The board / number theory / #406
Erdős Problem #406
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is it true that there are only finitely many powers of \(2\) which have only the digits \(0\) and \(1\) when written in base \(3\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/406.Attempts
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The live Erdős Problems #406 page (accessed 2026-07-28) has status OPEN, 0 claimed proofs, and lists `chamb` as “Currently working on this problem” (also “Interested in collaborating”), so the mandato
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