[ExI] two new ones
spike
spike66 at att.net
Mon Sep 8 05:47:01 UTC 2008
> Damien Broderick
> Subject: Re: [ExI] two new ones
>
> At 08:32 PM 9/7/2008 -0700, Spike wrote:
> >
> >Yesterday a *second* new Mersenne prime was discovered, so now there
> >are two in the process of verification...
> >Can life get much better?
>
> Yes, if they fit your famous prime pattern generating
> algorithm. Or was that long-ago exploded into vapormath?
>
> Damien Broderick
Well, Damien since you brought up that topic, I will explain as best I can.
In 1999 I did a superposition of probability functions calculation which had
me very excited, for it appeared to have correctly predicted the approximate
timing of the appearance of three primes in a row. In retrospect I am
forced to conclude that I was just stupid lucky all three times.
At a math party in Palo Alto in 2002, there were some excellent
mathematicians there for whom I am unworthy to clean their boots with my
wretched tongue, so deficient am I in mathematical skills. We discussed my
lines of reasoning, accumulated probability, a model of the growth rate of
GIMPS, and several other assumptions that went into that calculation. As it
turns out from a 2008 vantage point, primes are as weird and unpredictable
as ever, and Mersenne primes are just as weird and unpredictable. This
confirms that which the royal smart persons were able to convince me in
2002.
For instance, in 1999 I modeled the growth of GIMPS to be exponential, as it
was from 1996 to 1999. That was wrong; GIMPS went into an S curve as the
planet exhausted its supply of computer-hip math geeks. The project still
grows, but it isn't exponential. I modeled the computing power of
microprocessors as continuing to increase as they had since 1960: wrong
again, that wonderful trend slowed somewhat in the 00s. I modeled the
probability of any particular prime being a Mersenne as uniform, which I
knew wasn't right, but no one knows how to model that, and some assumption
must be made.
With nearly all my assumptions wrong, I still ended up with roughly
compensating errors, so the predictions were sorta correct but misleading.
No one can predict where or when the Mersennes will be found, no one! Of
course anyone is allowed to get stupid lucky. Page 86 of The Spike need not
be rewritten; the theory worked well enough. You could add a footnote if
you wish, explaining that a bunch of wrongs somehow made a right. {8^D But
it was sheer luck, of which my life has had an unexplainable superabundance,
both in love and in math.
Consider the interval that was being searched in the 1999 to 2002 timeframe:
by straight calculation we would expect five Mersennes; that interval
yielded only two. The interval being searched in the past five years would
be expected to yield two Mersennes already has five confirmed, and now two
more have been announced. The slot sized for five has two, and the slot for
sized two has seven? My model would have gone seriously astray had I
maintained its verity after 2003. Is god screwing with our minds? I am
utterly without explanation, but I am with these observations: prime numbers
are cool, and nature doesn't do what we expect in this area of study.
spike
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