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• 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
Message 1 of 2 , Jan 2, 2009
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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.

Thanks for reading! Have a nice day!
• ... 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
Message 1 of 2 , Jan 2, 2009
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--- 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
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