio R Paula02/2014
55323*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
553319551^19268+19268^1955183773Hans Havermann05/2017
553420625^11522+11522^2062583770Hans Havermann05/2017
5535(44*10^83768-791)/983769Robert Price10/2017
5536(87^43189+1)/8883764Paul Bourdelais08/2017
55372^278235-4983758Lelio R Paula06/2012
553823543^3610+3610^2354383755Hans Havermann05/2017
554018^66711-9183741Lelio R Paula11/2015
55394*10^83740-8983741Robert Price08/2017
5541(3*2^278172-1)/1183738Lelio R Paula02/2014
5542(15*29^57251+2561)/2883724Curtis Bright05/2015
55434*7^99059-983716Lelio R Paula10/2014
5544(2^278128-3)/12684472414983714Lelio R Paula12/2012
55452^278077+186721183710Enzo Doria03/2016
55462^278059-2783705Lelio R Paula06/2012
5547214^35917+35917^21483702Norbert Schneider12/2014
5548(23*10^83693+7)/383694Robert Price10/2015
554985^43375-283689Lelio R Paula09/2013
55505*3^175360+483669Lelio R Paula07/2014
5551(23^61441-1)/2283665Robert Price01/2012
555220091^14596+14596^2009183664Hans Havermann03/2017
55532^277907-11062983659Enzo Doria05/2014
555419522^19283+19283^1952283656Hans Havermann04/2017
55558*5^119664-383643Lelio R Paula10/2014
55568*3^175299-783640Lelio R Paula07/2014
5557(26*10^83638-413)/983639Robert Price10/2017
55583^175250+2283616Robert Price12/2013
556011^80285+3083609Lelio R Paula10/2015
555926870^1293+1293^2687083609Hans Havermann03/2017
55612^277691+187442383594Enzo Doria06/2016
556213^75022-6083571Lelio R Paula11/2015
556314^72905-5183559Lelio R Paula11/2015
5564(17*2^277565-1)/54383554Lelio R Paula02/2014
55655^119532-1283550Lelio R Paula10/2015
55666^107358-1625383541Enzo Doria02/2013
55672^277478-46021183530Enzo Doria06/2015
5568(22*10^83525-7)/383526Erik Branger09/2014
5569(30^56543+1)/3183520Robert Price07/2013
55702^277417-46078383511Paul Bourdelais04/2013
5571(22699*2^277387+1)/21983504Lelio R Paula06/2014
5572(31*2^277383-1)/24783500Lelio R Paula02/2014
557321368^8085+8085^2136883500Hans Havermann04/2017
5574(9*2^277342+1)/1383489Lelio R Paula12/2012
55755^119439-6683485Lelio R Paula10/2015
5576(14*10^83471-101)/383472Robert Price04/2017
55775*6^107263+783468Lelio R Paula10/2014
5578(64*10^83461-1)/983462Serge Batalov11/2010
55792^277244-17570983459Hans Havermann10/2018
558017^67796-9283420Lelio R Paula11/2015
55812^277106-11005783418Enzo Doria04/2014
55826^107200-1983418Lelio R Paula12/2015
558311^80096-183083412Enzo Doria12/2012
55843^174801+5683402Lelio R Paula12/2015
55852^277033-11197383396Enzo Doria05/2014
5586120^40105-11983386Norbert Schneider09/2018
558720519^11572+11572^2051983378Hans Havermann03/2017
558820850^9971+9971^2085083374Hans Havermann03/2017
55896^107122-1886383358Enzo Doria03/2013
55904*10^83354-8983355Robert Price08/2017
55913^174697-3483352Robert Price11/2013
5592(9787*2^276855-1)/234583343Lelio R Paula04/2015
55932^276825+7522783333Enzo Doria04/2016
55945^119214+8483328Lelio R Paula10/2015
55952^276803-15983327Lelio R Paula06/2012
5596(3*2^276753-1)/2583311Lelio R Paula02/2014
5597114^40495+40495^11483295Norbert Schneider12/2014
559839967!2+102483282Robert Price02/2015
55992^276641+5783278Lelio R Paula06/2012
560035^53934-341483278Enzo Doria03/2013
5601(2^276655+78557)/36542583276Lelio R Paula12/2012
56022^276615-403583270Lelio R Paula08/2013
56032^276588+115583262Lelio R Paula08/2013
56052^276587-93783261Yves Minet10/2009
56042^276584-11318383261Enzo Doria07/2014
5606(2^276592-1017)/1384373983256Lelio R Paula12/2012
56072^276547-10959183249Enzo Doria04/2014
560813^74733-3283249Lelio R Paula11/2015
56092^276523-258783242Yves Minet07/2014
561018^66311-4383239Lelio R Paula11/2015
561111^79919-153083228Enzo Doria12/2012
56122^276468-10974583226Enzo Doria04/2014
56132^276462+538583224Lelio R Paula08/2013
5614(9787*2^276422-1)/383215Lelio R Paula04/2015
56152^276391-1583202Lelio R Paula06/2012
5616(4*10^83201+173)/383202Robert Price01/2017
56172^276316-10965583180Enzo Doria04/2014
56182^276305-11206383177Enzo Doria06/2014
5619(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
562074913!4-283161Robert Price07/2017
56212^276227-183720783153Enzo Doria05/2015
5622(2^276227+3)/783152Lelio R Paula12/2012
56232^276184-6338983140Paul Bourdelais02/2012
56242^276066-11160383105Enzo Doria05/2014
5625(2^276028-3)*6-783094Gilbert Mozzo09/2016
56262^275926-469183063Yves Minet05/2019
5627(2^275897+9)/115383051Lelio R Paula12/2012
56282^275879-10980783048Enzo Doria04/2014
5630F(397379)83047Henri Lifchitz08/2003
5629U(397379)83047Serge Batalov03/2015
56323^174040-1483039Robert Price08/2013
5631(86*10^83038-221)/983039Robert Price06/2017
56332^275841-688383037Lelio R Paula07/2011
56343^174002-14083021Lelio R Paula12/2015
56356^106681+7783014Lelio R Paula12/2015
5636187^36539-283011Lelio R Paula10/2017
563711^79701-315083001Enzo Doria12/2012
5638(55459*2^275657+1)/2182985Lelio R Paula06/2014
5639(7*10^82960-457)/982960Robert Price09/2017
56402^275535-685582945Lelio R Paula08/2013
56413^173828-1482938Robert Price08/2013
56422^275512-10967782938Enzo Doria04/2014
56432^275446-11004582918Enzo Doria04/2014
5644(2^275473+47)/2952609744782916Lelio R Paula12/2012
56453^173755-1482903Robert Price08/2013
5646(182*10^82898+43)/982900Robert Price11/2017
56472^275363-11230982893Enzo Doria06/2014
564861^46427-6082888Norbert Schneider10/2014
56493*10^82880-7^8288082881Mike Oakes02/2010
56512^275290+9019582871Lelio R Paula07/2013
5650(35*10^82870-71)/982871Robert Price05/2015
56522^275270-185962182865Enzo Doria03/2016
56532^275259+8182862Henri Lifchitz01/2007
5654(113703^16384+1)/282834Richard Fischer04/2018
56557^98003+98003^7+182823Robert Price05/2014
565610^82790+12604382791Patrick De Geest07/2013
565710^82790-4782790Robert Price05/2011
56582^274985-11266382779Enzo Doria06/2014
56592^274935+1501582764Lelio R Paula07/2013
5660(17*2^274922+1)/382761Lelio R Paula12/2012
5661(43*10^82752-61)/982753Robert Price06/2015
5662(3*2^274862+1)/102782740Lelio R Paula12/2012
5663(31*2^274848-1)/406582736Lelio R Paula02/2014
5664(4^137405+23)/382726Robert Price02/2017
56652^274791-11049182721Enzo Doria05/2014
5666(11*2^274776-1)/9582715Lelio R Paula02/2014
5667(47*10^82706-119)/982707Robert Price09/2017
56682^274704-11139582695Enzo Doria05/2014
56692^274686-391182689Yves Minet04/2017
5670(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
5671(3^173263-5)/1449882664Lelio R Paula12/2012
56722^274511-6487582637Lelio R Paula08/2013
567312^76572-8382636Lelio R Paula11/2015
56743^173191-2^17319182634Mike Oakes02/2004
567514^72072-1582604Lelio R Paula11/2015
5676(55459*2^274339+1)/382589Lelio R Paula06/2014
56772^274351+12382588Lelio R Paula06/2012
5678(1017*2^274339-1)/351582584Lelio R Paula04/2015
56796^106086+11382551Lelio R Paula12/2015
5680(17*10^82540-377)/982541Robert Price11/2017
56812^274093-5869582511Lelio R Paula07/2013
56827*10^82509-4782510Robert Price02/2017
56832^274081-655582507Lelio R Paula07/2013
56842^274074-274074+182505Robert Price10/2014
568514^71985+4782505Lelio R Paula11/2015
56865*10^82504+2182505Robert Price01/2017
56876^106014-13982495Lelio R Paula12/2015
5688(2^274046+47)/75382494Lelio R Paula12/2012
56892^274008-183809982485Enzo Doria05/2015
56902^273981-11002982477Enzo Doria04/2014
569119^64490-3082467Lelio R Paula12/2015
56932^273785+1171582418Lelio R Paula07/2013
56928*10^82417+5182418Robert Price05/2017
569411^79133-1082409Theodore Burton11/2005
569591^42063+9082404Norbert Schneider01/2016
56972^273662-6382381Lelio R Paula06/2012
56962^273661+25582381Lelio R Paula07/2013
5698(62*10^82377-17)/982378Robert Price09/2015
56992^273608+52428782365Paul Underwood08/2018
57008*10^82360-5182361Robert Price10/2017
5701(79*10^82347-1)/382349Robert Price11/2017
5702(11*10^82323+91)/382323Robert Price02/2017
5703(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
5704(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
570515^69984+3282308Lelio R Paula11/2015
57069*6^105746+782288Lelio R Paula10/2014
570789^42211-8882286Norbert Schneider01/2016
5708gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
5709(19*10^82270-43)/382271Robert Price10/2017
57102^273282-11024182267Enzo Doria05/2014
5711(13^73849+4^73849)/1782263Robert Price05/2013
571210^82254+9^(82254+1)82255Robert Price08/2016
571310^82254+45777382255Patrick De Geest12/2016
571410^82254-9960982254Patrick De Geest12/2016
5715(754*10^82250-7)/982252Robert Price11/2017
571618^65524+1382251Lelio R Paula11/2015
57172^273206-10782244Lelio R Paula06/2012
57182^273193-45914582240Enzo Doria05/2015
57202^273126+3693782220Yves Minet06/2010
571939505!2+12882220Robert Price03/2015
57212^273053-11211182198Enzo Doria06/2014
57222^273016+118582187Lelio R Paula07/2013
5723(2^273008+3)/782183Lelio R Paula12/2012
57245^117554-1538682167Enzo Doria02/2013
5725(38*10^82161+403)/982162Robert Price11/2017
57262^272907-11143982154Enzo Doria05/2014
5727(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
57282^272875-6982144Lelio R Paula06/2012
57297^97197+482141Robert Price01/2014
5730(4*6^105554+1)/582137Serge Batalov10/2014
57312^272826-443382129Yves Minet03/2019
57326^105531-10982120Lelio R Paula12/2015
57332^272766-6582111Lelio R Paula06/2012
573419^64205-7882103Lelio R Paula12/2015
57352^272702+186997982092Enzo Doria05/2016
5736(29*2^272687-1)/982088Lelio R Paula02/2014
5737(5*10^82085-119)/382086Robert Price04/2016
57382^272660-11004982079Enzo Doria04/2014
57396^105474+6782075Lelio R Paula12/2015
57402^272637+8287582072Lelio R Paula07/2013
57412^272587-3182057Lelio R Paula06/2012
5742(41*10^82044-59)/982045Robert Price10/2017
57438*5^117368+982038Lelio R Paula10/2014
5744(101525^16384+1)/13107482023Lelio R Paula11/2011
57454*5^117343-782020Lelio R Paula10/2014
5746(265*10^81990+17)/381992Robert Price05/2016
57473^171843+1081990Robert Price10/2013
5748(7*10^81985+107)/381986Robert Price02/2017
5749(3*2^272356+1)/17716381983Lelio R Paula12/2012
57502^272296-11114981970Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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