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There are 25 primes smaller than 100. What is the closest to a 5 x 5 magic square I can construct with them? By "closest" I mean the one with the most columns, rows, and diagonals (12 in all) adding to the same amount.

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1 Answer 1

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I'll get things started with

10 lines with common sum 215:

    23 47 31 43 71
    89 41 67 11  7
    13 29 17 97 59
    53 79  2 61  5
    37 19 83  3 73


You can achieve

12 lines with distinct primes, here with common sum 283:

  13 107  79  37  47
  97  19   7  71  89
  29  17 131  23  83
 113   3   5 109  53
  31 137  61  43  11

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    $\begingroup$ This is clearly optimal: the row/column containing 2 will have an even sum, all others will have an odd sum. $\endgroup$ Sep 4, 2022 at 17:52
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    $\begingroup$ Followup: By choosing any 25 primes (not necessarily the 25 smallest), can you achieve 11 or even 12 matching sums? $\endgroup$
    – Ed Murphy
    Sep 5, 2022 at 7:02
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    $\begingroup$ @EdMurphy I updated my answer to address this. $\endgroup$
    – RobPratt
    Sep 5, 2022 at 16:16
  • $\begingroup$ mathworld.wolfram.com/PrimeMagicSquare.html $\endgroup$ Sep 5, 2022 at 17:09

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