grandes-ecoles 2024 Q17a

grandes-ecoles · France · x-ens-maths-a__mp Number Theory Prime Counting and Distribution
The objective of this question is to prove that if $n$ is a non-zero natural integer, then $\prod_{\substack{p \leqslant n \\ p \text{ prime}}} p \leqslant 4^n$.
Handle the cases $n \in \{1, 2, 3\}$.
The objective of this question is to prove that if $n$ is a non-zero natural integer, then $\prod_{\substack{p \leqslant n \\ p \text{ prime}}} p \leqslant 4^n$.

Handle the cases $n \in \{1, 2, 3\}$.