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BB(6) Is Hard (Antihydra) (2024)

Note: All Discord links are for the https://bbchallenge.org/ Discord server.

@mxdys has simulated this iteration out to \(2^{31} = 2\,147\,483\,648\) steps at which point \(b = 1\,073\,720\,884\) (only 20940 below the expected value if this were a random walk) ( Discord link). As with Hydra and Bigfoot, if we treat this iteration as a random walk, it has a miniscule chance of ever returning to \(b = 0\) and thus of ever halting. On Tuesday, we at bbchallenge.org announced a Coq proof of the BB(5) problem(and Ben Brubaker at Quanta wrote a lovely article describing the 60 year journey!).

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