--- On Fri, 1/2/09, moralesjohnvince <

moralesjohnvince@...> wrote:

> Hi everyone...I am John Vincent from the Philippines, I am

> looking for

> some number theory conjectures over the internet and this

> site was one

> of the results I got. Anyway, I am fascinated by the

> Goldbach

> conjecture so much that I decided to look for a possible

> proof.

>

> Anyway, I have this conjecture, and I have tested it only

> for very

> small numbers. I would be glad if you can provide a proof

> or a

> counterexample using your high-performing computers. The

> cojecture

> goes like this

>

> "for every natural number k greater than or equal to

> 4, there exist a

> natural number r such that

> k - r and k + r are both primes"

>

> This is about equidistant primes from a fixed natural

> number.

I.e. for every natural number k>=4, 2k is the sum of 2 primes. This is just a reformulation of Goldbach's conjecture.

High-performing computers will probably never provide a proof or disproof of this, but perhaps high-performing mathematicians will instead.

Phil