We've finished the primes quilt!

Each square in this quilt corresponds to a number between 1 and 841.  They are arranged from top left to bottom right working across rows from left to right.  Each square is colored by its smallest prime divisor.  So the background grid of gray is all of the multiples of 2.  The light blue is multiples of 3 and the aqua is multiples of 5.  The white squares are primes larger than 29 (and 1).

One of the most visible parts of this quilt is the light blue and aqua diagonals that go from top left to bottom right and the dark blue diagonals from top right to bottom left.  Why do think that is happening?