An illegal prime is a prime number which encodes information that is illegal to possess - specifically, in one case, a gzip file of the source code of DeCSS, a piece of software to decrypt copy-protected DVDs.
Your task has two phases:
Build a source file that implements DeCSS in as few bytes as possible. This can be done in any language.
Compress this source file (using your favourite compression algorithm), and iterate through possible files that decompress to the same thing (using Dirichlet's theorem if it helps) until primality is reached.
The person with the smallest probable prime wins.