Mori–Mukai's characterization conjecture for projective space

Let $X$ be a smooth Fano variety of dimension $n$ over an algebraically closed field, and let $C\subseteq X$ be a rational curve. Mori–Mukai's characterization conjecture. If

$$(-K_X\cdot C)\ge n+1$$

for every rational curve $C\subseteq X$, then $X$ is isomorphic to the $n$-dimensional projective space $\mathbf{P}^n$. This conjecture proposes a numerical characterization of projective space among smooth Fano varieties. The supplied text gives no resolution status.