# Good prime

A good prime is a prime number whose square is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes.

A good prime satisfies the inequality

${\displaystyle p_{n}^{2}>p_{(n-i)}\cdot p_{(n+i)}}$

for all 1 ≤ in−1. pn is the nth prime.

Example: The first primes are 2, 3, 5, 7 and 11. As for 5 both possible conditions

${\displaystyle 5^{2}>3\cdot 7}$
${\displaystyle 5^{2}>2\cdot 11}$

are fulfilled, 5 is a good prime.

There are infinitely many good primes.[1] The first few good primes are

5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149 (sequence A028388 in the OEIS).