PRP Records

Probable Primes Top 10000

(218736 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
5751(5*2^256274-1)/214177144Lelio R Paula02/2014
575219^60321+8277136Lelio R Paula03/2015
57535*2^256233-377135Lelio R Paula06/2014
57543*2^256149+777110Lelio R Paula06/2014
57553^161594-10677100Lelio R Paula02/2015
57562^256114-18577098Lelio R Paula03/2012
57578^85349-85349^877078Norbert Schneider05/2017
57582^256043-278637777077Enzo Doria03/2016
57592^255973+186994777056Enzo Doria05/2016
576012^71393-4377046Lelio R Paula02/2015
576115^65490+4477023Lelio R Paula02/2015
5762(3^161411-7)/94077010Lelio R Paula10/2012
5764lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5763(570^27943-1)/56977005Serge Batalov12/2016
57652^255750-7576989Lelio R Paula03/2012
57663*6^98926-576980Lelio R Paula10/2014
576718^61320-143376974Enzo Doria03/2013
57686^98916-1709376972Enzo Doria02/2013
57692^255659-11013176962Enzo Doria04/2014
577012^71303+9176949Lelio R Paula02/2015
577118^61298+5976946Lelio R Paula02/2015
5772(223^32768+1)/13107476945Lelio R Paula02/2009
5773(2^255613-5)/28151776942Lelio R Paula10/2012
577418^61290-1176936Lelio R Paula02/2015
577663^42752-276926Lelio R Paula08/2013
5775(11*2^255545-1)/11776926Lelio R Paula02/2014
57772^255517+5638776919Yves Minet02/2011
57782^255499-11256776913Enzo Doria06/2014
57792^255492+34576911Lelio R Paula06/2013
578010^76875+21759176876Patrick De Geest05/2013
578210^76875-5376875Robert Price05/2011
578111^73819-588076875Enzo Doria01/2013
57832^255313+1891576857Lelio R Paula06/2013
5784(2^255320-1017)/144666776853Lelio R Paula10/2012
57852^255296+577576852Lelio R Paula06/2013
578614^67052-2976851Lelio R Paula02/2015
5787(8*10^76840+43)/376841Robert Price10/2017
5788(7*10^76818-313)/976818Robert Price11/2016
578910^76801+6976802Robert Price03/2011
579010^76801-8094376801Patrick De Geest06/2013
57912^255105+5776795Lelio R Paula03/2012
5792(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5793(2^255097-7)/2002005576785Lelio R Paula10/2012
57942^255055+186935376780Enzo Doria05/2016
579517^62396-9076776Lelio R Paula03/2015
57967^90833-6076763Lelio R Paula02/2015
579713^68901-5676752Lelio R Paula03/2015
57982^254961+186991776751Enzo Doria05/2016
57999*5^109791-876742Lelio R Paula10/2014
580082^40089+40089^8276723Serge Batalov02/2012
58012^254861-279001376721Enzo Doria03/2016
580210^76705+1376706Robert Price01/2011
580310^76705-9407776705Patrick De Geest06/2013
5804(5*2^254785-1)/99976696Lelio R Paula02/2014
58052^254758-11040576690Enzo Doria05/2014
58062^254716-377976678Yves Minet04/2017
58072^254708-11050776675Enzo Doria05/2014
5808(47*10^76672+133)/976673Robert Price04/2017
58092^254670-11290176664Enzo Doria06/2014
5810(3^160665+7)/98135076651Lelio R Paula10/2012
58112^254598-11318376642Enzo Doria07/2014
581219^59932+2276639Lelio R Paula01/2015
58132^254569-11221376633Enzo Doria06/2014
58142*5^109626+976626Lelio R Paula10/2014
58152^254521+187252776619Enzo Doria05/2016
5816(76*10^76615+167)/976616Robert Price08/2016
581725^54799-24^5479976606Robert Price07/2012
5818(24737*2^254464+1)/976605Lelio R Paula06/2014
581912^70961-8576580Lelio R Paula02/2015
58207^90590-3876558Lelio R Paula02/2015
58212^254304+522776554Lelio R Paula06/2013
5822(76*10^76547-211)/976548Robert Price10/2017
582318^60979-536376546Enzo Doria03/2013
5824(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5825(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5826(7*10^76536-313)/976536Robert Price11/2016
58282^254239-2776534Lelio R Paula03/2012
58272^254238-184176534Yves Minet03/2013
5829(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
58302^254189-11222576519Enzo Doria06/2014
583118^60938-139776494Enzo Doria03/2013
58322^254075-278841776485Enzo Doria03/2016
58337*10^76483-2376484Robert Price04/2016
58342^254042-11291376475Enzo Doria06/2014
583514^66723-3776474Lelio R Paula02/2015
58362^254037-11030576473Enzo Doria05/2014
58372^253931-11110976441Enzo Doria05/2014
58382^253926-116776440Lelio R Paula05/2013
5839(49*10^76438-13)/976439Robert Price07/2015
5840(21*2^253845-1)/14376415Lelio R Paula02/2014
584110^76374+3176375Robert Price03/2011
584210^76374-22215976374Patrick De Geest05/2013
58432^253561-11053376330Enzo Doria05/2014
5844gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
58459*5^109182+276316Lelio R Paula10/2014
584611^73279-369076313Enzo Doria12/2012
5847(598*10^76309-31)/976311Robert Price02/2017
584811^73274-2400076308Enzo Doria12/2012
58497^90291-676305Theodore Burton11/2005
5850(21181*2^253432+1)/2143776291Lelio R Paula06/2014
58516^98025+14576279Lelio R Paula01/2015
58522^253355+115576268Lelio R Paula05/2013
5853(73*10^76262+413)/976263Robert Price10/2017
58542^253292-7121976249Enzo Doria04/2016
58557^90221-3676246Lelio R Paula02/2015
585618^60727-347376229Enzo Doria03/2013
5857(78557*2^253184+1)/376221Lelio R Paula06/2014
5858(8*10^76220-83)/376221Robert Price10/2017
5859(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
586011^73163-201076192Enzo Doria12/2012
58612^253060+5461576179Lelio R Paula05/2013
58622^253029+186976176170Enzo Doria05/2016
58632^252955-11100776148Enzo Doria05/2014
58642*5^108931+776140Lelio R Paula10/2014
5865(86*10^76128+121)/976129Robert Price03/2017
586622154*29^52050+976123Curtis Bright05/2015
58673^159530-11235876116Enzo Doria06/2014
586811^73089-4876115Lelio R Paula02/2015
586986^39337-8576098Norbert Schneider10/2015
5870(3^159505-7)/31329731676095Lelio R Paula06/2012
58716^97783+7776090Lelio R Paula01/2015
58722^252712-10576074Lelio R Paula03/2012
5873(10^76069-19)/976069Robert Price10/2017
5875131^35927+276068Lelio R Paula05/2013
5874(41*10^76067+373)/976068Robert Price04/2017
58762^252683-13976066Lelio R Paula03/2012
5877137^35597-13676061Norbert Schneider05/2015
58783^159413+10676060Lelio R Paula01/2015
58799^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
5880(2^252557-9)/7176026Lelio R Paula07/2012
5881(85*10^76021-103)/976022Robert Price10/2017
588211^72989+8076011Lelio R Paula02/2015
58832^252449-45952375995Enzo Doria05/2015
588420^58408+7375991Lelio R Paula01/2015
58852^252418-142175986Yves Minet01/2013
5886(11*2^252396-1)/575980Lelio R Paula02/2014
58872^252365-11068975970Enzo Doria05/2014
588811^72949-102075969Enzo Doria11/2012
5889(2^252294+47)/654975945Lelio R Paula07/2012
58902^252261-11059575939Enzo Doria05/2014
58917^89853+7675935Lelio R Paula01/2015
58923^159132+5675926Lelio R Paula01/2015
5893730^26513+26513^73075916Norbert Schneider11/2016
5894(27*2^252163-1)/194575907Lelio R Paula01/2014
58955^108596-1484675906Enzo Doria02/2013
58965^108560-1484675881Enzo Doria02/2013
58972^252051-11035975875Enzo Doria05/2014
58982^251971-11050975851Enzo Doria05/2014
5899(42457^16384+1)/32768275819Lelio R Paula11/2011
590099655!6-275811Robert Price07/2017
590114*10^75798+108975800Jens K. Andersen11/2007
59022^251784-45575795Yves Minet03/2012
59032^251780-128975794Yves Minet01/2013
59042^251760-21560975788Paul Bourdelais03/2013
590599^37973+275781Lelio R Paula05/2013
5906(185*10^75777+7)/375779Robert Price02/2017
59075*2^251690+375767Lelio R Paula06/2014
59086^97366+9575766Lelio R Paula01/2015
5909s(23010)75760Hans Havermann11/2017
59108*6^97337-775744Lelio R Paula10/2014
59112^251588-11167775736Enzo Doria05/2014
59125^108346-1325675731Enzo Doria02/2013
5913(31^50777+1)/3275726Robert Price07/2013
5914(10^75707+77)/375707Robert Price01/2017
5915(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
59162^251466+19375699Lelio R Paula03/2012
5917(5*2^251464+1)/942375695Lelio R Paula07/2012
59182^251422-10999175686Enzo Doria04/2014
59194*5^108245-375661Lelio R Paula10/2014
592012^70067-11^7006775615Jean-Louis Charton11/2006
592112^70066+9575614Lelio R Paula02/2015
5922-E20534/206375607Thomas Ritschel02/2017
592319^59120-5075600Lelio R Paula01/2015
592418^60222-469775596Enzo Doria03/2013
592518^60211-435575582Enzo Doria03/2013
59267*2^251014-975564Lelio R Paula06/2014
59276^97101-2575560Lelio R Paula01/2015
59288^83663-7^8366375556Jean-Louis Charton01/2004
59293^158331-14075544Lelio R Paula01/2015
5931(37^48157-1)/3675519Robert Price03/2012
5930(19*10^75518-43)/375519Robert Price10/2017
59322^250868-422975519Yves Minet08/2018
593310^75516+3146775517Patrick De Geest03/2016
593510^75516-10^2256-175516Serge Batalov01/2011
593410^75516-6659175516Patrick De Geest03/2016
59362^250851-18775514Lelio R Paula03/2012
5937(43*10^75498-7)/975499Robert Price12/2014
5938(3^158244-5)/24791675497Lelio R Paula06/2012
59394*5^107971-375470Lelio R Paula10/2014
5940(25*10^75465+71)/375466Robert Price01/2017
5941(5*2^250681-1)/99975461Lelio R Paula01/2014
5942(182*10^75456+1)/375458Robert Price02/2017
5943(2^250669-9)/9889772975451Lelio R Paula07/2012
594410^75441+1375442Robert Price01/2011
594510^75441-992375441Patrick De Geest05/2013
5946(27*2^250546-1)/645775420Lelio R Paula01/2014
59475*7^89231-675410Lelio R Paula10/2014
59492^250503-1699575409Lelio R Paula05/2013
594811^72411-2875409Lelio R Paula02/2015
59503*5^107860-875392Lelio R Paula10/2014
5951(34*10^75387-403)/975388Robert Price10/2017
59532^250426+2983575386Lelio R Paula05/2013
59528*3^157999-775386Lelio R Paula05/2014
5954(88*10^75381-43)/975382Robert Price11/2015
59552^250382-11175575373Enzo Doria05/2014
59562^250374-279805175371Eric Chen03/2016
5957(22*10^75368-1)/375369Robert Price12/2014
5958(19*10^75338+119)/375339Robert Price02/2017
59592^250223-185916775325Enzo Doria03/2016
5960(3^157854-7)/6602528275308Lelio R Paula06/2012
59613^157831-9875305Lelio R Paula01/2015
5962(46^45281+11^45281)/5775290Serge Batalov12/2016
596392^38335-9175282Norbert Schneider01/2016
59642^250020+1891575264Lelio R Paula05/2013
59652^250002+819375259Lelio R Paula05/2013
5966(11*2^249977-7)/1575251Renaud Lifchitz02/2011
5967(2^249968+78557)/6375247Lelio R Paula07/2012
5968(5*10^75244+91)/375245Robert Price11/2016
5969(10489!)^2+Prime(10489)75242Robert Price08/2014
597014^65644+6775237Lelio R Paula01/2015
5971(2^249928-5)/1185905975229Lelio R Paula06/2012
5972129^35638+275218Lelio R Paula05/2013
59732^249853-11047575214Enzo Doria05/2014
59742^249762+7540975186Enzo Doria04/2016
5975565^27318+27318^56575181Norbert Schneider12/2016
5976(2^249741-7)/68575177Lelio R Paula06/2012
59772^249726-11218175176Enzo Doria06/2014
59782^249721+1171575174Lelio R Paula05/2013
5979(38661^16384+1)/275158Lelio R Paula11/2011
59802^249658-4735575155Lelio R Paula05/2013
5981155^34311+275153Lelio R Paula05/2013
5982(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
5983(23*2^249602+1)/9375138Lelio R Paula08/2012
59842^249522+841575114Lelio R Paula05/2013
59852^249489-11091175104Enzo Doria05/2014
5986(28*10^75078+131)/375079Robert Price02/2017
5987(206*10^75073-17)/975075Robert Price03/2017
59882^249368-11057375068Enzo Doria05/2014
5989NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
5990(2^249375+78557)/4505612575062Lelio R Paula07/2012
5991(26*10^75055-173)/375056Robert Price10/2017
59922^249272+19375039Lelio R Paula03/2012
599314^65468+4375035Lelio R Paula01/2015
599437^47844+3675030Norbert Schneider05/2014
5995(52*10^75027-7)/975028Robert Price12/2014
599620^57653+8975009Lelio R Paula01/2015
59972^249061-186835374975Enzo Doria04/2016
59987^88713+2*3^8871374972Mike Oakes07/2010
59992*6^96313+574947Lelio R Paula10/2014
6000(8*10^74944+49)/374945Robert Price03/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!