 However Littlewood showed in 1914 that there are infinitely many sign changes for the function

so the lead in the race switches back and forth infinitely many times.The phenomenon that is ahead most of the time is called Chebyshev's bias.The prime number race generalizes to other moduli and is the subject of much research; Pál Turán asked whether it is always the case that and change places when and are coprime to .