• 1 Dalhousie University [Halifax]

We prove in this paper that for $y=x^{\theta}, \frac{11}{20}<\theta\leq\frac{7}{12}$ and $x$ large enough, we have $0.99\frac{y}{\log x}\leq\pi(x)-\pi(x-y)\leq1.01\frac{y}{\log x}$.