  Let $\mathfrak{sp}_{2n}(\mathbb {K})$ be the symplectic Lie algebra over an
algebraically closed field of characteristic zero. We prove that for any
nonzero nilpotent element $X \in \mathfrak{sp}_{2n}(\mathbb {K})$ there exists
a nilpotent element $Y \in \mathfrak{sp}_{2n}(\mathbb {K})$ such that $X$ and
$Y$ generate $\mathfrak{sp}_{2n}(\mathbb {K})$.
