I was plotting the Ulam spiral (https://en.wikipedia.org/wiki/Ulam_spiral), and decided to isolate twin/cousin/sexy primes on the Ulam spiral.
Although plotting twin primes offered no obvious lines, isolating cousin primes seemed to yield distinctly prime-rich lines (and not always on 45 degree angles, as are common in the Ulam spiral). How do you feel? Do you think these lines are significant? Look under the orange dotted lines.
Cousin primes on the Ulam spiral (from 1 - 500000)