PRP Records

Probable Primes Top 10000

(252538 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 ?
85022^199872+9360168Donovan Johnson06/2008
85016^77321+7760168Lelio R Paula04/2013
8503(86*10^60165-77)/960166Robert Price05/2016
8504(2^199868+78557)/2337360162Lelio R Paula05/2012
85057^71180+8260155Lelio R Paula04/2013
85072^199814-11229560151Enzo Doria06/2014
8506(51^35227-1)/5060151Paul Bourdelais08/2017
850842964!3-8160135Robert Price09/2014
85092^199709-5160119Lelio R Paula05/2011
85102^199700-11162360116Enzo Doria05/2014
8511(15185*2^199681-1)/15960112Lelio R Paula04/2015
85122^199672+253360108Henri Lifchitz09/2004
851320^46198-1160105Lelio R Paula04/2013
85142^199657+9325760103Yves Minet03/2010
85153^125967-11060102Lelio R Paula10/2012
85162^199654-1881360102Enzo Doria05/2013
8517(29*10^60100+19)/360101Robert Price01/2017
85182^199615-2*199615+160091Robert Price04/2018
8519129^28468+28468^12960085Serge Batalov05/2014
85202^199572-1587360078Enzo Doria04/2013
85219*2^199559+760075Lelio R Paula03/2014
85222^199527-11191960064Enzo Doria05/2014
85232^199522+8287560063Lelio R Paula10/2012
85245^85928-7260062Lelio R Paula10/2012
852539^37749+3860062Norbert Schneider05/2014
85266^77182-14360060Lelio R Paula10/2012
85272^199502-214560057Lelio R Paula06/2011
85282^199493+425760054Lelio R Paula06/2011
85292^199488+4075560052Lelio R Paula06/2011
8530(2^199451+9)/2561960037Lelio R Paula02/2012
85312^199425-6160033Lelio R Paula05/2011
8532(85*10^60026+23)/960027Robert Price11/2015
853365^33107+6260021Lelio R Paula01/2016
85352^199362-121560014Lelio R Paula06/2011
85342^199362-11163360014Enzo Doria05/2014
85361537^18832+18832^153760012Serge Batalov05/2014
85372^199324-1743360003Enzo Doria05/2013
853810^60000+20433160001Milton L. Brown04/2006
853910^60000+8712960001Milton L. Brown04/2006
8540143^27838-260001Lelio R Paula10/2017
855910^59999+6519760000Patrick De Geest04/2005
855810^60000-3252960000Patrick De Geest08/2009
8554(10^60000+2249)/960000Makoto Morimoto09/2016
8555((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
8556(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
8557(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
8541(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
8542(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
8543(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
8544(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
8545(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
8546(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
8547(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
8548(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
8549(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
8550(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
8551(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
8552(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
8553(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
856210^59999-51626759999Patrick De Geest06/2009
856120^46116-4159999Lelio R Paula03/2013
8560(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
8563(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
85646^77100-5559996Lelio R Paula10/2012
8566(19*2^199274+1)/16159987Lelio R Paula07/2012
8565(23^44053+1)/2459987Robert Price06/2013
85679^62848+6^62848-2^6284859973Mike Oakes08/2010
856815852^6061+6061^1585259961Hans Havermann08/2016
856919^46880-2059948Lelio R Paula03/2013
85702^199107-1773759938Enzo Doria05/2013
8571(13*10^59928+83)/359929Robert Price09/2016
857210^59913+10893143159914Marisa Kirisame02/2015
857310^59913+4861959914Patrick De Geest04/2016
857410^59913-7412359913Patrick De Geest03/2016
8575t(199528)59890Robert Price01/2015
85762^198903-1790159876Enzo Doria05/2013
85779*10^59862-1959863Robert Price10/2017
8578gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
8579(3^125447+7)/259854Lelio R Paula04/2012
85805^85630+4^(85630-1)59853Robert Price03/2016
85812^198824-213559852Yves Minet06/2013
8582(124^28591-1)/12359851Richard Fischer10/2017
85832^198799-1611759845Enzo Doria04/2013
85847^70811+6^(70811+1)59843Robert Price07/2016
85852^198774-1594559837Enzo Doria04/2013
85862^198753-1587359831Enzo Doria04/2013
8587(31*2^198748-1)/4559829Lelio R Paula01/2014
85882^198725+6959823Lelio R Paula04/2011
8589(68*10^59821+31)/959822Robert Price10/2015
8590(37*25^42785+1867)/859812Curtis Bright05/2015
85913^125354+266059810Lelio R Paula10/2012
8592105^29591-10459810Norbert Schneider08/2013
85934*5^85565-359808Lelio R Paula09/2014
859413963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
8596125330^3+3^12533059798Anatoly F. Selevich06/2010
85952^198643-318959798Yves Minet10/2014
8597(13*10^59797+191)/359798Robert Price08/2017
8598(7*10^59796-1)/359797Erik Branger03/2014
85992^198595+15359784Lelio R Paula04/2011
8600(19*10^59766+161)/959767Robert Price07/2016
86012^198510-196559758Lelio R Paula06/2011
86022^198506-1907759757Enzo Doria05/2013
86032^198484-1600559750Enzo Doria04/2013
86042^198473-1682159747Enzo Doria05/2013
8605(2^198481-5)/2831159745Lelio R Paula02/2012
86062^198400-18959725Lelio R Paula04/2011
86072^198384-1283759720Enzo Doria10/2012
860842694!3-72959719Robert Price09/2014
86092^198320-1871759701Enzo Doria05/2013
861020^45881-118359693Enzo Doria03/2013
86112^198224-685559672Lelio R Paula05/2011
86122^198181-1910159659Enzo Doria05/2013
86135*10^59650+4159651Robert Price08/2017
86142^198149-11221359649Enzo Doria06/2014
86152^198138+7369959646Enzo Doria04/2016
86162^198129-5559643Lelio R Paula04/2011
86175^85318-1463659635Enzo Doria02/2013
8618(2^198119+47)/156093559634Lelio R Paula02/2012
86192^198090-1609759632Enzo Doria04/2013
86209*10^59617+8959618Robert Price11/2016
862142625!3+8159612Robert Price09/2014
86225^85277-8459607Lelio R Paula10/2012
8623(871*10^59599-7)/959601Robert Price11/2017
86242^197984-1824559600Enzo Doria05/2013
862512202^14583-14583^1220259593Norbert Schneider01/2019
86262^197951-213759590Yves Minet06/2013
8627(38*10^59589+187)/959590Robert Price11/2017
862866^32749-65^3274959589Robert Price09/2013
86295*10^59586-359587Dmitry Domanov11/2010
8630(35*10^59584-197)/959585Robert Kinser10/2017
86312^197932-395959584Yves Minet04/2017
86322^197909-1896159577Enzo Doria05/2013
8633(3^124871+2)/4503159574Lelio R Paula04/2012
86342^197872+8159566Henri Lifchitz10/2005
86352^197873-1846959566Enzo Doria05/2013
8636(22*10^59558-31)/959559Robert Price04/2015
86382^197840-46559556Lelio R Paula05/2011
8637(31*2^197856-1)/388960559556Lelio R Paula01/2014
86392^197808-1780559547Enzo Doria05/2013
86402^197781-1790559539Enzo Doria05/2013
86412^197777-1747359537Enzo Doria05/2013
86426^76507-14959535Lelio R Paula10/2012
8644Phi(61456,109)59526Enzo Doria05/2012
864318^47420+2359526Lelio R Paula03/2013
8645(59^33613+1)/6059522Paul Bourdelais08/2017
86463^124747+9459520Lelio R Paula10/2012
864717^48370+1859517Lelio R Paula03/2013
864820^45740-152359510Enzo Doria03/2013
8649(47*10^59509+493)/959510Robert Price11/2017
8650(7*2^197642-1)/305159494Lelio R Paula01/2014
865118^47390-185359488Enzo Doria03/2013
8652(2^197581-7)/191559475Lelio R Paula02/2012
8653(24737*2^197559+1)/7759474Lelio R Paula06/2014
86542^197540-245959466Yves Minet07/2014
8655(44*10^59454+1)/959455Serge Batalov11/2010
86562^197494-1780559452Enzo Doria05/2013
86572^197482-1682159449Enzo Doria05/2013
86582^197485+7576759449Enzo Doria04/2016
8659(3*2^197483+1)/2559448Lelio R Paula07/2012
86602^197466-186835159444Enzo Doria04/2016
86612^197411-1778159427Enzo Doria05/2013
8662(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
86632^197392-11462959421Enzo Doria05/2015
86642^197355-15759410Lelio R Paula04/2011
86655^84992-8459407Lelio R Paula10/2012
86662*3^124504-559404Lelio R Paula04/2014
86672^197307-1916559396Enzo Doria05/2013
86692^197303+3276959395Lelio R Paula05/2011
86682*10^59394-6959395Robert Price07/2017
8670(53*10^59389+1)/959390Serge Batalov11/2010
86716^76316-3559386Lelio R Paula10/2012
86722^197259-292959381Yves Minet09/2014
8673lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
867417^48253-659373Lelio R Paula03/2013
86752^197156-1583759350Enzo Doria04/2013
86762^197152-429559349Yves Minet08/2018
86772^197149-1848159348Enzo Doria05/2013
86782^197142-1715759346Enzo Doria05/2013
8680(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
8679(8^65707-5^65707)/359339Robert Price12/2012
8681(2*14283^14283+1)/792549797559334David Broadhurst09/2010
86822^197012-11171959307Enzo Doria05/2014
86832^196975+51359296Lelio R Paula05/2011
8684(61*10^59294+119)/959295Robert Price09/2017
86854*10^59292+3959293Robert Price11/2017
86862^196960+9759291Lelio R Paula04/2011
86879^62116+8^(62116-1)59274Robert Price03/2016
86882^196900-9730559273Lelio R Paula09/2011
86895*6^76155+759261Lelio R Paula09/2014
869015^50385-1459258Wojciech Florek06/2006
8691(136777#-1)/882358147759254Donovan Johnson05/2006
8692(2^196744-3)*6-759227Gilbert Mozzo05/2016
8693(67607*2^196696+1)/359216Lelio R Paula05/2014
86942^196696-11296759212Enzo Doria06/2014
869520^45508-422359208Enzo Doria03/2013
8696gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
869714^51651-8159199Lelio R Paula03/2013
86982^196650-145159198Yves Minet08/2012
86992^196636-279779959194Enzo Doria04/2016
87001111*2^196610-55559189Henri Lifchitz04/2005
87013^124041+65859183Lelio R Paula10/2012
87022^196590-11179759180Enzo Doria05/2014
8703(10^59174-13)/359174Robert Price02/2017
8704(2*10^59174-113)/359174Robert Price09/2017
8705(9179*2^196533-1)/78359164Lelio R Paula04/2015
8706379*10^59152+959155Arkadiusz Wesolowski10/2011
8707(404*10^59149-53)/959151Robert Price11/2017
870813^53095+4059145Lelio R Paula03/2013
87102*F(282999)-159144Henri Lifchitz12/2009
87094*7^69984+359144Lelio R Paula09/2014
8711(5*10^59142+1)/359143Erik Branger12/2013
87122^196463+571159142Lelio R Paula10/2011
87132^196453-9730559139Lelio R Paula09/2011
8714(28*10^59135+53)/959136Serge Batalov11/2008
8715(28*10^59133+113)/359134Robert Price03/2016
87162^196434+759133Lelio R Paula04/2011
8717(8*10^59127-29)/359128Robert Price05/2016
87182^196414+25559127Lelio R Paula05/2011
87195^84586-9259124Lelio R Paula10/2012
87202^196388-1717759119Enzo Doria05/2013
872179427!6-659119Robert Price08/2018
87223^123890+2059111Lelio R Paula10/2012
87232^196355-102177759109Paul Bourdelais11/2012
872411^56754-141059104Enzo Doria11/2012
8725(7*2^196297-1)/120040759087Lelio R Paula01/2014
8726(16*10^59062-19)/359063Robert Price03/2016
872735^38249-122859060Enzo Doria03/2013
87285^84475-1859046Lelio R Paula10/2012
87292^196123-1770159039Enzo Doria05/2013
873012^54702-3159034Lelio R Paula03/2013
87312^196101-17559033Lelio R Paula04/2011
87322^196085+577559028Lelio R Paula05/2011
87332^196034+1171559013Lelio R Paula05/2011
87342^196018-1848559008Enzo Doria05/2013
87352^195984-216358998Yves Minet08/2013
87363^123645-1658994Lelio R Paula10/2012
873739^37078-3858994Norbert Schneider05/2014
87382^195958-1685358990Enzo Doria05/2013
87392^195930-307158981Yves Minet10/2014
87402^195924+51358980Lelio R Paula05/2011
87412^195863+15558961Lelio R Paula04/2011
8742(28*10^58956+113)/358957Robert Price03/2016
874311^56612-930058956Enzo Doria02/2013
87442^195833-1717358952Enzo Doria05/2013
8745(27*2^195833-1)/5358952Lelio R Paula01/2014
8746(13*2^195821-1)/12242558945Lelio R Paula01/2014
8747139^27504-13858942Norbert Schneider10/2015
8748(418*10^58923+23)/958925Robert Price08/2017
87493^123495+4458923Lelio R Paula10/2012
87502^195737-1856558923Enzo Doria05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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