PRP Records

Probable Primes Top 10000

(253476 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 ?
65012^257044-11288377378Enzo Doria06/2014
65022*7^91553+977372Lelio R Paula10/2014
6503713^27118+27118^71377371Norbert Schneider12/2016
65042^256920-11115577341Enzo Doria05/2014
65052^256896-655577334Lelio R Paula06/2013
6506(52*10^77322-7)/977323Robert Price12/2014
65072^256849-11293977320Enzo Doria06/2014
6508(4*10^77309-31)/977309Erik Branger05/2011
6509(3^161988+7)/4186477284Lelio R Paula10/2012
6510(14^67421-1)/1377272Paul Bourdelais09/2008
65115*3^161923-477258Lelio R Paula06/2014
65122^256552-149977230Yves Minet05/2013
65132^256460-11275777203Enzo Doria06/2014
65142^256398+2329977184Yves Minet02/2011
65152^256391-1155*25639177182Henri Lifchitz03/2005
6516(2^256391-9)/5659377177Lelio R Paula10/2012
6517(2^256308+9)/1058577153Lelio R Paula10/2012
651921^58348-277149Lelio R Paula08/2013
6518(17*2^256291-1)/478577149Lelio R Paula02/2014
6520(5*2^256274-1)/214177144Lelio R Paula02/2014
652119^60321+8277136Lelio R Paula03/2015
65225*2^256233-377135Lelio R Paula06/2014
65233*2^256149+777110Lelio R Paula06/2014
65243^161594-10677100Lelio R Paula02/2015
65252^256114-18577098Lelio R Paula03/2012
65268^85349-85349^877078Norbert Schneider05/2017
65272^256043-278637777077Enzo Doria03/2016
65282^255973+186994777056Enzo Doria05/2016
652912^71393-4377046Lelio R Paula02/2015
653015^65490+4477023Lelio R Paula02/2015
6531(3^161411-7)/94077010Lelio R Paula10/2012
6532lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
6533(570^27943-1)/56977005Serge Batalov12/2016
65342^255750-7576989Lelio R Paula03/2012
65353*6^98926-576980Lelio R Paula10/2014
653618^61320-143376974Enzo Doria03/2013
65376^98916-1709376972Enzo Doria02/2013
65382^255659-11013176962Enzo Doria04/2014
653912^71303+9176949Lelio R Paula02/2015
654018^61298+5976946Lelio R Paula02/2015
6541(223^32768+1)/13107476945Lelio R Paula02/2009
6542(2^255613-5)/28151776942Lelio R Paula10/2012
654318^61290-1176936Lelio R Paula02/2015
654563^42752-276926Lelio R Paula08/2013
6544(11*2^255545-1)/11776926Lelio R Paula02/2014
65462^255517+5638776919Yves Minet02/2011
65472^255499-11256776913Enzo Doria06/2014
65482^255492+34576911Lelio R Paula06/2013
654910^76875+21759176876Patrick De Geest05/2013
655110^76875-5376875Robert Price05/2011
655011^73819-588076875Enzo Doria01/2013
65522^255313+1891576857Lelio R Paula06/2013
6553(2^255320-1017)/144666776853Lelio R Paula10/2012
65542^255296+577576852Lelio R Paula06/2013
655514^67052-2976851Lelio R Paula02/2015
6556(8*10^76840+43)/376841Robert Price10/2017
6557(7*10^76818-313)/976818Robert Price11/2016
655810^76801+6976802Robert Price03/2011
655910^76801-8094376801Patrick De Geest06/2013
65602^255105+5776795Lelio R Paula03/2012
6561(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
6562(2^255097-7)/2002005576785Lelio R Paula10/2012
65632^255055+186935376780Enzo Doria05/2016
656417^62396-9076776Lelio R Paula03/2015
65657^90833-6076763Lelio R Paula02/2015
656613^68901-5676752Lelio R Paula03/2015
65672^254961+186991776751Enzo Doria05/2016
65689*5^109791-876742Lelio R Paula10/2014
656982^40089+40089^8276723Serge Batalov02/2012
65702^254861-279001376721Enzo Doria03/2016
6571(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/2045977974176718Makoto Kamada03/2019
657210^76705+1376706Robert Price01/2011
657310^76705-9407776705Patrick De Geest06/2013
6574(5*2^254785-1)/99976696Lelio R Paula02/2014
65752^254758-11040576690Enzo Doria05/2014
65762^254716-377976678Yves Minet04/2017
65772^254708-11050776675Enzo Doria05/2014
6578(47*10^76672+133)/976673Robert Price04/2017
65792^254670-11290176664Enzo Doria06/2014
6580(3^160665+7)/98135076651Lelio R Paula10/2012
65812^254598-11318376642Enzo Doria07/2014
658219^59932+2276639Lelio R Paula01/2015
65832^254569-11221376633Enzo Doria06/2014
65842*5^109626+976626Lelio R Paula10/2014
65852^254521+187252776619Enzo Doria05/2016
6586(76*10^76615+167)/976616Robert Price08/2016
658725^54799-24^5479976606Robert Price07/2012
6588(24737*2^254464+1)/976605Lelio R Paula06/2014
658912^70961-8576580Lelio R Paula02/2015
65907^90590-3876558Lelio R Paula02/2015
65912^254304+522776554Lelio R Paula06/2013
6592(76*10^76547-211)/976548Robert Price10/2017
659318^60979-536376546Enzo Doria03/2013
6594(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
6596(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
6595(7*10^76536-313)/976536Robert Price11/2016
65982^254239-2776534Lelio R Paula03/2012
65972^254238-184176534Yves Minet03/2013
6599(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
66002^254189-11222576519Enzo Doria06/2014
660118^60938-139776494Enzo Doria03/2013
66022^254075-278841776485Enzo Doria03/2016
66037*10^76483-2376484Robert Price04/2016
66042^254042-11291376475Enzo Doria06/2014
660514^66723-3776474Lelio R Paula02/2015
66062^254037-11030576473Enzo Doria05/2014
66072^253931-11110976441Enzo Doria05/2014
66082^253926-116776440Lelio R Paula05/2013
6609(49*10^76438-13)/976439Robert Price07/2015
6610(21*2^253845-1)/14376415Lelio R Paula02/2014
661110^76374+3176375Robert Price03/2011
661210^76374-22215976374Patrick De Geest05/2013
66132^253561-11053376330Enzo Doria05/2014
6614gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
66159*5^109182+276316Lelio R Paula10/2014
661611^73279-369076313Enzo Doria12/2012
6617(598*10^76309-31)/976311Robert Price02/2017
661811^73274-2400076308Enzo Doria12/2012
66197^90291-676305Theodore Burton11/2005
6620(21181*2^253432+1)/2143776291Lelio R Paula06/2014
66216^98025+14576279Lelio R Paula01/2015
66222^253355+115576268Lelio R Paula05/2013
6623(73*10^76262+413)/976263Robert Price10/2017
66242^253292-7121976249Enzo Doria04/2016
66257^90221-3676246Lelio R Paula02/2015
662618^60727-347376229Enzo Doria03/2013
6627(78557*2^253184+1)/376221Lelio R Paula06/2014
6628(8*10^76220-83)/376221Robert Price10/2017
6629(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
663011^73163-201076192Enzo Doria12/2012
66312^253060+5461576179Lelio R Paula05/2013
66322^253029+186976176170Enzo Doria05/2016
66332^252955-11100776148Enzo Doria05/2014
66342*5^108931+776140Lelio R Paula10/2014
6635(86*10^76128+121)/976129Robert Price03/2017
663622154*29^52050+976123Curtis Bright05/2015
66373^159530-11235876116Enzo Doria06/2014
663811^73089-4876115Lelio R Paula02/2015
663986^39337-8576098Norbert Schneider10/2015
6640(3^159505-7)/31329731676095Lelio R Paula06/2012
66416^97783+7776090Lelio R Paula01/2015
66422^252712-10576074Lelio R Paula03/2012
6643(10^76069-19)/976069Robert Price10/2017
6645131^35927+276068Lelio R Paula05/2013
6644(41*10^76067+373)/976068Robert Price04/2017
66462^252683-13976066Lelio R Paula03/2012
6647137^35597-13676061Norbert Schneider05/2015
66483^159413+10676060Lelio R Paula01/2015
66499^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
6650(2^252557-9)/7176026Lelio R Paula07/2012
6651(85*10^76021-103)/976022Robert Price10/2017
665211^72989+8076011Lelio R Paula02/2015
665399877!6-3675996Robert Price11/2018
66542^252449-45952375995Enzo Doria05/2015
665520^58408+7375991Lelio R Paula01/2015
66562^252418-142175986Yves Minet01/2013
6657(11*2^252396-1)/575980Lelio R Paula02/2014
66582^252365-11068975970Enzo Doria05/2014
665911^72949-102075969Enzo Doria11/2012
6660(2^252294+47)/654975945Lelio R Paula07/2012
66612^252261-11059575939Enzo Doria05/2014
66627^89853+7675935Lelio R Paula01/2015
66633^159132+5675926Lelio R Paula01/2015
6664730^26513+26513^73075916Norbert Schneider11/2016
6665(27*2^252163-1)/194575907Lelio R Paula01/2014
66665^108596-1484675906Enzo Doria02/2013
66675^108560-1484675881Enzo Doria02/2013
66682^252051-11035975875Enzo Doria05/2014
66692^251971-11050975851Enzo Doria05/2014
6670(42457^16384+1)/32768275819Lelio R Paula11/2011
66712^251842-471575812Yves Minet05/2019
667299655!6-275811Robert Price07/2017
667314*10^75798+108975800Jens K. Andersen11/2007
66742^251784-45575795Yves Minet03/2012
66752^251780-128975794Yves Minet01/2013
66762^251760-21560975788Paul Bourdelais03/2013
667799^37973+275781Lelio R Paula05/2013
6678(185*10^75777+7)/375779Robert Price02/2017
66795*2^251690+375767Lelio R Paula06/2014
66806^97366+9575766Lelio R Paula01/2015
6681s(23010)75760Hans Havermann11/2017
66828*6^97337-775744Lelio R Paula10/2014
66832^251588-11167775736Enzo Doria05/2014
66845^108346-1325675731Enzo Doria02/2013
6685(31^50777+1)/3275726Robert Price07/2013
6686(10^75707+77)/375707Robert Price01/2017
6687(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
66882^251466+19375699Lelio R Paula03/2012
6689(5*2^251464+1)/942375695Lelio R Paula07/2012
66902^251422-10999175686Enzo Doria04/2014
669191*(10^23+1)*(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)75680Makoto Kamada03/2019
66924*5^108245-375661Lelio R Paula10/2014
669312^70067-11^7006775615Jean-Louis Charton11/2006
669412^70066+9575614Lelio R Paula02/2015
6695-E20534/206375607Thomas Ritschel02/2017
669619^59120-5075600Lelio R Paula01/2015
669718^60222-469775596Enzo Doria03/2013
669818^60211-435575582Enzo Doria03/2013
66997*2^251014-975564Lelio R Paula06/2014
67006^97101-2575560Lelio R Paula01/2015
67018^83663-7^8366375556Jean-Louis Charton01/2004
67023^158331-14075544Lelio R Paula01/2015
6705(37^48157-1)/3675519Robert Price03/2012
6703(19*10^75518-43)/375519Robert Price10/2017
67042^250868-422975519Yves Minet08/2018
670610^75516+3146775517Patrick De Geest03/2016
670810^75516-10^2256-175516Serge Batalov01/2011
670710^75516-6659175516Patrick De Geest03/2016
67092^250851-18775514Lelio R Paula03/2012
6710(43*10^75498-7)/975499Robert Price12/2014
6711(3^158244-5)/24791675497Lelio R Paula06/2012
67124*5^107971-375470Lelio R Paula10/2014
6713(25*10^75465+71)/375466Robert Price01/2017
6714(5*2^250681-1)/99975461Lelio R Paula01/2014
6715(182*10^75456+1)/375458Robert Price02/2017
6716(2^250669-9)/9889772975451Lelio R Paula07/2012
671710^75441+1375442Robert Price01/2011
671810^75441-992375441Patrick De Geest05/2013
6719(27*2^250546-1)/645775420Lelio R Paula01/2014
67205*7^89231-675410Lelio R Paula10/2014
67222^250503-1699575409Lelio R Paula05/2013
672111^72411-2875409Lelio R Paula02/2015
67233*5^107860-875392Lelio R Paula10/2014
6724(34*10^75387-403)/975388Robert Price10/2017
67262^250426+2983575386Lelio R Paula05/2013
67258*3^157999-775386Lelio R Paula05/2014
6727(88*10^75381-43)/975382Robert Price11/2015
67282^250382-11175575373Enzo Doria05/2014
67292^250374-279805175371Eric Chen03/2016
6730(22*10^75368-1)/375369Robert Price12/2014
67312^250369-454375369Yves Minet03/2019
6732(19*10^75338+119)/375339Robert Price02/2017
67332^250223-185916775325Enzo Doria03/2016
6734(3^157854-7)/6602528275308Lelio R Paula06/2012
67353^157831-9875305Lelio R Paula01/2015
6736(46^45281+11^45281)/5775290Serge Batalov12/2016
673792^38335-9175282Norbert Schneider01/2016
67382^250020+1891575264Lelio R Paula05/2013
67392^250002+819375259Lelio R Paula05/2013
6740(11*2^249977-7)/1575251Renaud Lifchitz02/2011
6741(2^249968+78557)/6375247Lelio R Paula07/2012
6742(5*10^75244+91)/375245Robert Price11/2016
6743(10489!)^2+Prime(10489)75242Robert Price08/2014
674414^65644+6775237Lelio R Paula01/2015
6745(2^249928-5)/1185905975229Lelio R Paula06/2012
6746129^35638+275218Lelio R Paula05/2013
67472^249853-11047575214Enzo Doria05/2014
67482^249762+7540975186Enzo Doria04/2016
6749565^27318+27318^56575181Norbert Schneider12/2016
6750(2^249741-7)/68575177Lelio R Paula06/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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