PRP Records

Probable Primes Top 10000

(277054 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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(2^398398+774)/2119930Stefano Morozzi09/2020
3002(10^119880+179)/9119880Serge Batalov12/2014
3003(9*2^398145+1)/73119853Lelio R Paula04/2014
3004(10^119836+77)/3119836Robert Price01/2018
30052^398029+1872527119819Enzo Doria05/2016
30062^397897-113541119779Enzo Doria08/2014
3007(2^397696+1042)/2119719Stefano Morozzi09/2020
3008(19*10^119716+101)/3119717Robert Price09/2019
3009(21*2^397661-1)/27593119705Lelio R Paula04/2014
301077*10^119688+3119690Robert Price06/2020
3011(2^397504+1698)/2119661Stefano Morozzi09/2020
3012(58^67853-1)/57119653Paul Bourdelais09/2017
30132^397426+73849119638Enzo Doria04/2016
30142^396933-112723119489Enzo Doria06/2014
301511^114738-150119488Enzo Doria10/2012
3016(4*10^119474+149)/9119474Robert Price04/2018
30172^396790-21119446Lelio R Paula04/2013
3018(2^396633-7)/5119398Lelio R Paula04/2014
3019(2^396577+2522)/2119382Stefano Morozzi09/2020
3020(2^396492+2230)/2119356Stefano Morozzi01/2021
3022105^59050+104119352Norbert Schneider11/2016
3021126^56824-125119352Norbert Schneider12/2018
3023139^55690-138119345Norbert Schneider04/2019
3024790^41179+41179^790119322Norbert Schneider04/2019
30252^396374+73729119321Enzo Doria04/2016
302688*10^119295+3119297Robert Price05/2020
30272^396258-459491119286Enzo Doria05/2015
3028(2^396248+3126)/2119283Stefano Morozzi09/2020
30292^396128-396128-1119247Karsten Bonath06/2018
3030(28*10^119206-67)/3119207Robert Price10/2020
3031(2^395986+5)/76881119199Lelio R Paula04/2014
3032(23*2^395942-1)/91119190Lelio R Paula04/2014
3033(2^395902+202)/2119179Stefano Morozzi09/2020
3034(2^395825+582)/2119155Stefano Morozzi09/2020
3035(2^395733+1130)/2119128Stefano Morozzi09/2020
3036(11*2^395548+1)/3119073Lelio R Paula04/2014
3037(30^80599+1)/31119054Robert Price07/2013
3038(43*10^119024-403)/9119025Robert Price01/2019
30396*10^118964+43118965Robert Price07/2020
3040(8*10^118960+49)/3118961Robert Price05/2020
3041(194*10^118925-17)/3118927Robert Price09/2020
30422^395062-109121118926Enzo Doria04/2014
30432^395055-4627118924Yves Minet05/2019
3044(2^395054+702)/2118923Stefano Morozzi09/2020
3045(2^395011+2526)/2118910Stefano Morozzi09/2020
3046(2^394918+78557)/3118882Lelio R Paula01/2015
3047(2^394858+1018)/2118864Stefano Morozzi09/2020
3048(16*10^118852+77)/3118853Robert Price03/2019
3049(2^394739+3)/1883118826Lelio R Paula04/2014
305010^118772-40000000001118772Robert Price09/2020
3051(2^394513+2034)/2118760Stefano Morozzi09/2020
30522^394266+71389118686Enzo Doria04/2016
30532^394215-51261118671Tony Prest / Never Odd Or Even04/2018
3054(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
3055(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
3056(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
3057(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
3058(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
3059(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
3060(2^394131+2214)/2118645Stefano Morozzi09/2020
3061(17*10^118635+13)/3118636Robert Price01/2019
30625^169727+2118635Lelio R Paula08/2013
30632^394034-3118617M. Frind & P. Underwood09/2002
3064(7*10^118607+179)/3118608Robert Price09/2018
30653^248572-6242118599Enzo Doria05/2014
3066(3*2^393964-1)/181118594Lelio R Paula04/2014
30677^140303-6118570Robert Price11/2014
3068(2^393864+2686)/2118565Stefano Morozzi09/2020
3069(2^393862+3150)/2118564Stefano Morozzi09/2020
3070(2^393849+3762)/2118561Stefano Morozzi01/2021
3071(2^393661+2666)/2118504Stefano Morozzi09/2020
3072(2^393650+1614)/2118501Stefano Morozzi09/2020
307310^118485-50001118485Robert Price08/2020
3074(2^393528+1030)/2118464Stefano Morozzi09/2020
30752^393427+75683118434Enzo Doria04/2016
30762^393376-114749118418Enzo Doria04/2015
3077(2^393234+2010)/2118375Stefano Morozzi09/2020
3078(2^393205+3030)/2118367Stefano Morozzi09/2020
3079(2^393191+2174)/2118362Stefano Morozzi09/2020
30802^393180+73118359Lelio R Paula04/2013
3081p(23881)#/2+256118328Robert Price05/2017
3082(10^118324+359)/9118324Serge Batalov12/2014
3083(2^393048+570)/2118319Stefano Morozzi09/2020
3084p(23879)#/2+64118317Robert Price03/2017
3085(238*10^118265-1)/3118267Robert Price04/2020
3087(53*10^118216+1)/9118217Serge Batalov11/2010
3086(2^392707+1710)/2118217Stefano Morozzi09/2020
3088(7*2^392697+1)/15118214Renaud Lifchitz03/2011
3089(157^53819-1)/156118179Alexander Zhirkov06/2016
3090(2^392567+2750)/2118175Stefano Morozzi01/2021
3091(19*2^392551+1)/3118171Lelio R Paula04/2014
30922^392516-29219118160Enzo Doria07/2015
309366*10^118155+7118157Robert Price07/2020
3094Phi(177231,10)118152Maksym Voznyy09/2015
30952^392413-112123118129Enzo Doria06/2014
3096(2^392342+5)/27118106Lelio R Paula04/2014
3097(2^392333+1782)/2118104Stefano Morozzi01/2021
30982^392300-1841429118095Enzo Doria06/2015
30992^392220+75241118070Enzo Doria04/2016
310010^118009+664447118010Patrick De Geest07/2018
310110^118009-20001118009Robert Price01/2018
3102(14*10^117991+61)/3117992Robert Price12/2018
31032^391933+5897117984Yves Minet02/2011
31042^391912-1849259117978Enzo Doria08/2015
3105(2^391812+5)/14181117944Lelio R Paula04/2014
3106(7*10^117930-79)/9117930Robert Price01/2021
3107(46*10^117902+683)/9117903Robert Price03/2019
3108(7*2^391521+1)/285117858Lelio R Paula04/2014
31092^391324+90901117801Yves Minet02/2011
31102^391301-1859923117794Enzo Doria03/2016
31112^391261-4131117782Yves Minet02/2018
3112(2^391211+554)/2117766Stefano Morozzi09/2020
311338434^1157+1157^38434117737Hans Havermann01/2021
3114(2^391115-7)/11791117734Lelio R Paula04/2014
3115(85*10^117719+473)/9117720Robert Price01/2020
3116(2^391049+582)/2117718Stefano Morozzi09/2020
31172^390960+1880881117691Enzo Doria11/2016
31182^390897-1860553117672Enzo Doria11/2015
31192^390889-115003117670Enzo Doria06/2015
31202^390779-30337117637Paul Bourdelais02/2012
312111^112916-780117590Enzo Doria12/2012
3122(2^390473+1002)/2117544Stefano Morozzi09/2020
3123(16^97613-5^97613)/11117537Robert Price07/2013
3124(2^390438+1774)/2117534Stefano Morozzi01/2021
3125(2^390418+1722)/2117528Stefano Morozzi09/2020
3126(2^390403+654)/2117523Stefano Morozzi09/2020
3127(2^390343+2246)/2117505Stefano Morozzi01/2021
3128(17*2^390272+1)/1983117482Lelio R Paula04/2014
312931^78759-30117459Theodore Burton02/2007
3130(2^390176+1222)/2117455Stefano Morozzi09/2020
3131(2^390133+1242)/2117442Stefano Morozzi09/2020
3132(2^390013+2634)/2117406Stefano Morozzi09/2020
31333*10^117402+61117403Robert Price09/2020
31342^389998+37117402Lelio R Paula03/2013
3135(2^389977+314)/2117395Stefano Morozzi09/2020
3136(2^389921+342)/2117378Stefano Morozzi01/2021
3137(2^389768+1582)/2117332Stefano Morozzi09/2020
313829^80192-1*80192^29117273Dylan Delgado12/2019
3139(13*10^117249+161)/3117250Robert Price11/2018
31402^389478+43117245Lelio R Paula03/2013
3141(298*10^117229-7)/3117231Robert Price06/2020
3142(2^389416+342)/2117226Stefano Morozzi01/2021
3143(29*2^389351-1)/9117207Lelio R Paula04/2014
31445*10^117205+23117206Robert Price03/2019
3145(2^389341-7)/3865117200Lelio R Paula03/2014
3146(2^389276+2650)/2117184Stefano Morozzi09/2020
314710^117142+209223117143Patrick De Geest04/2018
314910^117142-1000000001117142Robert Price03/2018
314810^117142-966057117142Patrick De Geest04/2018
315010^117135+360577117136Patrick De Geest07/2018
315110^117135-401117135Robert Price01/2018
31524*10^117123+79117124Robert Price08/2018
31532^389033-12797413117111Enzo Doria04/2016
3154(2^388987+2634)/2117097Stefano Morozzi09/2020
31552^388960-109505117089Enzo Doria04/2014
31567*10^117082-57117083Robert Price06/2020
3157(2^388928-5)/569117077Lelio R Paula03/2014
31582^388888-1529117067Yves Minet01/2013
315910^117059+28879117060Patrick De Geest05/2016
3160(10^117059-71)/1117059Serge Batalov12/2014
3161(2^388854+3630)/2117057Stefano Morozzi09/2020
3162(2^388842+2098)/2117053Stefano Morozzi09/2020
3163(2^388789+3150)/2117037Stefano Morozzi09/2020
3164(693^41189-1)/692117005Michael Stocker05/2020
3165(26*10^116999-503)/9117000Robert Price07/2018
3166(2^388609+1554)/2116983Stefano Morozzi09/2020
31673^245154-6256116969Enzo Doria05/2014
31685*10^116966-43116967Robert Price01/2019
31692^388536-113495116961Enzo Doria08/2014
31702^388469-43116941Lelio R Paula03/2013
3171(7*2^388372-1)/111116911Lelio R Paula04/2014
3172(7*2^388335-1)/25116900Lelio R Paula04/2014
31732^388180+93116854Donovan Johnson07/2008
3174(2^388167+2510)/2116850Stefano Morozzi09/2020
3175(85*10^116842+293)/9116843Robert Price12/2019
3176(2^388081+7)/1179116821Lelio R Paula03/2014
31772^387946-113261116784Enzo Doria07/2014
31782^387745+75557116723Enzo Doria04/2016
3179(206*10^116687-17)/9116689Robert Price01/2020
3180(7*10^116684+179)/3116685Robert Price09/2018
31812^387554+71455116666Enzo Doria04/2016
3182(2^387447+78557)/365116631Lelio R Paula12/2014
3183(145*10^116610-1)/9116612Serge Batalov12/2014
3184(25*10^116601-331)/9116602Robert Price08/2018
3185(17*2^387284-1)/59116584Lelio R Paula04/2014
3186(2^387284+3726)/2116584Stefano Morozzi09/2020
318710^116557+987654321116558Robert Price12/2019
318810^116557+9141116558Patrick De Geest02/2020
318910^116557-609431116557Patrick De Geest02/2020
3190(2^387076+2046)/2116522Stefano Morozzi09/2020
3191(2^387073+2570)/2116521Stefano Morozzi09/2020
3192(31*2^386968+1)/7116490Lelio R Paula03/2014
31932^386947+1869143116483Enzo Doria05/2016
3194(30^78857-1)/29116480Robert Price12/2011
3195(2^386903-3)/5116469Lelio R Paula03/2014
31962^386389-1864783116315Enzo Doria03/2016
3197(31*2^386231-1)/1711116266Lelio R Paula03/2014
3198297^47012+47012^297116250Norbert Schneider07/2018
3199(2^386087-5)/40959116220Lelio R Paula03/2014
3200(2^386054+714)/2116214Stefano Morozzi09/2020
32012^385969-823116189Yves Minet05/2012
320257^66162+2116173Lelio R Paula08/2013
32032^385854+75049116154Enzo Doria04/2016
3204(2^385832+2590)/2116147Stefano Morozzi09/2020
32052^385775-109587116130Enzo Doria04/2014
3206(14*10^116112-101)/3116113Robert Price02/2019
3207Phi(236354,10)/24817171116109Makoto Kamada08/2019
32082^385622+71839116084Enzo Doria04/2016
32102^385564+781116067Lelio R Paula01/2012
3209(2^385565+1562)/2116067Stefano Morozzi09/2020
3211(2^385557+2214)/2116064Stefano Morozzi09/2020
3212(266*10^116024-17)/3116026Robert Price07/2020
32132^385410+71893116020Enzo Doria04/2016
3214(25*2^385091+1)/27115924Lelio R Paula04/2014
3215(11*10^115910-131)/3115911Robert Price09/2018
32162^384953-111943115883Paul Bourdelais02/2012
321743^70942-2115882Lelio R Paula04/2014
3218(94*10^115879-7)/3115881Robert Price03/2020
32197*10^115863+3115864Robert Price08/2015
32202^384834+93115847Donovan Johnson07/2008
32212^384809+71297115840Enzo Doria04/2016
3222(7*2^384759-1)/5115825Lelio R Paula04/2014
3223(71*10^115810-17)/9115811Ray Chandler08/2011
3224(97*10^115794-1)/3115796Serge Batalov12/2014
32252*10^115784-27115785Robert Price05/2018
322610^115773+126739115774Patrick De Geest04/2018
322810^115773-1000000001115773Robert Price03/2018
322710^115773-396221115773Patrick De Geest04/2018
3229(2^384582+778)/2115771Stefano Morozzi09/2020
32302^384530+1874305115756Enzo Doria06/2016
3231(3*2^384524-1)/7631115750Lelio R Paula03/2014
3232(44*10^115697-413)/9115698Robert Price03/2019
3233(2^384317+1026)/2115691Stefano Morozzi09/2020
32342^384312+81091115690Yves Minet02/2010
3235(2^384265+2150)/2115675Stefano Morozzi09/2020
3236(2^384246+2182)/2115670Stefano Morozzi09/2020
3237(4*10^115668-79)/3115669Robert Price02/2018
3238(2^384193+242)/2115654Stefano Morozzi09/2020
3239(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
3240(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
324118^92125-92125^18115642Dylan Delgado08/2019
32423^242337-4042115625Enzo Doria05/2014
3243(2^383931+674)/2115575Stefano Morozzi09/2020
32447*10^115561+79115562Robert Price07/2019
3245(2^383872+3046)/2115557Stefano Morozzi09/2020
3246(11*2^383859-13)/15115553Renaud Lifchitz03/2011
32472^383780-3149115530Yves Minet10/2014
3248(41*10^115523-383)/9115524Robert Price11/2018
3249(2^383618+618)/2115481Stefano Morozzi09/2020
32502^383560-455115464Yves Minet03/2012


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!