Proving the concept will indeed be difficult -- in fact it will be impossible. Randomness is inherently unproveable.
A true random number generator could, in theory, put out the first 100 digits of pi at the time of observation*, and still be truly random; pseudorandom number generators are generally designed to never produce such a pattern (and hence are designed to be specifically not random.)
* "Extremely unlikely!" you cry. Yet it's as likely as 100 1's in a row, or any other 100-digit sequence. The odds of a truly random number generator producing any such sequence is exactly 1/10^100. You wouldn't be too suprised to see a random number generator generate 3 1 4, yet you'd suspect it if it generated 1 1 1. The point is, we observe finite phenomena, and randomness is an infinite property. One school of thought holds that a true random number generator, left to run for an infinite period of time, would produce every numeric pattern there is, including all of the digits of pi, an infinite number of 1's in a row, etc. Of course, that's not necessarily the case (see random.)