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Goldbach conjecture prime-closeness query

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  • WarrenS
    Goldbach conjecture: every even number 2 is a sum of two primes: 2N=p+q. Quantitative version: let f(N) be the least value of |p-q| such that 2N=p+q with p,q
    Message 1 of 1 , Sep 18, 2012
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      Goldbach conjecture: every even number>2 is a sum of two primes: 2N=p+q.

      Quantitative version: let f(N) be the least value of |p-q| such that
      2N=p+q with p,q prime. [If no such p,q exist then let f(N)=infinity.]

      Has there been computational effort devoted to determining the behavior of f(N)?
      I presume/guess that
      f(N)=(logN)^(3+o(1))
      is a valid stronger version of Goldbach conjecture.
      If all record-breaking f(N) were computed for N=1..10^12
      then we'd have some evidence on this question.
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