The site's strict bound fails at $(n,k)=(4,2)$: $\binom42=6$ has the prime divisors $2$ and $3$, and no prime is below $4/2=2$. It fails again at $\binom62=15$, whose prime divisors are $3=n/2$ and $5$. A complete computation of the least prime factor of $\binom nk$ for $1<k<n-1$ and $n<600$ finds the strict bound false at 31 pairs: the listed exception at $(7,3)$ and $(7,4)$, and 29 pairs in the rows $n=2q$ with $q$ prime, from $(4,2)$, $(6,2)$, $(6,4)$ and $(14,2)$ up to $(542,2)$, at each of which $q$ is the least prime factor of $\binom nk$; the bound $p\leq n/2$ fails only at $(7,3)$ and $(7,4)$. In every row that is not twice a prime the two bounds agree, since a prime $p\leq n/2$ is then below $n/2$. The change replaces "$p<n/2$" by "$p\leq n/2$"; nothing else changes. The evidence is first the posers' own words. Erdős and Graham [ErGr80], printed p. 73, report that Ecklund [Ec69] proved the least prime factor of $\binom nk$ to be below $n/2$ for $k>1$ "with the unique exception of" $\binom73$, "thus settling a conjecture of Erdős and Selfridge"; their strict sign is the site's, but both their statements about instances of the question, a single exception and a settlement by Ecklund's theorem, hold only for the non-strict bound, since under the strict one $\binom42$ is a second exception and Ecklund's theorem proves only $p\leq\max\{n/k,n/2\}$. Ecklund's paper, printed p. 267, states the problem Erdős suggested with the non-strict bound: if $n\geq2k$, then $\binom nk$ has a prime divisor $p\leq n/2$. Guy [Gu04], section B33, printed p. 134, states Ecklund's theorem the same way, and the site's commentary credits the proof to Ecklund. The defect is not the site's alone: the strict sign is already in [ErGr80], and the site's wording copies it. A comment in the site's discussion thread pointed out on 2026-02-04 that Ecklund's bound is $p\leq n/2$. The results about the site's wording answer it (a prime $p<n/2$), not the corrected Statement ($p\leq n/2$), so they do not count toward the problem's standing: the Lean file Erdos384.lean of Boris Alexeev's repository of Lean proofs (first committed 2026-08-17; the link pins its 2026-09-15 revision; with the AI systems Codex and GPT-5.6 Sol named as its formal authors), which proves the strict wording false from $\binom42=6$ and whose claim page, Alexeev 2026, is rejected; and this page's own witness $\binom62=15$.