For a positive real number x, let π‎(x) be the number of primes less than or equal to x. The prime number theorem says that, as x → ∞,

This gives, in a sense, an idea of what proportion of integers are prime. It was suspected since the time of Gauss and Legendre and first proved in 1896 by Jacques Hadamard and Charles De La Vallée-Poussin independently.