---

Claim. V. Kovač and F. Luca, On the number of divisors of Mersenne numbers, Experimental Mathematics (online 20 May 2026; card), Theorem 3 (v4 numbering; v1 states it as Theorems 2 and 3, one per conjecture): if Conjecture 1 or Conjecture 2 holds, then $f(2n)/f(n)\to\infty$, which under the problem page's Formulation answers Problem 893 yes.

Hypothesis. Conjecture 1: along the indices $N$ with $\tau(2^N-1)>\tau(2^m-1)$ for all $m<N$, $\tau(2^N+1)/N\to\infty$. Conjecture 2: $\omega(\Phi_d(2))\le10\log d$ for all $d\ge2$ with at most finitely many exceptions. Both are unproven, and the paper supports them numerically; the page settles no standing.

Depends on. No page of this wiki.

Acceptance. As on the unconditional page: refereed, Experimental Mathematics; the site labels the problem OPEN, so its commentary is not acceptance.