The fact that the difference of the numbers in consecutive rows forms the arithmetic progression (3, 5, 7, 9, 11,...) is a side note - those are not the numbers of primary interest.

The numbers of interest are the ones in the 2-d array:
4, 7, 10, 13, ...
7, 12, 17, 22, ...
10, 17, 24, 31, ...
...

For any number N in the 2-d array, 2N + 1 is composite. Similarly for any number N not in the array, 2N + 1 is prime.