Forwarded message:
From: "Blake Buzzini" <bab282@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@ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------