PRP Records

Probable Primes Top 10000

(193013 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 ?
77512^200607-1712160389Enzo Doria05/2013
775211^57975-162060375Enzo Doria11/2012
7753(9913*2^200538-1)/380160369Lelio R Paula04/2015
77545^86342+6460351Lelio R Paula04/2013
7755(14*10^60346-23)/960347Robert Price04/2015
77562^200457-829560344Lelio R Paula09/2011
77576^77546+11360343Lelio R Paula04/2013
775937^38461-36^3846160315Robert Price06/2012
77582^200361-1759360315Enzo Doria05/2013
776010103^15059-10660304Enzo Doria07/2012
77612^200301-1740160297Enzo Doria05/2013
7762(37*10^60290+71)/960291Robert Price04/2015
77632^200266-9439560287Lelio R Paula09/2011
77642^200261-11161360285Enzo Doria05/2014
776546^36238-4560256Norbert Schneider07/2014
776613^54091+9460255Lelio R Paula05/2013
7767311^24171-15460253Enzo Doria07/2012
77682^200120-8108960243Paul Bourdelais01/2012
77693^126262+868060243Lelio R Paula04/2013
777043031!3-5904960239Robert Price12/2015
77712^200100-11126960237Enzo Doria05/2014
7772(29*2^200069-1)/537360225Lelio R Paula01/2014
777320^46283-192360216Enzo Doria03/2013
77742^200011-11207560210Enzo Doria05/2014
77752^200002+7453960207Enzo Doria04/2016
7776(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
7777(28*10^60180+149)/360181Robert Price10/2017
77782^199872+9360168Donovan Johnson06/2008
77796^77321+7760168Lelio R Paula04/2013
7780(86*10^60165-77)/960166Robert Price05/2016
7781(2^199868+78557)/2337360162Lelio R Paula05/2012
77827^71180+8260155Lelio R Paula04/2013
77842^199814-11229560151Enzo Doria06/2014
7783(51^35227-1)/5060151Paul Bourdelais08/2017
778542964!3-8160135Robert Price09/2014
77862^199709-5160119Lelio R Paula05/2011
77872^199700-11162360116Enzo Doria05/2014
7788(15185*2^199681-1)/15960112Lelio R Paula04/2015
77892^199672+253360108Henri Lifchitz09/2004
779020^46198-1160105Lelio R Paula04/2013
77912^199657+9325760103Yves Minet03/2010
77923^125967-11060102Lelio R Paula10/2012
77932^199654-1881360102Enzo Doria05/2013
7794(29*10^60100+19)/360101Robert Price01/2017
7795129^28468+28468^12960085Serge Batalov05/2014
77962^199572-1587360078Enzo Doria04/2013
77979*2^199559+760075Lelio R Paula03/2014
77982^199527-11191960064Enzo Doria05/2014
77992^199522+8287560063Lelio R Paula10/2012
78005^85928-7260062Lelio R Paula10/2012
780139^37749+3860062Norbert Schneider05/2014
78026^77182-14360060Lelio R Paula10/2012
78032^199502-214560057Lelio R Paula06/2011
78042^199493+425760054Lelio R Paula06/2011
78052^199488+4075560052Lelio R Paula06/2011
7806(2^199451+9)/2561960037Lelio R Paula02/2012
78072^199425-6160033Lelio R Paula05/2011
7808(85*10^60026+23)/960027Robert Price11/2015
780965^33107+6260021Lelio R Paula01/2016
78102^199362-121560014Lelio R Paula06/2011
78112^199362-11163360014Enzo Doria05/2014
78121537^18832+18832^153760012Serge Batalov05/2014
78132^199324-1743360003Enzo Doria05/2013
781410^60000+20433160001Milton L. Brown04/2006
781510^60000+8712960001Milton L. Brown04/2006
7816143^27838-260001Lelio R Paula10/2017
783510^59999+6519760000Patrick De Geest04/2005
783410^60000-3252960000Patrick De Geest08/2009
7830(10^60000+2249)/960000Makoto Morimoto09/2016
7831((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
7832(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
7833(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
7817(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
7818(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
7819(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
7820(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
7821(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
7822(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
7823(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
7824(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
7825(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
7826(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
7827(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
7828(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
7829(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
783910^59999-51626759999Patrick De Geest06/2009
783820^46116-4159999Lelio R Paula03/2013
7836(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
7837(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
78406^77100-5559996Lelio R Paula10/2012
7842(19*2^199274+1)/16159987Lelio R Paula07/2012
7841(23^44053+1)/2459987Robert Price06/2013
78439^62848+6^62848-2^6284859973Mike Oakes08/2010
784415852^6061+6061^1585259961Hans Havermann08/2016
784519^46880-2059948Lelio R Paula03/2013
78462^199107-1773759938Enzo Doria05/2013
7847(13*10^59928+83)/359929Robert Price09/2016
784910^59913+10893143159914Marisa Kirisame02/2015
784810^59913+4861959914Patrick De Geest04/2016
785010^59913-7412359913Patrick De Geest03/2016
7851t(199528)59890Robert Price01/2015
78522^198903-1790159876Enzo Doria05/2013
78539*10^59862-1959863Robert Price10/2017
7854gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
7855(3^125447+7)/259854Lelio R Paula04/2012
78565^85630+4^(85630-1)59853Robert Price03/2016
78572^198824-213559852Yves Minet06/2013
7858(124^28591-1)/12359851Richard Fischer10/2017
78592^198799-1611759845Enzo Doria04/2013
78607^70811+6^(70811+1)59843Robert Price07/2016
78612^198774-1594559837Enzo Doria04/2013
78622^198753-1587359831Enzo Doria04/2013
7863(31*2^198748-1)/4559829Lelio R Paula01/2014
78642^198725+6959823Lelio R Paula04/2011
7865(68*10^59821+31)/959822Robert Price10/2015
7866(37*25^42785+1867)/859812Curtis Bright05/2015
78673^125354+266059810Lelio R Paula10/2012
7868105^29591-10459810Norbert Schneider08/2013
78694*5^85565-359808Lelio R Paula09/2014
787013963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
7872125330^3+3^12533059798Anatoly F. Selevich06/2010
78712^198643-318959798Yves Minet10/2014
7873(13*10^59797+191)/359798Robert Price08/2017
7874(7*10^59796-1)/359797Erik Branger03/2014
78752^198595+15359784Lelio R Paula04/2011
7876(19*10^59766+161)/959767Robert Price07/2016
78772^198510-196559758Lelio R Paula06/2011
78782^198506-1907759757Enzo Doria05/2013
78792^198484-1600559750Enzo Doria04/2013
78802^198473-1682159747Enzo Doria05/2013
7881(2^198481-5)/2831159745Lelio R Paula02/2012
78822^198400-18959725Lelio R Paula04/2011
78832^198384-1283759720Enzo Doria10/2012
788442694!3-72959719Robert Price09/2014
78852^198320-1871759701Enzo Doria05/2013
788620^45881-118359693Enzo Doria03/2013
78872^198224-685559672Lelio R Paula05/2011
78882^198181-1910159659Enzo Doria05/2013
78895*10^59650+4159651Robert Price08/2017
78902^198149-11221359649Enzo Doria06/2014
78912^198138+7369959646Enzo Doria04/2016
78922^198129-5559643Lelio R Paula04/2011
78935^85318-1463659635Enzo Doria02/2013
7894(2^198119+47)/156093559634Lelio R Paula02/2012
78952^198090-1609759632Enzo Doria04/2013
78969*10^59617+8959618Robert Price11/2016
789742625!3+8159612Robert Price09/2014
78985^85277-8459607Lelio R Paula10/2012
7899(871*10^59599-7)/959601Robert Price11/2017
79002^197984-1824559600Enzo Doria05/2013
79012^197951-213759590Yves Minet06/2013
7902(38*10^59589+187)/959590Robert Price11/2017
790366^32749-65^3274959589Robert Price09/2013
79045*10^59586-359587Dmitry Domanov11/2010
7905(35*10^59584-197)/959585Robert Kinser10/2017
79062^197932-395959584Yves Minet04/2017
79072^197909-1896159577Enzo Doria05/2013
7908(3^124871+2)/4503159574Lelio R Paula04/2012
79092^197872+8159566Henri Lifchitz10/2005
79102^197873-1846959566Enzo Doria05/2013
7911(22*10^59558-31)/959559Robert Price04/2015
79132^197840-46559556Lelio R Paula05/2011
7912(31*2^197856-1)/388960559556Lelio R Paula01/2014
79142^197808-1780559547Enzo Doria05/2013
79152^197781-1790559539Enzo Doria05/2013
79162^197777-1747359537Enzo Doria05/2013
79176^76507-14959535Lelio R Paula10/2012
7919Phi(61456,109)59526Enzo Doria05/2012
791818^47420+2359526Lelio R Paula03/2013
7920(59^33613+1)/6059522Paul Bourdelais08/2017
79213^124747+9459520Lelio R Paula10/2012
792217^48370+1859517Lelio R Paula03/2013
792320^45740-152359510Enzo Doria03/2013
7924(47*10^59509+493)/959510Robert Price11/2017
7925(7*2^197642-1)/305159494Lelio R Paula01/2014
792618^47390-185359488Enzo Doria03/2013
7927(2^197581-7)/191559475Lelio R Paula02/2012
7928(24737*2^197559+1)/7759474Lelio R Paula06/2014
79292^197540-245959466Yves Minet07/2014
7930(44*10^59454+1)/959455Serge Batalov11/2010
79312^197494-1780559452Enzo Doria05/2013
79322^197482-1682159449Enzo Doria05/2013
79332^197485+7576759449Enzo Doria04/2016
7934(3*2^197483+1)/2559448Lelio R Paula07/2012
79352^197466-186835159444Enzo Doria04/2016
79362^197411-1778159427Enzo Doria05/2013
7937(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
79382^197392-11462959421Enzo Doria05/2015
79392^197355-15759410Lelio R Paula04/2011
79405^84992-8459407Lelio R Paula10/2012
79412*3^124504-559404Lelio R Paula04/2014
79422^197307-1916559396Enzo Doria05/2013
79432^197303+3276959395Lelio R Paula05/2011
79442*10^59394-6959395Robert Price07/2017
7945(53*10^59389+1)/959390Serge Batalov11/2010
79466^76316-3559386Lelio R Paula10/2012
79472^197259-292959381Yves Minet09/2014
7948lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
794917^48253-659373Lelio R Paula03/2013
79502^197156-1583759350Enzo Doria04/2013
79512^197149-1848159348Enzo Doria05/2013
79522^197142-1715759346Enzo Doria05/2013
7954(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
7953(8^65707-5^65707)/359339Robert Price12/2012
7955(2*14283^14283+1)/792549797559334David Broadhurst09/2010
79562^197012-11171959307Enzo Doria05/2014
79572^196975+51359296Lelio R Paula05/2011
7958(61*10^59294+119)/959295Robert Price09/2017
79594*10^59292+3959293Robert Price11/2017
79602^196960+9759291Lelio R Paula04/2011
79619^62116+8^(62116-1)59274Robert Price03/2016
79622^196900-9730559273Lelio R Paula09/2011
79635*6^76155+759261Lelio R Paula09/2014
796415^50385-1459258Wojciech Florek06/2006
7965(136777#-1)/882358147759254Donovan Johnson05/2006
7966(2^196744-3)*6-759227Gilbert Mozzo05/2016
7967(67607*2^196696+1)/359216Lelio R Paula05/2014
79682^196696-11296759212Enzo Doria06/2014
796920^45508-422359208Enzo Doria03/2013
7970gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
797114^51651-8159199Lelio R Paula03/2013
79722^196650-145159198Yves Minet08/2012
79732^196636-279779959194Enzo Doria04/2016
79741111*2^196610-55559189Henri Lifchitz04/2005
79753^124041+65859183Lelio R Paula10/2012
79762^196590-11179759180Enzo Doria05/2014
7977(10^59174-13)/359174Robert Price02/2017
7978(2*10^59174-113)/359174Robert Price09/2017
7979(9179*2^196533-1)/78359164Lelio R Paula04/2015
7980379*10^59152+959155Arkadiusz Wesolowski10/2011
7981(404*10^59149-53)/959151Robert Price11/2017
798213^53095+4059145Lelio R Paula03/2013
79832*F(282999)-159144Henri Lifchitz12/2009
79844*7^69984+359144Lelio R Paula09/2014
7985(5*10^59142+1)/359143Erik Branger12/2013
79862^196463+571159142Lelio R Paula10/2011
79872^196453-9730559139Lelio R Paula09/2011
7988(28*10^59135+53)/959136Serge Batalov11/2008
7989(28*10^59133+113)/359134Robert Price03/2016
79902^196434+759133Lelio R Paula04/2011
7991(8*10^59127-29)/359128Robert Price05/2016
79922^196414+25559127Lelio R Paula05/2011
79935^84586-9259124Lelio R Paula10/2012
79942^196388-1717759119Enzo Doria05/2013
79953^123890+2059111Lelio R Paula10/2012
79962^196355-102177759109Paul Bourdelais11/2012
799711^56754-141059104Enzo Doria11/2012
7998(7*2^196297-1)/120040759087Lelio R Paula01/2014
7999(16*10^59062-19)/359063Robert Price03/2016
800035^38249-122859060Enzo Doria03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 09 2017 09:21 (Time in France)

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