PRP Records

Probable Primes Top 10000

(218736 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 ?
225110^117059+28879117060Patrick De Geest05/2016
2252(10^117059-71)/1117059Serge Batalov12/2014
2253(26*10^116999-503)/9117000Robert Price07/2018
22543^245154-6256116969Enzo Doria05/2014
22552^388536-113495116961Enzo Doria08/2014
22562^388469-43116941Lelio R Paula03/2013
2257(7*2^388372-1)/111116911Lelio R Paula04/2014
2258(7*2^388335-1)/25116900Lelio R Paula04/2014
22592^388180+93116854Donovan Johnson07/2008
2260(2^388081+7)/1179116821Lelio R Paula03/2014
22612^387946-113261116784Enzo Doria07/2014
22622^387745+75557116723Enzo Doria04/2016
22632^387554+71455116666Enzo Doria04/2016
2264(2^387447+78557)/365116631Lelio R Paula12/2014
2265(145*10^116610-1)/9116612Serge Batalov12/2014
2266(17*2^387284-1)/59116584Lelio R Paula04/2014
2267(31*2^386968+1)/7116490Lelio R Paula03/2014
22682^386947+1869143116483Enzo Doria05/2016
2269(30^78857-1)/29116480Robert Price12/2011
2270(2^386903-3)/5116469Lelio R Paula03/2014
22712^386389-1864783116315Enzo Doria03/2016
2272(31*2^386231-1)/1711116266Lelio R Paula03/2014
2273297^47012+47012^297116250Norbert Schneider07/2018
2274(2^386087-5)/40959116220Lelio R Paula03/2014
22752^385969-823116189Yves Minet05/2012
227657^66162+2116173Lelio R Paula08/2013
22772^385854+75049116154Enzo Doria04/2016
22782^385775-109587116130Enzo Doria04/2014
22792^385622+71839116084Enzo Doria04/2016
22802^385564+781116067Lelio R Paula01/2012
22812^385410+71893116020Enzo Doria04/2016
2282(25*2^385091+1)/27115924Lelio R Paula04/2014
22832^384953-111943115883Paul Bourdelais02/2012
228443^70942-2115882Lelio R Paula04/2014
22857*10^115863+3115864Robert Price08/2015
22862^384834+93115847Donovan Johnson07/2008
22872^384809+71297115840Enzo Doria04/2016
2288(7*2^384759-1)/5115825Lelio R Paula04/2014
2289(71*10^115810-17)/9115811Ray Chandler08/2011
2290(97*10^115794-1)/3115796Serge Batalov12/2014
22912*10^115784-27115785Robert Price05/2018
229210^115773+126739115774Patrick De Geest04/2018
229410^115773-1000000001115773Robert Price03/2018
229310^115773-396221115773Patrick De Geest04/2018
22952^384530+1874305115756Enzo Doria06/2016
2296(3*2^384524-1)/7631115750Lelio R Paula03/2014
22972^384312+81091115690Yves Minet02/2010
2298(4*10^115668-79)/3115669Robert Price02/2018
2299(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
23003^242337-4042115625Enzo Doria05/2014
2301(11*2^383859-13)/15115553Renaud Lifchitz03/2011
23022^383780-3149115530Yves Minet10/2014
23032^383560-455115464Yves Minet03/2012
2304(2^383544+5)/3115458Lelio R Paula03/2014
230589^59221-88^59221115445Robert Price06/2015
23062^383347+1869413115399Enzo Doria05/2016
2307(2^383130-7)/131793115329Lelio R Paula03/2014
2308(12^106859+1)/13115320Paul Bourdelais02/2010
23092^383039+1869509115307Enzo Doria05/2016
2310(13*2^382968+1)/7115286Lelio R Paula04/2014
23112^382633+73697115185Enzo Doria04/2016
23122^382509-113593115147Enzo Doria08/2014
23132^382502-2791721115145Enzo Doria03/2016
23149^120590-120590115073Robert Price03/2014
23152^382198+9115054Lelio R Paula03/2013
23162^381883-59197114959Enzo Doria10/2015
23182^381806-4481114936Yves Minet07/2011
23172^381808-1851507114936Enzo Doria08/2015
23192^381774-112373114926Enzo Doria06/2014
23202^381555-109051114860Enzo Doria04/2014
23212^381546-113501114857Enzo Doria08/2014
23222^381360-110429114801Enzo Doria05/2014
2323(66^63079+1)/67114774Paul Bourdelais09/2017
23242^381252-115079114769Enzo Doria06/2015
23252^381209-29323114756Enzo Doria07/2015
2326569^41651-568^41651114754Jean-Louis Charton11/2009
23272^381201+1873205114753Enzo Doria06/2016
23282^380974-112991114685Enzo Doria07/2014
232988^58949-87114626Norbert Schneider11/2015
23302^380700+91114603Lelio R Paula03/2013
233210^114575+3^114576114576Mike Oakes09/2010
233110^114575+66561114576Patrick De Geest02/2017
233310^114575-581081114575Patrick De Geest02/2017
23342^380587-115315114569Enzo Doria06/2015
23352^380513-216925114546Enzo Doria05/2014
23362^380451-1840087114528Enzo Doria06/2015
2337(15*2^380388-1)/539114507Lelio R Paula04/2014
23382^380279-461347114476Enzo Doria07/2015
23392^380021+1871147114398Enzo Doria05/2016
23402^380005+1869707114393Enzo Doria05/2016
23412^379958-113297114379Enzo Doria07/2014
23422^379881-109105114356Enzo Doria04/2014
2343(21*2^379857-1)/13114349Lelio R Paula03/2014
2344(4*10^114340+83)/3114341Robert Price02/2018
2345(4*10^114296+149)/9114296Robert Price04/2018
234688^58773-87114284Norbert Schneider11/2015
23472^379529-2790283114250Enzo Doria03/2016
23482^379522+1869115114248Enzo Doria05/2016
2349(145*10^114226-1)/9114228Serge Batalov12/2014
23502^379317-115033114186Enzo Doria06/2015
2351(17*2^379246-1)/17407114162Lelio R Paula03/2014
2352(4*10^114076+143)/3114077Robert Price03/2018
23532*10^113941+9113942Dmitry Domanov11/2010
23542^378272-16565113872Enzo Doria04/2013
23552^378217-109075113855Enzo Doria04/2014
23562^378198+67113849Lelio R Paula03/2013
23572^378173-3249113842Yves Minet12/2014
2358(2^378155-5)/6597113833Lelio R Paula03/2014
235992941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
23602^378128-262977113828Enzo Doria05/2014
23612^378123-113215113827Enzo Doria07/2014
23626^146274-18893113824Enzo Doria03/2013
23632^378078+75113813Lelio R Paula03/2013
23642^377940+63113772Lelio R Paula03/2013
23652^377941-2785843113772Enzo Doria04/2016
23662^377810+1875109113733Enzo Doria09/2016
23672^377803-1838635113731Enzo Doria05/2015
23682^377799+52223113729Yves Minet08/2010
236911^109190-270113710Enzo Doria12/2012
23707*10^113693+9113694Robert Price09/2015
2371(2*10^113631+529)/9113631Robert Price01/2018
23722^377408-2798279113612Enzo Doria04/2016
23732^377222+93679113556Yves Minet02/2011
2374262147#+316847113552Makoto Morimoto02/2016
23752^377026-458903113497Enzo Doria04/2015
237635^73477-34^73477113454Robert Price05/2012
23772^376790+27113426Lelio R Paula03/2013
23782^376786-112701113424Enzo Doria06/2014
23792^376731+21113408Lelio R Paula03/2013
23802^376634+1871245113379Enzo Doria05/2016
2381(4^188318+17)/3113379Robert Price02/2017
23822^376576-344369113361Enzo Doria07/2015
2383(17*2^376526-1)/223113345Lelio R Paula03/2014
2384(27*2^376441-1)/811113319Lelio R Paula03/2014
23852^376128-21237113226Enzo Doria06/2013
23862^375638-1787171113079Enzo Doria03/2016
23872^375537+4847113048Yves Minet02/2011
2388(17^91837+16^91837)/33113000Robert Price08/2013
23895*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
23902^375350-3221112992Yves Minet07/2011
2392(13*2^375306+1)/7112979Lelio R Paula03/2014
23912^375305+76757112979Enzo Doria05/2016
23932^375258+1874989112964Enzo Doria07/2016
2394(29^77237-1)/28112950Robert Price04/2012
23952^375154+74959112933Enzo Doria04/2016
23962^374993-2787163112885Enzo Doria11/2015
2397123^53970+2112793Lelio R Paula06/2013
2398p(22852)#/2+512112745Robert Price05/2017
23992^374441-21049112718Enzo Doria06/2013
2400(2^374321+1)/3112682H.&R. Lifchitz12/2000
2401(13^101089-1)/12112607Paul Bourdelais03/2010
24023^236011-8828112606Enzo Doria05/2014
240339^70666+2112435Lelio R Paula11/2013
2404(2^373350-7)/3112390Lelio R Paula03/2014
24052^373306-1840931112377Enzo Doria06/2015
24062^373117+1872107112320Enzo Doria05/2016
24072^373040+2792761112297Enzo Doria03/2016
2408EPrime(112280)112280Eric W. Weisstein10/2010
24092^372950+7112270Lelio R Paula03/2013
24102^372945+1872167112268Enzo Doria05/2016
24112^372695+72113112193Enzo Doria04/2016
24122^372689-2563112191Yves Minet07/2014
24132^372638-1859441112176Enzo Doria03/2016
24143^235074-113056112159Enzo Doria07/2014
2415(91*10^112098-1)/9112100Robert Price04/2015
24162^372310-85061112077Paul Bourdelais02/2012
2417(10^112067+53)/9112067Serge Batalov07/2015
241875^59760+2112054Lelio R Paula08/2013
24192^372108+74221112016Enzo Doria04/2016
24202^371970-459491111975Enzo Doria05/2015
242141^69427-40^69427111971Robert Price07/2012
2422(10^111902+71)/9111902Serge Batalov07/2015
24232^371440-112865111815Enzo Doria06/2014
24242^371426-459161111811Enzo Doria05/2015
24252^371276-461267111766Enzo Doria07/2015
24262^371098-113261111712Enzo Doria07/2014
2427(7*10^111706-61)/9111706Erik Branger01/2011
24282^371044+1869391111696Enzo Doria05/2016
242988^57416+87111645Norbert Schneider11/2015
24302^370829-109693111631Enzo Doria04/2014
243115^94906-2111619Lelio R Paula11/2013
24332^370643-37111575Yves Minet01/2012
2432(2^370655-5)/2439111575Lelio R Paula03/2014
24342^370610-3911111565Yves Minet04/2017
2435286^45405+45405^286111532Norbert Schneider04/2015
24364*5^159563-9111531Lelio R Paula11/2014
24372^370393-2797093111500Enzo Doria03/2016
2438(21*2^370382-1)/629111495Lelio R Paula03/2014
24392^370292-2791979111469Enzo Doria03/2016
24402^370177-461551111435Enzo Doria07/2015
2441109^54683-108111413Norbert Schneider02/2017
2442numbpart(10^10+76282)111391Serge Batalov04/2015
24432^369974+733111374Lelio R Paula05/2013
24442^369915-286267111356Enzo Doria07/2015
24452^369855-1615111338Lelio R Paula05/2017
24467*10^111325+3111326Robert Price08/2015
244751^65176+2111293Lelio R Paula08/2013
24482^369643-1865767111274Enzo Doria03/2016
24492^369603+885111262Lelio R Paula05/2017
2450L(532277)111240Renaud Lifchitz03/2004
2451105^55033-2111233Lelio R Paula10/2017
2452(35*10^111232-737)/9111233Robert Price07/2018
24532^369392+29835111199Lelio R Paula05/2017
24542^369354-3413111187Yves Minet12/2016
24552^369296-27111170Lelio R Paula02/2013
24562^369239-109837111153Enzo Doria05/2014
24572^369224-291839111148Enzo Doria07/2015
24582^369216+2798881111146Enzo Doria04/2016
245910^111111+163849111112Patrick De Geest03/2017
246010^111111-312911111111Patrick De Geest03/2017
24612^369092-216923111108Enzo Doria05/2014
24622^369081-55111105Lelio R Paula02/2013
246388^57124-87111077Norbert Schneider11/2015
24642^368980+753111075Lelio R Paula05/2013
24652^368946-3623111064Yves Minet03/2017
24662^368929+29835111059Lelio R Paula05/2017
24674^184463-3^184463111058Jean-Louis Charton12/2004
2468111^54298+110111057Norbert Schneider04/2017
2469(4*10^111032-7)/3111033Ray Chandler04/2011
24702^368641-460303110972Enzo Doria06/2015
24712^368619-109087110966Enzo Doria04/2014
24723*2^368489+7110927Lelio R Paula09/2014
247397411!4-2110913Robert Price07/2017
2474(9179*2^368330-1)/35110881Lelio R Paula05/2015
2475(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
24762^368050-64875110795Lelio R Paula05/2017
24772^368048+25110794Lelio R Paula02/2013
247869^60239-2110771Lelio R Paula10/2013
2479(23*2^367952+1)/15717110762Lelio R Paula03/2014
24802^367924-69110757Lelio R Paula02/2013
24812^367709-109723110692Enzo Doria04/2014
2482(3*2^367644-1)/107110671Lelio R Paula03/2014
2483(23*2^367398+1)/57963110595Lelio R Paula03/2014
24842^367215+1879223110543Enzo Doria09/2016
24852^367141+41110521Lelio R Paula02/2013
24862^367126+29835110516Lelio R Paula05/2017
2487(11*10^110496+49)/3110497Robert Price07/2018
2488(31*2^366976+1)/7110472Lelio R Paula03/2014
24892^366853+5711110434Lelio R Paula05/2017
2490(21181*2^366833+1)/3110432Lelio R Paula07/2014
24912^366816+315110423Lelio R Paula05/2017
24922^366775-2787037110411Enzo Doria03/2016
2493(112*10^110405-1)/3110407Serge Batalov12/2014
24942^366751+2797553110404Enzo Doria03/2016
24952^366748+255110403Lelio R Paula05/2017
24962^366738-2985110400Yves Minet09/2014
2497(23*2^366739+1)/74575110396Lelio R Paula03/2014
24982^366716+1871791110393Enzo Doria05/2016
24992^366649+1871687110373Enzo Doria05/2016
25002^366629-351205110367Enzo Doria06/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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