For, \(p\) and \(q\) both prime, is
\(p+q=2n\), \(n\gt 2,\,\in\mathbb{Z}^+\)
true for all \(n\).
if,
\(p=q\)
\(p+q=2p=2n\)
\(p=n\)
but not all \(n\) are prime as such \(p\neq q\).
So previously where \(n_o=n_q\), cannot hold.