From: ichudov@Algebra.COM (Igor Chudov @ home)
Date: Sat, 21 Nov 1998 02:14:15 +0800
To: ravage@EINSTEIN.ssz.com (Jim Choate)
Subject: Re: More Goldbach's Conjecture
In-Reply-To: <199811200702.BAA09369@einstein.ssz.com>
Message-ID: <199811201742.LAA18097@manifold.algebra.com>
MIME-Version: 1.0
Content-Type: text



Jim Choate wrote:
> 
> 
> Well there are two more definitions, from the same book [1], that are not
> equivalent:
> 
> pp. 335
> 
> For all natural numbers x, if x is even, non-zero, and not 2, then there
> exist prime numbers y and z such that x is the sum of y and z.
> 
> pp. 673
> 
> ...every even number, n>6 (it at least takes care of my question about 4),
>  is the sum of two odd primes.

These conjectures are equivalent for numbers > 6. I think that the
discussion of whether numbers 4 and 6 can be expressed as sum of
two primes is completely uninteresting.

Also, since 6 = 3+3, I question why they put strict inequality (> 6)
in the definition on p 673. I think that they could say n > 4. Not that
it matters in any respect.

So I do not see them as "substantially" different, and the difference
between these conjectures does not lead us to any profound thoughts.

	- Igor.