The board / number theory / #1062
Erdős Problem #1062
OPENdatabase updated 2025-09-28
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).
A set `A` of positive integers is fork-free if no element divides two distinct other elements of `A`.
The extremal function from Erdős problem 1062: the largest size of a fork-free subset of `{1,...,n}`.
Erdős asked whether the limiting density `f n / n` exists and, if so, whether it is irrational.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1062.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA038372
Original pageerdosproblems.com/1062
Attempts
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Exact computational values f(n) are independently reproduced through n=200 (extending OEIS n=45..200), with f(200)=136 and an explicit checked witness; irrationality remains open and requires a unifor
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