PRP Records

Probable Primes Top 10000

(202622 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
77512^201560+10560676Lelio R Paula08/2011
7752(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
77532^201545-1802160672Enzo Doria05/2013
77542^201543+1171560671Lelio R Paula09/2011
77552^201512-11175560662Enzo Doria05/2014
7756p(13013)#/2+6460662Robert Price03/2017
775711^58248+1660660Lelio R Paula05/2013
77582^201496-2760657Lelio R Paula08/2011
77595*10^60655+5760656Robert Price11/2017
7760(7*10^60643+197)/360644Robert Price07/2017
77612^201426-1609760636Enzo Doria04/2013
7762(17*10^60631-11)/360632Robert Price07/2015
77636^77916-7760631Lelio R Paula04/2013
7764(27*2^201410-1)/49160630Lelio R Paula01/2014
77655^86727+9860620Lelio R Paula04/2013
776617^49266-2660620Lelio R Paula05/2013
776720^46589-3360614Lelio R Paula05/2013
77686^77889+6560610Lelio R Paula04/2013
7769139901#+14838760595Nicolas PALAU09/2016
77702^201285-11172360593Enzo Doria05/2014
777146199*2^201268+12964760593Paul Vanderveen11/2016
77723^126991-10060591Lelio R Paula04/2013
77732^201278-11162360591Enzo Doria05/2014
77745^86682-1600460589Enzo Doria05/2014
7775(865*10^60583-1)/960585Robert Price11/2017
7776(58*10^60579+221)/960580Robert Price02/2017
77779*2^201231-560578Lelio R Paula04/2014
77784*10^60572-8960573Robert Price08/2017
7779(78557*2^201207+1)/1306760571Lelio R Paula06/2014
77802^201186-6694560564Lelio R Paula09/2011
77812^201186-9439560564Lelio R Paula09/2011
778265^33403+3260557Lelio R Paula01/2016
7783103^30079+10260545Norbert Schneider10/2016
7784(1000159^10091+1)/100016060541Faysal YAtim08/2008
77852^201098-1771760537Enzo Doria05/2013
7786(3^126881+8)/482960534Lelio R Paula03/2012
77872^201074+7504960530Enzo Doria04/2016
778811^58111-129060517Enzo Doria11/2012
7789(509203*2^201012-1)/960516Lelio R Paula04/2015
77902^200911+571160481Lelio R Paula10/2011
7791(2^200912-3)/2360480Lelio R Paula03/2012
779218^48179-17^4817960478Jean-Louis Charton12/2010
779438^38281-37^3828160476Robert Price09/2012
77934*7^71560-360476Lelio R Paula09/2014
7795(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7796lucasV(1,2,401712)+260464Mike Oakes01/2017
77972^200833-1849360457Enzo Doria05/2013
779820^46465-504360453Enzo Doria03/2013
77992^200810-1825760450Enzo Doria05/2013
78005^86466-1433660438Enzo Doria02/2013
7801Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7802(29*2^200703-1)/23160417Lelio R Paula01/2014
78032^200682-101683160412Paul Bourdelais11/2012
78042^200617-1788160392Enzo Doria05/2013
7805(25^43201+1)/2660391Robert Price06/2013
78072^200609-13360390Lelio R Paula08/2011
78062^200608-1283760390Enzo Doria10/2012
78082^200607-1712160389Enzo Doria05/2013
780911^57975-162060375Enzo Doria11/2012
7810(9913*2^200538-1)/380160369Lelio R Paula04/2015
78115^86342+6460351Lelio R Paula04/2013
7812(14*10^60346-23)/960347Robert Price04/2015
78132^200457-829560344Lelio R Paula09/2011
78146^77546+11360343Lelio R Paula04/2013
781637^38461-36^3846160315Robert Price06/2012
78152^200361-1759360315Enzo Doria05/2013
781710103^15059-10660304Enzo Doria07/2012
78182^200301-1740160297Enzo Doria05/2013
7819(37*10^60290+71)/960291Robert Price04/2015
78202^200266-9439560287Lelio R Paula09/2011
78212^200261-11161360285Enzo Doria05/2014
782246^36238-4560256Norbert Schneider07/2014
782313^54091+9460255Lelio R Paula05/2013
7824311^24171-15460253Enzo Doria07/2012
78252^200120-8108960243Paul Bourdelais01/2012
78263^126262+868060243Lelio R Paula04/2013
782743031!3-5904960239Robert Price12/2015
78282^200100-11126960237Enzo Doria05/2014
7829(29*2^200069-1)/537360225Lelio R Paula01/2014
783020^46283-192360216Enzo Doria03/2013
78312^200011-11207560210Enzo Doria05/2014
78322^200002+7453960207Enzo Doria04/2016
7833(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
7834(28*10^60180+149)/360181Robert Price10/2017
78352^199872+9360168Donovan Johnson06/2008
78366^77321+7760168Lelio R Paula04/2013
7837(86*10^60165-77)/960166Robert Price05/2016
7838(2^199868+78557)/2337360162Lelio R Paula05/2012
78397^71180+8260155Lelio R Paula04/2013
78412^199814-11229560151Enzo Doria06/2014
7840(51^35227-1)/5060151Paul Bourdelais08/2017
784242964!3-8160135Robert Price09/2014
78432^199709-5160119Lelio R Paula05/2011
78442^199700-11162360116Enzo Doria05/2014
7845(15185*2^199681-1)/15960112Lelio R Paula04/2015
78462^199672+253360108Henri Lifchitz09/2004
784720^46198-1160105Lelio R Paula04/2013
78482^199657+9325760103Yves Minet03/2010
78493^125967-11060102Lelio R Paula10/2012
78502^199654-1881360102Enzo Doria05/2013
7851(29*10^60100+19)/360101Robert Price01/2017
7852129^28468+28468^12960085Serge Batalov05/2014
78532^199572-1587360078Enzo Doria04/2013
78549*2^199559+760075Lelio R Paula03/2014
78552^199527-11191960064Enzo Doria05/2014
78562^199522+8287560063Lelio R Paula10/2012
78575^85928-7260062Lelio R Paula10/2012
785839^37749+3860062Norbert Schneider05/2014
78596^77182-14360060Lelio R Paula10/2012
78602^199502-214560057Lelio R Paula06/2011
78612^199493+425760054Lelio R Paula06/2011
78622^199488+4075560052Lelio R Paula06/2011
7863(2^199451+9)/2561960037Lelio R Paula02/2012
78642^199425-6160033Lelio R Paula05/2011
7865(85*10^60026+23)/960027Robert Price11/2015
786665^33107+6260021Lelio R Paula01/2016
78682^199362-121560014Lelio R Paula06/2011
78672^199362-11163360014Enzo Doria05/2014
78691537^18832+18832^153760012Serge Batalov05/2014
78702^199324-1743360003Enzo Doria05/2013
787210^60000+20433160001Milton L. Brown04/2006
787310^60000+8712960001Milton L. Brown04/2006
7871143^27838-260001Lelio R Paula10/2017
787410^59999+6519760000Patrick De Geest04/2005
788810^60000-3252960000Patrick De Geest08/2009
7889(10^60000+2249)/960000Makoto Morimoto09/2016
7890((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
7891(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
7892(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
7875(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
7876(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
7877(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
7878(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
7879(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
7880(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
7881(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
7882(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
7883(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
7884(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
7885(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
7886(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
7887(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
789510^59999-51626759999Patrick De Geest06/2009
789620^46116-4159999Lelio R Paula03/2013
7893(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
7894(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
78976^77100-5559996Lelio R Paula10/2012
7899(19*2^199274+1)/16159987Lelio R Paula07/2012
7898(23^44053+1)/2459987Robert Price06/2013
79009^62848+6^62848-2^6284859973Mike Oakes08/2010
790115852^6061+6061^1585259961Hans Havermann08/2016
790219^46880-2059948Lelio R Paula03/2013
79032^199107-1773759938Enzo Doria05/2013
7904(13*10^59928+83)/359929Robert Price09/2016
790510^59913+10893143159914Marisa Kirisame02/2015
790610^59913+4861959914Patrick De Geest04/2016
790710^59913-7412359913Patrick De Geest03/2016
7908t(199528)59890Robert Price01/2015
79092^198903-1790159876Enzo Doria05/2013
79109*10^59862-1959863Robert Price10/2017
7911gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
7912(3^125447+7)/259854Lelio R Paula04/2012
79135^85630+4^(85630-1)59853Robert Price03/2016
79142^198824-213559852Yves Minet06/2013
7915(124^28591-1)/12359851Richard Fischer10/2017
79162^198799-1611759845Enzo Doria04/2013
79177^70811+6^(70811+1)59843Robert Price07/2016
79182^198774-1594559837Enzo Doria04/2013
79192^198753-1587359831Enzo Doria04/2013
7920(31*2^198748-1)/4559829Lelio R Paula01/2014
79212^198725+6959823Lelio R Paula04/2011
7922(68*10^59821+31)/959822Robert Price10/2015
7923(37*25^42785+1867)/859812Curtis Bright05/2015
79243^125354+266059810Lelio R Paula10/2012
7925105^29591-10459810Norbert Schneider08/2013
79264*5^85565-359808Lelio R Paula09/2014
792713963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
7929125330^3+3^12533059798Anatoly F. Selevich06/2010
79282^198643-318959798Yves Minet10/2014
7930(13*10^59797+191)/359798Robert Price08/2017
7931(7*10^59796-1)/359797Erik Branger03/2014
79322^198595+15359784Lelio R Paula04/2011
7933(19*10^59766+161)/959767Robert Price07/2016
79342^198510-196559758Lelio R Paula06/2011
79352^198506-1907759757Enzo Doria05/2013
79362^198484-1600559750Enzo Doria04/2013
79372^198473-1682159747Enzo Doria05/2013
7938(2^198481-5)/2831159745Lelio R Paula02/2012
79392^198400-18959725Lelio R Paula04/2011
79402^198384-1283759720Enzo Doria10/2012
794142694!3-72959719Robert Price09/2014
79422^198320-1871759701Enzo Doria05/2013
794320^45881-118359693Enzo Doria03/2013
79442^198224-685559672Lelio R Paula05/2011
79452^198181-1910159659Enzo Doria05/2013
79465*10^59650+4159651Robert Price08/2017
79472^198149-11221359649Enzo Doria06/2014
79482^198138+7369959646Enzo Doria04/2016
79492^198129-5559643Lelio R Paula04/2011
79505^85318-1463659635Enzo Doria02/2013
7951(2^198119+47)/156093559634Lelio R Paula02/2012
79522^198090-1609759632Enzo Doria04/2013
79539*10^59617+8959618Robert Price11/2016
795442625!3+8159612Robert Price09/2014
79555^85277-8459607Lelio R Paula10/2012
7956(871*10^59599-7)/959601Robert Price11/2017
79572^197984-1824559600Enzo Doria05/2013
79582^197951-213759590Yves Minet06/2013
7959(38*10^59589+187)/959590Robert Price11/2017
796066^32749-65^3274959589Robert Price09/2013
79615*10^59586-359587Dmitry Domanov11/2010
7962(35*10^59584-197)/959585Robert Kinser10/2017
79632^197932-395959584Yves Minet04/2017
79642^197909-1896159577Enzo Doria05/2013
7965(3^124871+2)/4503159574Lelio R Paula04/2012
79662^197872+8159566Henri Lifchitz10/2005
79672^197873-1846959566Enzo Doria05/2013
7968(22*10^59558-31)/959559Robert Price04/2015
79702^197840-46559556Lelio R Paula05/2011
7969(31*2^197856-1)/388960559556Lelio R Paula01/2014
79712^197808-1780559547Enzo Doria05/2013
79722^197781-1790559539Enzo Doria05/2013
79732^197777-1747359537Enzo Doria05/2013
79746^76507-14959535Lelio R Paula10/2012
7976Phi(61456,109)59526Enzo Doria05/2012
797518^47420+2359526Lelio R Paula03/2013
7977(59^33613+1)/6059522Paul Bourdelais08/2017
79783^124747+9459520Lelio R Paula10/2012
797917^48370+1859517Lelio R Paula03/2013
798020^45740-152359510Enzo Doria03/2013
7981(47*10^59509+493)/959510Robert Price11/2017
7982(7*2^197642-1)/305159494Lelio R Paula01/2014
798318^47390-185359488Enzo Doria03/2013
7984(2^197581-7)/191559475Lelio R Paula02/2012
7985(24737*2^197559+1)/7759474Lelio R Paula06/2014
79862^197540-245959466Yves Minet07/2014
7987(44*10^59454+1)/959455Serge Batalov11/2010
79882^197494-1780559452Enzo Doria05/2013
79892^197482-1682159449Enzo Doria05/2013
79902^197485+7576759449Enzo Doria04/2016
7991(3*2^197483+1)/2559448Lelio R Paula07/2012
79922^197466-186835159444Enzo Doria04/2016
79932^197411-1778159427Enzo Doria05/2013
7994(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
79952^197392-11462959421Enzo Doria05/2015
79962^197355-15759410Lelio R Paula04/2011
79975^84992-8459407Lelio R Paula10/2012
79982*3^124504-559404Lelio R Paula04/2014
79992^197307-1916559396Enzo Doria05/2013
80002*10^59394-6959395Robert Price07/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!