- Let N be an even number that is the first counter-example of GC

Thus N - 2 must be an even number, the sum of two prime numbers.

Thus N - 1 is an odd number, which is not the sum of a prime number + an even number which is not one less than a prime number.

However, as N - 2 is an even number which is the sum of two prime numbers, N -1 must be an odd number, the sum of a prime number + an even number, which is one less than a prime number. Contradiction.

Therefore N cannot be the first counter-example of GC

[Non-text portions of this message have been removed] - --- In primenumbers@yahoogroups.com, Bob Gilson <bobgillson@...> wrote:
>

If N-2 is an even number which is the sum of two prime numbers, N -1 must be an odd number,which the sum of a prime number + an even number, which is one MORE than a prime number. There is no contradiction!

> Let N be an even number that is the first counter-example of GC

>

> Thus N - 2ï¿½must beï¿½an even number, the sum of two prime numbers.

>

> Thus N - 1 is an odd number, which is not the sum of a prime number + an even number which is not one less than a prime number.ï¿½

>

> However, as N - 2 is an even number which is the sum of two prime numbers, N -1 must be an odd number,ï¿½the sum of a prime number + an even number, which is one less than a prime number. Contradiction.

>

> Therefore N cannotï¿½be the first counter-example of GC

>

> [Non-text portions of this message have been removed]

>

Jean