PRP Records

Probable Primes Top 10000

(252402 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 ?
2251(9*2^398145+1)/73119853Lelio R Paula04/2014
2252(10^119836+77)/3119836Robert Price01/2018
22532^398029+1872527119819Enzo Doria05/2016
22542^397897-113541119779Enzo Doria08/2014
2255(21*2^397661-1)/27593119705Lelio R Paula04/2014
2256(58^67853-1)/57119653Paul Bourdelais09/2017
22572^397426+73849119638Enzo Doria04/2016
22582^396933-112723119489Enzo Doria06/2014
225911^114738-150119488Enzo Doria10/2012
2260(4*10^119474+149)/9119474Robert Price04/2018
22612^396790-21119446Lelio R Paula04/2013
2262(2^396633-7)/5119398Lelio R Paula04/2014
2263105^59050+104119352Norbert Schneider11/2016
22642^396374+73729119321Enzo Doria04/2016
22652^396258-459491119286Enzo Doria05/2015
22662^396128-396128-1119247Karsten Bonath06/2018
2267(2^395986+5)/76881119199Lelio R Paula04/2014
2268(23*2^395942-1)/91119190Lelio R Paula04/2014
2269(11*2^395548+1)/3119073Lelio R Paula04/2014
2270(30^80599+1)/31119054Robert Price07/2013
22712^395062-109121118926Enzo Doria04/2014
2272(2^394918+78557)/3118882Lelio R Paula01/2015
2273(2^394739+3)/1883118826Lelio R Paula04/2014
22742^394266+71389118686Enzo Doria04/2016
22752^394215-51261118671Tony Prest / Never Odd Or Even04/2018
2276(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
2277(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
2278(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
2279(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
2280(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
2281(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
22825^169727+2118635Lelio R Paula08/2013
22832^394034-3118617M. Frind & P. Underwood09/2002
2284(7*10^118607+179)/3118608Robert Price09/2018
22853^248572-6242118599Enzo Doria05/2014
2286(3*2^393964-1)/181118594Lelio R Paula04/2014
22877^140303-6118570Robert Price11/2014
22882^393427+75683118434Enzo Doria04/2016
22892^393376-114749118418Enzo Doria04/2015
22902^393180+73118359Lelio R Paula04/2013
2291p(23881)#/2+256118328Robert Price05/2017
2292(10^118324+359)/9118324Serge Batalov12/2014
2293p(23879)#/2+64118317Robert Price03/2017
2294(53*10^118216+1)/9118217Serge Batalov11/2010
2295(7*2^392697+1)/15118214Renaud Lifchitz03/2011
2296(157^53819-1)/156118179Alexander Zhirkov06/2016
2297(19*2^392551+1)/3118171Lelio R Paula04/2014
22982^392516-29219118160Enzo Doria07/2015
2299Phi(177231,10)118152Maksym Voznyy09/2015
23002^392413-112123118129Enzo Doria06/2014
2301(2^392342+5)/27118106Lelio R Paula04/2014
23022^392300-1841429118095Enzo Doria06/2015
23032^392220+75241118070Enzo Doria04/2016
230410^118009+664447118010Patrick De Geest07/2018
230510^118009-20001118009Robert Price01/2018
2306(14*10^117991+61)/3117992Robert Price12/2018
23072^391933+5897117984Yves Minet02/2011
23082^391912-1849259117978Enzo Doria08/2015
2309(2^391812+5)/14181117944Lelio R Paula04/2014
2310(7*2^391521+1)/285117858Lelio R Paula04/2014
23112^391324+90901117801Yves Minet02/2011
23122^391301-1859923117794Enzo Doria03/2016
23132^391261-4131117782Yves Minet02/2018
2314(2^391115-7)/11791117734Lelio R Paula04/2014
23152^390960+1880881117691Enzo Doria11/2016
23162^390897-1860553117672Enzo Doria11/2015
23172^390889-115003117670Enzo Doria06/2015
23182^390779-30337117637Paul Bourdelais02/2012
231911^112916-780117590Enzo Doria12/2012
2320(16^97613-5^97613)/11117537Robert Price07/2013
2321(17*2^390272+1)/1983117482Lelio R Paula04/2014
232231^78759-30117459Theodore Burton02/2007
23232^389998+37117402Lelio R Paula03/2013
2324(13*10^117249+161)/3117250Robert Price11/2018
23252^389478+43117245Lelio R Paula03/2013
2326(29*2^389351-1)/9117207Lelio R Paula04/2014
2327(2^389341-7)/3865117200Lelio R Paula03/2014
232810^117142+209223117143Patrick De Geest04/2018
233010^117142-1000000001117142Robert Price03/2018
232910^117142-966057117142Patrick De Geest04/2018
233110^117135+360577117136Patrick De Geest07/2018
233210^117135-401117135Robert Price01/2018
23334*10^117123+79117124Robert Price08/2018
23342^389033-12797413117111Enzo Doria04/2016
23352^388960-109505117089Enzo Doria04/2014
2336(2^388928-5)/569117077Lelio R Paula03/2014
23372^388888-1529117067Yves Minet01/2013
233810^117059+28879117060Patrick De Geest05/2016
2339(10^117059-71)/1117059Serge Batalov12/2014
2340(26*10^116999-503)/9117000Robert Price07/2018
23413^245154-6256116969Enzo Doria05/2014
23422^388536-113495116961Enzo Doria08/2014
23432^388469-43116941Lelio R Paula03/2013
2344(7*2^388372-1)/111116911Lelio R Paula04/2014
2345(7*2^388335-1)/25116900Lelio R Paula04/2014
23462^388180+93116854Donovan Johnson07/2008
2347(2^388081+7)/1179116821Lelio R Paula03/2014
23482^387946-113261116784Enzo Doria07/2014
23492^387745+75557116723Enzo Doria04/2016
2350(7*10^116684+179)/3116685Robert Price09/2018
23512^387554+71455116666Enzo Doria04/2016
2352(2^387447+78557)/365116631Lelio R Paula12/2014
2353(145*10^116610-1)/9116612Serge Batalov12/2014
2354(25*10^116601-331)/9116602Robert Price08/2018
2355(17*2^387284-1)/59116584Lelio R Paula04/2014
2356(31*2^386968+1)/7116490Lelio R Paula03/2014
23572^386947+1869143116483Enzo Doria05/2016
2358(30^78857-1)/29116480Robert Price12/2011
2359(2^386903-3)/5116469Lelio R Paula03/2014
23602^386389-1864783116315Enzo Doria03/2016
2361(31*2^386231-1)/1711116266Lelio R Paula03/2014
2362297^47012+47012^297116250Norbert Schneider07/2018
2363(2^386087-5)/40959116220Lelio R Paula03/2014
23642^385969-823116189Yves Minet05/2012
236557^66162+2116173Lelio R Paula08/2013
23662^385854+75049116154Enzo Doria04/2016
23672^385775-109587116130Enzo Doria04/2014
23682^385622+71839116084Enzo Doria04/2016
23692^385564+781116067Lelio R Paula01/2012
23702^385410+71893116020Enzo Doria04/2016
2371(25*2^385091+1)/27115924Lelio R Paula04/2014
2372(11*10^115910-131)/3115911Robert Price09/2018
23732^384953-111943115883Paul Bourdelais02/2012
237443^70942-2115882Lelio R Paula04/2014
23757*10^115863+3115864Robert Price08/2015
23762^384834+93115847Donovan Johnson07/2008
23772^384809+71297115840Enzo Doria04/2016
2378(7*2^384759-1)/5115825Lelio R Paula04/2014
2379(71*10^115810-17)/9115811Ray Chandler08/2011
2380(97*10^115794-1)/3115796Serge Batalov12/2014
23812*10^115784-27115785Robert Price05/2018
238210^115773+126739115774Patrick De Geest04/2018
238410^115773-1000000001115773Robert Price03/2018
238310^115773-396221115773Patrick De Geest04/2018
23852^384530+1874305115756Enzo Doria06/2016
2386(3*2^384524-1)/7631115750Lelio R Paula03/2014
23872^384312+81091115690Yves Minet02/2010
2388(4*10^115668-79)/3115669Robert Price02/2018
2389(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
23903^242337-4042115625Enzo Doria05/2014
2391(11*2^383859-13)/15115553Renaud Lifchitz03/2011
23922^383780-3149115530Yves Minet10/2014
2393(41*10^115523-383)/9115524Robert Price11/2018
23942^383560-455115464Yves Minet03/2012
2395(2^383544+5)/3115458Lelio R Paula03/2014
239689^59221-88^59221115445Robert Price06/2015
23972^383347+1869413115399Enzo Doria05/2016
2398(2^383130-7)/131793115329Lelio R Paula03/2014
2399(12^106859+1)/13115320Paul Bourdelais02/2010
24002^383039+1869509115307Enzo Doria05/2016
2401(13*2^382968+1)/7115286Lelio R Paula04/2014
24022^382633+73697115185Enzo Doria04/2016
24032^382509-113593115147Enzo Doria08/2014
24042^382502-2791721115145Enzo Doria03/2016
24059^120590-120590115073Robert Price03/2014
24062^382198+9115054Lelio R Paula03/2013
24072^381883-59197114959Enzo Doria10/2015
24092^381806-4481114936Yves Minet07/2011
24082^381808-1851507114936Enzo Doria08/2015
24102^381774-112373114926Enzo Doria06/2014
24112^381555-109051114860Enzo Doria04/2014
24122^381546-113501114857Enzo Doria08/2014
24132^381360-110429114801Enzo Doria05/2014
2414(66^63079+1)/67114774Paul Bourdelais09/2017
24152^381252-115079114769Enzo Doria06/2015
24162^381209-29323114756Enzo Doria07/2015
2417569^41651-568^41651114754Jean-Louis Charton11/2009
24182^381201+1873205114753Enzo Doria06/2016
24192^380974-112991114685Enzo Doria07/2014
242088^58949-87114626Norbert Schneider11/2015
24212^380700+91114603Lelio R Paula03/2013
242310^114575+3^114576114576Mike Oakes09/2010
242210^114575+66561114576Patrick De Geest02/2017
242410^114575-581081114575Patrick De Geest02/2017
24252^380587-115315114569Enzo Doria06/2015
24262^380513-216925114546Enzo Doria05/2014
24272^380451-1840087114528Enzo Doria06/2015
2428(15*2^380388-1)/539114507Lelio R Paula04/2014
24292^380279-461347114476Enzo Doria07/2015
24302^380021+1871147114398Enzo Doria05/2016
24312^380005+1869707114393Enzo Doria05/2016
24322^379958-113297114379Enzo Doria07/2014
24332^379881-109105114356Enzo Doria04/2014
2434(21*2^379857-1)/13114349Lelio R Paula03/2014
2435(4*10^114340+83)/3114341Robert Price02/2018
2436(4*10^114296+149)/9114296Robert Price04/2018
243788^58773-87114284Norbert Schneider11/2015
24382^379529-2790283114250Enzo Doria03/2016
24392^379522+1869115114248Enzo Doria05/2016
2440(145*10^114226-1)/9114228Serge Batalov12/2014
24412^379317-115033114186Enzo Doria06/2015
2442(17*2^379246-1)/17407114162Lelio R Paula03/2014
2443(4*10^114076+143)/3114077Robert Price03/2018
24442*10^113941+9113942Dmitry Domanov11/2010
24454*10^113905+91113906Robert Price08/2018
24464*10^113874-21113875Robert Price09/2018
24472^378272-16565113872Enzo Doria04/2013
24482^378217-109075113855Enzo Doria04/2014
24492^378198+67113849Lelio R Paula03/2013
24502^378173-3249113842Yves Minet12/2014
2451(2^378155-5)/6597113833Lelio R Paula03/2014
245292941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
24532^378128-262977113828Enzo Doria05/2014
24542^378123-113215113827Enzo Doria07/2014
24556^146274-18893113824Enzo Doria03/2013
24562^378078+75113813Lelio R Paula03/2013
24572^377940+63113772Lelio R Paula03/2013
24582^377941-2785843113772Enzo Doria04/2016
24592^377810+1875109113733Enzo Doria09/2016
24602^377803-1838635113731Enzo Doria05/2015
24612^377799+52223113729Yves Minet08/2010
246211^109190-270113710Enzo Doria12/2012
24637*10^113693+9113694Robert Price09/2015
2464(2*10^113631+529)/9113631Robert Price01/2018
24652^377408-2798279113612Enzo Doria04/2016
24662^377222+93679113556Yves Minet02/2011
2467262147#+316847113552Makoto Morimoto02/2016
24682^377026-458903113497Enzo Doria04/2015
246935^73477-34^73477113454Robert Price05/2012
24702^376790+27113426Lelio R Paula03/2013
24712^376786-112701113424Enzo Doria06/2014
24722^376731+21113408Lelio R Paula03/2013
24742^376634+1871245113379Enzo Doria05/2016
2473(4^188318+17)/3113379Robert Price02/2017
24752^376576-344369113361Enzo Doria07/2015
2476(17*2^376526-1)/223113345Lelio R Paula03/2014
2477(27*2^376441-1)/811113319Lelio R Paula03/2014
24782^376128-21237113226Enzo Doria06/2013
24792^375638-1787171113079Enzo Doria03/2016
24802^375537+4847113048Yves Minet02/2011
2481(17^91837+16^91837)/33113000Robert Price08/2013
24825*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
24832^375350-3221112992Yves Minet07/2011
2485(13*2^375306+1)/7112979Lelio R Paula03/2014
24842^375305+76757112979Enzo Doria05/2016
24862^375258+1874989112964Enzo Doria07/2016
2487(29^77237-1)/28112950Robert Price04/2012
24882^375154+74959112933Enzo Doria04/2016
24892^374993-2787163112885Enzo Doria11/2015
2490123^53970+2112793Lelio R Paula06/2013
2491p(22852)#/2+512112745Robert Price05/2017
2492(11*10^112742-131)/3112743Robert Price09/2018
24932^374441-21049112718Enzo Doria06/2013
2494(2^374321+1)/3112682H.&R. Lifchitz12/2000
2495(13^101089-1)/12112607Paul Bourdelais03/2010
24963^236011-8828112606Enzo Doria05/2014
249739^70666+2112435Lelio R Paula11/2013
2498(2^373350-7)/3112390Lelio R Paula03/2014
24992^373306-1840931112377Enzo Doria06/2015
25002^373117+1872107112320Enzo Doria05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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