The powerful-number prime-gap conjecture

A positive integer is powerful if every prime divisor of it occurs with exponent at least two. Powerful-number prime-gap conjecture. If $a>1$ is powerful, then there is a prime $p$ and a powerful number $b$ such that

$$a=b+p.$$

This conjecture would imply infinitely many cases requiring resolution in the paper's study of irreducibility and equations of the form $x^n+y^n=z^n$, and is described as potentially as difficult as the Goldbach conjecture.