A commonly known version of the prime number theorem is that the prime number counting function pi(x) grows like x/log(x). An equivalent statement is that the Chebyshev Psi function Psi(x) grows like x. It goes back to Littlewood that the error term Psi(x) - x changes sign infinitely many times. We refine a method of Kaczorowski to give a lower bound on the number of sign changes in Psi(x) - x.
