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.
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.
- 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.
- The magic sums are 70,681, 59,807, 48,933, 38,059, 27,185 and 16,311 respectively.
- There is a common difference between these magic sums of 10,874.
- This common difference is also the same as that between the magic sum of the 3 x 3 and the centre number, 5437.
- The centre number is exactly half of the common difference between each magic sum.
Madachy’s Mathematical Recreations (Joseph Madachy 1979)