[QUOTE=axn;399290]I don't understand this statement. Why can't B2 exceed square of B1 (for both P-1 and ECM)?[/QUOTE]

I think you do understand the statement- it's just that it's incorrect. I went back and skimmed both the Silverman and Montgomery papers looking for support for my statement, and found nothing. Then I ran ECM with B1 = 1e5 and B2 = 1e12, and it ran fine. So, I'm simply mistaken.

I distinctly remember reading about this relationship... I'll keep looking, but perhaps I am only recalling a claim that B2 > B1^2 is always suboptimal; that is, to find a factor most quickly, B2 should be selected to be less than the square of B1.

My apologies for spreading misinformation.
Edit: Found the reference! [url]http://mersenneforum.org/showthread.php?t=15486[/url]

So, very incorrect statement, but that's where my poor B1^2 recollection came from.

Actually, for example for P-1, you do powering in stage 1 to compute b^E, which you store. Then in stage 2 you "add" more primes to this powering with a single multiplication. You compute something like b^(E*R) for different R=product of k primes*. The trick is that you can test more primes (as possible factors of q-1, where q is the factor you try to find) with a single multiplication. That is why you can extend stage 2 (B2) higher. As you waste about the same time to do a squaring as you waste to do a multiplication, the right cutting point should be something like B2=k*B1^2, where k is the number of primes in R.

Well, this ignores a lot of other things, like for example, the prime numbers have a... cheesy distribution, you pick one prime q by random, what is the probability that q-1 has all factors lower than B1 except exactly one factor which is higher? How many (even) numbers (in percent) of an indicated size are product of only a big prime and some small prime? etc...

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*yeah, I know you take some "constellation" only, which also will contain non-primes, this is not the point here

My P-1 runs in the 1.5M range (with B1=10M, B2=200M) are finding a lot of factors with the Brent-Suyama extention:
[code][Sun Apr 12 00:16:52 2015]
P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PCVICTOR, M1567483 has a factor: 10229405036637564504977 (P-1, B1=10000000, B2=200000000, E=12)
[/code]k = 3263003501995736 = 2^3 × 29 × 28027 × [B]501,825,749[/B]
23 digits 73.115 bits

And a day later another one!
[code]
[Mon Apr 13 11:35:49 2015]
P-1 found a factor in stage #2, B1=10000000, B2=200000000, E=12.
UID: VictordeHollander/PCVICTOR, M1584157 has a factor: 6061174682472739845780233437247 (P-1, B1=10000000, B2=200000000, E=12)[/code]k = 1913059968952805765394539 = 137 × 60943 × 9,442,729 × [B]24,265,355,701[/B]
31 digits 102.257 bits

P-1 found a factor in stage #1, B1=700000.
UID: Jwb52z/Clay, M77025833 has a factor: 36815836598984416959313 (P-1, B1=700000),

I haven't been able to do P-1 in over a year until the last few days, so I was very pleased to find a factor again.

Welcome back! :smile:

P-1 found a factor in stage #2, B1=670000, B2=12730000.
UID: firejuggler, M76039529 has a factor: 27414116836656177011399 (74.537 bits)
k=7^2 × 344237 × 10686887

Thank you. :) I was looking back at some of my past found factors and I can't for the life of me remember how I figured out or obtained the bits for the factors.

log(factor)/log(2)

I didn't remember having to do math to figure it out and then I found a saved URL to a page on the Mersenne website, but it no longer works. It was at: [url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=[/url]

I wonder if it's another page now or if there is no page like this now. If I remember correctly, it figured out the bits for you when you input the factor found.

[url]http://www.mersenne.ca/[/url] lower right box

Thank you! :) I can't edit that post anymore, so I'll just put it here: 74.963 bits