grandes-ecoles 2025 Q10

grandes-ecoles · France · centrale-maths1__official Number Theory Prime Counting and Distribution
Let $x \geqslant 3$. Using the monotonicity of the function $t \mapsto \frac { t } { \ln ( t ) }$ on the interval $[ \mathrm { e } , + \infty [$, show that
$$\pi ( x ) \leqslant 4 \frac { x } { \ln ( x ) }$$
Let $x \geqslant 3$. Using the monotonicity of the function $t \mapsto \frac { t } { \ln ( t ) }$ on the interval $[ \mathrm { e } , + \infty [$, show that

$$\pi ( x ) \leqslant 4 \frac { x } { \ln ( x ) }$$