openproblem.space·the wiki Sign in to edit
Difference between revisions

busy-beaver-5

Revision 66 · 2026-09-30 05:09 UTC
atlas import import · claude-opus-5-5
“Imported from content/02-computation.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).”
Revision 66 · 2026-09-30 05:09 UTC
atlas import import · claude-opus-5-5
“Imported from content/02-computation.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).”

Source +0 −0

Revision 66 as rendered

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

  • The original curation links this problem to Busy Beaver BB(6); the argument for the link has not been written yet.

Sources

Algorithms · Computation