PRP Records

Probable Primes Top 10000

(301745 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 ?
6251(65*10^118417+493)/9118418Robert Price08/2021
625230960^6671+6671^30960118397Hans Havermann02/2021
6253(2^393234+2010)/2118375Stefano Morozzi09/2020
6254(2^393205+3030)/2118367Stefano Morozzi09/2020
6255(2^393191+2174)/2118362Stefano Morozzi09/2020
62562^393180+73118359Lelio R Paula04/2013
62573*2^393125+5118343Jon Grantham07/2023
625827546^19771+19771^27546118339Hans Havermann02/2021
6259822^40595-40595^822118330Norman Luhn09/2024
6260p(23881)#/2+256118328Robert Price05/2017
6261(10^118324+359)/9118324Serge Batalov12/2014
6262(2^393048+570)/2118319Stefano Morozzi09/2020
6263p(23879)#/2+64118317Robert Price03/2017
62642^393033+20147118315Enzo Doria08/2023
62658*10^118308+59118309Robert Price11/2021
62669*10^118282+29118283Robert Price03/2022
6267(9*35^76602+12877)/34118279Eric Chen05/2025
6268(238*10^118265-1)/3118267Robert Price04/2020
6270(53*10^118216+1)/9118217Serge Batalov11/2010
6269(2^392707+1710)/2118217Stefano Morozzi09/2020
6271(7*2^392697+1)/15118214Renaud Lifchitz03/2011
6272(157^53819-1)/156118179Alexander Zhirkov06/2016
6273(2^392567+2750)/2118175Stefano Morozzi01/2021
627455*10^118172+3118174Robert Price07/2022
6275(19*2^392551+1)/3118171Lelio R Paula04/2014
627627185^22222+22222^27185118168Hans Havermann01/2021
62772^392516-29219118160Enzo Doria07/2015
627866*10^118155+7118157Robert Price07/2020
6279Phi(177231,10)118152Maksym Voznyy09/2015
62802^392413-112123118129Enzo Doria06/2014
628127491^19798+19798^27491118119Hans Havermann02/2021
6282(49*10^118109-319)/9118110Robert Price10/2021
6283(2^392342+5)/27118106Lelio R Paula04/2014
6284(2^392333+1782)/2118104Stefano Morozzi01/2021
62852^392300-1841429118095Enzo Doria06/2015
62863*2^392260-5118083Jon Grantham07/2023
62872^392220+75241118070Enzo Doria04/2016
628827836^17409+17409^27836118047Hans Havermann02/2021
6289(13^118026)%(10^118026)118026Henri Lifchitz05/2025
629010^118009+664447118010Patrick De Geest07/2018
629110^118009-20001118009Robert Price01/2018
6292(14*10^117991+61)/3117992Robert Price12/2018
62932^391933+5897117984Yves Minet02/2011
62942^391912-1849259117978Enzo Doria08/2015
6295(2*34^77029+1043)/11117968Eric Chen08/2023
62965*2^391836-3117956Jon Grantham07/2023
629728357^14440+14440^28357117953Hans Havermann02/2021
6298(2^391812+5)/14181117944Lelio R Paula04/2014
629985^61124-61124^85117934Norman Luhn09/2024
6300(7*10^117930-79)/9117930Robert Price01/2021
630127531^19168+19168^27531117904Hans Havermann02/2021
6302(46*10^117902+683)/9117903Robert Price03/2019
630326349^26668-26668^26349117893Frank Doornink03/2024
630427670^18189+18189^27670117869Hans Havermann02/2021
6305(7*2^391521+1)/285117858Lelio R Paula04/2014
6306(56*10^117856+583)/9117857Robert Price08/2021
630732169^4606+4606^32169117846Hans Havermann02/2021
6308(71*10^117803-143)/9117804Robert Price10/2021
63092^391324+90901117801Yves Minet02/2011
63102^391301-1859923117794Enzo Doria03/2016
63112^391261-4131117782Yves Minet02/2018
6312(2^391211+554)/2117766Stefano Morozzi09/2020
6313816^40445-40445^816117764Norman Luhn09/2024
631438434^1157+1157^38434117737Hans Havermann01/2021
6315(2^391115-7)/11791117734Lelio R Paula04/2014
6316(85*10^117719+473)/9117720Robert Price01/2020
6317(2^391049+582)/2117718Stefano Morozzi09/2020
6318(21*23^86445-197)/22117715Eric Chen08/2023
631931083^6122+6122^31083117709Hans Havermann02/2021
63202^390960+1880881117691Enzo Doria11/2016
6321(71*10^117685+91)/9117686Robert Price04/2022
63232^390897-1860553117672Enzo Doria11/2015
6322(61*10^117671+47)/9117672Robert Price07/2022
63242^390889-115003117670Enzo Doria06/2015
632512^109010+35117642Riley Fisher08/2023
63262^390779-30337117637Paul Bourdelais02/2012
6327(2^390735+378)/2117623Stefano Morozzi02/2021
632811^112916-780117590Enzo Doria12/2012
632927641^17916+17916^27641117564Hans Havermann02/2021
633027906^16321+16321^27906117561Hans Havermann02/2021
633127294^20275+20275^27294117555Hans Havermann02/2021
6332(2^390473+1002)/2117544Stefano Morozzi09/2020
633335912^1875+1875^35912117541Hans Havermann02/2021
6334(16^97613-5^97613)/11117537Robert Price07/2013
6335(2^390438+1774)/2117534Stefano Morozzi01/2021
6336(2^390418+1722)/2117528Stefano Morozzi09/2020
6337(2^390403+654)/2117523Stefano Morozzi09/2020
6338(2^390343+2246)/2117505Stefano Morozzi01/2021
633928043^15478+15478^28043117493Hans Havermann02/2021
6340(17*2^390272+1)/1983117482Lelio R Paula04/2014
634137077^1474+1474^37077117479Hans Havermann01/2021
634231^78759-30117459Theodore Burton02/2007
6343(2^390176+1222)/2117455Stefano Morozzi09/2020
6344(2^390133+1242)/2117442Stefano Morozzi09/2020
6345(2^390013+2634)/2117406Stefano Morozzi09/2020
63463*10^117402+61117403Robert Price09/2020
63472^389998+37117402Lelio R Paula03/2013
6348(2^389977+314)/2117395Stefano Morozzi09/2020
6349(2^389921+342)/2117378Stefano Morozzi01/2021
635071830^43+43^71830117333Hans Havermann01/2021
6351(2^389768+1582)/2117332Stefano Morozzi09/2020
635233802^2951+2951^33802117292Hans Havermann02/2021
6353(2^561185)%L(561185)117281Henri Lifchitz05/2025
635426789^23866+23866^26789117277Hans Havermann02/2021
635529^80192-1*80192^29117273Dylan Delgado12/2019
6356(101*10^117260+7)/9117262Robert Price02/2022
6357(13*10^117249+161)/3117250Robert Price11/2018
63582^389478+43117245Lelio R Paula03/2013
6359(298*10^117229-7)/3117231Robert Price06/2020
6360(2^389416+342)/2117226Stefano Morozzi01/2021
6361(29*2^389351-1)/9117207Lelio R Paula04/2014
63625*10^117205+23117206Robert Price03/2019
6363(2^389341-7)/3865117200Lelio R Paula03/2014
636427272^19827+19827^27272117195Hans Havermann01/2021
6365(2^389276+2650)/2117184Stefano Morozzi09/2020
6366(844*10^117175-7)/9117177Robert Price05/2021
636710^117142+209223117143Patrick De Geest04/2018
636910^117142-1000000001117142Robert Price03/2018
636810^117142-966057117142Patrick De Geest04/2018
637010^117135+360577117136Patrick De Geest07/2018
637110^117135-401117135Robert Price01/2018
637226415^26488-26488^26415117126Norbert Schneider05/2021
63734*10^117123+79117124Robert Price08/2018
63742^389033-12797413117111Enzo Doria04/2016
6375(2^388987+2634)/2117097Stefano Morozzi09/2020
63762^388960-109505117089Enzo Doria04/2014
63777*10^117082-57117083Robert Price06/2020
6378791^40398-40398^791117081Norman Luhn09/2024
6379(2^388928-5)/569117077Lelio R Paula03/2014
63802^388888-1529117067Yves Minet01/2013
638110^117059+28879117060Patrick De Geest05/2016
6382(10^117059-71)/1117059Serge Batalov12/2014
6383(2^388854+3630)/2117057Stefano Morozzi09/2020
6384(2^388842+2098)/2117053Stefano Morozzi09/2020
6385(2^388789+3150)/2117037Stefano Morozzi09/2020
6386(2^388748+378)/2117025Stefano Morozzi02/2021
6387(693^41189-1)/692117005Michael Stocker05/2020
6388(26*10^116999-503)/9117000Robert Price07/2018
638920^89917-21116985Anonymous09/2024
6390(2^388609+1554)/2116983Stefano Morozzi09/2020
639138496^1093+1093^38496116975Hans Havermann02/2021
63923^245154-6256116969Enzo Doria05/2014
63935*10^116966-43116967Robert Price01/2019
63942^388536-113495116961Enzo Doria08/2014
6395(2^388512+382)/2116954Stefano Morozzi02/2021
6396(8*32^77701+271)/31116952Eric Chen11/2023
63972^388469-43116941Lelio R Paula03/2013
639827417^18416+18416^27417116939Hans Havermann02/2021
6399(2^388438+1842)/2116932Stefano Morozzi02/2021
6400(7*2^388372-1)/111116911Lelio R Paula04/2014
6401(7*2^388335-1)/25116900Lelio R Paula04/2014
64022^388180+93116854Donovan Johnson07/2008
6403(2^388167+2510)/2116850Stefano Morozzi09/2020
6404(85*10^116842+293)/9116843Robert Price12/2019
640535296^2043+2043^35296116840Hans Havermann02/2021
6406(2^388081+7)/1179116821Lelio R Paula03/2014
640738633^1056+1056^38633116814Hans Havermann02/2021
64082^387946-113261116784Enzo Doria07/2014
640928*36^75009+305116739Eric Chen12/2022
641028363^13056+13056^28363116737Hans Havermann02/2021
64112^387745+75557116723Enzo Doria04/2016
6412(29*10^116719+313)/9116720Robert Price04/2021
641329622^8699+8699^29622116695Hans Havermann02/2021
6414(206*10^116687-17)/9116689Robert Price01/2020
6415(7*10^116684+179)/3116685Robert Price09/2018
64162^387554+71455116666Enzo Doria04/2016
6417(602*10^116647-71)/9116649Robert Price12/2021
64183^244461-10116638Tyler NeSmith09/2022
6419(2^387447+78557)/365116631Lelio R Paula12/2014
6420(2*10^116620+43)/9116620Serge Batalov11/2022
6421(19*10^116617+287)/9/12893116614Alfred Reich11/2022
6422(145*10^116610-1)/9116612Serge Batalov12/2014
6423(25*10^116601-331)/9116602Robert Price08/2018
642425791^26428-26428^25791116587Frank Doornink03/2024
6426(17*2^387284-1)/59116584Lelio R Paula04/2014
6425(2^387284+3726)/2116584Stefano Morozzi09/2020
64272^387211+111546435116563Paul Bourdelais10/2021
642810^116557+987654321116558Robert Price12/2019
642910^116557+9141116558Patrick De Geest02/2020
643010^116557-609431116557Patrick De Geest02/2020
6431209^50234-50234^209116551Norman Luhn09/2024
6432(28*10^116546+41)/3116547Robert Price07/2021
6433(2^387123+1814)/2116536Stefano Morozzi02/2021
6434(2^387076+2046)/2116522Stefano Morozzi09/2020
6435(2^387073+2570)/2116521Stefano Morozzi09/2020
6436(7*10^116514-1)/3116515Robert Price08/2022
6437(26*32^77406-390071011)/31116508Eric Chen11/2023
643828846^10931+10931^28846116500Hans Havermann02/2021
643910^116496+3593037116497Paul Bourdelais10/2021
6440272^47851-47851^272116497Norman Luhn09/2024
6441(31*2^386968+1)/7116490Lelio R Paula03/2014
6442(944^39157+1)/945116489Jinyuan Wang12/2024
64432^386947+1869143116483Enzo Doria05/2016
6444(30^78857-1)/29116480Robert Price12/2011
6445(2^386903-3)/5116469Lelio R Paula03/2014
644628107^13892+13892^28107116441Hans Havermann02/2021
644729110^9957+9957^29110116386Hans Havermann02/2021
644826469^24838+24838^26469116335Hans Havermann01/2021
64492^386389-1864783116315Enzo Doria03/2016
6450(8*32^77250-163)/31116273Eric Chen11/2023
6451(31*2^386231-1)/1711116266Lelio R Paula03/2014
6452297^47012+47012^297116250Norbert Schneider07/2018
6453(35*10^116223-341)/9116224Robert Price08/2021
6454(2^386087-5)/40959116220Lelio R Paula03/2014
6455(2^386054+714)/2116214Stefano Morozzi09/2020
6456(10^116201+7)/39623116197Alfred Reich06/2021
64572^385969-823116189Yves Minet05/2012
645857^66162+2116173Lelio R Paula08/2013
64592^385854+75049116154Enzo Doria04/2016
6460(2^385832+2590)/2116147Stefano Morozzi09/2020
64612^385775-109587116130Enzo Doria04/2014
6462(14*10^116112-101)/3116113Robert Price02/2019
6463Phi(236354,10)/24817171116109Makoto Kamada08/2019
64643*10^116107+23116108Robert Price03/2022
646528729^10990+10990^28729116094Hans Havermann02/2021
64662^385622+71839116084Enzo Doria04/2016
64672^385564+781116067Lelio R Paula01/2012
6468(2^385565+1562)/2116067Stefano Morozzi09/2020
6469(2^385563+378)/2116066Stefano Morozzi02/2021
6470(2^385557+2214)/2116064Stefano Morozzi09/2020
647129431^8776+8776^29431116056Hans Havermann01/2021
6472(266*10^116024-17)/3116026Robert Price07/2020
647330263^6820+6820^30263116022Hans Havermann02/2021
64742^385410+71893116020Enzo Doria04/2016
647538225^1084+1084^38225116014Hans Havermann02/2021
647626548^23433+23433^26548116011Hans Havermann02/2021
647712^107422-11115928Riley Fisher12/2023
6478(25*2^385091+1)/27115924Lelio R Paula04/2014
6479(11*10^115910-131)/3115911Robert Price09/2018
64802^384953-111943115883Paul Bourdelais02/2012
648143^70942-2115882Lelio R Paula04/2014
6482(94*10^115879-7)/3115881Robert Price03/2020
64837*10^115863+3115864Robert Price08/2015
64842^384834+93115847Donovan Johnson07/2008
64852^384809+71297115840Enzo Doria04/2016
6486(55*10^115829+323)/9115830Robert Price10/2021
6487(7*2^384759-1)/5115825Lelio R Paula04/2014
648831348^4951+4951^31348115822Hans Havermann02/2021
6489(793*10^115810+53)/9115812Robert Price01/2022
6490(71*10^115810-17)/9115811Ray Chandler08/2011
6491(97*10^115794-1)/3115796Serge Batalov12/2014
649231115^5266+5266^31115115794Hans Havermann02/2021
64932*10^115784-27115785Robert Price05/2018
649410^115773+126739115774Patrick De Geest04/2018
649610^115773-1000000001115773Robert Price03/2018
649510^115773-396221115773Patrick De Geest04/2018
6497(2^384582+778)/2115771Stefano Morozzi09/2020
649830537^6178+6178^30537115762Hans Havermann01/2021
64992^384530+1874305115756Enzo Doria06/2016
6500(3*2^384524-1)/7631115750Lelio R Paula03/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 15 2025 20:38 (Time in France)

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