I'm looking to write a program to investigate a few random number algorithms. Basically I am looking to see if the spread of numbers is indeed randomly distributed enough. What kind of statistical analysis would I be looking to do?

This is good...very good. Anything a bit lighter and just for fun? I'm more interested in the theory than the actual results.
– DanDanSep 29 '10 at 19:22

I don't know whether Knuth, The Art Of Computer Programming, is light, but it is fun, and Volume 2, Seminumerical Algorithms, goes into the theory of randomness in some detail.
– Gerry MyersonSep 30 '10 at 5:16