Strong prime

In mathematics, a strong prime is a prime number with certain special properties. The definitions of strong primes are different in cryptography and number theory.

In number theory, a strong prime is a prime number that is greater than the arithmetic mean of the nearest prime above and below (in other words, it's closer to the following than to the preceding prime). Or to put it algebraically, given a prime number ${\displaystyle p_{n}}$, where n is its index in the ordered set of prime numbers, ${\displaystyle p_{n}>{{p_{n-1}+p_{n+1}} \over 2}}$. The first few strong primes are

For example, 17 is the seventh prime. The sixth and eighth primes, 13 and 19, add up to 32, and half that is 16. That is less than 17, thus 17 is a strong prime.

In a twin prime pair (p, p + 2) with p > 5, p is always a strong prime, since 3 must divide p − 2 which cannot be prime.

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