Construct a magic square made up of the primes 5, 17, 29, 47, 59, 71, 89, 101, and 113, so that all rows, columns, and diagonals have the same sum.
Note that the sum of all the numbers is 531, so each row (hence, each column and diagonal) must total 1/3 of 531, or 177. Further note that 59 is the middle number, and the differences between successive numbers on either side of 59 are symmetric. A good strategy is to start with the middle number in the middle of the square and then balance numbers on opposite ends in every direction. If you need to do some trial-and-error, a spreadsheet is an efficient way to proceed. Here’s a solution that works:
| 47 | 29 | 101 |
| 113 | 59 | 5 |
| 17 | 89 | 71 |