> ------------------------------
>
> Date: Thu, 14 Oct 1999 20:44:16 -0400 (EDT)
> From: Darxus <[EMAIL PROTECTED]>
> Subject: Mersenne: types of work to request - 10m digit prime vs. next prime
>
> As soon as I heard that there was a $100,000 prize available for finding a
> prime, I decided to switch to the 10m digit test, even though my chances
> of finding it were extreemly small. I mean, the tiny chance of winning
> that cash is better than leaving your idle CPU time idle, right ?
>
> Unfortunately, this cash prize had clouded my thoughts, as I fortunately
> realized when my girlfriend told me she opted not to switch to the 10m
> digit tests, because she was more interested in getting her name in the
> history books than getting $100,000, and there was is a significantly
> greater chance of finding the next prime than there is of finding the 1st
> 10m digit prime.
I too am more interested in fame than fortune (and incidentally don't put
much stock in the Islands) and to this end I've been latching on to
smallish exponents.
Speaking of fortune - for a few short weeks in April and May, joining
GIMPS really was a positive-expectation bet. I could test one exponent in
the 4-5M range a week for a 1-in-35000-more-or-less shot at the prize, for
roughly $1 electricity per exponent (less than 2 KWH/day at 8c each, with
the monitor off when I wasn't at the keyboard). Of course that meant it
was more a lottery than research, and it was bound to end within a couple
months.
[snip]
> It was what, half a million dollars total ? I think it would havebeen
> much better to award $25k per new prime discovered for the next 20 primes.
The purpose of the EFF awards was not to help GIMPS; it was to inspire
people to find better ways to find big primes, and, more generally,
encourage fresh mathematical thought.
Conjecture time: The prime number earning the $150K prize will not be a
Mersenne.
Why do I say that? Even with processor speeds increasing, we have a good
idea how long it'll take to find big primes by Lucas-Lehmer. Even for the
10M-digit prime it'll be a damn long time the way we are doing it now.
Finding the monsters requires an intellectual leap by someone - possibly
in processor design, more likely in number theory. Admittedly this leap
may well be a better version of L-L in which case Mersennes will still be
the record primes for a long while to come. But my hunch is that there is
a better chance of finding some new way to either construct primes, or to
test some other special-form number, than there is of dramatically
improving on Lucas-Lehmer. Just a hunch. I might be wrong. I hope I live
long enough to see all of the EFF prizes awarded, whether to Mersennes or
not.
Gordon Bower
PS - On an unrelated note --- what is the smallest natural number that is
not known whether it is prime or composite? Surely *someone* out there is
trying to work from the bottom up and factor every number. (I don't know
the answer. I am guessing the it is a smallish number of maybe 15 or
so decimal digits?)
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