--- On Fri, 1/2/09, moralesjohnvince <moralesjohnvince@...
> 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
> conjecture so much that I decided to look for a possible
> 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
> 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
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.