On 19 Jul 99, at 3:57, [EMAIL PROTECTED] wrote:
> *) Somebody finds how to parallelize the FFT using little
> communication. The wall-clock time might be reduced 10-fold,
> but the CPU time increased 16-fold. This could be
> great for verifying a new Mersenne prime, but
> does it qualify for the money?
Surely that's been done - long since - for application on massively
parallel processors (vector machines).
>
> *) Somebody finds a novel way to choose elliptic
> curves modulo Mp, using the information that
> its prime factors are == 1 (mod p) and that 2, -p
> are quadratic residues modulo any factor of Mp.
> This lets the trial division phase search 10 bits higher,
> such as searching to 2^74 rather than 2^64.
> Does its finder get any money?
I think this would speed us up only a few percent at best.
Nevertheless it's a novel approach & could have other useful
ramifications.
I mentioned to George that I think the best way to decide which
improvements are eligible for any share of an award would be to have
a vote with the electorate consisting of previous Mersenne prime
discoverers.
> *) Somebody finds a way to verify the output of the LL test
> without a complete rerun (cf. verification of digital signatures).
> If this eliminates the need for double-checks, does it qualify?
That sounds interesting! Of course, if we could find a _quick_ way of
computing a few bits of the residual, we could use this as a filter
which would remove a large proportion of the contenders - never mind
about being a quick check on a result. I think this really _should_
qualify for an award!
Regards
Brian Beesley
_________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
