PRP Records

Probable Primes Top 10000

(172751 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 ?
72512^200011-11207560210Enzo Doria05/2014
72522^200002+7453960207Enzo Doria04/2016
7253(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
72542^199872+9360168Donovan Johnson06/2008
72556^77321+7760168Lelio R Paula04/2013
7256(86*10^60165-77)/960166Robert Price05/2016
7257(2^199868+78557)/2337360162Lelio R Paula05/2012
72587^71180+8260155Lelio R Paula04/2013
72592^199814-11229560151Enzo Doria06/2014
726042964!3-8160135Robert Price09/2014
72612^199709-5160119Lelio R Paula05/2011
72622^199700-11162360116Enzo Doria05/2014
7263(15185*2^199681-1)/15960112Lelio R Paula04/2015
72642^199672+253360108Henri Lifchitz09/2004
726520^46198-1160105Lelio R Paula04/2013
72662^199657+9325760103Yves Minet03/2010
72673^125967-11060102Lelio R Paula10/2012
72682^199654-1881360102Enzo Doria05/2013
7269(29*10^60100+19)/360101Robert Price01/2017
7270129^28468+28468^12960085Serge Batalov05/2014
72712^199572-1587360078Enzo Doria04/2013
72729*2^199559+760075Lelio R Paula03/2014
72732^199527-11191960064Enzo Doria05/2014
72742^199522+8287560063Lelio R Paula10/2012
72755^85928-7260062Lelio R Paula10/2012
727639^37749+3860062Norbert Schneider05/2014
72776^77182-14360060Lelio R Paula10/2012
72782^199502-214560057Lelio R Paula06/2011
72792^199493+425760054Lelio R Paula06/2011
72802^199488+4075560052Lelio R Paula06/2011
7281(2^199451+9)/2561960037Lelio R Paula02/2012
72822^199425-6160033Lelio R Paula05/2011
7283(85*10^60026+23)/960027Robert Price11/2015
728465^33107+6260021Lelio R Paula01/2016
72852^199362-121560014Lelio R Paula06/2011
72862^199362-11163360014Enzo Doria05/2014
72871537^18832+18832^153760012Serge Batalov05/2014
72882^199324-1743360003Enzo Doria05/2013
728910^60000+20433160001Milton L. Brown04/2006
729010^60000+8712960001Milton L. Brown04/2006
729110^59999+6519760000Patrick De Geest04/2005
730910^60000-3252960000Patrick De Geest08/2009
7305(10^60000+2249)/960000Makoto Morimoto09/2016
7306((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
7307(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
7308(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
7292(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
7293(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
7294(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
7295(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
7296(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
7297(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
7298(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
7299(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
7300(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
7301(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
7302(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
7303(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
7304(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
731110^59999-51626759999Patrick De Geest06/2009
731220^46116-4159999Lelio R Paula03/2013
7310(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
7313(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
73146^77100-5559996Lelio R Paula10/2012
7316(19*2^199274+1)/16159987Lelio R Paula07/2012
7315(23^44053+1)/2459987Robert Price06/2013
73179^62848+6^62848-2^6284859973Mike Oakes08/2010
731815852^6061+6061^1585259961Hans Havermann08/2016
731919^46880-2059948Lelio R Paula03/2013
73202^199107-1773759938Enzo Doria05/2013
7321(13*10^59928+83)/359929Robert Price09/2016
732310^59913+10893143159914Marisa Kirisame02/2015
732210^59913+4861959914Patrick De Geest04/2016
732410^59913-7412359913Patrick De Geest03/2016
7325t(199528)59890Robert Price01/2015
73262^198903-1790159876Enzo Doria05/2013
7327gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
7328(3^125447+7)/259854Lelio R Paula04/2012
73295^85630+4^(85630-1)59853Robert Price03/2016
73302^198824-213559852Yves Minet06/2013
73312^198799-1611759845Enzo Doria04/2013
73327^70811+6^(70811+1)59843Robert Price07/2016
73332^198774-1594559837Enzo Doria04/2013
73342^198753-1587359831Enzo Doria04/2013
7335(31*2^198748-1)/4559829Lelio R Paula01/2014
73362^198725+6959823Lelio R Paula04/2011
7337(68*10^59821+31)/959822Robert Price10/2015
7338(37*25^42785+1867)/859812Curtis Bright05/2015
73393^125354+266059810Lelio R Paula10/2012
7340105^29591-10459810Norbert Schneider08/2013
73414*5^85565-359808Lelio R Paula09/2014
734213963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
7344125330^3+3^12533059798Anatoly F. Selevich06/2010
73432^198643-318959798Yves Minet10/2014
7345(7*10^59796-1)/359797Erik Branger03/2014
73462^198595+15359784Lelio R Paula04/2011
7347(19*10^59766+161)/959767Robert Price07/2016
73482^198510-196559758Lelio R Paula06/2011
73492^198506-1907759757Enzo Doria05/2013
73502^198484-1600559750Enzo Doria04/2013
73512^198473-1682159747Enzo Doria05/2013
7352(2^198481-5)/2831159745Lelio R Paula02/2012
73532^198400-18959725Lelio R Paula04/2011
73542^198384-1283759720Enzo Doria10/2012
735542694!3-72959719Robert Price09/2014
73562^198320-1871759701Enzo Doria05/2013
735720^45881-118359693Enzo Doria03/2013
73582^198224-685559672Lelio R Paula05/2011
73592^198181-1910159659Enzo Doria05/2013
73602^198149-11221359649Enzo Doria06/2014
73612^198138+7369959646Enzo Doria04/2016
73622^198129-5559643Lelio R Paula04/2011
73635^85318-1463659635Enzo Doria02/2013
7364(2^198119+47)/156093559634Lelio R Paula02/2012
73652^198090-1609759632Enzo Doria04/2013
73669*10^59617+8959618Robert Price11/2016
736742625!3+8159612Robert Price09/2014
73685^85277-8459607Lelio R Paula10/2012
73692^197984-1824559600Enzo Doria05/2013
73702^197951-213759590Yves Minet06/2013
737166^32749-65^3274959589Robert Price09/2013
73725*10^59586-359587Dmitry Domanov11/2010
73732^197909-1896159577Enzo Doria05/2013
7374(3^124871+2)/4503159574Lelio R Paula04/2012
73752^197872+8159566Henri Lifchitz10/2005
73762^197873-1846959566Enzo Doria05/2013
7377(22*10^59558-31)/959559Robert Price04/2015
73792^197840-46559556Lelio R Paula05/2011
7378(31*2^197856-1)/388960559556Lelio R Paula01/2014
73802^197808-1780559547Enzo Doria05/2013
73812^197781-1790559539Enzo Doria05/2013
73822^197777-1747359537Enzo Doria05/2013
73836^76507-14959535Lelio R Paula10/2012
7385Phi(61456,109)59526Enzo Doria05/2012
738418^47420+2359526Lelio R Paula03/2013
73863^124747+9459520Lelio R Paula10/2012
738717^48370+1859517Lelio R Paula03/2013
738820^45740-152359510Enzo Doria03/2013
7389(7*2^197642-1)/305159494Lelio R Paula01/2014
739018^47390-185359488Enzo Doria03/2013
7391(2^197581-7)/191559475Lelio R Paula02/2012
7392(24737*2^197559+1)/7759474Lelio R Paula06/2014
73932^197540-245959466Yves Minet07/2014
7394(44*10^59454+1)/959455Serge Batalov11/2010
73952^197494-1780559452Enzo Doria05/2013
73962^197482-1682159449Enzo Doria05/2013
73972^197485+7576759449Enzo Doria04/2016
7398(3*2^197483+1)/2559448Lelio R Paula07/2012
73992^197466-186835159444Enzo Doria04/2016
74002^197411-1778159427Enzo Doria05/2013
7402(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
74012^197392-11462959421Enzo Doria05/2015
74032^197355-15759410Lelio R Paula04/2011
74045^84992-8459407Lelio R Paula10/2012
74052*3^124504-559404Lelio R Paula04/2014
74062^197307-1916559396Enzo Doria05/2013
74072^197303+3276959395Lelio R Paula05/2011
7408(53*10^59389+1)/959390Serge Batalov11/2010
74096^76316-3559386Lelio R Paula10/2012
74102^197259-292959381Yves Minet09/2014
7411lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
741217^48253-659373Lelio R Paula03/2013
74132^197156-1583759350Enzo Doria04/2013
74142^197149-1848159348Enzo Doria05/2013
74152^197142-1715759346Enzo Doria05/2013
7417(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
7416(8^65707-5^65707)/359339Robert Price12/2012
7418(2*14283^14283+1)/792549797559334David Broadhurst09/2010
74192^197012-11171959307Enzo Doria05/2014
74202^196975+51359296Lelio R Paula05/2011
74212^196960+9759291Lelio R Paula04/2011
74229^62116+8^(62116-1)59274Robert Price03/2016
74232^196900-9730559273Lelio R Paula09/2011
74245*6^76155+759261Lelio R Paula09/2014
742515^50385-1459258Wojciech Florek06/2006
7426(136777#-1)/882358147759254Donovan Johnson05/2006
7427(2^196744-3)*6-759227Gilbert Mozzo05/2016
7428(67607*2^196696+1)/359216Lelio R Paula05/2014
74292^196696-11296759212Enzo Doria06/2014
743020^45508-422359208Enzo Doria03/2013
7431gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
743214^51651-8159199Lelio R Paula03/2013
74332^196650-145159198Yves Minet08/2012
74342^196636-279779959194Enzo Doria04/2016
74351111*2^196610-55559189Henri Lifchitz04/2005
74363^124041+65859183Lelio R Paula10/2012
74372^196590-11179759180Enzo Doria05/2014
7438(10^59174-13)/359174Robert Price02/2017
7439(9179*2^196533-1)/78359164Lelio R Paula04/2015
7440379*10^59152+959155Arkadiusz Wesolowski10/2011
744113^53095+4059145Lelio R Paula03/2013
74432*F(282999)-159144Henri Lifchitz12/2009
74424*7^69984+359144Lelio R Paula09/2014
7444(5*10^59142+1)/359143Erik Branger12/2013
74452^196463+571159142Lelio R Paula10/2011
74462^196453-9730559139Lelio R Paula09/2011
7447(28*10^59135+53)/959136Serge Batalov11/2008
7448(28*10^59133+113)/359134Robert Price03/2016
74492^196434+759133Lelio R Paula04/2011
7450(8*10^59127-29)/359128Robert Price05/2016
74512^196414+25559127Lelio R Paula05/2011
74525^84586-9259124Lelio R Paula10/2012
74532^196388-1717759119Enzo Doria05/2013
74543^123890+2059111Lelio R Paula10/2012
74552^196355-102177759109Paul Bourdelais11/2012
745611^56754-141059104Enzo Doria11/2012
7457(7*2^196297-1)/120040759087Lelio R Paula01/2014
7458(16*10^59062-19)/359063Robert Price03/2016
745935^38249-122859060Enzo Doria03/2013
74605^84475-1859046Lelio R Paula10/2012
74612^196123-1770159039Enzo Doria05/2013
746212^54702-3159034Lelio R Paula03/2013
74632^196101-17559033Lelio R Paula04/2011
74642^196085+577559028Lelio R Paula05/2011
74652^196034+1171559013Lelio R Paula05/2011
74662^196018-1848559008Enzo Doria05/2013
74672^195984-216358998Yves Minet08/2013
74683^123645-1658994Lelio R Paula10/2012
746939^37078-3858994Norbert Schneider05/2014
74702^195958-1685358990Enzo Doria05/2013
74712^195930-307158981Yves Minet10/2014
74722^195924+51358980Lelio R Paula05/2011
74732^195863+15558961Lelio R Paula04/2011
7474(28*10^58956+113)/358957Robert Price03/2016
747511^56612-930058956Enzo Doria02/2013
74762^195833-1717358952Enzo Doria05/2013
7477(27*2^195833-1)/5358952Lelio R Paula01/2014
7478(13*2^195821-1)/12242558945Lelio R Paula01/2014
7479139^27504-13858942Norbert Schneider10/2015
74803^123495+4458923Lelio R Paula10/2012
74812^195737-1856558923Enzo Doria05/2013
748214^51407+4758920Lelio R Paula03/2013
74832^195691-9958909Lelio R Paula04/2011
74842^195667-185982758902Enzo Doria04/2016
74852^195642+7549958895Enzo Doria04/2016
74868*6^75678+558890Lelio R Paula09/2014
74872^195618+7318958887Enzo Doria04/2016
7488(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
7489t(197953)58881Robert Price12/2014
74902^195581-1610558876Enzo Doria04/2013
7491(8*10^58872+67)/358873Robert Price01/2017
74927*2^195542-558865Lelio R Paula03/2014
74932*10^58861+9^5886158862Mike Oakes04/2011
749411^56513-162058853Enzo Doria11/2012
74952^195496+16558851Lelio R Paula04/2011
74965^84187+6658845Lelio R Paula10/2012
7497(28*10^58843-43)/358844Robert Price04/2016
74982^195462-1756558840Enzo Doria05/2013
74992^195435+5927358832Yves Minet01/2011
75002^195424-1860558829Enzo Doria05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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