The unproven Riemann hypothesis, dating from 1859, states that except for s = −2, −4, ..., all zeroes of the ζ-function have real part equal to 1/2. The connection to prime numbers is that it essentially says that the primes are as regularly distributed as possible.[clarification needed] From a physical viewpoint, it roughly states that the irregularity in the distribution of primes only comes from random noise. From a mathematical viewpoint, it roughly states that the asymptotic distribution of primes (about x/log x of numbers less than x are primes, the prime number theorem) also holds for much shorter intervals of length about the square root of x (for intervals near x). This hypothesis is generally believed to be correct. In particular, the simplest assumption is that primes should have no significant irregularities without good reason.
According to the Riemann hypothesis, all zeroes of the ζ-function have real part equal to 1/2 except for what values of s?
s = −2, −4, ..., −2, −4, ..., −2, −4 s = −2, −4