To: WSFAlist at keithlynch.net
Date: Wed, 19 Jun 2002 02:15:13 -0400
Subject: [WSFA] Re: Goldbach's Conjecture
From: ronkean at juno.com
Reply-To: WSFA members <WSFAlist at keithlynch.net>

On Wed, 19 Jun 2002 01:34:38 -0400 (EDT) "Keith F. Lynch"
<kfl at keithlynch.net> writes:
> According to http://front.math.ucdavis.edu/math.GM/0206033
> Goldbach's conjecture (i.e. that every even number greater
> than two is the sum of two primes) has finally been proven.
>
> Nobody on the newsgroups seems to have noticed yet.
> --

I don't know if 1 is strictly prime, but 1 is not evenly divisible by any
integer but itself (or, trivially, 1) and

2 = 1 + 1

and

4 = 2 + 2
6 = 3 + 3
8 = 5 + 3
10 = 5 + 5
12 = 7 + 5
14 = 11 + 3
16 = 13 + 3
18 = 13 + 5
20 = 13 + 7

so it looks like Goldbach's Conjecture is true for the even numbers up to
20.

Continuing further by hand would be increasingly tedious, but presumably
a modern computer could extend the computations to some very large
number.  But, since a computer could never count to infinity (in a finite
time), it seems that it would be impossible for a computer to prove the
conjecture for all even numbers.  But, a human has allegedly done so.
Assuming that has been done, what is the difference between a human
mathematician and a computer which explains why the human can do what the
computer cannot?

Ron Kean

.

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