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

for all 1 ≤ i ≤ n−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. The first good primes are

References

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