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OP-6813Status unassessedLogic and foundations

The sixth Busy Beaver number

TheoremDB P9418 · Candidate awaiting source review

MSC 03 · Mathematical logic and foundations

Inferred from the community field; finer classification has not been reviewed.

Source candidate · not reviewedAs of 2026-09-08Source & evidence ↓
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Problem statement

A Turing machine is a mathematical model of computation consisting of a finite set of states, a finite tape alphabet, a transition function, and a designated start state. A machine is halting if it eventually reaches a halting configuration. For a halting machine, the halting number is the total number of steps (or tape shifts) taken before halting. For each positive integer nn, the Busy Beaver number BB(n)BB(n) is defined as the maximum halting number among all halting Turing machines with exactly nn states and exactly 22 tape symbols, when started on an initially blank tape. It is known that BB(1)=1BB(1) = 1, BB(2)=6BB(2) = 6, BB(3)=21BB(3) = 21, BB(4)=107BB(4) = 107, and BB(5)=47176870BB(5) = 47176870. Determine the exact value of BB(6)BB(6).

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Formal statement

Lean 4
theorem BB_6 : BB 6 = answer(sorry)

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Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

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References
  1. [1]TheoremDB P9418 link
  2. [2]Source formal statement (not locally verified) link

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