Riemann hypothesis
Number theory
The conjecture that every nontrivial zero of the Riemann zeta function has real part exactly 1/2.
What is usually left out
The trivial zeros are the negative even integers −2, −4, −6, and so on; they come from the functional equation and are not at issue. The hypothesis is equivalent to a sharp bound on how far the count of primes below x can stray from the logarithmic integral, which is why it is described as being about the regularity of the primes. Billions of zeros have been computed and all lie on the critical line, which is evidence and not proof.
Related terms
In the atlas
- Riemann hypothesis — Number theory, open
- Generalized Riemann hypothesis for Selberg class — Number theory, open