The fifth Busy Beaver number BB(5)
This page delivers no verdict; it presents claims and evidence with their sources. No theory in science is absolute. Method
For everyone
The "Busy Beaver" question asks how many steps a Turing machine with a given number of states can take before halting. For five states the answer was unknown for 60 years. In 2024 an online volunteer collaboration showed the answer is 47,176,870 and published a computer-verified proof.
For specialists
The function S(n), defined by Radó (1962), is uncomputable and grows faster than any computable function. The proof uses "decider" algorithms showing that each of 181,385,789 five-state machines either halts or never halts. The whole chain is formalised in the Coq/Rocq proof assistant (Coq-BB5). The value matches the machine found by Marxen and Buntrock in 1990.
Claims
- S(5) = 47,176,870.[1]
Evidence
Supporting
The proof has been machine-checked in the Coq proof assistant.[1]
Challenging
—
Connections
Sources
- Preprint (2025). Determination of the fifth Busy Beaver valuearXiv:2509.12337archive
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Cite this page
Athena contributors. (2026). The fifth Busy Beaver number BB(5). Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/bb5/
@misc{athena_bb5,
title = {The fifth Busy Beaver number BB(5)},
author = {{Athena contributors}},
year = {2026},
howpublished = {\url{https://latifkedi.github.io/athena/en/d/bb5/}},
note = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}Added: September 27, 2026 · Last changed: September 27, 2026 · Page history