On the existence of twin prime in an interval

Shaon Sahoo

Let $S_{(x,y]}=\left\{\frac{p_n}{p_{n+1}-2}:n\in I\right\}$, where $I=\left\{n:x<p_n\le y\right\}$, $p_n$ is the $n$-th prime and $x,y\in {\mathbb{R}}_{>0}$. If $M_α(x…