Find a 4×4 magic square consisting of 16 different positive semiprimes less than 100. A semiprime is a positive integer with exactly two, not necessarily different, prime factors. (For example, both 21 = 3×7 and 25 = 52 are semiprimes.) In a magic square, the entries in each column, row, and major diagonal have the same sum (known as the magic sum). We want a magic square for which, in addition, the four center entries, the four corners, and each of the four quadrants also exhibit the same magic sum, making a total of 16 ways to get the magic sum. We want the square with the smallest magic sum for such a square. Present your answer as four rows of four integers each.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95
| | | | sum --- | --- | --- | --- | --- | 8 | 1 | 6 | 15 | 3 | 5 | 7 | 15 | 4 | 9 | 2 | 15 sum | 15 | 15 | 15 | 15
Online Ecyclopedia of Integer Series, https://oeis.org/A001358