PRP Records

Probable Primes Top 10000

(271067 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 ?
3001(25*2^385091+1)/27115924Lelio R Paula04/2014
3002(11*10^115910-131)/3115911Robert Price09/2018
30032^384953-111943115883Paul Bourdelais02/2012
300443^70942-2115882Lelio R Paula04/2014
3005(94*10^115879-7)/3115881Robert Price03/2020
30067*10^115863+3115864Robert Price08/2015
30072^384834+93115847Donovan Johnson07/2008
30082^384809+71297115840Enzo Doria04/2016
3009(7*2^384759-1)/5115825Lelio R Paula04/2014
3010(71*10^115810-17)/9115811Ray Chandler08/2011
3011(97*10^115794-1)/3115796Serge Batalov12/2014
30122*10^115784-27115785Robert Price05/2018
301310^115773+126739115774Patrick De Geest04/2018
301510^115773-1000000001115773Robert Price03/2018
301410^115773-396221115773Patrick De Geest04/2018
3016(2^384582+778)/2115771Stefano Morozzi09/2020
30172^384530+1874305115756Enzo Doria06/2016
3018(3*2^384524-1)/7631115750Lelio R Paula03/2014
3019(44*10^115697-413)/9115698Robert Price03/2019
3020(2^384317+1026)/2115691Stefano Morozzi09/2020
30212^384312+81091115690Yves Minet02/2010
3022(2^384265+2150)/2115675Stefano Morozzi09/2020
3023(2^384246+2182)/2115670Stefano Morozzi09/2020
3024(4*10^115668-79)/3115669Robert Price02/2018
3025(2^384193+242)/2115654Stefano Morozzi09/2020
3026(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
3027(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
302818^92125-92125^18115642Dylan Delgado08/2019
30293^242337-4042115625Enzo Doria05/2014
3030(2^383931+674)/2115575Stefano Morozzi09/2020
30317*10^115561+79115562Robert Price07/2019
3032(2^383872+3046)/2115557Stefano Morozzi09/2020
3033(11*2^383859-13)/15115553Renaud Lifchitz03/2011
30342^383780-3149115530Yves Minet10/2014
3035(41*10^115523-383)/9115524Robert Price11/2018
3036(2^383618+618)/2115481Stefano Morozzi09/2020
30372^383560-455115464Yves Minet03/2012
3038(2^383544+5)/3115458Lelio R Paula03/2014
303989^59221-88^59221115445Robert Price06/2015
30402^383347+1869413115399Enzo Doria05/2016
3041(103*10^115366+17)/3115368Robert Price08/2020
3042(2^383232+750)/2115365Stefano Morozzi09/2020
3043(2^383130-7)/131793115329Lelio R Paula03/2014
3044(12^106859+1)/13115320Paul Bourdelais02/2010
30452^383039+1869509115307Enzo Doria05/2016
3046(13*2^382968+1)/7115286Lelio R Paula04/2014
3047(2^382945+2046)/2115278Stefano Morozzi09/2020
3048(2^382789+3182)/2115231Stefano Morozzi09/2020
30496*10^115211+79115212Robert Price09/2020
3050(2^382722+3598)/2115211Stefano Morozzi09/2020
3051(2^382699+2090)/2115204Stefano Morozzi09/2020
30522^382633+73697115185Enzo Doria04/2016
30532^382509-113593115147Enzo Doria08/2014
30542^382502-2791721115145Enzo Doria03/2016
30559^120590-120590115073Robert Price03/2014
30562^382198+9115054Lelio R Paula03/2013
3057(89*10^115030-179)/9115031Robert Price12/2019
30582^381883-59197114959Enzo Doria10/2015
3059(2^381820+1626)/2114939Stefano Morozzi09/2020
30612^381806-4481114936Yves Minet07/2011
30602^381808-1851507114936Enzo Doria08/2015
3062(2^381792+2502)/2114931Stefano Morozzi09/2020
30632^381774-112373114926Enzo Doria06/2014
30642^381555-109051114860Enzo Doria04/2014
30652^381546-113501114857Enzo Doria08/2014
3066(2^381436+1182)/2114824Stefano Morozzi09/2020
30673^240644+16114817Robert Price04/2020
30682^381360-110429114801Enzo Doria05/2014
3069(17*10^114795+79)/3114796Robert Price04/2019
3070(66^63079+1)/67114774Paul Bourdelais09/2017
30712^381252-115079114769Enzo Doria06/2015
3072(2^381251+3186)/2114768Stefano Morozzi09/2020
30732^381209-29323114756Enzo Doria07/2015
3074569^41651-568^41651114754Jean-Louis Charton11/2009
30752^381201+1873205114753Enzo Doria06/2016
3076(85*10^114737+293)/9114738Robert Price12/2019
3077(265*10^114736+17)/3114738Robert Price03/2020
3078(2^381062+2170)/2114711Stefano Morozzi09/2020
30792^380974-112991114685Enzo Doria07/2014
308088^58949-87114626Norbert Schneider11/2015
3081(2^380773+662)/2114624Stefano Morozzi09/2020
30822^380700+91114603Lelio R Paula03/2013
3083(2^380632+2578)/2114582Stefano Morozzi09/2020
308510^114575+3^114576114576Mike Oakes09/2010
308410^114575+66561114576Patrick De Geest02/2017
308610^114575-581081114575Patrick De Geest02/2017
30872^380587-115315114569Enzo Doria06/2015
30882^380513-216925114546Enzo Doria05/2014
30892^380451-1840087114528Enzo Doria06/2015
3090(2^380426+1510)/2114520Stefano Morozzi09/2020
3091(15*2^380388-1)/539114507Lelio R Paula04/2014
30922^380279-461347114476Enzo Doria07/2015
30932^380021+1871147114398Enzo Doria05/2016
30942^380005+1869707114393Enzo Doria05/2016
30952^379958-113297114379Enzo Doria07/2014
30962^379881-109105114356Enzo Doria04/2014
3097(21*2^379857-1)/13114349Lelio R Paula03/2014
3098(4*10^114340+83)/3114341Robert Price02/2018
3099(26*10^114317-77)/3114318Robert Price11/2019
3100(4*10^114296+149)/9114296Robert Price04/2018
310188^58773-87114284Norbert Schneider11/2015
31022^379529-2790283114250Enzo Doria03/2016
31032^379522+1869115114248Enzo Doria05/2016
3104(145*10^114226-1)/9114228Serge Batalov12/2014
31052^379317-115033114186Enzo Doria06/2015
3106(17*2^379246-1)/17407114162Lelio R Paula03/2014
3107(2^379192+226)/2114148Stefano Morozzi09/2020
31086*10^114091+23114092Robert Price09/2020
3109(4*10^114076+143)/3114077Robert Price03/2018
3110(2^378754+2058)/2114017Stefano Morozzi09/2020
3111(46*10^113969+683)/9113970Robert Price03/2019
31122*10^113941+9113942Dmitry Domanov11/2010
3113(2^378478+1642)/2113933Stefano Morozzi09/2020
31144*10^113905+91113906Robert Price08/2018
311510^113894-10000001113894Robert Price09/2020
31164*10^113874-21113875Robert Price09/2018
31172^378272-16565113872Enzo Doria04/2013
31182^378217-109075113855Enzo Doria04/2014
31192^378198+67113849Lelio R Paula03/2013
31202^378173-3249113842Yves Minet12/2014
3121(2^378155-5)/6597113833Lelio R Paula03/2014
312292941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
31232^378128-262977113828Enzo Doria05/2014
31242^378123-113215113827Enzo Doria07/2014
31256^146274-18893113824Enzo Doria03/2013
31262^378078+75113813Lelio R Paula03/2013
31272^377940+63113772Lelio R Paula03/2013
31282^377941-2785843113772Enzo Doria04/2016
31292^377810+1875109113733Enzo Doria09/2016
31302^377803-1838635113731Enzo Doria05/2015
31312^377799+52223113729Yves Minet08/2010
313211^109190-270113710Enzo Doria12/2012
31337*10^113693+9113694Robert Price09/2015
3134(82*10^113681+161)/9113682Robert Price10/2019
31354*10^113658+49113659Robert Price01/2019
3136(2*10^113631+529)/9113631Robert Price01/2018
31372^377408-2798279113612Enzo Doria04/2016
31385*10^113586+57113587Robert Price12/2018
31392^377222+93679113556Yves Minet02/2011
3140262147#+316847113552Makoto Morimoto02/2016
3141(2^377131+2018)/2113528Stefano Morozzi09/2020
31422^377026-458903113497Enzo Doria04/2015
3143(2^377014+2202)/2113493Stefano Morozzi09/2020
3144(2^376967+258)/2113479Stefano Morozzi09/2020
3145(29*10^113468-17)/3113469Robert Price09/2019
314635^73477-34^73477113454Robert Price05/2012
3147(14*10^113451-89)/3113452Robert Price05/2020
31482^376790+27113426Lelio R Paula03/2013
31492^376786-112701113424Enzo Doria06/2014
31502^376731+21113408Lelio R Paula03/2013
31512^376634+1871245113379Enzo Doria05/2016
3152(4^188318+17)/3113379Robert Price02/2017
31532^376576-344369113361Enzo Doria07/2015
31542^376549-4543113353Yves Minet03/2019
3155(17*2^376526-1)/223113345Lelio R Paula03/2014
3156(27*2^376441-1)/811113319Lelio R Paula03/2014
3157(2^376350+3538)/2113293Stefano Morozzi09/2020
3158(2*10^113248+73)/3113248Robert Price09/2020
31592^376128-21237113226Enzo Doria06/2013
31605*10^113224-81113225Robert Price01/2019
316110^113220-1000001113220Robert Price08/2020
3162(2^376102+1578)/2113218Stefano Morozzi09/2020
3163(2^375996+3102)/2113186Stefano Morozzi09/2020
3164(94*10^113176+11)/3113178Robert Price04/2020
3165(46*10^113162+521)/9113163Robert Price02/2019
3166(2^375885+3614)/2113153Stefano Morozzi09/2020
3167(2^375873+2006)/2113149Stefano Morozzi09/2020
3168(2^375726+694)/2113105Stefano Morozzi09/2020
31692^375638-1787171113079Enzo Doria03/2016
3170(2^375563+2178)/2113056Stefano Morozzi09/2020
31712^375537+4847113048Yves Minet02/2011
3172(17^91837+16^91837)/33113000Robert Price08/2013
31735*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
31742^375350-3221112992Yves Minet07/2011
3175(13*2^375306+1)/7112979Lelio R Paula03/2014
31762^375305+76757112979Enzo Doria05/2016
31772^375258+1874989112964Enzo Doria07/2016
3178(29^77237-1)/28112950Robert Price04/2012
31792^375154+74959112933Enzo Doria04/2016
3180(266*10^112930-17)/3112932Robert Price07/2020
3181(2^375134+778)/2112927Stefano Morozzi09/2020
3182(85*10^112919+293)/9112920Robert Price12/2019
3183(2^375022+1210)/2112893Stefano Morozzi09/2020
31842^374993-2787163112885Enzo Doria11/2015
3185123^53970+2112793Lelio R Paula06/2013
31862^374640-4685112778Yves Minet05/2019
3187(2^374556+682)/2112753Stefano Morozzi09/2020
3188p(22852)#/2+512112745Robert Price05/2017
3189(11*10^112742-131)/3112743Robert Price09/2018
31902^374441-21049112718Enzo Doria06/2013
31914*10^112706-93112707Robert Price07/2020
3192(2^374321+1)/3112682H.&R. Lifchitz12/2000
3193(2^374213+1766)/2112650Stefano Morozzi09/2020
3194(2^374094+2674)/2112614Stefano Morozzi09/2020
3195(13^101089-1)/12112607Paul Bourdelais03/2010
31963^236011-8828112606Enzo Doria05/2014
3197(2^373748+1090)/2112510Stefano Morozzi09/2020
319839^70666+2112435Lelio R Paula11/2013
3199(134*10^112400+7)/3112402Robert Price02/2020
3200(2^373365+326)/2112394Stefano Morozzi09/2020
3201(2^373350-7)/3112390Lelio R Paula03/2014
32022^373306-1840931112377Enzo Doria06/2015
3203(2^373262+270)/2112363Stefano Morozzi09/2020
3204(142*10^112352-7)/9112354Robert Price12/2019
32052^373117+1872107112320Enzo Doria05/2016
32062^373040+2792761112297Enzo Doria03/2016
3207EPrime(112280)112280Eric W. Weisstein10/2010
32082^372950+7112270Lelio R Paula03/2013
32092^372945+1872167112268Enzo Doria05/2016
3210(2^372754+3094)/2112210Stefano Morozzi09/2020
32116*10^112208+43112209Robert Price07/2020
3212(2^372728+3058)/2112203Stefano Morozzi09/2020
32132^372695+72113112193Enzo Doria04/2016
32142^372689-2563112191Yves Minet07/2014
32152^372638-1859441112176Enzo Doria03/2016
32163^235074-113056112159Enzo Doria07/2014
3217131^52949-130112108Norbert Schneider02/2019
3218(91*10^112098-1)/9112100Robert Price04/2015
32192^372310-85061112077Paul Bourdelais02/2012
3220(10^112067+53)/9112067Serge Batalov07/2015
3221(2^372237+2082)/2112055Stefano Morozzi09/2020
322275^59760+2112054Lelio R Paula08/2013
3223(2^372200+1710)/2112044Stefano Morozzi09/2020
3224(2^372161+2574)/2112032Stefano Morozzi09/2020
32258*10^112018-49112019Robert Price08/2019
32272^372108+74221112016Enzo Doria04/2016
3226(2^372109+2046)/2112016Stefano Morozzi09/2020
3228(184*10^112007-1)/3112009Robert Price02/2020
32295*10^112003+81112004Robert Price03/2019
3230215^48018+48018^215112000Norbert Schneider10/2018
32312^371970-459491111975Enzo Doria05/2015
323241^69427-40^69427111971Robert Price07/2012
3233(10^111902+71)/9111902Serge Batalov07/2015
3234(2^371625+1610)/2111870Stefano Morozzi09/2020
32352^371440-112865111815Enzo Doria06/2014
32362^371426-459161111811Enzo Doria05/2015
3237(94*10^111770+11)/3111772Robert Price04/2020
32382^371276-461267111766Enzo Doria07/2015
32396*10^111760+43111761Robert Price07/2020
324098079!4-1024111747Robert Price11/2019
3241(2^371186+3162)/2111738Stefano Morozzi09/2020
32422^371098-113261111712Enzo Doria07/2014
3243(7*10^111706-61)/9111706Erik Branger01/2011
32442^371044+1869391111696Enzo Doria05/2016
324588^57416+87111645Norbert Schneider11/2015
32462^370829-109693111631Enzo Doria04/2014
324715^94906-2111619Lelio R Paula11/2013
3248(2^370726+1198)/2111600Stefano Morozzi09/2020
32492^370695-4627111591Yves Minet05/2019
32507*10^111579-87111580Robert Price06/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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