Mathematicians will never stop proving the Prime Number Theorem 6 years ago
The classic formula derived from it, n/log(n), is always above the actual number of primes
No? pi(100) = 25, but 100 / log(100) = 21.7
The logarithmic integral is larger than pi for "small" arguments. But there is a pretty famous proof that li(x) - pi(x) changes signs infinitely often.