Goldbach's Conjecture (fwd)

Jim Choate ravage at EINSTEIN.ssz.com
Thu Nov 19 19:56:28 PST 1998



Forwarded message:

> From: "Blake Buzzini" <bab282 at psu.edu>
> Subject: RE: Goldbach's Conjecture
> Date: Thu, 19 Nov 1998 22:17:54 -0500

> I could be wrong, but I thought Goldbach's conjecture was that every even
> number could be expressed as the sum of *two* primes. This doesn't prohibit

No, that was Fermat, Goldbach just says every even number greater than two
can be represented as a sum of primes. Basicaly Fermat says that if we have
n primes we can reduce them to 2 primes only, in all cases. Which happens to
exclude using equilateral triangles as a test bed since you can't tile a
equilateral with only two other equilaterals, you could use rectangles though.
So basicaly from a geometric perspective Fermat says that given a rectangle of
even area it is possible to divide it with a bisector into two rectangles of
prime area.

It's interesting that Fermat doesn't mention that the only prime that can
use two as a factor is 4. And you can't factor 2 at all since we eliminate
1 as a potential candidate (another issue of symmetry breaking simply so we
don't have to write '....works for every prime but 1' on all our theorems).

> repetition. Therefore, under Goldbach's conjecture:
> 
> 4 -> 2 + 2
> 6 -> 3 + 3 but NOT 2 + 2 + 2
> 8 -> 5 + 3 but NOT 2 + 2 + 2

The real issue for me is the interaction of primes (ie n * 1 = n) and the
identity theorem (ie n * 1 = n). They're opposite sides of the same coin.

It doesn't really matter now since it doesn't look like I'm going to get a
copy of EURISKO in this lifetime to play with.


    ____________________________________________________________________
 
            Lawyers ask the wrong questions when they don't want
            the right answers.

                                        Scully (X-Files)

       The Armadillo Group       ,::////;::-.          James Choate
       Austin, Tx               /:'///// ``::>/|/      ravage at ssz.com
       www.ssz.com            .',  ||||    `/( e\      512-451-7087
                           -====~~mm-'`-```-mm --'-
    --------------------------------------------------------------------






More information about the cypherpunks-legacy mailing list