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[PrimeNumbers] Re: distance between prime tuples

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  • Jens Kruse Andersen
    ... I have computed the 4 smallest x such that these 14 are all primes: x +/- 2, 4, 8, 16, 32, 64, 128 A PrimeForm/GW input file with x values in {. . . .} :
    Message 1 of 7 , Jun 1, 2005
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      Mark Underwood wrote:

      > And for the tuple
      >
      > x-64, x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32, x+64
      >
      > x must have a factor of 3,5,7,11,13.

      I have computed the 4 smallest x such that these 14 are all primes:
      x +/- 2, 4, 8, 16, 32, 64, 128

      A PrimeForm/GW input file with x values in {. . . .} :

      ABC2 $b+2^$a & $b-2^$a
      a: from 1 to 7
      b: in {93487500801880185 539493168332973855 635219113875010665
      892427005980104595}

      My tuplet finder used 5 GHz hours with prp'ing by the GMP library.
      I was surprised to see that the primes are consecutive for the smallest,
      x = 93487500801880185.

      --
      Jens Kruse Andersen
    • Jens Kruse Andersen
      ... A Google search on 93487500801880185 reveals that it was first found by Jim: http://www.primepuzzles.net/puzzles/puzz_167.htm Phil then found
      Message 2 of 7 , Jun 1, 2005
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        I wrote:
        > x +/- 2, 4, 8, 16, 32, 64, 128
        > x = 93487500801880185.

        A Google search on 93487500801880185 reveals that it was first found by Jim:
        http://www.primepuzzles.net/puzzles/puzz_167.htm

        Phil then found 64606701602327559675 +/- 2, 4, 8, 16, 32, 64, 128, 256

        So I'm 3 years late and didn't even rediscover the best result :-(
        Extending to +/- 512 is too hard for me.

        --
        Jens Kruse Andersen
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