PRP Records

Probable Primes Top 10000

(294627 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 ?
525110^118009+664447118010Patrick De Geest07/2018
525210^118009-20001118009Robert Price01/2018
5253(14*10^117991+61)/3117992Robert Price12/2018
52542^391933+5897117984Yves Minet02/2011
52552^391912-1849259117978Enzo Doria08/2015
5256(2*34^77029+1043)/11117968Eric Chen08/2023
52575*2^391836-3117956Jon Grantham07/2023
525828357^14440+14440^28357117953Hans Havermann02/2021
5259(2^391812+5)/14181117944Lelio R Paula04/2014
5260(7*10^117930-79)/9117930Robert Price01/2021
526127531^19168+19168^27531117904Hans Havermann02/2021
5262(46*10^117902+683)/9117903Robert Price03/2019
526327670^18189+18189^27670117869Hans Havermann02/2021
5264(7*2^391521+1)/285117858Lelio R Paula04/2014
5265(56*10^117856+583)/9117857Robert Price08/2021
526632169^4606+4606^32169117846Hans Havermann02/2021
5267(71*10^117803-143)/9117804Robert Price10/2021
52682^391324+90901117801Yves Minet02/2011
52692^391301-1859923117794Enzo Doria03/2016
52702^391261-4131117782Yves Minet02/2018
5271(2^391211+554)/2117766Stefano Morozzi09/2020
527238434^1157+1157^38434117737Hans Havermann01/2021
5273(2^391115-7)/11791117734Lelio R Paula04/2014
5274(85*10^117719+473)/9117720Robert Price01/2020
5275(2^391049+582)/2117718Stefano Morozzi09/2020
5276(21*23^86445-197)/22117715Eric Chen08/2023
527731083^6122+6122^31083117709Hans Havermann02/2021
52782^390960+1880881117691Enzo Doria11/2016
5279(71*10^117685+91)/9117686Robert Price04/2022
52812^390897-1860553117672Enzo Doria11/2015
5280(61*10^117671+47)/9117672Robert Price07/2022
52822^390889-115003117670Enzo Doria06/2015
528312^109010+35117642Riley Fisher08/2023
52842^390779-30337117637Paul Bourdelais02/2012
5285(2^390735+378)/2117623Stefano Morozzi02/2021
528611^112916-780117590Enzo Doria12/2012
528727641^17916+17916^27641117564Hans Havermann02/2021
528827906^16321+16321^27906117561Hans Havermann02/2021
528927294^20275+20275^27294117555Hans Havermann02/2021
5290(2^390473+1002)/2117544Stefano Morozzi09/2020
529135912^1875+1875^35912117541Hans Havermann02/2021
5292(16^97613-5^97613)/11117537Robert Price07/2013
5293(2^390438+1774)/2117534Stefano Morozzi01/2021
5294(2^390418+1722)/2117528Stefano Morozzi09/2020
5295(2^390403+654)/2117523Stefano Morozzi09/2020
5296(2^390343+2246)/2117505Stefano Morozzi01/2021
529728043^15478+15478^28043117493Hans Havermann02/2021
5298(17*2^390272+1)/1983117482Lelio R Paula04/2014
529937077^1474+1474^37077117479Hans Havermann01/2021
530031^78759-30117459Theodore Burton02/2007
5301(2^390176+1222)/2117455Stefano Morozzi09/2020
5302(2^390133+1242)/2117442Stefano Morozzi09/2020
5303(2^390013+2634)/2117406Stefano Morozzi09/2020
53043*10^117402+61117403Robert Price09/2020
53052^389998+37117402Lelio R Paula03/2013
5306(2^389977+314)/2117395Stefano Morozzi09/2020
5307(2^389921+342)/2117378Stefano Morozzi01/2021
530871830^43+43^71830117333Hans Havermann01/2021
5309(2^389768+1582)/2117332Stefano Morozzi09/2020
531033802^2951+2951^33802117292Hans Havermann02/2021
531126789^23866+23866^26789117277Hans Havermann02/2021
531229^80192-1*80192^29117273Dylan Delgado12/2019
5313(101*10^117260+7)/9117262Robert Price02/2022
5314(13*10^117249+161)/3117250Robert Price11/2018
53152^389478+43117245Lelio R Paula03/2013
5316(298*10^117229-7)/3117231Robert Price06/2020
5317(2^389416+342)/2117226Stefano Morozzi01/2021
5318(29*2^389351-1)/9117207Lelio R Paula04/2014
53195*10^117205+23117206Robert Price03/2019
5320(2^389341-7)/3865117200Lelio R Paula03/2014
532127272^19827+19827^27272117195Hans Havermann01/2021
5322(2^389276+2650)/2117184Stefano Morozzi09/2020
5323(844*10^117175-7)/9117177Robert Price05/2021
532410^117142+209223117143Patrick De Geest04/2018
532610^117142-1000000001117142Robert Price03/2018
532510^117142-966057117142Patrick De Geest04/2018
532710^117135+360577117136Patrick De Geest07/2018
532810^117135-401117135Robert Price01/2018
532926415^26488-26488^26415117126Norbert Schneider05/2021
53304*10^117123+79117124Robert Price08/2018
53312^389033-12797413117111Enzo Doria04/2016
5332(2^388987+2634)/2117097Stefano Morozzi09/2020
53332^388960-109505117089Enzo Doria04/2014
53347*10^117082-57117083Robert Price06/2020
5335(2^388928-5)/569117077Lelio R Paula03/2014
53362^388888-1529117067Yves Minet01/2013
533710^117059+28879117060Patrick De Geest05/2016
5338(10^117059-71)/1117059Serge Batalov12/2014
5339(2^388854+3630)/2117057Stefano Morozzi09/2020
5340(2^388842+2098)/2117053Stefano Morozzi09/2020
5341(2^388789+3150)/2117037Stefano Morozzi09/2020
5342(2^388748+378)/2117025Stefano Morozzi02/2021
5343(693^41189-1)/692117005Michael Stocker05/2020
5344(26*10^116999-503)/9117000Robert Price07/2018
5345(2^388609+1554)/2116983Stefano Morozzi09/2020
534638496^1093+1093^38496116975Hans Havermann02/2021
53473^245154-6256116969Enzo Doria05/2014
53485*10^116966-43116967Robert Price01/2019
53492^388536-113495116961Enzo Doria08/2014
5350(2^388512+382)/2116954Stefano Morozzi02/2021
5351(8*32^77701+271)/31116952Eric Chen11/2023
53522^388469-43116941Lelio R Paula03/2013
535327417^18416+18416^27417116939Hans Havermann02/2021
5354(2^388438+1842)/2116932Stefano Morozzi02/2021
5355(7*2^388372-1)/111116911Lelio R Paula04/2014
5356(7*2^388335-1)/25116900Lelio R Paula04/2014
53572^388180+93116854Donovan Johnson07/2008
5358(2^388167+2510)/2116850Stefano Morozzi09/2020
5359(85*10^116842+293)/9116843Robert Price12/2019
536035296^2043+2043^35296116840Hans Havermann02/2021
5361(2^388081+7)/1179116821Lelio R Paula03/2014
536238633^1056+1056^38633116814Hans Havermann02/2021
53632^387946-113261116784Enzo Doria07/2014
536428*36^75009+305116739Eric Chen12/2022
536528363^13056+13056^28363116737Hans Havermann02/2021
53662^387745+75557116723Enzo Doria04/2016
5367(29*10^116719+313)/9116720Robert Price04/2021
536829622^8699+8699^29622116695Hans Havermann02/2021
5369(206*10^116687-17)/9116689Robert Price01/2020
5370(7*10^116684+179)/3116685Robert Price09/2018
53712^387554+71455116666Enzo Doria04/2016
5372(602*10^116647-71)/9116649Robert Price12/2021
53733^244461-10116638Tyler NeSmith09/2022
5374(2^387447+78557)/365116631Lelio R Paula12/2014
5375(2*10^116620+43)/9116620Serge Batalov11/2022
5376(19*10^116617+287)/9/12893116614Alfred Reich11/2022
5377(145*10^116610-1)/9116612Serge Batalov12/2014
5378(25*10^116601-331)/9116602Robert Price08/2018
5379(17*2^387284-1)/59116584Lelio R Paula04/2014
5380(2^387284+3726)/2116584Stefano Morozzi09/2020
53812^387211+111546435116563Paul Bourdelais10/2021
538210^116557+987654321116558Robert Price12/2019
538310^116557+9141116558Patrick De Geest02/2020
538410^116557-609431116557Patrick De Geest02/2020
5385(28*10^116546+41)/3116547Robert Price07/2021
5386(2^387123+1814)/2116536Stefano Morozzi02/2021
5387(2^387076+2046)/2116522Stefano Morozzi09/2020
5388(2^387073+2570)/2116521Stefano Morozzi09/2020
5389(7*10^116514-1)/3116515Robert Price08/2022
5390(26*32^77406-390071011)/31116508Eric Chen11/2023
539128846^10931+10931^28846116500Hans Havermann02/2021
539210^116496+3593037116497Paul Bourdelais10/2021
5393(31*2^386968+1)/7116490Lelio R Paula03/2014
53942^386947+1869143116483Enzo Doria05/2016
5395(30^78857-1)/29116480Robert Price12/2011
5396(2^386903-3)/5116469Lelio R Paula03/2014
539728107^13892+13892^28107116441Hans Havermann02/2021
539829110^9957+9957^29110116386Hans Havermann02/2021
539926469^24838+24838^26469116335Hans Havermann01/2021
54002^386389-1864783116315Enzo Doria03/2016
5401(8*32^77250-163)/31116273Eric Chen11/2023
5402(31*2^386231-1)/1711116266Lelio R Paula03/2014
5403297^47012+47012^297116250Norbert Schneider07/2018
5404(35*10^116223-341)/9116224Robert Price08/2021
5405(2^386087-5)/40959116220Lelio R Paula03/2014
5406(2^386054+714)/2116214Stefano Morozzi09/2020
5407(10^116201+7)/39623116197Alfred Reich06/2021
54082^385969-823116189Yves Minet05/2012
540957^66162+2116173Lelio R Paula08/2013
54102^385854+75049116154Enzo Doria04/2016
5411(2^385832+2590)/2116147Stefano Morozzi09/2020
54122^385775-109587116130Enzo Doria04/2014
5413(14*10^116112-101)/3116113Robert Price02/2019
5414Phi(236354,10)/24817171116109Makoto Kamada08/2019
54153*10^116107+23116108Robert Price03/2022
541628729^10990+10990^28729116094Hans Havermann02/2021
54172^385622+71839116084Enzo Doria04/2016
54192^385564+781116067Lelio R Paula01/2012
5418(2^385565+1562)/2116067Stefano Morozzi09/2020
5420(2^385563+378)/2116066Stefano Morozzi02/2021
5421(2^385557+2214)/2116064Stefano Morozzi09/2020
542229431^8776+8776^29431116056Hans Havermann01/2021
5423(266*10^116024-17)/3116026Robert Price07/2020
542430263^6820+6820^30263116022Hans Havermann02/2021
54252^385410+71893116020Enzo Doria04/2016
542638225^1084+1084^38225116014Hans Havermann02/2021
542726548^23433+23433^26548116011Hans Havermann02/2021
542812^107422-11115928Riley Fisher12/2023
5429(25*2^385091+1)/27115924Lelio R Paula04/2014
5430(11*10^115910-131)/3115911Robert Price09/2018
54312^384953-111943115883Paul Bourdelais02/2012
543243^70942-2115882Lelio R Paula04/2014
5433(94*10^115879-7)/3115881Robert Price03/2020
54347*10^115863+3115864Robert Price08/2015
54352^384834+93115847Donovan Johnson07/2008
54362^384809+71297115840Enzo Doria04/2016
5437(55*10^115829+323)/9115830Robert Price10/2021
5438(7*2^384759-1)/5115825Lelio R Paula04/2014
543931348^4951+4951^31348115822Hans Havermann02/2021
5440(793*10^115810+53)/9115812Robert Price01/2022
5441(71*10^115810-17)/9115811Ray Chandler08/2011
5442(97*10^115794-1)/3115796Serge Batalov12/2014
544331115^5266+5266^31115115794Hans Havermann02/2021
54442*10^115784-27115785Robert Price05/2018
544510^115773+126739115774Patrick De Geest04/2018
544710^115773-1000000001115773Robert Price03/2018
544610^115773-396221115773Patrick De Geest04/2018
5448(2^384582+778)/2115771Stefano Morozzi09/2020
544930537^6178+6178^30537115762Hans Havermann01/2021
54502^384530+1874305115756Enzo Doria06/2016
5451(3*2^384524-1)/7631115750Lelio R Paula03/2014
545228275^12406+12406^28275115748Hans Havermann01/2021
5453(44*10^115697-413)/9115698Robert Price03/2019
545431408^4825+4825^31408115692Hans Havermann02/2021
5455(2^384317+1026)/2115691Stefano Morozzi09/2020
54562^384312+81091115690Yves Minet02/2010
5457(2^384265+2150)/2115675Stefano Morozzi09/2020
5458(2^384246+2182)/2115670Stefano Morozzi09/2020
5459(4*10^115668-79)/3115669Robert Price02/2018
5460(2^384193+242)/2115654Stefano Morozzi09/2020
5461(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
5462(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
546318^92125-92125^18115642Dylan Delgado08/2019
54643^242337-4042115625Enzo Doria05/2014
5465(2^383931+674)/2115575Stefano Morozzi09/2020
54667*10^115561+79115562Robert Price07/2019
5467(2^383872+3046)/2115557Stefano Morozzi09/2020
5468(11*2^383859-13)/15115553Renaud Lifchitz03/2011
54692^383780-3149115530Yves Minet10/2014
5470(41*10^115523-383)/9115524Robert Price11/2018
547127316^16923+16923^27316115506Hans Havermann02/2021
5472(2^383618+618)/2115481Stefano Morozzi09/2020
54732^383560-455115464Yves Minet03/2012
5474(2^383544+5)/3115458Lelio R Paula03/2014
5475(22*10^115454+119)/3115455Robert Price04/2021
547689^59221-88^59221115445Robert Price06/2015
5477(7^136559-5^136559)/2115406Jon Grantham08/2023
54782^383347+1869413115399Enzo Doria05/2016
5479(103*10^115366+17)/3115368Robert Price08/2020
5480(2^383232+750)/2115365Stefano Morozzi09/2020
5481(2^383130-7)/131793115329Lelio R Paula03/2014
5482(12^106859+1)/13115320Paul Bourdelais02/2010
548329961^7060+7060^29961115315Hans Havermann01/2021
54852^383039+1869509115307Enzo Doria05/2016
548432918^3183+3183^32918115307Hans Havermann01/2021
548636964^1315+1315^36964115288Hans Havermann02/2021
5487(13*2^382968+1)/7115286Lelio R Paula04/2014
5488(22*10^115282+29)/3115283Robert Price02/2021
5489(2^382945+2046)/2115278Stefano Morozzi09/2020
5490(2^382789+3182)/2115231Stefano Morozzi09/2020
549130416^6141+6141^30416115224Hans Havermann02/2021
54926*10^115211+79115212Robert Price09/2020
5493(2^382722+3598)/2115211Stefano Morozzi09/2020
549427987^13078+13078^27987115210Hans Havermann02/2021
5495(2^382699+2090)/2115204Stefano Morozzi09/2020
5496(22*10^115188-193)/9115189Robert Price07/2022
54972^382633+73697115185Enzo Doria04/2016
54982^382509-113593115147Enzo Doria08/2014
54992^382502-2791721115145Enzo Doria03/2016
5500(2^382495+1274)/2115143Stefano Morozzi01/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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