Problem 1673. Pandiagonal Prime Magic Square Verification

Verify if an NxN matrix is a Pandiagonal Prime Magic Square.

Required properties:

1) N^2 prime values ( No repeats, 1 is a non-prime )
2) Every row, column, diagonal, anti-diagonal, broken diagonals sum to same value
3) Magic Constant is the sum of a row/column/diagonal

Input: M (Matrix NxN)

Output: Magic Constant ( 0 if invalid )

Example:

m=[7 107 23 103;89 37 73 41;97 17 113 13;47 79 31 83]; Magic is 240

Rows;Columns; Diags 7+37+113+83, 107+73+13+47, 23+41+97+79, 103+89+17+31;

Anti-Diag 103+73+17+47, 23+37+97+83, 107+89+13+31, 7+41+113+79

Related:

1) Kurchan Evaluation has similar array processing

2) Create Minimum Pandiagonal Prime Magic Squares (6:20) Bonus for 14