Prime squares and square squares
Hello Math-Fun, today we'll look for "prime squares" and "square squares". Definition 1 A "prime square" is a prime which is the sum of 4 integers. Those integers must occupy the 4 vertices of a geometric square formed by 4 cell-centers properly chosen on an infinite grid A (the 4 integers hereunder in the upper left corner, for instance, sum up to 11, which is prime). The type-A infinite grid is an infinite sector of the plane where the cells are labeled by the successive anti-diagonals like below: + --- + ---+--- + ---+--- + ---+--- + ---+--- + ---+--- + ---+--- + ---+--- + ---+---+---+ | 1 | 3 | 6 | 10| 15 | 21| 28 | 36| 45 | 55| 66 | 78| 91 |105| 120 | | + ---+--- + ---+--- + ---+--- + ---+--- + ---+--- + ---+--- + ---+--- + ---+---+. | 2 | 5 | 9 | 14 | 20| 27 | 35| 44 | 54| 65 | 77| 90 |104| 119 | | | + --- + ---+--- + ---+--- + ---+--- + ---+--- + ---+--- + ---+--- + ---+---+---+ | 4 | 8 | 13 | 19| 2