What is the smallest possible constant of a 3×3 magic square containing nine distinct noncomposite numbers only?
As Steven pointed out below, noncomposite does not mean the values have to be positive. As all negative numbers are not, by definition, composite, nor are 0 or 1, the smallest possible constant would wind up being
zero
2 1 3
5 0 5
3 1 2
The above square is 9 distinct terms, none of which are composite, which fits the requirements set forth by the problem.
If we instead hold to primes, as the problem title suggests, allowing no negative terms, the smallest constant would be 177
17 89 71
113 59 5
47 29 101
Finally, if we allow 0 and 1, but still no negative values, our smallest constant becomes 111
7 61 43
73 37 1
31 13 67

Posted by Justin
on 20180929 16:11:21 