After I've read and I've understand  (I have no free access), I would like to know if is it possible to prove or discard that the sequence A025528, that counts the number of prime powers less than or equal to a fixed integer $n\geq 1$ in OEIS has gaps between their terms arbitraly large, as same as than occurs in the sequence of prime numbers.
With it, and calculations and reasoning of the author should be easy to deduce, in case that the sequence of gaps is unbounded, the irrationality of a real number following the proof in the article.
Question. Are the gaps between consecutive terms in the sequence of prime powers A000961 arbitrarly large? I am asking if such sequence is unbounded. I think that should be well known. Thanks in advance.
As a detail, and as comparison with a reasoning in the article I know that, for instance, in the sequence $4!+1,4!+2,4!+3,4!+4$ the first term is a prime power, $25$.
 Cilleruelo, Una serie que converge a un número irracional, La Gaceta de la RSME, Vol. 18 (2015), No. 3, page 568.