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Happy new year to all

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  • 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
    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!
    • Phil Carmody
      ... 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 2 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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