A prime p_n is called "good" if p_n^2>p_(n - i) p_(n + i) for all 1<=i<=n - 1 (there is a typo in Guy 1994 in which the is are replaced by 1s). There are infinitely many good primes, and the first few are 5, 11, 17, 29, 37, 41, 53, ... (OEIS A028388).

Andrica's conjecture | Landau's problems | Pólya conjecture