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 ≤ i ≤ n−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).

References

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

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