PRP Records

Probable Primes Top 10000

(253476 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 ?
82512^214055-15964437Lelio R Paula08/2011
825210^64436-5364436Robert Price05/2011
8253(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
8254Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
82553^135027+10064425Lelio R Paula05/2013
8256(3^134972-7)/264398Lelio R Paula04/2012
82576*10^64387+764388Dmitry Domanov11/2010
82582^213864-1837764380Enzo Doria05/2013
825917929^3892+3892^1792964369Hans Havermann06/2019
8260(2^213821+9)/20964365Lelio R Paula04/2012
82612^213788+13564357Lelio R Paula08/2011
826217703^4316+4316^1770364352Hans Havermann06/2019
8263(3^134883+2)/4831364351Lelio R Paula04/2012
8264(49^38069-46^38069)/364344Serge Batalov12/2016
8265(11^61781+2^61781)/1364338Robert Price02/2013
82666^82670+3764330Lelio R Paula07/2013
8267(3^134839+4)/3231295964328Lelio R Paula04/2012
8268(22*10^64326+161)/364327Robert Price02/2017
826911^61767-405064324Enzo Doria12/2012
82702^213645-11485364314Enzo Doria05/2015
827113^57733+1864312Lelio R Paula07/2013
82722^213621+7270764307Enzo Doria04/2016
827310^64305+13679164306Patrick De Geest05/2011
827410^64305-964305Alexander Gramolin01/2011
8275V(307652)64295Serge Batalov03/2015
82764*10^64286-8964287Robert Price08/2017
8277(2^213546-5)/222164281Lelio R Paula04/2012
82782^213438-5869564252Lelio R Paula10/2011
82792^213367-10564230Lelio R Paula08/2011
8280595^23148+23148^59564225Norbert Schneider07/2016
82823^134601+868064221Lelio R Paula05/2013
8281(26*10^64220+61)/364221Robert Price06/2017
8283500^23793+23793^50064217Norbert Schneider08/2016
8284179^28504-264216Lelio R Paula10/2017
82852^213314-45564214Yves Minet02/2012
828639^40359-3864214Norbert Schneider05/2014
82872^213292-1608564208Enzo Doria04/2013
8288(72524!5+1)/2564203Joe McLean10/2018
82892^213274-7764202Lelio R Paula08/2011
829019^50203+7864198Lelio R Paula08/2013
8291(44*10^64192-233)/964193Robert Price10/2017
82922^213240-11286564192Enzo Doria06/2014
82932^213190-11239164177Enzo Doria06/2014
8294(9913*2^213184-1)/965764175Lelio R Paula04/2015
829514^55991+2764173Lelio R Paula07/2013
82962^213158-11258164167Enzo Doria06/2014
82972^213148+9164164Lelio R Paula08/2011
8298(96^32369+1)/9764163Paul Bourdelais08/2017
83006^82439+12564151Lelio R Paula07/2013
82997*2^213102+964151Lelio R Paula04/2014
8301L(306854)+F(306855)64129Henri Lifchitz01/2007
830215621^12736+12736^1562164125Hans Havermann07/2019
830315633^12622+12622^1563364113Hans Havermann07/2019
8304610^23017+23017^61064110Norbert Schneider07/2016
83052^212950-6487564105Lelio R Paula10/2011
8306(266*10^64102-17)/364104Robert Price06/2016
8307p(13679)#/2+6464097Robert Price03/2017
830819^50119+9464090Lelio R Paula08/2013
83092^212880-14764084Lelio R Paula08/2011
831011^61523-459064070Enzo Doria01/2013
83115^91663+3864070Lelio R Paula05/2013
83125^91650+5264061Lelio R Paula05/2013
83132^212770+6964051Lelio R Paula08/2011
8314(3^134227+1)/464042Paul Bourdelais11/2007
8315(2*10^64041-17)/364041Robert Price08/2014
8316(15^54449+1)/1664036Paul Bourdelais03/2010
8317(29*10^64027+91)/364028Robert Price03/2016
8318(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
831916878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
832015862^10863+10863^1586264019Hans Havermann06/2019
83212^212663+5364018Lelio R Paula08/2011
8322(4*10^64014+197)/364015Robert Price03/2017
832385402!6-364014Robert Price08/2018
8324(140^29819+1)/14163994Richard Fischer05/2018
832515313^15094+15094^1531363991Hans Havermann06/2019
832610^63986+6363987Robert Price01/2011
832710^63986-3155763986Patrick De Geest05/2013
832815699^11900+11900^1569963983Hans Havermann07/2019
832931487!2-2^3148763982Robert Price09/2015
8330(21*2^212522-1)/141632363971Lelio R Paula01/2014
83315^91517+9863968Lelio R Paula04/2013
8332(19*10^63960-43)/363961Robert Price10/2017
8333(62*10^63954-17)/963955Robert Price09/2015
83355^91493-4^9149363951Predrag Minovic04/2004
8334V(364793)63951Serge Batalov03/2015
833819^50004+5863943Lelio R Paula05/2013
83365*6^82172-763943Lelio R Paula09/2014
8337(56*10^63942+223)/963943Robert Price07/2016
833919^50000-2463938Lelio R Paula05/2013
8340(23*2^212374-1)/2701963928Lelio R Paula01/2014
8341(9*2^212355-1)/76163924Lelio R Paula01/2014
83432^212344-18363922Lelio R Paula08/2011
8342(58695*2^212336-1)/37963922Lelio R Paula04/2015
834410^63916+7963917Robert Price01/2011
834510^63916-7682363916Patrick De Geest05/2013
83462^212295-2563908Lelio R Paula08/2011
83472^212285-238363905Yves Minet10/2013
8348267^26336+26336^26763905Norbert Schneider09/2014
8349(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
835019^49962+6063890Lelio R Paula05/2013
83513^133906-11305663890Enzo Doria07/2014
8352(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
83533*6^82092+563881Lelio R Paula09/2014
835415441^13706+13706^1544163879Hans Havermann02/2017
83552^212154-77635163865Paul Bourdelais03/2013
835635^41359+263862Lelio R Paula05/2013
8357(61*10^63857-43)/963858Robert Price09/2015
8358(2^212131-3)/48563856Lelio R Paula04/2012
83592^212112-45999563853Enzo Doria06/2015
836015^54290+5863850Lelio R Paula05/2013
83613*2^212097-763849Lelio R Paula04/2014
836255^36683-5463842Norbert Schneider08/2014
8363(509203*2^212056-1)/363841Lelio R Paula04/2015
8364(3^133805-7)/17263839Lelio R Paula04/2012
83652^212049+14963834Lelio R Paula08/2011
83665^91318-1863829Lelio R Paula04/2013
836718468^2857+2857^1846863824Hans Havermann03/2017
8368(2^212024-5)/111163823Lelio R Paula04/2012
83692^211961+1291563807Lelio R Paula02/2013
8371(3^133707-7)/578063791Lelio R Paula04/2012
8370(44*10^63790-161)/963791Robert Price11/2017
8372747^22198+22198^74763782Norbert Schneider07/2016
83742^211800-1716963759Enzo Doria05/2013
8373(85*10^63757-1)/363759Robert Price07/2017
837585089!6-863757Robert Price08/2018
8376(14*10^63747-11)/363748Erik Branger09/2014
837791*19^49848+663746Curtis Bright05/2015
837818855^2402+2402^1885563741Hans Havermann03/2017
8379(142*10^63734-7)/963736Robert Price02/2017
83802^211699-11163728Lelio R Paula08/2011
838111^61192-555063725Enzo Doria01/2013
8382(11*10^63718+7)/963719Serge Batalov06/2011
83836^81872-1363709Lelio R Paula04/2013
83843^133522+9863707Lelio R Paula05/2013
83862^211607-6163701Lelio R Paula08/2011
83855^91135+863701Lelio R Paula04/2013
838711^61157-27063689Enzo Doria07/2012
838810^63685+114514191963686Marisa Kirisame03/2015
838910^63685+10383763686Patrick De Geest03/2016
839010^63685-13079763685Patrick De Geest03/2016
83912^211547+1155*21154763682Henri Lifchitz02/2005
83922^211543+4563681Lelio R Paula08/2011
83932^211534+4363679Lelio R Paula08/2011
839411^61140-6063671Enzo Doria07/2012
83952^211491-11232163666Enzo Doria06/2014
839619085^2164+2164^1908563654Hans Havermann03/2017
8397(2^211430-5)/85963644Lelio R Paula04/2012
83982^211401-9163639Lelio R Paula08/2011
8399(6883*2^211378-1)/6963634Lelio R Paula04/2015
8400(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
8401(29*2^211384-1)/5012262163627Lelio R Paula01/2014
84022^211333+1501563618Lelio R Paula01/2013
840333^41889-3263610Norbert Schneider03/2014
840413^57093+1863599Lelio R Paula05/2013
8405(5*2^211219-1)/963583Lelio R Paula01/2014
8406(107*10^63576-17)/963578Robert Price02/2017
840723^46687-102063575Enzo Doria08/2012
8408(67607*2^211188+1)/523431963573Lelio R Paula06/2014
8409(3^133243+7)/1072663570Lelio R Paula04/2012
8410(7*2^211181+1)/274563570Lelio R Paula06/2012
8412(20^48859-1)/1963566Paul Bourdelais03/2010
84112*3^133227+563566Lelio R Paula04/2014
84132^211155+11363564Lelio R Paula08/2011
84142^211134+34563558Lelio R Paula09/2011
84152^211121+1638563554Lelio R Paula09/2011
841616996^5483+5483^1699663549Hans Havermann02/2017
8417(2^211079+9)/36428363536Lelio R Paula03/2012
84183*10^63522+1363523Robert Price08/2017
841915852^10157+10157^1585263516Hans Havermann02/2017
84202^210948-1587363502Enzo Doria04/2013
84217^75136+663498Lelio R Paula04/2013
84222^210928+1291563496Lelio R Paula02/2013
84237*10^63493+3963494Robert Price07/2016
84242^210909+13563490Lelio R Paula08/2011
8425(3*2^210832+1)/763467Lelio R Paula07/2012
84268*7^75098-363467Lelio R Paula09/2014
842717683^3882+3882^1768363466Hans Havermann03/2017
8429Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
84282^210820-1690563464Enzo Doria05/2013
84305^90795-3663463Lelio R Paula04/2013
843184731!6-4863463Robert Price08/2018
84322^210816-1319763462Enzo Doria10/2012
84332^210750+13363443Lelio R Paula08/2011
8434291^25742+25742^29163426Norbert Schneider09/2014
8435(3^132908+8)/27985963408Lelio R Paula04/2012
84366^81480-13963404Lelio R Paula04/2013
84372^210576-17363390Lelio R Paula08/2011
843818^50497+5563388Lelio R Paula05/2013
84392^210545+1163381Lelio R Paula08/2011
84402^210543+6363380Lelio R Paula08/2011
8441155^28929-15463365Norbert Schneider12/2018
844283^33016+8263361Norbert Schneider04/2015
84432^210464+9876533163356Jason Earls12/2008
84447*10^63351+963352Dmitry Domanov11/2010
8445p(13534)#/2+51263348Robert Price05/2017
84461741^19546+19546^174163345Serge Batalov05/2014
844710^63336+1981963337Patrick De Geest12/2013
844810^63336-12288363336Patrick De Geest12/2013
8449(19^49523-2^49523)/1763327Robert Price09/2013
8450(2^210378+47)/9551693163323Lelio R Paula03/2012
845131191!2+25663316Robert Price01/2015
845216458^7031+7031^1645863315Hans Havermann01/2017
8453(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
8454156^28864+15563303Norbert Schneider12/2018
8455(2^210283+7)/169114563296Lelio R Paula03/2012
84562^210217+129963282Lelio R Paula09/2011
8457(2^210221-3)/26963281Lelio R Paula04/2012
8458Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
845996^31913-9563261Norbert Schneider04/2016
84603^132572+28063253Lelio R Paula04/2013
84613^132570-2^(132570-1)63252Robert Price01/2016
846211^60734-492063248Enzo Doria01/2013
84642^210061+2163235Donovan Johnson06/2006
846318^50375+9563235Lelio R Paula05/2013
846585^32773-263233Lelio R Paula08/2013
8466(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
8467(2^210054-1017)/67163230Lelio R Paula04/2012
84683*2^210022+563224Lelio R Paula04/2014
846915^53756+3263222Lelio R Paula05/2013
847117^51380+2263221Lelio R Paula05/2013
8470(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
847243^38700+4263216Norbert Schneider06/2014
84735^90431-9663209Lelio R Paula04/2013
8474(172*10^63202-1)/963204Serge Batalov12/2014
8475(43*10^63200+83)/963201Robert Price08/2017
84762^209914-1600563191Enzo Doria04/2013
84773*6^81190-563179Lelio R Paula09/2014
84782^209820+425763163Lelio R Paula10/2011
847999^31648+263158Lelio R Paula05/2013
848016976^5253+5253^1697663158Hans Havermann01/2017
84812^209790+6763154Lelio R Paula08/2011
8482145878#-p(145878)63152Henri Lifchitz12/2018
84832^209759+9019563144Lelio R Paula02/2013
8484145823#+21150763142Arkadiusz Wesolowski03/2013
84862^209707+51363129Lelio R Paula10/2011
8485(3^132314-8)/1763129Lelio R Paula04/2012
8487(2*10^63117+7)/963117Erik Branger03/2011
84889*2^209654-763114Lelio R Paula04/2014
848984304!6-963112Robert Price08/2018
849011^60598-1463107Lelio R Paula05/2013
849115103^15078+15078^1510363106Hans Havermann01/2017
849215346^12941+12941^1534663103Hans Havermann01/2017
84933^132253+7663101Lelio R Paula04/2013
8494(56*10^63100+403)/963101Robert Price10/2017
849517549^3936+3936^1754963090Hans Havermann01/2017
8496(55459*2^209553+1)/42363084Lelio R Paula06/2014
8497(331^25033-1)/33063077Eric Chen09/2017
849920^48480+3163074Lelio R Paula06/2013
8498(26*10^63073-23)/363074Robert Price08/2016
85002^209499+7625363066Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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