Definition:Balanced Prime/Definition 1

Definition

Let $\left({p_{n - 1}, p_n, p_{n + 1} }\right)$ be a triplet of consecutive prime numbers.

$p_n$ is a balanced prime if and only if:

$p_n = \dfrac {p_{n - 1} + p_{n + 1} } 2$

$p$ is a balanced prime if and only if it is the arithmetic mean of the prime numbers on either side of it.

Also see

• Equivalence of Definitions of Balanced Prime

• Results about balanced primes can be found here.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $257$