>From: George Woltman <[EMAIL PROTECTED]>
>To: "David Campeau" <[EMAIL PROTECTED]>, <[EMAIL PROTECTED]>
>Subject: Re: Mersenne: V20 beta #4 (will the beta never end?)
>Date: Thu, 20 Apr 2000 11:43:46 -0400
>
>Hi,
>
>At 07:47 AM 4/20/00 -0400, David Campeau wrote:
>>Seeing that not every time a stage 1 gcd will result in a factor found,
>>are
>>we not better to wait until the end of stage 2? This way, we could factor
>>deeper.
>
>Brian Beesley's timings showed that running the Stage 1 GCD will
>save time in the long run for exponents above 4 or 5 million.
This will, of course, be almost every exponent within a month or so of v20's
release to the public - as it stands, most of the lower exponents are being
taken by those of us who connect immediately after they expire.
>>some preleminary data (on my machine at home):
>>Total P-1 test = 91
>>Stage 1 factor = 2
>>Stage 2 factor = 1
>>
>>So on my machine the stage 1 gcd saved me 2 stage 2, so about 2 hour of
>>cpu,
>>but at the cost of about 90 * 230 sec of stage 1 gcd = 20700sec or 5:45
>>hours. Seems to me that we could save a little bit by forgoing stage 1
>>gcd.
Of course, some users will be inconvenienced by the memory usage in Stage 2
and may want to take that into consideration. Since I myself have 128 megs
of memory, and rarely run anything except Netscape, AIM, MS Office and
shareware games, P-1 for PrimeNet is not a major problem for me, aside from
the slight delay in my assignments when I get new work.
>
>I know you are working on the smallest double-checks (about 3 million
>or so). Thus, it is not surprising you would be better off not running
>the stage 1 GCD. First-time testers will be better off running the stage 1
>GCD, and most double-checkers will be neutral to slightly better off.
And, of course, double-checkers tend to be people who have more of an
interest in the project, and may be running multiple clients. They are,
therefore, more likely to take the time to analyze the documentation. Not
to be stereotyped, that's just a general pattern that my common sense leads
me to expect.
>
>The GCD cost grows at an N (log N)^2 rate. The stage 2 cost grows at
>N log N (the cost of an FFT multiply) times something (the stage 2
>bounds grow as N increases). I don't know if that something is
>O(N) or worse. It doesn't matter. It does show that at
>some point you are better off doing the stage 1 GCD for a 2%
>chance of saving the cost of stage 2.
>
>Regards,
>George
>
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