The Ulam Spiral is said to be somewhat of a mystery as to why the prime numbers seem to form diagonal lines. What's the mystery? Seeing that all primes are odd, (except 2), and that all the odd numbers form diagonal lines in this configuration, isn't it just this fact alone that causes this phenomenon?

I've seen this before, though I don't know much about it. The wikipedia article (your link) explains:

quote:

Since in the Ulam spiral adjacent diagonals are alternatively odd and even numbers, it is no surprise that all prime numbers lie in alternate diagonals of the Ulam spiral. What is startling is the tendency of prime numbers to lie on some diagonals more than others.

There is also an article on this at MathWorld.