PRP Records

Probable Primes Top 10000

(253466 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 ?
25012^391933+5897117984Yves Minet02/2011
25022^391912-1849259117978Enzo Doria08/2015
2503(2^391812+5)/14181117944Lelio R Paula04/2014
2504(46*10^117902+683)/9117903Robert Price03/2019
2505(7*2^391521+1)/285117858Lelio R Paula04/2014
25062^391324+90901117801Yves Minet02/2011
25072^391301-1859923117794Enzo Doria03/2016
25082^391261-4131117782Yves Minet02/2018
2509(2^391115-7)/11791117734Lelio R Paula04/2014
25102^390960+1880881117691Enzo Doria11/2016
25112^390897-1860553117672Enzo Doria11/2015
25122^390889-115003117670Enzo Doria06/2015
25132^390779-30337117637Paul Bourdelais02/2012
251411^112916-780117590Enzo Doria12/2012
2515(16^97613-5^97613)/11117537Robert Price07/2013
2516(17*2^390272+1)/1983117482Lelio R Paula04/2014
251731^78759-30117459Theodore Burton02/2007
25182^389998+37117402Lelio R Paula03/2013
2519(13*10^117249+161)/3117250Robert Price11/2018
25202^389478+43117245Lelio R Paula03/2013
2521(29*2^389351-1)/9117207Lelio R Paula04/2014
25225*10^117205+23117206Robert Price03/2019
2523(2^389341-7)/3865117200Lelio R Paula03/2014
252410^117142+209223117143Patrick De Geest04/2018
252610^117142-1000000001117142Robert Price03/2018
252510^117142-966057117142Patrick De Geest04/2018
252710^117135+360577117136Patrick De Geest07/2018
252810^117135-401117135Robert Price01/2018
25294*10^117123+79117124Robert Price08/2018
25302^389033-12797413117111Enzo Doria04/2016
25312^388960-109505117089Enzo Doria04/2014
2532(2^388928-5)/569117077Lelio R Paula03/2014
25332^388888-1529117067Yves Minet01/2013
253410^117059+28879117060Patrick De Geest05/2016
2535(10^117059-71)/1117059Serge Batalov12/2014
2536(26*10^116999-503)/9117000Robert Price07/2018
25373^245154-6256116969Enzo Doria05/2014
25385*10^116966-43116967Robert Price01/2019
25392^388536-113495116961Enzo Doria08/2014
25402^388469-43116941Lelio R Paula03/2013
2541(7*2^388372-1)/111116911Lelio R Paula04/2014
2542(7*2^388335-1)/25116900Lelio R Paula04/2014
25432^388180+93116854Donovan Johnson07/2008
2544(2^388081+7)/1179116821Lelio R Paula03/2014
25452^387946-113261116784Enzo Doria07/2014
25462^387745+75557116723Enzo Doria04/2016
2547(7*10^116684+179)/3116685Robert Price09/2018
25482^387554+71455116666Enzo Doria04/2016
2549(2^387447+78557)/365116631Lelio R Paula12/2014
2550(145*10^116610-1)/9116612Serge Batalov12/2014
2551(25*10^116601-331)/9116602Robert Price08/2018
2552(17*2^387284-1)/59116584Lelio R Paula04/2014
2553(31*2^386968+1)/7116490Lelio R Paula03/2014
25542^386947+1869143116483Enzo Doria05/2016
2555(30^78857-1)/29116480Robert Price12/2011
2556(2^386903-3)/5116469Lelio R Paula03/2014
25572^386389-1864783116315Enzo Doria03/2016
2558(31*2^386231-1)/1711116266Lelio R Paula03/2014
2559297^47012+47012^297116250Norbert Schneider07/2018
2560(2^386087-5)/40959116220Lelio R Paula03/2014
25612^385969-823116189Yves Minet05/2012
256257^66162+2116173Lelio R Paula08/2013
25632^385854+75049116154Enzo Doria04/2016
25642^385775-109587116130Enzo Doria04/2014
2565(14*10^116112-101)/3116113Robert Price02/2019
2566Phi(236354,10)/24817171116109Makoto Kamada08/2019
25672^385622+71839116084Enzo Doria04/2016
25682^385564+781116067Lelio R Paula01/2012
25692^385410+71893116020Enzo Doria04/2016
2570(25*2^385091+1)/27115924Lelio R Paula04/2014
2571(11*10^115910-131)/3115911Robert Price09/2018
25722^384953-111943115883Paul Bourdelais02/2012
257343^70942-2115882Lelio R Paula04/2014
25747*10^115863+3115864Robert Price08/2015
25752^384834+93115847Donovan Johnson07/2008
25762^384809+71297115840Enzo Doria04/2016
2577(7*2^384759-1)/5115825Lelio R Paula04/2014
2578(71*10^115810-17)/9115811Ray Chandler08/2011
2579(97*10^115794-1)/3115796Serge Batalov12/2014
25802*10^115784-27115785Robert Price05/2018
258110^115773+126739115774Patrick De Geest04/2018
258310^115773-1000000001115773Robert Price03/2018
258210^115773-396221115773Patrick De Geest04/2018
25842^384530+1874305115756Enzo Doria06/2016
2585(3*2^384524-1)/7631115750Lelio R Paula03/2014
2586(44*10^115697-413)/9115698Robert Price03/2019
25872^384312+81091115690Yves Minet02/2010
2588(4*10^115668-79)/3115669Robert Price02/2018
2589(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
2590(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
259118^92125-92125^18115642Dylan Delgado08/2019
25923^242337-4042115625Enzo Doria05/2014
25937*10^115561+79115562Robert Price07/2019
2594(11*2^383859-13)/15115553Renaud Lifchitz03/2011
25952^383780-3149115530Yves Minet10/2014
2596(41*10^115523-383)/9115524Robert Price11/2018
25972^383560-455115464Yves Minet03/2012
2598(2^383544+5)/3115458Lelio R Paula03/2014
259989^59221-88^59221115445Robert Price06/2015
26002^383347+1869413115399Enzo Doria05/2016
2601(2^383130-7)/131793115329Lelio R Paula03/2014
2602(12^106859+1)/13115320Paul Bourdelais02/2010
26032^383039+1869509115307Enzo Doria05/2016
2604(13*2^382968+1)/7115286Lelio R Paula04/2014
26052^382633+73697115185Enzo Doria04/2016
26062^382509-113593115147Enzo Doria08/2014
26072^382502-2791721115145Enzo Doria03/2016
26089^120590-120590115073Robert Price03/2014
26092^382198+9115054Lelio R Paula03/2013
26102^381883-59197114959Enzo Doria10/2015
26122^381806-4481114936Yves Minet07/2011
26112^381808-1851507114936Enzo Doria08/2015
26132^381774-112373114926Enzo Doria06/2014
26142^381555-109051114860Enzo Doria04/2014
26152^381546-113501114857Enzo Doria08/2014
26162^381360-110429114801Enzo Doria05/2014
2617(17*10^114795+79)/3114796Robert Price04/2019
2618(66^63079+1)/67114774Paul Bourdelais09/2017
26192^381252-115079114769Enzo Doria06/2015
26202^381209-29323114756Enzo Doria07/2015
2621569^41651-568^41651114754Jean-Louis Charton11/2009
26222^381201+1873205114753Enzo Doria06/2016
26232^380974-112991114685Enzo Doria07/2014
262488^58949-87114626Norbert Schneider11/2015
26252^380700+91114603Lelio R Paula03/2013
262610^114575+3^114576114576Mike Oakes09/2010
262710^114575+66561114576Patrick De Geest02/2017
262810^114575-581081114575Patrick De Geest02/2017
26292^380587-115315114569Enzo Doria06/2015
26302^380513-216925114546Enzo Doria05/2014
26312^380451-1840087114528Enzo Doria06/2015
2632(15*2^380388-1)/539114507Lelio R Paula04/2014
26332^380279-461347114476Enzo Doria07/2015
26342^380021+1871147114398Enzo Doria05/2016
26352^380005+1869707114393Enzo Doria05/2016
26362^379958-113297114379Enzo Doria07/2014
26372^379881-109105114356Enzo Doria04/2014
2638(21*2^379857-1)/13114349Lelio R Paula03/2014
2639(4*10^114340+83)/3114341Robert Price02/2018
2640(4*10^114296+149)/9114296Robert Price04/2018
264188^58773-87114284Norbert Schneider11/2015
26422^379529-2790283114250Enzo Doria03/2016
26432^379522+1869115114248Enzo Doria05/2016
2644(145*10^114226-1)/9114228Serge Batalov12/2014
26452^379317-115033114186Enzo Doria06/2015
2646(17*2^379246-1)/17407114162Lelio R Paula03/2014
2647(4*10^114076+143)/3114077Robert Price03/2018
2648(46*10^113969+683)/9113970Robert Price03/2019
26492*10^113941+9113942Dmitry Domanov11/2010
26504*10^113905+91113906Robert Price08/2018
26514*10^113874-21113875Robert Price09/2018
26522^378272-16565113872Enzo Doria04/2013
26532^378217-109075113855Enzo Doria04/2014
26542^378198+67113849Lelio R Paula03/2013
26552^378173-3249113842Yves Minet12/2014
2656(2^378155-5)/6597113833Lelio R Paula03/2014
265792941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
26582^378128-262977113828Enzo Doria05/2014
26592^378123-113215113827Enzo Doria07/2014
26606^146274-18893113824Enzo Doria03/2013
26612^378078+75113813Lelio R Paula03/2013
26622^377940+63113772Lelio R Paula03/2013
26632^377941-2785843113772Enzo Doria04/2016
26642^377810+1875109113733Enzo Doria09/2016
26652^377803-1838635113731Enzo Doria05/2015
26662^377799+52223113729Yves Minet08/2010
266711^109190-270113710Enzo Doria12/2012
26687*10^113693+9113694Robert Price09/2015
26694*10^113658+49113659Robert Price01/2019
2670(2*10^113631+529)/9113631Robert Price01/2018
26712^377408-2798279113612Enzo Doria04/2016
26725*10^113586+57113587Robert Price12/2018
26732^377222+93679113556Yves Minet02/2011
2674262147#+316847113552Makoto Morimoto02/2016
26752^377026-458903113497Enzo Doria04/2015
267635^73477-34^73477113454Robert Price05/2012
26772^376790+27113426Lelio R Paula03/2013
26782^376786-112701113424Enzo Doria06/2014
26792^376731+21113408Lelio R Paula03/2013
26802^376634+1871245113379Enzo Doria05/2016
2681(4^188318+17)/3113379Robert Price02/2017
26822^376576-344369113361Enzo Doria07/2015
26832^376549-4543113353Yves Minet03/2019
2684(17*2^376526-1)/223113345Lelio R Paula03/2014
2685(27*2^376441-1)/811113319Lelio R Paula03/2014
26862^376128-21237113226Enzo Doria06/2013
26875*10^113224-81113225Robert Price01/2019
2688(46*10^113162+521)/9113163Robert Price02/2019
26892^375638-1787171113079Enzo Doria03/2016
26902^375537+4847113048Yves Minet02/2011
2691(17^91837+16^91837)/33113000Robert Price08/2013
26925*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
26932^375350-3221112992Yves Minet07/2011
2694(13*2^375306+1)/7112979Lelio R Paula03/2014
26952^375305+76757112979Enzo Doria05/2016
26962^375258+1874989112964Enzo Doria07/2016
2697(29^77237-1)/28112950Robert Price04/2012
26982^375154+74959112933Enzo Doria04/2016
26992^374993-2787163112885Enzo Doria11/2015
2700123^53970+2112793Lelio R Paula06/2013
27012^374640-4685112778Yves Minet05/2019
2702p(22852)#/2+512112745Robert Price05/2017
2703(11*10^112742-131)/3112743Robert Price09/2018
27042^374441-21049112718Enzo Doria06/2013
2705(2^374321+1)/3112682H.&R. Lifchitz12/2000
2706(13^101089-1)/12112607Paul Bourdelais03/2010
27073^236011-8828112606Enzo Doria05/2014
270839^70666+2112435Lelio R Paula11/2013
2709(2^373350-7)/3112390Lelio R Paula03/2014
27102^373306-1840931112377Enzo Doria06/2015
27112^373117+1872107112320Enzo Doria05/2016
27122^373040+2792761112297Enzo Doria03/2016
2713EPrime(112280)112280Eric W. Weisstein10/2010
27142^372950+7112270Lelio R Paula03/2013
27152^372945+1872167112268Enzo Doria05/2016
27162^372695+72113112193Enzo Doria04/2016
27172^372689-2563112191Yves Minet07/2014
27182^372638-1859441112176Enzo Doria03/2016
27193^235074-113056112159Enzo Doria07/2014
2720131^52949-130112108Norbert Schneider02/2019
2721(91*10^112098-1)/9112100Robert Price04/2015
27222^372310-85061112077Paul Bourdelais02/2012
2723(10^112067+53)/9112067Serge Batalov07/2015
272475^59760+2112054Lelio R Paula08/2013
27252^372108+74221112016Enzo Doria04/2016
27265*10^112003+81112004Robert Price03/2019
2727215^48018+48018^215112000Norbert Schneider10/2018
27282^371970-459491111975Enzo Doria05/2015
272941^69427-40^69427111971Robert Price07/2012
2730(10^111902+71)/9111902Serge Batalov07/2015
27312^371440-112865111815Enzo Doria06/2014
27322^371426-459161111811Enzo Doria05/2015
27332^371276-461267111766Enzo Doria07/2015
27342^371098-113261111712Enzo Doria07/2014
2735(7*10^111706-61)/9111706Erik Branger01/2011
27362^371044+1869391111696Enzo Doria05/2016
273788^57416+87111645Norbert Schneider11/2015
27382^370829-109693111631Enzo Doria04/2014
273915^94906-2111619Lelio R Paula11/2013
27402^370695-4627111591Yves Minet05/2019
27422^370643-37111575Yves Minet01/2012
2741(2^370655-5)/2439111575Lelio R Paula03/2014
27432^370610-3911111565Yves Minet04/2017
2744286^45405+45405^286111532Norbert Schneider04/2015
27454*5^159563-9111531Lelio R Paula11/2014
2746(4^185225+23)/3111517Robert Price10/2018
27472^370393-2797093111500Enzo Doria03/2016
2748(21*2^370382-1)/629111495Lelio R Paula03/2014
27492^370292-2791979111469Enzo Doria03/2016
27502^370177-461551111435Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

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