Busy Beaver number $BB(3)$

The maximal number of steps that a $3$-state Turing machine can make on an initially blank tape before eventually halting.

Updates

• Lower bound: $21$
  Reference unknown
  [via Sequence A060843 in the OEIS]
• 1965-04-01 Upper bound: $21$
  Shen Lin and Tibor Rado. 1965. Computer Studies of Turing Machine Problems. J. ACM 12, 2 (April 1965), 196-212.
  [via Sequence A060843 in the OEIS]