Old log (2003)


December 31, 2003

By Hisanori Mishima (= me, December 30, 2003)

Wol1 (412) : 318374342413474731848149836073518516852486679938442947814238396766496475250619113620107726911440994360091381764557431356569527110007067050010150247514799 (c153)=
14254350629519738347268653 (p26) *
22335240004139107607084938214544959605419831108448603991473997556506446931388792199437089288953302767237830829380641844538062283 (c128)

Wol1 (440) : 7050727669286821324506519057212270604734383188532415233589152980342222003379837319921838127548583017476847634857850242747326184357065670727577308671710493577648401821 (c166)=
71371673408096128843531423 (p26) *
98788879853936755599468701545212076563241917361791418995736525597714038511006883386653906569363441494591764987717550105117868046073519605827 (c140)

Wol1 (529) : 34521964834087779959012580706924770501177443588575348597046790849411150282506429785107539112474747617735498530440823535980061517157477774687093311142907487523632524017078798514520485404818061325882586536071322867 (c212)=
6945191008291999498766849 (p25) *
4970628567719927409760618833098444696871298944261585658806321361327151632587936473497435064216333181362619321142069424053302177352339510759795720146019249291150356267850441146876178685683 (c187)

Wol1 (536) : 11449712777954538150375591732425855686536886770106232648011097680802780228072535950502526382257607037564954187872077190849568607204169111984923075420805867306285485918199825681040339248662033730466695295883514629076259432785653 (c227)=
1178032657910421797816763349 (p28) *
9719350903449384788358392462507640116347104874205635262940705771690094159189529382023541205705688694644894314979259547930736919625258809932393645502311728752485319841518330469293572145235754375579297 (c199)

Wol1 (581) : 14670902671387267647856234362915462707601395562346268856225606770085748280781160864174699441840263349398643603679926535308933779523637743387422592117101413556164160962484241269827022060408789369467181112749163222257647060151122462062385337247657417 (c248)=
1224321279015438856298239881338191 (p34) *
11982886292056568583380003861609390746470943543174323444889559719323387646603246447277150859297220267417788458795564366739289108716182701062805306323246874622636932110031888584741424936824712860104100054908337302887 (c215)

December 29, 2003

By Hisanori Mishima (= me, December 26, 2003)

#Pn+1

c 109 : 599 : 1677112828986089396946444699134393971234409713877195654708875854664975605451751075607661851611647259159233381017375505847474015551845205099450648535893906717311497755650536765716130081033589502463136619918606517 (c211)=
190883459271153022334840970773 (p30) *
8786056347625823691111383534521124896172840316511198336221135038106788227120208380917875518202863235761664389600591723596650259980557873085823826463284492775369060639520274017181729 (c181)


By Sean A. Irvine (December 19, 2003),

pi(131), pi(132) C110
11867444257312396824165348217581065703143719 (p44) *
1367796845918610240048347435605564570335668940406626975998006383429 (p67)
by GNFS, 2 days

December 13, 2003

By Sean A. Irvine (November 25, 2003),

!97 C118 =
2806086219469865361296006323835845391645130298311042021739 (p58) *
2331411033631616484345611765370372580434283837051405784144357 (p61)
by GNFS

November 24, 2003

By Donovan Johnson (November 23, 2003),

Reverse Smarandache consecutive prime sequences

rv_prime(61) : 1564937620624148229131946688599432703087526807483861587050261907538979145771761205716244006834678198489 (c103) =
16138716639540267077347782537646347750869 (p41) *
96967909876427917117386957106121190007596036747602856106484981 (p62)

Decimal expansion Euler gamma

egamma(110) : 197484523580330384354433390155602917382463404065882360582778131846035953653865648115171225004361083574411 (c105) =
59714912509794593604996731 (p26) *
3307122379990734552955002195256293957381227944311102116030530801899965970303281 (p79)

egamma(124 and 125) : 1390401698187318436667011793405804266113482072362160598542666335383807172561489716884489248438149331718611543 (c109) =
1244375892429245928967300135441 (p31) *
1117348629659647155996507159086725815582551471403269050405366920274714452520423 (p79)

egamma(133) : 154435266808805989852931237723520598636252222235722100550674590431235391186296734758020577972805550995137655911 (c111) =
59495314306211960689548782154787 (p32) *
2595755121385773754609577444777436789502796210307537569823107205611473649340653 (p79)

egamma(136) : 514049473580809928144270684187706755868976140894992786055263774854780022083797435949586106994169217756532739409 (c111) =
4421564533058459953190110185736201164227 (p40) *
116259633832650293559000419451587704440239206966230237209513386660600667 (p72)

egamma(150) : 597079727983050624299835203857476773897231150237779276729314701746984852590530064529749549272974004348477794680207934893163711590456797933 (c138) =
344428097543763787706738338871213 (p33) *
874457819229902363377702060187867 (p33) *
1982416427959383069197431654414542534717978612610542656895437282358421523 (p73)

egamma(182) : 22512236296267766627800502759594919813251947158751551133971489423248990930633679164926532241734562884662608769335279751725608577958353989431471385354245521061241 (c161) =
5141849788401460918430347276807807 (p34) *
4378236864688057984745864556839823089196177463599737932001844017544659581947400856976683504053318965516178402786335904405344263 (p127)

egamma(183) : 329706255921200009976789185003244845729617921027829519806609488590047941884238854042784504559805736320833310649123305569249020164285522969 (c138) =
811112136103299678893888960450113 (p33) *
406486651161646617795321500887353326073989274896777694136967574481391372855706806101648183870342856855513 (p105)

egamma(194) : 159801446788361476403625253881212026605521389895174988468843304382289182778878795215459309904993416830491127630656743283447672091695884792049185159194287 (c153) =
1449673127893217611139021246709871 (p34) *
110232743998364569353093052015784343510632172349690039714225842829103242995893471133396783749482477566632177210833640897 (p120)

egamma(195 and 196) : 12297340511036442821381984500347308991966535696250195094083121121004223889925534697153003299199445450597490470134054310647580582333223185917487754467613837957104070809929953 (c173) =
24290697870830860395418415687 (p29) *
1623054043758192895307956243381 (p31) *
311916411270394519426713434186032475753147329924663583387682765109376922246156701102661866691878495533167606259099 (c114)

egamma(197) : 125128010187314183873849105841752058462416524423932052323724881140963347798124188000042450301221088014891218064948810447414622522111606468447478388737590589424902523544945453599559075511583 (c189) =
8152168315808270139534118183 (p28) *
15349046454876589229751488887642482915922540614148485105172028155897297616709980552530728784356854119725661435883754283199191541125699723712508411765439770409801 (p161)

egamma(199) : 2239874524258955609648863368577425033147688536825469921636659817170615936273436829402200478431302869672609418897194732172916197184658683881351082645110296997491270212428938058741458838931297082837 (c196) =
581862967168399518772500191270322821 (p36) *
3849488024919626271269290248905479476104499298477322574049490149798267618779229059011330134369853099734210009913317651166054109402544697161297640218421815105297 (c160)


By Sean A. Irvine (November 20, 2003),

pi(129) C128 =
92961936886277006490094628597583160266697628297173 (p50) *
128495808233677881108095597469943022610206003555063421624970650949026441596891 (p78)
by SNFS, 8 days

November 09, 2003

By Donovan Johnson (November 01, 2003),

Smarandache consecutive prime sequences  

sm_prime(45) : 76035848941688042378755959793424765076768999906487197003519778294552810940295198618166683005780038425587 (c104) =
4816974392586326891872084844773520489505127 (p43) *
15784980932992446676485129331868006720498184905390623831448981 (p62)

sm_prime(66) : 2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271277281283293307311313317 (169) =
719496213832163304035156894278359085943 (p39) *
3276057985959286871096836415452067957776858665246311365616765176363487938478589627685667904261452904203097941728113730342088282819 (p130)

sm_prime(85) : 5386163818080899533075811183582210707195669136965739908887434831995339056823980060717817143545288386436247517206985020372306454144040622830646774836244452286966494799185887237441291374063374882353225140579649618067 (c214) =
938138966465927005668231226874933 (p33) *
5741328321934193723149115657357374392365078904908896416466269626590494391630765328198494888925304626136187644678563034520281856129055051798453709045769681084532276891466576731320999 (p181)

sm_prime(88) : 822204316052665490624293516377120348793686194386558717033450370940484654515132138755436444621587090296159794456167322636724966131224255912235744007129358853381376584544791801177436910038419320694664915571163679259339947 (c219) =
2710464426574355359207102208147 (p31) *
303344440897833788912801102627243903508730678399658794543979332762871506152763761544632319869733028538793052831369888545180167305552151471455313367978701620728616665737817976008833715659401 (c189)


Reverse Smarandache consecutive prime sequences

rv_prime(46) : 766494390381027843399937644526725765929139631799053346601041026484667587287725060165333663336251 (c96) =
1606468571835626548618972323451650419433980281 (p46) *
477130025335755745131310913072860269689878766892371 (p51)

rv_prime(48) : 284395351936538336903622013804630521537004150066284184113006502862655998270313210647905694141940453601 (c102) =
172266191420204510230566152849010267821976023136971 (p51) *
1650906365270594717268506934549014952293877906182531 (p52)

rv_prime(56) : 21709813759454546886436594814639289874568091503614731644490193914621476997131463092494095331990237024618493 (c107) =
68789862089102535788942220130059696452147771 (p44) *
315596122744571461194921635269112846546278413693335370079308583 (p63)

rv_prime(80) : 5849304207984962221518002980030503212440389805793798024806073117026956814136284829887332923839295638518170218511436617811953190998282316984234609067781607036673365288697013233025531252299415891 (c193) =
151015708185993506122507878495593 (p33) *
38733084645610905624075576983352943389820494901714870771781753889708788652895810088683752430943419837761176092906954187262684146380181837054759696859436998180187 (c161)

rv_prime(94) : 35617147610333169508462572930458785148874188361698471696344074084710687757267786063273108033963868450863595257405940174809232664354471127243542127687282771985418365498431625105517460946206350872417688671635590499658187587478156403859331 (c236) =
3084553936084647025262438529078371 (p34) *
11546936234009738419875885675410290538368463336965618151028740683046347994752142912993047848383707322676841244665470876951942314551346572115791029498283263388439983170745578655776203699996102368906289761 (c203)

rv_prime(100) : 11550319636426873980887655316887248533622241831610986026360100368732165568416167589665549709158735651571794354541256991069039441213340435916054215309608022358903319257430744397795544325847423094304579727746344969907 (c215) =
1473077246128308468292532940391 (p31) *
7840946336510593393882369102509236598198134996592335583589987735439049479786340928615738592162271198258821714205406556931357184961077445156724978307923840251696874911830748062585617877 (p184)


Decimal expansion of pi

pi(178) : 43378547775876936248689100796981885808463015830020761139058977102134702068276466329451461587365549 (c98) =
3066701668625813290440960889431301832173 (p40) *
14145017175835962830452697638426074511151431970214588210113 (p59)

pi(230) : 334042482998598611579631453729675408749685403429533132188862574407815730212596127076142794859321256826895762776874066321928320540652143112431097853182157030739550892310792806792207744905931750040257765991 (c204) =
7176797356030663837193688482587 (p31) *
46544784034887464906675327005063750049040575525585146389684592097678499144684106288570001839534791709800816587195901634897328109129370235849342917598674296510347111076464293 (c173)

October 23, 2003

By Eric Brier and Christophe Clavier (October 13, 2003),

NumeratorSumMoebius(349) = 85711 * 1042333 * 441983328758242916140415831 * c100
                         = 85711 * 1042333 * 441983328758242916140415831 * p39 * p61

c100 = 1337999964933850799175431891040949498928914886894280109064577042815153756236658658715524954229344719

p39 = 133999105227930918009955555607384892653
p61 = 9985141039993725595934239074569361978230861035614702794042923

October 12, 2003

By Donovan Johnson (October 08, 2003),

Decimal expansion of pi

pi(152) : 18724976406509085702506798269971107132895009947667608605683025701889145724514571605130681909626130605836585018561005244669149853384752329968790199 (c146) =
1207553142685778828505209347410873071 (p37) *
15506544386826684153288191271946947540722092963502685116472832255828367553839961651266453593380773921043037369 (p110)

pi(157) : 14803750492504118933568397901309071255416281656213384834369872486761407226174389934180416236708890078965146321203415446068262460712000937 (c137) =
2259864614896157251149056187655145909 (p37) *
268096620753598537265152880052986931161 (p39) *
24434192711933854450651117794533645172809326637935988399773613 (p62)

pi(163) and pi(164): 16085983889348659695149223672706107957998819249232492682923423411714369719847460310435406171746631172463635875644046629017377596567079274099976238648891352367897 (c161) =
79505051873425600355704675501 (p29) *
24463026450148952284697976321371867 (p35) *
230561605525245550298717213881008439 (p36) *
35872011615213920177923032254365901554725242399272730220066769 (p62)

pi(171) : 84072635839911083084952064853555894840378017249059647821310617567644847330563060367441500775901203094557470476528913060545577152790645657570679 (c143) =
21569901587347233434282156073936667 (p35) *
3897682866074250173518994552466340477290976844298056080427223267458190237282773734604094317590393579745742037 (c109)

pi(188): 1762381929329515192610161836876272679141108059028457843999537085028436385438872455511294568175984174173612693336716684822847479329677686119960984943755388897 (c157) =
243957365719807575465040506904051 (p33) *
7224139038104158842550448857241616139227283357094244166022647161124758805252291406069596937133695249753103112970527350723547 (c124)

pi(189) : 2753572766016765278317663992103604582235697324666722868460340877103360540840908529484719770095957186924398359091441395317247165429 (c130) =
8871575792756196685579961831861 (p31) *
310381473409166793585144293640538687260614167058701153296984523843789646815481866370749538143981889 (p99)

pi(199): 37522191372754961209246739808048991395534742725442519081531022211355500574988616586968762214115249287615963054685310403261134607937843217098209 (c143) =
785104609139512346303905301171549 (p33) *
47792601057176195102165785242434247783297148185337755398706433767253917394427936963003305569621414286202400341 (c110)


By Ryota (from Japan) (October 06, 2003),

#P63 - 1 = 1571 * 1847 * 46499920734701574780956751713981 * 
4650259363702349457361134214308129104057050712996780271476630865740615078822621739277

October 05, 2003

By Donovan Johnson (September 27, 2003),

Decimal expansion of pi

pi(138) : 6333555600240737178684632845484438478630146634261836088493270238588425622915256424280959233153430016765343101 (c109) =
259547268142248930064373476846436297 (p31) *
24402320415753839522038936745039592429894413102757236423786737329071974933 (p74)

pi(140) : 1060260477788613898758424513169319782062237910405198001928011349701413934483418044682620298420623970851706328558136972277 (c121) =
501073126975745520869197456573 (p30) *
2307819174811593592205993891347463027 (p37) *
916874055494699722268649960415379234756271621094568387 (p54)

pi(156) : 21371378595848933594983968593738114858484145573980311707312548246991948342083054412435611056749095700558830520498519092837373092581976749875682717062098511 (c155) =
2850809297215988044431817625021 (p31) *
7496600567677241407033655869984922713719784170172396724500416010398096070578977312943210144676509900775385624176139045629691 (p124)

pi(160) : 15707963267948966192313216916397514420985846996875529104874722961539082031431044993140174126710585339910740432566411533235469223047752911158626797040642405587251 (c161) =
1609397104148965849700544971573 (p31) *
9760153803840221516712852360614761538191252257302253242662826235086683752993634617350679394169821083864425144305164020965457874887 (c130)

pi(178) : 6827465596293043236005989382413968299311898592472080377998647488554518042077052748388146019767952178258054633997907947451944348481 (c130) =
157392673253341061059807576794469 (p33) *
43378547775876936248689100796981885808463015830020761139058977102134702068276466329451461587365549 (c98)

pi(196) : 53120450077209979382192629973276774562107713820468719361606026729263689390719858980778143700759400830081191299865404481298683901179840263 (c137) =
651321602496223077203528675021 (p30) *
81557942917328644010437832158340486172039242274701693942171679523658962932965103722742348180582375853991203 (p107)

pi(199) : 210677017322058453721851310496300774816471841862360751024814298590350107613993422132739810302952771735853034997772134753583456962715405361009853472588331471980422583490987547 (c174) =
5614731166128853075001456341883 (p31) *
37522191372754961209246739808048991395534742725442519081531022211355500574988616586968762214115249287615963054685310403261134607937843217098209 (c143)

UPDATE Sept 28, 2003
pi(158) and pi(159) : 7027646433017781743751568046163687209190271354307600325679366854627644330119289331827606416299314729763839287272463271 (c118) =
698225646938987668521752591471888923 (p36) *
401240133972980946960221959312887293333 (p39) *
25084747844403021118591433473785821314151569 (p44)

Reverse Smarandache consecutive prime sequences  

rv_prime(66) : 12311328227693219695343269246185493509414175889011293651729563877764060129666454255714670951949762511797743346070611087865192063321592331847135565612146687745993 (c161)
7414988455353286221620881128354702401 (p37) *
1660330060096721750292749164284704077165073170580742002796230584842166171192530998380596544783145470231641767804858947942793 (p124)

September 22, 2003

By John Dilick (September 19, 2003),

DecExpGamma(116)_C109 = 3985356826070059943652401227 * 1502879536503277035547512732207213045812202537854730508149754746946616457985812263
(B1=26000 sigma=2987076780)


By Eric Brier and Christophe Clavier (September 15, 2003),

Wolstenholme2(193) = 514921507 * 719988668710825504369 * 58696468410756153296430694389791839 * c103
                   = 514921507 * 719988668710825504369 * 58696468410756153296430694389791839 * p38 * p66

c103 = 2776520438548190467371766696805836769424719312441403594593984937191761303803681468501643564320063941293

p38 = 26389033943954098514625813791329754071
p66 = 105214933007591571465082376457273326625611594723096651393079475483


By Donovan Johnson (September 20, 2003),

Reverse Smarandache consecutive prime sequences

rv_prime(43) : 5728698402798127130737930585193541931342547537860787291012032562660129311576887125647307 (c88) =
116713367662855148561752006884036975853579 (p42) *
49083481331344753518433092671989963181080704833 (p47)

rv_prime(49) : 568058027997992982977952947932917907892877872847842827817782772767757754947459493429190398836858534328230797928279383 (c117) =
349861990565301958632269873 (p27) *
938133127024293971760278606286486485774326439 (p45) *
1730738550132222350258918319901476137725200289 (p46)

rv_prime(50) : 3600348685872879327687989035312831305616704193879195242486621388154979651695950443796001105449956796070682683 (c109) =
383650756287733427291486683 (p27) *
9384443082324230729233737823216261020301901551838110330452800701979718008833012001 (p82)

rv_prime(55) : 111421032187002280309632989856121034054599454982987492993026549279405928500272394028217993657968749321808098234173964502444935611 (c129) =
22874184939239723262444320549 (p29) *
4871038355376067771661851790054045267276535569218117437617670620986322591589816578983635334080255839 (p100)

rv_prime(60) : 27891414672608957543951820706603350598417481061955010823743652047342136602124387773143840839412151803481787991867770975571 (c122) =
12607180615885461216371981707 (p29) *
36371803279457107812112558769327 (p32) *
60825786648605084300111218796912583538486972082661669456702839 (p62)

rv_prime(61) : 13277213840422899913499418442524212466305973015201311704996302782039645389249124934871155663882428527022350959347988317387185416689 (c131) =
8484180880722589722880643801 (p28) *
1564937620624148229131946688599432703087526807483861587050261907538979145771761205716244006834678198489 (c103)

rv_prime(63) : 46167686192923247343855349489458905360522360279918215133985701437977933887482384346044913969 (c92) =
10088476492991905391424534717859 (p32) *
4576279304907360954640881960377460029870540888968831309163291 (p61)

rv_prime(72) : 2138765923590202044903850224912603848710985178715729772866503055473590253752553544754839266096126949201615427781828965870561467 (c127) =
7860377360666779793479181428566575831 (p37) *
450375446606864626540728435662056910153 (p39) *
604150520604540320934537226171028855960276657165269 (p51)

rv_prime(73) : 51247050018044101519351223886963240511589933216794439938794046264052400706883434406450141341328773390598622169124372124761052832865508217608267113858573373650488189099856834341320123223 (c185) =
6412884684411368832699302605439 (p31) *
7991263298811057314862289359865191975672613418455189598426097818571870854537523077460504506106924853965292260991625659133741434839417402905537849856258857 (c154)

rv_prime(85) : 10500456757035772276580337097663780483747494025212427721740763640936676706717599351356693927931039571937700760520313355074891836188493552611496431371372006900465619824639116852862344031961669882627 (c197) =
24267743087052276441885461707 (p29) *
432691936756086224578639148497942162732858831544251079736655310607971541475510475892550422180544239448452440377993898369438518693537271878244142122963669530285799195561 (p168)

rv_prime(86) : 222917194141527216536052571716016901802836394615940690271805236431244331904072001467925174100134856080793341078835019670107057378195615246784072530833615106697742325853930507413309999699830383172405302008629247831 (c213) =
3340427364071833505577568887871 (p31) *
66733136166685270102767102494831260488442693622905874073397696070054771170456069155618125487606534542631085593121021721033413482281704243310413524642325980204712228097554268840918761 (p182)

(September 14, 2003),

He has run 2900 curves with B1=3e6 on GMP-ECM 5.0 on the following numbers:
Sm(n)  n= 45, 49, 54, 58, 59, 62, 69 and 74
No additional factors were found.

Smarandache consecutive prime sequences  

sm_prime(52) : 32356858964550791309112011394145475479733032059659737394757372410541567333134701241312574811175413498461679310959867 (c116) =
53404874448534840071487306149359 (p32) *
605878382800663995141058117639985478719138243641595731501044246289517491841124709813 (p84)

sm_prime(53) : 1137057055760597992246686194114581051349348018590078744650422421653684860078712835577914239546000006364323082234828205994537 (c124) =
39081047667186446148508593173110063 (p35) *
50394127357598746888545910986174743077 (p38) *
577345959345270247313420614676929222255393278474587 (p51)

sm_prime(56) : 8014040351411677275139584117656322872572809300398934852780594722312967355501828754069845731092580601516913887026713 (c115) =
132638207270881221255323402440482150228239 (p42) *
60420300577833900197416080699725779483003888688559210047422222276838817367 (p74)

sm_prime(61) : 3887476271063651237571151075778921625700824078758758463435772861367413156370357029371952373897258017913167917083411793787696620534067827687903 (c142) =
88577547579846682973920668362263 (p32) *
120084327060080362294548390666359 (p33) *
120844217778287124562149093554238437561 (p39) *
3024348928732452974578444617240975133319 (p40)

sm_prime(62) : 135008380617007234878368449143488614318107508855094971482279232895992733784818784418532972860941702915012154144637334740204664599418709964102713286974127 (c153) =
81395714265253088040956686461583 (p32) *
1658666943778399757138220126720697437902439979943829089701530008529751846278440488019352365856102472586436640797664550369 (c121)

sm_prime(63) : 1255811048181699339391817274922865611143414968579417013120991377003324015066299151629628678031539874434227815406114321 (c118) =
7102067243719626554227868240167393 (p34) *
176823311450932229516940629409802081101703930041279701900641473843754633382230440497 (p84)

sm_prime(64) : 1011888947832152557374413749704826451159169439006027305162241508124623946313241105891803474079214323237615763605753382597119038472395134603752471660197072183 (c157) =
15436778485674892152416973119591 (p32) *
65550525893156458146993799938614834847553347735798507338900157168971276188901880668326696493200423495446036893939611652942513 (p125)

sm_prime(67) : 1045342515690804118964898189773990369986877526369841059133842612605188176029087429499037527557506772712705173436357176358491825219751986115691 (c142) =
1320859610392348153944861630769 (p31) *
791410765736334057497721631901506822030180462713167809014790668498563275204070321326862031885390393715795765339 (c111)

sm_prime(68) : 350547608588397263028371669248130674674498290774577814294185552471609459047300432025197567456003118011814481157743822832705940238011549640530174702940087 (c153) =
3015004170238185511004806931051461 (p34) *
116267702727822091483472269837864495956807733756797148311416887823025220899563534161909069758367262478558445728620200267 (p120)

sm_prime(69) : 6016214523859505226136593069299798522745865479553272265289739624576293010950729415783761346126017160534313061127512284966949105864348888225190466961728045767848024701 (c166) =
10014372271620700533397713773055971 (p35) *
600758026632243058398982286695184830224397954785808745757235920300738139551282434150698635093115906508337179375496689279838624217631 (c132)

sm_prime(73) : 68456051040642857836423897782181387602556669481100937551736050806231825824137743991167420052642698843725325087679738001188382547392526803869072693353701160259102623316147669320461 (c179) =
3897362220871782833539717852739 (p31) *
17564713557809938969614902878156556166407416855827676394970079514330231977359975148722754405441714326279652182240408180100206160165894521457393138799 (c149)

sm_prime(79) : 5847943553878086528704648914748974583967175809453995389961854968183260713505209496741279968411491479890133217668024714360246031384852035824042735891160106957532044598749061223595543027235423 (c190) =
687018636860794953485021121527 (p30) *
1341363587794985571347403706577 (p31) *
6345825721429516767962996790871904541074303880536743771758400771782756641776791142379505301112745816311404966767841395660488518537 (p130)

sm_prime(84) : 1186557285034828544703171369428088471553445826519918611494015126664773835730500993720250715791618494672141059671897569127480650929678695940883864324622205181278516674658048504108163216597191573205413549 (c202) =
1307827621652005575321294567353 (p31) *
907273455148475713073619753064686995562184831226179262880543302855533170059386086502876916206328896449478717135089826066914711509958106065962287312045290618964977921245333 (p171)

sm_prime(86) : 5820172766087887200405159234744728990058977448158029011862956722200655963478512583117651967790763192610994444205574953372685579051784850471966081836371359758100795575325241435667981601354790051 (c193) =
165832762044239387599737384054677 (p33) *
35096640098988602358426117417891760469805799314782469821964078260041060740556358345052741915392190543536489408380072626999648201863294650891165016887984965330263 (c161)

sm_prime(89) : 1152093682187113506643141879741895850910188062378387312259876968409714288666378845962888944844085135147055408598499956161819082975530339260579433970505738598406391452269605968507251694656539 (c190) =
207848368271252045878278225127 (p30) *
5542952738910012687745497110288852228277203935729668141853652678830218159374779521441472692434506608269237820616608652551758167097827835668802249077136202230957 (c160)

August 31, 2003

By Eric Brier and Christophe Clavier (August 26, 2003),

NumeratorSumLog2(339) = 509 * 653 * 61813 * 718171 * 898481 * 1192097 * 573240467801 * c104
                      = 509 * 653 * 61813 * 718171 * 898481 * 1192097 * 573240467801 * p37 * p67

c104 = 17814750668637755014003269179483959273194732404337832837054251482094954210480616728284928139443291407137

p37 = 2956352602718751512211953577860532503
p67 = 6025922162415528520672576633583294557657162410366474598917605279879


By Sean A. Irvine (August 25, 2003),

e(111), e(112), e(113) C111=
466704426641249074325700341346542812672357739686022249 (p54) *
1456104588519663169704829557275116260157514491194015717767 (p58)

August 13, 2003

By Eric Brier and Christophe Clavier (August 11, 2003),

ExpansionE(145) = 2 * 7 * 139 * 811 * 47521 * 5712554518722032579350362935093 * c104
                = 2 * 7 * 139 * 811 * 47521 * 5712554518722032579350362935093 * p37 * p68

c104 = 63447550901449416690354813949829559652215812340102960229849820330764470899909189746037082002403127256869

p37 = 2061498890404368057536789745175812127
p68 = 30777387849577752695061923434336109649904773513269460470239586674747

(August 04, 2003),

sm_prime(47) = 11 * 43 * 5483 * 733511 * c100
             = 11 * 43 * 5483 * 733511 * p29 * p31 * p40

c100 = 1239064959397344958709288840487940809660589640883722704327411919045274472736100816060343535916588239

p29 = 65892911291742926896163302121
p31 = 3125568541217689315277975113751
p40 = 6016256615536852144859495812015379557409

June 28, 2003

By Hisanori Mishima (= me, June 27, 2003)

Numerator of Sigma (Moeb(n)/n) 538 :
4874964899112372460358581791384750273890599470784740203987059700004802233952118117324716559475285987890738761820978515556127786751921040922075990699629446243073759198898010603689470162266264554434077808537087 (c208)=
79374701109660060064458599 (p26) *
61417111887796191909526401011589106198365028512125579235086909178577545994882675526321330528352590192100395194260951114963291518535431660069720892770453299600761117430450820008844713 (c182)


By John Dilick (June 26, 2003),

W1(394) = 4030764905976753326698287624083 *
13303454915663158655407709865857037751469547897082115321382077647255222224846398768212385261442919070049141080821751709855319297740737 (c134)

June 26, 2003

By Hisanori Mishima (= me, June 25, 2003)

Wol2 (297) : 3811502969888961854890590270554482002073461506130405074085020416957189343875470123898973976122373809651221284328648437489491573045655609760875416379948234842876719343200803785804296797584904507578482986940898438398621608279690307137075881839829649548853779903 (c259)=
13441724821699523137457167307089 (p32) *
283557580626550066944042097995759422245515560148554484833558442303975027998738138971921451805526950006199058255241591227289243220137925873454942308108746112280583679568677734454098304789867518298352700613284350167673007741696527 (c228)

log 2 (432) : 61981557038199737344863706789002752797113833907255577249839691382683556585257868532628662995748328070554429966019498054625468510335115742694289530760899 (c152)=
31491126464550777896634841601 (p29) *
1968222924891928174061752571327345088007303338146146712380486593604312257507301461919180184517863627388796871650852501602499 (p124)

sm_prime(100) : 54816542260286728226544994269678319008833465048862862956025886677468305561608166445655050539050725376585981377005191330912400912587238541006262122727471704495518867751565845054589519845566683101846125334823288591149335614731149847661801429382964639243988360546733058687 (c269)=
980763094841480316654607774669 (p30) *
55891726094308908461367256275435556930498574794195749936799803472303671719615153847450729790342299626751996861173939393862012812270684958898331610022406768511895766797735267847949252069412439171154790143794050398738666909209669509975417723 (c239)


By Sean A. Irvine (June 24, 2003),

by GNFS
pi(125) C115=
30899580435462147410542820672922039628357 (p41) *
253822469680412348251198675435958669434219988379646150451048380232285775743 (p75)

Compositorial(100)-1: C118=
13948046914431107377095937825626610981534469 (p44) *
118206984914353818471095171880306951413884491050908487378045990871781092821 (p75)


By Robert Backstrom (June 22, 2003),

By GMP-ECM 4c    c138 = p31 * c108
By GMP-ECM 5.0   c108 = p50 * p59

j(tau) 931 = 2 * 3^4 * 7^4 * 13 * 207275087 * 135995234261 * c138
c138 = 975951514039733416966803695195631221008082351088915710997961759531660253802105569414077912576811768364837773315326548986788233241515277559
=
p31:  2673695606015565136064417299873
c108: 365019679818425761359552408502464459078864683512751413615286789071499082390698961385164285032597293030949783

c108 = 365019679818425761359552408502464459078864683512751413615286789071499082390698961385164285032597293030949783
=
p50: 10268228385759161587975143556980119026573112440573
p59: 35548457446141887498996499669535117894408202462436293716771

June 21, 2003

By John Dilick (June 18, 2003),

W4(113)_C201 = 49663779435313861979204161 *
7286629950496313081601369289560441122582040164244795173838688413788283305240752310698183373414185399976962418192669486011264636637324921162300485034586746798903742162799077697 (p175)


By me (Hisanori Mishima, June 19, 2003)

Wol1 (588) : 8626662327127334652724182632411541856876013683327363862377014480985093488598717400365744164800342538309274347342479849490701507521811930134724151706997623698772367886111885261870985770429036264426338226120093132130615594501359423209830952866387039139 (c250)=
13300972372885036495812184181 (p29) *
648573809890274626663463026223184955433242328522380970269701908770900676678499495314630674348064871775808388366640627350442718463266726364551030936664321513787023997887028204534967560352890847809722947163055484906289473719 (c222)

Wol4 (108) : 952354788524482843559361580435730339279085957838411331549748812434342351342028493636501226840108521241627345808383958320105023498973356439698151117028423274585165761 (c165)=
335557985673969966881232631 (p27) *
2838122855612192559081980364894101617102940332989031425981783495381663931140480740563408216026225069359595588726470016031542619213051988231 (c139)

June 19, 2003

By John Dilick (June 18, 2003),

W4(133)_C200 = 6611929389362728504255493351 *
8181838099921545583138096537808108267084883909494654447050722680348078254442938229282145913579811600706321683863264077121415071504301073731818645518588781296628573243876267 (c172)

(June 17, 2003)
W4(117)_C173 = 157544163589898713532201917 *
70055165714803113390187705157336671460274644785631307108798759105913855640246541433193674880463212215355325847537862178974684986156940301895831213 (c146)


By Dr. Robert G. Wilson v (June 17, 2003),

(Fri, 13 Jun 2003 07:52:23 -0500 John Dilick)

# e157: 
320106891088296398536471463411241389380529398478113698094499890422138965958277429498210665433707991
= 1702562464496177673291021024204281 * 
188014770537668606293640128323600045074804763072531459430592568911.

June 17, 2003

Decimal digits of Pi, e, Euler gamma, Smarandache consecutive sequences and reverse 
are all checked with ecm5 B1=5e4, 300 times.

By me (Hisanori Mishima, June 16, 2003),

rv_prime(52):
3591716240565653103343003611657545018547948852803211968579647185022723206221275240810381,52
prime factor of 29 digits : 11153708989356800227491284821
prime cofactor 322019898850953993647920761543905231101642892928302951190361

rv_ prime 63
335237488629682640913713559667558269310389059128247605986666048405429002383688965784971055923242078043370645272763069 (117 digits)
prime factor of 25 digits: 7261301491887827714733901
Composite cofactor 46167686192923247343855349489458905360522360279918215133985701437977933887482384346044913969 (c92)

egamma 238
18832428305909405204347310266727737909566957590566569180317798565852462951694060158135339870212075389373410827138210097625782050909166028516200473958304731795009583258657894834626141527853581044179678452002433458730007268657377 (227 digits)
prime factor of 35 digits: 42604915115811254855561220321154247
Composite cofactor 442024781758582561463396344472344433965975527439480134123782323322082605088387376653718322253705785235845582009875828264695838551607861674195982957007769975359896894884866395024060314398784791 (c192)

June 15, 2003

Smarandache consecutive sequences extended to 100.
And following data were added.
Reverse Smarandache consecutive sequences,
numerator of partial sum of log2, numerator of Sigma (Moeb(n)/n).

By John Dilick (June 13, 2003),

e(157)_C99 =
1702562464496177673291021024204281 *
188014770537668606293640128323600045074804763072531459430592568911

e(145)_C135 = 5712554518722032579350362935093 *
63447550901449416690354813949829559652215812340102960229849820330764470899909189746037082002403127256869 (c104)

(June 12, 2003),
CPr(74)_C148 = 58902901917444574940765431 * C123


By me (Hisanori Mishima : June 15, 2003),

sm_prime(74):
8499715403394958160836443178289342284237532559797714810832052489943084361403027073966979111720645644755127820367165365714722340865281669295380384083 (c148)=
58902901917444574940765431 (p26) *
144300452553385966579730349309776704684318209783537762587096993952002889015622194231143294323604692442088170009296190729093 (c123)

egamma(231):
c205=
9455701486028872198970035877 (p28) *
938495423422766620682596755347356022826083248305170172501164922336153024718181626712824091784783806029058014866553792567084202176801284021700938532999846430680841735463657618497 (p177)

June 11, 2003

By John Dilick (June 10, 2003),

e(135)_C121 = 2546995124868158512832244593 *
515367678099845165040388689239551165504447844497773799438449384958288252955467615945160141561

e(138)_C116 = 212430901563970453594456491557 *
77862578686095477285752231223985556253118132409538904600022208308498779714300376695343

e(166)_C155 = 58270721104294168043248631233 *
699051856099797443221945078974058111834958803626708054305660004193384115746383582505921421992642771936784029911558680528007389

(June 10, 2003),

e(183)_C184 = 8218900069176377049205293941123731 *
330735476229174613169941197394489263394542052966131872079722382641016105224964234905549037285578381379252310797736160089909502046765773016780209062759 (c150)

e(162)_C139 = 1948208546264922475245156562343 *
2545589357773784387459734075715180152005163706165999368432401529087246707336649241527076558491325812504070833 (p109)

June 09, 2003

By John Dilick (June 06, 2003),

e(156)_C124 = 
398053064160126049411886990490431 *
497943384792713769699062503908851623 *
11130368909963174695603942585569125629623186003128141707


By Sean A. Irvine (June 04, 2003),

by GNFS
A89 C113 =
3252057283323157777789113242014000564108261 (p43) *
14000163506376778836919142950487935314415707211129135003645155641750303 (p71)

May 31, 2003

By Dr. Robert G. Wilson v (May 29, 2003),

gamma(107) = 
57721566490153286060651209008240243104215933593992359880576723488486772677766467093694706329174674951463144
= 2^3 * 419 * 569 * 64457914934471558841664607951 * 
469510792224465537229586664550201072015052647479386218570614666996114713

(May 26, 2003),

e105 : 
2718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466
= 2 * 3835744444367128389900043017797 * 
354335627397036242519197467470860300478977020702175898009897148758754463489

May 26, 2003

By Dr. Robert G. Wilson v (May 21, 2003),

Consecutive prime numbers,

44 : 193 : 2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193 (103)
    = 3 * 11 * 29 * 557 * 1747 * 192926646339376423418933347 * 
13119818895337440993411500987038164533394883458604413490415202369673

46 : 199 : 2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199 (109)
    = 3 * 13^3 * 197 * 105613 * 4330517801 * 
5502954190852198184124234451796585462038073 * 
721289234685133229945791017773141436234452113

c 58 : 271 : 2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271 (145)
    = 19 * 46838908157 * 
2648620458075372640494115621952835065077601496753193938561477911306072529232744531715396496605088997490602560473145406713491597980337
(c133)

60 : 281 : 2357111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271277281 (151)
    = 11 * 83 * 253307 * 107783930539 * 103547886614462293 * 
787665212805008428560409 * 89342055626849724105094049 * 
12976849313970273913900712520179840938131005023513939592155826413

May 12, 2003

New data added.

Decimal expansion of Mathematical constants
 Pi = 3.14159265358979323846 ...
 e = 2.71828182845904523536 ...
 Euler gamma = 0.57721566490153286060 ...

Pi and e results owe to Sean A. Irvine Ph.D. and Robert G. 'Bob' Wilson, V, Ph.D. (May 11, 2003).
On July 10, 2000 I received the case of Pi from Dr. Sean, but the results over 100 digits were not right,
so I checked Pi for up to 250 digits and e and Euler gamma as well.
The results for Euler gamma owe to me, and those of Pi and e also owe to me.

And I had received the Smarandache consecutive sequences (prime sequence) from Dr. Bob Wilson 
on September 12, 2001.

I'm very sorry for my poor correspondence and updates.

May 09, 2003

By Robert Backstrom (May 01, 2003),

By GMP-ECM 5.0c
j(tau) 659 = 2 * 3 * 31 * 51065267417401 * c122
c122 = 71907245253089113512919848208873596322010594818476937907950109538709105998466595463799120265104103497251752591514756685793

p40: 7189514302559602515752104691541184838563
p83: 10001683316422192766825674142619267664938060568942317529828327806770687474537623211

May 01, 2003

By Robert Backstrom (April 29, 2003),

By GMP-ECM 5.0c
Wolstenholme Number(339) = 1543 * 12408499 * c134
c134 = 65032313537234234560590404004023835479057256753957350796093965114199994488108016102838749359884060577727073320600554013098831985776109

p35: 21755020252874334234803630337510433
p100: 2989301447726392397692315617985355972598096878265101058524133713422511933426485692145518861580906573

By GMP-ECM 5.0c
Product of Pn - NextPrime (82) = 71206445269031 * c158
c158 = 41325288101164302124434820155180445392548416644795496890994410836120861712732944997367640274468720437356063836095833924784288465283652874055794921158540069289

p36: 204904080283287105646461555152016979
p123: 201681138042886389889264609936105000164385000021753137105729567299239603935210598172988186781720752802900731745113240479891

April 27, 2003

By Robert Backstrom (April 24, 2003),

By GMP-ECM 5.1-beta
j(tau) 788 = 2^15 * 5 * 151 * 864047 * 1244167566419 * 3999587553915809 * c110
c110 = 70676844682540910247096363400537566945907365029201623866796087875028147186489193416305700849024149557339403581

p35: 65857816038913767385095865662033347
p76: 1073173222761892029529591890193579267822806940514613134155941433061237997823

By GMP-ECM 5.0c
Product of Pn + NextPrime (81) = 11579 * 243631 * 121326342572784285151 * c140
c140 = 20421817568421420634903008099185778143090068128396782530199597528698701787171465618667379552136385560011026738906598171734369384262485710289

p36: 115031005728159607785433286726710741
p105: 177533156727170616857051668073469282321456294764109403828380929415489334359266301178535679559437229666829

(April 21, 2003),

By GMP-ECM 5.0c
Compositorial - NextComposite (120) = 11^2 * 61 * c149
c149 = 28671696796713756094177186834103546421574661281731381844884728073216051998171887458677106477645718523603657238837902322167606557377049180327868852459

p34: 2500085340660206790353421025293427
p45: 542441618696365031602237029271773890318199581
p71: 21141975171015301784922551947759587623579336238900145066092584851298557

(April 20, 2003),

By GMP-ECM 5.0c
Compositorial + NextComposite 121 = 2 * 109 * 2511541 * c146
c146 = 46768905347997106673204716350603681262434321255092995771473588640843052966285176635774906834386744115472579875224325253943952922882767295807925869

p37: 2913732827827924176300353946931451629
p110: 16051198964203429689448838874859643116564809708048988753415931766108818272074870463112675191203434724118578561

(April 18, 2003),

By GMP-ECM 5.0c
j(tau) 988 = 2^17 * 3^3 * 5^3 * 7^3 * 43 * 13565543 * 2817855671 * 3750829767796253 * 1115494947226259413103 * c104
c104 = 13408115689343943056502716171280068435872515267231541647146773220753675428065623037694174024340704228793

p35: 36257584928977552521256176240880547
p69: 369801676410829987627204288178519169061228504284130988979090375487219

By GMP-ECM 5.0c  c115 = p36 * c79
By PPMPQS v3.5   c79  = p34 * p45
Wolstenholme Number(332) = 2207 * 991889309 * 3713307486900719 * c115
c115 = 3171327016843901903814634343481401675120102757780115152838479690452591970050440429356338983969656438566723636899619

p34: 7368867444980563202833982802328289
p36: 858832821729841271211563625910545131
p45: 501108361806292258970448137766071621586621641

April 16, 2003

By Robert Backstrom (April 13, 2003),

By GMP-ECM 5.0c

j(tau) 916 = 2^15 * 3^3 * 7 * 14779 * 23753 * 209167241 * 93843420985079 * c126
c126 = 148438929245539576073651389713723680765491850412243211258016474737489729611088012528246727146643293638037398982628603554475011

p38: 19828643674000767413421412010753821321
p88: 7486085870823936575768045475271400263785822035528972705394385619443636392844279087918891

April 12, 2003

By Robert Backstrom (April 11, 2003),

By GMP-ECM 5.0c
Wolstenholme Number 2 (187) = 435371 * c150
c150 = 767791406939465622012776090572932416363199401644760745409722073917907313863971033836020537764627788060987778539778653298413122886398024728393451171523

p36: 266021141304262297770212450450218463
p115: 2886204469220370791406874153844694273867608536207878729951690865975961607472522623859466429085397913869411061662621

(April 10, 2003),

By GMP-ECM 5.0c
Wolstenholme Number 2 (157) = 1931 * 3863 * 56237 * c122
c122 = 84907553175557798661040632703430484431951743622287821290006561799155408974820059055891826908384330966684613257512109537873

p37: 3376317399249552316784966198145724129
p86: 25147977259018965436311103727131506100950244182795199847762560004834394203973701101937

By GMP-ECM 5.0c
Wolstenholme Number 2 (232) = 233 * 383 * 659 * 14815212791 * 148988906631422629 * 2697429230143075469 * c145
c145 = 3189135229677108362386002615840367090692742630717970765940876708072719001387227379182527075795538827496935179920453307199702050935404757735323531

p33: 928380722619046582964212202858143
p112: 3435158822212795831359156146545069238812068477490339139698836360546144158214246568944037596287097553347287245717

(April 09, 2003),

By GMP-ECM 5.0c
Product of Pn + NextPrime 76 = 609269 * 872947 * c145
c145 = 1238324113315471000582916085923610386008302157562859753845057976971080056609413672834187544008199611440151185677795963073884295048552213939845033

p34: 9172682259568195088829283139249591
p111: 135001309134386742497021851490551341134886432624653123443323502293577506728590215658955098198750920329117928863

By GMP-ECM 5.0c
j(tau) 844 = 2^16 * 3^3 * 29 * 53 * 103 * c145
c145 = 5709751163473979943982961594686199630014891196848401854469034003689993282094762283564550263834779641436083427872324105362640296081633847785144407

p34: 1116807572075483293620819402404203
p112: 5112564873519738912085012019931524444067640449738984075204584598568205235571120616464050446954067219706522364869

By GMP-ECM 5.0c
Compositorial + NextComposite 124 = 5^3 * 233 * 1558223 * 662393057603 * c139
c139 = 1585000055459068525495826929180087231680849753196507586660157878439747112953306817298349125212734461539475968490076334523425600268108549213

p31: 7986893518391091552820646539991
p108: 198450129804454512833176342449137677040837361767828486767817954441868712888183512817051707681015990835185643

April 09, 2003

By Robert Backstrom (April 06, 2003),

By GMP-ECM 5.0c

n! - Next (n+1) 101 = 2 * 3 * 17 * c158
c158 = 92411252547434896282859050240028791662375615634338664395371464249186054895257073299049880995998121048153171470623035290033036336300031999999999999999999999999

p35: 43611885324319153923313915322940217
p124: 2118946517909509171311785751602320348865012854998104169393096551232275881479184112581018349175719912227839645259962224819447

April 04, 2003

By Robert Backstrom (March 31, 2003),

By GMP-ECM 5.0c

Wolstenholme Number(434) = 1176787 * 759753302459 * 8191713824863 * c158
c158 = 26597812613759492943768703062808207241034094128869129793739920819434827967823249438008276450227963365093634603561317097490370559820680483786226266472868203773

p26: 12913587111198806288443357
p36: 114832408701246893132530662221269687
p98: 17936369865311472938351383876797806402546562668820639555638189481946569171621094029229750958905447

(March 30, 2003),

By GMP-ECM 5.0c

Wolstenholme Number 3 (134) = 4044310931621 * c158
c158 = 93593521433951100336762837718712409901973898126948108254714053183496785689773778263201069023258390520583776148809177556723312866360014494913492166908838087113

p33:  661646811835339415067105041379277
p126: 141455410590330526653379365787421341859898926909439082210759894751027388089084659830414210405254764192185590901032334055321069

By GMP-ECM 5.0c

Wolstenholme Number 2 (225) = 1962419 * 5372945089561060913082887 * c158
c158 = 39188872207082167662335887052894429084052759027414331200828686904852063980652644954472601208576752601944292129454422705555840731261998130645709520880968277613

p32:  14733720237885182390043593046631
p127: 2659808356230006523674858978445911134809818405706030803399242416320417702328757543040498683018574591525413963208290298545882123

By GMP-ECM 5.0c

!n (Sums of i! (from 0 to n-1)) 109 = 2 * 43465295731484059 * c158
c158 = 15380347917056356546267081808566880432897712731701231375772067230420632030383268382130686150473615936959053408435239322802324444594338956637265150021748975223

p33:  313113024435600845597668426436477
p125: 49120754222153705336452839990454932948676066123572088464718829722611034513029877007737225159905419731174624163259043638532099

March 26, 2003

By Robert Backstrom (March 24, 2003),

By GMP-ECM 5.0c
Wolstenholme Number(405) = 1777 * 39313 * 14704770989 * c156
c156 = 480610155106318511553691066546039656239500642209460642924931181502590271036301962753576299880848218939161681509898912430958378700893856594752003595981970939

p28: 2208022180855732466271486487
p129: 217665456114238451160370947451645434157775306831147015582661800282533147558988408983455382003534494960402773055470970618077259197


By GMP-ECM 5.0c
Product of Pn + NextPrime (83) = 2081 * 877734052767073 * c156
c156 = 694348398144877237325966368169688611319197195704701029667081203227815526893328282663171483602118048191510404611334954732846459102521883852337180886036431971

p34: 7899473900471013983985290504720219
p122: 87898055857045875403446499388126949985403424147787391573947114006155976973213200543557027455837306742568147803557057050009

(March 22, 2003),

By GMP-ECM 4c
Compositorial(144) - 145 = 5 * 29 * 1513751 * 10239474769019 * 12643749785169219006234167 * c149
c149 = 19503130489568862715852431070064025870405769931624967639413957089850419821119519926167125500920346237435801227938427820905617316971509347623736906013

p36: 237868749626647985181572505023714087
c113: 81991142258831481123314764983615213747556877167230191756783926348112725994050832890320798432794253273985579062299

(March 21, 2003),

By GMP-ECM 5.0c
n! + Next (n+1) 106 = 78193 * 1152791 * 651355591 * c151
c151 = 1952334955689095783689216093316820471278610031885933111702177998292983373677132076030012142913244538963171295691122667629946069260868212890816581181179

p29: 61227224929927128884696098153
c122: 31886713107175595848725844326701812311188256460949638520633353851303173135644985148352047594557650085004294115977252610243

March 21, 2003

By Robert Backstrom (March 20, 2003),

By GMP-ECM 5.0c
Wolstenholme Number 3 (125) = 3943 * c154
c154 = 2605835687994435428379776215392645058063801705970468255141806147804654140362319986216791967869730477112255495020607321091006378069491052307031793492912439

p34: 1276109866602128715758239661740489
p121: 2042015155742773220666815551864694725256831765448109521715264580625744577186716133634805686184402322400388108290206327551

(March 16, 2003),

By GMP-ECM 5.0c
j(tau) 957 = 2^7 * 3^7 * 5^3 * 11 * 251 * 2179 * c153
c153 = 131914571278268699201259107075909643086746734143986529613966296201114173557260685271633690781349812731969891208356467757872854078123356883560103669972051

p33: 346675075016118961567230391213303
p120: 380513572463019487486714063434474623263028183925843737884922591910892136242934966743457712685578631072774908094488285317

By GMP-ECM 5.0c
j(tau) 823 = 3^3 * 5 * c153
c153 = 125007620431511376071578962806258672946339533723171280135828754095163141968103243533479102425479754185595039778380447877578775635211200286746659341891207

p35: 17321494218890584531204847083288867
p118: 7216907436032843869631044183014605371983061677144179832169920663133735797404405590542338335704451721342142081343475021

March 16, 2003
News 1

J(tau) 500 series has completed.
Last composite number was factored by Sean Irvine (March 14, 2003).

News 2

I go long business trip to Vietnam, Germany, Singapore,
from March 16 to April 2.
I'll be in Japan from March 21 to 24,
but I'm not sure I can maintain the Web or not.


By Sean A. Irvine (March 14, 2003),

j(tau) 565 C119
3470994496423657454143675709808366055353820141513 (p49) *
18737866270165614571334752518722052574947897999791182432114852819901923 (p71)
by GNFS, 4 days


By Robert Backstrom (March 14, 2003),

By GMP-ECM 4c
Wolstenholme Number(402) = 1913 * 52609 * 143139317 * 298112231 * 663873209 * c141
c141 = 172975943297538066223207556991636140276735870658804093443441576579452326788490002132965630872967963822035920842279248560011496878636715686741
p33: 184880444195883928838198841194513
p51: 366115852312678489754005627240324138841935859506033
p58: 2555501840555247206203091511083715193230640403005509910229

By GMP-ECM 4c
Wolstenholme Number(439) = 3323 * 47378296453 * 794746093577 * 47801119289657 * c150
c150 = 493887297863208014011549041442122803497895200086825739983769395992701248119061244474321950040916522135238627954868219944125640454632691058103797526767
p34: 2720088812294951685363278675151641
p44: 15322726054127114193740608534331639519298659
p74: 11849737654503731765196412232662829126318862961785105980668565744041113293

March 14, 2003

By Robert Backstrom (March 11, 2003),

By GMP-ECM 5.0c
j(tau) 906 = 2^16 * 3^6 * 23 * 683 * c151
c151 = 1061348852290850868116420854216472190975787142075575158604264693884736268381274661625989874293176566456632617410650277446832379402357918332072848061989

p29: 10382088987552510758340778771
p123: 102228834058670001793384884481001342043277282990294036860797537645517531486572005053012498410480922406624005058844726499559

By GMP-ECM 5.0c
Numerator of sums of 1/p (88) = 661 * 225673197165833 * 2643804307152800069141 * c150
c150 = 115694606688991288073226849571628633780634569607841948980197255525815800198092359551638251876628036312563732882295930083855970030809150051447825330283

p32: 22623079802380757737136232274181
c118: 5114007805286355150593434105856355180943294411233248016725523544672820002322546384694353285410358237441830614499450543

March 10, 2003

By Sean A. Irvine (March 06, 2003),

j(tau) 591 C121
263100148220478610780225026550977089425847 (p42) *
6586211833053071713370509075901020667807609125637109701592750067076952436343357 (p79)
by GNFS, 7 days


By Robert Backstrom (March 05, 2003),

By GMP-ECM 4c
Compositorial(135) + 1 = 19437707 * 189067237 * 2887541871197297 * 4123217486131673836800154505583133923296257 * c107
c107 = 11692368258132293403867555890711521482174288031020496822745529767855535528706684225308168095559651182255191
     = p44: 98610279711255122090524533708099809849525341
     * p63: 118571494699834592950302065702999696909255870432199173385590851

(Wed, 5 Mar 2003 02:17:27 +1100)
By GMP-ECM 5.0c
Euler Number(152) = 5 * 47 * 25149009833 * 18051556174129735359181 * 3957666449530267510589053 * 438321334095183824658294709367 * c149
c149 = 13965855928973841139965472780340537434039457580258306891962403590314838680618490975777067831077295235994023072026465940264060807760093327653365897773
     = p34:  1767165620447279332603545521778737
     * p115: 7902969459896467561629440342971710640832059821111586575368404463345261317763357672435550860134160040014045085591229

March 05, 2003

By Robert Backstrom (March 02, 2003),

By GMP-ECM 4c
Wolstenholme Number 4 (102) = 103 * 1551961 * 3432237466963211 * c148
c148 = 4850492745696949910403024921117321695433015979164643396114167201592683362184490701088777457108813496607877891592818862726275229544463801180072695373
     = p32:  13728281948422683231745425076823
     * p117: 353321177691448078727374929647551552030938954671554446049705831157155348889547342751321655126534427306083701440953851

By GMP-ECM 4c
Wolstenholme Number 2 (206) = 5573 * 27799 * 3394691 * 58040906161875019 * c148
c148 = 6112679007314191880321191896704309742475927977983151759122133137849373527903120221786819967854960819052565023219003191156172546292534590607197942387
     = p29:  25084808105073417380740836679
     * p120: 243680516977042328266483841371191920438043540044805358556964175124191707440486131643375087841590637905887650844500129653

March 03, 2003

By Robert Backstrom

(March 02, 2003),

By GMP-ECM 4c  c146 = p32 * c115
By GMP-ECM 4c  c115 = p33 * c83
By PPSIQS      c83  = p37 * p47
Numerator of sums of 1/p (72) = c146
c146 = 67716345406116182666502711298537657766476568871138508325904399838588246626836961302256491823908939835231572644219200070269138634270480044366340573
     = p32: 10774822439848219544475069839689
     * p33: 122797736200334999541587307307277
     * p37: 2437316904825953681023538533923768491
     * p47: 20998149731197355908192993429290864403334372251

(March 01, 2003),

By GMP-ECM 4c
j(tau) 930 = 2^19 * 3^7 * 5^2 * 11 * 37 * 246713 * c146
c146 = 39363974936591111874029750136697196746957687142725988484022046337031772775805118879787921789476216576489473662603181393130842156529910786708975841
     = p36:  269681743755259371514737410158869613
     * p111: 145964552099286958376311506123403480179230670631633005283383079185478295974506013937972229973647616946394748357

By GMP-ECM 4c
j(tau) 895 = 3^6 * 5^3 * 592299848071 * c145
c145 = 1488475554386720396225859068612387466149044816276923790207727279288695544844460888477242342427545373514061113584470610884103398118130744251287367
     = p40:  1876646603207708549052938799131510607151
     * p105: 793157087670370982668595562830469480807791161537311851858221172897470046783243883846502979211635470995817

(February 27, 2003),

By GMP-ECM 4c
j(tau) 979 = 2^2 * 3^6 * 11 * 157 * 200793732872525562811 * c142
c142 = 2295659823173461298301905382906836889529221902560842468088654823350055609504555072090609816903183249421276489006844016838984699568167171008701
     = p35:  15225231226187688486743101851239093
     * p108: 150779964459579606186357186277754401396443058567368255619629641197657684172093752473087989690142441860442857

February 27, 2003

By Robert Backstrom

(February 26, 2003),
By GMP-ECM 4c  c132 = p30 * c102
By PPSIQS      c102 = p41 * p62
Wolstenholme Number(375) = 2991293 * 14745386317 * 226200387227189 * c132
c132 = 157775940052324384267457496555967508686839373216098605862993244951174827526643037966784277347149437403364379092532153130903514799641
     = p30: 376640966940288913618185914377
     * p41: 13861355773887662138481416664067482659459
     * p62: 30220908072151906094376584276200279895674903451499149258903387

(February 24, 2003),
By GMP-ECM 4c  c137 = p40 * c98
By PPSIQS      c98  = p42 * p56
j(tau) 961 = 2^2 * 3^4 * 31 * 53 * 15637595131 * 76296337332619 * c137
c137 = 98137616660391805182160665450331608110497003734817158740272713597052153029480468405464645193797136546380258955703124045802875234165327431
     = p40: 2730811235723978595576300333272104789429
     * p42: 725257120867853775657207761741371052222611
     * p56: 49550931599404303408225549205871232114085670475437137449

February 24, 2003

By Robert Backstrom

(February 22, 2003),
By GMP-ECM 4c
n! + Next (n+1) 115 = 2^2 * 29 * 11689 * 540619 * 832489733 * 21643402349501 * 43757760294852283 * c138
c138 = 506120146121131286429045000075219170319468420643583132327628740857710247610896046750754905383409203012106951271861367971692934877205916449
     = p31:  3077736003585121074931617358859
     * p108: 164445600770038072605509537507278217843412228185763167858637737005351896353551488863625446199923109993291011

(February 21, 2003),
By GMP-ECM 4c
n! + Next (n+1) 118 = 7 * 17 * 1093 * 59557 * 9648923 * 155167495397917391 * 2084416557145567040882033 * c137
c137 = 19377671890943492615358991152039997258788723811585825132264775522047395161413238609513155872525773268667781986362794249264844482336285429
     = p33:  849709758176204932853234945568499
     * p104: 22805048081988874428528508377659248661755187447996807143290836978397170017355006678871522411680142078071

February 22, 2003

By Robert Backstrom (February 19, 2003),

By GMP-ECM 4c
Wolstenholme Number(415) = 44843 * 462055437709 * 72642234787001353104382613 * c136
c136 = 3905013833937890885098102779921102698789246993717179299528008231318915199586747199922595171695455476306383391498813007023436486269586801
     = p33:  665319523657585669376479475368823
     * p103: 5869381094470408302245364323391458834392729377796850695437983861806725758790521723099661884640588390487

By GMP-ECM 4c
Wolstenholme Number 3 (115) = 36857 * 16367017957 * c136
c136 = 2876654269671447477263053543724904160556864204757853692411747139799753218106010225290017233532164200740713538892542751417221447280908879
     = p27: 773973187020471635517580319
     * p34: 1393986792345808714615949753660083
     * p76: 2666263668699495811656882967858393033117365025591002595152094719809011442027

(February 17, 2003),

By GMP-ECM 4c
!n 118 = 2 * 419429 * 5193701381694374115197159 * 667977353910046767904061117 * c136
c136 = 1375892862947247458445963100356237495669387001713634083089366292264346193749576650319002144747776574842879863964590008435972050071962811
     = p38: 12385176047424648952807657665926071129
     * p99: 111091910012320585885478017196578916541278012336707485204313031579073418861182222312613479752247859

By GMP-ECM 4c
!n 102 = 2 * 19759 * 929370670336517619127 * c135
c135 = 259216664054046526960068111093271923414926509024337950356502387712824650488344674864622343605423531899482132867085133812930492007891349
     = p31:  2171839665883231714832265273563
     * p105: 119353499305681817491384280773496599934319683979832065304263623724824694272615400530997917343321766623823

By GMP-ECM 4c
j(tau) 824 = 2^20 * 137 * 15173 * 91543073 * c135
c135 = 105183359466773734818959009689835707202616882723813435846579866761316478764965998799096878961517678584968335198159380322087207684123249
     = p31: 6904832762500332797203348727101
     * p35: 17209545297528758526479283918491533
     * p69: 885165498035980812528551069423846680387109991340263526690624245977753

February 17, 2003

By Robert Backstrom (February 17, 2003),

Wolstenholme Number(393) = 1039756704737 * 38135878911119730823639 * c134
c134 = 77855254515261145823118259825507895935168614965271740041194267562069664777256579877299481795200860260175860619706885812657601593072221
     = p32:  27841234916804877219028424777269
     * p103: 2796400904913451664490202757111964938818199971539174982780964682770038010237011450666031545349070467209

(February 16, 2003),

By GMP-ECM 4c  c132 = p37 * c96
By PPSIQS      c96  = p44 * p53
Wolstenholme Number(353) = 5176903 * 328479291093011 * c132
c132 = 568640774416618311218057691656564075373851129941754151106091254399824528695746926706998502071006399450765337953881210469874778326943
     = p37: 2135417189930656649556714964473166177
     * p44: 18542419324756116939063885039274668859542323
     * p53: 14361138315196752240719065706538504043949978829763333

(February 15, 2003),

By GMP-ECM 4c  c132 = p37 * c96
By PPSIQS      c96  = p46 * p50
j(tau) 951 = 3^6 * 7 * 19 * 9432617471009 * 10332868189974541 * c132
c132 = 871203665260912009336929226497576222730298831541949179721888713687691841429879497264009633185152182386042777190415263103268189547999
     = p37: 3170850932620019484147416773371458443
     * p46: 4106852924849171486975799533206820537042022053
     * p50: 66901324851213656806378898127387711856388458917881

(February 14, 2003),

By GMP-ECM 4c
Wolstenholme Number 4 (116) = 233 * 9399966696584690730167 * 442355249504309494209383 * 35241720973265923451802163 * c130
c130 = 2405923506483449915704186856640271081825197782717994523789933167787649344204887403473390765015416580259040378240378259537819602761
     = p27: 494713268903093149281763597
     * p36: 110243739585640141718461124684783099
     * p68: 44113784763856653115509509891438821906807061103740745087361916381687

By GMP-ECM 4c  c128 = p31 * c98
By PPSIQS      c98  = p45 * p54
n! + Next (n+1) 127 = 2^7 * 1499 * 233251 * 364801 * 10195000211621581304233 * 112110838660897826584207 * 2097168323572991834774989 * c128
c128 = 76982295511818969603573875716198425055239836835763887099832179711581911640345843707878279920407907135902462241655270834254295011
     = p31: 1836910936184685814680363443863
     * p45: 108130284800608582112629076040452606858203103
     * p54: 387574691854855934360392358358474211284876875654617099

February 15, 2003

By Robert Backstrom (February 13, 2003),

By GMP-ECM 4c
Wolstenholme Number 3 (122) = 477034109608206118268561 * c131
c131 = 34462262408471170117523588218048165423852049248068812433341146781375291490691632295861865446592153969657958514291985224104807001633
     = p34: 1509663713604475162448586942918941
     * p98: 22827774224094599791890433583396087354095909972333153748380059800043603455416125758012858177619413

By GMP-ECM 4c
j(tau) 756 = 2^20 * 3^9 * 7^2 * 11 * 29927 * c131
c131 = 16763646533538598211209110750071445101740690756085789546937109972195262963508102759535663674956478751460108287304522709837332752483
     = p37: 4088633565648727970251889363502328219
     * p94: 4100060879600682444350227284809288677723239091960925298338977184122847252688606514189296676057

(February 12, 2003),

By GMP-ECM 4c  c129 = p32 * c97
By PPSIQS      c97  = p44 * p54

Wolstenholme Number(417) = 16033 * 4078649 * 18250494362363 * 10964290733706398994728923 * c129
c129 = 449500065650138062180190036082723204956615256288079887849004269813312017119250406821481074125145884798401835157786831209268452307
     = p32: 83993672188828991076137683999177
     * p44: 10893781773237172401312291050864400199473523
     * p54: 491252212551345657057417280430555370938600379930270617

(February 12, 2003),

By GMP-ECM 4c

Compositorial - NextComposite 138 = 2^2 * 5 * 7 * 7489 * 6045383389729 * 88933969079300713 * 634335284915209789 * c131
c131 = 26852459049910499338475860282802303618675054872302884504599586968138931671707869465868800919233197392801332382439343358372134729747
     = p30:  292282983487931778582512783479
     * p101: 91871441605902535334287223113338140759096058131741356022331009526389378307035432668651907407852877893


By Sean A. Irvine

(February 14, 2003),

j(tau) 563 C116
351130558070835238547370618238989157840901 (p42) *
131620752614170596798308185726251279378950316298545842292727076409860380507 (p75)
by GNFS, 4 days

(February 11, 2003),

j(tau) 548 C116
26594500863305575014511156480477463915696856037 (p47) *
467484520831275678807572555737895282905647574617995207586161780444621 (p69)
by GNFS, 4 days

February 11, 2003

By Sean A. Irvine (February 10, 2003),

j(tau) 519 C118
13771832183240947037203355774265682431267293 (p44) *
152169913392466948768643497684647716146129408258899200318747444641006357621 (p75)
by GNFS, 7 days


By Robert Backstrom

(February 10, 2003),

!n 106 = 2 * 6814742569 * 352090088957 * 131410216066712117 * c130
c130 = 1731326710778318705088190815974607117337122386320690477211126844979387368985007287176461875277410471716374496562853937363336212837
     = p36: 200283901445803877013121558882274333
     * p94: 8644362818380635827270155811132043565794130702453595318342078954531924583965174822456271808489

j(tau) 843 = 2^2 * 3^6 * 5 * 23 * 73 * 3287359 * 2450253783841 * c130
c130 = 6539372159847692773479213142801066985110123967175859954134883551920759003312338000246275347026292560285742179966707806293807861523
     = p41: 43960251516543329379938454092252762435341
     * p90: 148756477368805894364996907432806242314600911035407868440669062738759345298715495412985503

!n 98 = 2 * 276179284055483149799083 * c129
c129 = 175963374360617491967807004107178221036496318484209133907555939701438496941993066582204394449036092388200101656249802046514922279
     = p35: 52271717499127267475571578695986659
     * p43: 2159928875033340292122144016373690879799907
     * p52: 1558533211365861660669978299273653506974902325788783

(February 09, 2003),

j(tau) 783 = 3^10 * 5^3 * 31 * 17176281031993 * c129
c129 = 626543972011807404906686023768414031571789130450530853028275704851508516508762678261614730127189790958634458351067413720169178667
     = p33: 356007682410228822145069384197323
     * p97: 1759916998897340443838918844709028601112559515567588937465098462147531382354691946674629757188129

Compositorial - NextComposite 133 = 2 * 306859872713 * 18927613069129 * 17292586213455190348309 * c129
c129 = 140787425008610693878107480664385280680187383193131827401709139243956692217021602404685455882024443578079854403325190776428916281
     = p37: 1893960893595071843177619655107865199
     * p92: 74334916568087806902505506053121824958142727580594345678618264897629462973107183802587522519

Kn 112 = 3^2 * 11 * 1319 * 486589 * 442501337 * 3226044975479 * 200405777703624325450997 * c128
c128 = 10960149743110906234879619670191736390792878094444137761128123187465558876908247707244994372341672231094755841241583181681358347
     = p32: 54558694028482977637903673518201
     * p38: 12428348366943282149091354546253465897
     * p59: 16163637560526557801385567656418220723284249049000243292651

(February 08, 2003),

# Product of Pn - NextPrime (93) =  2270071 * 100734575803747 * 302225186156696915091037 * 425519736344229699232883457343 * c128
# c128 = 17327106977413870622398913725739973207256562840197530854569506036853232318197551572079752595321493892598351868223096321087216257
#      = p35: 34410349027035202086980268200441819
#      * p93: 503543482334354435577153340592071882246622910030445934761994020311416306693129563103332533203

j(tau) 766 = 2^18 * 3^5 * 11 * 701 * 1515742643 * c128
c128 = 72398500060172023344345359500203092152327351209577162267417134400758095283929482599589221974501000429296937407587060296085013109
     = p32: 57006097851712835472303720799607
     * p37: 3494106111963603427461457994753002367
     * p60: 363473007783170060067523923723233291665115830627838265518861

(February 07, 2003),

j(tau) 770 = 2^17 * 5^2 * 7^2 * 11 * 47736512518663 * c127
c127 = 1577208702500696486428083859047114648751427498542233619323110453873869150867698061615263190198914088834640101343968651297181947
     = p29: 89591487315132237455220965377
     * p98: 17604448254698209426531534554578643644850478010775120830309870711131974827702289222637817540956411

(February 06, 2003),

j(tau) 740 = 2^16 * 3 * 5^2 * 71 * 9389259601919 * c125
c125 = 43838039229385185171630497207636524847266178752273389651915817014339769428485239548875111637572408460690780662827895046912911
     = p34: 4863822847332166057501649612103349
     * p91: 9013083042987594426937058395407399258920602180169418633718953519751104768202556013040162739

An 104 = 229 * 431173 * 10467401297 * 14764039052569203217 * 17806777365299125394615651399 * c101
c101 = 37542549183766327696669805442524725656799307149011714422749107177757747287935900829463893679199309557
     = p48: 390652581877305013602683191199123803926767322647
     * p53: 96102140176197730796878284064741781227227687153272531

(February 04, 2003),

j(tau) 749 = 2^7 * 7 * 1213442520231779 * 98695580776821508033676030473 * c101
c101 = 10538831553002348795160113154321814644977253826954691347959990620686175603846423838822477397179280957
     = p48: 435275506456935766674266527932940971323655103327
     * p53: 24211864432222570222476723010754120318020179207966691

95! + 96 = 2^5 * 3 * 97 * 463 * 1264631932355273299 * c124
c124 = 1894572874912624876545048795681656106035394085022591263381588816316772710659309501875951124715683274921887490109394621607509
     = p31: 4621153581208876165761748812953
     * p93: 409978340173886156068908523966992562677805303382045121824157798005602341320241474934055457053

j(tau) 864 = 2^26 * 3^11 * 6902849 * 361659308657159 * c124
c124 = 3903542493914240093027372475023982122831910270593975502770884602976296867619451830984608525147205198252009412618135995480613
     = p33: 635122946924719297815273674764231
     * p91: 6146121019269241423063032308772134705278175553111875572976703958716460344980568950505414323

February 05, 2003

By Robert Backstrom (February 03, 2003),

Wolstenholme Number 3 (116) = 173 * 76206181 * 262016771 * 664194857 * c123
c123 = 756339082989386674981525773652397914634600049192247471430446700839421067597073527406063696138925921588905262887183250863561
     = p31: 1288915283583447604166104281307
     * p93: 586802788843196604189054625188748871936357207450798477078537198254212362266139571737720820523


By Sean A. Irvine (February 03, 2003),

j(tau) 533 C115
27287430518473806294703795416335173396534049149 (p47) *
53234850049136683797737848479362139055717022787131954906234351141641 (p68)
by GNFS, 5 days

February 04, 2003

By Robert Backstrom

(February 02, 2003),

j(tau) 777 = 2^8 * 3^5 * 5 * 7^2 * 787 * 11743 * 39557691348797 * c123
c123 = 115249873213788897933710310515699906521230683994474447650555025978187399750238176331833127679445188776521043980474842934331
     = p34: 1947431755980085281980791261720871
     * p89: 59180442580277744921372492911249696606534664215918217621053499145107025669895186788397261

(February 01, 2003),

j(tau) 874 = 2^16 * 3^5 * 5 * 1363321651 * 180442077665182548571 * c122
c122 = 49411986873924450608238418918606479606427970333617822602687392428179806971421993494333067727060731322146163480290209349971
     = p35: 37754341265095784247612857106494123
     * p88: 1308776294810002704878249183468209976594511353053588614317551409952490680182598672067577

(January 31, 2003),

Wolstenholme Number 2 (218) = 269 * 9419 * 76561 * 170609 * 1373539 * 554400841 * 10706122337909 * 7698541041609895123 * c121
c121 = 3999884503190596969891566771064581448585882492534902573472824314658647826657940705061649333663598473841311879743336511683
     = p31: 4820741441067505150370823541139
     * p90: 829723923609738838856348787482304905375836362190306001967247058985908279287559090658490897

(January 30, 2003),

Numerator of sums of 1/p (56) = 353 * c104
c104 = 24504252652223706246697335419356503645611278111060814860990440468575203699995064346624457783271150292747
     = p32: 27281214795174369762755731429871
     * p72: 898209732821653319220542972742946383138820336943361179852397341671893157

j(tau) 630 = 2^15 * 3^9 * 5^2 * 7^2 * 643 * c121
c121 = 1061384911701968177193167881715487625242819021293954121201436814547068254638063919224503301973044313453536900936606354571
     = p35: 31674942064840995484345769585703907
     * p86: 33508661500603006886203528736557363110535107436401214121260362701754773559962364042553

# Compositorial(124) - 1 = 97 * 2791 * 1212551773681 * 26641125044957818017047 * c121
# c121 = 5448239308725180452521363488602368650924712646697711921254183354712890039872936851024414348901276094149123704423485522191
#      = p31: 7078317587567030354738937513559
#      * p90: 769708230991915299781326087404092183910508693477777021537158180032970507088601108713994249

January 31, 2003

By Robert Backstrom (January 30, 2003),

j(tau) 689 = 2^4 * 3 * 11 * 84395203 * 123066109099 * c120
c120 = 171496759760152038224348267695247679595904519075184211196459972872646071786462867657870890069676631659529659938099749489
     = p40: 1536959264743287310664431983782098516717
     * p81: 111581851057579275069713859745253441666489991815990630235213456001756505915760917


By Sean A. Irvine (January 28, 2003),

K98 C124
249005854215940273354849230153528526528320514781671 (p51) *
12554844335885269284014257210254854210399654907616875772919833182509389801 (p74)
by GNFS, 17 days

January 28, 2003

By Robert Backstrom

(January 27, 2003),
Wolstenholme Number 4 (82) = 83 * 1292587 * 136236313 * 88130331323755617353087 * c100
c100 = 5793443290084109525347575423241440888160231898301492737620325231688410132217478155094935241247010931
     = p47: 17303217840410217023929479610749816305867333633
     * p54: 334818837947818446819548023876418928855989512184123507

(January 26, 2003),
Compositorial(110) + 111 = 3 * 37 * 1153 * 4091 * 2576257 * c119
c119 = 42092031952386588204673548375007521535663876025934075851509086082099335890239901625269585953241933294913261353791235891
     = p33: 182196254248241991218982102124453
     * p87: 231025781106543981304162137907296366901446876433869339348851611710288117114262328032247

Wolstenholme Number 3 (106) = 107 * 107 * 1127030805343 * c118
c118 = 7108708343011430155967470437195128981055614418455451269682634226245212738970811075698982165629034582158118755468578707
     = p33: 200414552344377659577370377027947
     * p38: 20749919876018370834594294881710880651
     * p49: 1709405194120020574653953207879559542609925409931

January 27, 2003

By Robert Backstrom

(January 26, 2003),
Wolstenholme Number 3 (102) = 103 * 103 * 1035361 * c118
c118 = 7642137470999641994885519196452386930118072401846362402189960774784939739987562031939688415228930808330258245293964563
     = p26: 93602171089177370369825639
     * p92: 81644874067277422672067594021656021237675993358687743577054703490930332873199860253180883317

(January 25, 2003),
Wolstenholme Number 2 (145) = 86477 * c118
c118 = 1236519026597803769325553908033763104608146904941051378427978139483651429029700852293336489369617775009558088432818521
     = p37: 7868099745111937253040655226728687109
     * p81: 157155992762546270846346189104176881289387699907633311891122210605186201390912069

Kn(105) = 3^2 * 11 * 503 * 4549 * 1407181 * 214840051 * 2224323069242445590014673291 * c118
c118 = 7167359979555886087601592409601525119566468292172155604764330028799355659752955762179624016099620142054556076091015701
     = p34: 4099535860479868375392505964383273
     * p85: 1748334500168737553466101739372269658677857589989859185028021359348960489113764660237

(January 24, 2003),
Compositorial(111) - 1 = 53970003815150555423 * c117
c117 = 116772713392819996118683532613355373372627022632576663840523680048446946822782454864732989001146140683509632632116513
     = p34: 6683171270258856025862257208781871
     * p83: 17472650134297260848686541137655882526581597241981664073428267388173864252278697903


By Robert G. Wilson v (January 24, 2003),

Compositorial(126)-1=750448953620887367410573061184198797002054435486520653650279640059827577807585058764462842896400614348059994236655173989266694772621311999999999999999999999999999999
= 202841873114353460109307495936795922369 *
3699674737265992214167800204891032816490938467733505169338647940059707892260953051267923283887176764587395734878965088658702271
(Composite).

January 24, 2003

Tom Hill reported the performance of Tomabechi's PPSIQS.
Please see, here.

According to his report, we can factorize under 100 digits numbers within 80 hours,
and under 105 digits numbers within 10 days.

January 22, 2003

By Robert Backstrom (January 21, 2003),

j(tau) 736 = 2^26 * 3^6 * 19 * 53 * 140867 * 9112529 * 6567838214744546912971 * c99
c99 = 137673753031584652778589157679508828715970624248224635255823115799749077667777359988509528501155789
    = p40: 8632111313570112804846031023562587286051
    * p59: 15949024292023967995940263786486166879254827477991058709839


By Tetsuya Kobayashi (January 20, 2003),

by GMP-ECM 4c (B1=1000000)

#Comp+1(135) = 19437707 * 189067237 * 2887541871197297 *
4123217486131673836800154505583133923296257 (p43) *
11692368258132293403867555890711521482174288031020496822745529767855535528706684225308168095559651182255191
(c107)

#Comp-1(124) = 97 * 2791 * 1212551773681 * 26641125044957818017047 *
7078317587567030354738937513559 (p31) *
769708230991915299781326087404092183910508693477777021537158180032970507088601108713994249 (p90)

#Pn-Next(92) = 4326124537177 * 37014563287463 *
19840070481640014859714635964651 (p32) *
329344641854808872322267119303323765773051473744291522515972117467118913823370805039653444057872128954508727407973629115659559627331024595043
(c141)

#Pn-Next(93) = 2270071 * 100734575803747 * 302225186156696915091037 * 425519736344229699232883457343 *
34410349027035202086980268200441819 (p35) *
503543482334354435577153340592071882246622910030445934761994020311416306693129563103332533203 (p93)

#Pn-Next(95) = 701 * 1032276011783 *
60990521808162637156705302405977 (p32) *
2828787060845232390191557668850472950301653492824680904359486722225487496125393057796931244992804111602047422322557791965599361342827757543320107371728248971057
(c160)

An(122) = 4447 * 8748589 * 224671944757814893698923 *
5357184344026871433813454489 (p28) *
2091719404733295490351680008300975974728730624340763365262075427987433868905108531073887829988937579745498752250697148321959617959596130441219
(c142)

An(131) =
154897098711246670758585090356549 (p33) *
5427736110001685179268129029599304755566812992074805392783512471714883137814950643141765734812894922624675413349085385383019702445495653794220288618914149401236801733039806181590324776723969
(p190)

An(143) = 463 * 5779 * 93407 * 15687339179 * 171642157811 * 188516496362759704438837649 *
6311722240957283358780698522887 (p31) *
47801725768820889369093164548244418625112165529887798199530340609414703195999751574971166662779518845642087266243435905562077282158855413598697776214711959057
(p158)

!n(125) = 2 * 4003462951519339518498108071 *
735680089427823377647105992061 (p30) *
257767310423870387697020754829125512340977287275705425167916531658286344165374468173945706467412083644511220074994595730170505816160469822699703688647
(c150)

!n(150) = 2 * 193 * 4273 * 110967919 * 32305343490253 * 1318985116716816679014834977 *
2180905096301566573580878199 (p28) *
279076732153434584735416770874361 *
80785709818845671276248756464382131699447046700239233182323629574833995570217140386811826665880134629359506111469756127963961852589073707304515553
(c146)

January 21, 2003

By Robert Backstrom (January 17, 2003),

Wolstenholme Number(307) = 163169 * 638663 * 25984741 * c114
c114 = 920655861168153754244380005306615451610524615319253728366132633898198880594135287603121089091655080396693844163409
     = p40: 5822460904403726261068004897403933183499
     * p75: 158121432893062493176295690980213056288430228901994694073674948108498035091

January 18, 2003

By Robert Backstrom

(January 15, 2003),
Product of Pn (to 307) + NextPrime (311) = 46641022492394831 * c107
c107 = 13452543537395461112259458442956562510381049482201767353114972350599221210533519759701435848891506505035451
     = p37: 1594781337498366500444666194774775731
     * p70: 8435352998610845769087621355517704808144164903147152053413627676412121

Wolstenholme Number 4 (92) = 468121 * 2127659 * 192437515033114355107171771994237 * c112
c112 = 1507158229791904275026898464014431947359348143148892489843316684671779917468999121136044003143875969455203523831
     = p33: 170898020260958623826883176097757
     * p38: 55047726577495955307739585256102882153
     * p42: 160207347460097643346896656688679636168811

(January 13, 2003),
Compositorial(104) - 105 = 3 * 5 * 7 * 413100454723643 * c109
c109 = 9899522902581455841929453561164028654308521349125674464513077275593063091789918708216837834950213723374708493
     = p35: 27390769640106813323791770362124797
     * p75: 361418208858436865805513585299726415585930588006487622188869451784051967569

Compositorial(95) + 96 = 2^5 * 3 * 67 * c110
c110 = 67568952568969963358407790471050840601579775045442282298548352047615235063742278009786673671641791044776119403
     = p35: 56362682587459425664304945892015817
     * p76: 1198824283498598209040148187034901412486160476942530188593869069987507488659

# j(tau) 880 = 2^23 * 3^5 * 5^2 * 11 * 2309 * 164030729 * 257746603 * 8361174759925423014273453289747 * c97
# c97 = 7516590328496668658021725692319649864323343703693034963111899609417279443300537507810284570092607
#     = p44: 14231133037614394463193205016030561377668769
#     * p54: 528179331092578711125807227297127863403018993383892703

(January 12, 2003),
84! - 85 = 5 * 17 * 107358283884281839 * c108
c108 = 363186323364468719954231021472864342923532899954581296663756197699954672947155652437260116112564670337331441
     = p32: 24236617038454113533422134992671
     * p36: 205556603617541401961004470832022081
     * p41: 72899752162733702869324401861983712236591

# Compositorial(108) - 110 = 2 * 5 * 11 * 6927983577517 * 125058671905223691223 * c97
# c97 = 5415827332214524703294270230906356015967093370414505953509044682512715506268979340224733738188189
#     = p35: 61803396716849802286935449585397679
#     * p62: 87629930067225216235462107974324473353205515353928892076248691

# Compositorial(128) + NextComposite = 3 * 43 * 16747 *
# 31143370848253634183240832259787 * 20855172966451253480280903113298547 * c95
# c95 = 68458122157528457601734461987932230825160849619091573794468834784732470787765357069440463136947
#     = p42: 141870667492614961111651295564213563231307
#     * p54: 482538944571414147131838196419749468115446555552318521

Wolstenholme Number 3 (120) = 6511903610780083291 * 11998733936912481307934447 * c106
c106 = 1306429574432070123031309918690598566427514048115085442040486205930783199207382241955658387704767832302519
     = p34: 1966381222239770821732470375200281
     * p72: 664382653605695665167144810750338280376621945729966580946116640428638799

(January 10, 2003),
Wolstenholme Number(317) = 314816696171 * 1075057622600065015738171 * c105
c105 = 228453688027747334314019042520196931565126236553556990975144660396429492621522681497808581017812904750513
     = p35: 31680957502973075051528303342441549
     * p70: 7211072708465590850583457398845409905858415289006721015782876054126837

January 10, 2003

By Robert Backstrom

(January 09, 2003),

By GMP-ECM 4c
Fourier Coefficient of j(tau) 771 = 2^2 * 3^6 * 7 * 67 * 97 *
1879 * 82537603831 * 17196460053718019591851 * c105
c105 = 470881732592493221611266582297299104974137244181148249694836801849927839535383316364793053835194174921967
     = p34: 6464656237722114836647854553705381
     * p71: 72839407893777353915396615521689523457925319170795213756955141924770307

(January 09, 2003),

by GMP-ECM 4c
Wolstenholme Number 3 (121) = 4885214500670011 *
9389680761825277 * 82635410947934420671 * c103
c103 = 4337029378373928101755227590636203020151027989755218142695023737751511578834415082335175400732965664449
     = p33: 189260215174424633349063990521489
     * p71: 22915695062360921404236848178150179020908397060024314307442092538510641

(January 08, 2003),

By GMP-ECM 4c
Compositorial(95) - 96 = 2^5 * 3 * 113 * 3613 * 560212947149 * c95
c95 = 19793493039195221579629802825891852422286641657909803853748898716852650846879986992374214920679
    = p34: 3339391946217065346867232966551151
    * p61: 5927274593094025406774611374565893071898812253297485508792329

(Craig Kitchen also found the same on January 08, 2003.)


(January 07, 2003),

By PPSIQS
sigma1/p(78) = 1237 * 40087 * 193883 * 71681682691 *
8335042497553 * 6407545381506250342667407731823103 * c91
c91 = 5689314168309031342231826397897965391542806274540336831495552706674506256675085214342451431
    = p37: 1632270826911851865940901782780510543
    * p55: 3485520953084015089408978297978029742545759973873885417

# by GMP-ECM 4c
# j(tau) 697 = 2^4 * 3^6 * 5 * 7^3 * 43 * 8111 * 12415537 *
#       1144089409405671344165873 * c98
# c98 = 63498898956136569676361041374523823843093020084154132847028511520126400145125804280229008982928879
#     = p34: 4638142558143609080428027750747549
#     * p65: 13690588023139946989063405859682446878977342193743599882390002171

Jtau(697) had already factored by Craig Kitchen on January 06, 2003.

January 07, 2003

By Robert Backstrom (January 06, 2003),

An(113) = 797 * 1597 * 7069 * 370298209 * 114868714856832773 *
3138375181864537532903 * 1909887851191940824724911 *
14124799454310769615865729533 * c75

c75 = 682560842725053885024416907579776362920132741227303027183990502737463569257
= p32: 27251376958639689372790837924693
* p44: 25046838688591732939372977442441017704030149


By Craig Kitchen (January 06, 2003),

Compositorial + NextComposite
128 : 3 * 43 * 16747 * 31143370848253634183240832259787 * 
20855172966451253480280903113298547 * c95

68458122157528457601734461987932230825160849619091573794468834784732470787765357069440463136947 
= P42 * P54
P42 = 141870667492614961111651295564213563231307
P54 = 482538944571414147131838196419749468115446555552318521

Compositorial - NextComposite
108 : 2 * 5 * 11 * 6927983577517 * 125058671905223691223 * c97
c97=P35*P62
P35 = 61803396716849802286935449585397679
P62 = 87629930067225216235462107974324473353205515353928892076248691

Fourier Coefficients of j(tau)
697 : 2^4 * 3^6 * 5 * 7^3 * 43 * 8111 * 12415537 * 1144089409405671344165873 
* c98
c98=P34*P65
P34 = 4638142558143609080428027750747549
P65 = 13690588023139946989063405859682446878977342193743599882390002171

880 : 2^23 * 3^5 * 5^2 * 11 * 2309 * 164030729 * 257746603 * 
8361174759925423014273453289747 * c97

7516590328496668658021725692319649864323343703693034963111899609417279443300537507810284570092607 
= P44 * P54
P44 = 14231133037614394463193205016030561377668769
P54 = 528179331092578711125807227297127863403018993383892703

January 05, 2003

By Tetsuya Kobayashi (January 04, 2003),

by GMP-ECM 4c (B1=1000000)

#Comp+1(117) = 131 * 3637 * 5197 * 566723 * 1314301 *
358473660602236012406528777728115441 (p36) *
189962617379527320217393001166104734305921591120129356285202416445009644151031618522893773 (p90)

n!+Next(117) = 2 * 59 * 131 * 13694830133 * 14771319743 *
672343202835731160870873402989 (p30) *
1888266820449328486691369383092577039861500980961304229409347758794904196459314902467505720559144186738309990545020032694277171850251632581 (c139)

#Comp+Next(148) = 2 * 3 * 5^2 * 373 * 2521 * 1539125097616588429 * 2149566039415057103669 * 361415009257544929102862351 *
221745566391564723228483385261 (p30) *
6825295745457943527254950973201495998423940653753499999401012690378739550081244123213128320981267527 (p100)

#Comp-Next(143) = 2^4 * 3^2 * 241 * 631 * 1973 * 2671 * 395803 * 924091788387166833769 *
35271184305299614289806438669 (p29) *
2585197638130466404568275876317803032524845157485586054635218387622164082023440916541047314344753751899078569929542696750221 (p124)

1/p(78) = 1237 * 40087 * 193883 * 71681682691 * 8335042497553 *
6407545381506250342667407731823103 (p34) *
5689314168309031342231826397897965391542806274540336831495552706674506256675085214342451431 (c91)

1/p(82) =
1661985439636800100353810329 (p28) *
3662340516341827979805102472827870140531528770092670458420063857766283446068410877779522825093555556860420624371915401164131650949909634417456337 (p145)

1/p(87) = 22872332994788361786551293 *
25987476354575450930279719647919 (p32) *
167793996132539906099828270232104622236652156556833860118612001922544826314420977338204156451012291765462757975286708579632925091 (c129)

1/p(93) = 9874409 * 317261207 * 1621581182314216397737 * 75055123084717598199732809 *
2990329531573746494550783541261 (p31) *
935252261652296943251416638495342671801163235247312779755820634057672079631596512239675007097507821241958223 (p108)

An(104) = 229 * 431173 * 10467401297 * 14764039052569203217 *
17806777365299125394615651399 (p29) *
37542549183766327696669805442524725656799307149011714422749107177757747287935900829463893679199309557 (c101)

An(113) = 797 * 1597 * 7069 * 370298209 * 114868714856832773 * 3138375181864537532903 *
14124799454310769615865729533 (p29) *
682560842725053885024416907579776362920132741227303027183990502737463569257 (c75)

An(129) = 193201 * 424769 * 36874181 *
4052576929889020795880741833 (p28) *
4025135711316721056700461409085320525804225720474278464940882561971002905389284401231769792378759975480939828481637200968478440664063636985721759407258552585447960137074313 (c172)

An(138) = 641 * 4683383041823 * 10097677219369 * 116831796825979753459 *
1696577794723594035652714717 (p28) *
114302985988768439323439359692790743700124905908341429426490914373552458526330809400892884961641272407355327600189210167604396357771802899017376810646219902197819 (c162)

An(143) = 463 * 5779 * 93407 * 15687339179 * 171642157811 *
188516496362759704438837649 (p27) *
301711215691207702606975624686093768735701322649262169815377588236767935731873059551170564529802780592460462345797104228058616137370841453907814750603938698699095127726400781999973921437559 (c189)

!n(150) = 2 * 193 * 4273 * 110967919 * 32305343490253 * 1318985116716816679014834977 *
279076732153434584735416770874361 (p33) *
176185966252260031028280134264004497087035929680758540244179614475016854081021310966725594931799122448657123549078733985742205290876998268148968226341830532920710007994129047 (c174)

Kn(105) = 3 * 3 * 11 * 503 * 4549 * 1407181 * 214840051 *
2224323069242445590014673291 (p28) *
7167359979555886087601592409601525119566468292172155604764330028799355659752955762179624016099620142054556076091015701 (c118)

Kn(132) = 3 * 3 * 11 * 307 * 761 * 2105315952144649 *
229671244617957421569367963 (p27) *
10075325366431025321114491890460448009418876296736595650198116061244127449859988873546232795327824789170821626134267424836131104423800900894783039359003828323349502936698626163 (c176)

Kn(137) = 3 * 3 * 11 * 271 * 433 * 501036959 * 26883657461 * 43972500175363 * 16210933606229969 * 12764765239107309599 *
1064405444760785092405786303 (p28) *
3332040674557017226396689491872435807810220266574514391130881558664232264460563131792083599336689881539697767994025573907143803254749 (c133)

Kn(141) = 3 * 3 * 11 * 331 * 6373 *
2078618825775576423279277 (p25) *
4403909376190031338841748472765171636858489326412036806137308360334186690387918602503436382299721805986579452784181416963477771557048278895390241821874401006132118354213058502685653484634251967800418711591138137 (c211)

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