Let $p_1, p_2, p_3, \dots \in \mathbb{N}$ be the D4180: Prime integer sequence such that

(i)	$P = \{ p_1, p_2, p_3, \ldots \}$ is the D2276: Set of prime integers

Then \begin{equation} \# \left\{ N \in 1, 2, 3, \ldots : 1 + \prod_{n = 1}^N p_n \in P \right\} = \infty \end{equation}