[extropy-chat] Goldbach's Conjecture Resolved! A Story
spike66 at comcast.net
Fri Oct 13 04:25:54 UTC 2006
> bounces at lists.extropy.org] On Behalf Of Anders Sandberg
> Subject: Re: [extropy-chat] Goldbach's Conjecture Resolved! A Story
> spike wrote:
> > Let P(n) be the number of different ways a positive even integer n can
> > expressed as the sum of two primes.
> > I have found that P(n) ~ .15*n^0.75
> Is that a numerical estimate?
> http://homepage.mac.com/billtomlinson/primes.html has a neat graph of
> P(n). It seems that numbers divisible by different small primes have their
> own "paths", I wonder if they all have 0.75 as exponent?...
Hmm, good question. This I will be able to answer as soon as I get back
from vacation. The wicked cool thing I discovered is a really fast way to
calculate S(n). I will adapt Tomlinson's terminology here, S(n) instead of
P(n). I will share this approximately Monday evening if I get time to post.
Oh it is cool, oh my.
Anders thanks for the sites. That graph is one of the cool things I
discovered while playing with this algorithm. I discovered the striations
(which Tomlinson calls streaks). I have been puzzled until my puzzler is
sore, more baffled than was the Grinch that time the Whos were singing
cheerfully after he had ransacked Whoville.
After I get back, anyone here who wants to play with those numbers can have
at em. We might discover even more cool way stuff.
> Fun! Thanks, Spike for bringing it up!
> Anders Sandberg...
There's more. I will share the algorithm, or if you prefer a table of S(n)
to 500,000. That table is too big to post on the ExI list, so I might make
a website and post it there, or just email it to anyone who wants it.
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