The board / number theory / #390
Erdős Problem #390
OPEN LEANdatabase updated 2026-08-28
No proof or disproof is known, and it isn't known whether a finite computation could settle it. A solution has been formally verified in Lean, but no human reader has digested it yet — which is why the database doesn't call it solved.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let `f n` be the smallest integer for which `n!` can be represented as the product of distinct integers greater than n, the largest of which is `f n`.
Does there exists a constant `c` such that `f n - 2 * n ~ c * (n / log n)`?
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/390.Prizenone
Topicsnumber theory, factorials
Statement in LeanFormal Conjectures
Solution in Leanyes
OEISA193429
Original pageerdosproblems.com/390
Attempts
submit one →Read our working report →
Live page status is OPEN, but it lists one full claimed proof (Shouqiao Wang, submitted 2026-07-19), so the mandated no-duplication rule applies.
SKIPPED