The board / number theory / #377
Erdős Problem #377
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).
The sum of the inverses of all primes smaller than \(n\), which don't divide the central binom coefficient.
Is there some absolute constant \(C > 0\) such that \[ \sum_{p \leq n} 1_{p\nmid {2n \choose n}}\frac{1}{p} \leq C \] for all \(n\)?
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/377.Attempts
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Exactly certified max_{n<=10^8} f(n)=f(3250)=1.1792429057944813969965..., found the omitted Sander log-weighted theorem, and reduced the unresolved issue precisely to a uniform small-prime/digit-depth
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