Busy beaver
BB(n) is the maximum number of 1s printed by a 2-state n-symbol Turing Machine when it halts
BB(n) for n < 5 are known.
BB(5) >= 47,176,870 there are several programs where the halting is unknown. There is a collaborative effort to determine BB(5) https://bbchallenge.org/
BB(n) is larger than any computable function.
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