PRP Records

Probable Primes Top 10000

(224660 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 ?
82512^199522+8287560063Lelio R Paula10/2012
82525^85928-7260062Lelio R Paula10/2012
825339^37749+3860062Norbert Schneider05/2014
82546^77182-14360060Lelio R Paula10/2012
82552^199502-214560057Lelio R Paula06/2011
82562^199493+425760054Lelio R Paula06/2011
82572^199488+4075560052Lelio R Paula06/2011
8258(2^199451+9)/2561960037Lelio R Paula02/2012
82592^199425-6160033Lelio R Paula05/2011
8260(85*10^60026+23)/960027Robert Price11/2015
826165^33107+6260021Lelio R Paula01/2016
82632^199362-121560014Lelio R Paula06/2011
82622^199362-11163360014Enzo Doria05/2014
82641537^18832+18832^153760012Serge Batalov05/2014
82652^199324-1743360003Enzo Doria05/2013
826710^60000+20433160001Milton L. Brown04/2006
826810^60000+8712960001Milton L. Brown04/2006
8266143^27838-260001Lelio R Paula10/2017
826910^59999+6519760000Patrick De Geest04/2005
828310^60000-3252960000Patrick De Geest08/2009
8284(10^60000+2249)/960000Makoto Morimoto09/2016
8285((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
8286(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
8287(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
8270(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
8271(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
8272(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
8273(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
8274(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
8275(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
8276(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
8277(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
8278(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
8279(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
8280(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
8281(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
8282(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
829110^59999-51626759999Patrick De Geest06/2009
829020^46116-4159999Lelio R Paula03/2013
8288(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
8289(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
82926^77100-5559996Lelio R Paula10/2012
8294(19*2^199274+1)/16159987Lelio R Paula07/2012
8293(23^44053+1)/2459987Robert Price06/2013
82959^62848+6^62848-2^6284859973Mike Oakes08/2010
829615852^6061+6061^1585259961Hans Havermann08/2016
829719^46880-2059948Lelio R Paula03/2013
82982^199107-1773759938Enzo Doria05/2013
8299(13*10^59928+83)/359929Robert Price09/2016
830010^59913+10893143159914Marisa Kirisame02/2015
830110^59913+4861959914Patrick De Geest04/2016
830210^59913-7412359913Patrick De Geest03/2016
8303t(199528)59890Robert Price01/2015
83042^198903-1790159876Enzo Doria05/2013
83059*10^59862-1959863Robert Price10/2017
8306gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
8307(3^125447+7)/259854Lelio R Paula04/2012
83085^85630+4^(85630-1)59853Robert Price03/2016
83092^198824-213559852Yves Minet06/2013
8310(124^28591-1)/12359851Richard Fischer10/2017
83112^198799-1611759845Enzo Doria04/2013
83127^70811+6^(70811+1)59843Robert Price07/2016
83132^198774-1594559837Enzo Doria04/2013
83142^198753-1587359831Enzo Doria04/2013
8315(31*2^198748-1)/4559829Lelio R Paula01/2014
83162^198725+6959823Lelio R Paula04/2011
8317(68*10^59821+31)/959822Robert Price10/2015
8318(37*25^42785+1867)/859812Curtis Bright05/2015
83193^125354+266059810Lelio R Paula10/2012
8320105^29591-10459810Norbert Schneider08/2013
83214*5^85565-359808Lelio R Paula09/2014
832213963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
8324125330^3+3^12533059798Anatoly F. Selevich06/2010
83232^198643-318959798Yves Minet10/2014
8325(13*10^59797+191)/359798Robert Price08/2017
8326(7*10^59796-1)/359797Erik Branger03/2014
83272^198595+15359784Lelio R Paula04/2011
8328(19*10^59766+161)/959767Robert Price07/2016
83292^198510-196559758Lelio R Paula06/2011
83302^198506-1907759757Enzo Doria05/2013
83312^198484-1600559750Enzo Doria04/2013
83322^198473-1682159747Enzo Doria05/2013
8333(2^198481-5)/2831159745Lelio R Paula02/2012
83342^198400-18959725Lelio R Paula04/2011
83352^198384-1283759720Enzo Doria10/2012
833642694!3-72959719Robert Price09/2014
83372^198320-1871759701Enzo Doria05/2013
833820^45881-118359693Enzo Doria03/2013
83392^198224-685559672Lelio R Paula05/2011
83402^198181-1910159659Enzo Doria05/2013
83415*10^59650+4159651Robert Price08/2017
83422^198149-11221359649Enzo Doria06/2014
83432^198138+7369959646Enzo Doria04/2016
83442^198129-5559643Lelio R Paula04/2011
83455^85318-1463659635Enzo Doria02/2013
8346(2^198119+47)/156093559634Lelio R Paula02/2012
83472^198090-1609759632Enzo Doria04/2013
83489*10^59617+8959618Robert Price11/2016
834942625!3+8159612Robert Price09/2014
83505^85277-8459607Lelio R Paula10/2012
8351(871*10^59599-7)/959601Robert Price11/2017
83522^197984-1824559600Enzo Doria05/2013
83532^197951-213759590Yves Minet06/2013
8354(38*10^59589+187)/959590Robert Price11/2017
835566^32749-65^3274959589Robert Price09/2013
83565*10^59586-359587Dmitry Domanov11/2010
8357(35*10^59584-197)/959585Robert Kinser10/2017
83582^197932-395959584Yves Minet04/2017
83592^197909-1896159577Enzo Doria05/2013
8360(3^124871+2)/4503159574Lelio R Paula04/2012
83612^197872+8159566Henri Lifchitz10/2005
83622^197873-1846959566Enzo Doria05/2013
8363(22*10^59558-31)/959559Robert Price04/2015
83652^197840-46559556Lelio R Paula05/2011
8364(31*2^197856-1)/388960559556Lelio R Paula01/2014
83662^197808-1780559547Enzo Doria05/2013
83672^197781-1790559539Enzo Doria05/2013
83682^197777-1747359537Enzo Doria05/2013
83696^76507-14959535Lelio R Paula10/2012
8371Phi(61456,109)59526Enzo Doria05/2012
837018^47420+2359526Lelio R Paula03/2013
8372(59^33613+1)/6059522Paul Bourdelais08/2017
83733^124747+9459520Lelio R Paula10/2012
837417^48370+1859517Lelio R Paula03/2013
837520^45740-152359510Enzo Doria03/2013
8376(47*10^59509+493)/959510Robert Price11/2017
8377(7*2^197642-1)/305159494Lelio R Paula01/2014
837818^47390-185359488Enzo Doria03/2013
8379(2^197581-7)/191559475Lelio R Paula02/2012
8380(24737*2^197559+1)/7759474Lelio R Paula06/2014
83812^197540-245959466Yves Minet07/2014
8382(44*10^59454+1)/959455Serge Batalov11/2010
83832^197494-1780559452Enzo Doria05/2013
83842^197482-1682159449Enzo Doria05/2013
83852^197485+7576759449Enzo Doria04/2016
8386(3*2^197483+1)/2559448Lelio R Paula07/2012
83872^197466-186835159444Enzo Doria04/2016
83882^197411-1778159427Enzo Doria05/2013
8389(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
83902^197392-11462959421Enzo Doria05/2015
83912^197355-15759410Lelio R Paula04/2011
83925^84992-8459407Lelio R Paula10/2012
83932*3^124504-559404Lelio R Paula04/2014
83942^197307-1916559396Enzo Doria05/2013
83962^197303+3276959395Lelio R Paula05/2011
83952*10^59394-6959395Robert Price07/2017
8397(53*10^59389+1)/959390Serge Batalov11/2010
83986^76316-3559386Lelio R Paula10/2012
83992^197259-292959381Yves Minet09/2014
8400lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
840117^48253-659373Lelio R Paula03/2013
84022^197156-1583759350Enzo Doria04/2013
84032^197152-429559349Yves Minet08/2018
84042^197149-1848159348Enzo Doria05/2013
84052^197142-1715759346Enzo Doria05/2013
8407(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
8406(8^65707-5^65707)/359339Robert Price12/2012
8408(2*14283^14283+1)/792549797559334David Broadhurst09/2010
84092^197012-11171959307Enzo Doria05/2014
84102^196975+51359296Lelio R Paula05/2011
8411(61*10^59294+119)/959295Robert Price09/2017
84124*10^59292+3959293Robert Price11/2017
84132^196960+9759291Lelio R Paula04/2011
84149^62116+8^(62116-1)59274Robert Price03/2016
84152^196900-9730559273Lelio R Paula09/2011
84165*6^76155+759261Lelio R Paula09/2014
841715^50385-1459258Wojciech Florek06/2006
8418(136777#-1)/882358147759254Donovan Johnson05/2006
8419(2^196744-3)*6-759227Gilbert Mozzo05/2016
8420(67607*2^196696+1)/359216Lelio R Paula05/2014
84212^196696-11296759212Enzo Doria06/2014
842220^45508-422359208Enzo Doria03/2013
8423gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
842414^51651-8159199Lelio R Paula03/2013
84252^196650-145159198Yves Minet08/2012
84262^196636-279779959194Enzo Doria04/2016
84271111*2^196610-55559189Henri Lifchitz04/2005
84283^124041+65859183Lelio R Paula10/2012
84292^196590-11179759180Enzo Doria05/2014
8430(10^59174-13)/359174Robert Price02/2017
8431(2*10^59174-113)/359174Robert Price09/2017
8432(9179*2^196533-1)/78359164Lelio R Paula04/2015
8433379*10^59152+959155Arkadiusz Wesolowski10/2011
8434(404*10^59149-53)/959151Robert Price11/2017
843513^53095+4059145Lelio R Paula03/2013
84372*F(282999)-159144Henri Lifchitz12/2009
84364*7^69984+359144Lelio R Paula09/2014
8438(5*10^59142+1)/359143Erik Branger12/2013
84392^196463+571159142Lelio R Paula10/2011
84402^196453-9730559139Lelio R Paula09/2011
8441(28*10^59135+53)/959136Serge Batalov11/2008
8442(28*10^59133+113)/359134Robert Price03/2016
84432^196434+759133Lelio R Paula04/2011
8444(8*10^59127-29)/359128Robert Price05/2016
84452^196414+25559127Lelio R Paula05/2011
84465^84586-9259124Lelio R Paula10/2012
84472^196388-1717759119Enzo Doria05/2013
844879427!6-659119Robert Price08/2018
84493^123890+2059111Lelio R Paula10/2012
84502^196355-102177759109Paul Bourdelais11/2012
845111^56754-141059104Enzo Doria11/2012
8452(7*2^196297-1)/120040759087Lelio R Paula01/2014
8453(16*10^59062-19)/359063Robert Price03/2016
845435^38249-122859060Enzo Doria03/2013
84555^84475-1859046Lelio R Paula10/2012
84562^196123-1770159039Enzo Doria05/2013
845712^54702-3159034Lelio R Paula03/2013
84582^196101-17559033Lelio R Paula04/2011
84592^196085+577559028Lelio R Paula05/2011
84602^196034+1171559013Lelio R Paula05/2011
84612^196018-1848559008Enzo Doria05/2013
84622^195984-216358998Yves Minet08/2013
84633^123645-1658994Lelio R Paula10/2012
846439^37078-3858994Norbert Schneider05/2014
84652^195958-1685358990Enzo Doria05/2013
84662^195930-307158981Yves Minet10/2014
84672^195924+51358980Lelio R Paula05/2011
84682^195863+15558961Lelio R Paula04/2011
8469(28*10^58956+113)/358957Robert Price03/2016
847011^56612-930058956Enzo Doria02/2013
84712^195833-1717358952Enzo Doria05/2013
8472(27*2^195833-1)/5358952Lelio R Paula01/2014
8473(13*2^195821-1)/12242558945Lelio R Paula01/2014
8474139^27504-13858942Norbert Schneider10/2015
8475(418*10^58923+23)/958925Robert Price08/2017
84763^123495+4458923Lelio R Paula10/2012
84772^195737-1856558923Enzo Doria05/2013
847879185!6-1658921Robert Price08/2018
847914^51407+4758920Lelio R Paula03/2013
84802^195691-9958909Lelio R Paula04/2011
84812^195667-185982758902Enzo Doria04/2016
84822^195642+7549958895Enzo Doria04/2016
8483(299*10^58893+1)/358895Robert Price11/2017
84848*6^75678+558890Lelio R Paula09/2014
84862^195618+7318958887Enzo Doria04/2016
8485(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
8487t(197953)58881Robert Price12/2014
84882^195581-1610558876Enzo Doria04/2013
8489(8*10^58872+67)/358873Robert Price01/2017
84907*2^195542-558865Lelio R Paula03/2014
84912*10^58861+9^5886158862Mike Oakes04/2011
849211^56513-162058853Enzo Doria11/2012
84932^195496+16558851Lelio R Paula04/2011
84945^84187+6658845Lelio R Paula10/2012
8495(28*10^58843-43)/358844Robert Price04/2016
84962^195462-1756558840Enzo Doria05/2013
84972^195449-417158837Yves Minet02/2018
84982^195435+5927358832Yves Minet01/2011
84992^195424-1860558829Enzo Doria05/2013
85002^195385-11158817Lelio R Paula04/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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