Re: Goldbach Conjecture equivalency


lynto008@xxxxxxxxxxx wrote:
> Hi,
>
> Playing around with the Goldbach conjecture (that an even number is a
> sum of two primes) I came to the interesting and I would assume more
> general conjecture that provided no prime is 2, the sum of p primes is
> odd if p is odd and even if p is even. I came to this conclusion as
> follows:
>
> Assuming the goldbach conjecture, then an even number is the sum of two
> primes.
> Then an even number + 1 = prime + prime + 1.
> Or, equivalently, an odd number = prime + (prime + 1).
> But, given that the prime is not two, then (prime + 1) is an even
> number.
> And, an even number is the sum of two primes, so, the sum of three
> primes is an odd number, if and only if none of the primes are two.
> Then, an odd number + 1 = prime + prime + (prime + 1) and we can start
> over using the same method.
>
> Can anyone see a problem with this or does anyone know if this has
> already been documented? I figure that this is reasonably significant
> if it is correct.
>
> Thanks for your time,
>
> Lynton

I was a little confused about what your conjecture is saying. Let me
try to rephrase:

Conjecture: Every even number can be written as the sum of an even
number of primes, and every odd number can be written as the sum of an
odd number of primes.

Is this what you meant?

.

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