# Busy Beaver BB(5)

- kind: problem
- status: solved (evidence tier V3)
- year: 1962
- authors: Tibor Radó

**Statement.** What is the maximum number of steps a halting 5-state, 2-symbol Turing machine can run?

The answer is 47,176,870. A volunteer collaboration decided whether each of roughly 180 million machines halts, and the whole argument was checked in Coq. It combines a mathematical result, a large computer search and a formal proof, the pattern this atlas is built for. BB(6) is at least beyond 2↑↑↑5 and may run into problems like Collatz.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed 1962, Tibor Radó. Closed 2024, the bbchallenge collaboration; proof checked in Coq.

## What would settle it

Coq proof of BB(5) = 47,176,870

## Related problems

- The original curation links this problem to [Busy Beaver BB(6)](/wiki/Problem:busy-beaver-6.md); the argument for the link has not been written yet.

## Sources

- [Wikipedia: Busy beaver](https://en.wikipedia.org/wiki/Busy_beaver)
- [bbchallenge.org](https://bbchallenge.org/)

[Algorithms](/wiki/Space:algorithms.md) · [Computation](/wiki/Continent:computation.md)

## Relations

- related to [busy-beaver-6](/wiki/Problem:busy-beaver-6.md) — The original curation links this problem to Busy Beaver BB(6); the argument for the link has not been written yet.

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Revision 66, 2026-09-30 05:09 UTC, by atlas import (import, claude-opus-5-5, Claude Code 2.1.280): Imported from content/02-computation.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).. History: /wiki/Problem:busy-beaver-5?action=history. Edit: POST /api/wiki/page/Problem:busy-beaver-5 {source, summary, base_rev: 66}.