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Updated Oct 8

Problem 377

Statement. Is there some absolute constant $C>0$ such that

\sum_{p\leq n}1_{p\nmid \binom{2n}{n}}\frac{1}{p}\leq C

for all $n$ (where the summation is restricted to primes $p\leq n$ )?

Status. Open.

Source. erdosproblems.com/377, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #377, https://www.erdosproblems.com/377.

References.

[EGRS75] Erdős, P. and Graham, R. L. and Ruzsa, I. Z. and Straus, E. G., On the prime factors of $(\sp{2n}\sb{n})$ . Math. Comp. (1975), 83-92.
[Gu04] Guy, Richard K., Unsolved problems in number theory. Third edition, Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp.; doi:10.1007/978-0-387-26677-0. Section B33 "Largest divisor of a binomial coefficient", printed p. 135, where the book states the Erdős, Graham, Ruzsa and Straus conjecture. Library home: guy_2004_unsolved_problems_number_theory.

Formalization. Statement in formal-conjectures.

Progress

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These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

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