[QUOTE=retina;263494]It was easier and faster than factoring it. :wink:[/QUOTE]

Sure, but is verification any faster than proof?

[QUOTE=jyb;263484]Specifically, given any composite C with no known factors, it follows immediately that 2[sup]C[/sup]-1 is also composite, and chances are good that no factors of [I]it[/I] are known either. .[/QUOTE]

Chances ares ZERO that no factor is known. If C is even, then
2^C-1 splits as the difference of two squares. If C = ab is odd, then
2^C-1 is known to have the factors 2^a-1 and 2^b-1.

[QUOTE=R.D. Silverman;263509]Chances ares ZERO that no factor is known. If C is even, then
2^C-1 splits as the difference of two squares. If C = ab is odd, then
2^C-1 is known to have the factors 2^a-1 and 2^b-1.[/QUOTE]

Why don't you read my post again (just the part you quoted) and see if you can figure out why this is incorrect?

How much ECM has been done on M1277, M1619, M1753, M2137?

A *huge* amount....someone else will have to say how much that means.....to the point where the probably effort to find factors that way exceeds the effort to run NFS on it and get the factors with certainty.

[QUOTE=lorgix;264576]How much ECM has been done on M1277, M1619, M1753, M2137?[/QUOTE]Your answer lies here: [url]http://v5www.mersenne.org/report_ECM/[/url]
These are best left to a big sieving project.

Are you seriously saying that those numbers are ready for SNFS?
That no more ECM should be done?

I'd like to know if anyone has completed t65.

[QUOTE=lorgix;264626]Are you seriously saying that those numbers are ready for SNFS?
That no more ECM should be done?[/QUOTE]
[QUOTE=R.D. Silverman;262950]After Bruce's work and EPFL's latest pass, the chances of finding a factor
from 2^n-1 for n < 1200 is [i]miniscule[/i]. For most of these numbers, ECM
does [b]not[/b] have the "best chance" per GHz/day. Instead, with high
probability, NFS will succeed with less work. And it is guaranteed.

If NFS@Home were to attempt a larger number than M1061, some additional
ECM work might be done on that number as a pre-screen. Otherwise,
further ECM work on these numbers does not have a lot of value.[/QUOTE]
Bob said it.

I would be surprised were even M1277 'ready for SNFS' in a useful way.

The PS3 ECM implementation in [url]http://eprint.iacr.org/2010/338.pdf[/url] stopped at 1200 bits, so I don't think they've done their B1=3e9 magic on M1277.

(their largest reported-failure was 142162 curves at 3e9 on M1193)

It looks as if we would need a better siever (larger large primes, in any case) to be able to find relations for M1277 at any sort of usable speed; maxed-out parameters for gnfs-lasieve4I16e get me about one relation a minute and we need a billion.

(which suggests that 'ready for SNFS' would be about 200 million minutes of ECM, which is a few million curves at PS3-speed ... so wait for a better siever first)

I don't think Bob said 1200 > 1277 though.

I left out M1061 because it's already in sieving.

Thank you, fivemack.

I'm assuming 85e7~29e8 should be used.

Just finished P-1 to B1=10^12, B2=10^14, reported and got 122GHz-days credit. :smile:
[code]
Manual Testing 1061 NF-PM1 2011-11-21 02:02 B1=1000000000000, B2=100000000000000 122.3257
[/code]

Yeah, I know about all the efforts, as discussed in few threads around, like [URL="http://www.mersenneforum.org/showthread.php?t=14822"]here[/URL], and [URL="http://www.mersenneforum.org/showthread.php?t=14236"]here[/URL], and the current thread, and I know about nfs@home sieving it already, in a word, I know the futility of my action. I just had an antediluvian computer who crunched it for two months and half, phase two had to process 2400 primes and needed just few MB of memory. So I let it run. I even forgot about it, till I saw the primenet report in the morning, when I was looking for my eventually GPU-2-72 new factors :D, the report is few days old already... and it took the older numbers to 3 levels of magnitude higher.