ECM on small Mersenne Numbers

Erich · 2012-03-09, 17:28

I have a question about the ECM test on small Mersenne numbers. What is the purpose of finding factors of these numbers, since the entire exponent range in which ECM is being performed has already been checked by either LL or factoring? I'm guessing there must be a reason to run ECM; is finding more factors in this lower range useful in some way?

bcp19 · 2012-03-09, 18:19

Quote:

Originally Posted by Erich

I have a question about the ECM test on small Mersenne numbers. What is the purpose of finding factors of these numbers, since the entire exponent range in which ECM is being performed has already been checked by either LL or factoring? I'm guessing there must be a reason to run ECM; is finding more factors in this lower range useful in some way?

The main purpose is to find all of the factors of the number. If you use the number 60, you can say it has a factor of 2 and stop, or you can take it all the way and say it has factors 2,2,3,5.

Erich · 2012-03-09, 18:46

OK, so it is an attempt to find all of the factors of each Mersenne number, as opposed to any factor.

Prime95 · 2012-03-09, 19:23

Quote:

Originally Posted by Erich

OK, so it is an attempt to find all of the factors of each Mersenne number, as opposed to any factor.

No, it is much more an attempt to find any factor (although a few users do some ECM on the really, really, small Mersenne numbers in hopes of finding all factors).

You are right in that this does not help at all in the goal of finding new Mersenne primes. But some of us find a known factor more satisfying than a couple of matching LL results.

CRGreathouse · 2012-03-10, 02:49

It is useful to have the full factorization of the first X Mersenne numbers for certain number-theoretic algorithms. Jan Feitsma used factorizations of this type to speed his search for pseudoprimes up to 2^64, for example.

cheesehead · 2012-03-10, 03:47

Quote:

Originally Posted by Erich

OK, so it is an attempt to find all of the factors of each Mersenne number, as opposed to any factor.

The exponents PrimeNet will give you if you request an ECM assignment are those of Mersenne numbers for which no factor has yet been found. So it's still a matter of finding the first (or any) factor in those cases.

It is possible to do ECM on Mersennes for which a factor is already known, but it's more complicated to get PrimeNet to register an assignment in this case -- one can't just simply ask PrimeNet for an ECM assignment. The procedure to follow in order to get an assignment registered in such cases is described here: http://www.mersenneforum.org/showthread.php?t=11308

LaurV · 2012-03-16, 16:31

This is to report a small "misbehavior" of the server when ECM for small mersenne is reported. I did not want to create a new topic, as we have already one and it seems to be in the right subforum too.

So, I found by mistake (related to my activity in the last days, see this thread) that one can do multiple reports for the same ECM result he gets. For example, once you have a "valid" ECM result ready to be reported like this (the assignment keys made up):

Code:

[Fri Mar 16 11:53:26 2012]
UID: LaurV/pinch, M6620423 completed 3 ECM curves, B1=50000, B2=5000000, We4: AB3A7E78, AID: EE233FA52592387CD6D97C67F58FD73E

then you can report it multiple times and get an infinite amount of credit. The credit itself is not a big deal (why should I care if one gets billions of GHzdays of ECM work??? He does not take them from my pocket!) but it seems that PrimeNet considers each report as DIFFERENT curves, according with the increasing amount of credit he gave for each report, so in fact, I could report I did 30 curves, but in fact I only reported 10 time the SAME 3 curves. This could be bad for the project, for example make us to believe there are thousands of curves done for some expo (like 1061 or 1277) and therefore no factors can have lower then 60 digits, but in fact... well you got the point.

As a sample:

Code:

Manual testing    6622997    NF-ECM    2012-03-16 16:26    0.0    3 curves, B1=50000, B2=5000000    0.9947
Manual testing    6622997    NF-ECM    2012-03-16 15:52    0.0    3 curves, B1=50000, B2=5000000    0.9947
pinch             6622997    NF-ECM    2012-03-16 13:42    5.2    3 curves, B1=50000, B2=5000000    0.8550

Not clear yet if there is only a difference between manual reports and the initial P95 report in calculus, anyhow it seems as manual reports are more advantageous :D

This is the same 3 curves, reported 3 time. I swear I did not run 9 curves :D I reported it second time by mistake, then I wanted to verify third time to check if is only maximum one manual report and one automatic report, as the credit was different, seems it is not limited, I tried the third just a minute ago, and it went on, gaving me another buck. Till morning I could go to be first in the ECM top producers :P

Just FYI, maybe this is known already.

Dubslow · 2012-03-16, 18:12

My guess would be that it is known, and the assumption is that only those who actually care for factors (and therefore not credit) would do ECM that doesn't help the project's initial goal, and therefore won't cheat. If someone who wouldn't do ECM otherwise does this just to inflate the credits, well, no one will die if we miss a factor.

cheesehead · 2012-03-16, 21:47

ISTM repetitious ECM result reporting will just cause PrimeNet to go to higher B1/B2 values sooner than ordinarily warranted.

TObject · 2012-09-19, 00:00

Say, when doing multiple ECM curves on a single exponent; and the computer is configured for stage two only on high memory. What is there to prevent Prime95 from starting stage one of the next curve while waiting for high memory for stage two?

Is it just that this feature is not implemented, or is there a fundamental obstacle?

Thanks.

LaurV · 2012-09-19, 03:19

Quote:

Originally Posted by TObject

What is there to prevent Prime95

Nothing. It works like that, and that's the reason of max high workers parameter in the ini file. I discussed before if I queue P-1 assignments for 30 days on 8 workers (say 200 exponents), but allow only 2 workers to stage 2, then it ends up after about 18 days with all of expos stage 1 done, few of them completed (stage 2 done), two workers doind stage 2, and .... 6 workers waiting. The discussion was where I was arguing to increase B1 manually, until you get a balance, i.e. the time needed to stage1 be about 3 times longer than the time needed for stage2. In this case (increasing B1) you increase your chances better then BRS-extension, and also get bigger PrimeNet credit

You always have to work the best compromise B1/B2 for your system and expo ranges. If you have lots of memory, give it to P95 and let it chose automatically. Or use less workers, but give more cores to each worker. In this way you can max your chances without limiting the memory for stage2 too much.

2012-03-09, 17:28	#1
Erich Mar 2012 Northeast US 2₁₆ Posts	ECM on small Mersenne Numbers I have a question about the ECM test on small Mersenne numbers. What is the purpose of finding factors of these numbers, since the entire exponent range in which ECM is being performed has already been checked by either LL or factoring? I'm guessing there must be a reason to run ECM; is finding more factors in this lower range useful in some way?

2012-03-16, 16:31	#7
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 7×1,423 Posts	This is to report a small "misbehavior" of the server when ECM for small mersenne is reported. I did not want to create a new topic, as we have already one and it seems to be in the right subforum too. So, I found by mistake (related to my activity in the last days, see this thread) that one can do multiple reports for the same ECM result he gets. For example, once you have a "valid" ECM result ready to be reported like this (the assignment keys made up): Code: [Fri Mar 16 11:53:26 2012] UID: LaurV/pinch, M6620423 completed 3 ECM curves, B1=50000, B2=5000000, We4: AB3A7E78, AID: EE233FA52592387CD6D97C67F58FD73E then you can report it multiple times and get an infinite amount of credit. The credit itself is not a big deal (why should I care if one gets billions of GHzdays of ECM work??? He does not take them from my pocket!) but it seems that PrimeNet considers each report as DIFFERENT curves, according with the increasing amount of credit he gave for each report, so in fact, I could report I did 30 curves, but in fact I only reported 10 time the SAME 3 curves. This could be bad for the project, for example make us to believe there are thousands of curves done for some expo (like 1061 or 1277) and therefore no factors can have lower then 60 digits, but in fact... well you got the point. As a sample: Code: Manual testing 6622997 NF-ECM 2012-03-16 16:26 0.0 3 curves, B1=50000, B2=5000000 0.9947 Manual testing 6622997 NF-ECM 2012-03-16 15:52 0.0 3 curves, B1=50000, B2=5000000 0.9947 pinch 6622997 NF-ECM 2012-03-16 13:42 5.2 3 curves, B1=50000, B2=5000000 0.8550 Not clear yet if there is only a difference between manual reports and the initial P95 report in calculus, anyhow it seems as manual reports are more advantageous :D This is the same 3 curves, reported 3 time. I swear I did not run 9 curves :D I reported it second time by mistake, then I wanted to verify third time to check if is only maximum one manual report and one automatic report, as the credit was different, seems it is not limited, I tried the third just a minute ago, and it went on, gaving me another buck. Till morning I could go to be first in the ECM top producers :P Just FYI, maybe this is known already. Last fiddled with by LaurV on 2012-03-16 at 16:37

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2012-03-09, 18:46	#3
Erich Mar 2012 Northeast US 2 Posts	OK, so it is an attempt to find all of the factors of each Mersenne number, as opposed to any factor.

2012-03-10, 02:49	#5
CRGreathouse Aug 2006 3·1,993 Posts	It is useful to have the full factorization of the first X Mersenne numbers for certain number-theoretic algorithms. Jan Feitsma used factorizations of this type to speed his search for pseudoprimes up to 2^64, for example.

2012-03-16, 18:12	#8
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3·29·83 Posts	My guess would be that it is known, and the assumption is that only those who actually care for factors (and therefore not credit) would do ECM that doesn't help the project's initial goal, and therefore won't cheat. If someone who wouldn't do ECM otherwise does this just to inflate the credits, well, no one will die if we miss a factor.

2012-03-16, 21:47	#9
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	ISTM repetitious ECM result reporting will just cause PrimeNet to go to higher B1/B2 values sooner than ordinarily warranted.

2012-09-19, 00:00	#10
TObject Feb 2012 3⁴×5 Posts	Say, when doing multiple ECM curves on a single exponent; and the computer is configured for stage two only on high memory. What is there to prevent Prime95 from starting stage one of the next curve while waiting for high memory for stage two? Is it just that this feature is not implemented, or is there a fundamental obstacle? Thanks.