Cramér's conjecture on gaps between consecutive primes

Let $p_n$ denote the $n$-th prime. Cramér's conjecture. There exist absolute constants $n_0,c>0$ such that if $n>n_0$, then

$$p_{n+1}-p_n\leq c(\log p_n)^2.$$

This conjectural bound on maximal gaps between consecutive primes would provide a more reasonable worst-case running time for locating neighboring primes in the algorithm; it is not known unconditionally.