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

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

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

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

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


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