Another one - ECM by yoyo@home factored sigma(467^82) from t500, saving a NFS project at RSALS:
[code]
P46: 4947726040857185102516007340686396523695536351
P126: 197980050742278097899395439860325470417890258230103933976904713646031677407406127407817964809934399087195852992396007380977469[/code]

Someone asked to post factors: And so I shall.
[code]
PRP34: 1742550337291198113097072330267531
PRP66: 411513693526501507341276223561159325575633489664251957113289013551
[/code]

Added in moderation:
[code]
These are factors of
sigma(2264332996616837246388092345997233854542506549933913545440618343701^2)[/code]

ECM result:[code]3413115876788156351831 | σ(5^856)[/code]leaving a c577.

The extension to the 3- Cunningham table at [url]http://homes.cerias.purdue.edu/%7Essw/cun/xtend/index.html[/url] contains a few useful factors.

3^643-1 90409139288880820194533925917030434583969676709199.P199
3^709-1 274491592643873035641589597480400693593.P254
3^743-1 184299732531199558664226573204873006690059.P294
3^757-1 50970551620807604645290420443828540446885807.P274

I'm just listing the factors not in the checkfacts.txt I downloaded yesterday.

Chris K

From t600, sigma(55333^36)
[code]
P55: 5772850333194165742399366695533974156755488478114146383
P97: 4302159248392553378277227194838786969127481890710031995131839100487726245576069187545045634945563
[/code]

Looking around the Cunningham tables at [url]http://mersennewiki.org/index.php/Cunningham_Tables[/url] I found that 11^271-1 has factor 265948315388080203780860845505259306067883090581971551.

I also noticed that the 5- table has several gaps that could be filled in from checkfacts.txt.

Chris K

From t1200:[code]sigma(11^570) = 34662384377922958688821 * c572[/code]

From t600:
[code]sigma(98138549979439469138489095158515442021127198477956313572191080279412141989^2)

P57: 347271086486080023804331816431473226151245600889600438633
P70: 3670800929233225374509510925591831822281584379173731045884131554080251[/code]

From t800
[code]
sigma(1974702993887119^16)

P36: 427400677767892344459685769683326007
P210: 125081576765096503175958783912156103008834717129461343070555283898472131234550878404444174334046277495146108186380177421306455039647273189566125955574825678889097197713561486460410176218625110941357568355334663[/code]

From t600. The large base was factored by Thomas Ruley. The three small bases had

yoyo@home ECM through t50
RSALS SNFS sieving
Post processing by Lionel Debroux and friends

[code]
sigma(127^96)
P61: 2669288262465371351142217904830390312669440703472876824768621
P122: 90006165658164357452474271860412832398522063081759977262154301800900539029717493099426699511980359765377811879658989392541

sigma(127^106)
P81: 805844980755184303074789047450029080808385302121960517970444522982374628442566923
P104: 28396258574775401289886522521644954210909214813391321811252362454811570386595446111122098973735211268889

sigma(317^82)
P57: 165667218838975386148774892995435465309692858238108067371
P141: 286102346475574942343939350064162581360252014941224495489125227496633578133038075313273250691509585282235734692497546077855303910941363844701

sigma(354639323684545612988577649^6)
P54: 113781224932787570877235380486520835574225640096154453
P74: 14503526244684274281329089150662849919767136152563411201282184896373300911
[/code]

Can RSALS work by giving each PC a number to process and having it do all the work for that number? I could generate SNFS polynomials for everything in t1200.txt that will take less than a week or so to factor.

Chris K