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Re: [PrimeNumbers] Re: Prime Talisman Squares

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  • Craig Pennington
    ... Cool. And in general for an arbitrary prime Talisman Square the maximum k will be p_M-p_m where m is the lowest prime index and M = m + (floor((N+1)/2))^2
    Message 1 of 6 , Jan 28, 2003
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      On Tue, Jan 28, 2003 at 04:29:11PM -0000, jbrennen <jack@...> wrote:
      > --- Jon Perry wrote:
      > It is easy to prove that k=9 is maximal, because you can't place
      > 2,3,5,7, and 11 in a 4x4 square such that none of them touch.

      Cool. And in general for an arbitrary prime Talisman Square the
      maximum k will be p_M-p_m where m is the lowest prime index and

      M = m + (floor((N+1)/2))^2

      for an NxN matrix.

      Using your example:

      p_0=2
      p_1=3
      p_2=5
      p_3=7
      p_4=11

      m=0
      M=4

      And for a 5x5 matrix starting at p_0, the maximal k is:

      p_9 - p_0 = 29 - 2 = 27

      This would work for a Talisman Square drawn from any ordered sequence.

      Cheers,
      Craig

      --
      Corollary to Clarke's Third Law:
      Any technology distinguishable from magic is insufficiently
      advanced.
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