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Could AlphaEvolve find the sixth busy beaver ?

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Hi,

What we thought:

Prediction 5 . It will never be proved that
Σ(5) = 4,098 and S(5) = 47,176,870.
-- Allen H. Brady, 1990  .

How it started:

To investigate AlphaEvolve’s breadth, we applied
the system to over 50 open problems in mathematical
analysis, geometry, combinatorics and number theory.
The system’s flexibility enabled us to set up most
experiments in a matter of hours. In roughly 75% of
cases, it rediscovered state-of-the-art solutions, to
the best of our knowledge.
https://deepmind.google/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/

How its going:

We prove that S(5) = 47, 176, 870 using the Coq proof
assistant. The Busy Beaver value S(n) is the maximum
number of steps that an n-state 2-symbol Turing machine
can perform from the all-zero tape before halting, and
S was historically introduced by Tibor Radó in 1962 as
one of the simplest examples of an uncomputable function.
The proof enumerates 181,385,789 Turing machines with 5
states and, for each machine, decides whether it halts or
not. Our result marks the first determination of a new
Busy Beaver value in over 40 years and the first Busy
Beaver value ever to be formally verified, attesting to the
effectiveness of massively collaborative online research
https://arxiv.org/pdf/2509.12337

They claim not having used much AI. But could for
example AlphaEvolve do it somehow nevertheless, more or
less autonomously, and find the sixth busy beaver?

Bye

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Could AlphaEvolve find the sixth busy beaver ? Mild Shock <janburse@fastmail.fm> - 2025-11-30 13:36 +0100
  An old Busy Beaver ASIC (Application-Specific Integrated Circuit) (Re: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-11-30 13:56 +0100
  Re: Could AlphaEvolve find the sixth busy beaver ? Jeff Barnett <jbb@notatt.com> - 2025-12-01 14:29 -0700
    Re: Could AlphaEvolve find the sixth busy beaver ? Mild Shock <janburse@fastmail.fm> - 2025-12-02 00:14 +0100
      FYI: The Busy Beaver Frontier / Scott Aaronson (Was: Could AlphaEvolve find the sixth busy beaver ?) Mild Shock <janburse@fastmail.fm> - 2025-12-02 00:17 +0100
        2024 claim of BB(5) (Was: FYI: The Busy Beaver Frontier / Scott Aaronson ) Mild Shock <janburse@fastmail.fm> - 2025-12-02 00:22 +0100

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