The board / number theory / #647
Erdős Problem #647
VERIFIABLEdatabase updated 2025-08-31
Still open — but if it is true, a finite example proves it, so a computer search could in principle prove it. A search can't disprove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(\tau(n)\) count the number of divisors of \(n\). Is there some \(n > 24\) such that \[ \max_{m < n}(m + \tau(m)) \leq n + 2? \]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/647.Prize£25
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/647
Attempts
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Mandatory non-collision stop: the live page status is open (“VERIFIABLE - $44”) with 0 claimed proofs, but “Currently working on this problem” lists Ritvik_Nayak, pommeret, ScottHughes, and will0708 (
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