[105693] in Cypherpunks
Re: Goldbach's Conjecture - a question about prime sums of odd numbers...
daemon@ATHENA.MIT.EDU (Igor Chudov @ home)
Thu Nov 19 10:47:54 1998
To: ravage@einstein.ssz.com (Jim Choate)
Date: Thu, 19 Nov 1998 09:26:56 -0600 (CST)
Cc: cypherpunks@einstein.ssz.com, cypherpunks@manifold.algebra.com
In-Reply-To: <199811190522.XAA01164@einstein.ssz.com> from "Jim Choate" at Nov 18, 98 11:22:04 pm
From: ichudov@Algebra.Com (Igor Chudov @ home)
Reply-To: ichudov@Algebra.Com (Igor Chudov @ home)
Jim Choate wrote:
>
>
> Hi,
>
> I have a question related to Goldbach's Conjecture:
>
> All even numbers greater than two can be represented as the sum of primes.
Hold on right here, Jim.
Do you mean a sum of DIFFERENT primes?
Because any number greater than 1 can be represented as a sum of some 2s
and some 3s.
E.g. 8 = 3+3+2, 9 = 3+3+3, 10 = 3+3+2+2, etc.
Since this is so boring, I assume that the primes must be different.
> Is there any work on whether odd numbers can always be represented as the
> sum of primes?
Well, take 11, for example, it cannot be repsesented as a sum of different
primes. It cannot, pure and simple.
So, the above hypothesis is incorrect. No need for high powered math here.
> This of course implies that the number of prime members
> must be odd and must exclude 1 (unless you can have more than a single
> instance of a given prime). Has this been examined?
Why, let's say 5 = 3+2, it is a sum of an even number of primes.
I suggest that first "examination" should always include playing
with trivial examples.
> I'm assuming, since I can't find it explicitly stated anywhere, that
> Goldbachs Conjecture allows those prime factors to occur in multiple
> instances.
If multiple instances are allowed, it is an enormously boring conjecture
for 5 grade school students.
any number above 1 may be represented as a sum of some 3s and some
2s. Big deal.
> I've pawed through my number theory books and can't find anything relating
> to this as regards odd numbers.
- Igor.
