ECM - why 3 curves?

James Heinrich · 2017-11-13, 02:22

Just playing around with different assignment types I added one worker to do ECM ("ECM on Mersenne cofactors" specifically in my case), and I see that I'm assigned 3 curves each on a bunch of different exponents. Is there a particular reason for this instead of assigning me 10 or 100 curves on the same exponent?

VictordeHolland · 2017-11-13, 12:15

It makes sure assignments are returned swiftly, other than that I cant think of any good reason.

Advanced users can just edit the number of curves/bounds in their worktodo lines.

GP2 · 2017-11-13, 20:30

I have one core doing that too. It's being assigned exponents typically in the 17M range (rarely 15M or 11M) and it's also doing only a few curves (1 or more rarely 3).

In those ranges, exponents have typically never had a single ECM test done. So the strategy seems to be breadth rather than depth.

Among other things, if there's a smallish factor that should have been found by TF but wasn't, then even a small number of ECM curves at t=25 might uncover it. And we might discover some unreliable machines that way too.

LaurV · 2017-11-14, 13:59

There is nothing wrong with assigning 3 curves, or either 2, or 1. Think about it like that, every curve is (somehow) equivalent with doing a P-1 test. Your chance to find factors is the same if you do 10 curves for one expo or 1 single curve for each of 10 different expos (well with reasonable assumptions about expo ranges and ecm boundaries).

Of course, you can do how many you want, a hundred, or a thousand, and report them.

Lower number of curves will ensure people finish their assignments and report something, instead of giving up without any report after half of the scheduled 100 curves.

2017-11-13, 02:22	#1
James Heinrich "James Heinrich" May 2004 ex-Northern Ontario 3,271 Posts	ECM - why 3 curves? Just playing around with different assignment types I added one worker to do ECM ("ECM on Mersenne cofactors" specifically in my case), and I see that I'm assigned 3 curves each on a bunch of different exponents. Is there a particular reason for this instead of assigning me 10 or 100 curves on the same exponent?

2017-11-14, 13:59	#4
LaurV Romulan Interpreter Jun 2011 Thailand 22073₈ Posts	There is nothing wrong with assigning 3 curves, or either 2, or 1. Think about it like that, every curve is (somehow) equivalent with doing a P-1 test. Your chance to find factors is the same if you do 10 curves for one expo or 1 single curve for each of 10 different expos (well with reasonable assumptions about expo ranges and ecm boundaries). Of course, you can do how many you want, a hundred, or a thousand, and report them. Lower number of curves will ensure people finish their assignments and report something, instead of giving up without any report after half of the scheduled 100 curves. Last fiddled with by LaurV on 2017-11-14 at 14:02

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2017-11-13, 12:15	#2
VictordeHolland "Victor de Hollander" Aug 2011 the Netherlands 2³·3·7² Posts	It makes sure assignments are returned swiftly, other than that I cant think of any good reason. Advanced users can just edit the number of curves/bounds in their worktodo lines.

2017-11-13, 20:30	#3
GP2 Sep 2003 3²·7·41 Posts	I have one core doing that too. It's being assigned exponents typically in the 17M range (rarely 15M or 11M) and it's also doing only a few curves (1 or more rarely 3). In those ranges, exponents have typically never had a single ECM test done. So the strategy seems to be breadth rather than depth. Among other things, if there's a smallish factor that should have been found by TF but wasn't, then even a small number of ECM curves at t=25 might uncover it. And we might discover some unreliable machines that way too.