busy beaver

from The Free On-line Dictionary of Computing (8 July 2008)

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.

   (1994-10-24)