PRP Records

Probable Primes Top 10000

(290751 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 ?
425138496^1093+1093^38496116975Hans Havermann02/2021
42523^245154-6256116969Enzo Doria05/2014
42535*10^116966-43116967Robert Price01/2019
42542^388536-113495116961Enzo Doria08/2014
4255(2^388512+382)/2116954Stefano Morozzi02/2021
42562^388469-43116941Lelio R Paula03/2013
425727417^18416+18416^27417116939Hans Havermann02/2021
4258(2^388438+1842)/2116932Stefano Morozzi02/2021
4259(7*2^388372-1)/111116911Lelio R Paula04/2014
4260(7*2^388335-1)/25116900Lelio R Paula04/2014
42612^388180+93116854Donovan Johnson07/2008
4262(2^388167+2510)/2116850Stefano Morozzi09/2020
4263(85*10^116842+293)/9116843Robert Price12/2019
426435296^2043+2043^35296116840Hans Havermann02/2021
4265(2^388081+7)/1179116821Lelio R Paula03/2014
426638633^1056+1056^38633116814Hans Havermann02/2021
42672^387946-113261116784Enzo Doria07/2014
426828363^13056+13056^28363116737Hans Havermann02/2021
42692^387745+75557116723Enzo Doria04/2016
4270(29*10^116719+313)/9116720Robert Price04/2021
427129622^8699+8699^29622116695Hans Havermann02/2021
4272(206*10^116687-17)/9116689Robert Price01/2020
4273(7*10^116684+179)/3116685Robert Price09/2018
42742^387554+71455116666Enzo Doria04/2016
4275(602*10^116647-71)/9116649Robert Price12/2021
4276(2^387447+78557)/365116631Lelio R Paula12/2014
4277(145*10^116610-1)/9116612Serge Batalov12/2014
4278(25*10^116601-331)/9116602Robert Price08/2018
4279(17*2^387284-1)/59116584Lelio R Paula04/2014
4280(2^387284+3726)/2116584Stefano Morozzi09/2020
42812^387211+111546435116563Paul Bourdelais10/2021
428210^116557+987654321116558Robert Price12/2019
428310^116557+9141116558Patrick De Geest02/2020
428410^116557-609431116557Patrick De Geest02/2020
4285(28*10^116546+41)/3116547Robert Price07/2021
4286(2^387123+1814)/2116536Stefano Morozzi02/2021
4287(2^387076+2046)/2116522Stefano Morozzi09/2020
4288(2^387073+2570)/2116521Stefano Morozzi09/2020
428928846^10931+10931^28846116500Hans Havermann02/2021
429010^116496+3593037116497Paul Bourdelais10/2021
4291(31*2^386968+1)/7116490Lelio R Paula03/2014
42922^386947+1869143116483Enzo Doria05/2016
4293(30^78857-1)/29116480Robert Price12/2011
4294(2^386903-3)/5116469Lelio R Paula03/2014
429528107^13892+13892^28107116441Hans Havermann02/2021
429629110^9957+9957^29110116386Hans Havermann02/2021
429726469^24838+24838^26469116335Hans Havermann01/2021
42982^386389-1864783116315Enzo Doria03/2016
4299(31*2^386231-1)/1711116266Lelio R Paula03/2014
4300297^47012+47012^297116250Norbert Schneider07/2018
4301(35*10^116223-341)/9116224Robert Price08/2021
4302(2^386087-5)/40959116220Lelio R Paula03/2014
4303(2^386054+714)/2116214Stefano Morozzi09/2020
4304(10^116201+7)/39623116197Alfred Reich06/2021
43052^385969-823116189Yves Minet05/2012
430657^66162+2116173Lelio R Paula08/2013
43072^385854+75049116154Enzo Doria04/2016
4308(2^385832+2590)/2116147Stefano Morozzi09/2020
43092^385775-109587116130Enzo Doria04/2014
4310(14*10^116112-101)/3116113Robert Price02/2019
4311Phi(236354,10)/24817171116109Makoto Kamada08/2019
43123*10^116107+23116108Robert Price03/2022
431328729^10990+10990^28729116094Hans Havermann02/2021
43142^385622+71839116084Enzo Doria04/2016
43152^385564+781116067Lelio R Paula01/2012
4316(2^385565+1562)/2116067Stefano Morozzi09/2020
4317(2^385563+378)/2116066Stefano Morozzi02/2021
4318(2^385557+2214)/2116064Stefano Morozzi09/2020
431929431^8776+8776^29431116056Hans Havermann01/2021
4320(266*10^116024-17)/3116026Robert Price07/2020
432130263^6820+6820^30263116022Hans Havermann02/2021
43222^385410+71893116020Enzo Doria04/2016
432338225^1084+1084^38225116014Hans Havermann02/2021
432426548^23433+23433^26548116011Hans Havermann02/2021
4325(25*2^385091+1)/27115924Lelio R Paula04/2014
4326(11*10^115910-131)/3115911Robert Price09/2018
43272^384953-111943115883Paul Bourdelais02/2012
432843^70942-2115882Lelio R Paula04/2014
4329(94*10^115879-7)/3115881Robert Price03/2020
43307*10^115863+3115864Robert Price08/2015
43312^384834+93115847Donovan Johnson07/2008
43322^384809+71297115840Enzo Doria04/2016
4333(55*10^115829+323)/9115830Robert Price10/2021
4334(7*2^384759-1)/5115825Lelio R Paula04/2014
433531348^4951+4951^31348115822Hans Havermann02/2021
4336(793*10^115810+53)/9115812Robert Price01/2022
4337(71*10^115810-17)/9115811Ray Chandler08/2011
4338(97*10^115794-1)/3115796Serge Batalov12/2014
433931115^5266+5266^31115115794Hans Havermann02/2021
43402*10^115784-27115785Robert Price05/2018
434110^115773+126739115774Patrick De Geest04/2018
434310^115773-1000000001115773Robert Price03/2018
434210^115773-396221115773Patrick De Geest04/2018
4344(2^384582+778)/2115771Stefano Morozzi09/2020
434530537^6178+6178^30537115762Hans Havermann01/2021
43462^384530+1874305115756Enzo Doria06/2016
4347(3*2^384524-1)/7631115750Lelio R Paula03/2014
434828275^12406+12406^28275115748Hans Havermann01/2021
4349(44*10^115697-413)/9115698Robert Price03/2019
435031408^4825+4825^31408115692Hans Havermann02/2021
4351(2^384317+1026)/2115691Stefano Morozzi09/2020
43522^384312+81091115690Yves Minet02/2010
4353(2^384265+2150)/2115675Stefano Morozzi09/2020
4354(2^384246+2182)/2115670Stefano Morozzi09/2020
4355(4*10^115668-79)/3115669Robert Price02/2018
4356(2^384193+242)/2115654Stefano Morozzi09/2020
4357(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
4358(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
435918^92125-92125^18115642Dylan Delgado08/2019
43603^242337-4042115625Enzo Doria05/2014
4361(2^383931+674)/2115575Stefano Morozzi09/2020
43627*10^115561+79115562Robert Price07/2019
4363(2^383872+3046)/2115557Stefano Morozzi09/2020
4364(11*2^383859-13)/15115553Renaud Lifchitz03/2011
43652^383780-3149115530Yves Minet10/2014
4366(41*10^115523-383)/9115524Robert Price11/2018
436727316^16923+16923^27316115506Hans Havermann02/2021
4368(2^383618+618)/2115481Stefano Morozzi09/2020
43692^383560-455115464Yves Minet03/2012
4370(2^383544+5)/3115458Lelio R Paula03/2014
4371(22*10^115454+119)/3115455Robert Price04/2021
437289^59221-88^59221115445Robert Price06/2015
43732^383347+1869413115399Enzo Doria05/2016
4374(103*10^115366+17)/3115368Robert Price08/2020
4375(2^383232+750)/2115365Stefano Morozzi09/2020
4376(2^383130-7)/131793115329Lelio R Paula03/2014
4377(12^106859+1)/13115320Paul Bourdelais02/2010
437829961^7060+7060^29961115315Hans Havermann01/2021
43802^383039+1869509115307Enzo Doria05/2016
437932918^3183+3183^32918115307Hans Havermann01/2021
438136964^1315+1315^36964115288Hans Havermann02/2021
4382(13*2^382968+1)/7115286Lelio R Paula04/2014
4383(22*10^115282+29)/3115283Robert Price02/2021
4384(2^382945+2046)/2115278Stefano Morozzi09/2020
4385(2^382789+3182)/2115231Stefano Morozzi09/2020
438630416^6141+6141^30416115224Hans Havermann02/2021
43876*10^115211+79115212Robert Price09/2020
4388(2^382722+3598)/2115211Stefano Morozzi09/2020
438927987^13078+13078^27987115210Hans Havermann02/2021
4390(2^382699+2090)/2115204Stefano Morozzi09/2020
43912^382633+73697115185Enzo Doria04/2016
43922^382509-113593115147Enzo Doria08/2014
43932^382502-2791721115145Enzo Doria03/2016
4394(2^382495+1274)/2115143Stefano Morozzi01/2021
439526752^20065+20065^26752115099Hans Havermann02/2021
439626383^23008+23008^26383115080Hans Havermann02/2021
43979^120590-120590115073Robert Price03/2014
439828203^12016+12016^28203115062Hans Havermann02/2021
43992^382198+9115054Lelio R Paula03/2013
440030101^6630+6630^30101115032Hans Havermann01/2021
4401(89*10^115030-179)/9115031Robert Price12/2019
4402(2^381935+2774)/2114974Stefano Morozzi02/2021
440327300^16271+16271^27300114972Hans Havermann02/2021
44042^381883-59197114959Enzo Doria10/2015
440527423^15542+15542^27423114944Hans Havermann02/2021
4406(2^381820+1626)/2114939Stefano Morozzi09/2020
44082^381806-4481114936Yves Minet07/2011
44072^381808-1851507114936Enzo Doria08/2015
4409(2^381792+2502)/2114931Stefano Morozzi09/2020
44102^381774-112373114926Enzo Doria06/2014
441126341^22980+22980^26341114883Hans Havermann01/2021
44122^381555-109051114860Enzo Doria04/2014
44132^381546-113501114857Enzo Doria08/2014
4414(7*10^114845-19)/3114846Robert Price10/2020
441526675^20178+20178^26675114833Hans Havermann02/2021
4416(2^381436+1182)/2114824Stefano Morozzi09/2020
44173^240644+16114817Robert Price04/2020
44182^381360-110429114801Enzo Doria05/2014
4419(17*10^114795+79)/3114796Robert Price04/2019
4420(66^63079+1)/67114774Paul Bourdelais09/2017
44212^381252-115079114769Enzo Doria06/2015
4422(2^381251+3186)/2114768Stefano Morozzi09/2020
44232^381209-29323114756Enzo Doria07/2015
44242^381207-111546435114755Paul Bourdelais10/2021
4425569^41651-568^41651114754Jean-Louis Charton11/2009
44262^381201+1873205114753Enzo Doria06/2016
4427(85*10^114737+293)/9114738Robert Price12/2019
4428(265*10^114736+17)/3114738Robert Price03/2020
4429(2^381062+2170)/2114711Stefano Morozzi09/2020
44302^380974-112991114685Enzo Doria07/2014
443137097^1234+1234^37097114679Hans Havermann02/2021
443288^58949-87114626Norbert Schneider11/2015
4433(2^380773+662)/2114624Stefano Morozzi09/2020
443429913^6782+6782^29913114608Hans Havermann02/2021
4435(331*10^114605-7)/9114607Robert Price04/2022
44362^380700+91114603Lelio R Paula03/2013
4437(2^380632+2578)/2114582Stefano Morozzi09/2020
44387*10^114577+27114578Robert Price11/2020
444010^114575+3^114576114576Mike Oakes09/2010
443910^114575+66561114576Patrick De Geest02/2017
444110^114575-581081114575Patrick De Geest02/2017
44422^380587-115315114569Enzo Doria06/2015
444331874^3927+3927^31874114558Hans Havermann02/2021
44442^380513-216925114546Enzo Doria05/2014
44452^380451-1840087114528Enzo Doria06/2015
4446(2^380426+1510)/2114520Stefano Morozzi09/2020
4447(15*2^380388-1)/539114507Lelio R Paula04/2014
44482^380279-461347114476Enzo Doria07/2015
4449(331*10^114454-7)/9114456Robert Price04/2022
445027121^16590+16590^27121114447Hans Havermann01/2021
445125966^25555+25555^25966114445Hans Havermann01/2021
4452(11*10^114400+529)/9114401Robert Price09/2021
44532^380021+1871147114398Enzo Doria05/2016
44542^380005+1869707114393Enzo Doria05/2016
44552^379958-113297114379Enzo Doria07/2014
4456(2^379897+1274)/2114361Stefano Morozzi01/2021
44572^379881-109105114356Enzo Doria04/2014
4458(21*2^379857-1)/13114349Lelio R Paula03/2014
4459(4*10^114340+83)/3114341Robert Price02/2018
4460(26*10^114317-77)/3114318Robert Price11/2019
4461(4*10^114296+149)/9114296Robert Price04/2018
446288^58773-87114284Norbert Schneider11/2015
446327764^13065+13065^27764114280Hans Havermann01/2021
44642^379529-2790283114250Enzo Doria03/2016
44652^379522+1869115114248Enzo Doria05/2016
4466(145*10^114226-1)/9114228Serge Batalov12/2014
44672^379317-115033114186Enzo Doria06/2015
4468(22*10^114178+47)/3114179Robert Price06/2021
4469(17*2^379246-1)/17407114162Lelio R Paula03/2014
4470(2^379192+226)/2114148Stefano Morozzi09/2020
44716*10^114091+23114092Robert Price09/2020
4472(4*10^114076+143)/3114077Robert Price03/2018
4473(2^378820+3226)/2114036Stefano Morozzi01/2021
4474(2^378754+2058)/2114017Stefano Morozzi09/2020
4476(46*10^113969+683)/9113970Robert Price03/2019
4475(83*10^113969+133)/9113970Robert Price08/2021
447732226^3439+3439^32226113966Hans Havermann02/2021
4478(77*10^113963-149)/9113964Robert Price03/2022
447978*10^113954-7113956Robert Price10/2020
44802*10^113941+9113942Dmitry Domanov11/2010
448110^113933+145897113934Patrick De Geest02/2021
4484(2^378478+1642)/2113933Stefano Morozzi09/2020
448210^113933-8000000001113933Robert Price11/2020
448310^113933-66167113933Patrick De Geest02/2021
44852339662057597*10^113903+9113916Robert Price03/2021
44864*10^113905+91113906Robert Price08/2018
448710^113894+76609113895Patrick De Geest02/2021
448910^113894-10000001113894Robert Price09/2020
448810^113894-373947113894Patrick De Geest02/2021
449033933^2270+2270^33933113881Hans Havermann02/2021
44914*10^113874-21113875Robert Price09/2018
44922^378272-16565113872Enzo Doria04/2013
44932^378217-109075113855Enzo Doria04/2014
44942^378198+67113849Lelio R Paula03/2013
44952^378173-3249113842Yves Minet12/2014
4496(2^378155-5)/6597113833Lelio R Paula03/2014
449792941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
449830030^6173+6173^30030113829Hans Havermann01/2021
44992^378128-262977113828Enzo Doria05/2014
45002^378123-113215113827Enzo Doria07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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