[extropy-chat] Goldbach's Conjecture Resolved! A Story

[spike]

> 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
> be
> > expressed as the sum of two primes.
> ...
> > I have found that P(n) ~ .15*n^0.75
> 
> Is that a numerical estimate?

Yes.

> 
> 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.

spike