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The Busy Beaver problem is about finding the sequence of n-state Turing Machines writing the most 1's on a tape.
3
votes
Wanted: Concrete Example of Busy Beaver Holdout
Skelet has 43 holdouts (those with type = ----).
At least No. 827123 (the very first in the lists) is still open, afaik.
My "feeling" is that all but 6 (no idea, which!) have been shown to be infinite …
1
vote
Goldbach Conjecture and Busy Beaver numbers?
The Goldbach conjecture can be falsified (if actually false) by such a TM program; it can not be proven correct in this way (an insightful mathematician, however, might do this).
Knowing BB(27) would …