Prime Number Theorem

Theorem (bound for $x > 55$)

Let $\pi(x)$ denote the number of primes less than some integer $x$. For $x>55$, $$\frac{x}{\log x} \leq \pi(x)\leq \frac{x}{\log x - 4}$$

References:

1. https://www.chrismusco.com/amlds2023/notes/lecture03.html
2. https://mathworld.wolfram.com/PrimeNumberTheorem.html
3. https://en.wikipedia.org/wiki/Prime_number_theorem