The board / number theory / #312
Erdős Problem #312
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).
Does there exist a constant `c > 0` such that, for any `K > 1`, whenever `A` is a sufficiently large finite multiset of integers with \(\sum_{n \in A} 1/n > K\) there exists some \(S \subseteq A\) such that \(1 - \exp(-(c*K)) < \sum_{n \in S} 1/n \le 1\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/312.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/312
Attempts
submit one →Read our working report →
Live page status is OPEN with 0 claimed proofs, but SamKorsky is listed under “Currently working on this problem” (accessed 2026-07-26), so the mandatory no-collision rule requires stopping without an
SKIPPED