Old log (2005)


December 31, 2005

By Sean A. Irvine (December 29, 2005),

A100 C125=
6323653886959229380845623497003053099857 (p40) *
15065998423079630399753455176676726982352540152749808915358829005761157502572450237391 (p86)
Using B1=11000000, B2=25577181640, polynomial Dickson(12), sigma=2953734571 


By Takahiro Nohara (December 24, 2005),

GMP-ECM 6.0
Using B1=3000000, B2=4016636513, polynomial Dickson(6), sigma=3711289225
#Pn-1 : 107 : 587 : 2113 * 7036640657 * c226
c226 =
13249058166170065954638883746672779 (p35) *
451504654777480332725514621461529908680110632399071787534123806875964925120699863737099864782732659889124100266729075092169882366533558604949193789517993608378275807510054738171188398074333211 (p192)

December 14, 2005

By Takahiro Nohara (December 10, 2005),

GMP-ECM 6.0 B1=3e6 B2=4016636513, polynomial Dickson(6), sigma=896626848

#Pn-1:102 : 557 : 53563779143263213754862638009468737 *  
82602029648398188445386287742234111403 * c153

c153=
7516041202205203365829856242410078083 (p37) *
43170824554563778543954012893292726573573914583070159291706566047481518155928638841550438499893617689248620663398493 (p116)

(December 09, 2005),

GMP-ECM 6.0 B1=3e6 sigma=2969523850
#Pn-1:101 : 547 : 1777 * 748371367 * 104001413863 * 545012941449887 * c185 
c185 =
18969792870295254937433709703595027 (p35) *
1802490532401299547724997820789090035797977349168135114438810286524852275250684607182019690492307971921698932083391949806041217017127173129655465576713 (c151)

GMP-ECM 6.0 B1=3e6 sigma=1279422167(p35) sigma=2859957466(p38)
#Pn-1:102 : 557 : c226 
c226 =
53563779143263213754862638009468737 (p35) *
82602029648398188445386287742234111403 (p38) *
324473696085273455177408620610156556411529631988694898169556606160819531302196815249511269341121173159169579467545167557676843692882329421483948274528919 (c153)

December 08, 2005

By Sean A. Irvine (December 06, 2005),

A(91) C124 = 14555122524822466500886923353644326686917 (p41) *
72319000454312489530004603582161560345310985046684040594569720061990517675629144463 (p83)
Using B1=11000000, B2=25577181640, polynomial Dickson(12), sigma=2549924231

December 05, 2005

By Daniel Morel (December 03, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1
353 :
p39 = 126190244698738480545705939566276703301
p94 = 2368803961066147764491828774350811163030082966931116082433704521724664372928952548336484746187


By Takahiro Nohara (November 27, 2005),

GMP_ECM 6.0 B1=3e6 sigma=4233617732(p35)/457382280(p41)

#Pn-1 : 99 : 523 : 563 * 225889 * 306587 * 715834581677 * c192
c192 = 
10418196554442817047806293540750981 (p35) *
92652652358338027441793024490911721607621 (p41) *
323281867970993977783809081897877479544850652894137062773178465898647806746635511493120926634064979187016427070659173 (p117)

November 25, 2005

By Takahiro Nohara (November 19, 2005),

GMP-ECM 6.0 B1=3e6 sigma=2236901319

#Pn-1 : 87 : 449 : 1594387 * 6566983041745360901 * c160
c160=
3849821945755297700069276502505219 (p34) *
1189637556684698747565091073363640408460918656192308353018449063606469878820247822075107345051121071049123570173392064935350653 (p127)


By Tyler Cadigan (November 18, 2005),

log2(296) : 50903805695542610381163733395650812773199716625122600221840278827300235701138485861308072337665861131711525905205816829331237 (c125)=
43267149219667183972539909621498892605434016535607 (p50) *
1176500107208453806080252343277346196766867869286877935098261037723143113091 (p76)

November 02, 2005

By Sean A. Irvine (October 31, 2005),

An(124)=
11735342201837191361539337041175429 (p35) *
127315706614553567473637722865181003712837767523673423465059674636259703216604317070648988593850611585939394164624895389603819257103845203730242337504924434488235652971643711 (c174)

October 29, 2005

By Sean A. Irvine (October 25, 2005),

Smarandache factors

Sm90 C154
5469640487155071172064105436159054827205011884517193846381587779057 (p67) *
323974513721871489318385733207245357406204798917206286895918649972193592038458818136011 (p87)
by SNFS, 32 days

Sm91 C129
3581874457050057021838729610409482762969149632972915379 (p55) *
267535593139950330755907265689770024664090795106497661308268157342396003221 (p75)
by GNFS, 4 days

October 21, 2005

By Takahiro Nohara (October 11, 2005),

GMP-ECM 6.0 B1=3000000, sigma=865746042

#Pn+1

109 : 599 : 154006033 * 74119649873 * 1650289933478587 * 
190883459271153022334840970773 * c181 

c181 =
280818180154859694807701663308663035067 (p39) *
31287348784828227314024928001758099249285416881733304087248867485320089557888388230230494319575002170766366000142329442881077584276509595352787 (c143)

October 08, 2005

By Samuel Chong (October 06, 2005),

prSm(73) : C149 = P59 * P91
14311578668849306832064176821408791945900114506618448115473 (p59) *
1227307899724677528169696576941663375461295118312494677251376824180964822377749437208968063 (p91)

prSm(74) : C123 = P48 * P75
744185509071912604429600817249568778913156967011 (p48) *
193903873153006845303017952557072775598878161951060566046538018201411273463 (p75)

October 07, 2005

By Sean A. Irvine (September 26, 2005),

Eu102 C139
198943119321654388058500384086517043195558620394228397755851 (p60) *
7047149416458071487967246745672316954994551826273995139785075734373341685377233 (p79)
by GNFS, 7 days

Eu124 C137
340434085979481287216483227078798002216360327742620827466139 (p60) *
44413952531259741407329119806185226325218923696798983508326220755665292925241 (p77)
by GNFS, 10 days

September 19, 2005

By Sean A. Irvine (September 16, 2005),

pi(161) C122 =
4527705705970663951905199136808845955456189777215099928379 (p58) *
20342160442335063733742077236518001174173671789847306412587431043 (p65)
by GNFS, 2 days

September 13, 2005

By Sean A. Irvine (September 12, 2005),

Sm87 C145=
101784611215757903569658774280830604745279416597473 (p51) *
58398250025786270255235847423735930777973447337337804788906368149837276410666257137526766841721 (p95)
by SNFS, 14 days

Sm88 C153=
462668377429470430246269302055630668010673 (p42)
B1=11000000, sigma=1512552247
144494999796935291164027251780366969508458166480331 (p51) *
3718931833006826909360514481439595803175244655637881136348103 (p61)
by GNFS, 8 hours


By Takahiro Nohara (September 09, 2005),

GMP-ECM 6.0 B1=3000000, sigma=1326032457

#Pn+1 : 91 : 467 : 718713552547 * 460510058368076603383799 * c160
c160 =
16156803036090201905385238636184905319 (p38) *
408488243051779645854430946252515353238147389749753196825278209716589309102056100230817149742283216455301303602054263772153 (c123)

September 04, 2005

By Takahiro Nohara (September 01, 2005),

GMP-ECM 6.0 B1=3000000, sigma=3921292590

#Pn+1 : 85 : 439 : 1291 * 6673 * 139650775093 * c162
c162 =
19969104182482670740236140786422824137 (p38) *
10034958528788396564004501968711967973119867610519000155529138535763559699681389007849498417348666003660967218272626506797137 (c125)


By Sean A. Irvine (August 30, 2005),

Sm83 C134
21875480270521598141087357354188092945840550359281483 (p53) *
3966169790267211790412249283896602109358687165012835285295541472324348526743126307 (p82)
by SNFS, 8 days

Sm85 C158 =
120549814855596987772827562271063563633851059 (p45) *
2112809210944968177871685727287164545437750155430310661 (p55) *
197843626412162026434764405036310959588059884460495810550047 (p60)
by GNFS, 1 day

Sm86 C154 =
718252229986396496762902999331863301257 (p39) *
10828687641092318839822035841363590407263202742239027773 (p56) *
1089075252400674157091531724111232381528208779232955680665273 (p61)
by GNFS, 2 days

Others with B1=1e6:
Sm114 8678622406220213516465050301044327
Sm159 45941358846148651407783221723920871719
Sm171 40202471819457246557501649563881337
Sm193 5167315927941164272437909427556797

August 17, 2005

By Takahiro Nohara (August 13, 2005),

GMP-ECM 6.0 B1=3000000 sigma=3622833556
#Pn+1 : 90 : 463 : 983 * 190369 * 729293 * 100282859827 * 398078244463 *
1107468799967598177002554891344421 * c123
c123 =
80260386060361641572501935020349314640391 (p41) *
9659026917024052721831744862518962349908991929318819821433353718411415563363604891 (p82)

GMP-ECM 6.0 B1=3000000 sigma=2879898706
#Pn+1 : 70 : 349 : 44953 * 141817427570657 * c122
c122 =
77724772359105367603657162406342181371251 (p41) *
527839044097742938651735469124709889688504597419577097506875696336826710286115001 (p81)

GMP-ECM 6.0 B1=3000000 sigma=2349546992
#Pn+1 : 79 : 401 : 356647 * 106472237 * 176879825310092531660311384621 * c121
c121 =
686296752057535768615870183262908809835739 (p42) *
8848111170777672369264653969664674390436544386049279331460052279209563209215751 (p79)

August 09, 2005

By Takahiro Nohara (August 07, 2005),

GMP-ECM 6.0 B1=3000000 sigma=3838602697

#Pn+1 : 107 : 587 : 1033 * 39461 * 315883 * 286066602745434780680837711 * c200
c200 =
1660393570870141125306133982905353653 (p37) *
14542505790899495331676035395961467283593678099942532725645947228011463511145888769713042029641505451142893238247487145900368877514723901177230976575091626242239983 (c164)

August 05, 2005

By Sean A. Irvine (August 05, 2005),

Sm78 C139=
205155431830422787082756234197593935249202704547671264423 (p57) *
17403902113720391120287411398887911225298966708915583006414519403038472992542973083 (p83)
by GNFS, 9 days

Sm89  496118159817126721484175235476073
Sm89  26459905787227421825352754831024262009257.P64
Sm92  46731404628893905607210235741707
Sm93  19544056951015647623992763251
Sm95  244987542265129586458446183157595351.P141
Sm100 970447246795177523033247400823.P118
Sm106 95383501607400293616004374931
Sm106 54259599094002572583355411045946413
Sm108 132761751746390611923240080737166083.P161
Sm109 9943216978062352390003139833531
Sm114 2042059881000388200555074336219
Sm116 9787002048140152171263515060558503699.P198
Sm121 105299178204417486675841093021769.P214
Sm123 12347002211187670552593982429
Sm123 2829927788416784955921382453753
Sm125 295999706346724665505289
Sm137 144065103514544138702103468451
Sm148 8817212782626223819399721069204897.P254
Sm152 4103096315830350734534473515557
Sm152 12805089500421274253268517941967
Sm152 17815076027044127272632744936161.P205
Sm154 32063206397901252963254536935569
Sm159 11855111297257593607972759339201
Sm160 64603936118676024484144135734907
Sm162 22260247937572504750086047
Sm164 1039418554780603268384723777072953
Sm165 13183356310254866666237435750357.P328
Sm176 1011379313630785579015894871
Sm183 553245689211853052761209813199
Sm184 677008100402429325901609057.P342
Sm187 1080829169904060835770214147747.P411
Sm193 419908232491384495189
Sm195 165897663095213559529993681.P412
Sm198 14158849264684185910199571953

with ECM B1=1e6


By Robert Backstrom (August 04, 2005),
Version: GGNFS-0.77.1

Numerator of sums of 1/p
88 : 457 : 5114007805286355150593434105856355180943294411233248016725523544672820002322546384694353285410358237441830614499450543 (c118)=
3966979363543508505733804381051749268934302913 (p46) *
1289144040496914074686936387595825971847492738371301408841827655832774511 (p73)

(July 31, 2005),

Compositorial - 1
143 : 93089088076902061345405263916294652269849231431718776059613972924411476323122717906388563045148718363115396339291567713 (c119)=
1447345271264845328858211337003783744943861621902103 (p52) *
64317125930532695247337661969468151147410456483218525960925023212871 (p68)

(July 30, 2005),

j(tau) 804 : 95446502719482969505270435601595515189072919166224468531268320035728217284399746219514419999965213444930397215666307181 (c119)=
7597977844925814119112729478698898180013123047 (p46) *
12562092791995354841000098043399059116942794342939793121829475051873629323 (p74)

July 30, 2005

By Robert Backstrom (July 30, 2005),

j(tau) 896 : 33070122493551474326429028586770268145455668268605539571596936841913129050422975320567776805010275117094193790869277937 (c119)=
1181331343195781103579661923510215331051820922028047441 (p55) *
27993943176085516963946888104498669682834640034515866451173981857 (p65)
Version: GGNFS-0.77.1

An (85) : 29315020531556479448429138741028061319464905386507863966292659907512929508706251989116335322509196707913921465953652923 (c119)=
12194986532161980689130284753627383518703248922670572861 (p56) *
2403858376902970146877304304849110010659979876398829839102745943 (p64)
Version: GGNFS-0.77.1

(July 29, 2005),

Numerator of sums of 1/p
66 : 317 : 1182655751698719951370900766132534145383371084750972319652981861648329701504590118296007633405107336268872581649684283 (c118)=
303909666003986239876228859266842827787705817105239453149 (p57) *
3891471328467741507057433841812285282114821235137598083531767 (p61)
Version: GGNFS-0.77.1

Numerator of partial sum of log2
345 : 10818669946626402202625871018449493162394206784078156194072427654172897113669264627035468290217218462751735851927102047 (c119)=
427500883306985127706085821818637 (p33) *
10142505879304971145212796807506953 (p35) *
2495120860308713979572376656717009102965011637735427 (p52)
Version: GGNFS-0.77.1


#Pn+1 : 71 : 353 : 81154480902099611233153511142160470616627175020897792950288308775569035448766719057771760324009668149273219856764473473 (c119)=
1081837917202245668794906709903751665982461 (p43) *
75015378562413685326482273680311001741744170108833695241420007074182850548693 (p77)
Version: GGNFS-0.73.4

By Takahiro Nohara (July 24, 2005),

#Pn+1 : 89 : 461 : 44159768129 * C180
11015237372786104937627672290033 (p32) *
621586378274104762712676521655722011 (p36) *
33412574625271012134414729953620091172963231498103816474576876697302747887791334055729070825458559932860708322073 (p113)
GMP-ECM 6.0 B1=3000000

July 18, 2005

By Sean A. Irvine (July 13, 2005),

pi(160) C130=
108170872899832181171943799499558717639 (p39) *
90229038022816617652814372359006809358122140644520797791447679884698341145599374402308735233 (p92)
ECM, sigma=1724727943, B1=3e6

July 11, 2005

By Sean A. Irvine (July 07, 2005),

pi(154) : C123
10789634420987857010775029383748023977737397438325309257953 (p59) *
52534340926224154858301028796087331808920451927923056676637799277 (p65)
by GNFS, 2 days


By Robert Backstrom (July 07, 2005),

Decimal expansion pi
155 : 1580360827013248215564850232045270285102248915761849967196045585900905141732882909277422392782305524578538994401845053 (c118)=
22630320596212777239949971354349164035682841071031305313 (p56) *
69833779874851808158971138966537527611703272650713319909541981 (p62)

Numerator of partial sum of log2
474 : 441560459715388641476998120680047056847226775229911750411366614793854177341512225604208095361908235451891055523023113 (c117)=
13426967095903928842393387969121839 (p35) *
32886090846986018881491736980506688852057335867558515292734889167203811256466884167 (p83)

(July 06, 2005),

j(tau) 885 : 356555639147864504602165661143636008605219647847134365819169173523755123405888020035957603102141188324242144458385183 (c117)=
404008281901783447339819739476496082348091 (p42) *
882545371271733158516473630526165229456259434931744410536615073313926460013 (p75)

Wol2 (174) : 286037196844385053010204965918575732308982226586612693387491605514153249537115974655520971282190177776011986150655907 (c117)=
250636991615596538777207823434161061 (p36) *
1141240943727420818504681555523585148674117490033186921512395199386710012707787687 (p82)

(July 05, 2005),

Decimal expansion Euler gamma
128 : 337550641544807621964871902336240624414858505142949523716568701114987153768904102315222579701616538927802929248332391 (c117)=
207743855106573133146456500425883725903 (p39) *
1624840558444644597492368949108572570751047073658745750538663061668034849326697 (p79)

j(tau) 776 : 291084741877149267583179968519759520005144831934722411164475489383251357977495869562662504544228090248144968109029419 (c117)=
67848595323674198101485284626646203248589 (p41) *
4290210290847126488123981777321784946841419932424731508182584564030549696471 (p76)

Decimal expansion e
120 : 135988885309872691748476035387096027703099059167540125817548032804246166909477592404391524264603853490793255887338189 (c117)=
7618884955083303490358532668456717389152828163212192779 (p55) *
17848922265080430555557156153743192270481701628733213194150791 (p62)

Wol4 (96) : 47793747705918663096873476091697077978868038906346452480185327137487648101587521336540073073319723611469222073589027 (c116)=
17078196754614161379498618259581535030676881 (p44) *
2798524246595637832702765676062050866884697482331133922646112489811998067 (p73)

(July 04, 2005),

#Pn - 1 : 67 : 331 : 910675235536071757006445921898228450290550588923012013909402003948003546381545086023326034032187234177532585995714971 (c117)=
542761405340834519889048924121682813868448697091022417 (p54) *
1677855548635040965457455394319465295335704380797332131732933163 (p64)

Wol2 (169) : 18201922714509118935113396379234922083886441727716242256515599703509322335690331628774673238224858361283107955548973 (c116)=
96551038586784477190417825035100147 (p35) *
188521252395937725793069921952070090164394543474962531044480949034784019203364959 (p81)

July 04, 2005

By Robert Backstrom (July 03, 2005),

Numerator of sums of 1/p
62 : 293 : 51225057461582337756141841953688309824879677243404855408671659040356492890811985473060076317744188025804448531505123 (c116)=
43536091344561600390559851581507045347 (p38) *
1176611309824928053490878945094978144486298527042995833457706217116182238251009 (p79)

Reverse Smarandache consecutive prime sequences
64 : 311 : 14303490983299113224836122126542170400843945529360302119558259561863755813205709953862907140789683488352776036079313 (c116)=
2974840379652901657238841261821759493810175620159929453 (p55) *
4808154105050844962121810633134115273898496369509949529013621 (p61)

(July 02, 2005),

#Pn + 1 : 69 : 99015111342459742852316153206930392934740995862203525595575907225684909370971652351415777357475716659408079165832763 (c116)=
2676767005233908515724708358526628401592806758287 (p49) *
36990560309826942070521832749917907651082187806062449398287631104149 (p68)

j(tau) 922 : 55955251693256210527527521979137459922304663364181882230967981446836321024725559450966778486604147932595546205730213 (c116)=
94175219397797459737011225662525729 (p35) *
594161097272313594068158680533649189975554116135294933404740571055925399314030597 (p81)

Numerator of Sigma (Moeb(n)/n)
353 : 31089676661959953787895190953613265269236987250846811698363547006419779757612478084049342971026204458791185365471071 (c116)=
9671515331741527070876976348665445215121893 (p43) *
3214561068824952032159919025786733499435594233889934095650212391111669747 (p73)

n! - Next (n+1)
116 : 22588228947233477899214636825212819585289291528075985829325282250843481802794891141298057960955648563814096428693483 (c116)=
2351713433091689251072828057431051002299153 (p43) *
9605009109267949573105222474405748622943288905958729553488614882439287611 (p73)

July 02, 2005

By Robert Backstrom (July 01, 2005),

Numerator of Sigma (Moeb(n)/n)
301 : 33615956869857348574229072027885891299094710067029757070435929418947878057764777173531903447978788599344796064068467 (c116)=
1254197991432597174646654276071279773317 (p40) *
26802751319558248344085642148486574262564892984296260930910151583585535532951 (p77)

j(tau) 845 : 12151020642860360116453597752255201299402117015679992060495444347447582573673810112973863455776150137353211572844991 (c116)=
14987923561225763934656790944124140464549773811039146271 (p56) *
810720750824713163870365345840653608124756252161919304852321 (p60)

n! - Next (n+1)
81 : 14880374403199757652765616048939912792203842181444794571478828718258005194526164084213810017530958669753736055567249 (c116)=
23939035186380516755040509499141836329 (p38) *
621594575025544661569474467763053303429195717007663370915278553589336604317481 (p78)

Decimal expansion e
175 : 51907556204762650789357627824006314292847095049900196344587204037898172296692116322974582535605318652450366307846291 (c116)=
1451339981644257956251617797290551222134621820154651 (p52) *
35765263040542252875521351843065778176013284048718672124276465641 (p65)

(June 30, 2005),

j(tau) 671 : 44609124596036621490105328361430212451627959167061653812033042504842411372166397134029346092113640965372440358263721 (c116)=
89103838919173681549794586282501605157 (p38) *
500642005295660399544421435685902231593540516930339975713920156453215925587253 (p78)

Compositorial + 1
125 : 83699003594839944595086799054805768863087278598474231157156095044248605390358442545677115575092318551783556469510613 (c116)=
438232951578275129562452139648834437 (p36) *
190992035841672709643750659212183753474662064445467933485810250417682126248453649 (p81)

Wol (325) : 3763779868002642781812437837107648756689530013942580777711741215092499363807847931880551439747416009400898600923499 (c115)=
38849115941961773998359807797466927748421344497041 (p50) *
96881995297537836391973014841029343122126698222747444007831322939 (p65)

June 30, 2005

By Robert Backstrom (June 29, 2005),

Wol (390) : 3573497828465137338973011216213066046360155358820416552191521965961282147311205149765369290155150427139542906837253 (c115)=
3686850289712335568294613596109644468029 (p40) *
969254932438267654282894186857171964758048026592154211846141970802433412457 (p75)

Numerator of Sigma (Moeb(n)/n)
371 : 5295692613557488362300244738345461187376775776190880013773045566034239807510682868697797026704521356980364795387247 (c115)=
6955232303342175348471979651673930436012051519554267 (p52) *
761396942991072529530545929016626330088776253834478480059666941 (p63)

Numerator of Sigma (Moeb(n)/n)
354 : 1691674667957070685280134219174794588944847694689868467730900511669582110243787800693083182595022312256661973118959 (c115)=
720449197551251039451471178180022143792494180636112798973 (p57) *
2348083214898339837206969930239888859451420208001464955483 (p58)

Wol (331) : 534541949017974663356482798279900374817915460700632144228123110816672423499421207674187212669391273650119918143197 (c114)=
245967104240266351812151695685364430367487944052679503 (p54) *
2173225361452488110339538565806169063551799060522556468090899 (p61)

An (97) : 8229605319761098762937867932186950698778264180505861112745893482398697188365380530635440227880012788693712875576997 (c115)=
190070679887515448939267118931772719752412327 (p45) *
43297605525646619891584200584159454053392068427535261624426011963488211 (p71)

(June 28, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1
441 : 2 : 9729238166075362426536499565068245866287789090112352693536428520200507490961825543825004255861141267878058481243797 (c115)=
35682703613693630234254251405926173 (p35) *
272659781372106013869259461509568750038375537404726805941885273334848490415612889 (p81)

Compositorial - NextComposite
118 : 1719330846187847473841838016110079082355463525541701127948024090521045331439987260938556230736931301308546218117831 (c115)=
1998318412641678876414167004359290504208076281836658047 (p55) *
860388832585982365691563278735867629439243937790021834393273 (p60)

(June 27, 2005),

#Pn + 1 : 72 : 359 : 4796100052757314705339332429010272727278993031197470793713287684138765824112122607290910881664819236642967857186739 (c115)=
179124080758411776021912407933366040466777179234105959669 (p57) *
26775294714427093707672113583710320686632583467959421473031 (p59)

Wol (308) : 266832534479428652819032181349369959084874688607360114833992120804748716251455477518364446783469299312595384857257 (c114)=
1923896111701956254463328263360450817981417376317 (p49) *
138693837394046089531682457681199293422317221925207672729987353821 (p66)

j(tau) 967 : 839953412191544446532470624221817224802097665603262289089505558360007323957156042404209572251717839846713199197739 (c114)=
3040340442331243818590665332824001013 (p37) *
276269525773071920297525038929174262319714035176037414891636538248951025791903 (p78)

(June 26, 2005),

n! - Next (n+1)
91 : 365956522747376742233265979094359227781843170618965902228529791068354105117309120871985977140430769896272075900701 (c114)=
41966691417146796544168791203613342050193239 (p44) *
8720166169636470963044890732210151240440342341409335292937623815436459 (p70)

June 27, 2005

By Robert Backstrom (June 26, 2005),

j(tau) 672 : 866800935378219260097480740084941195827303157432509754864852736948863332786265041793639144123134390115543781986723 (c114)=
9798943243286631143421269195717542008298663 (p43) *
88458613735932654028628908778226574109477829572639095660169699979859621 (p71)

Wol (427) : 36211672257089805244775681206524503756508391967523268324523909402107707115518334628144116539487654572172662223189 (c113)=
258749825155088796518029370818171324759503852826813 (p51) *
139948586382175707397539599245490553264051159873146520931141753 (p63)

Decimal expansion Euler gamma
145 : 120365434349850793203885064389313745240546131648368816532377889470726432835754556935623180166547329223153809003507 (c114)=
36491583309232631939190519424513724513790198280130762383 (p56) *
3298443735089934456904501123218744931586861899079376436829 (p58)

Decimal expansion Euler gamma
195,196 : 311916411270394519426713434186032475753147329924663583387682765109376922246156701102661866691878495533167606259099 (c114)=
34601348911601063571401135892180719847362103534539 (p50) *
9014573740095313925717629946349249310426136426314400649740637041 (p64)

(June 25, 2005),

j(tau) 866 : 24370521968048174120183449284747740305598177468698482462863616064715204790628996984857272338742281618435425542447 (c113)=
21014485913421864002110776669069662720909 (p41) *
1159701078030313554697016066314832246224967551347726852266136356773223083 (p73)

Wol (316) : 22337490343111019427467957064608405499063292594975130445701778386248011049074933221659415389467666395204755307723 (c113)=
220630579288768152147048451697336528880102499283591327 (p54) *
101243854841513236243830801226440843619190515326825152600149 (p60)

(June 24, 2005),

j(tau) 812 : 47369688682929942917762477506115562623161728201037272201172197559253167341283307136857702499752259785138624796181 (c113)=
2878261827800807998229805743857161048722168817647773 (p52) *
16457741344234716842701594005260802673927809817560626728961497 (p62)

j(tau) 807 : 36894057288309845232446327028866599165077211785397120623538057534159032149775523272260792698865696356408392098969 (c113)=
67640257762352529765368096236199174527249 (p41) *
545445249749543075174583601496364746003082173010607549200658557105558281 (p72)

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1
317 : 22337490343111019427467957064608405499063292594975130445701778386248011049074933221659415389467666395204755307723 (c113)=
220630579288768152147048451697336528880102499283591327 (p54) *
101243854841513236243830801226440843619190515326825152600149 (p60)

Compositorial + NextComposite
115 : 36497797485870570426489812900513535120174597151506772886252225358203431794825180627751581447750610187523709633639 (c113)=
132026036241268613867582494546371183485635710571297 (p51) *
276443938824106818554355352885233417398654388897805729397796487 (p63)

Compositorial - NextComposite
144 : 81991142258831481123314764983615213747556877167230191756783926348112725994050832890320798432794253273985579062299 (c113)=
277108014125166528786441406222971542451620666970533627 (p54) *
295881526623033780264025774470867182297058382488871016490337 (p60)

(June 23, 2005),

Numerator of partial sum of log2
342 : 2792251583055766373725119242614584643655820667481584804795429570568483202960252748427953804724326500774626414413 (c112)=
3656306081077561178050829496650878414713757420682922449 (p55) *
763681027008781865058318344495005687182914425906715906237 (p57)

n! - Next (n+1)
102 : 2294350144367389139997841274796485953847396153855191192241712943074880777362658223492536278321200428451407289879 (c112)=
108383195635476009638288100196469581414600272495833 (p51) *
21168873374835258909089457466569414067866070128676275744842863 (p62)

j(tau) 884 : 3791029845266166465039907819843775949197406967334647524343399377283678846561872596416173584771703311405230783891 (c112)=
1463839284408098139274844338659079459272149829678004721 (p55) *
2589785562968454804545077503248932028524909301933347064771 (p58)

j(tau) 970 : 6612431006887761365088988591593916810223738782780411547603943861201797585207634241635906748999134478183282033391 (c112)=
325237757984898227810154858679345173170021 (p42) *
20331068101861643394859247562167023403410832255517383768791435858283971 (p71)

(June 22, 2005),

Compositorial + 1
116 : 146056863859630566342193847731376801333506909310722895881003398507471651288215054915158686265874957203816264063 (c111)=
2276740073143445748890381959954906806448993207734620411 (p55) *
64151751700831186747789229742558271208151612529697235533 (p56)

j(tau) 857 : 3358400714581445343668420508311543850141888100440600586834181894305615730027081623838841913388762335047775282477 (c112)=
2656176537610717193658608004498774462427319683 (p46) *
1264374060619627544594963364276687046728205273710977585789169349519 (p67)

# Smarandache consecutive prime sequences
# 67 : 331 : 791410765736334057497721631901506822030180462713167809014790668498563275204070321326862031885390393715795765339 (c111)=
# 216923389236198609558821678067350492090000009865599 (p51) *
# 3648342248952235810314115497899698981790456018322548372756261 (p61)

(June 21, 2005),

Decimal expansion Euler gamma
181 : 524208005840817722439592028959388238385744574675253690038404605351035698761855480852591653341809230337723947863 (c111)=
106264722984427016894148083739803465200854774467763167 (p54) *
4933038840346291148388126409202794818338095015702698078089 (p58)

Numerator of partial sum of log2
373 : 139243795794198724117485398867117875555486081094861370957221429478345972737111554654501110350048193222290448883 (c111)=
134513346721689599135962457310703951231 (p39) *
1035167135364615561324847336516137594321048082685420365923187709280132493 (p73)

Wol (354) : 17715406743632780198363311478440400403575184590938605012350994192066103558822250127353977131785980918324123687 (c110)=
514320465766932005957756894820023387 (p36) *
34444296742530644981840363782119353354834609009998870398013383124041796901 (p74)

# Smarandache consecutive prime sequences
# 54 : 251 : 39072383268838818724194101852294011252795990578608801856164243487895076093578454199830597276364044586973855069 (c110)=
# 54290725767198980123376315097824574442986607719 (p47) *
# 719687989370098249238915678281457138366570340161328675020170651 (p63)

Wol2(154) : 43330468483762813708032919079909928529604577192021095290463325562255433512147611576155692195556490097200169483 (c110)=
8346228885109033674892817848816201368513397293551491 (p52) *
5191622357861655029809255817320795636185348770262106961113 (p58)

n! + Next (n+1)
94 : 16470094612230191368575174978605666672430747060376083190904388376629005564478118529587973827736246440472146969 (c110)=
76148279016093531176977904190680324693698933 (p44) *
216289781266748327043570207564139980770551122623358872073405081493 (p66)

(June 20, 2005),

# Smarandache consecutive prime sequences
# 49 : 227 : 15927916540958381020446558046173111013678994720507242458067807967018546666926991609716921536181021508538681181 (c110)=
# 146136279270895280678880836744405148990333772191301 (p51) *
# 108993582021015698823608956587424819120928097943488149645881 (p60)

j(tau) 716 : 16616685232406425631242818525065793285099465470001978717515009603174109348509703055885001789466559014855550973 (c110)=
4290346855916447496307293168099518192443433534009 (p49) *
3873040057237280822995337305337312615575587744842816342016997 (p61)

j(tau) 641 : 11537930459879667769628185599188296290980852465159013734631439037644386724483122903061007051596743851945096723 (c110)=
8069123415565284297497905354175228565743801201 (p46) *
1429886477832657538613789756449723396973105972844589248758749123 (p64)

j(tau) 602 : 85573284197455735003590146885949304337976165176924184716063726278240101057754079736699623686756041563382815777 (c110)=
300936064303648302834455758739237907236954589678797 (p51) *
284357025787082822762940358370016695184968661706573172018341 (p60)

(June 19, 2005),

Decimal expansion e
136 : 27714658188127855026824304482096297417859991249350847009018308028060279806629899128782319585892893509404491277 (c110)=
62993530833567718300607218756139237220329159 (p44) *
439960386747513265299578568283959662991812252854482805899211608203 (p66)

Wol2(152) : 1503179121691027488582907353112208876617680900401214275943226609031914533254179206958963909050662059600577111 (c109)=
6950896107606540523834724261897202757222000401941591 (p52) *
216256882338675836273198174815024533430065619051882590721 (p57)

Decimal expansion pi
199 : 47792601057176195102165785242434247783297148185337755398706433767253917394427936963003305569621414286202400341 (c110)=
71723686423433640381591900075479245638009733474409 (p50) *
666343344024789902706694741748553217109959505473410431252749 (p60)

Numerator of Sigma (Moeb(n)/n)
323 : c109
769804650769428357500809546783546571 (p36) *
12539117582634222037880205814991260134915090865747143973602011569083988417 (p74)

(June 18, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1
376 : c109
16401798969443029846837863892954431163719655823685857 (p53) *
318323295195293419319656735675722015437223675170780398531 (p57)

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1
377 : c109
730379173952626873537233990616746145080601271 (p45) *
3345274781673635154885780895651576507920502606751221720155389623 (p64)

# Numerator of partial sum of log2
# 402 : c109
# 5875607580369964436535523341158277467 (p37) *
# 461503216104808264773648106386475214742726052333372480358632832432135689 (p72)

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1
361 : 1578619901923171202535373641553885366034933344606238186153516229864503098534771897251698268109608635844890291 (c109)=
107504445723986304623772768419287095127 (p39) *
14684229022269641933905334771026201166556028411621461034147728192419333 (p71)

j(tau) 712 : 3925579604871391311975401696731516512427597392996040806247388321044224181300932571338338427839631367836079499 (c109)=
37178015617607314894581779489364803666638665928221049 (p53) *
105588734085427012990252976889907164068534432148671894051 (p57)

Decimal expansion pi
171 : 3897682866074250173518994552466340477290976844298056080427223267458190237282773734604094317590393579745742037 (c109)=
358554847971751083950167495287357849832852032790553 (p51) *
10870534558722047991065335471744534053381515402392875072029 (p59)

(June 17, 2005),

Compositorial - NextComposite
111 : 7139854933473346865404417821258606884387358459697368650140252246584773355733341044099075355739140666136618879 (c109)=
208143619428604189198370181913662033698727964201355327 (p54) *
34302540491386066995643185647282710163027818905600938177 (p56)

June 17, 2005

By Robert Backstrom (June 16, 2005),

Compositorial - NextComposite
98 : 8037936766702853905530337259734386401500408698706339671395573248283449562893481198492451774105196822932246467 (c109)=
4600798500987782110251363579752503656321916529 (p46) *
1747074288295200317569266539270021731669746679433910536553124723 (p64)

Wol4 (76) : 130964031668092516139601951613444375622303612354448996042945647267543373754246858671070698590862134538823067  (c108)=
394864655446961643757317071454116918391217516243 (p48) *
331668154800660931498014803317744359773849829075761959846169 (p60)

(June 15, 2005),

Numerator of Sigma (Moeb(n)/n)
335 : 176474793713835254810842601328999570637766417315703941688186962353289219076814094264894616407169131676687629 (c108)=
502671255137074860363028374217705984851044471 (p45) *
351073971129922356990782453761292723716542247879553673990835099 (p63)

j(tau) 713 : 26256691609543804931544765935848686307479095886438648174880713476115522602673876496197080381119927496366221 (c107)=
84291339062731357613857041427271564284159743477740527 (p53) *
311499282150483243201333486189529704348217584567488323 (p54)

j(tau) 937 : 21982378994979046043815035463300792088083574474229217318275773572543846010493205753150814178928111299486509 (c107)=
1667288628546594418037965694953628699337147933713 (p49) *
13184507240441915844224387902211168580254246973630974982493 (p59)

Compositorial - NextComposite
105 : 122475610124590659918952950856702562561362465781915478881112593193535751005606200507052753108486760779327 (c105)=
4800793152898190213090792290547175519644190828343 (p49) *
25511536578211742842340940656450351296633604596851557689 (p56)

Product of Pn - NextPrime
76 : 383 : 9536190424504557457424559891996712529337950671153442927207611167824407606054351671676084392773716049547079 (c106)=
6051348818640501147598322857722446675548617577 (p46) *
1575878487640539362081653014162164365171939119518102943092527 (p61)

(June 14, 2005),

Wol(335) : 3325217979957081833295642411465095088793768203856018341932091007122223938781500898857838077260557978815437 (c106)=
978032807504176901039866941780664194049896689 (p45) *
3399904332905397725476690345789229928070990041867233616562333 (p61)

Wol2 (177) : 2535249397382545212637953365913824777373914073321390951401435859757500756542869240959079886408086105226087 (c106)=
161345456674978279873906152797686287628691 (p42) *
15713175007398369959588753613445692915251179215900909349812177757 (p65)

Numerator of partial sum of log2
348 : 4456951021183051616406555353906693301775103831745751988155091879908662124630639398201035512077358390903019 (c106)=
32257809133627322361077684155899457601 (p38) *
138166575501771434392991948397413539852420887611978841118210981848619 (p69)

June 14, 2005

By Robert Backstrom (June 13, 2005),

by GGNFS-0.77.1

j(tau) 817 : c106
2909178803821596509774330944351681218747348674375977 (p52) *
491395106134383857831542113628463608049743067873256343 (p54)

Wol1(302) : 584232289008998799860344971544752127949585726562575417836294025009027509683574242234505990298111495573759 (c105)=
11830412996258272899814227827665044667563757 (p44) *
49383930146291595196414982112215538670460611152281560612021787 (p62)

(June 12, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1.
320 : 930391123778138997315036818412094005845108363534818717653889429221763219473647708261115102012552323418439 (c105)=
9760178623440409559475837112181423442616061045452343 (p52) *
95325214801261620461377250817960492382025102474261873 (p53)

June 12, 2005

By Robert Backstrom (June 11, 2005),

by GGNFS-0.77.1

j(tau) 882 : c105
684952983615279352492336740971238603954326371486541 (p51) *
525684097059935235505569232549641055362987429465451537 (p54)

j(tau) 871 : c105
269085595863552455211747211021395536697361 (p42) *
526659305324107733291583295577935989295036422745867120869086341 (p63)

Decimal expansion e
c 130 : 142328323195032581858705614011076680269865126505167009448537251678827881925865144952832803327471395741481 (c105)=
701177765609534526827064986655919418801 (p39) *
202984649793203909416391112161175161242591274325425154022877138681 (p66)

(June 10, 2005),

Numerator of Sigma (Moeb(n)/n)
c 391 : 89497337694351314404011506076854642964384171906099199256708123640844153574627232980463998452398872935081 (c104)=
37620694757248189875150800487878259920411063 (p44) *
2378938992802845909239261864656929833437569688339194199920287 (p61)

j(tau) 829 : 49500652945608771100855669020041206847741169942391035985826676073144694470860969363980763103459633805513 (c104)=
935340427234076154438970745438751285248167 (p42) *
52922606041939905368454407079186071992471943521740488622881039 (p62)

(June 09, 2005),

j(tau) 790 : 53127882444826488751689500362652958819924427771707586884133309778701634370802738836009171044781409525933 (c104)=
5707644708663758907745821404509274940996366233178709 (p52) *
9308197191072967878059480703081415396841492684889337 (p52)

N = int((Euler gamma)*(10^n))
c 129 : 10088127127767241117572754316788990814558211369269470715012933711756090686151 (c104)=
3170426086997585354242379652595025322383857 (p43) *
3739905504299704703581505250837101753559098961174437840037943 (p61)

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1.
534 : 311030244866026730669899403339021199418968814685137316539267163703758647508691  (c103)=
269378861866716221346894620307638296099 (p39) *
11546200867829000582276599678960603372462890319503091668055074991 (p65)


By Donovan Johnson (May 14, 2005),

Decimal expansion e
e 130 : c105 = p39 * p66
701177765609534526827064986655919418801 (p39) *
202984649793203909416391112161175161242591274325425154022877138681 (p66)


By Jim Howell (May 14, 2005),

Smarandache consecutive prime sequences
sm 277 : c105 = p44 * p61
28475493197611851339024962994788029096409041 (p44) *
6233492256636919081614074752809064000781307721607111804489561 (p61)


By Sam Chong (May 14, 2005),

Smarandache consecutive prime sequences
sm 227 : c110 = p51 * p60
146136279270895280678880836744405148990333772191301 (p51) *
108993582021015698823608956587424819120928097943488149645881 (p60)

sm 251 : c110 = p47 * p63
54290725767198980123376315097824574442986607719 (p47) *
719687989370098249238915678281457138366570340161328675020170651 (p63)

sm 271 : c133 = p52 * p82
2461933169125535769713639083639611578977677394990241 (p52) *
1075829551870470595060810398407988637537982828486834255418641410187071177046512657 (p82)

sm 293 : c121 = p59 * p62
83393752462669798268233009801219995235992915589571746867579 (p59) *
19889582790040319807543211319311059885444058391783370159133011 (p62)

sm 331 : c111 = p51 * p61
216923389236198609558821678067350492090000009865599 (p51) *
3648342248952235810314115497899698981790456018322548372756261 (p61)

sm 347 : c132 = p49 * p84
1497562954541046535930805880040033899375103265867 (p49) *
401157109830054192006553622718777650367687499798190796333310008050388958430563876093 (p84)

June 09, 2005

By Robert Backstrom (June 08, 2005),

by GGNFS

n! - Next (n+1) : 92 : 402009715850915467674776585327198415150342953750804104217479005958448095249531 (c103)=
3259598756981910700011153017795546402381831011 (p46) *
1233310434266883725889393158777027824053018578025407311291 (p58)

j(tau) 928 : 7051800321767262803522846821120014624169270699439761263189222105499730049986099104279727311526481993109 (c103)=
134431169436410657856760777255433147 (p36) *
52456586901172072713746931207944677934033663708788307748068478801647 (p68)

(June 07, 2005),

j(tau) : 801 : 375654881493468349265354134937562189585027261006141739229063560152326749864712265063297575665885114181 (c102)=
538888245866437601253843298166443646633068756886939 (p51) *
697092364465068843997274448846555911140481820114079 (p51)

j(tau) : 726 : 168680283135942585553188805068934815240121393503315858882524011032227950554422682082116760544194835453 (c102)=
123970064547849622463602159827163002305911 (p42) *
1360653346040937460682638598199615201365048793833867353204523 (p61)

(June 06, 2005),

Smarandache consecutive prime sequences

59 : 277 : 177501766351230737991566110614697827654621213440228057985389411598588402677204439958522366115887070521001 (c105)=
28475493197611851339024962994788029096409041 (p44) *
6233492256636919081614074752809064000781307721607111804489561 (p61)

Numerator of partial sum of log 2

402 : 2711611794910529292256241048945879058739648545163158556453521753389997176176107776831378520239010835255219763 (c109)=
5875607580369964436535523341158277467 (p37) *
461503216104808264773648106386475214742726052333372480358632832432135689 (p72)

May 31, 2005

By Hisanori Mishima (= me, May 30, 2005)

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1

368 : 365414789325862528168158428144738883188489935014894933345658145497770848153180397601662772354577152252271774764365564140885410377722967227140129 (c144)
1359303118903545256461189213179 (p31) *
268825094450321778236249895774591302175413168431747366725784279642859790731479394747407606075937885514239851292051 (p114)

c 376 : 11154632152841253435261238990219918420396029371835661667898074498151392246734979295572652499413352567797367290619791132090561335407114766716810345857249557 (c155)
2136462855692215284472545933462592599336466471 (p46) *
5221074695083872979364925507456374936973610198263407103465439069296121729299914485171386372991700727808276067 (c109)

384 : 47965710844270515171907548476129018601221830003766370259485836509162826437688533324898532358290831982935488007608604992705807270459299211476681547 (c146)
481363912063010562403143930620747 (p33) *
99645423435880255602362885345694584917605119552353709576236180866161529909559675968443442964834706658051302246401 (p113)

483 : 9667840080172097706800619227151341532885535514028011036359257518932139482028708302743576336035351324023020034273932080141825556695121303318549519440906767465201 (c160)
2372143335675690838117391767297382263 (p37) *
4075571629577886066738742517051523975785026323013104342303626699346072059662358170286509799942786188737698311167393573120727 (p124)


By Sean A. Irvine (May 23, 2005),

pi(153) C139 =
976359038311791530372478550517862439745255797 (p45) *
Using B1=11000000, B2=25577181640, sigma=2971692226
9336951683883073922629400330994417449641707571 (p46) *
249189099714380420698937789850842663897905224827 (p48)
by MPQS


By Daniel Morel (May 23, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1 : 324
203147175518924862731697436199346709853 (p39) *
157710357443847388221081975977837570292996663076839427186965041876715617 (p72)

May 22, 2005

By Daniel Morel (May 16, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1 : 323
180643380389065460022902706385886849539651 (p42) *
1766330673667203602816678605695998256665552431544594884926875771165950157 (p73)


By Sean A. Irvine (May 16, 2005),

118!+1 = 46757 * 82219 * 1871263 * 11294645177647665140920980967 (Andrew Walker, 1998) *
26722464573695888110450933578985133184055013159596413387712641189727401257 *
215755998310817447135361660925170571172035520281882810599201805043440117717351

May 04, 2005

By Sean A. Irvine (May 02, 2005),

#P59+1 C108 =
18723894480431431244395492728567362363491163 (p44) *
19259944724657631476770666783798472381845864907898574445238683029 (p65)
by GNFS


By Robert Backstrom (April 30, 2005),

by GGNFS

Numerator of Sigma (Moeb(n)/n) :
317 : c102
53437626858863901988806898028066597062981 (p41) *
4177650219320707986597531350198111788646911367336837414040127 (p61)

(April 29, 2005),

De_Gamma(168) c101 = p50 * p52
11722338869822263694059758486196989489567930201953 (p50) *
2276755801653486268164419781540467835910286085471911 (p52)

April 29, 2005

By Robert Backstrom (April 29, 2005),

by GGNFS-0.76.7

Numerator of Sigma (Moeb(n)/n):

449 : c100
49350967780435495167954892564595982288995083 (p44) *
127534561282217876439720481957791148565473170914352982429 (p57)

#Pn - 1:

69 : 347 : c100
70480562484942995076658042377709050174599947903 (p47) *
48381310515443473764559893110550856049139646739260231 (p53)

April 07, 2005

By Sean A. Irvine (March 30, 2005),

!100 C117 =
1884076705873106460846681401289627891055695967 (p46) *
399185297631919524093813088285580868154108386990703259795475857191152331 (p72)
by GNFS, 2 days

March 11, 2005

By Daniel Morel (March 09, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1 : 315
1232827122718990273563198595630536581 (p37) *
11526067057709428771259691403482478386405100195656791498812773542863392483473 (p77)

(March 08, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1 : 301
29762669397705986089705232481001890669086623 (p44) *
17763104562592975546980878619138912928227958905891035073076433621212489 (p71)


By Sean A. Irvine (March 08, 2005),

pi(149) c133 =
201265413594481461362159450636255507 * 
8195878150882451442411275530077576034278876386853299457257470477282087761163969880910561278737543

(March 07, 2005),

pi(144) C134 =
6460724926242404313133972681735106778274913 (p43) *
5661526311202224431186163832029359287700684130038956598108043482255087785695468690840870049 (p91)
by GNFS, 7 days


By Tyler Cadigan (March 05, 2005),

log2_279
803111368988845617343256117638865146493530148022959720845614886060725746352341762482809670812285230572940156079607979 (c117)
1187559694642886647156248613785257127792567192337 (p49) *
676270315178009453263884613454269230758850391541269829977874780342267 (p69)

March 02, 2005

By Tyler Cadigan (March 01, 2005),

log2_270
697957153906248132562379431028604476373837216382573166096549695038121360349276640606010833354885204453411000407 (c111)
241925368237708472403653722677816817276081 (p42) *
2885010195460183266645161513254185315471643335534114524965240401696647 (p70)

Sigma (Moeb(n)n) 282
78921231421538183141733904580129006436572384119637384419106055104949786106272354298530399253660407277 (c101)
100422733105511161750867003092498386480241501482183 (p51) *
785890096604102639195588673714364528504287838792619 (p51)

Sigma (Moeb(n)n) 283
32129154087299019138922925030027397840937917592193603110727841938306518293713544644153176200406606426679 (c104)
62194172833363673878620173394050167651816759 (p44) *
516594282448009919858082340220155309095536004892601833818881 (p60)

Sigma (Moeb(n)n) 293
2987397391352753092001147922643178620725714360443364434207257576923373138513572937823261610642184440536427351713 (c112)
497493298042610932582516546068684783970867 (p42) *
6004899770723903727253955079844891160186059528778097427520051296843739 (p70)

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1 : 294
92241578283944685050275093295839542481908968597712085791442139247975320816494086725436467496307524639935260175887 (c113)
14973467017255433069226545456639598734174287187 (p47) *
6160335357044926910567642308760411556659843450131718961340991910101 (p67)

(February 22, 2005),

log2_275
101478651430299825083769428290201247872466697311269177343201977121665481341572769348384132919371831373 (c102)
196207743089013680129314754037808050782537498747 (p48) *
517200034171240360678222461457627105199478027930239959 (p54)

February 21, 2005

By Daniel Morel (February 17, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1

358 : c99 = p43 * p57
p43 = 6215932820276088407049951544334436427674259
p57 = 158372088238673566357098870786130795824701153458586356759

561 : c228 = p31 * p197
p31 = 5421654433405748071759906011943
p197 = 35998435614306037760690767416361319688907261845899084987315689048080055684789601876003987626178971431732443901258106111212063743419072939526349893533911327820015204316960515944107728381541768262509

February 13, 2005

By Tyler Cadigan (February 09, 2005),

log2_245 : 41109900178980375410777297738796820333773615291314628594829958175632133435856417364136399957167008687 (c101)
142395222366879106723269450527595678004717654012643 (p51) *
288702805442877486727697590036882729395684350714309 (p51)

February 04, 2005

By Daniel Morel (February 02, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1

407: c123 = p30 * p93
p30 = 360804280516777216543370629853
p93 = 26893982313992058982652122949407744212679989601829543024859715008659292111894052462153082713

417: c164 = p30 * p135
p30 = 105438089850069130177434955807
p135 = 888620494896723142642140516080701905904986630195859046368662164942125418782208375869119861365900532477144096236023890504625377586221607

February 02, 2005

By Daniel Morel (January 31, 2005),

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1
340 : c99 = p44 * p55
p44 = 24410023694925534140391855068803312133966107
p55 = 9468923303940961503320011988580720135071031226356291091

(January 27, 2005),

336 : c99 = p38 * p62
p38 = 12543634785423810885088475985019547461
p62 = 17749170789100631267034275397065259177807883123379497286654777

534 : c135 = p32 * c103
p32 = 90398943039553849836490168760911
c103 = 3110302448660267306698994033390211994189688146851373165392671637037586475086913218197515399520907760109

(January 21, 2005),

c 454 : 1 : 3934311087587104886022408351271609393518918160698398255383548562990464262243572521171803516506182247115080986014108116415933788634757132817431296991233146877885879698952879588985392493740151 (190)
    = 227 * 28433 * 120349 * 151049 * 85642955428295087753602499043191 * 391532816307551934169538573430085188244175427143102087505597344345393066249809029260346477017197800499647741200511185465852949292549341331871 (c141)

461 : 2 : 1272331469161511996192155511097711449697440386959592700800538970999871957489839314048794457354018513786340695902573008119148459290781525828450960810758657463596101523914950359882502420045449623 (193)
    = 17301397 * 1007013130360416051802729906033 * 73027084763193864062470347106555827241924349970568919068475678392965958252498483666311424652398156335095924390712153603591921129040775890324960385144273323

474 : 2 : 65315168584332634282655072222956801490856044164844272170735890027559474777716027895997863194337352419673556373594186640161668628060221832236952023691301180340700008585954254031362264226008126773 (194)
    = 3 * 1848138983046485218571860393 * 159290215995899685791184682156091 * 73955260045287882237821065129907302487417997020436017349017853773884108748851476834481880001788793686269363188132401707350897592429757

c 486 : 1 : 1152769050892054595234280319344727806756285202945596358130451121759044422975726398683624341177928435114455051169815786283620359960635433622860974936278629848801907238699031932761547821764295555297715223 (202)
    = 3^4 * 2705069 * 1585672072883 * 17089900378388916821660908865791783 * 194144920943987155154806217119965622518747737706912298661082786867981638627067408743725772060149428437158425666599517638102345781000741891670838663 (c147)

c 488 : 2 : 297640494160897205444144588107096987790694875685968038079797047206052764547356732046371950218045823786409785770200587396790420727047474691984166925530866420653061442291403320895838290109859400639771021147 (204)
    = 332183 * 5685150774680454617980631927 * 5627894384491138986812472480299 * 28004426824642207882623132832038584700010877290716722725034981115527996393160088527506358170592948786783407057600216885792055389491168801633 (c140)

January 11, 2005

By Daniel Morel (January 10, 2005),

(with ECM 5.03)

Numerator of sigma (1/i) 1 to m, where gcd(i,m)=1
-------------------------------------------------
N=m^p.n

m : p : n (alen) = factors

290 : 2 : 1136266232709363957704149781794636466138356029420624917626758517649237519917371910825828260297995767056936324992692124 (118)
    = 22 * 853 * 27521056043849 * 41914893203719087475161205726986204333 * 288693907948514687456648150016432121647164816133226361724902431

296 : 2 : 37313093963629312466314523688452375817730670258838236535733576957733404944461039620883776162893628821138142953799138381081 (122)
    = 1092430193 * 587136435314616870202204599261202439 * 58173947571977173517603594809052832194738155573543766983963999565788321050703

299 : 2 : 21706203009888445920506438603880764029930739927215474653819157704576006752979706769142424614047527848149427479318339696807 (122)
    = 19455341 * 1238669637322888744428552158444017 * 900719408871244068379967739589623673370707348785867398621761622151979425599277331

387 : 2 : 1153403160597213791079262620864543014924394587886004969876155733143006652059040185427582078413005567506787297934144370814179745917540369435665980263465416511887 (160)
    = 3 * 10531 * 25981 * 61351567141260516412183144154059 * 22903863464782195111700993888899629931865581780451195823454681595607581086582999364875362544144712873446525166570502121
c 388 : 2 : 372273498775558576421707970522221693772760784488679598253706521676327086868404419022801816094679980186448023326392758282583098192355774698421764240937622915448 (159)
    = 23 * 523 * 573163818473024834130222685863911 * 155235726247407702979413744918725986388844056702113632793215912857923855738456521384850191137938870142533533833908546332427 (c123)

Old log (2004) index Old log (2006)

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima