BusyBeaver(6) Is Quite Large

10 months ago

The author reflects on the increasing difficulty of focusing on research due to the current state of the world, but finds solace in breakthroughs like those in Busy Beaver research.
In 2022, it was discovered that BB(6) > 10^36,534, later improved to BB(6) > 15^10, showcasing the rapid growth of the Busy Beaver function.
The Busy Beaver function BB(n) represents the maximum steps a Turing machine with n states can take before halting on an all-0 input tape.
Recent improvements show BB(6) > 10,000,000^10 and later BB(6) > 2 tetrated to the 2 tetrated to the 2 tetrated to the 9, demonstrating its enormous size.
The author speculates that BB(n) might become independent of ZFC axioms at n=7, 8, or 9, much earlier than previously thought (currently known at n=745).
The author attended STOC’2025 in Prague, presenting a plenary lecture on 'The Status of Quantum Speedups,' with slides available online.

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