Problems & Puzzles: Puzzles

Puzzle 663 Pandiagonal prime magic squares

Natalia Makarova sent the following puzzle:

While there are known the minimal solutions (minimal magic constant)for the pandiagonal prime magic squares nxn for n=4, 5 & 6, it remains unknown the minimal solution for n=7.

Remember that: A square table NxN, filled with natural numbers, is called pan-diagonal magic square of order N, if the sum of the numbers in all rows, columns, main and broken diagonals are equal.

Natalia sent one 7x7 solution (not the minimal)

 191 89 397 409 43 157 311 379 103 101 491 17 313 193 317 241 109 163 439 47 281 223 383 227 107 541 37 79 331 337 7 139 167 563 53 83 347 389 277 127 307 67 73 97 367 11 263 173 613

whose magical constant is 1597

Q. Find a 7x7 solution with a smaller constant than 1597, if the  minimal the better.

On May 19, 2013, Natalia sent the following contribution:

This all that I know about pandiagonal squares of prime numbers (see attachment). This is not about minimum squares.

Required to find the squares with a minimal magic constant. I did not find the square of order 14, 17, 19, 21, 22, 23.

The squares of orders 17, 19 can be composed of arithmetic progressions J. Wroblewski

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On July 2013, Natalia wrote: