The short-interval prime conjecture

For a real number $\theta>0$ and sufficiently large $x$, the interval $[x,x+x^\theta]$ contains a prime number. The short-interval prime conjecture. Given $\theta>0$, for all sufficiently large $x$, the interval

$$[x,x+x^\theta]$$

contains a prime number. This is a conjecture from prime number theory; the source notes that it is known for all $\theta>0.525$, while the paper assumes it in proving its main theorem.