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Re: [PrimeNumbers] Prime differences

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  • Jens Kruse Andersen
    ... I assume you mean: Are there primes q and p for all even N such that p-q = N ? This is conjectured, also for consecutive q and p, but has not been proved
    Message 1 of 2 , Mar 30 2:00 AM
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      Bob Gilson wrote:

      > Can anyone tell me if, p minus q = N, where N is the set of even integers,
      > and p and q are primes, has ever been proved?
      >
      > Example: 5 - 3 = 2, 7 - 3 = 4, 13 - 7 = 6, 13 - 5 = 8, 23 - 13 = 10 ...

      I assume you mean:
      Are there primes q and p for all even N such that p-q = N ?
      This is conjectured, also for consecutive q and p, but has not been proved as
      far as I know.

      It was also asked in:
      http://groups.yahoo.com/group/primenumbers/message/15636

      I verified it for N<10^12.
      The latest first appearance of a satisfying q for N < 10^12 is N = 496562420542
      which first appears for q = 3307.

      Some associated sequences are in OEIS:
      http://www.research.att.com/projects/OEIS?Anum=A101042

      --
      Jens Kruse Andersen
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