Construct a 3x3 magic square using the primes 5, 17, 29, 47, 59, 71, 89, 101, and 113. That means all rows, columns, and diagonals have the same sum.
Solution
The sum of all the numbers in this magic square will be 531, so each row (and likewise each column and diagonal) must be a third of this or 177. Furthermore, as 59 is the central number in the given list, it must be the middle number in the square, and the differences between the numbers on either side of 59 must balance out to the sum 177.
So, start with the middle number and balance the numbers in opposite directions. You can program a spreadsheet to assist you. Place 59 in the middle of a 3x3 array and program the spreadsheet to fill in the last column while you make trial entries in the first column.
Here is one solution:
