PRP Records

Probable Primes Top 10000

(291192 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 ?
42512^392413-112123118129Enzo Doria06/2014
425227491^19798+19798^27491118119Hans Havermann02/2021
4253(49*10^118109-319)/9118110Robert Price10/2021
4254(2^392342+5)/27118106Lelio R Paula04/2014
4255(2^392333+1782)/2118104Stefano Morozzi01/2021
42562^392300-1841429118095Enzo Doria06/2015
42572^392220+75241118070Enzo Doria04/2016
425827836^17409+17409^27836118047Hans Havermann02/2021
425910^118009+664447118010Patrick De Geest07/2018
426010^118009-20001118009Robert Price01/2018
4261(14*10^117991+61)/3117992Robert Price12/2018
42622^391933+5897117984Yves Minet02/2011
42632^391912-1849259117978Enzo Doria08/2015
426428357^14440+14440^28357117953Hans Havermann02/2021
4265(2^391812+5)/14181117944Lelio R Paula04/2014
4266(7*10^117930-79)/9117930Robert Price01/2021
426727531^19168+19168^27531117904Hans Havermann02/2021
4268(46*10^117902+683)/9117903Robert Price03/2019
426927670^18189+18189^27670117869Hans Havermann02/2021
4270(7*2^391521+1)/285117858Lelio R Paula04/2014
4271(56*10^117856+583)/9117857Robert Price08/2021
427232169^4606+4606^32169117846Hans Havermann02/2021
4273(71*10^117803-143)/9117804Robert Price10/2021
42742^391324+90901117801Yves Minet02/2011
42752^391301-1859923117794Enzo Doria03/2016
42762^391261-4131117782Yves Minet02/2018
4277(2^391211+554)/2117766Stefano Morozzi09/2020
427838434^1157+1157^38434117737Hans Havermann01/2021
4279(2^391115-7)/11791117734Lelio R Paula04/2014
4280(85*10^117719+473)/9117720Robert Price01/2020
4281(2^391049+582)/2117718Stefano Morozzi09/2020
428231083^6122+6122^31083117709Hans Havermann02/2021
42832^390960+1880881117691Enzo Doria11/2016
4284(71*10^117685+91)/9117686Robert Price04/2022
42862^390897-1860553117672Enzo Doria11/2015
4285(61*10^117671+47)/9117672Robert Price07/2022
42872^390889-115003117670Enzo Doria06/2015
42882^390779-30337117637Paul Bourdelais02/2012
4289(2^390735+378)/2117623Stefano Morozzi02/2021
429011^112916-780117590Enzo Doria12/2012
429127641^17916+17916^27641117564Hans Havermann02/2021
429227906^16321+16321^27906117561Hans Havermann02/2021
429327294^20275+20275^27294117555Hans Havermann02/2021
4294(2^390473+1002)/2117544Stefano Morozzi09/2020
429535912^1875+1875^35912117541Hans Havermann02/2021
4296(16^97613-5^97613)/11117537Robert Price07/2013
4297(2^390438+1774)/2117534Stefano Morozzi01/2021
4298(2^390418+1722)/2117528Stefano Morozzi09/2020
4299(2^390403+654)/2117523Stefano Morozzi09/2020
4300(2^390343+2246)/2117505Stefano Morozzi01/2021
430128043^15478+15478^28043117493Hans Havermann02/2021
4302(17*2^390272+1)/1983117482Lelio R Paula04/2014
430337077^1474+1474^37077117479Hans Havermann01/2021
430431^78759-30117459Theodore Burton02/2007
4305(2^390176+1222)/2117455Stefano Morozzi09/2020
4306(2^390133+1242)/2117442Stefano Morozzi09/2020
4307(2^390013+2634)/2117406Stefano Morozzi09/2020
43083*10^117402+61117403Robert Price09/2020
43092^389998+37117402Lelio R Paula03/2013
4310(2^389977+314)/2117395Stefano Morozzi09/2020
4311(2^389921+342)/2117378Stefano Morozzi01/2021
431271830^43+43^71830117333Hans Havermann01/2021
4313(2^389768+1582)/2117332Stefano Morozzi09/2020
431433802^2951+2951^33802117292Hans Havermann02/2021
431526789^23866+23866^26789117277Hans Havermann02/2021
431629^80192-1*80192^29117273Dylan Delgado12/2019
4317(101*10^117260+7)/9117262Robert Price02/2022
4318(13*10^117249+161)/3117250Robert Price11/2018
43192^389478+43117245Lelio R Paula03/2013
4320(298*10^117229-7)/3117231Robert Price06/2020
4321(2^389416+342)/2117226Stefano Morozzi01/2021
4322(29*2^389351-1)/9117207Lelio R Paula04/2014
43235*10^117205+23117206Robert Price03/2019
4324(2^389341-7)/3865117200Lelio R Paula03/2014
432527272^19827+19827^27272117195Hans Havermann01/2021
4326(2^389276+2650)/2117184Stefano Morozzi09/2020
4327(844*10^117175-7)/9117177Robert Price05/2021
432810^117142+209223117143Patrick De Geest04/2018
433010^117142-1000000001117142Robert Price03/2018
432910^117142-966057117142Patrick De Geest04/2018
433110^117135+360577117136Patrick De Geest07/2018
433210^117135-401117135Robert Price01/2018
433326415^26488-26488^26415117126Norbert Schneider05/2021
43344*10^117123+79117124Robert Price08/2018
43352^389033-12797413117111Enzo Doria04/2016
4336(2^388987+2634)/2117097Stefano Morozzi09/2020
43372^388960-109505117089Enzo Doria04/2014
43387*10^117082-57117083Robert Price06/2020
4339(2^388928-5)/569117077Lelio R Paula03/2014
43402^388888-1529117067Yves Minet01/2013
434110^117059+28879117060Patrick De Geest05/2016
4342(10^117059-71)/1117059Serge Batalov12/2014
4343(2^388854+3630)/2117057Stefano Morozzi09/2020
4344(2^388842+2098)/2117053Stefano Morozzi09/2020
4345(2^388789+3150)/2117037Stefano Morozzi09/2020
4346(2^388748+378)/2117025Stefano Morozzi02/2021
4347(693^41189-1)/692117005Michael Stocker05/2020
4348(26*10^116999-503)/9117000Robert Price07/2018
4349(2^388609+1554)/2116983Stefano Morozzi09/2020
435038496^1093+1093^38496116975Hans Havermann02/2021
43513^245154-6256116969Enzo Doria05/2014
43525*10^116966-43116967Robert Price01/2019
43532^388536-113495116961Enzo Doria08/2014
4354(2^388512+382)/2116954Stefano Morozzi02/2021
43552^388469-43116941Lelio R Paula03/2013
435627417^18416+18416^27417116939Hans Havermann02/2021
4357(2^388438+1842)/2116932Stefano Morozzi02/2021
4358(7*2^388372-1)/111116911Lelio R Paula04/2014
4359(7*2^388335-1)/25116900Lelio R Paula04/2014
43602^388180+93116854Donovan Johnson07/2008
4361(2^388167+2510)/2116850Stefano Morozzi09/2020
4362(85*10^116842+293)/9116843Robert Price12/2019
436335296^2043+2043^35296116840Hans Havermann02/2021
4364(2^388081+7)/1179116821Lelio R Paula03/2014
436538633^1056+1056^38633116814Hans Havermann02/2021
43662^387946-113261116784Enzo Doria07/2014
436728363^13056+13056^28363116737Hans Havermann02/2021
43682^387745+75557116723Enzo Doria04/2016
4369(29*10^116719+313)/9116720Robert Price04/2021
437029622^8699+8699^29622116695Hans Havermann02/2021
4371(206*10^116687-17)/9116689Robert Price01/2020
4372(7*10^116684+179)/3116685Robert Price09/2018
43732^387554+71455116666Enzo Doria04/2016
4374(602*10^116647-71)/9116649Robert Price12/2021
4375(2^387447+78557)/365116631Lelio R Paula12/2014
4376(145*10^116610-1)/9116612Serge Batalov12/2014
4377(25*10^116601-331)/9116602Robert Price08/2018
4378(17*2^387284-1)/59116584Lelio R Paula04/2014
4379(2^387284+3726)/2116584Stefano Morozzi09/2020
43802^387211+111546435116563Paul Bourdelais10/2021
438110^116557+987654321116558Robert Price12/2019
438210^116557+9141116558Patrick De Geest02/2020
438310^116557-609431116557Patrick De Geest02/2020
4384(28*10^116546+41)/3116547Robert Price07/2021
4385(2^387123+1814)/2116536Stefano Morozzi02/2021
4386(2^387076+2046)/2116522Stefano Morozzi09/2020
4387(2^387073+2570)/2116521Stefano Morozzi09/2020
4388(7*10^116514-1)/3116515Robert Price08/2022
438928846^10931+10931^28846116500Hans Havermann02/2021
439010^116496+3593037116497Paul Bourdelais10/2021
4391(31*2^386968+1)/7116490Lelio R Paula03/2014
43922^386947+1869143116483Enzo Doria05/2016
4393(30^78857-1)/29116480Robert Price12/2011
4394(2^386903-3)/5116469Lelio R Paula03/2014
439528107^13892+13892^28107116441Hans Havermann02/2021
439629110^9957+9957^29110116386Hans Havermann02/2021
439726469^24838+24838^26469116335Hans Havermann01/2021
43982^386389-1864783116315Enzo Doria03/2016
4399(31*2^386231-1)/1711116266Lelio R Paula03/2014
4400297^47012+47012^297116250Norbert Schneider07/2018
4401(35*10^116223-341)/9116224Robert Price08/2021
4402(2^386087-5)/40959116220Lelio R Paula03/2014
4403(2^386054+714)/2116214Stefano Morozzi09/2020
4404(10^116201+7)/39623116197Alfred Reich06/2021
44052^385969-823116189Yves Minet05/2012
440657^66162+2116173Lelio R Paula08/2013
44072^385854+75049116154Enzo Doria04/2016
4408(2^385832+2590)/2116147Stefano Morozzi09/2020
44092^385775-109587116130Enzo Doria04/2014
4410(14*10^116112-101)/3116113Robert Price02/2019
4411Phi(236354,10)/24817171116109Makoto Kamada08/2019
44123*10^116107+23116108Robert Price03/2022
441328729^10990+10990^28729116094Hans Havermann02/2021
44142^385622+71839116084Enzo Doria04/2016
44152^385564+781116067Lelio R Paula01/2012
4416(2^385565+1562)/2116067Stefano Morozzi09/2020
4417(2^385563+378)/2116066Stefano Morozzi02/2021
4418(2^385557+2214)/2116064Stefano Morozzi09/2020
441929431^8776+8776^29431116056Hans Havermann01/2021
4420(266*10^116024-17)/3116026Robert Price07/2020
442130263^6820+6820^30263116022Hans Havermann02/2021
44222^385410+71893116020Enzo Doria04/2016
442338225^1084+1084^38225116014Hans Havermann02/2021
442426548^23433+23433^26548116011Hans Havermann02/2021
4425(25*2^385091+1)/27115924Lelio R Paula04/2014
4426(11*10^115910-131)/3115911Robert Price09/2018
44272^384953-111943115883Paul Bourdelais02/2012
442843^70942-2115882Lelio R Paula04/2014
4429(94*10^115879-7)/3115881Robert Price03/2020
44307*10^115863+3115864Robert Price08/2015
44312^384834+93115847Donovan Johnson07/2008
44322^384809+71297115840Enzo Doria04/2016
4433(55*10^115829+323)/9115830Robert Price10/2021
4434(7*2^384759-1)/5115825Lelio R Paula04/2014
443531348^4951+4951^31348115822Hans Havermann02/2021
4436(793*10^115810+53)/9115812Robert Price01/2022
4437(71*10^115810-17)/9115811Ray Chandler08/2011
4438(97*10^115794-1)/3115796Serge Batalov12/2014
443931115^5266+5266^31115115794Hans Havermann02/2021
44402*10^115784-27115785Robert Price05/2018
444110^115773+126739115774Patrick De Geest04/2018
444310^115773-1000000001115773Robert Price03/2018
444210^115773-396221115773Patrick De Geest04/2018
4444(2^384582+778)/2115771Stefano Morozzi09/2020
444530537^6178+6178^30537115762Hans Havermann01/2021
44462^384530+1874305115756Enzo Doria06/2016
4447(3*2^384524-1)/7631115750Lelio R Paula03/2014
444828275^12406+12406^28275115748Hans Havermann01/2021
4449(44*10^115697-413)/9115698Robert Price03/2019
445031408^4825+4825^31408115692Hans Havermann02/2021
4451(2^384317+1026)/2115691Stefano Morozzi09/2020
44522^384312+81091115690Yves Minet02/2010
4453(2^384265+2150)/2115675Stefano Morozzi09/2020
4454(2^384246+2182)/2115670Stefano Morozzi09/2020
4455(4*10^115668-79)/3115669Robert Price02/2018
4456(2^384193+242)/2115654Stefano Morozzi09/2020
4457(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
4458(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
445918^92125-92125^18115642Dylan Delgado08/2019
44603^242337-4042115625Enzo Doria05/2014
4461(2^383931+674)/2115575Stefano Morozzi09/2020
44627*10^115561+79115562Robert Price07/2019
4463(2^383872+3046)/2115557Stefano Morozzi09/2020
4464(11*2^383859-13)/15115553Renaud Lifchitz03/2011
44652^383780-3149115530Yves Minet10/2014
4466(41*10^115523-383)/9115524Robert Price11/2018
446727316^16923+16923^27316115506Hans Havermann02/2021
4468(2^383618+618)/2115481Stefano Morozzi09/2020
44692^383560-455115464Yves Minet03/2012
4470(2^383544+5)/3115458Lelio R Paula03/2014
4471(22*10^115454+119)/3115455Robert Price04/2021
447289^59221-88^59221115445Robert Price06/2015
44732^383347+1869413115399Enzo Doria05/2016
4474(103*10^115366+17)/3115368Robert Price08/2020
4475(2^383232+750)/2115365Stefano Morozzi09/2020
4476(2^383130-7)/131793115329Lelio R Paula03/2014
4477(12^106859+1)/13115320Paul Bourdelais02/2010
447829961^7060+7060^29961115315Hans Havermann01/2021
44802^383039+1869509115307Enzo Doria05/2016
447932918^3183+3183^32918115307Hans Havermann01/2021
448136964^1315+1315^36964115288Hans Havermann02/2021
4482(13*2^382968+1)/7115286Lelio R Paula04/2014
4483(22*10^115282+29)/3115283Robert Price02/2021
4484(2^382945+2046)/2115278Stefano Morozzi09/2020
4485(2^382789+3182)/2115231Stefano Morozzi09/2020
448630416^6141+6141^30416115224Hans Havermann02/2021
44876*10^115211+79115212Robert Price09/2020
4488(2^382722+3598)/2115211Stefano Morozzi09/2020
448927987^13078+13078^27987115210Hans Havermann02/2021
4490(2^382699+2090)/2115204Stefano Morozzi09/2020
4491(22*10^115188-193)/9115189Robert Price07/2022
44922^382633+73697115185Enzo Doria04/2016
44932^382509-113593115147Enzo Doria08/2014
44942^382502-2791721115145Enzo Doria03/2016
4495(2^382495+1274)/2115143Stefano Morozzi01/2021
449626752^20065+20065^26752115099Hans Havermann02/2021
449726383^23008+23008^26383115080Hans Havermann02/2021
44989^120590-120590115073Robert Price03/2014
449928203^12016+12016^28203115062Hans Havermann02/2021
45002^382198+9115054Lelio R Paula03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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