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    Riemann Hypothesis

    Statement

    The Riemann hypothesis posits that the nontrivial zeros of the Riemann zeta function ζ(s) all lie on the critical line Re(s) = 1/2.

    Formal statement

    for all _(n, n element Z ∧ n!=0)Re(ρ_n) = 1/2

    History

    formulation date | 1859 (166 years ago)
formulator | Bernhard Riemann
status | open

    Associated equation

    Re(ρ_n) = 1/2

    Current evidence

    It has been verified that the first 1×10^13 nontrivial zeros of the zeta function lie on the critical line.
Conrey (1989) proved that at least 40% of the nontrivial zeros of the zeta function lie on the critical line.

    Associated prizes

    prize offered for solution | $1 million "Millennium Prize Problem" of The Clay Mathematics Institute.

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