20130223, 16:51  #13  
Aug 2010
Kansas
547 Posts 
Quote:
The bank called the other day and said I had an outstanding account. I was pleased I hadn't kept that large of a balance, and for them to take time out of their day to tell me it was outstanding was a real egoboost. The gal went on, sadly, to tell me that it meant I had a negative balance. I started to freak out. Now I'm REALLY broke. Like, I'm so broke, when people offer free mix tapes on the streets, I have to turn them down. They say its $0.00, but I'm so broke I can't afford that much! 

20130223, 22:38  #14  
Feb 2012
195_{16} Posts 
Quote:
Please do not smack axn, though; I certainly hope we can correct and supplement each other with more respect than a pack of raging baboons. Thanks again for the paper. 

20130228, 10:58  #15  
Jun 2003
4842_{10} Posts 
Quote:
Can you point me to the part where the paper discusses the above? 

20130228, 12:45  #16  
Nov 2003
2^{2}×5×373 Posts 
Clearly, the referrees did before the paper was published. Several other
computational number theorists have sent comments to me..... Quote:
the optimal B1/B2 params for just one curve apply to P1. Indeed, if running just one curve P1 is faster....... 

20130228, 14:03  #17  
Jun 2003
2×3^{2}×269 Posts 
Quote:
I saw a statement to this effect. However, given the context of this thread, I was expecting something more. 

20130228, 14:40  #18  
Nov 2003
2^{2}·5·373 Posts 
Quote:
Running P1 is the same as running ECM with just one curve. (only faster!) Indeed. P1 has a benefit over ECM when running only one curve for certain sets of numbers: those known to have P1 lie in a certain congruence class. [such as Cunninghams (and extensions), Fibonacci/Lucas, etc] 

20130228, 18:42  #19 
Tribal Bullet
Oct 2004
110111001110_{2} Posts 
The 10x rule of thumb for P1 stage 1 is used only because P1 stage 1 is computationally faster than ECM stage 1, and if you are willing to commit to performing ECM for that long then you may as well let P1 run for that long as well.
It has nothing to do with the relative probability of P1 finding a factor, compared to ECM. For stage 2, you can use a method whose runtime is linear in the stage 2 bound (this is the 'classical' stage 2 that Bob's paper analyzes) or if you have a ton of memory then you can use fast algorithms that allow B2 to be ~B1^2 instead of a fixed multiple of B1, and still take the same time. The second choice is not suitable for large Mersenne numbers, as it would require huge batches of them. 
20130301, 17:48  #20 
"Nancy"
Aug 2002
Alexandria
4643_{8} Posts 
I've been wondering about that... current Mp candidates have residues of about 48MB each, so on a contemporary system, you could fit on the order of 2^10 residues. That would be enough to make a multipoint evaluation stage 2 worthwhile. We'd need a fast convolution product, however... knowing that 2 is a pth principal root of unity is intriguing, if only p were not prime! A prime length FFT is considerably less intriguing, and generic convolution algorithms would blow up memory use by a factor of several, probably making the polynomial stage 2 uncompetitive. Maybe an external FFT would do the trick.

20140523, 19:06  #21 
Aug 2002
Dawn of the Dead
5·47 Posts 
Can anyone recommend an ECM test for me? I like running bizarre work, the kind others won't touch. I am intrigued by ECM on low Mersenne numbers, such that I have a chance (albeit small) of finding a monster factor. Current box is a cheap work HP and sometime soon I will build a much nicer personal box dedicated for ECM.
I wish I had time to read the linked material, alas I am Dirctor of Operations for a new and rapidly growing mining company and am currently developing two small mines simultaneously (lack of sleep is an issue). I can allocate 1350 MB of ram and don't care if the test takes months. I want to find a monster. I used to like P1, but the gpu crowd effectively ruined that and TF as well. Last fiddled with by PageFault on 20140523 at 19:06 
20140523, 21:50  #22 
ἀβουλία
"Mr. Meeseeks"
Jan 2012
California, USA
879_{16} Posts 
GPU's have ""ruined"" TF but not P1. Not many people use GPU's to P1 at the moment.

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