You'll find that when the number of columns is a multiple of 6 you'll get obvious columns in the dots, and if it's +1 or -1 modulo 6 the columns become diagonal stripes (the process sort of continues for ±2 and at ±3 it's pretty broken down).

It's a fairly straightforward number theory result that every prime > 3 is congruent to ±1 modulo 6 so that's probably what you're seeing. (Can't be +2 or +4 because that's divisible by 2, can't be +3 because that's divisible by 3, leaving +1 and +5 aka -1.)