A prime number greater than 3 must leave a remainder 1 or 5 when divided by 6. In other words:

If n is prime and n > 3, then n ≡ 1 (mod 6) or n ≡ 5 (mod 6).

Or more succinctly:

n ≡ ±1 (mod 6).

So when the total number of columns is a multiple of 6, all the primes greater than 3 line up on the nth columns for n = 1, 5, 7, 11, etc.