Chaitin's Constant
An Irrational Number 
which gives the probability that for any set of instructions, a Universal TuringMachine will halt. The digits in are random and cannot be computed ahead of time.
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/chaitin/chaitin.html Gardner, M. ``The Random Number Gardner, M. ``Chaitin's Omega.'' Ch. 21 in Fractal Music, Hypercards, and More Mathematical Recreations from Scientific American Magazine. New York: W. H. Freeman, 1992. Kobayashi, K. ``Sigma(N)O-Complete Properties of Programs and Lartin-Lof Randomness.'' Information Proc. Let. 46, 37-42, 1993. Bids Fair to Hold the Mysteries of the Universe.'' Sci. Amer. 241, 20-34, Nov. 1979.
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