PRP Records

Probable Primes Top 10000

(181746 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 ?
52512^256460-11275777203Enzo Doria06/2014
52522^256398+2329977184Yves Minet02/2011
52532^256391-1155*25639177182Henri Lifchitz03/2005
5254(2^256391-9)/5659377177Lelio R Paula10/2012
5255(2^256308+9)/1058577153Lelio R Paula10/2012
525621^58348-277149Lelio R Paula08/2013
5257(17*2^256291-1)/478577149Lelio R Paula02/2014
5258(5*2^256274-1)/214177144Lelio R Paula02/2014
525919^60321+8277136Lelio R Paula03/2015
52605*2^256233-377135Lelio R Paula06/2014
52613*2^256149+777110Lelio R Paula06/2014
52623^161594-10677100Lelio R Paula02/2015
52632^256114-18577098Lelio R Paula03/2012
52648^85349-85349^877078Norbert Schneider05/2017
52652^256043-278637777077Enzo Doria03/2016
52662^255973+186994777056Enzo Doria05/2016
526712^71393-4377046Lelio R Paula02/2015
526815^65490+4477023Lelio R Paula02/2015
5269(3^161411-7)/94077010Lelio R Paula10/2012
5270lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5271(570^27943-1)/56977005Serge Batalov12/2016
52722^255750-7576989Lelio R Paula03/2012
52733*6^98926-576980Lelio R Paula10/2014
527418^61320-143376974Enzo Doria03/2013
52756^98916-1709376972Enzo Doria02/2013
52762^255659-11013176962Enzo Doria04/2014
527712^71303+9176949Lelio R Paula02/2015
527818^61298+5976946Lelio R Paula02/2015
5279(223^32768+1)/13107476945Lelio R Paula02/2009
5280(2^255613-5)/28151776942Lelio R Paula10/2012
528118^61290-1176936Lelio R Paula02/2015
528363^42752-276926Lelio R Paula08/2013
5282(11*2^255545-1)/11776926Lelio R Paula02/2014
52842^255517+5638776919Yves Minet02/2011
52852^255499-11256776913Enzo Doria06/2014
52862^255492+34576911Lelio R Paula06/2013
528710^76875+21759176876Patrick De Geest05/2013
528910^76875-5376875Robert Price05/2011
528811^73819-588076875Enzo Doria01/2013
52902^255313+1891576857Lelio R Paula06/2013
5291(2^255320-1017)/144666776853Lelio R Paula10/2012
52922^255296+577576852Lelio R Paula06/2013
529314^67052-2976851Lelio R Paula02/2015
5294(7*10^76818-313)/976818Robert Price11/2016
529510^76801+6976802Robert Price03/2011
529610^76801-8094376801Patrick De Geest06/2013
52972^255105+5776795Lelio R Paula03/2012
5298(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5299(2^255097-7)/2002005576785Lelio R Paula10/2012
53002^255055+186935376780Enzo Doria05/2016
530117^62396-9076776Lelio R Paula03/2015
53027^90833-6076763Lelio R Paula02/2015
530313^68901-5676752Lelio R Paula03/2015
53042^254961+186991776751Enzo Doria05/2016
53059*5^109791-876742Lelio R Paula10/2014
530682^40089+40089^8276723Serge Batalov02/2012
53072^254861-279001376721Enzo Doria03/2016
530810^76705+1376706Robert Price01/2011
530910^76705-9407776705Patrick De Geest06/2013
5310(5*2^254785-1)/99976696Lelio R Paula02/2014
53112^254758-11040576690Enzo Doria05/2014
53122^254716-377976678Yves Minet04/2017
53132^254708-11050776675Enzo Doria05/2014
5314(47*10^76672+133)/976673Robert Price04/2017
53152^254670-11290176664Enzo Doria06/2014
5316(3^160665+7)/98135076651Lelio R Paula10/2012
53172^254598-11318376642Enzo Doria07/2014
531819^59932+2276639Lelio R Paula01/2015
53192^254569-11221376633Enzo Doria06/2014
53202*5^109626+976626Lelio R Paula10/2014
53212^254521+187252776619Enzo Doria05/2016
5322(76*10^76615+167)/976616Robert Price08/2016
532325^54799-24^5479976606Robert Price07/2012
5324(24737*2^254464+1)/976605Lelio R Paula06/2014
532512^70961-8576580Lelio R Paula02/2015
53267^90590-3876558Lelio R Paula02/2015
53272^254304+522776554Lelio R Paula06/2013
532818^60979-536376546Enzo Doria03/2013
5329(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5331(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5330(7*10^76536-313)/976536Robert Price11/2016
53322^254239-2776534Lelio R Paula03/2012
53332^254238-184176534Yves Minet03/2013
5334(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
53352^254189-11222576519Enzo Doria06/2014
533618^60938-139776494Enzo Doria03/2013
53372^254075-278841776485Enzo Doria03/2016
53387*10^76483-2376484Robert Price04/2016
53392^254042-11291376475Enzo Doria06/2014
534014^66723-3776474Lelio R Paula02/2015
53412^254037-11030576473Enzo Doria05/2014
53422^253931-11110976441Enzo Doria05/2014
53432^253926-116776440Lelio R Paula05/2013
5344(49*10^76438-13)/976439Robert Price07/2015
5345(21*2^253845-1)/14376415Lelio R Paula02/2014
534610^76374+3176375Robert Price03/2011
534710^76374-22215976374Patrick De Geest05/2013
53482^253561-11053376330Enzo Doria05/2014
5349gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
53509*5^109182+276316Lelio R Paula10/2014
535111^73279-369076313Enzo Doria12/2012
5352(598*10^76309-31)/976311Robert Price02/2017
535311^73274-2400076308Enzo Doria12/2012
53547^90291-676305Theodore Burton11/2005
5355(21181*2^253432+1)/2143776291Lelio R Paula06/2014
53566^98025+14576279Lelio R Paula01/2015
53572^253355+115576268Lelio R Paula05/2013
53582^253292-7121976249Enzo Doria04/2016
53597^90221-3676246Lelio R Paula02/2015
536018^60727-347376229Enzo Doria03/2013
5361(78557*2^253184+1)/376221Lelio R Paula06/2014
5362(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
536311^73163-201076192Enzo Doria12/2012
53642^253060+5461576179Lelio R Paula05/2013
53652^253029+186976176170Enzo Doria05/2016
53662^252955-11100776148Enzo Doria05/2014
53672*5^108931+776140Lelio R Paula10/2014
5368(86*10^76128+121)/976129Robert Price03/2017
536922154*29^52050+976123Curtis Bright05/2015
53703^159530-11235876116Enzo Doria06/2014
537111^73089-4876115Lelio R Paula02/2015
537286^39337-8576098Norbert Schneider10/2015
5373(3^159505-7)/31329731676095Lelio R Paula06/2012
53746^97783+7776090Lelio R Paula01/2015
53752^252712-10576074Lelio R Paula03/2012
5376131^35927+276068Lelio R Paula05/2013
5377(41*10^76067+373)/976068Robert Price04/2017
53782^252683-13976066Lelio R Paula03/2012
5379137^35597-13676061Norbert Schneider05/2015
53803^159413+10676060Lelio R Paula01/2015
53819^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
5382(2^252557-9)/7176026Lelio R Paula07/2012
538311^72989+8076011Lelio R Paula02/2015
53842^252449-45952375995Enzo Doria05/2015
538520^58408+7375991Lelio R Paula01/2015
53862^252418-142175986Yves Minet01/2013
5387(11*2^252396-1)/575980Lelio R Paula02/2014
53882^252365-11068975970Enzo Doria05/2014
538911^72949-102075969Enzo Doria11/2012
5390(2^252294+47)/654975945Lelio R Paula07/2012
53912^252261-11059575939Enzo Doria05/2014
53927^89853+7675935Lelio R Paula01/2015
53933^159132+5675926Lelio R Paula01/2015
5394730^26513+26513^73075916Norbert Schneider11/2016
5395(27*2^252163-1)/194575907Lelio R Paula01/2014
53965^108596-1484675906Enzo Doria02/2013
53975^108560-1484675881Enzo Doria02/2013
53982^252051-11035975875Enzo Doria05/2014
53992^251971-11050975851Enzo Doria05/2014
5400(42457^16384+1)/32768275819Lelio R Paula11/2011
540199655!6-275811Robert Price07/2017
540214*10^75798+108975800Jens K. Andersen11/2007
54032^251784-45575795Yves Minet03/2012
54042^251780-128975794Yves Minet01/2013
54052^251760-21560975788Paul Bourdelais03/2013
540699^37973+275781Lelio R Paula05/2013
5407(185*10^75777+7)/375779Robert Price02/2017
54085*2^251690+375767Lelio R Paula06/2014
54096^97366+9575766Lelio R Paula01/2015
54108*6^97337-775744Lelio R Paula10/2014
54112^251588-11167775736Enzo Doria05/2014
54125^108346-1325675731Enzo Doria02/2013
5413(31^50777+1)/3275726Robert Price07/2013
5414(10^75707+77)/375707Robert Price01/2017
54152^251466+19375699Lelio R Paula03/2012
5416(5*2^251464+1)/942375695Lelio R Paula07/2012
54172^251422-10999175686Enzo Doria04/2014
54184*5^108245-375661Lelio R Paula10/2014
541912^70067-11^7006775615Jean-Louis Charton11/2006
542012^70066+9575614Lelio R Paula02/2015
5421-E20534/206375607Thomas Ritschel02/2017
542219^59120-5075600Lelio R Paula01/2015
542318^60222-469775596Enzo Doria03/2013
542418^60211-435575582Enzo Doria03/2013
54257*2^251014-975564Lelio R Paula06/2014
54266^97101-2575560Lelio R Paula01/2015
54278^83663-7^8366375556Jean-Louis Charton01/2004
54283^158331-14075544Lelio R Paula01/2015
5429(37^48157-1)/3675519Robert Price03/2012
543010^75516+3146775517Patrick De Geest03/2016
543210^75516-10^2256-175516Serge Batalov01/2011
543110^75516-6659175516Patrick De Geest03/2016
54332^250851-18775514Lelio R Paula03/2012
5434(43*10^75498-7)/975499Robert Price12/2014
5435(3^158244-5)/24791675497Lelio R Paula06/2012
54364*5^107971-375470Lelio R Paula10/2014
5437(25*10^75465+71)/375466Robert Price01/2017
5438(5*2^250681-1)/99975461Lelio R Paula01/2014
5439(182*10^75456+1)/375458Robert Price02/2017
5440(2^250669-9)/9889772975451Lelio R Paula07/2012
544110^75441+1375442Robert Price01/2011
544210^75441-992375441Patrick De Geest05/2013
5443(27*2^250546-1)/645775420Lelio R Paula01/2014
54445*7^89231-675410Lelio R Paula10/2014
54462^250503-1699575409Lelio R Paula05/2013
544511^72411-2875409Lelio R Paula02/2015
54473*5^107860-875392Lelio R Paula10/2014
54492^250426+2983575386Lelio R Paula05/2013
54488*3^157999-775386Lelio R Paula05/2014
5450(88*10^75381-43)/975382Robert Price11/2015
54512^250382-11175575373Enzo Doria05/2014
54522^250374-279805175371Eric Chen03/2016
5453(22*10^75368-1)/375369Robert Price12/2014
5454(19*10^75338+119)/375339Robert Price02/2017
54552^250223-185916775325Enzo Doria03/2016
5456(3^157854-7)/6602528275308Lelio R Paula06/2012
54573^157831-9875305Lelio R Paula01/2015
5458(46^45281+11^45281)/5775290Serge Batalov12/2016
545992^38335-9175282Norbert Schneider01/2016
54602^250020+1891575264Lelio R Paula05/2013
54612^250002+819375259Lelio R Paula05/2013
5462(11*2^249977-7)/1575251Renaud Lifchitz02/2011
5463(2^249968+78557)/6375247Lelio R Paula07/2012
5464(5*10^75244+91)/375245Robert Price11/2016
5465(10489!)^2+Prime(10489)75242Robert Price08/2014
546614^65644+6775237Lelio R Paula01/2015
5467(2^249928-5)/1185905975229Lelio R Paula06/2012
5468129^35638+275218Lelio R Paula05/2013
54692^249853-11047575214Enzo Doria05/2014
54702^249762+7540975186Enzo Doria04/2016
5471565^27318+27318^56575181Norbert Schneider12/2016
5472(2^249741-7)/68575177Lelio R Paula06/2012
54732^249726-11218175176Enzo Doria06/2014
54742^249721+1171575174Lelio R Paula05/2013
5475(38661^16384+1)/275158Lelio R Paula11/2011
54762^249658-4735575155Lelio R Paula05/2013
5477155^34311+275153Lelio R Paula05/2013
5478(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
5479(23*2^249602+1)/9375138Lelio R Paula08/2012
54802^249522+841575114Lelio R Paula05/2013
54812^249489-11091175104Enzo Doria05/2014
5482(28*10^75078+131)/375079Robert Price02/2017
5483(206*10^75073-17)/975075Robert Price03/2017
54842^249368-11057375068Enzo Doria05/2014
5485NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
5486(2^249375+78557)/4505612575062Lelio R Paula07/2012
54872^249272+19375039Lelio R Paula03/2012
548814^65468+4375035Lelio R Paula01/2015
548937^47844+3675030Norbert Schneider05/2014
5490(52*10^75027-7)/975028Robert Price12/2014
549120^57653+8975009Lelio R Paula01/2015
54922^249061-186835374975Enzo Doria04/2016
54937^88713+2*3^8871374972Mike Oakes07/2010
54942*6^96313+574947Lelio R Paula10/2014
5495(8*10^74944+49)/374945Robert Price03/2016
5496300^30247+30247^30074926Norbert Schneider11/2014
54972^248866-17174917Lelio R Paula03/2012
54986*5^107168-774908Lelio R Paula10/2014
549911^71926+7874904Lelio R Paula02/2015
55002^248824+186939174904Enzo Doria05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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