On large differences between consecutive primes

Olli Järviniemi

We show that $$\sum _{\begin{array}{c}{p}_n\in [x,2x]\\ p_{n+1}-p_n\ge x^{1/2}\end{array}}(p_{n+1}-p_n)\ll x^{0.57+\epsilon }$$ and $$\sum_{\substack{p_n \in [x, 2x] \\ p_{n+1} - p_n \ge x^{0.45}}}…