At 02:55 AM 2/27/2000 -0800, Paul Leyland <[EMAIL PROTECTED]> wrote:
>BJB wrote:
>
>> Yes - I think we need this database - with or without savefiles,
>> it's a waste of effort to inadvertently duplicate work done before.
>> Since P-1 is deterministic (like trial factoring, but unlike
>> Pollard's rho or ECM) you should get the same result every if you use
>> the same limits on the same exponent.
>
...
>
>
>The degree of freedom in choosing an elliptic curve for ECM is probably what
>you're hinting at. I'd suggest that a database of number of curves at run
>each B1/B2 limit is still useful. George keeps such a database for small
>exponents.
>
>
>Paul
It's my understanding that the choice of curve is randomized intentionally,
and that the space of possible curves for each exponent is so large that
it is more efficient to check random curves than to attempt to eliminate
the very
small chance of calculating the same curve more than once.
This approach is used not only in GIMPS, but in George's implementation of
Richard Crandall's program for searching for factors of Fermat primes.
It is not necessary or advisable to run all possible curves.
In fact, for F16, my runs produced in sequence, the following seed numbers,
many of which found the factor 825753601:
Attacking 2^65536 + 1
Selecting elliptic curve seed s = 1561883045:
Selecting elliptic curve seed s = 630999867:
Selecting elliptic curve seed s = 1921480920:
Selecting elliptic curve seed s = 1664751173:
Selecting elliptic curve seed s = 671100398:
Selecting elliptic curve seed s = 2008555722:
Selecting elliptic curve seed s = 112071784:
Selecting elliptic curve seed s = 1157242418:
Selecting elliptic curve seed s = 690847237:
Selecting elliptic curve seed s = 823396944:
Selecting elliptic curve seed s = 1372799571:
Selecting elliptic curve seed s = 244007149:
Selecting elliptic curve seed s = 2013596788:
Selecting elliptic curve seed s = 1958155050:
Selecting elliptic curve seed s = 441279715:
Selecting elliptic curve seed s = 248788694:
Selecting elliptic curve seed s = 831355685:
Note that they go to at least 2 x 10^9.
Ken
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