---

Claim. For $k=14$ there is an $n$ with $\prod_{0\le i\le 14}(n-i)\mid\binom{2n}{n}$, as Problem 396 asks: the least such $n$ is $359503904702190$, the term $a(14)$ of the OEIS entry A375077, which its extension line credits to Justin Dehorty and Sharvil Kesarwani on 3 April 2026. The thread post of 3 April 2026 by the user wibble132 reports the value from a run of Kesarwani's search program lasting about two and a half days; Dehorty's reply of 4 April 2026 says the same value was computed on 1 April 2026 by Dehorty, with the algorithm Dehorty and Kesarwani developed together, and by a third party, so the term was found three times independently. A witness is checked through Kummer's theorem, as Stephan's page explains.

Submission note. Posted to the site's forum by Justin Dehorty on 4 April 2026:

Really awesome to see this result. This matches the exact result computed on April 1st by myself (using Rust and the algorithm Sharvil and I co-developed) and I understand from the ongoing OEIS discussion thread that Sharvil's friend also computed it on the same day (triple confirmation!)

Re: The recent optimizations you alluded to...

Moving forward, moderators have requested that we continue algorithmic discussions along those lines at a separate location so we don't spam the comments section of this problem. As such, I have set up a GitHub Gist for further discussion and have compiled all information exchanged on this thread and GitHub so that others may get up to speed and contribute to these recent advances more easily in the future:

Search Algorithm Optimizations for A375077

I have done my best to source everything and provide accurate sources/attributions, but mistakes or omissions are possible. @Sharvil and others - please let me know in the comments section of that Gist if there is anything there that needs to be adjusted or added.

Covers. The instance $k=14$ of the question, with the answer yes by an explicit witness.

Depends on. No page of this wiki.

Standing. The entry is an edited database record and the thread posts unrefereed announcements; the site's commentary on a problem it labels OPEN points to the entry without accepting a result. The claim stays claimed.