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Goldbach conjecture variation

  1. Feb 22, 2010 #1

    mathman

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    4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?
     
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  3. Feb 22, 2010 #2

    CRGreathouse

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    There is almost surely no other case, but a proof is far beyond reach.
     
  4. Feb 22, 2010 #3
    A quick&dirty computer program shows no cases up to a hundred thousand.
     
  5. Feb 22, 2010 #4

    CRGreathouse

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    I can verify that there are no further exceptions up to http://www.research.att.com/~njas/sequences/A025018 [Broken](67) = 906030579562279642 ≈ 9 × 1017.

    Edit: According to Tomás Oliveira e Silva, this bound is good up to 1.609 × 1018.
     
    Last edited by a moderator: May 4, 2017
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