Compression of random binary data

[danceswithnumbers at gmail.com]

In Short, I cannot find a single mathematical proof that says you cannot compress random numbers. Pigeon hole and other conjectures are just that. In fact, the biggest fallacy when people start talking about compression is to say that all compression alg rely on redundancies, or repetitive sequences. The million random digits is compressed down to 415,241 kb. I have been only able to compress that down to 352,954 kb. A very small amount. It has taken six years to come up with that small amount.