Definition:Balanced Prime/Definition 2

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 :

for some $d \in \Z$.

That is, $p_n$ is the middle term of a $3$-term arithmetic progression in which the $1$st and last terms are the previous and following primes.

Also see

 * Equivalence of Definitions of Balanced Prime