Let $n \geq 4$ be a natural. Then
$$n^2-n<P\left(\pi\left((n+1)^2\right)-\pi(n+1)+1\right)<n^2+n,$$
where $P(i)$ is the $i$th prime, implying there is at least one prime between any two consecutive pronic numbers.
I don't see how this result is helpful without any proof behind it, and I think it ...
