Primally Magic Squares

[elendiastarman]

A Primally Magic Square (PMS) is exactly like a traditional magic square with a change of criteria. Where a traditional magic square is one where the sum of each row, column, and both diagonals are some number, usually 15 (uses 1-9). By contrast, a PMS is one where all rows, columns, and both diagonals form a prime number. Note: if a number is prime either forward or back, it counts.

Example:

|1|3|7|
|3|9|7|
|7|7|9|

137, 397, 977, 797, and 199 are all prime, so this square is a PMS.

How many 3x3 PMS's are there?

How many 4x4 PMS's are there?

How many 5x5 PMS's are there?

How many 9x9 PMS's are there?