PrimeCoin searches for prime chains. For example 6 is at the center of a bitwin prime chain of length 2.

6 - 1 = 5, prime 6 + 1 = 7, prime 6 * 2 - 1 = 11, prime 6 * 2 + 1 = 13, prime

The design paper is a light and interesting read:

http://ppcoin.org/static/primecoin-paper.pdf

Also:

http://en.wikipedia.org/wiki/Cunningham_chain