Fun to see that prime numbers of columns causes stripy patterns, and some stripe to the left and some stripe to the right. Probably some deep number theoretic reason for that.
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.)