PRP Records

Probable Primes Top 10000

(295148 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 ?
5501(2^388987+2634)/2117097Stefano Morozzi09/2020
55022^388960-109505117089Enzo Doria04/2014
55037*10^117082-57117083Robert Price06/2020
5504(2^388928-5)/569117077Lelio R Paula03/2014
55052^388888-1529117067Yves Minet01/2013
550610^117059+28879117060Patrick De Geest05/2016
5507(10^117059-71)/1117059Serge Batalov12/2014
5508(2^388854+3630)/2117057Stefano Morozzi09/2020
5509(2^388842+2098)/2117053Stefano Morozzi09/2020
5510(2^388789+3150)/2117037Stefano Morozzi09/2020
5511(2^388748+378)/2117025Stefano Morozzi02/2021
5512(693^41189-1)/692117005Michael Stocker05/2020
5513(26*10^116999-503)/9117000Robert Price07/2018
5514(2^388609+1554)/2116983Stefano Morozzi09/2020
551538496^1093+1093^38496116975Hans Havermann02/2021
55163^245154-6256116969Enzo Doria05/2014
55175*10^116966-43116967Robert Price01/2019
55182^388536-113495116961Enzo Doria08/2014
5519(2^388512+382)/2116954Stefano Morozzi02/2021
5520(8*32^77701+271)/31116952Eric Chen11/2023
55212^388469-43116941Lelio R Paula03/2013
552227417^18416+18416^27417116939Hans Havermann02/2021
5523(2^388438+1842)/2116932Stefano Morozzi02/2021
5524(7*2^388372-1)/111116911Lelio R Paula04/2014
5525(7*2^388335-1)/25116900Lelio R Paula04/2014
55262^388180+93116854Donovan Johnson07/2008
5527(2^388167+2510)/2116850Stefano Morozzi09/2020
5528(85*10^116842+293)/9116843Robert Price12/2019
552935296^2043+2043^35296116840Hans Havermann02/2021
5530(2^388081+7)/1179116821Lelio R Paula03/2014
553138633^1056+1056^38633116814Hans Havermann02/2021
55322^387946-113261116784Enzo Doria07/2014
553328*36^75009+305116739Eric Chen12/2022
553428363^13056+13056^28363116737Hans Havermann02/2021
55352^387745+75557116723Enzo Doria04/2016
5536(29*10^116719+313)/9116720Robert Price04/2021
553729622^8699+8699^29622116695Hans Havermann02/2021
5538(206*10^116687-17)/9116689Robert Price01/2020
5539(7*10^116684+179)/3116685Robert Price09/2018
55402^387554+71455116666Enzo Doria04/2016
5541(602*10^116647-71)/9116649Robert Price12/2021
55423^244461-10116638Tyler NeSmith09/2022
5543(2^387447+78557)/365116631Lelio R Paula12/2014
5544(2*10^116620+43)/9116620Serge Batalov11/2022
5545(19*10^116617+287)/9/12893116614Alfred Reich11/2022
5546(145*10^116610-1)/9116612Serge Batalov12/2014
5547(25*10^116601-331)/9116602Robert Price08/2018
554825791^26428-26428^25791116587Frank Doornink03/2024
5550(17*2^387284-1)/59116584Lelio R Paula04/2014
5549(2^387284+3726)/2116584Stefano Morozzi09/2020
55512^387211+111546435116563Paul Bourdelais10/2021
555210^116557+987654321116558Robert Price12/2019
555310^116557+9141116558Patrick De Geest02/2020
555410^116557-609431116557Patrick De Geest02/2020
5555(28*10^116546+41)/3116547Robert Price07/2021
5556(2^387123+1814)/2116536Stefano Morozzi02/2021
5557(2^387076+2046)/2116522Stefano Morozzi09/2020
5558(2^387073+2570)/2116521Stefano Morozzi09/2020
5559(7*10^116514-1)/3116515Robert Price08/2022
5560(26*32^77406-390071011)/31116508Eric Chen11/2023
556128846^10931+10931^28846116500Hans Havermann02/2021
556210^116496+3593037116497Paul Bourdelais10/2021
5563(31*2^386968+1)/7116490Lelio R Paula03/2014
55642^386947+1869143116483Enzo Doria05/2016
5565(30^78857-1)/29116480Robert Price12/2011
5566(2^386903-3)/5116469Lelio R Paula03/2014
556728107^13892+13892^28107116441Hans Havermann02/2021
556829110^9957+9957^29110116386Hans Havermann02/2021
556926469^24838+24838^26469116335Hans Havermann01/2021
55702^386389-1864783116315Enzo Doria03/2016
5571(8*32^77250-163)/31116273Eric Chen11/2023
5572(31*2^386231-1)/1711116266Lelio R Paula03/2014
5573297^47012+47012^297116250Norbert Schneider07/2018
5574(35*10^116223-341)/9116224Robert Price08/2021
5575(2^386087-5)/40959116220Lelio R Paula03/2014
5576(2^386054+714)/2116214Stefano Morozzi09/2020
5577(10^116201+7)/39623116197Alfred Reich06/2021
55782^385969-823116189Yves Minet05/2012
557957^66162+2116173Lelio R Paula08/2013
55802^385854+75049116154Enzo Doria04/2016
5581(2^385832+2590)/2116147Stefano Morozzi09/2020
55822^385775-109587116130Enzo Doria04/2014
5583(14*10^116112-101)/3116113Robert Price02/2019
5584Phi(236354,10)/24817171116109Makoto Kamada08/2019
55853*10^116107+23116108Robert Price03/2022
558628729^10990+10990^28729116094Hans Havermann02/2021
55872^385622+71839116084Enzo Doria04/2016
55892^385564+781116067Lelio R Paula01/2012
5588(2^385565+1562)/2116067Stefano Morozzi09/2020
5590(2^385563+378)/2116066Stefano Morozzi02/2021
5591(2^385557+2214)/2116064Stefano Morozzi09/2020
559229431^8776+8776^29431116056Hans Havermann01/2021
5593(266*10^116024-17)/3116026Robert Price07/2020
559430263^6820+6820^30263116022Hans Havermann02/2021
55952^385410+71893116020Enzo Doria04/2016
559638225^1084+1084^38225116014Hans Havermann02/2021
559726548^23433+23433^26548116011Hans Havermann02/2021
559812^107422-11115928Riley Fisher12/2023
5599(25*2^385091+1)/27115924Lelio R Paula04/2014
5600(11*10^115910-131)/3115911Robert Price09/2018
56012^384953-111943115883Paul Bourdelais02/2012
560243^70942-2115882Lelio R Paula04/2014
5603(94*10^115879-7)/3115881Robert Price03/2020
56047*10^115863+3115864Robert Price08/2015
56052^384834+93115847Donovan Johnson07/2008
56062^384809+71297115840Enzo Doria04/2016
5607(55*10^115829+323)/9115830Robert Price10/2021
5608(7*2^384759-1)/5115825Lelio R Paula04/2014
560931348^4951+4951^31348115822Hans Havermann02/2021
5610(793*10^115810+53)/9115812Robert Price01/2022
5611(71*10^115810-17)/9115811Ray Chandler08/2011
5612(97*10^115794-1)/3115796Serge Batalov12/2014
561331115^5266+5266^31115115794Hans Havermann02/2021
56142*10^115784-27115785Robert Price05/2018
561510^115773+126739115774Patrick De Geest04/2018
561710^115773-1000000001115773Robert Price03/2018
561610^115773-396221115773Patrick De Geest04/2018
5618(2^384582+778)/2115771Stefano Morozzi09/2020
561930537^6178+6178^30537115762Hans Havermann01/2021
56202^384530+1874305115756Enzo Doria06/2016
5621(3*2^384524-1)/7631115750Lelio R Paula03/2014
562228275^12406+12406^28275115748Hans Havermann01/2021
5623(44*10^115697-413)/9115698Robert Price03/2019
562431408^4825+4825^31408115692Hans Havermann02/2021
5625(2^384317+1026)/2115691Stefano Morozzi09/2020
56262^384312+81091115690Yves Minet02/2010
5627(2^384265+2150)/2115675Stefano Morozzi09/2020
5628(2^384246+2182)/2115670Stefano Morozzi09/2020
5629(4*10^115668-79)/3115669Robert Price02/2018
5630(2^384193+242)/2115654Stefano Morozzi09/2020
5631(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
5632(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
563318^92125-92125^18115642Dylan Delgado08/2019
56343^242337-4042115625Enzo Doria05/2014
5635(17699*31^77516-29)/30115608Eric Chen05/2024
5636(2^383931+674)/2115575Stefano Morozzi09/2020
56377*10^115561+79115562Robert Price07/2019
5638(2^383872+3046)/2115557Stefano Morozzi09/2020
5639(11*2^383859-13)/15115553Renaud Lifchitz03/2011
56402^383780-3149115530Yves Minet10/2014
5641(41*10^115523-383)/9115524Robert Price11/2018
564227316^16923+16923^27316115506Hans Havermann02/2021
5643(2^383618+618)/2115481Stefano Morozzi09/2020
56442^383560-455115464Yves Minet03/2012
5645(2^383544+5)/3115458Lelio R Paula03/2014
5646(22*10^115454+119)/3115455Robert Price04/2021
564789^59221-88^59221115445Robert Price06/2015
5648(7^136559-5^136559)/2115406Jon Grantham08/2023
56492^383347+1869413115399Enzo Doria05/2016
5650(103*10^115366+17)/3115368Robert Price08/2020
5651(2^383232+750)/2115365Stefano Morozzi09/2020
5652(2^383130-7)/131793115329Lelio R Paula03/2014
5653(12^106859+1)/13115320Paul Bourdelais02/2010
565429961^7060+7060^29961115315Hans Havermann01/2021
56562^383039+1869509115307Enzo Doria05/2016
565532918^3183+3183^32918115307Hans Havermann01/2021
565736964^1315+1315^36964115288Hans Havermann02/2021
5658(13*2^382968+1)/7115286Lelio R Paula04/2014
5659(22*10^115282+29)/3115283Robert Price02/2021
5660(2^382945+2046)/2115278Stefano Morozzi09/2020
5661(2^382789+3182)/2115231Stefano Morozzi09/2020
566230416^6141+6141^30416115224Hans Havermann02/2021
56636*10^115211+79115212Robert Price09/2020
5664(2^382722+3598)/2115211Stefano Morozzi09/2020
566527987^13078+13078^27987115210Hans Havermann02/2021
5666(2^382699+2090)/2115204Stefano Morozzi09/2020
5667(22*10^115188-193)/9115189Robert Price07/2022
56682^382633+73697115185Enzo Doria04/2016
56692^382509-113593115147Enzo Doria08/2014
56702^382502-2791721115145Enzo Doria03/2016
5671(2^382495+1274)/2115143Stefano Morozzi01/2021
56722^382464+22741115134Enzo Doria09/2023
567326752^20065+20065^26752115099Hans Havermann02/2021
567426383^23008+23008^26383115080Hans Havermann02/2021
56759^120590-120590115073Robert Price03/2014
567628203^12016+12016^28203115062Hans Havermann02/2021
56772^382198+9115054Lelio R Paula03/2013
567818268*31^77131+22839115035Eric Chen05/2024
567930101^6630+6630^30101115032Hans Havermann01/2021
5680(89*10^115030-179)/9115031Robert Price12/2019
568125554^26089-26089^25554114987Frank Doornink02/2024
568225142^26129-26129^25142114979Frank Doornink12/2023
5683(2^381935+2774)/2114974Stefano Morozzi02/2021
568427300^16271+16271^27300114972Hans Havermann02/2021
5685(23*10^114962+7)/3114963Robert Price05/2023
56862^381883-59197114959Enzo Doria10/2015
568727423^15542+15542^27423114944Hans Havermann02/2021
5688(2^381820+1626)/2114939Stefano Morozzi09/2020
56902^381806-4481114936Yves Minet07/2011
56892^381808-1851507114936Enzo Doria08/2015
5691(2^381792+2502)/2114931Stefano Morozzi09/2020
56922^381774-112373114926Enzo Doria06/2014
569326341^22980+22980^26341114883Hans Havermann01/2021
56942^381555-109051114860Enzo Doria04/2014
56952^381551+213683114859Enzo Doria09/2023
56962^381546-113501114857Enzo Doria08/2014
5697(7*10^114845-19)/3114846Robert Price10/2020
569826675^20178+20178^26675114833Hans Havermann02/2021
5699(2^381436+1182)/2114824Stefano Morozzi09/2020
57003^240644+16114817Robert Price04/2020
57012^381360-110429114801Enzo Doria05/2014
5702(17*10^114795+79)/3114796Robert Price04/2019
5703(66^63079+1)/67114774Paul Bourdelais09/2017
57042^381252-115079114769Enzo Doria06/2015
5705(2^381251+3186)/2114768Stefano Morozzi09/2020
57062^381209-29323114756Enzo Doria07/2015
57072^381207-111546435114755Paul Bourdelais10/2021
5708569^41651-568^41651114754Jean-Louis Charton11/2009
57092^381201+1873205114753Enzo Doria06/2016
5710(85*10^114737+293)/9114738Robert Price12/2019
5711(265*10^114736+17)/3114738Robert Price03/2020
5712(2^381062+2170)/2114711Stefano Morozzi09/2020
57132^380974-112991114685Enzo Doria07/2014
571437097^1234+1234^37097114679Hans Havermann02/2021
5715(26*10^114658-119)/3114659Robert Price07/2023
571688^58949-87114626Norbert Schneider11/2015
5717(2^380773+662)/2114624Stefano Morozzi09/2020
5718Phi(155285,10)/242674820198201114610Makoto Kamada02/2024
571929913^6782+6782^29913114608Hans Havermann02/2021
5720(331*10^114605-7)/9114607Robert Price04/2022
57212^380700+91114603Lelio R Paula03/2013
5722(2^380632+2578)/2114582Stefano Morozzi09/2020
57237*10^114577+27114578Robert Price11/2020
572510^114575+3^114576114576Mike Oakes09/2010
572410^114575+66561114576Patrick De Geest02/2017
572610^114575-581081114575Patrick De Geest02/2017
57272^380587-115315114569Enzo Doria06/2015
572831874^3927+3927^31874114558Hans Havermann02/2021
57292^380513-216925114546Enzo Doria05/2014
57302^380451-1840087114528Enzo Doria06/2015
5731(2^380426+1510)/2114520Stefano Morozzi09/2020
5732(15*2^380388-1)/539114507Lelio R Paula04/2014
57332^380279-461347114476Enzo Doria07/2015
5734(331*10^114454-7)/9114456Robert Price04/2022
573527121^16590+16590^27121114447Hans Havermann01/2021
573625966^25555+25555^25966114445Hans Havermann01/2021
5737(611*32^76029-53)/31114437Eric Chen11/2023
5738(11*10^114400+529)/9114401Robert Price09/2021
57392^380021+1871147114398Enzo Doria05/2016
57402^380005+1869707114393Enzo Doria05/2016
57412^379958-113297114379Enzo Doria07/2014
5742(2^379897+1274)/2114361Stefano Morozzi01/2021
57432^379881-109105114356Enzo Doria04/2014
5744(21*2^379857-1)/13114349Lelio R Paula03/2014
5745(4*10^114340+83)/3114341Robert Price02/2018
5746(26*10^114317-77)/3114318Robert Price11/2019
5747(4*10^114296+149)/9114296Robert Price04/2018
574888^58773-87114284Norbert Schneider11/2015
574927764^13065+13065^27764114280Hans Havermann01/2021
57502^379529-2790283114250Enzo Doria03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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