PRP Records

Probable Primes Top 10000

(173006 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 ?
72512^201426-1609760636Enzo Doria04/2013
7252(17*10^60631-11)/360632Robert Price07/2015
72536^77916-7760631Lelio R Paula04/2013
7254(27*2^201410-1)/49160630Lelio R Paula01/2014
72555^86727+9860620Lelio R Paula04/2013
725617^49266-2660620Lelio R Paula05/2013
725720^46589-3360614Lelio R Paula05/2013
72586^77889+6560610Lelio R Paula04/2013
7259139901#+14838760595Nicolas PALAU09/2016
72602^201285-11172360593Enzo Doria05/2014
726146199*2^201268+12964760593Paul Vanderveen11/2016
72633^126991-10060591Lelio R Paula04/2013
72622^201278-11162360591Enzo Doria05/2014
72645^86682-1600460589Enzo Doria05/2014
7265(58*10^60579+221)/960580Robert Price02/2017
72669*2^201231-560578Lelio R Paula04/2014
7267(78557*2^201207+1)/1306760571Lelio R Paula06/2014
72682^201186-6694560564Lelio R Paula09/2011
72692^201186-9439560564Lelio R Paula09/2011
727065^33403+3260557Lelio R Paula01/2016
7271103^30079+10260545Norbert Schneider10/2016
7272(1000159^10091+1)/100016060541Faysal YAtim08/2008
72732^201098-1771760537Enzo Doria05/2013
7274(3^126881+8)/482960534Lelio R Paula03/2012
72752^201074+7504960530Enzo Doria04/2016
727611^58111-129060517Enzo Doria11/2012
7277(509203*2^201012-1)/960516Lelio R Paula04/2015
72782^200911+571160481Lelio R Paula10/2011
7279(2^200912-3)/2360480Lelio R Paula03/2012
728018^48179-17^4817960478Jean-Louis Charton12/2010
728238^38281-37^3828160476Robert Price09/2012
72814*7^71560-360476Lelio R Paula09/2014
7283(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7284lucasV(1,2,401712)+260464Mike Oakes01/2017
72852^200833-1849360457Enzo Doria05/2013
728620^46465-504360453Enzo Doria03/2013
72872^200810-1825760450Enzo Doria05/2013
72885^86466-1433660438Enzo Doria02/2013
7289Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7290(29*2^200703-1)/23160417Lelio R Paula01/2014
72912^200682-101683160412Paul Bourdelais11/2012
72922^200617-1788160392Enzo Doria05/2013
7293(25^43201+1)/2660391Robert Price06/2013
72952^200609-13360390Lelio R Paula08/2011
72942^200608-1283760390Enzo Doria10/2012
72962^200607-1712160389Enzo Doria05/2013
729711^57975-162060375Enzo Doria11/2012
7298(9913*2^200538-1)/380160369Lelio R Paula04/2015
72995^86342+6460351Lelio R Paula04/2013
7300(14*10^60346-23)/960347Robert Price04/2015
73012^200457-829560344Lelio R Paula09/2011
73026^77546+11360343Lelio R Paula04/2013
730437^38461-36^3846160315Robert Price06/2012
73032^200361-1759360315Enzo Doria05/2013
730510103^15059-10660304Enzo Doria07/2012
73062^200301-1740160297Enzo Doria05/2013
7307(37*10^60290+71)/960291Robert Price04/2015
73082^200266-9439560287Lelio R Paula09/2011
73092^200261-11161360285Enzo Doria05/2014
731046^36238-4560256Norbert Schneider07/2014
731113^54091+9460255Lelio R Paula05/2013
7312311^24171-15460253Enzo Doria07/2012
73132^200120-8108960243Paul Bourdelais01/2012
73143^126262+868060243Lelio R Paula04/2013
731543031!3-5904960239Robert Price12/2015
73162^200100-11126960237Enzo Doria05/2014
7317(29*2^200069-1)/537360225Lelio R Paula01/2014
731820^46283-192360216Enzo Doria03/2013
73192^200011-11207560210Enzo Doria05/2014
73202^200002+7453960207Enzo Doria04/2016
7321(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
73222^199872+9360168Donovan Johnson06/2008
73236^77321+7760168Lelio R Paula04/2013
7324(86*10^60165-77)/960166Robert Price05/2016
7325(2^199868+78557)/2337360162Lelio R Paula05/2012
73267^71180+8260155Lelio R Paula04/2013
73272^199814-11229560151Enzo Doria06/2014
732842964!3-8160135Robert Price09/2014
73292^199709-5160119Lelio R Paula05/2011
73302^199700-11162360116Enzo Doria05/2014
7331(15185*2^199681-1)/15960112Lelio R Paula04/2015
73322^199672+253360108Henri Lifchitz09/2004
733320^46198-1160105Lelio R Paula04/2013
73342^199657+9325760103Yves Minet03/2010
73353^125967-11060102Lelio R Paula10/2012
73362^199654-1881360102Enzo Doria05/2013
7337(29*10^60100+19)/360101Robert Price01/2017
7338129^28468+28468^12960085Serge Batalov05/2014
73392^199572-1587360078Enzo Doria04/2013
73409*2^199559+760075Lelio R Paula03/2014
73412^199527-11191960064Enzo Doria05/2014
73422^199522+8287560063Lelio R Paula10/2012
73435^85928-7260062Lelio R Paula10/2012
734439^37749+3860062Norbert Schneider05/2014
73456^77182-14360060Lelio R Paula10/2012
73462^199502-214560057Lelio R Paula06/2011
73472^199493+425760054Lelio R Paula06/2011
73482^199488+4075560052Lelio R Paula06/2011
7349(2^199451+9)/2561960037Lelio R Paula02/2012
73502^199425-6160033Lelio R Paula05/2011
7351(85*10^60026+23)/960027Robert Price11/2015
735265^33107+6260021Lelio R Paula01/2016
73542^199362-121560014Lelio R Paula06/2011
73532^199362-11163360014Enzo Doria05/2014
73551537^18832+18832^153760012Serge Batalov05/2014
73562^199324-1743360003Enzo Doria05/2013
735710^60000+20433160001Milton L. Brown04/2006
735810^60000+8712960001Milton L. Brown04/2006
735910^59999+6519760000Patrick De Geest04/2005
737710^60000-3252960000Patrick De Geest08/2009
7360(10^60000+2249)/960000Makoto Morimoto09/2016
7361((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
7362(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
7363(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
7364(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
7365(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
7366(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
7367(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
7368(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
7369(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
7370(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
7371(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
7372(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
7373(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
7374(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
7375(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
7376(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
738110^59999-51626759999Patrick De Geest06/2009
737920^46116-4159999Lelio R Paula03/2013
7380(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
7378(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
73826^77100-5559996Lelio R Paula10/2012
7384(19*2^199274+1)/16159987Lelio R Paula07/2012
7383(23^44053+1)/2459987Robert Price06/2013
73859^62848+6^62848-2^6284859973Mike Oakes08/2010
738615852^6061+6061^1585259961Hans Havermann08/2016
738719^46880-2059948Lelio R Paula03/2013
73882^199107-1773759938Enzo Doria05/2013
7389(13*10^59928+83)/359929Robert Price09/2016
739110^59913+10893143159914Marisa Kirisame02/2015
739010^59913+4861959914Patrick De Geest04/2016
739210^59913-7412359913Patrick De Geest03/2016
7393t(199528)59890Robert Price01/2015
73942^198903-1790159876Enzo Doria05/2013
7395gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
7396(3^125447+7)/259854Lelio R Paula04/2012
73975^85630+4^(85630-1)59853Robert Price03/2016
73982^198824-213559852Yves Minet06/2013
73992^198799-1611759845Enzo Doria04/2013
74007^70811+6^(70811+1)59843Robert Price07/2016
74012^198774-1594559837Enzo Doria04/2013
74022^198753-1587359831Enzo Doria04/2013
7403(31*2^198748-1)/4559829Lelio R Paula01/2014
74042^198725+6959823Lelio R Paula04/2011
7405(68*10^59821+31)/959822Robert Price10/2015
7406(37*25^42785+1867)/859812Curtis Bright05/2015
74083^125354+266059810Lelio R Paula10/2012
7407105^29591-10459810Norbert Schneider08/2013
74094*5^85565-359808Lelio R Paula09/2014
741013963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
7412125330^3+3^12533059798Anatoly F. Selevich06/2010
74112^198643-318959798Yves Minet10/2014
7413(7*10^59796-1)/359797Erik Branger03/2014
74142^198595+15359784Lelio R Paula04/2011
7415(19*10^59766+161)/959767Robert Price07/2016
74162^198510-196559758Lelio R Paula06/2011
74172^198506-1907759757Enzo Doria05/2013
74182^198484-1600559750Enzo Doria04/2013
74192^198473-1682159747Enzo Doria05/2013
7420(2^198481-5)/2831159745Lelio R Paula02/2012
74212^198400-18959725Lelio R Paula04/2011
74222^198384-1283759720Enzo Doria10/2012
742342694!3-72959719Robert Price09/2014
74242^198320-1871759701Enzo Doria05/2013
742520^45881-118359693Enzo Doria03/2013
74262^198224-685559672Lelio R Paula05/2011
74272^198181-1910159659Enzo Doria05/2013
74282^198149-11221359649Enzo Doria06/2014
74292^198138+7369959646Enzo Doria04/2016
74302^198129-5559643Lelio R Paula04/2011
74315^85318-1463659635Enzo Doria02/2013
7432(2^198119+47)/156093559634Lelio R Paula02/2012
74332^198090-1609759632Enzo Doria04/2013
74349*10^59617+8959618Robert Price11/2016
743542625!3+8159612Robert Price09/2014
74365^85277-8459607Lelio R Paula10/2012
74372^197984-1824559600Enzo Doria05/2013
74382^197951-213759590Yves Minet06/2013
743966^32749-65^3274959589Robert Price09/2013
74405*10^59586-359587Dmitry Domanov11/2010
74412^197932-395959584Yves Minet04/2017
74422^197909-1896159577Enzo Doria05/2013
7443(3^124871+2)/4503159574Lelio R Paula04/2012
74442^197872+8159566Henri Lifchitz10/2005
74452^197873-1846959566Enzo Doria05/2013
7446(22*10^59558-31)/959559Robert Price04/2015
74482^197840-46559556Lelio R Paula05/2011
7447(31*2^197856-1)/388960559556Lelio R Paula01/2014
74492^197808-1780559547Enzo Doria05/2013
74502^197781-1790559539Enzo Doria05/2013
74512^197777-1747359537Enzo Doria05/2013
74526^76507-14959535Lelio R Paula10/2012
7454Phi(61456,109)59526Enzo Doria05/2012
745318^47420+2359526Lelio R Paula03/2013
74553^124747+9459520Lelio R Paula10/2012
745617^48370+1859517Lelio R Paula03/2013
745720^45740-152359510Enzo Doria03/2013
7458(7*2^197642-1)/305159494Lelio R Paula01/2014
745918^47390-185359488Enzo Doria03/2013
7460(2^197581-7)/191559475Lelio R Paula02/2012
7461(24737*2^197559+1)/7759474Lelio R Paula06/2014
74622^197540-245959466Yves Minet07/2014
7463(44*10^59454+1)/959455Serge Batalov11/2010
74642^197494-1780559452Enzo Doria05/2013
74652^197482-1682159449Enzo Doria05/2013
74662^197485+7576759449Enzo Doria04/2016
7467(3*2^197483+1)/2559448Lelio R Paula07/2012
74682^197466-186835159444Enzo Doria04/2016
74692^197411-1778159427Enzo Doria05/2013
7470(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
74712^197392-11462959421Enzo Doria05/2015
74722^197355-15759410Lelio R Paula04/2011
74735^84992-8459407Lelio R Paula10/2012
74742*3^124504-559404Lelio R Paula04/2014
74752^197307-1916559396Enzo Doria05/2013
74762^197303+3276959395Lelio R Paula05/2011
7477(53*10^59389+1)/959390Serge Batalov11/2010
74786^76316-3559386Lelio R Paula10/2012
74792^197259-292959381Yves Minet09/2014
7480lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
748117^48253-659373Lelio R Paula03/2013
74822^197156-1583759350Enzo Doria04/2013
74832^197149-1848159348Enzo Doria05/2013
74842^197142-1715759346Enzo Doria05/2013
7486(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
7485(8^65707-5^65707)/359339Robert Price12/2012
7487(2*14283^14283+1)/792549797559334David Broadhurst09/2010
74882^197012-11171959307Enzo Doria05/2014
74892^196975+51359296Lelio R Paula05/2011
74902^196960+9759291Lelio R Paula04/2011
74919^62116+8^(62116-1)59274Robert Price03/2016
74922^196900-9730559273Lelio R Paula09/2011
74935*6^76155+759261Lelio R Paula09/2014
749415^50385-1459258Wojciech Florek06/2006
7495(136777#-1)/882358147759254Donovan Johnson05/2006
7496(2^196744-3)*6-759227Gilbert Mozzo05/2016
7497(67607*2^196696+1)/359216Lelio R Paula05/2014
74982^196696-11296759212Enzo Doria06/2014
749920^45508-422359208Enzo Doria03/2013
7500gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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