PRP Records

Probable Primes Top 10000

(288949 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 ?
4001(7*10^117930-79)/9117930Robert Price01/2021
400227531^19168+19168^27531117904Hans Havermann02/2021
4003(46*10^117902+683)/9117903Robert Price03/2019
400427670^18189+18189^27670117869Hans Havermann02/2021
4005(7*2^391521+1)/285117858Lelio R Paula04/2014
4006(56*10^117856+583)/9117857Robert Price08/2021
400732169^4606+4606^32169117846Hans Havermann02/2021
4008(71*10^117803-143)/9117804Robert Price10/2021
40092^391324+90901117801Yves Minet02/2011
40102^391301-1859923117794Enzo Doria03/2016
40112^391261-4131117782Yves Minet02/2018
4012(2^391211+554)/2117766Stefano Morozzi09/2020
401338434^1157+1157^38434117737Hans Havermann01/2021
4014(2^391115-7)/11791117734Lelio R Paula04/2014
4015(85*10^117719+473)/9117720Robert Price01/2020
4016(2^391049+582)/2117718Stefano Morozzi09/2020
401731083^6122+6122^31083117709Hans Havermann02/2021
40182^390960+1880881117691Enzo Doria11/2016
40192^390897-1860553117672Enzo Doria11/2015
40202^390889-115003117670Enzo Doria06/2015
40212^390779-30337117637Paul Bourdelais02/2012
4022(2^390735+378)/2117623Stefano Morozzi02/2021
402311^112916-780117590Enzo Doria12/2012
402427641^17916+17916^27641117564Hans Havermann02/2021
402527906^16321+16321^27906117561Hans Havermann02/2021
402627294^20275+20275^27294117555Hans Havermann02/2021
4027(2^390473+1002)/2117544Stefano Morozzi09/2020
402835912^1875+1875^35912117541Hans Havermann02/2021
4029(16^97613-5^97613)/11117537Robert Price07/2013
4030(2^390438+1774)/2117534Stefano Morozzi01/2021
4031(2^390418+1722)/2117528Stefano Morozzi09/2020
4032(2^390403+654)/2117523Stefano Morozzi09/2020
4033(2^390343+2246)/2117505Stefano Morozzi01/2021
403428043^15478+15478^28043117493Hans Havermann02/2021
4035(17*2^390272+1)/1983117482Lelio R Paula04/2014
403637077^1474+1474^37077117479Hans Havermann01/2021
403731^78759-30117459Theodore Burton02/2007
4038(2^390176+1222)/2117455Stefano Morozzi09/2020
4039(2^390133+1242)/2117442Stefano Morozzi09/2020
4040(2^390013+2634)/2117406Stefano Morozzi09/2020
40413*10^117402+61117403Robert Price09/2020
40422^389998+37117402Lelio R Paula03/2013
4043(2^389977+314)/2117395Stefano Morozzi09/2020
4044(2^389921+342)/2117378Stefano Morozzi01/2021
404571830^43+43^71830117333Hans Havermann01/2021
4046(2^389768+1582)/2117332Stefano Morozzi09/2020
404733802^2951+2951^33802117292Hans Havermann02/2021
404826789^23866+23866^26789117277Hans Havermann02/2021
404929^80192-1*80192^29117273Dylan Delgado12/2019
4050(13*10^117249+161)/3117250Robert Price11/2018
40512^389478+43117245Lelio R Paula03/2013
4052(298*10^117229-7)/3117231Robert Price06/2020
4053(2^389416+342)/2117226Stefano Morozzi01/2021
4054(29*2^389351-1)/9117207Lelio R Paula04/2014
40555*10^117205+23117206Robert Price03/2019
4056(2^389341-7)/3865117200Lelio R Paula03/2014
405727272^19827+19827^27272117195Hans Havermann01/2021
4058(2^389276+2650)/2117184Stefano Morozzi09/2020
4059(844*10^117175-7)/9117177Robert Price05/2021
406010^117142+209223117143Patrick De Geest04/2018
406210^117142-1000000001117142Robert Price03/2018
406110^117142-966057117142Patrick De Geest04/2018
406310^117135+360577117136Patrick De Geest07/2018
406410^117135-401117135Robert Price01/2018
406526415^26488-26488^26415117126Norbert Schneider05/2021
40664*10^117123+79117124Robert Price08/2018
40672^389033-12797413117111Enzo Doria04/2016
4068(2^388987+2634)/2117097Stefano Morozzi09/2020
40692^388960-109505117089Enzo Doria04/2014
40707*10^117082-57117083Robert Price06/2020
4071(2^388928-5)/569117077Lelio R Paula03/2014
40722^388888-1529117067Yves Minet01/2013
407310^117059+28879117060Patrick De Geest05/2016
4074(10^117059-71)/1117059Serge Batalov12/2014
4075(2^388854+3630)/2117057Stefano Morozzi09/2020
4076(2^388842+2098)/2117053Stefano Morozzi09/2020
4077(2^388789+3150)/2117037Stefano Morozzi09/2020
4078(2^388748+378)/2117025Stefano Morozzi02/2021
4079(693^41189-1)/692117005Michael Stocker05/2020
4080(26*10^116999-503)/9117000Robert Price07/2018
4081(2^388609+1554)/2116983Stefano Morozzi09/2020
408238496^1093+1093^38496116975Hans Havermann02/2021
40833^245154-6256116969Enzo Doria05/2014
40845*10^116966-43116967Robert Price01/2019
40852^388536-113495116961Enzo Doria08/2014
4086(2^388512+382)/2116954Stefano Morozzi02/2021
40872^388469-43116941Lelio R Paula03/2013
408827417^18416+18416^27417116939Hans Havermann02/2021
4089(2^388438+1842)/2116932Stefano Morozzi02/2021
4090(7*2^388372-1)/111116911Lelio R Paula04/2014
4091(7*2^388335-1)/25116900Lelio R Paula04/2014
40922^388180+93116854Donovan Johnson07/2008
4093(2^388167+2510)/2116850Stefano Morozzi09/2020
4094(85*10^116842+293)/9116843Robert Price12/2019
409535296^2043+2043^35296116840Hans Havermann02/2021
4096(2^388081+7)/1179116821Lelio R Paula03/2014
409738633^1056+1056^38633116814Hans Havermann02/2021
40982^387946-113261116784Enzo Doria07/2014
409928363^13056+13056^28363116737Hans Havermann02/2021
41002^387745+75557116723Enzo Doria04/2016
4101(29*10^116719+313)/9116720Robert Price04/2021
410229622^8699+8699^29622116695Hans Havermann02/2021
4103(206*10^116687-17)/9116689Robert Price01/2020
4104(7*10^116684+179)/3116685Robert Price09/2018
41052^387554+71455116666Enzo Doria04/2016
4106(602*10^116647-71)/9116649Robert Price12/2021
4107(2^387447+78557)/365116631Lelio R Paula12/2014
4108(145*10^116610-1)/9116612Serge Batalov12/2014
4109(25*10^116601-331)/9116602Robert Price08/2018
4110(17*2^387284-1)/59116584Lelio R Paula04/2014
4111(2^387284+3726)/2116584Stefano Morozzi09/2020
41122^387211+111546435116563Paul Bourdelais10/2021
411310^116557+987654321116558Robert Price12/2019
411410^116557+9141116558Patrick De Geest02/2020
411510^116557-609431116557Patrick De Geest02/2020
4116(28*10^116546+41)/3116547Robert Price07/2021
4117(2^387123+1814)/2116536Stefano Morozzi02/2021
4118(2^387076+2046)/2116522Stefano Morozzi09/2020
4119(2^387073+2570)/2116521Stefano Morozzi09/2020
412028846^10931+10931^28846116500Hans Havermann02/2021
412110^116496+3593037116497Paul Bourdelais10/2021
4122(31*2^386968+1)/7116490Lelio R Paula03/2014
41232^386947+1869143116483Enzo Doria05/2016
4124(30^78857-1)/29116480Robert Price12/2011
4125(2^386903-3)/5116469Lelio R Paula03/2014
412628107^13892+13892^28107116441Hans Havermann02/2021
412729110^9957+9957^29110116386Hans Havermann02/2021
412826469^24838+24838^26469116335Hans Havermann01/2021
41292^386389-1864783116315Enzo Doria03/2016
4130(31*2^386231-1)/1711116266Lelio R Paula03/2014
4131297^47012+47012^297116250Norbert Schneider07/2018
4132(35*10^116223-341)/9116224Robert Price08/2021
4133(2^386087-5)/40959116220Lelio R Paula03/2014
4134(2^386054+714)/2116214Stefano Morozzi09/2020
4135(10^116201+7)/39623116197Alfred Reich06/2021
41362^385969-823116189Yves Minet05/2012
413757^66162+2116173Lelio R Paula08/2013
41382^385854+75049116154Enzo Doria04/2016
4139(2^385832+2590)/2116147Stefano Morozzi09/2020
41402^385775-109587116130Enzo Doria04/2014
4141(14*10^116112-101)/3116113Robert Price02/2019
4142Phi(236354,10)/24817171116109Makoto Kamada08/2019
414328729^10990+10990^28729116094Hans Havermann02/2021
41442^385622+71839116084Enzo Doria04/2016
41452^385564+781116067Lelio R Paula01/2012
4146(2^385565+1562)/2116067Stefano Morozzi09/2020
4147(2^385563+378)/2116066Stefano Morozzi02/2021
4148(2^385557+2214)/2116064Stefano Morozzi09/2020
414929431^8776+8776^29431116056Hans Havermann01/2021
4150(266*10^116024-17)/3116026Robert Price07/2020
415130263^6820+6820^30263116022Hans Havermann02/2021
41522^385410+71893116020Enzo Doria04/2016
415338225^1084+1084^38225116014Hans Havermann02/2021
415426548^23433+23433^26548116011Hans Havermann02/2021
4155(25*2^385091+1)/27115924Lelio R Paula04/2014
4156(11*10^115910-131)/3115911Robert Price09/2018
41572^384953-111943115883Paul Bourdelais02/2012
415843^70942-2115882Lelio R Paula04/2014
4159(94*10^115879-7)/3115881Robert Price03/2020
41607*10^115863+3115864Robert Price08/2015
41612^384834+93115847Donovan Johnson07/2008
41622^384809+71297115840Enzo Doria04/2016
4163(55*10^115829+323)/9115830Robert Price10/2021
4164(7*2^384759-1)/5115825Lelio R Paula04/2014
416531348^4951+4951^31348115822Hans Havermann02/2021
4166(71*10^115810-17)/9115811Ray Chandler08/2011
4167(97*10^115794-1)/3115796Serge Batalov12/2014
416831115^5266+5266^31115115794Hans Havermann02/2021
41692*10^115784-27115785Robert Price05/2018
417010^115773+126739115774Patrick De Geest04/2018
417210^115773-1000000001115773Robert Price03/2018
417110^115773-396221115773Patrick De Geest04/2018
4173(2^384582+778)/2115771Stefano Morozzi09/2020
417430537^6178+6178^30537115762Hans Havermann01/2021
41752^384530+1874305115756Enzo Doria06/2016
4176(3*2^384524-1)/7631115750Lelio R Paula03/2014
417728275^12406+12406^28275115748Hans Havermann01/2021
4178(44*10^115697-413)/9115698Robert Price03/2019
417931408^4825+4825^31408115692Hans Havermann02/2021
4180(2^384317+1026)/2115691Stefano Morozzi09/2020
41812^384312+81091115690Yves Minet02/2010
4182(2^384265+2150)/2115675Stefano Morozzi09/2020
4183(2^384246+2182)/2115670Stefano Morozzi09/2020
4184(4*10^115668-79)/3115669Robert Price02/2018
4185(2^384193+242)/2115654Stefano Morozzi09/2020
4186(266947#+1267)/(7^2*181)115647Makoto Morimoto06/2019
4187(266947#+273808)/(2*109*157)115646Makoto Morimoto10/2017
418818^92125-92125^18115642Dylan Delgado08/2019
41893^242337-4042115625Enzo Doria05/2014
4190(2^383931+674)/2115575Stefano Morozzi09/2020
41917*10^115561+79115562Robert Price07/2019
4192(2^383872+3046)/2115557Stefano Morozzi09/2020
4193(11*2^383859-13)/15115553Renaud Lifchitz03/2011
41942^383780-3149115530Yves Minet10/2014
4195(41*10^115523-383)/9115524Robert Price11/2018
419627316^16923+16923^27316115506Hans Havermann02/2021
4197(2^383618+618)/2115481Stefano Morozzi09/2020
41982^383560-455115464Yves Minet03/2012
4199(2^383544+5)/3115458Lelio R Paula03/2014
4200(22*10^115454+119)/3115455Robert Price04/2021
420189^59221-88^59221115445Robert Price06/2015
42022^383347+1869413115399Enzo Doria05/2016
4203(103*10^115366+17)/3115368Robert Price08/2020
4204(2^383232+750)/2115365Stefano Morozzi09/2020
4205(2^383130-7)/131793115329Lelio R Paula03/2014
4206(12^106859+1)/13115320Paul Bourdelais02/2010
420729961^7060+7060^29961115315Hans Havermann01/2021
42092^383039+1869509115307Enzo Doria05/2016
420832918^3183+3183^32918115307Hans Havermann01/2021
421036964^1315+1315^36964115288Hans Havermann02/2021
4211(13*2^382968+1)/7115286Lelio R Paula04/2014
4212(22*10^115282+29)/3115283Robert Price02/2021
4213(2^382945+2046)/2115278Stefano Morozzi09/2020
4214(2^382789+3182)/2115231Stefano Morozzi09/2020
421530416^6141+6141^30416115224Hans Havermann02/2021
42166*10^115211+79115212Robert Price09/2020
4217(2^382722+3598)/2115211Stefano Morozzi09/2020
421827987^13078+13078^27987115210Hans Havermann02/2021
4219(2^382699+2090)/2115204Stefano Morozzi09/2020
42202^382633+73697115185Enzo Doria04/2016
42212^382509-113593115147Enzo Doria08/2014
42222^382502-2791721115145Enzo Doria03/2016
4223(2^382495+1274)/2115143Stefano Morozzi01/2021
422426752^20065+20065^26752115099Hans Havermann02/2021
422526383^23008+23008^26383115080Hans Havermann02/2021
42269^120590-120590115073Robert Price03/2014
422728203^12016+12016^28203115062Hans Havermann02/2021
42282^382198+9115054Lelio R Paula03/2013
422930101^6630+6630^30101115032Hans Havermann01/2021
4230(89*10^115030-179)/9115031Robert Price12/2019
4231(2^381935+2774)/2114974Stefano Morozzi02/2021
423227300^16271+16271^27300114972Hans Havermann02/2021
42332^381883-59197114959Enzo Doria10/2015
423427423^15542+15542^27423114944Hans Havermann02/2021
4235(2^381820+1626)/2114939Stefano Morozzi09/2020
42372^381806-4481114936Yves Minet07/2011
42362^381808-1851507114936Enzo Doria08/2015
4238(2^381792+2502)/2114931Stefano Morozzi09/2020
42392^381774-112373114926Enzo Doria06/2014
424026341^22980+22980^26341114883Hans Havermann01/2021
42412^381555-109051114860Enzo Doria04/2014
42422^381546-113501114857Enzo Doria08/2014
4243(7*10^114845-19)/3114846Robert Price10/2020
424426675^20178+20178^26675114833Hans Havermann02/2021
4245(2^381436+1182)/2114824Stefano Morozzi09/2020
42463^240644+16114817Robert Price04/2020
42472^381360-110429114801Enzo Doria05/2014
4248(17*10^114795+79)/3114796Robert Price04/2019
4249(66^63079+1)/67114774Paul Bourdelais09/2017
42502^381252-115079114769Enzo Doria06/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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