[seqfan] Re: Poll: Sequences Suitable For Crunchers vs. Formula Finding Algorithms

[Charles Greathouse]

> Perhaps such a sequence as A006945 could be thrown onto the BOINC
> world (since many participants crunch simply for the points).

Yes, that would be nice.  But this search should not be done by brute
force (sieve + test); Jan Feitsma et. al. have a good technique that
improves on that by orders of magnitude.

> Aside: With the advent of AKS, how long will the Miller-Rabin terms be
> useful (a guess)?

I would guess 100+ years.  AKS has been dramatically improved by
Bernstein and others, but it's not currently competitive at any
feasible size.  In any case it will never be as fast as Miller-Rabin,
which is useful for determining whether a number is likely to be prime
(before proving it with ECPP, APR-CL, or AKS).

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Thu, Aug 26, 2010 at 11:57 AM, Donald Alan Morrison
<donmorrison at gmail.com> wrote:
> On Thu, Aug 26, 2010 at 4:39 AM, Richard Mathar
> <mathar at strw.leidenuniv.nl> wrote:
>> dm> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> dm> Subject: [seqfan] Poll: Sequences Suitable For Crunchers vs. Formula Finding Algorithms
>> various reasons) which deserve to be extended. One of my favorites are the
>> A006945 Miller-Rabin terms, which from a very practical point of view provide
>> a "safe net" for primality testing, and can reduce computing time on a
>> world-wide scale.
>> Finding more terms is, however, not sexy, because there are
>> essentially no discoveries to be made nor any prizes to be won. I guess
>
> Perhaps such a sequence as A006945 could be thrown onto the BOINC
> world (since many participants crunch simply for the points).
>
> Aside: With the advent of AKS, how long will the Miller-Rabin terms be
> useful (a guess)?
>
>> similar things may be said about more prominent number chases in
>> the Mersenne prime, aliquot sequence etc area (for which similar
>> applications may be missing...?) Competing with these is no fun.
>
> No fun for those who can engineer superseeker style searches.
>
> Again, I think a lot of BOINC crunchers do it just for "putting points
> on the board", so they will sign up regardless.  Look at the Collatz
> Project(!) it's not even looking for a counter-example(!) yet people
> donate ridiculous sums of electricity and time to it.  I think the
> seqfan folks such as yourself could "dip into" this waste and get some
> useful terms from such brute force means, while still pursuing other,
> more directed, thoughtful and effective ways of finding interesting
> terms such as with superseeker et al.  Plus, it would give me
> something to do. :^)
>
> http://boinc.thesonntags.com/collatz/
>
>> So the question aside from keyword issues is: which extension would
>> be most beneficial from a math community point of view?
>
> I agree, and I'm willing to donate programming time for more naive
> brute-force-like efforts that agree with this, since I'm just a
> programmer, not a superseeker architect (though I'd love to learn over
> time).
>
> Cheers,
> Don
>
>
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