Primitive Roots In Short Intervals

Let $p\ge 2$ be a large prime, and let $N\gg (\log p{)}^{1+\epsilon }$. This note proves the existence of primitive roots in the short interval $[M,M+N]$, where $M\ge 2$ is a fixed number, and $\epsilon >0$ is a small number. In particular, the least primitive root $g(p)=O((\log p{)}^{1+\epsilon })$, and the least prime primitive root $g^{\ast }(p)=O((\log p{)}^{1+\epsilon })$ unconditionally.