The board / number theory / #66
Erdős Problem #66
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 there and \(A \subset \mathbb{N}\) is such that \[\lim_{n\to \infty}\frac{1_A\ast 1_A(n)}{\log n}\] exists and is \(\ne 0\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/66.Prize$500
Topicsnumber theory, additive basis
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/66
Attempts
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The live page status is “OPEN - $500” with 0 claimed proofs, but it lists Mahmudsudo and quintessen as “Currently working on this problem”; stopped before any mathematical attempt to avoid colliding w
SKIPPED