RE: Goldbach's Conjecture (fwd)

[Jim Choate <ravage@EINSTEIN.ssz.com>]

Forwarded message:

> Date: Fri, 20 Nov 1998 09:41:01 -0600
> From: Mark Hahn <mhahn@tcbtech.com>
> Subject: RE: Goldbach's Conjecture (fwd)

> At 09:39 PM 11/19/98 -0600, Jim Choate instructed:
> >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).
> 
> I thought I was following along until I got here, and got very lost. First
> question: I think the first sentence implies 4 is prime, so I must have
> the emphasis wrong.

No, I made a typo. I got so focused on primes last nite that I seem to have
typed it in instead of 'even'. I didn't notice it when I saw it posted to
the list. My mistake, sorry for the confusion.

What started this whole enquiry for me was the realization that the
multiplication identity axiom is related to the definition of a prime. Then
add on top of that the reason we exclude 1 is so we don't have to write
'...except for the prime 1' on the end of lots of number theory (re Richard
Feynman's comment during the Challenger Investigation). It was the 
realization that if we go ahead and include 1 so the axioms are in line with
each other (and use our cut&paste feature for the '...1...') then perhaps it
would provide a more consistent base and just maybe some of the extant
problems in number theory might become solvable in other ways. My original
intention was to get a copy of Doug Lenat's EURISKO theorem proving program
and change the definition of prime in its database and note the results
(after converting it to Perl from LISP). What started all that is that I'm
slowly going through 'An Introduction to Algebraic Structures' by J. Landin
(Dover) creating a cheat-sheet of number theory that eventualy I hope to post
on my webpage for reference.


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