PRP Records

Probable Primes Top 10000

(252675 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 ?
62517^90833-6076763Lelio R Paula02/2015
625213^68901-5676752Lelio R Paula03/2015
62532^254961+186991776751Enzo Doria05/2016
62549*5^109791-876742Lelio R Paula10/2014
625582^40089+40089^8276723Serge Batalov02/2012
62562^254861-279001376721Enzo Doria03/2016
6257(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/2045977974176718Makoto Kamada03/2019
625810^76705+1376706Robert Price01/2011
625910^76705-9407776705Patrick De Geest06/2013
6260(5*2^254785-1)/99976696Lelio R Paula02/2014
62612^254758-11040576690Enzo Doria05/2014
62622^254716-377976678Yves Minet04/2017
62632^254708-11050776675Enzo Doria05/2014
6264(47*10^76672+133)/976673Robert Price04/2017
62652^254670-11290176664Enzo Doria06/2014
6266(3^160665+7)/98135076651Lelio R Paula10/2012
62672^254598-11318376642Enzo Doria07/2014
626819^59932+2276639Lelio R Paula01/2015
62692^254569-11221376633Enzo Doria06/2014
62702*5^109626+976626Lelio R Paula10/2014
62712^254521+187252776619Enzo Doria05/2016
6272(76*10^76615+167)/976616Robert Price08/2016
627325^54799-24^5479976606Robert Price07/2012
6274(24737*2^254464+1)/976605Lelio R Paula06/2014
627512^70961-8576580Lelio R Paula02/2015
62767^90590-3876558Lelio R Paula02/2015
62772^254304+522776554Lelio R Paula06/2013
6278(76*10^76547-211)/976548Robert Price10/2017
627918^60979-536376546Enzo Doria03/2013
6280(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
6282(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
6281(7*10^76536-313)/976536Robert Price11/2016
62842^254239-2776534Lelio R Paula03/2012
62832^254238-184176534Yves Minet03/2013
6285(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
62862^254189-11222576519Enzo Doria06/2014
628718^60938-139776494Enzo Doria03/2013
62882^254075-278841776485Enzo Doria03/2016
62897*10^76483-2376484Robert Price04/2016
62902^254042-11291376475Enzo Doria06/2014
629114^66723-3776474Lelio R Paula02/2015
62922^254037-11030576473Enzo Doria05/2014
62932^253931-11110976441Enzo Doria05/2014
62942^253926-116776440Lelio R Paula05/2013
6295(49*10^76438-13)/976439Robert Price07/2015
6296(21*2^253845-1)/14376415Lelio R Paula02/2014
629710^76374+3176375Robert Price03/2011
629810^76374-22215976374Patrick De Geest05/2013
62992^253561-11053376330Enzo Doria05/2014
6300gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
63019*5^109182+276316Lelio R Paula10/2014
630211^73279-369076313Enzo Doria12/2012
6303(598*10^76309-31)/976311Robert Price02/2017
630411^73274-2400076308Enzo Doria12/2012
63057^90291-676305Theodore Burton11/2005
6306(21181*2^253432+1)/2143776291Lelio R Paula06/2014
63076^98025+14576279Lelio R Paula01/2015
63082^253355+115576268Lelio R Paula05/2013
6309(73*10^76262+413)/976263Robert Price10/2017
63102^253292-7121976249Enzo Doria04/2016
63117^90221-3676246Lelio R Paula02/2015
631218^60727-347376229Enzo Doria03/2013
6313(78557*2^253184+1)/376221Lelio R Paula06/2014
6314(8*10^76220-83)/376221Robert Price10/2017
6315(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
631611^73163-201076192Enzo Doria12/2012
63172^253060+5461576179Lelio R Paula05/2013
63182^253029+186976176170Enzo Doria05/2016
63192^252955-11100776148Enzo Doria05/2014
63202*5^108931+776140Lelio R Paula10/2014
6321(86*10^76128+121)/976129Robert Price03/2017
632222154*29^52050+976123Curtis Bright05/2015
63233^159530-11235876116Enzo Doria06/2014
632411^73089-4876115Lelio R Paula02/2015
632586^39337-8576098Norbert Schneider10/2015
6326(3^159505-7)/31329731676095Lelio R Paula06/2012
63276^97783+7776090Lelio R Paula01/2015
63282^252712-10576074Lelio R Paula03/2012
6329(10^76069-19)/976069Robert Price10/2017
6331131^35927+276068Lelio R Paula05/2013
6330(41*10^76067+373)/976068Robert Price04/2017
63322^252683-13976066Lelio R Paula03/2012
6333137^35597-13676061Norbert Schneider05/2015
63343^159413+10676060Lelio R Paula01/2015
63359^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
6336(2^252557-9)/7176026Lelio R Paula07/2012
6337(85*10^76021-103)/976022Robert Price10/2017
633811^72989+8076011Lelio R Paula02/2015
633999877!6-3675996Robert Price11/2018
63402^252449-45952375995Enzo Doria05/2015
634120^58408+7375991Lelio R Paula01/2015
63422^252418-142175986Yves Minet01/2013
6343(11*2^252396-1)/575980Lelio R Paula02/2014
63442^252365-11068975970Enzo Doria05/2014
634511^72949-102075969Enzo Doria11/2012
6346(2^252294+47)/654975945Lelio R Paula07/2012
63472^252261-11059575939Enzo Doria05/2014
63487^89853+7675935Lelio R Paula01/2015
63493^159132+5675926Lelio R Paula01/2015
6350730^26513+26513^73075916Norbert Schneider11/2016
6351(27*2^252163-1)/194575907Lelio R Paula01/2014
63525^108596-1484675906Enzo Doria02/2013
63535^108560-1484675881Enzo Doria02/2013
63542^252051-11035975875Enzo Doria05/2014
63552^251971-11050975851Enzo Doria05/2014
6356(42457^16384+1)/32768275819Lelio R Paula11/2011
635799655!6-275811Robert Price07/2017
635814*10^75798+108975800Jens K. Andersen11/2007
63592^251784-45575795Yves Minet03/2012
63602^251780-128975794Yves Minet01/2013
63612^251760-21560975788Paul Bourdelais03/2013
636299^37973+275781Lelio R Paula05/2013
6363(185*10^75777+7)/375779Robert Price02/2017
63645*2^251690+375767Lelio R Paula06/2014
63656^97366+9575766Lelio R Paula01/2015
6366s(23010)75760Hans Havermann11/2017
63678*6^97337-775744Lelio R Paula10/2014
63682^251588-11167775736Enzo Doria05/2014
63695^108346-1325675731Enzo Doria02/2013
6370(31^50777+1)/3275726Robert Price07/2013
6371(10^75707+77)/375707Robert Price01/2017
6372(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
63732^251466+19375699Lelio R Paula03/2012
6374(5*2^251464+1)/942375695Lelio R Paula07/2012
63752^251422-10999175686Enzo Doria04/2014
637691*(10^23+1)*(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)75680Makoto Kamada03/2019
63774*5^108245-375661Lelio R Paula10/2014
637812^70067-11^7006775615Jean-Louis Charton11/2006
637912^70066+9575614Lelio R Paula02/2015
6380-E20534/206375607Thomas Ritschel02/2017
638119^59120-5075600Lelio R Paula01/2015
638218^60222-469775596Enzo Doria03/2013
638318^60211-435575582Enzo Doria03/2013
63847*2^251014-975564Lelio R Paula06/2014
63856^97101-2575560Lelio R Paula01/2015
63868^83663-7^8366375556Jean-Louis Charton01/2004
63873^158331-14075544Lelio R Paula01/2015
6389(37^48157-1)/3675519Robert Price03/2012
6390(19*10^75518-43)/375519Robert Price10/2017
63882^250868-422975519Yves Minet08/2018
639110^75516+3146775517Patrick De Geest03/2016
639310^75516-10^2256-175516Serge Batalov01/2011
639210^75516-6659175516Patrick De Geest03/2016
63942^250851-18775514Lelio R Paula03/2012
6395(43*10^75498-7)/975499Robert Price12/2014
6396(3^158244-5)/24791675497Lelio R Paula06/2012
63974*5^107971-375470Lelio R Paula10/2014
6398(25*10^75465+71)/375466Robert Price01/2017
6399(5*2^250681-1)/99975461Lelio R Paula01/2014
6400(182*10^75456+1)/375458Robert Price02/2017
6401(2^250669-9)/9889772975451Lelio R Paula07/2012
640210^75441+1375442Robert Price01/2011
640310^75441-992375441Patrick De Geest05/2013
6404(27*2^250546-1)/645775420Lelio R Paula01/2014
64055*7^89231-675410Lelio R Paula10/2014
64072^250503-1699575409Lelio R Paula05/2013
640611^72411-2875409Lelio R Paula02/2015
64083*5^107860-875392Lelio R Paula10/2014
6409(34*10^75387-403)/975388Robert Price10/2017
64112^250426+2983575386Lelio R Paula05/2013
64108*3^157999-775386Lelio R Paula05/2014
6412(88*10^75381-43)/975382Robert Price11/2015
64132^250382-11175575373Enzo Doria05/2014
64142^250374-279805175371Eric Chen03/2016
6415(22*10^75368-1)/375369Robert Price12/2014
64162^250369-454375369Yves Minet03/2019
6417(19*10^75338+119)/375339Robert Price02/2017
64182^250223-185916775325Enzo Doria03/2016
6419(3^157854-7)/6602528275308Lelio R Paula06/2012
64203^157831-9875305Lelio R Paula01/2015
6421(46^45281+11^45281)/5775290Serge Batalov12/2016
642292^38335-9175282Norbert Schneider01/2016
64232^250020+1891575264Lelio R Paula05/2013
64242^250002+819375259Lelio R Paula05/2013
6425(11*2^249977-7)/1575251Renaud Lifchitz02/2011
6426(2^249968+78557)/6375247Lelio R Paula07/2012
6427(5*10^75244+91)/375245Robert Price11/2016
6428(10489!)^2+Prime(10489)75242Robert Price08/2014
642914^65644+6775237Lelio R Paula01/2015
6430(2^249928-5)/1185905975229Lelio R Paula06/2012
6431129^35638+275218Lelio R Paula05/2013
64322^249853-11047575214Enzo Doria05/2014
64332^249762+7540975186Enzo Doria04/2016
6434565^27318+27318^56575181Norbert Schneider12/2016
6435(2^249741-7)/68575177Lelio R Paula06/2012
64362^249726-11218175176Enzo Doria06/2014
64372^249721+1171575174Lelio R Paula05/2013
6438(38661^16384+1)/275158Lelio R Paula11/2011
64392^249658-4735575155Lelio R Paula05/2013
6440155^34311+275153Lelio R Paula05/2013
6441(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
6442(23*2^249602+1)/9375138Lelio R Paula08/2012
64432^249522+841575114Lelio R Paula05/2013
64442^249489-11091175104Enzo Doria05/2014
6445(28*10^75078+131)/375079Robert Price02/2017
6446(206*10^75073-17)/975075Robert Price03/2017
64472^249368-11057375068Enzo Doria05/2014
6448NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
6449(2^249375+78557)/4505612575062Lelio R Paula07/2012
6450(26*10^75055-173)/375056Robert Price10/2017
64512^249272+19375039Lelio R Paula03/2012
645214^65468+4375035Lelio R Paula01/2015
645337^47844+3675030Norbert Schneider05/2014
6454(52*10^75027-7)/975028Robert Price12/2014
645520^57653+8975009Lelio R Paula01/2015
64562^249061-186835374975Enzo Doria04/2016
64577^88713+2*3^8871374972Mike Oakes07/2010
64582*6^96313+574947Lelio R Paula10/2014
6459(8*10^74944+49)/374945Robert Price03/2016
6460300^30247+30247^30074926Norbert Schneider11/2014
64612^248866-17174917Lelio R Paula03/2012
64626*5^107168-774908Lelio R Paula10/2014
646311^71926+7874904Lelio R Paula02/2015
64642^248824+186939174904Enzo Doria05/2016
64652^248816+111174902Lelio R Paula01/2011
6466V(388219)74890Serge Batalov03/2015
6467159^34017+15874885Norbert Schneider12/2018
64682*F(358297)-174880Henri Lifchitz12/2009
6469(22*10^74874-31)/974875Robert Price04/2015
647011^71892-7680000074868Enzo Doria01/2013
64719*5^107107-474866Lelio R Paula10/2014
64722^248678-71011174860Paul Bourdelais03/2013
6473(14*10^74858+211)/974859Robert Price11/2017
647413^67194+1274851Lelio R Paula01/2015
6475(7*2^248634+1)/7174846Lelio R Paula08/2012
647611^71867-309074842Enzo Doria12/2012
64772^248609+26214574839Lelio R Paula05/2013
64783^156852+5074838Lelio R Paula01/2015
647918^59607-1174824Lelio R Paula01/2015
64802^248556-11050774823Enzo Doria05/2014
64817^88531-3674818Lelio R Paula01/2015
6482p(15738)#/2+102474814Robert Price07/2017
64834*3^156740-574785Lelio R Paula05/2014
6484(32*10^74773-41)/974774Robert Price05/2015
6485(29*2^248384-1)/1374772Lelio R Paula01/2014
648619401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
64872^248357-1279741374763Enzo Doria03/2016
648842^46057+4174762Lelio R Paula07/2012
648911^71784-300074756Enzo Doria12/2012
649019^58458+1874754Lelio R Paula01/2015
649112^69265-3574750Lelio R Paula02/2015
649211^71771-4800074742Enzo Doria12/2012
6493(7*10^74741+197)/374742Robert Price07/2017
6494(2^248282-5)/5012974736Lelio R Paula06/2012
64952^248252-11010574732Enzo Doria04/2014
6496(7*10^74729+71)/374730Robert Price03/2016
64973^156614-5074724Lelio R Paula01/2015
6498(7*2^248213+1)/13574719Lelio R Paula07/2012
6499(2^248173+78557)/76774705Lelio R Paula07/2012
6500125^35622+12474697Norbert Schneider02/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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