Open: the site labels the problem OPEN (page last edited 19 October 2025). Neither question is answered. The first is proved for every $\epsilon>1/5$ by Filaseta and Trifonov (1992), claimed for every $\epsilon>1/5-\eta$, with some $\eta>0$, in Pandey's 2024 preprint (a pending partial claim), and proved for every $\epsilon>0$ under the abc conjecture by Granville (1998); the second is open, and Erdős's 1951 lower bound shows that its constant $\pi^2/6$ could not be lowered. The claim pages under claims/ record these results.