Your description here does not quite match your linked code, in that it is not that the N-th pack contains integers spaced out by N. Rather, packs on the N-th row contain integers spaced out by N. For example, the third pack does not contain "every third integer", but rather draws alternating integers just like the second pack, because it is on the second row. The second pack contains (first cell of the second row) contains {101, 103, 105, ..., 299} and the third pack (second cell of the second row) contains {102, 104, 106, ..., 300}.

With this in mind, the seeming patterns of the figure you link to are explained by https://news.ycombinator.com/item?id=17106193

My one quibble with the comment I linked is about asymptotics. By the Prime Number Theorem, asymptotically, the density of black squares should approach zero and the density of red squares should approach 100% (including among the left diagonal which is entirely black in the displayed window, and including losing the regular appearance of rows that are entirely black except for their last cell. These black line patterns in the displayed window are both small number phenomena caused by (1 - 1/ln(R))^100 being nearly zero for small R, which stops and then goes the other way for large R.)