Gaps between integers with the same prime factors

We give numerical and theoretical evidence in support of the conjecture of Dressler that between any two positive integers having the same prime factors there is a prime. In particular, it is shown that the abc conjecture implies that the gap between two consecutive such numbers $a <c$ is $\gg a^{1/2 - \epsilon }$, and it is shown that this lower bound is best possible. Dressler's conjecture is verified for values of $a$ and $c$ up to $7\cdot 10^{13}$.