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Re: distance between prime tuples

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  • Mark Underwood
    Some trivia: As it turns out, for a tuple of the form x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32 x must indeed have a factor of 3,5,7 and 11 And for
    Message 1 of 7 , Jun 1, 2005
      Some trivia:

      As it turns out, for a tuple of the form

      x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32

      x must indeed have a factor of 3,5,7 and 11

      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.

      However, breaking the trend, the 16 term tuple doesn't require that x
      has a factor of 17, only 3,5,7 and 11. But the 18 term tuple does
      require x to have a factor of 19 (as well as 3,5,7,11,and 13).


      Mark



      --- In primenumbers@yahoogroups.com, "Mark Underwood"
      <mark.underwood@s...> wrote:
      >
      > I just took a look and find that a tuple of the form
      > x-8, x-4, x-2, x+2, x+4, x+8
      > must have x = 3*5*7*k.
      >
      > Extrapolating, perhaps a tentuple of the form
      > x-32, x-16, x-8, x-4, x-2, x+2, x+4, x+8, x+16, x+32
      > must have x = 3*5*7*11*k. I'll soon see.
      >
    • 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 2 of 7 , Jun 1, 2005
        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 3 of 7 , Jun 1, 2005
          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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