Erdős Problem #5 — Limit points of the normalized prime gaps $d_n/\log n$

Let $2 = p_1 < p_2 < \cdots$ be the sequence of consecutive primes. [...] $p_{n+1} - p_n = d_n$. [...] It seems likely that $d_n/\log n$ is everywhere dense in $(0, \infty)$. Ricci [13] and I proved independently that the limit points of $d_n/\log n$ form a set of positive Lebesgue measure, but the only known limit point of this set is $\infty$. In particular I do not know if $d_n/\log n$ has a rational limit point.