Abstract
The Busy Beaver function, with its incomprehensibly rapid growth, has captivated generations of computer scientists, mathematicians, and hobbyists. In this survey, I o er a personal view of the BB function 58 years after its introduction, emphasizing lesser-known insights, recent progress, and especially favorite open problems. Examples of such problems include: when does the BB function rst exceed the Ackermann function? Is the value of BB(20) independent of set theory? Can we prove that BB(n + 1) > 2BB(n) for large enough n? Given BB(n), how many advice bits are needed to compute BB(n + 1)? Do all Busy Beavers halt on all inputs, not just the 0 input? Is it decidable, given n, whether BB(n) is even or odd?
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