\begin{definition}[Definition:Balanced Prime/Definition 1]
Let $\left({p_{n - 1}, p_n, p_{n + 1} }\right)$ be a triplet of consecutive prime numbers.
$p_n$ is a '''balanced prime''' {{iff}}:
:$p_n = \dfrac {p_{n - 1} + p_{n + 1} } 2$
$p$ is a '''balanced prime''' {{iff}} it is the arithmetic mean of the prime numbers on either side of it.
\end{definition}