8 x 8 Prime Bordered Magic Square

The following prime magic square has a magic sum of exactly 19,000!

In addition, it is also a bordered prime magic square.

The inner 4 x 4 square, (shaded red) is a prime magic square with a magic sum of 9,500, exactly half of the magic sum of the 8 x 8 square.

Furthermore, the inner 6 x 6 square is also a prime magic square with a magic sum of 14,250. Exactly three quarters of the magic sum of the 8 x 8 square.

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Journal of Recreational Mathematics ( A.W.Johnson Jr Vol 15:2, 1982-83)

13 x 13 Prime Bordered Magic Square

The following 13 x 13 Prime Magic Square contains an amazing number of features.

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  1. This is a bordered prime magic square. Each of the 11 x 11, 9 x 9, 7 x 7, 5x 5, and 3 x 3 squares are also prime magic squares.
  2. The magic sums are 70,681, 59,807, 48,933, 38,059, 27,185 and 16,311 respectively.
  3. There is a common difference between these magic sums of 10,874.
  4. This common difference is also the same as that between the magic sum of the 3 x 3 and the centre number, 5437.
  5. The centre number is exactly half of the common difference between each magic sum.

Madachy’s Mathematical Recreations (Joseph Madachy 1979)