## \$ Π (x) ge log log x \$ holds \$ 2 le x e e {{e ^ 3} <5.3 times 10 ^ 8 \$?

The book Theory of Numbers by G H Hardy, et al. test $$π (x) ge log log x$$ for $$x> e ^ {e ^ 3}$$. There is a way to try out that also goes for $$2 le x e e ^ {e ^ 3}$$ otherwise (in the worst case) some valuable source to verify this numerically?