Cunningham ECM Now Futile?

[R.D. Silverman]

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?

[xilman]

Originally Posted by R.D. Silverman

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.

[Batalov]

B+K as well as Cyril Bouvier are finding some factors (the last one today) for 5+-, 6+- extensions... However, all of the last ones were ... well, futile. [/tautology]

[R.D. Silverman]

Originally Posted by Batalov

B+K as well as Cyril Bouvier are finding some factors (the last one today) for 5+-, 6+- extensions... However, all of the last ones were ... well, futile. [/tautology]

Well, yes. From the extensions. When the tables get extended
there is always some low hanging fruit.....

[bdodson]

Originally Posted by R.D. Silverman

Rhetorical question: Are we wasting our time running ECM on the
(older part of the) Cunningham tables?

On the contrary; there may still be a few p<58 factors left
on the oldest parts above c290. It is the 3- and 3+ extensions
that have been getting 100000s of curves with no factors. I've
been running t60's on the smaller ones (under c234 for sure, under
c250 mostly) and 2t55's on the larger ones. Virtually nothing left
by Sam's and PaulZ's runs after the proposed extension was announced,
before the official extension.

Mostly everything under C250 is ready to sieve, with perhaps a few
exceptions of the hardest gnfs --- running ecm after t60 has failed,
say to 3t60 or some larger fraction of t65 looks extremely un-promising
with current resources. PaulZ keeps observing that we have sufficient
hardware to find a given p65, on a particular number; but I don't see
anyone running 2nd or 3rd t60's after the first t60 failed on a larger pool
of possible candidates.

-Bruce (I'd be happy to be proved wrong ...)