Busy Beaver
<theory> (BB) One of a series of sets of Turing Machine programs.
The BBs in the Nth set are programs of N states that produce a larger finite number of ones on an initially blank tape than any other program of N states.
There is no program that, given input N, can deduce the productivity (number of ones output) of the BB of size N.
The productivity of the BB of size 1 is 1.
Some work has been done to figure out productivities of bigger Busy Beavers - the 7th is in the thousands.
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