PRP Records

Probable Primes Top 10000

(280932 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 ?
3501(2^388438+1842)/2116932Stefano Morozzi02/2021
3502(7*2^388372-1)/111116911Lelio R Paula04/2014
3503(7*2^388335-1)/25116900Lelio R Paula04/2014
35042^388180+93116854Donovan Johnson07/2008
3505(2^388167+2510)/2116850Stefano Morozzi09/2020
3506(85*10^116842+293)/9116843Robert Price12/2019
350735296^2043+2043^35296116840Hans Havermann02/2021
3508(2^388081+7)/1179116821Lelio R Paula03/2014
350938633^1056+1056^38633116814Hans Havermann02/2021
35102^387946-113261116784Enzo Doria07/2014
351128363^13056+13056^28363116737Hans Havermann02/2021
35122^387745+75557116723Enzo Doria04/2016
351329622^8699+8699^29622116695Hans Havermann02/2021
3514(206*10^116687-17)/9116689Robert Price01/2020
3515(7*10^116684+179)/3116685Robert Price09/2018
35162^387554+71455116666Enzo Doria04/2016
3517(2^387447+78557)/365116631Lelio R Paula12/2014
3518(145*10^116610-1)/9116612Serge Batalov12/2014
3519(25*10^116601-331)/9116602Robert Price08/2018
3520(17*2^387284-1)/59116584Lelio R Paula04/2014
3521(2^387284+3726)/2116584Stefano Morozzi09/2020
352210^116557+987654321116558Robert Price12/2019
352310^116557+9141116558Patrick De Geest02/2020
352410^116557-609431116557Patrick De Geest02/2020
3525(2^387123+1814)/2116536Stefano Morozzi02/2021
3526(2^387076+2046)/2116522Stefano Morozzi09/2020
3527(2^387073+2570)/2116521Stefano Morozzi09/2020
352828846^10931+10931^28846116500Hans Havermann02/2021
3529(31*2^386968+1)/7116490Lelio R Paula03/2014
35302^386947+1869143116483Enzo Doria05/2016
3531(30^78857-1)/29116480Robert Price12/2011
3532(2^386903-3)/5116469Lelio R Paula03/2014
353328107^13892+13892^28107116441Hans Havermann02/2021
353429110^9957+9957^29110116386Hans Havermann02/2021
353526469^24838+24838^26469116335Hans Havermann01/2021
35362^386389-1864783116315Enzo Doria03/2016
3537(31*2^386231-1)/1711116266Lelio R Paula03/2014
3538297^47012+47012^297116250Norbert Schneider07/2018
3539(2^386087-5)/40959116220Lelio R Paula03/2014
3540(2^386054+714)/2116214Stefano Morozzi09/2020
35412^385969-823116189Yves Minet05/2012
354257^66162+2116173Lelio R Paula08/2013
35432^385854+75049116154Enzo Doria04/2016
3544(2^385832+2590)/2116147Stefano Morozzi09/2020
35452^385775-109587116130Enzo Doria04/2014
3546(14*10^116112-101)/3116113Robert Price02/2019
3547Phi(236354,10)/24817171116109Makoto Kamada08/2019
354828729^10990+10990^28729116094Hans Havermann02/2021
35492^385622+71839116084Enzo Doria04/2016
35512^385564+781116067Lelio R Paula01/2012
3550(2^385565+1562)/2116067Stefano Morozzi09/2020
3552(2^385563+378)/2116066Stefano Morozzi02/2021
3553(2^385557+2214)/2116064Stefano Morozzi09/2020
355429431^8776+8776^29431116056Hans Havermann01/2021
3555(266*10^116024-17)/3116026Robert Price07/2020
355630263^6820+6820^30263116022Hans Havermann02/2021
35572^385410+71893116020Enzo Doria04/2016
355838225^1084+1084^38225116014Hans Havermann02/2021
355926548^23433+23433^26548116011Hans Havermann02/2021
3560(25*2^385091+1)/27115924Lelio R Paula04/2014
3561(11*10^115910-131)/3115911Robert Price09/2018
35622^384953-111943115883Paul Bourdelais02/2012
356343^70942-2115882Lelio R Paula04/2014
3564(94*10^115879-7)/3115881Robert Price03/2020
35657*10^115863+3115864Robert Price08/2015
35662^384834+93115847Donovan Johnson07/2008
35672^384809+71297115840Enzo Doria04/2016
3568(7*2^384759-1)/5115825Lelio R Paula04/2014
356931348^4951+4951^31348115822Hans Havermann02/2021
3570(71*10^115810-17)/9115811Ray Chandler08/2011
3571(97*10^115794-1)/3115796Serge Batalov12/2014
357231115^5266+5266^31115115794Hans Havermann02/2021
35732*10^115784-27115785Robert Price05/2018
357410^115773+126739115774Patrick De Geest04/2018
357610^115773-1000000001115773Robert Price03/2018
357510^115773-396221115773Patrick De Geest04/2018
3577(2^384582+778)/2115771Stefano Morozzi09/2020
357830537^6178+6178^30537115762Hans Havermann01/2021
35792^384530+1874305115756Enzo Doria06/2016
3580(3*2^384524-1)/7631115750Lelio R Paula03/2014
358128275^12406+12406^28275115748Hans Havermann01/2021
3582(44*10^115697-413)/9115698Robert Price03/2019
358331408^4825+4825^31408115692Hans Havermann02/2021
3584(2^384317+1026)/2115691Stefano Morozzi09/2020
35852^384312+81091115690Yves Minet02/2010
3586(2^384265+2150)/2115675Stefano Morozzi09/2020
3587(2^384246+2182)/2115670Stefano Morozzi09/2020
3588(4*10^115668-79)/3115669Robert Price02/2018
3589(2^384193+242)/2115654Stefano Morozzi09/2020
3590(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
3591(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
359218^92125-92125^18115642Dylan Delgado08/2019
35933^242337-4042115625Enzo Doria05/2014
3594(2^383931+674)/2115575Stefano Morozzi09/2020
35957*10^115561+79115562Robert Price07/2019
3596(2^383872+3046)/2115557Stefano Morozzi09/2020
3597(11*2^383859-13)/15115553Renaud Lifchitz03/2011
35982^383780-3149115530Yves Minet10/2014
3599(41*10^115523-383)/9115524Robert Price11/2018
360027316^16923+16923^27316115506Hans Havermann02/2021
3601(2^383618+618)/2115481Stefano Morozzi09/2020
36022^383560-455115464Yves Minet03/2012
3603(2^383544+5)/3115458Lelio R Paula03/2014
360489^59221-88^59221115445Robert Price06/2015
36052^383347+1869413115399Enzo Doria05/2016
3606(103*10^115366+17)/3115368Robert Price08/2020
3607(2^383232+750)/2115365Stefano Morozzi09/2020
3608(2^383130-7)/131793115329Lelio R Paula03/2014
3609(12^106859+1)/13115320Paul Bourdelais02/2010
361029961^7060+7060^29961115315Hans Havermann01/2021
36122^383039+1869509115307Enzo Doria05/2016
361132918^3183+3183^32918115307Hans Havermann01/2021
361336964^1315+1315^36964115288Hans Havermann02/2021
3614(13*2^382968+1)/7115286Lelio R Paula04/2014
3615(22*10^115282+29)/3115283Robert Price02/2021
3616(2^382945+2046)/2115278Stefano Morozzi09/2020
3617(2^382789+3182)/2115231Stefano Morozzi09/2020
361830416^6141+6141^30416115224Hans Havermann02/2021
36196*10^115211+79115212Robert Price09/2020
3620(2^382722+3598)/2115211Stefano Morozzi09/2020
362127987^13078+13078^27987115210Hans Havermann02/2021
3622(2^382699+2090)/2115204Stefano Morozzi09/2020
36232^382633+73697115185Enzo Doria04/2016
36242^382509-113593115147Enzo Doria08/2014
36252^382502-2791721115145Enzo Doria03/2016
3626(2^382495+1274)/2115143Stefano Morozzi01/2021
362726752^20065+20065^26752115099Hans Havermann02/2021
362826383^23008+23008^26383115080Hans Havermann02/2021
36299^120590-120590115073Robert Price03/2014
363028203^12016+12016^28203115062Hans Havermann02/2021
36312^382198+9115054Lelio R Paula03/2013
363230101^6630+6630^30101115032Hans Havermann01/2021
3633(89*10^115030-179)/9115031Robert Price12/2019
3634(2^381935+2774)/2114974Stefano Morozzi02/2021
363527300^16271+16271^27300114972Hans Havermann02/2021
36362^381883-59197114959Enzo Doria10/2015
363727423^15542+15542^27423114944Hans Havermann02/2021
3638(2^381820+1626)/2114939Stefano Morozzi09/2020
36402^381806-4481114936Yves Minet07/2011
36392^381808-1851507114936Enzo Doria08/2015
3641(2^381792+2502)/2114931Stefano Morozzi09/2020
36422^381774-112373114926Enzo Doria06/2014
364326341^22980+22980^26341114883Hans Havermann01/2021
36442^381555-109051114860Enzo Doria04/2014
36452^381546-113501114857Enzo Doria08/2014
3646(7*10^114845-19)/3114846Robert Price10/2020
364726675^20178+20178^26675114833Hans Havermann02/2021
3648(2^381436+1182)/2114824Stefano Morozzi09/2020
36493^240644+16114817Robert Price04/2020
36502^381360-110429114801Enzo Doria05/2014
3651(17*10^114795+79)/3114796Robert Price04/2019
3652(66^63079+1)/67114774Paul Bourdelais09/2017
36532^381252-115079114769Enzo Doria06/2015
3654(2^381251+3186)/2114768Stefano Morozzi09/2020
36552^381209-29323114756Enzo Doria07/2015
3656569^41651-568^41651114754Jean-Louis Charton11/2009
36572^381201+1873205114753Enzo Doria06/2016
3658(85*10^114737+293)/9114738Robert Price12/2019
3659(265*10^114736+17)/3114738Robert Price03/2020
3660(2^381062+2170)/2114711Stefano Morozzi09/2020
36612^380974-112991114685Enzo Doria07/2014
366237097^1234+1234^37097114679Hans Havermann02/2021
366388^58949-87114626Norbert Schneider11/2015
3664(2^380773+662)/2114624Stefano Morozzi09/2020
366529913^6782+6782^29913114608Hans Havermann02/2021
36662^380700+91114603Lelio R Paula03/2013
3667(2^380632+2578)/2114582Stefano Morozzi09/2020
36687*10^114577+27114578Robert Price11/2020
367010^114575+3^114576114576Mike Oakes09/2010
366910^114575+66561114576Patrick De Geest02/2017
367110^114575-581081114575Patrick De Geest02/2017
36722^380587-115315114569Enzo Doria06/2015
367331874^3927+3927^31874114558Hans Havermann02/2021
36742^380513-216925114546Enzo Doria05/2014
36752^380451-1840087114528Enzo Doria06/2015
3676(2^380426+1510)/2114520Stefano Morozzi09/2020
3677(15*2^380388-1)/539114507Lelio R Paula04/2014
36782^380279-461347114476Enzo Doria07/2015
367927121^16590+16590^27121114447Hans Havermann01/2021
368025966^25555+25555^25966114445Hans Havermann01/2021
36812^380021+1871147114398Enzo Doria05/2016
36822^380005+1869707114393Enzo Doria05/2016
36832^379958-113297114379Enzo Doria07/2014
3684(2^379897+1274)/2114361Stefano Morozzi01/2021
36852^379881-109105114356Enzo Doria04/2014
3686(21*2^379857-1)/13114349Lelio R Paula03/2014
3687(4*10^114340+83)/3114341Robert Price02/2018
3688(26*10^114317-77)/3114318Robert Price11/2019
3689(4*10^114296+149)/9114296Robert Price04/2018
369088^58773-87114284Norbert Schneider11/2015
369127764^13065+13065^27764114280Hans Havermann01/2021
36922^379529-2790283114250Enzo Doria03/2016
36932^379522+1869115114248Enzo Doria05/2016
3694(145*10^114226-1)/9114228Serge Batalov12/2014
36952^379317-115033114186Enzo Doria06/2015
3696(17*2^379246-1)/17407114162Lelio R Paula03/2014
3697(2^379192+226)/2114148Stefano Morozzi09/2020
36986*10^114091+23114092Robert Price09/2020
3699(4*10^114076+143)/3114077Robert Price03/2018
3700(2^378820+3226)/2114036Stefano Morozzi01/2021
3701(2^378754+2058)/2114017Stefano Morozzi09/2020
3702(46*10^113969+683)/9113970Robert Price03/2019
370332226^3439+3439^32226113966Hans Havermann02/2021
370478*10^113954-7113956Robert Price10/2020
37052*10^113941+9113942Dmitry Domanov11/2010
370610^113933+145897113934Patrick De Geest02/2021
3709(2^378478+1642)/2113933Stefano Morozzi09/2020
370710^113933-8000000001113933Robert Price11/2020
370810^113933-66167113933Patrick De Geest02/2021
37102339662057597*10^113903+9113916Robert Price03/2021
37114*10^113905+91113906Robert Price08/2018
371210^113894+76609113895Patrick De Geest02/2021
371410^113894-10000001113894Robert Price09/2020
371310^113894-373947113894Patrick De Geest02/2021
371533933^2270+2270^33933113881Hans Havermann02/2021
37164*10^113874-21113875Robert Price09/2018
37172^378272-16565113872Enzo Doria04/2013
37182^378217-109075113855Enzo Doria04/2014
37192^378198+67113849Lelio R Paula03/2013
37202^378173-3249113842Yves Minet12/2014
3721(2^378155-5)/6597113833Lelio R Paula03/2014
372292941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
372330030^6173+6173^30030113829Hans Havermann01/2021
37242^378128-262977113828Enzo Doria05/2014
37252^378123-113215113827Enzo Doria07/2014
37266^146274-18893113824Enzo Doria03/2013
372734596^1949+1949^34596113815Hans Havermann02/2021
37282^378078+75113813Lelio R Paula03/2013
372926273^21448+21448^26273113799Hans Havermann02/2021
37312^377940+63113772Lelio R Paula03/2013
37302^377941-2785843113772Enzo Doria04/2016
37322^377810+1875109113733Enzo Doria09/2016
37332^377803-1838635113731Enzo Doria05/2015
37342^377799+52223113729Yves Minet08/2010
3735(2^377791+3258)/2113727Stefano Morozzi02/2021
373611^109190-270113710Enzo Doria12/2012
373728206^10739+10739^28206113698Hans Havermann01/2021
37387*10^113693+9113694Robert Price09/2015
373913899^27442+27442^13899113692Norbert Schneider12/2020
3740(82*10^113681+161)/9113682Robert Price10/2019
374126121^22478+22478^26121113673Hans Havermann01/2021
37424*10^113658+49113659Robert Price01/2019
3743(2*10^113631+529)/9113631Robert Price01/2018
37442^377408-2798279113612Enzo Doria04/2016
374513706^27459+27459^13706113596Norbert Schneider12/2020
37465*10^113586+57113587Robert Price12/2018
3747(2^377242+2794)/2113561Stefano Morozzi02/2021
37482^377222+93679113556Yves Minet02/2011
3750262147#+316847113552Makoto Morimoto02/2016
374927172^15101+15101^27172113552Hans Havermann01/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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