This just shows the reduced residues mod n. There are n squares in the nth row from the top. Color the kth square of the nth row black if gcd(k,n)=1, color it red otherwise.
You're correct. The correspondence just seems to be due to some bound on the prime gap for arithmetic progressions (or perhaps something even more trivial that I'm missing). A cursory search suggests it might be a consequence of Ingham's bound. In any case, it doesn't yield much of interest.
No, it isn't plotting a prime spiral. Each square in their triangle is a block of 75 numbers. Within the nth row the numbers are sorted by residue mod n.
