PRP Records

Probable Primes Top 10000

(247113 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 ?
60012^255659-11013176962Enzo Doria04/2014
600212^71303+9176949Lelio R Paula02/2015
600318^61298+5976946Lelio R Paula02/2015
6004(223^32768+1)/13107476945Lelio R Paula02/2009
6005(2^255613-5)/28151776942Lelio R Paula10/2012
600618^61290-1176936Lelio R Paula02/2015
600863^42752-276926Lelio R Paula08/2013
6007(11*2^255545-1)/11776926Lelio R Paula02/2014
60092^255517+5638776919Yves Minet02/2011
60102^255499-11256776913Enzo Doria06/2014
60112^255492+34576911Lelio R Paula06/2013
601210^76875+21759176876Patrick De Geest05/2013
601410^76875-5376875Robert Price05/2011
601311^73819-588076875Enzo Doria01/2013
60152^255313+1891576857Lelio R Paula06/2013
6016(2^255320-1017)/144666776853Lelio R Paula10/2012
60172^255296+577576852Lelio R Paula06/2013
601814^67052-2976851Lelio R Paula02/2015
6019(8*10^76840+43)/376841Robert Price10/2017
6020(7*10^76818-313)/976818Robert Price11/2016
602110^76801+6976802Robert Price03/2011
602210^76801-8094376801Patrick De Geest06/2013
60232^255105+5776795Lelio R Paula03/2012
6024(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
6025(2^255097-7)/2002005576785Lelio R Paula10/2012
60262^255055+186935376780Enzo Doria05/2016
602717^62396-9076776Lelio R Paula03/2015
60287^90833-6076763Lelio R Paula02/2015
602913^68901-5676752Lelio R Paula03/2015
60302^254961+186991776751Enzo Doria05/2016
60319*5^109791-876742Lelio R Paula10/2014
603282^40089+40089^8276723Serge Batalov02/2012
60332^254861-279001376721Enzo Doria03/2016
603410^76705+1376706Robert Price01/2011
603510^76705-9407776705Patrick De Geest06/2013
6036(5*2^254785-1)/99976696Lelio R Paula02/2014
60372^254758-11040576690Enzo Doria05/2014
60382^254716-377976678Yves Minet04/2017
60392^254708-11050776675Enzo Doria05/2014
6040(47*10^76672+133)/976673Robert Price04/2017
60412^254670-11290176664Enzo Doria06/2014
6042(3^160665+7)/98135076651Lelio R Paula10/2012
60432^254598-11318376642Enzo Doria07/2014
604419^59932+2276639Lelio R Paula01/2015
60452^254569-11221376633Enzo Doria06/2014
60462*5^109626+976626Lelio R Paula10/2014
60472^254521+187252776619Enzo Doria05/2016
6048(76*10^76615+167)/976616Robert Price08/2016
604925^54799-24^5479976606Robert Price07/2012
6050(24737*2^254464+1)/976605Lelio R Paula06/2014
605112^70961-8576580Lelio R Paula02/2015
60527^90590-3876558Lelio R Paula02/2015
60532^254304+522776554Lelio R Paula06/2013
6054(76*10^76547-211)/976548Robert Price10/2017
605518^60979-536376546Enzo Doria03/2013
6056(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
6057(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
6058(7*10^76536-313)/976536Robert Price11/2016
60602^254239-2776534Lelio R Paula03/2012
60592^254238-184176534Yves Minet03/2013
6061(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
60622^254189-11222576519Enzo Doria06/2014
606318^60938-139776494Enzo Doria03/2013
60642^254075-278841776485Enzo Doria03/2016
60657*10^76483-2376484Robert Price04/2016
60662^254042-11291376475Enzo Doria06/2014
606714^66723-3776474Lelio R Paula02/2015
60682^254037-11030576473Enzo Doria05/2014
60692^253931-11110976441Enzo Doria05/2014
60702^253926-116776440Lelio R Paula05/2013
6071(49*10^76438-13)/976439Robert Price07/2015
6072(21*2^253845-1)/14376415Lelio R Paula02/2014
607310^76374+3176375Robert Price03/2011
607410^76374-22215976374Patrick De Geest05/2013
60752^253561-11053376330Enzo Doria05/2014
6076gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
60779*5^109182+276316Lelio R Paula10/2014
607811^73279-369076313Enzo Doria12/2012
6079(598*10^76309-31)/976311Robert Price02/2017
608011^73274-2400076308Enzo Doria12/2012
60817^90291-676305Theodore Burton11/2005
6082(21181*2^253432+1)/2143776291Lelio R Paula06/2014
60836^98025+14576279Lelio R Paula01/2015
60842^253355+115576268Lelio R Paula05/2013
6085(73*10^76262+413)/976263Robert Price10/2017
60862^253292-7121976249Enzo Doria04/2016
60877^90221-3676246Lelio R Paula02/2015
608818^60727-347376229Enzo Doria03/2013
6089(78557*2^253184+1)/376221Lelio R Paula06/2014
6090(8*10^76220-83)/376221Robert Price10/2017
6091(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
609211^73163-201076192Enzo Doria12/2012
60932^253060+5461576179Lelio R Paula05/2013
60942^253029+186976176170Enzo Doria05/2016
60952^252955-11100776148Enzo Doria05/2014
60962*5^108931+776140Lelio R Paula10/2014
6097(86*10^76128+121)/976129Robert Price03/2017
609822154*29^52050+976123Curtis Bright05/2015
60993^159530-11235876116Enzo Doria06/2014
610011^73089-4876115Lelio R Paula02/2015
610186^39337-8576098Norbert Schneider10/2015
6102(3^159505-7)/31329731676095Lelio R Paula06/2012
61036^97783+7776090Lelio R Paula01/2015
61042^252712-10576074Lelio R Paula03/2012
6105(10^76069-19)/976069Robert Price10/2017
6107131^35927+276068Lelio R Paula05/2013
6106(41*10^76067+373)/976068Robert Price04/2017
61082^252683-13976066Lelio R Paula03/2012
6109137^35597-13676061Norbert Schneider05/2015
61103^159413+10676060Lelio R Paula01/2015
61119^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
6112(2^252557-9)/7176026Lelio R Paula07/2012
6113(85*10^76021-103)/976022Robert Price10/2017
611411^72989+8076011Lelio R Paula02/2015
611599877!6-3675996Robert Price11/2018
61162^252449-45952375995Enzo Doria05/2015
611720^58408+7375991Lelio R Paula01/2015
61182^252418-142175986Yves Minet01/2013
6119(11*2^252396-1)/575980Lelio R Paula02/2014
61202^252365-11068975970Enzo Doria05/2014
612111^72949-102075969Enzo Doria11/2012
6122(2^252294+47)/654975945Lelio R Paula07/2012
61232^252261-11059575939Enzo Doria05/2014
61247^89853+7675935Lelio R Paula01/2015
61253^159132+5675926Lelio R Paula01/2015
6126730^26513+26513^73075916Norbert Schneider11/2016
6127(27*2^252163-1)/194575907Lelio R Paula01/2014
61285^108596-1484675906Enzo Doria02/2013
61295^108560-1484675881Enzo Doria02/2013
61302^252051-11035975875Enzo Doria05/2014
61312^251971-11050975851Enzo Doria05/2014
6132(42457^16384+1)/32768275819Lelio R Paula11/2011
613399655!6-275811Robert Price07/2017
613414*10^75798+108975800Jens K. Andersen11/2007
61352^251784-45575795Yves Minet03/2012
61362^251780-128975794Yves Minet01/2013
61372^251760-21560975788Paul Bourdelais03/2013
613899^37973+275781Lelio R Paula05/2013
6139(185*10^75777+7)/375779Robert Price02/2017
61405*2^251690+375767Lelio R Paula06/2014
61416^97366+9575766Lelio R Paula01/2015
6142s(23010)75760Hans Havermann11/2017
61438*6^97337-775744Lelio R Paula10/2014
61442^251588-11167775736Enzo Doria05/2014
61455^108346-1325675731Enzo Doria02/2013
6146(31^50777+1)/3275726Robert Price07/2013
6147(10^75707+77)/375707Robert Price01/2017
6148(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
61492^251466+19375699Lelio R Paula03/2012
6150(5*2^251464+1)/942375695Lelio R Paula07/2012
61512^251422-10999175686Enzo Doria04/2014
61524*5^108245-375661Lelio R Paula10/2014
615312^70067-11^7006775615Jean-Louis Charton11/2006
615412^70066+9575614Lelio R Paula02/2015
6155-E20534/206375607Thomas Ritschel02/2017
615619^59120-5075600Lelio R Paula01/2015
615718^60222-469775596Enzo Doria03/2013
615818^60211-435575582Enzo Doria03/2013
61597*2^251014-975564Lelio R Paula06/2014
61606^97101-2575560Lelio R Paula01/2015
61618^83663-7^8366375556Jean-Louis Charton01/2004
61623^158331-14075544Lelio R Paula01/2015
6164(37^48157-1)/3675519Robert Price03/2012
6165(19*10^75518-43)/375519Robert Price10/2017
61632^250868-422975519Yves Minet08/2018
616610^75516+3146775517Patrick De Geest03/2016
616810^75516-10^2256-175516Serge Batalov01/2011
616710^75516-6659175516Patrick De Geest03/2016
61692^250851-18775514Lelio R Paula03/2012
6170(43*10^75498-7)/975499Robert Price12/2014
6171(3^158244-5)/24791675497Lelio R Paula06/2012
61724*5^107971-375470Lelio R Paula10/2014
6173(25*10^75465+71)/375466Robert Price01/2017
6174(5*2^250681-1)/99975461Lelio R Paula01/2014
6175(182*10^75456+1)/375458Robert Price02/2017
6176(2^250669-9)/9889772975451Lelio R Paula07/2012
617710^75441+1375442Robert Price01/2011
617810^75441-992375441Patrick De Geest05/2013
6179(27*2^250546-1)/645775420Lelio R Paula01/2014
61805*7^89231-675410Lelio R Paula10/2014
61822^250503-1699575409Lelio R Paula05/2013
618111^72411-2875409Lelio R Paula02/2015
61833*5^107860-875392Lelio R Paula10/2014
6184(34*10^75387-403)/975388Robert Price10/2017
61862^250426+2983575386Lelio R Paula05/2013
61858*3^157999-775386Lelio R Paula05/2014
6187(88*10^75381-43)/975382Robert Price11/2015
61882^250382-11175575373Enzo Doria05/2014
61892^250374-279805175371Eric Chen03/2016
6190(22*10^75368-1)/375369Robert Price12/2014
6191(19*10^75338+119)/375339Robert Price02/2017
61922^250223-185916775325Enzo Doria03/2016
6193(3^157854-7)/6602528275308Lelio R Paula06/2012
61943^157831-9875305Lelio R Paula01/2015
6195(46^45281+11^45281)/5775290Serge Batalov12/2016
619692^38335-9175282Norbert Schneider01/2016
61972^250020+1891575264Lelio R Paula05/2013
61982^250002+819375259Lelio R Paula05/2013
6199(11*2^249977-7)/1575251Renaud Lifchitz02/2011
6200(2^249968+78557)/6375247Lelio R Paula07/2012
6201(5*10^75244+91)/375245Robert Price11/2016
6202(10489!)^2+Prime(10489)75242Robert Price08/2014
620314^65644+6775237Lelio R Paula01/2015
6204(2^249928-5)/1185905975229Lelio R Paula06/2012
6205129^35638+275218Lelio R Paula05/2013
62062^249853-11047575214Enzo Doria05/2014
62072^249762+7540975186Enzo Doria04/2016
6208565^27318+27318^56575181Norbert Schneider12/2016
6209(2^249741-7)/68575177Lelio R Paula06/2012
62102^249726-11218175176Enzo Doria06/2014
62112^249721+1171575174Lelio R Paula05/2013
6212(38661^16384+1)/275158Lelio R Paula11/2011
62132^249658-4735575155Lelio R Paula05/2013
6214155^34311+275153Lelio R Paula05/2013
6215(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
6216(23*2^249602+1)/9375138Lelio R Paula08/2012
62172^249522+841575114Lelio R Paula05/2013
62182^249489-11091175104Enzo Doria05/2014
6219(28*10^75078+131)/375079Robert Price02/2017
6220(206*10^75073-17)/975075Robert Price03/2017
62212^249368-11057375068Enzo Doria05/2014
6222NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
6223(2^249375+78557)/4505612575062Lelio R Paula07/2012
6224(26*10^75055-173)/375056Robert Price10/2017
62252^249272+19375039Lelio R Paula03/2012
622614^65468+4375035Lelio R Paula01/2015
622737^47844+3675030Norbert Schneider05/2014
6228(52*10^75027-7)/975028Robert Price12/2014
622920^57653+8975009Lelio R Paula01/2015
62302^249061-186835374975Enzo Doria04/2016
62317^88713+2*3^8871374972Mike Oakes07/2010
62322*6^96313+574947Lelio R Paula10/2014
6233(8*10^74944+49)/374945Robert Price03/2016
6234300^30247+30247^30074926Norbert Schneider11/2014
62352^248866-17174917Lelio R Paula03/2012
62366*5^107168-774908Lelio R Paula10/2014
623711^71926+7874904Lelio R Paula02/2015
62382^248824+186939174904Enzo Doria05/2016
62392^248816+111174902Lelio R Paula01/2011
6240V(388219)74890Serge Batalov03/2015
62412*F(358297)-174880Henri Lifchitz12/2009
6242(22*10^74874-31)/974875Robert Price04/2015
624311^71892-7680000074868Enzo Doria01/2013
62449*5^107107-474866Lelio R Paula10/2014
62452^248678-71011174860Paul Bourdelais03/2013
6246(14*10^74858+211)/974859Robert Price11/2017
624713^67194+1274851Lelio R Paula01/2015
6248(7*2^248634+1)/7174846Lelio R Paula08/2012
624911^71867-309074842Enzo Doria12/2012
62502^248609+26214574839Lelio R Paula05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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