Is it true that given any fixed $\epsilon > 0$, there exists $k > 0$ such that for all integers $n \geq k$, it follows that there exists a prime $p$ between $n$ and $(1 + \epsilon)n$?
If it is true, who discovered this result and where might I obtain a proof of it?
If it is not true, what would be one of the best extensions of Nagura's Theorem that is currently known?