grandes-ecoles 2025 Q2

grandes-ecoles · France · centrale-maths1__official Number Theory Prime Counting and Distribution
Show that, for all $n \in \mathbb { N } ^ { * }$,
$$\prod _ { \substack { p \leqslant n \\ p \text { prime } } } p < 4 ^ { n } .$$
One may proceed by induction and perform the inductive step by discussing according to the parity of $n$.
Show that, for all $n \in \mathbb { N } ^ { * }$,

$$\prod _ { \substack { p \leqslant n \\ p \text { prime } } } p < 4 ^ { n } .$$

One may proceed by induction and perform the inductive step by discussing according to the parity of $n$.