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Is this why all Even Numbers >2 are the Sum of Two Primes?

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  • Bob Gilson
    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,
    Message 1 of 2 , Aug 3, 2009
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      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]
    • Jean Penné
      ... 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
      Message 2 of 2 , Aug 3, 2009
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        --- In primenumbers@yahoogroups.com, Bob Gilson <bobgillson@...> wrote:
        >
        > 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]
        >

        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!
        Jean
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