The board / number theory / #1196
Erdős Problem #1196
PROVED LEANdatabase updated 2026-04-16
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
A set is primitive if no non-associated elements of the set divide each other.
Is it true that, for any \(x\), if \(A\subset [x,\infty)\) is a primitive set of integers (so that no distinct elements of \(A\) divide each other) then\[\sum_{a\in A}\frac{1}{a\log a}< 1+o(1),\]where the \(o(1)\) term \(\to 0\) as \(x\to \infty\)? -
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/1196.Prizenone
Topicsnumber theory, primitive sets
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/1196
Attempts
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