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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
Busy Beaver
(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.
(1994-10-24)