I've been experimenting with the function $π(x)$ such that $π(x)$ counts the number of primes from $1$ to $x$.
I found that after $10$, $π(x^2) - π(\lfloor \frac{x^2}{2} \rfloor)$ is always larger than $x$.
However, after doing some research (see Prime Number Theorem), I'm a bit confused because the number of primes grows more and more slowly.
Wouldn't this mean, at some point, $x$ will be greater than $π(x^2) - π(\lfloor \frac{x^2}{2} \rfloor)$ again or am I just being stupid?