Chaitins Omega

GregoryChaitin, working with AlgorithmicInformationTheory formulated a number called Omega, a number with unsurpassible complexity. Basically, define the SimplestTuringMachine, iterate through every possible n-bit program as n goes from 1 to inf, output a 1 if it halts, a 0 if it doesn't. The most difficult serious to compute.

See also: GeneralPurposeComputer