On Sat, 16 Oct 1999, Darxus wrote:
> On Fri, 15 Oct 1999, Jud McCranie wrote:
>
> > At 05:45 PM 10/15/99 -0400, you wrote:
> >
> > >I've put a graph of these "pairs" up on my web page.
> >
> > You can't really tell much from that graph - most of the points are hugging
> > the x-axis.
>
> Most of those are pretty random... like, the higher your numbers get, the
> more grouped they are.
>
> I have more thoughts on this, from reading
> http://www.utm.edu/research/primes/notes/faq/NextMersenne.html
> a few times, but I gotta get going.
Okay, that page is a bit overwhelming for me, but it looks like it's
saying that, when you graph log(log(p)) vs. n, where the logs are base 2,
p is part of 2^p-1, and n is the number of the mersenne prime (did I say
that right?), you'll get an approximation of a straight line. All
mersenne primes will fit that pattern, but they are less likely to be *on*
the line than they are to be *near* the line.
Geez, I'm having difficulty putting this into words.
Like... primes are not likely to fall extreemly close to the line,
but they're probably going to be near it -- like, they're magnetically
repelled from the line. This would cause random clumping.
It would also cause random clumping when you graph P vs. N (where P is
part of 2^P-1, and N is the number of the merseene prime).
I have no idea what would cause this, but if it's correct, we should be
able to calculate the probability of the distance from the line (if you're
doing the log log thing, or if you're fitting an exponential curve), and
predict more accurately where a prime would fall (you'd be predicting 2
points, one on either side of the line).
Gonna go regression test (proper term?) the extrapolations I've been
playing with assuming the distribution is totally random but approximating
an exponential curve....
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