A few more smallest numbers from t1200 by Carlos Pinho using YAFU

[code]
sigma(3366749619659150960221042883^6)
P59 : 15235177240850052146612276878410221254337199225620022218449
P41 : 97703474017730135628692260767320008436827

sigma(1702594318846587302612149397633956098232821964830541308689471261574742435735740202028681151991904136514102080427414590891286507761207244895097707413821121)
P60 : 122905588319431830112748007785394790443743188132452214932167
P41 : 13085504011593720920284511813544010752971

sigma(2643566058636238661059790529652952868159565618778261835950411821^2)
P45 : 451390135277541146096643374256357023317536361
P55 : 4007131247035756595292962337889197968059488894939371323

sigma(10291769043128655374740490724787519517494742647433109544467657857169143978218395874748554169^2)
P49 : 7417829203168776436629828856165169504489286754477
P51 : 253535748661567152076424165247296162007788189473717


sigma(167839883042054675512869703384715005675078076766230905975932716751647521^2)
P53 : 98296826709875298709212297704079195775020254431544659
P47 : 25386542339479763974540394141042158765939661101
[/code]

I've already reserved the smallest composites in t1200.txt with Pascal Ochem at [URL]http://www.lri.fr/~ochem/opn/[/URL] and found most of the factorizations above. I also added them to factordb.com before they appeared here.

Anyway, I feel very lucky that William posted the factors here, especially considering that he didn't usually post small factorizations (like those I sent him). Otherwise, I'd waste much more resources.

[QUOTE=warut;224882]I've already reserved the smallest composites in t1200.txt with Pascal Ochem at [URL]http://www.lri.fr/~ochem/opn/[/URL] and found most of the factorizations above.[/QUOTE]

Sorry, that was my fault. I was advising Carlos on factoring tasks, and I forgot to check Pascal's page for reservations. I'll be more careful in the future.

I always post factorizations from Pascal's lists on this thread, although I like to group them to keep the post count down. I also keep my own list of small composites from various OPN factorings - some of these feed the OPN composites page when they have had enough ECM, others are handed out by email. I post those factorizations only when they also occur in Pascal's lists. Currently my list starts at 103 digit composites.

William

Here are a few more numbers that Carlos Pinho factored with YAFU from among the smallest of t1200. Carlos moved to slightly larger numbers quickly after becoming aware of warut's reservation with Pascal. I'm embarrassed that I had directed Carlos into warut's range. To the best of my knowledge, neither Carlos nor warut are currently factoring small numbers from t1200.
[code]
sigma(20701496952978549865985589014277656713219688240766093450394182426709^2)
P50: 14491634098671266692665845737599358797694186120177
P51: 229713223508379694443075572703661040864322968379127

sigma(215037657498809482451765813083169598451853320637716556861^2)
P41: 15500571021297438496674599099739144527449
P60: 215930372312043063191522428520943088502313142556556430660807

sigma(41191321607477420982171263209861331^4)
P31: 9817297281573876786555236007961
P69: 344557642784558059914066991975566591449493197546500114506882816949951

sigma(6773396221406784379729251352961^4)
P48: 381885494535718490984295202940560822510328454431
P53: 30894712119291134294936632106886866599730542649701861

sigma(590385607384351^10)
P49: 1266216608063344007246226524622919833314288469203
P53: 10585149482510673698257043497801731563775179265942401

sigma(1507037281339563840594209968921^4)
P40 = 4729972067065577210833611704891427691501
P61 = 4424172680258274209229635269842554313024682726172051378257721
[/code]

[QUOTE=wblipp;224821][code]P26: 11318127709881100296762883
P28: 8709472493279809677543843709
P45: 646555076222326204672887005617748263663956703
[/code][/QUOTE]

How much ECM has been run on the small numbers?

Some t1200 factorizations by warut and Carlos Pinho

[code]by warut

sigma(3870273363029323250851^6)
P55: 2485871283820573885216352356033253900659587167483616601
P70: 3276335037979689181119237247315390207360270224358374071202031880745607

sigma(7937912597072012839301^6)
P41: 14316299918895968709199362178012082451131
P75: 443774980802385030646251596801480611142447062281817034994767518752533057531



by Carlos Pinho

sigma(48629241577256062625838748375894551966977617104148322647^2)
P47: 33089027219408454915334449328519109235976178119
P54: 716665713355166734160669977128002409838082318498379901

sigma(252773247712614597680142554168925040769775199^4)
P30: 708235825474879503392247019061
P71: 37424663228097643302803671600210750081756529790907960058167206832634671

sigma(16731903133168141693322425258023067^4)
P36: 169423106268285774444782863634150551
P66: 164853853963914940211802084289992110255722503861428073536504762581

sigma(77641447575886912537878903491957184131386078491541340916198683459^2)
P50: 15078965905521851018734699349519105808243736522867
P52: 2298846839746395125904885457021181782215426307236331

sigma(1458398614405596945559445082471045997269960327174338728156523640961^2)
P46: 4658745841663812282876729804952816750847695933
P55: 7645463225990568242011672429536839102186796836095591099

sigma(57288824639910345063732204967313473^4)
P42: 500626890388845581250401319616841703396571
P59: 80027672573960211630172816191741995612473268557174177234631

sigma(10556013436628536491472810118960827906484636377291805158586758073665118344151174067934495493872692190857587921807196800936816718328230808949)
P46: 1066269921400493386823891022817945786031258251
P56: 40634449104647207021561394533723528037848191513035317033

sigma(4359977845598272757076518581118691539852489438400131^2)
P47 = 47824108000342125391768788390332417666796760267
P54 = 917981206567007339636067114141506928684975294752855863

sigma(5568980230140338976462439^6)
P46: 2378601071232421654339121113340059248914985133
P56: 18993958435083341742946739293899386860515151903483122751

sigma(1630954578528106158097259780845944093769939317863135626697854967^2)
P49: 1383971778882162457550660597684110831794964614229
P53: 33316863856553720544798572587129378593937883291293117

sigma(11263883599936683984204999714504018039950712684617892255536959811641^2)
P41: 22821823195971589922097717226260792960007
P61: 2025333509122951539254607664271762980990916862153608715014071

sigma(2166925471028702160318130234776077456815367485156244235818604434644718236693281092050147152663897346923285320538654370618398817011289621)
P42: 139674960649498336741623588557211552058663
P60: 407678858046178698103373805560966203633689298115052297714647

sigma(6591064979223121842783091913720467836620027635880327917^2)
P33: 735991999807277813855605577551273
P68: 83361343130537898445077262870290189332803835252401910149707891094117
[/code]

More t1200 factors by Carlos Pinho
[code]sigma(3954811924355567256296299810005903141495629348920228356242944974308293^2)
P44: 96832337122757210622607843067947213102308031
P57: 649675212392185197138094711098920027475595385271440929777

sigma(9800602068292171582695670195872101044562282268159708236489089023384833761690891199103406311556538113296641252014099878493078441370423454051960198264838485580937588909568748361)
P47: 97621261277456294696015045249991392178637608239
P54: 702364765541756394992455108362536965996332497312551403

sigma(805806360637093144343288020427145164309248943228418129152830826227689289512678808485045219667967323818060202210934292501107799735406871867583131368351126474309)
P56: 48167520778196172610393605132898424110771956601830062011
P46: 1584516692548919351638248517413528613759848037

sigma(3543811998365921041862473467411438251519710130925469106120520513833^2)
P45: 271089370510539447953762278485940637751696793
P57: 294744325938964503165318352326373159489767689008233751387

sigma(9133932443979032517937463330850753467467584790448941318549^2)
P43: 2597735745053294553836673766123358665001917
P59: 43522511452155258616146903004213363014305250361103755460989

sigma(13061966247138294279496504049^6)
P42: 279031890725392454294931084180935925117761
P60: 412452304717630024578233590219349053957299640919509273633993

sigma(148537339219715195541779726605907378119990403172905626985725679^2)
P49: 3017894207307710659929031472117062291998716870353
P53: 56500934625535958372135182287650159903122220254878967

sigma(1191257338224814653076011327363739164618986355649255308404216911930163311157617292145632913132199464280943057247218648383899134452547561542422693924310582721)
P50: 35092568742159665294197592686236863247081260132777
P52: 5135200656633819681327833225570630342640327273109609

sigma(300769820001773419578552841160525897^4)
P40: 8035762001874151030270775009430915430631
P65: 12708815928661147871125548985467016165575330130962794864529336101

sigma(584559257636395879275679^6)
P40: 5907359170549799663080158830589389315003
P65: 21863352887149918993245285818027792784902364951404850434225052097
[/code]

More t1200 factors by Carlos Pinho
[code]sigma(28147894399958175520997236651014413102068118761730337662566901383619833883394250548689^2)
P46: 3348255454686042654028979503272390094287625231
P56: 70158304399931817874623965093718369976170183986322264487

sigma(77568368415953747512579265204067182113^4)
P45: 435789748441368946989123161991537542830443421
P57: 565290331657776569438725821681270073762688372699548862351

sigma(21000245145752398227637515381885577114461751159703142921292850141262027755333541879525642063997393869841^2)
P49: 2279764014043541174743115758967070407926683385369
P54: 125995287583301849356518617922004425790336528111703377

sigma(2010712798704091664137247425058269005588556606765011916813^2)
P64: 1214460207452075193941618124378382359876530215999334667132818947
P42: 109370569925672381734375188936022256806141

sigma(279823724714479347106098038351903865304656195929369449^2)
P45: 184185551248116827864249148488609624348655271
P60: 734234765792631986910475701270920893697419788989235351555439

sigma(63433699405463538473685663515381959718164762390196566014961317811^2)
P46: 8256038890217970300470773504158354740865466357
P59: 16897994275198956819156286509520038301231983358787228732023

sigma(1419039133962591418795945563103299403426784352618069268027^2)
P44: 29931732849818590139902207869878547864037633
P59: 10713994770512051524089429260999096403686243418090484211401

sigma(13206260735204461656258377447877660737815072249^4)
P47: 26278823067140597900052253074717037029402414991
P56: 16179966830414737443392779000601761281724562825089013561

sigma(5939213080142536720797511^6)
P42: 369128392271919832897011858113077176060341
P61: 1385155180776529561860005676495413663914228149911157982714229

sigma(20054087300384132354438712651988057254615218610261134681835315400332673^2)
P43: 7497079629103728153225712422298577913222493
P59: 69433502216552087300217330881104501292582167869851658609133

sigma(23030881817328391685820905621870074530938345237^4)
P52: 1207366189130403397633081977886922328551499583901911
P54: 147018587134802307984706668279930874845125337035730481

sigma(607453794248251^12)
P50: 21454987390487794278090742150188062278517598028597
P56: 11368801873569191810219574859673608158560279344908652399[/code]

This is the last set of t1200 factorizations from Carlos for a while. His processing power is switching over to SNFS post processing for RSALS.

The t1200 (and other t-lists) are dynamic because every factorization opens up new factor chains, and those chains may have incomplete factorizations that qualify for the lists. These factors all come from newly created small entries in the files.

[code]sigma(7362739400916016285054774606883417740884002979504684488481709247968717584701440429^2)
P37: 4493839426948533329741717443597400839
P46: 1571603195198616784321743131725165564796575399

sigma(28794707161850002920661968558268836346817399836148446551503715053225695685282036539312259074276402083892674127193^2)
P37: 1118544349330750412054708929975790857
P52: 3887520485906844369361797414808982711962036650729679

sigma(158890236728741463715008247758940435941464817681909119^2)
P28: 2304592606786298380857643717
P61: 2651543452826178567488106610948128624844325233935048368204911

sigma(19918689331707481608093934777074440675711053521139529124559411886055315388003^2)
P43: 2855166123366392250912749233841048697425059
P49: 8858488984275953547408850833051508610827852263241

sigma(716665713355166734160669977128002409838082318498379901^2)
P30 = 295170118557943473718791292003
P63 = 219297158180794183095847372777415137706354122249364387254068901[/code]

sigma(10801628845957255866230679727801511422754413486734974487148132766971^4)
5*11*8179631 *3061185761*376358629801501*C236

frmky has just posted the factorization of sigma(3^562), which is in [URL="http://www.lri.fr/~ochem/opn/t600.txt"]t600.txt[/URL].

[url]http://www.mersenneforum.org/showpost.php?p=226559&postcount=73[/url]