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Old 2012-04-24, 18:45   #2
xilman's Avatar
May 2003
Down not across

3·3,529 Posts

Originally Posted by R.D. Silverman View Post
Food for thought:

Has running ECM on the Cunningham tables (except for recent extensions)
now become a waste of time? Consider that since the beginning of the
year all factors except for two have been from the extensions.

EPFL ran something like 27000 curves with B1 = 10^9 on the 2+ tables
and turned up very little. They ran step 1 to 3 x 10^9 on the 2- tables.

Bruce has done extensive runs on all of the tables.
[Kudos to EPFL and Bruce]

I just finished a run of 1000 curves with first limit 500million on the 2LM
tables. As expected, nothing turned up. 1000 curves per composite
isn't a lot, but the step 1 limits were fairly high. It took me since last
summer with the resources that I have.

Rhetorical question: Are we wasting our time running ECM on the
(older part of the) Cunningham tables?
You may very well be correct.

Bruce and EPFL between them long ago persuaded me to move elsewhere. One of my first Cunningham results was finding a Most Wanted with ECM; those days are long past.

Shameless plug: the (Generalized) Cullen & Woodall numbers are still good candidates for ECM work with relatively little investment of time and hardware. The homogeneous Cunninghams are still churning out ECM factors at a reasonable rate in the p45-p55 range.
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