PRP Records

Probable Primes Top 10000

(174961 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 ?
72512^202182+13560863Lelio R Paula08/2011
72522^202176+8560862Lelio R Paula08/2011
72535183^16384+5182^1638460860Henri Lifchitz01/2007
7254(31*2^202163+1)/360859Lelio R Paula03/2012
725514708^13707+13707^1470860847Hans Havermann12/2016
72562^202112+202112^2-160842Robert Price04/2014
7257(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
725864743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7259(19*2^202098-1)/679560836Lelio R Paula01/2014
7260(6^78175-11)/560832Paul Bourdelais11/2011
72612^202063+160560828Lelio R Paula09/2011
72622^202058+85960826Lelio R Paula09/2011
72631576^19021+19021^157660821Serge Batalov05/2014
7264(2^202009+3)/600560807Lelio R Paula03/2012
726510^60776+360777Robert Price01/2011
726610^60776-1481960776Patrick De Geest12/2012
7267(6883*2^201869-1)/3560771Lelio R Paula04/2015
7268(27*2^201841-1)/4360760Lelio R Paula01/2014
72692^201822-17760755Lelio R Paula08/2011
7270(13*10^60744+17)/360745Robert Price06/2015
7271(31*2^201754-1)/9960734Lelio R Paula01/2014
7272(26*10^60717-71)/960718Robert Price03/2015
727337^38712-260709Lelio R Paula08/2013
72742^201657-11200360705Enzo Doria05/2014
7275(10^60703+3^60703)/1360702Robert Price01/2013
72762^201622-11281760695Enzo Doria06/2014
72772^201620-1717760694Enzo Doria05/2013
7278(2^201615-3)*6-760693Gilbert Mozzo05/2016
72792^201609-4978960691Henri Lifchitz03/2005
72802^201582-1906160683Enzo Doria05/2013
728143316!3+2760679Robert Price09/2014
7282(509203*2^201564-1)/506760679Lelio R Paula04/2015
72832^201560+10560676Lelio R Paula08/2011
7284(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
72852^201545-1802160672Enzo Doria05/2013
72862^201543+1171560671Lelio R Paula09/2011
72872^201512-11175560662Enzo Doria05/2014
7288p(13013)#/2+6460662Robert Price03/2017
728911^58248+1660660Lelio R Paula05/2013
72902^201496-2760657Lelio R Paula08/2011
72912^201426-1609760636Enzo Doria04/2013
7292(17*10^60631-11)/360632Robert Price07/2015
72936^77916-7760631Lelio R Paula04/2013
7294(27*2^201410-1)/49160630Lelio R Paula01/2014
72955^86727+9860620Lelio R Paula04/2013
729617^49266-2660620Lelio R Paula05/2013
729720^46589-3360614Lelio R Paula05/2013
72986^77889+6560610Lelio R Paula04/2013
7299139901#+14838760595Nicolas PALAU09/2016
73012^201285-11172360593Enzo Doria05/2014
730046199*2^201268+12964760593Paul Vanderveen11/2016
73033^126991-10060591Lelio R Paula04/2013
73022^201278-11162360591Enzo Doria05/2014
73045^86682-1600460589Enzo Doria05/2014
7305(58*10^60579+221)/960580Robert Price02/2017
73069*2^201231-560578Lelio R Paula04/2014
7307(78557*2^201207+1)/1306760571Lelio R Paula06/2014
73082^201186-6694560564Lelio R Paula09/2011
73092^201186-9439560564Lelio R Paula09/2011
731065^33403+3260557Lelio R Paula01/2016
7311103^30079+10260545Norbert Schneider10/2016
7312(1000159^10091+1)/100016060541Faysal YAtim08/2008
73132^201098-1771760537Enzo Doria05/2013
7314(3^126881+8)/482960534Lelio R Paula03/2012
73152^201074+7504960530Enzo Doria04/2016
731611^58111-129060517Enzo Doria11/2012
7317(509203*2^201012-1)/960516Lelio R Paula04/2015
73182^200911+571160481Lelio R Paula10/2011
7319(2^200912-3)/2360480Lelio R Paula03/2012
732018^48179-17^4817960478Jean-Louis Charton12/2010
732238^38281-37^3828160476Robert Price09/2012
73214*7^71560-360476Lelio R Paula09/2014
7323(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7324lucasV(1,2,401712)+260464Mike Oakes01/2017
73252^200833-1849360457Enzo Doria05/2013
732620^46465-504360453Enzo Doria03/2013
73272^200810-1825760450Enzo Doria05/2013
73285^86466-1433660438Enzo Doria02/2013
7329Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7330(29*2^200703-1)/23160417Lelio R Paula01/2014
73312^200682-101683160412Paul Bourdelais11/2012
73322^200617-1788160392Enzo Doria05/2013
7333(25^43201+1)/2660391Robert Price06/2013
73352^200609-13360390Lelio R Paula08/2011
73342^200608-1283760390Enzo Doria10/2012
73362^200607-1712160389Enzo Doria05/2013
733711^57975-162060375Enzo Doria11/2012
7338(9913*2^200538-1)/380160369Lelio R Paula04/2015
73395^86342+6460351Lelio R Paula04/2013
7340(14*10^60346-23)/960347Robert Price04/2015
73412^200457-829560344Lelio R Paula09/2011
73426^77546+11360343Lelio R Paula04/2013
734437^38461-36^3846160315Robert Price06/2012
73432^200361-1759360315Enzo Doria05/2013
734510103^15059-10660304Enzo Doria07/2012
73462^200301-1740160297Enzo Doria05/2013
7347(37*10^60290+71)/960291Robert Price04/2015
73482^200266-9439560287Lelio R Paula09/2011
73492^200261-11161360285Enzo Doria05/2014
735046^36238-4560256Norbert Schneider07/2014
735113^54091+9460255Lelio R Paula05/2013
7352311^24171-15460253Enzo Doria07/2012
73532^200120-8108960243Paul Bourdelais01/2012
73543^126262+868060243Lelio R Paula04/2013
735543031!3-5904960239Robert Price12/2015
73562^200100-11126960237Enzo Doria05/2014
7357(29*2^200069-1)/537360225Lelio R Paula01/2014
735820^46283-192360216Enzo Doria03/2013
73592^200011-11207560210Enzo Doria05/2014
73602^200002+7453960207Enzo Doria04/2016
7361(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
73622^199872+9360168Donovan Johnson06/2008
73636^77321+7760168Lelio R Paula04/2013
7364(86*10^60165-77)/960166Robert Price05/2016
7365(2^199868+78557)/2337360162Lelio R Paula05/2012
73667^71180+8260155Lelio R Paula04/2013
73672^199814-11229560151Enzo Doria06/2014
736842964!3-8160135Robert Price09/2014
73692^199709-5160119Lelio R Paula05/2011
73702^199700-11162360116Enzo Doria05/2014
7371(15185*2^199681-1)/15960112Lelio R Paula04/2015
73722^199672+253360108Henri Lifchitz09/2004
737320^46198-1160105Lelio R Paula04/2013
73742^199657+9325760103Yves Minet03/2010
73753^125967-11060102Lelio R Paula10/2012
73762^199654-1881360102Enzo Doria05/2013
7377(29*10^60100+19)/360101Robert Price01/2017
7378129^28468+28468^12960085Serge Batalov05/2014
73792^199572-1587360078Enzo Doria04/2013
73809*2^199559+760075Lelio R Paula03/2014
73812^199527-11191960064Enzo Doria05/2014
73822^199522+8287560063Lelio R Paula10/2012
73835^85928-7260062Lelio R Paula10/2012
738439^37749+3860062Norbert Schneider05/2014
73856^77182-14360060Lelio R Paula10/2012
73862^199502-214560057Lelio R Paula06/2011
73872^199493+425760054Lelio R Paula06/2011
73882^199488+4075560052Lelio R Paula06/2011
7389(2^199451+9)/2561960037Lelio R Paula02/2012
73902^199425-6160033Lelio R Paula05/2011
7391(85*10^60026+23)/960027Robert Price11/2015
739265^33107+6260021Lelio R Paula01/2016
73942^199362-121560014Lelio R Paula06/2011
73932^199362-11163360014Enzo Doria05/2014
73951537^18832+18832^153760012Serge Batalov05/2014
73962^199324-1743360003Enzo Doria05/2013
739710^60000+20433160001Milton L. Brown04/2006
739810^60000+8712960001Milton L. Brown04/2006
739910^59999+6519760000Patrick De Geest04/2005
740010^60000-3252960000Patrick De Geest08/2009
7414(10^60000+2249)/960000Makoto Morimoto09/2016
7415((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
7416(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
7417(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
7401(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
7402(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
7403(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
7404(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
7405(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
7406(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
7407(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
7408(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
7409(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
7410(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
7411(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
7412(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
7413(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
742110^59999-51626759999Patrick De Geest06/2009
742020^46116-4159999Lelio R Paula03/2013
7418(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
7419(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
74226^77100-5559996Lelio R Paula10/2012
7424(19*2^199274+1)/16159987Lelio R Paula07/2012
7423(23^44053+1)/2459987Robert Price06/2013
74259^62848+6^62848-2^6284859973Mike Oakes08/2010
742615852^6061+6061^1585259961Hans Havermann08/2016
742719^46880-2059948Lelio R Paula03/2013
74282^199107-1773759938Enzo Doria05/2013
7429(13*10^59928+83)/359929Robert Price09/2016
743010^59913+10893143159914Marisa Kirisame02/2015
743110^59913+4861959914Patrick De Geest04/2016
743210^59913-7412359913Patrick De Geest03/2016
7433t(199528)59890Robert Price01/2015
74342^198903-1790159876Enzo Doria05/2013
7435gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
7436(3^125447+7)/259854Lelio R Paula04/2012
74375^85630+4^(85630-1)59853Robert Price03/2016
74382^198824-213559852Yves Minet06/2013
74392^198799-1611759845Enzo Doria04/2013
74407^70811+6^(70811+1)59843Robert Price07/2016
74412^198774-1594559837Enzo Doria04/2013
74422^198753-1587359831Enzo Doria04/2013
7443(31*2^198748-1)/4559829Lelio R Paula01/2014
74442^198725+6959823Lelio R Paula04/2011
7445(68*10^59821+31)/959822Robert Price10/2015
7446(37*25^42785+1867)/859812Curtis Bright05/2015
74483^125354+266059810Lelio R Paula10/2012
7447105^29591-10459810Norbert Schneider08/2013
74494*5^85565-359808Lelio R Paula09/2014
745013963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
7452125330^3+3^12533059798Anatoly F. Selevich06/2010
74512^198643-318959798Yves Minet10/2014
7453(7*10^59796-1)/359797Erik Branger03/2014
74542^198595+15359784Lelio R Paula04/2011
7455(19*10^59766+161)/959767Robert Price07/2016
74562^198510-196559758Lelio R Paula06/2011
74572^198506-1907759757Enzo Doria05/2013
74582^198484-1600559750Enzo Doria04/2013
74592^198473-1682159747Enzo Doria05/2013
7460(2^198481-5)/2831159745Lelio R Paula02/2012
74612^198400-18959725Lelio R Paula04/2011
74622^198384-1283759720Enzo Doria10/2012
746342694!3-72959719Robert Price09/2014
74642^198320-1871759701Enzo Doria05/2013
746520^45881-118359693Enzo Doria03/2013
74662^198224-685559672Lelio R Paula05/2011
74672^198181-1910159659Enzo Doria05/2013
74682^198149-11221359649Enzo Doria06/2014
74692^198138+7369959646Enzo Doria04/2016
74702^198129-5559643Lelio R Paula04/2011
74715^85318-1463659635Enzo Doria02/2013
7472(2^198119+47)/156093559634Lelio R Paula02/2012
74732^198090-1609759632Enzo Doria04/2013
74749*10^59617+8959618Robert Price11/2016
747542625!3+8159612Robert Price09/2014
74765^85277-8459607Lelio R Paula10/2012
74772^197984-1824559600Enzo Doria05/2013
74782^197951-213759590Yves Minet06/2013
747966^32749-65^3274959589Robert Price09/2013
74805*10^59586-359587Dmitry Domanov11/2010
74812^197932-395959584Yves Minet04/2017
74822^197909-1896159577Enzo Doria05/2013
7483(3^124871+2)/4503159574Lelio R Paula04/2012
74852^197872+8159566Henri Lifchitz10/2005
74842^197873-1846959566Enzo Doria05/2013
7486(22*10^59558-31)/959559Robert Price04/2015
74882^197840-46559556Lelio R Paula05/2011
7487(31*2^197856-1)/388960559556Lelio R Paula01/2014
74892^197808-1780559547Enzo Doria05/2013
74902^197781-1790559539Enzo Doria05/2013
74912^197777-1747359537Enzo Doria05/2013
74926^76507-14959535Lelio R Paula10/2012
7494Phi(61456,109)59526Enzo Doria05/2012
749318^47420+2359526Lelio R Paula03/2013
74953^124747+9459520Lelio R Paula10/2012
749617^48370+1859517Lelio R Paula03/2013
749720^45740-152359510Enzo Doria03/2013
7498(7*2^197642-1)/305159494Lelio R Paula01/2014
749918^47390-185359488Enzo Doria03/2013
7500(2^197581-7)/191559475Lelio R Paula02/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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