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 ?
2251Phi(177231,10)118152Maksym Voznyy09/2015
22522^392413-112123118129Enzo Doria06/2014
2253(2^392342+5)/27118106Lelio R Paula04/2014
22542^392300-1841429118095Enzo Doria06/2015
22552^392220+75241118070Enzo Doria04/2016
225610^118009+664447118010Patrick De Geest07/2018
225710^118009-20001118009Robert Price01/2018
22582^391933+5897117984Yves Minet02/2011
22592^391912-1849259117978Enzo Doria08/2015
2260(2^391812+5)/14181117944Lelio R Paula04/2014
2261(7*2^391521+1)/285117858Lelio R Paula04/2014
22622^391324+90901117801Yves Minet02/2011
22632^391301-1859923117794Enzo Doria03/2016
22642^391261-4131117782Yves Minet02/2018
2265(2^391115-7)/11791117734Lelio R Paula04/2014
22662^390960+1880881117691Enzo Doria11/2016
22672^390897-1860553117672Enzo Doria11/2015
22682^390889-115003117670Enzo Doria06/2015
22692^390779-30337117637Paul Bourdelais02/2012
227011^112916-780117590Enzo Doria12/2012
2271(16^97613-5^97613)/11117537Robert Price07/2013
2272(17*2^390272+1)/1983117482Lelio R Paula04/2014
227331^78759-30117459Theodore Burton02/2007
22742^389998+37117402Lelio R Paula03/2013
22752^389478+43117245Lelio R Paula03/2013
2276(29*2^389351-1)/9117207Lelio R Paula04/2014
2277(2^389341-7)/3865117200Lelio R Paula03/2014
227810^117142+209223117143Patrick De Geest04/2018
228010^117142-1000000001117142Robert Price03/2018
227910^117142-966057117142Patrick De Geest04/2018
228110^117135+360577117136Patrick De Geest07/2018
228210^117135-401117135Robert Price01/2018
22834*10^117123+79117124Robert Price08/2018
22842^389033-12797413117111Enzo Doria04/2016
22852^388960-109505117089Enzo Doria04/2014
2286(2^388928-5)/569117077Lelio R Paula03/2014
22872^388888-1529117067Yves Minet01/2013
228810^117059+28879117060Patrick De Geest05/2016
2289(10^117059-71)/1117059Serge Batalov12/2014
2290(26*10^116999-503)/9117000Robert Price07/2018
22913^245154-6256116969Enzo Doria05/2014
22922^388536-113495116961Enzo Doria08/2014
22932^388469-43116941Lelio R Paula03/2013
2294(7*2^388372-1)/111116911Lelio R Paula04/2014
2295(7*2^388335-1)/25116900Lelio R Paula04/2014
22962^388180+93116854Donovan Johnson07/2008
2297(2^388081+7)/1179116821Lelio R Paula03/2014
22982^387946-113261116784Enzo Doria07/2014
22992^387745+75557116723Enzo Doria04/2016
2300(7*10^116684+179)/3116685Robert Price09/2018
23012^387554+71455116666Enzo Doria04/2016
2302(2^387447+78557)/365116631Lelio R Paula12/2014
2303(145*10^116610-1)/9116612Serge Batalov12/2014
2304(25*10^116601-331)/9116602Robert Price08/2018
2305(17*2^387284-1)/59116584Lelio R Paula04/2014
2306(31*2^386968+1)/7116490Lelio R Paula03/2014
23072^386947+1869143116483Enzo Doria05/2016
2308(30^78857-1)/29116480Robert Price12/2011
2309(2^386903-3)/5116469Lelio R Paula03/2014
23102^386389-1864783116315Enzo Doria03/2016
2311(31*2^386231-1)/1711116266Lelio R Paula03/2014
2312297^47012+47012^297116250Norbert Schneider07/2018
2313(2^386087-5)/40959116220Lelio R Paula03/2014
23142^385969-823116189Yves Minet05/2012
231557^66162+2116173Lelio R Paula08/2013
23162^385854+75049116154Enzo Doria04/2016
23172^385775-109587116130Enzo Doria04/2014
23182^385622+71839116084Enzo Doria04/2016
23192^385564+781116067Lelio R Paula01/2012
23202^385410+71893116020Enzo Doria04/2016
2321(25*2^385091+1)/27115924Lelio R Paula04/2014
2322(11*10^115910-131)/3115911Robert Price09/2018
23232^384953-111943115883Paul Bourdelais02/2012
232443^70942-2115882Lelio R Paula04/2014
23257*10^115863+3115864Robert Price08/2015
23262^384834+93115847Donovan Johnson07/2008
23272^384809+71297115840Enzo Doria04/2016
2328(7*2^384759-1)/5115825Lelio R Paula04/2014
2329(71*10^115810-17)/9115811Ray Chandler08/2011
2330(97*10^115794-1)/3115796Serge Batalov12/2014
23312*10^115784-27115785Robert Price05/2018
233210^115773+126739115774Patrick De Geest04/2018
233410^115773-1000000001115773Robert Price03/2018
233310^115773-396221115773Patrick De Geest04/2018
23352^384530+1874305115756Enzo Doria06/2016
2336(3*2^384524-1)/7631115750Lelio R Paula03/2014
23372^384312+81091115690Yves Minet02/2010
2338(4*10^115668-79)/3115669Robert Price02/2018
2339(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
23403^242337-4042115625Enzo Doria05/2014
2341(11*2^383859-13)/15115553Renaud Lifchitz03/2011
23422^383780-3149115530Yves Minet10/2014
23432^383560-455115464Yves Minet03/2012
2344(2^383544+5)/3115458Lelio R Paula03/2014
234589^59221-88^59221115445Robert Price06/2015
23462^383347+1869413115399Enzo Doria05/2016
2347(2^383130-7)/131793115329Lelio R Paula03/2014
2348(12^106859+1)/13115320Paul Bourdelais02/2010
23492^383039+1869509115307Enzo Doria05/2016
2350(13*2^382968+1)/7115286Lelio R Paula04/2014
23512^382633+73697115185Enzo Doria04/2016
23522^382509-113593115147Enzo Doria08/2014
23532^382502-2791721115145Enzo Doria03/2016
23549^120590-120590115073Robert Price03/2014
23552^382198+9115054Lelio R Paula03/2013
23562^381883-59197114959Enzo Doria10/2015
23582^381806-4481114936Yves Minet07/2011
23572^381808-1851507114936Enzo Doria08/2015
23592^381774-112373114926Enzo Doria06/2014
23602^381555-109051114860Enzo Doria04/2014
23612^381546-113501114857Enzo Doria08/2014
23622^381360-110429114801Enzo Doria05/2014
2363(66^63079+1)/67114774Paul Bourdelais09/2017
23642^381252-115079114769Enzo Doria06/2015
23652^381209-29323114756Enzo Doria07/2015
2366569^41651-568^41651114754Jean-Louis Charton11/2009
23672^381201+1873205114753Enzo Doria06/2016
23682^380974-112991114685Enzo Doria07/2014
236988^58949-87114626Norbert Schneider11/2015
23702^380700+91114603Lelio R Paula03/2013
237210^114575+3^114576114576Mike Oakes09/2010
237110^114575+66561114576Patrick De Geest02/2017
237310^114575-581081114575Patrick De Geest02/2017
23742^380587-115315114569Enzo Doria06/2015
23752^380513-216925114546Enzo Doria05/2014
23762^380451-1840087114528Enzo Doria06/2015
2377(15*2^380388-1)/539114507Lelio R Paula04/2014
23782^380279-461347114476Enzo Doria07/2015
23792^380021+1871147114398Enzo Doria05/2016
23802^380005+1869707114393Enzo Doria05/2016
23812^379958-113297114379Enzo Doria07/2014
23822^379881-109105114356Enzo Doria04/2014
2383(21*2^379857-1)/13114349Lelio R Paula03/2014
2384(4*10^114340+83)/3114341Robert Price02/2018
2385(4*10^114296+149)/9114296Robert Price04/2018
238688^58773-87114284Norbert Schneider11/2015
23872^379529-2790283114250Enzo Doria03/2016
23882^379522+1869115114248Enzo Doria05/2016
2389(145*10^114226-1)/9114228Serge Batalov12/2014
23902^379317-115033114186Enzo Doria06/2015
2391(17*2^379246-1)/17407114162Lelio R Paula03/2014
2392(4*10^114076+143)/3114077Robert Price03/2018
23932*10^113941+9113942Dmitry Domanov11/2010
23944*10^113905+91113906Robert Price08/2018
23954*10^113874-21113875Robert Price09/2018
23962^378272-16565113872Enzo Doria04/2013
23972^378217-109075113855Enzo Doria04/2014
23982^378198+67113849Lelio R Paula03/2013
23992^378173-3249113842Yves Minet12/2014
2400(2^378155-5)/6597113833Lelio R Paula03/2014
240192941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
24022^378128-262977113828Enzo Doria05/2014
24032^378123-113215113827Enzo Doria07/2014
24046^146274-18893113824Enzo Doria03/2013
24052^378078+75113813Lelio R Paula03/2013
24062^377940+63113772Lelio R Paula03/2013
24072^377941-2785843113772Enzo Doria04/2016
24082^377810+1875109113733Enzo Doria09/2016
24092^377803-1838635113731Enzo Doria05/2015
24102^377799+52223113729Yves Minet08/2010
241111^109190-270113710Enzo Doria12/2012
24127*10^113693+9113694Robert Price09/2015
2413(2*10^113631+529)/9113631Robert Price01/2018
24142^377408-2798279113612Enzo Doria04/2016
24152^377222+93679113556Yves Minet02/2011
2416262147#+316847113552Makoto Morimoto02/2016
24172^377026-458903113497Enzo Doria04/2015
241835^73477-34^73477113454Robert Price05/2012
24192^376790+27113426Lelio R Paula03/2013
24202^376786-112701113424Enzo Doria06/2014
24212^376731+21113408Lelio R Paula03/2013
24222^376634+1871245113379Enzo Doria05/2016
2423(4^188318+17)/3113379Robert Price02/2017
24242^376576-344369113361Enzo Doria07/2015
2425(17*2^376526-1)/223113345Lelio R Paula03/2014
2426(27*2^376441-1)/811113319Lelio R Paula03/2014
24272^376128-21237113226Enzo Doria06/2013
24282^375638-1787171113079Enzo Doria03/2016
24292^375537+4847113048Yves Minet02/2011
2430(17^91837+16^91837)/33113000Robert Price08/2013
24315*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
24322^375350-3221112992Yves Minet07/2011
2434(13*2^375306+1)/7112979Lelio R Paula03/2014
24332^375305+76757112979Enzo Doria05/2016
24352^375258+1874989112964Enzo Doria07/2016
2436(29^77237-1)/28112950Robert Price04/2012
24372^375154+74959112933Enzo Doria04/2016
24382^374993-2787163112885Enzo Doria11/2015
2439123^53970+2112793Lelio R Paula06/2013
2440p(22852)#/2+512112745Robert Price05/2017
2441(11*10^112742-131)/3112743Robert Price09/2018
24422^374441-21049112718Enzo Doria06/2013
2443(2^374321+1)/3112682H.&R. Lifchitz12/2000
2444(13^101089-1)/12112607Paul Bourdelais03/2010
24453^236011-8828112606Enzo Doria05/2014
244639^70666+2112435Lelio R Paula11/2013
2447(2^373350-7)/3112390Lelio R Paula03/2014
24482^373306-1840931112377Enzo Doria06/2015
24492^373117+1872107112320Enzo Doria05/2016
24502^373040+2792761112297Enzo Doria03/2016
2451EPrime(112280)112280Eric W. Weisstein10/2010
24522^372950+7112270Lelio R Paula03/2013
24532^372945+1872167112268Enzo Doria05/2016
24542^372695+72113112193Enzo Doria04/2016
24552^372689-2563112191Yves Minet07/2014
24562^372638-1859441112176Enzo Doria03/2016
24573^235074-113056112159Enzo Doria07/2014
2458(91*10^112098-1)/9112100Robert Price04/2015
24592^372310-85061112077Paul Bourdelais02/2012
2460(10^112067+53)/9112067Serge Batalov07/2015
246175^59760+2112054Lelio R Paula08/2013
24622^372108+74221112016Enzo Doria04/2016
24632^371970-459491111975Enzo Doria05/2015
246441^69427-40^69427111971Robert Price07/2012
2465(10^111902+71)/9111902Serge Batalov07/2015
24662^371440-112865111815Enzo Doria06/2014
24672^371426-459161111811Enzo Doria05/2015
24682^371276-461267111766Enzo Doria07/2015
24692^371098-113261111712Enzo Doria07/2014
2470(7*10^111706-61)/9111706Erik Branger01/2011
24712^371044+1869391111696Enzo Doria05/2016
247288^57416+87111645Norbert Schneider11/2015
24732^370829-109693111631Enzo Doria04/2014
247415^94906-2111619Lelio R Paula11/2013
24762^370643-37111575Yves Minet01/2012
2475(2^370655-5)/2439111575Lelio R Paula03/2014
24772^370610-3911111565Yves Minet04/2017
2478286^45405+45405^286111532Norbert Schneider04/2015
24794*5^159563-9111531Lelio R Paula11/2014
2480(4^185225+23)/3111517Robert Price10/2018
24812^370393-2797093111500Enzo Doria03/2016
2482(21*2^370382-1)/629111495Lelio R Paula03/2014
24832^370292-2791979111469Enzo Doria03/2016
24842^370177-461551111435Enzo Doria07/2015
2485109^54683-108111413Norbert Schneider02/2017
2486numbpart(10^10+76282)111391Serge Batalov04/2015
24872^369974+733111374Lelio R Paula05/2013
24882^369915-286267111356Enzo Doria07/2015
24892^369855-1615111338Lelio R Paula05/2017
24907*10^111325+3111326Robert Price08/2015
249151^65176+2111293Lelio R Paula08/2013
24922^369643-1865767111274Enzo Doria03/2016
24932^369603+885111262Lelio R Paula05/2017
2494L(532277)111240Renaud Lifchitz03/2004
2495105^55033-2111233Lelio R Paula10/2017
2496(35*10^111232-737)/9111233Robert Price07/2018
24972^369392+29835111199Lelio R Paula05/2017
24982^369354-3413111187Yves Minet12/2016
24992^369296-27111170Lelio R Paula02/2013
25002^369239-109837111153Enzo Doria05/2014


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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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