Guy, Richard K., Unsolved problems in number theory. 3rd ed., Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp. Section B46 "The largest prime factor of $n$", printed p. 154, which the site's remark names, states the question in terms of the largest prime factor $P(p-1)$ of $p-1$: are there infinitely many primes $p$ with $(p-1)/P(p-1)=2^k$, or $=2^k\cdot 3^l$? Library home: Guy 2004.