Links

Imathination.net by Dick Boland. The contents of this website have been removed (temporarily I hope) from the web, but I'm keeping the link here to credit the author. This website used to include what was (so far as I know) the first published pictures of the number spiral and product curves. Dick discovered these things independently of me, conceiving them and rendering them as helical spirals on a cone. When the cone was viewed from above, it looked identical for practical purposes to my version of the number spiral.

Divisor Plot by Jeffrey Ventrella. This website contains a fascinating visual investigation of the patterns formed by factors on a certain type of two-dimensional graph which is different from the number spiral. Towards the bottom of the home page, the author rolls his graph into a three-dimensional coil, stands it on end, and glues it to the number spiral, thereby extending the number spiral into a third dimension. This site is beautifully presented and extremely interesting.

Ulam's Spirals: Towards an Explanation by Didier van der Straten. This paper offers an explanation of the fact that some curves of form n^2+n+k (in my lingo, offset curves of angle 1/2) are denser in primes than others.

Natural Numbers. This new site offers software for prime hunters, including a program for investigating offset sequences and other features of the number spiral. Also contains lists of factorizations and other useful info.

More Prime Patterns by Harvey Heinz. This is a smorgasbord of prime topics, with tasty introductions to eighteen different patterns. For each pattern there is an illustration to convey the idea quickly, plus a brief discussion and references for more information. Among the topics covered is the Ulam Spiral.

The Prime Pages by Chris Caldwell. Huge well-organized site with links and references to everything involving primes. Frequently updated.