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19780Re: [PrimeNumbers] Happy new year to all

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  • Phil Carmody
    Jan 2, 2009
      --- 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.

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