I have been thinking a lot recently about the distribution of prime numbers — in particular, I’ve been trying to figure out if there is a way to predict the sequence of gap sizes between primes. But anyway, in the course of that investigation I came across a really cool site about number spirals in which the author develops a set of formulas and insights from them based on a particular way of aligning numbers in spirals. It’s a very interesting, visual, site that anyone who knows basic algebra can understand. I wonder if some of the properties of these spirals relate to physics — particularly the orbits of planets or the positions of particles?
I also found this site which has several illustrations on it of various spatial visualizations of primes — the one I found most interesting is the “Golbach Folding at Multiples of 30,” a way to make the primes line up (with one minor catch!).
This is another interesting site that provides music generated by prime number sequences that sounds suspiciously like free-jazz.
As long as we’re on the subject — I just found this obscure research paper that shows the prime numbers at work in nature — they find that predator-prey interactions obey patterns that tend to favor prime numbers. Interesting. This adds to my hunch that the primes play an important role in nature — and that they may be fundamental to understanding the patterns at work in chaotic dynamical systems.