\begin{definition}[Definition:Balanced Prime/Definition 2]
Let $\paren {p_{n - 1}, p_n, p_{n + 1} }$ be a triplet of consecutive prime numbers.
$p_n$ is a '''balanced prime''' {{iff}}:
{{begin-eqn}}
{{eqn | l = p_{n - 1} + d
      | r = p_n
      | c = 
}}
{{eqn | l = p_{n - 1} + 2 d
      | r = p_{n + 1}
      | c = 
}}
{{end-eqn}}
for some $d \in \Z$.
That is, {{iff}} $p_n$ is the middle term of a $3$-term arithmetic sequence in which the $1$st and last terms are the previous and following primes.
\end{definition}