PRP Records

Probable Primes Top 10000

(252675 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 ?
8501(10^60703+3^60703)/1360702Robert Price01/2013
85022^201622-11281760695Enzo Doria06/2014
85032^201620-1717760694Enzo Doria05/2013
8504(2^201615-3)*6-760693Gilbert Mozzo05/2016
85052^201609-4978960691Henri Lifchitz03/2005
85062^201582-1906160683Enzo Doria05/2013
850743316!3+2760679Robert Price09/2014
8508(509203*2^201564-1)/506760679Lelio R Paula04/2015
85092^201560+10560676Lelio R Paula08/2011
8510(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
85112^201545-1802160672Enzo Doria05/2013
85122^201543+1171560671Lelio R Paula09/2011
85132^201512-11175560662Enzo Doria05/2014
8514p(13013)#/2+6460662Robert Price03/2017
851511^58248+1660660Lelio R Paula05/2013
85162^201496-2760657Lelio R Paula08/2011
85175*10^60655+5760656Robert Price11/2017
8518(7*10^60643+197)/360644Robert Price07/2017
85192^201426-1609760636Enzo Doria04/2013
8520(17*10^60631-11)/360632Robert Price07/2015
85216^77916-7760631Lelio R Paula04/2013
8522(27*2^201410-1)/49160630Lelio R Paula01/2014
85235^86727+9860620Lelio R Paula04/2013
852417^49266-2660620Lelio R Paula05/2013
852520^46589-3360614Lelio R Paula05/2013
85266^77889+6560610Lelio R Paula04/2013
8527139901#+14838760595Nicolas PALAU09/2016
85282^201285-11172360593Enzo Doria05/2014
852946199*2^201268+12964760593Paul Vanderveen11/2016
85303^126991-10060591Lelio R Paula04/2013
85312^201278-11162360591Enzo Doria05/2014
85325^86682-1600460589Enzo Doria05/2014
8533(865*10^60583-1)/960585Robert Price11/2017
8534(58*10^60579+221)/960580Robert Price02/2017
85359*2^201231-560578Lelio R Paula04/2014
85364*10^60572-8960573Robert Price08/2017
8537(78557*2^201207+1)/1306760571Lelio R Paula06/2014
85382^201186-6694560564Lelio R Paula09/2011
85392^201186-9439560564Lelio R Paula09/2011
854065^33403+3260557Lelio R Paula01/2016
8541103^30079+10260545Norbert Schneider10/2016
8542(1000159^10091+1)/100016060541Faysal YAtim08/2008
85432^201098-1771760537Enzo Doria05/2013
8544(3^126881+8)/482960534Lelio R Paula03/2012
85452^201074+7504960530Enzo Doria04/2016
854611^58111-129060517Enzo Doria11/2012
8547(509203*2^201012-1)/960516Lelio R Paula04/2015
854814447^14544-14544^1444760500Norbert Schneider12/2018
85492^200911+571160481Lelio R Paula10/2011
8550(2^200912-3)/2360480Lelio R Paula03/2012
855118^48179-17^4817960478Jean-Louis Charton12/2010
855238^38281-37^3828160476Robert Price09/2012
85534*7^71560-360476Lelio R Paula09/2014
8554(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
8555lucasV(1,2,401712)+260464Mike Oakes01/2017
85562^200833-1849360457Enzo Doria05/2013
855720^46465-504360453Enzo Doria03/2013
85582^200810-1825760450Enzo Doria05/2013
8559((2)^(2*100400-1)+(2)^(100400-1)+1)+2667260447Faysal YAtim04/2018
85605^86466-1433660438Enzo Doria02/2013
8561Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
8562(29*2^200703-1)/23160417Lelio R Paula01/2014
85632^200682-101683160412Paul Bourdelais11/2012
85642^200617-1788160392Enzo Doria05/2013
8565(25^43201+1)/2660391Robert Price06/2013
85672^200609-13360390Lelio R Paula08/2011
85662^200608-1283760390Enzo Doria10/2012
85682^200607-1712160389Enzo Doria05/2013
856911^57975-162060375Enzo Doria11/2012
8570(9913*2^200538-1)/380160369Lelio R Paula04/2015
85715^86342+6460351Lelio R Paula04/2013
857213088^14659-14659^1308860350Norbert Schneider03/2019
8573(14*10^60346-23)/960347Robert Price04/2015
85742^200457-829560344Lelio R Paula09/2011
85756^77546+11360343Lelio R Paula04/2013
857737^38461-36^3846160315Robert Price06/2012
85762^200361-1759360315Enzo Doria05/2013
857810103^15059-10660304Enzo Doria07/2012
85792^200301-1740160297Enzo Doria05/2013
8580(37*10^60290+71)/960291Robert Price04/2015
85812^200266-9439560287Lelio R Paula09/2011
85822^200261-11161360285Enzo Doria05/2014
858313717^14570-14570^1371760280Norbert Schneider01/2019
85842^200191-459760264Yves Minet03/2019
858546^36238-4560256Norbert Schneider07/2014
858613^54091+9460255Lelio R Paula05/2013
8587311^24171-15460253Enzo Doria07/2012
85882^200120-8108960243Paul Bourdelais01/2012
85893^126262+868060243Lelio R Paula04/2013
859043031!3-5904960239Robert Price12/2015
85912^200100-11126960237Enzo Doria05/2014
8592(29*2^200069-1)/537360225Lelio R Paula01/2014
859320^46283-192360216Enzo Doria03/2013
85942^200011-11207560210Enzo Doria05/2014
85952^200002+7453960207Enzo Doria04/2016
8596(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
8597(28*10^60180+149)/360181Robert Price10/2017
85992^199872+9360168Donovan Johnson06/2008
85986^77321+7760168Lelio R Paula04/2013
8600(86*10^60165-77)/960166Robert Price05/2016
8601(2^199868+78557)/2337360162Lelio R Paula05/2012
86027^71180+8260155Lelio R Paula04/2013
86042^199814-11229560151Enzo Doria06/2014
8603(51^35227-1)/5060151Paul Bourdelais08/2017
860542964!3-8160135Robert Price09/2014
86062^199709-5160119Lelio R Paula05/2011
86072^199700-11162360116Enzo Doria05/2014
8608(15185*2^199681-1)/15960112Lelio R Paula04/2015
86092^199672+253360108Henri Lifchitz09/2004
861020^46198-1160105Lelio R Paula04/2013
86112^199657+9325760103Yves Minet03/2010
86123^125967-11060102Lelio R Paula10/2012
86132^199654-1881360102Enzo Doria05/2013
8614(29*10^60100+19)/360101Robert Price01/2017
86152^199615-2*199615+160091Robert Price04/2018
8616129^28468+28468^12960085Serge Batalov05/2014
86172^199572-1587360078Enzo Doria04/2013
86189*2^199559+760075Lelio R Paula03/2014
86192^199527-11191960064Enzo Doria05/2014
86202^199522+8287560063Lelio R Paula10/2012
86215^85928-7260062Lelio R Paula10/2012
862239^37749+3860062Norbert Schneider05/2014
86236^77182-14360060Lelio R Paula10/2012
86242^199502-214560057Lelio R Paula06/2011
86252^199493+425760054Lelio R Paula06/2011
86262^199488+4075560052Lelio R Paula06/2011
8627(2^199451+9)/2561960037Lelio R Paula02/2012
86282^199425-6160033Lelio R Paula05/2011
8629(85*10^60026+23)/960027Robert Price11/2015
863065^33107+6260021Lelio R Paula01/2016
86322^199362-121560014Lelio R Paula06/2011
86312^199362-11163360014Enzo Doria05/2014
86331537^18832+18832^153760012Serge Batalov05/2014
86342^199324-1743360003Enzo Doria05/2013
863510^60000+20433160001Milton L. Brown04/2006
863610^60000+8712960001Milton L. Brown04/2006
8637143^27838-260001Lelio R Paula10/2017
865110^59999+6519760000Patrick De Geest04/2005
865210^60000-3252960000Patrick De Geest08/2009
8653(10^60000+2249)/960000Makoto Morimoto09/2016
8654((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
8655(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
8656(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
8638(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
8639(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
8640(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
8641(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
8642(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
8643(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
8644(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
8645(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
8646(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
8647(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
8648(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
8649(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
8650(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
866010^59999-51626759999Patrick De Geest06/2009
865920^46116-4159999Lelio R Paula03/2013
8657(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
8658(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
86616^77100-5559996Lelio R Paula10/2012
8663(19*2^199274+1)/16159987Lelio R Paula07/2012
8662(23^44053+1)/2459987Robert Price06/2013
86649^62848+6^62848-2^6284859973Mike Oakes08/2010
866515852^6061+6061^1585259961Hans Havermann08/2016
866619^46880-2059948Lelio R Paula03/2013
86672^199107-1773759938Enzo Doria05/2013
8668(13*10^59928+83)/359929Robert Price09/2016
866910^59913+10893143159914Marisa Kirisame02/2015
867010^59913+4861959914Patrick De Geest04/2016
867110^59913-7412359913Patrick De Geest03/2016
8672t(199528)59890Robert Price01/2015
86732^198903-1790159876Enzo Doria05/2013
86749*10^59862-1959863Robert Price10/2017
8675gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
8676(3^125447+7)/259854Lelio R Paula04/2012
86775^85630+4^(85630-1)59853Robert Price03/2016
86782^198824-213559852Yves Minet06/2013
8679(124^28591-1)/12359851Richard Fischer10/2017
86802^198799-1611759845Enzo Doria04/2013
86817^70811+6^(70811+1)59843Robert Price07/2016
86822^198774-1594559837Enzo Doria04/2013
86832^198753-1587359831Enzo Doria04/2013
8684(31*2^198748-1)/4559829Lelio R Paula01/2014
86852^198725+6959823Lelio R Paula04/2011
8686(68*10^59821+31)/959822Robert Price10/2015
8687(37*25^42785+1867)/859812Curtis Bright05/2015
86893^125354+266059810Lelio R Paula10/2012
8688105^29591-10459810Norbert Schneider08/2013
86904*5^85565-359808Lelio R Paula09/2014
869113963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
8693125330^3+3^12533059798Anatoly F. Selevich06/2010
86922^198643-318959798Yves Minet10/2014
8694(13*10^59797+191)/359798Robert Price08/2017
8695(7*10^59796-1)/359797Erik Branger03/2014
86962^198595+15359784Lelio R Paula04/2011
8697(19*10^59766+161)/959767Robert Price07/2016
86982^198510-196559758Lelio R Paula06/2011
86992^198506-1907759757Enzo Doria05/2013
87002^198484-1600559750Enzo Doria04/2013
87012^198473-1682159747Enzo Doria05/2013
8702(2^198481-5)/2831159745Lelio R Paula02/2012
87032^198400-18959725Lelio R Paula04/2011
87042^198384-1283759720Enzo Doria10/2012
870542694!3-72959719Robert Price09/2014
87062^198320-1871759701Enzo Doria05/2013
870720^45881-118359693Enzo Doria03/2013
87082^198224-685559672Lelio R Paula05/2011
87092^198181-1910159659Enzo Doria05/2013
87105*10^59650+4159651Robert Price08/2017
87112^198149-11221359649Enzo Doria06/2014
87122^198138+7369959646Enzo Doria04/2016
87132^198129-5559643Lelio R Paula04/2011
87145^85318-1463659635Enzo Doria02/2013
8715(2^198119+47)/156093559634Lelio R Paula02/2012
87162^198090-1609759632Enzo Doria04/2013
87179*10^59617+8959618Robert Price11/2016
871842625!3+8159612Robert Price09/2014
87195^85277-8459607Lelio R Paula10/2012
8720(871*10^59599-7)/959601Robert Price11/2017
87212^197984-1824559600Enzo Doria05/2013
872212202^14583-14583^1220259593Norbert Schneider01/2019
87232^197951-213759590Yves Minet06/2013
8724(38*10^59589+187)/959590Robert Price11/2017
872566^32749-65^3274959589Robert Price09/2013
87265*10^59586-359587Dmitry Domanov11/2010
8727(35*10^59584-197)/959585Robert Kinser10/2017
87282^197932-395959584Yves Minet04/2017
87292^197909-1896159577Enzo Doria05/2013
8730(3^124871+2)/4503159574Lelio R Paula04/2012
87322^197872+8159566Henri Lifchitz10/2005
87312^197873-1846959566Enzo Doria05/2013
8733(22*10^59558-31)/959559Robert Price04/2015
873412003^14600-14600^1200359558Norbert Schneider02/2019
87362^197840-46559556Lelio R Paula05/2011
8735(31*2^197856-1)/388960559556Lelio R Paula01/2014
87372^197808-1780559547Enzo Doria05/2013
87382^197781-1790559539Enzo Doria05/2013
87392^197777-1747359537Enzo Doria05/2013
87406^76507-14959535Lelio R Paula10/2012
8742Phi(61456,109)59526Enzo Doria05/2012
874118^47420+2359526Lelio R Paula03/2013
8743(59^33613+1)/6059522Paul Bourdelais08/2017
87443^124747+9459520Lelio R Paula10/2012
874517^48370+1859517Lelio R Paula03/2013
874620^45740-152359510Enzo Doria03/2013
8747(47*10^59509+493)/959510Robert Price11/2017
8748(7*2^197642-1)/305159494Lelio R Paula01/2014
874918^47390-185359488Enzo Doria03/2013
8750(2^197581-7)/191559475Lelio R Paula02/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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