Good prime

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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

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

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).


  1. ^ Weisstein, Eric W. "Good Prime". MathWorld.