The board / number theory / #413
Erdős Problem #413
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).
`IsBarrier f n` means `n` is a barrier for the real-valued function `f`, i.e. `(m : ℝ) + f m ≤ (n : ℝ)` for all `m < n`.
Are there infinitely many barriers for `ω`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/413.Prizenone
Topicsnumber theory, iterated functions
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA005236
Original pageerdosproblems.com/413
Attempts
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Live page status OPEN (last edited 17 April 2026; accessed 2026-07-28), with 0 claimed proofs, but “Currently working on this problem” lists conglu and RaziqStark; stopped to avoid colliding with curr
SKIPPED