[jona-f]

If you select 30, 60 or 90 columns you get the clearest patterns. It kinda seems that the more divisors the number of columns has, the clearer the vertical clusters are. And somehow 30, 60 and 90 stand out. Number theory is so weird. I expected more randomness.

[susam]

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.

[jacobtomlinson]

I just set the column width to 6 to verify this for myself. What a neat tool!

[jona-f]

Oh yes, thanks!

[dgacmu]

If you can do 210 you'll see even more.

Any primorial will give you the strongest patterns. (Primorials are the products of the first N primes, so 2, 6, 30, 210, etc.)

[Daub]

Very cool. Go from 30 to 31 to see this ‘pattern’ twist in on itself.

[ainiriand]

Go for 258 and be ready to get your mind blown.

[calrain]

210 columns is stripes