The board / number theory / #164
Erdős Problem #164
PROVED LEANdatabase updated 2026-04-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
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A set \(A\subset \mathbb{N}\) is primitive if no member of \(A\) divides another. Is the sum \[\sum_{n\in A}\frac{1}{n\log n}\] maximised over all primitive sets when \(A\) is the set of primes? Erdős [Er35] proved that this sum always converges for a primitive set. Lichtman [Li23] proved that the answer is yes. An alternative, simpler, proof is given by Alexeev, Barreto, Li, Lichtman, Price, Shah, Tang, and Tao [ABLLPSTT26].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/164.Prizenone
Topicsnumber theory, primitive sets
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA137245
Original pageerdosproblems.com/164
Attempts
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