Strange behaviour of prime numbers

[ttw]

One has to be careful using empirical counting with prime numbers. The function Li(x) is the integral from 2 to x of dt/ln(t). It has been proven that the difference between Li(x) and Pi(x), which is the prime counting function of all primes less than x, changes sign infinitely many times. However the first sign change isn't known. It's know to happen at a big number.

Lots of other weird things happen.