On the Maximal Gap between Primes

In this paper, we show some results about the gap between a prime number and its consecutive prime number for large enough prime numbers. We show that the gap between a prime number $p_n$ and its consecutive prime number is not larger than $2{\log }^2{p}_n$. We also show that the result implies the existence of a prime number in a certain type of interval for large enough numbers as a consequence.