It looks as though primes tend to concentrate in certain curves that swoop away to the northwest and southwest, like the curve marked by the blue arrow. (The numbers on that curve are of the form x(x+1) + 41, the famous prime-generating formula discovered by Euler in 1774.)

Some clips from a wonderfully-done exploration of this curious mathematical construct (also known as the Ulam Spiral). To date, it is not fully understood exactly why more primes tend to fall along certain "curves" in the spiral than others, but the elusive quest for a simple prime-generating formula keeps the deceptively-simple spiral intriguing to number theorists.

Great stuff Jason, thanks for sharing.

btw, did you know that "the spiral" had always been an universal symbol of "generative force", a kind of "life source" and thus "mother nature", as well as the "universal order", according to Marija Gimbutas' research on the iconography of Early Neolitihic settlements of Europe? Pretty interesting. I love mathematics!