ThmDex – An index of mathematical definitions, results, and conjectures.
Conjecture C7 on D1671: Euclid number
Euclid number conjecture
Formulation 0
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}