The book Theory of Numbers by G H Hardy, et al. proves $ π(x) \ge \log \log x$ for $ x > e^{e^3}$ . Is there a way to *prove* that it also holds for $ 2 \le x \le e^{e^3}$ otherwise (at worst) any valuable source to check this numerically?

# Tag: $\log

## Does finding a cycle with $\log n$ length in $\text{P}$ ?

Let $ G$ be an arbitrary graph with $ n$ vertices and we want to find a cycle with $ \log n$ length. Is there exists a known polynomial algorithm for this problem?