The reason vertical clusters appear in these examples is that all your chosen numbers are multiples of 6. A prime number greater than 3 leaves a remainder of e

The reason vertical clusters appear in these examples is that all your chosen numbers are multiples of 6. A prime number greater than 3 leaves a remainder of either 1 or 5 when divided by 6. In other words: For all primes p greater than 3, p ≡ ±1 (mod 6). Therefore, when the total number of columns is a multiple of 6, all primes except 2 fall into the same columns, namely 1, 5, 7, 11, 13, 17 and so on.