20120424, 18:34  #1 
"Bob Silverman"
Nov 2003
North of Boston
5^{2}×13×23 Posts 
Cunningham ECM Now Futile?
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? 
20120424, 18:45  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11,489 Posts 
Quote:
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 p45p55 range. 

20120424, 19:53  #4  
"Bob Silverman"
Nov 2003
North of Boston
16463_{8} Posts 
Quote:
there is always some low hanging fruit..... 

20120425, 02:45  #5  
Jun 2005
lehigh.edu
1024_{10} Posts 
Quote:
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 unpromising 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 ...) 

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