[ExI] 2^57885161-1

[spike]

>... On Behalf Of Dave Sill
Subject: Re: [ExI] 2^57885161-1

On Fri, Feb 8, 2013 at 10:39 AM, spike <spike66 at att.net> wrote:
> ...

>...One problem is that busy CPUs consume more power than ones, so the
unused cycles aren't free. Another problem is that most CPU chips have
multiple cores, so keeping only one of them busy won't tell whether there's
a virus running on another one. So you have to keep all of the cores busy.
Combine the first problem with the second problem and you a third potential
problem: overheating...

OK, so take all your new computers and run this app for a couple months, see
if they overheat.  If so, collect on the warranty.


>...But your proposed practical application of large primes doesn't answer
the question about their mathematical importance.

-Dave
_______________________________________________

Ja, I didn't really attempt that one at all.  Mostly they are an engineering
and entertainment thing, but look at a possible indirect benefit to
mathematics: young people notice how cool is this whole exercise and become
inspired to study mathematics in college.  Then perhaps they go on to
graduate school and post-grad, and then perhaps greatness.  Or perhaps they
figure out some cool statistical model (stretching a bit to call this
mathematics) to use superposition of probability distribution functions to
derive a method to predict the approximate time interval until the next
record prime is discovered, as I did thrice in 1998, 2000 and 2001, which
resulted in my eventually finding myself in Damien's completely
coincidentally wildly cool excellent book The Spike, which was not named
after me.

I know another benefit to mathematics that is as far as I know my only
completely original invention: imagine that some technologically advanced
society intercepts our signals and decide to invade earth to devour the
biota and savage our civilization, but they know nothing of our defensive
resources.  On their way inbound, they learn that the earthlings have
discovered 48 Mersenne primes.  Mersenne primes are fundamental; they would
be an interesting curiosity in any number base.  In the unlikely but
possible event that the invaders, even if advanced, never discovered the
Lucas Lehmer algorithm, even a technologically wildly advanced society would
only know about 15 to perhaps 20 MPs.  If they find we have 48 of them, they
would be astonished at the sheer volume of computing cycles we use on what
is apparently just play.  The warlike invaders would assume that the
earthlings are like themselves, and would extrapolate 1000 times as much
computing power dedicated to home-planet defense, at which time they
immediately call off the invasion and flee in terror, which saves the human
mathematicians from becoming alien excrement, advancing mathematics,
therefore Mersenne Primes are of great mathematical importance QED.

I call this the pyramid argument, for it is in a sense analogous to the
ancient Egyptian creating these enormous squared-off clearly manmade
mountains.  The endemic desert invaders see those things at some distance,
and extrapolate the presence of either some incomprehensible technology or
seething masses of men to build those things, those astonishing numbers of
men whose rock-carving skills could easily be temporarily diverted to
ass-whooping skills, elegantly sufficient to rid the desert of paltry
numbers of invaders before lunchtime, scarcely impacting schedule, and hey
sarge, perhaps we should wheel these camels through pi radians and gallop on
off to invade elsewhere.  I have the notion that this is why the Egyptian
drew all those figures with the sideways feet and hands: every invader they
ever saw noticed the pyramids and walked like an Egyptian, right on out of
Dodge forthwith.  The pyramids were the negative thirtieth century nukes:
you don't need to use 'em, you just need to have 'em.  The Mersenne Primes
would show we are smart enough to defend ourselves if called upon to do so.

Alternately, a really smart and peaceful nearby alien species intercept our
signals and learn that we know 48 MPs, and decide that we as a species are
sufficiently intelligent to be interesting, so they send us signals, share
with us all the cool mathematics they have discovered, and mathematics as a
scientific discipline is greatly advanced, consequently MPs are of great
mathematical importance QED.

spike