Riemann hypothesis: Quick Facts

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Photos

A graph illustrating the Riemann hypothesis, with a horizontal real axis and a vertical imaginary axis. The critical strip, where the real part of S is between 0 and 1, is shaded, and the critical line at real part 1/2 is marked. Trivial zeros are shown at negative even integers on the real axis.

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Topics

Bohr–Landau theorem prime number theorem Riemann zeta function number theory Millennium Problem P versus NP problem Poincaré conjecture Navier-Stokes equation Yang-Mills theory Hodge conjecture Birch and Swinnerton-Dyer conjecture twin prime conjecture amicable numbers Fermat’s last theorem perfect number

Key People

Bernhard Riemann, lithograph after a portrait, artist unknown, 1863.

Bernhard Riemann

German mathematician

Equations written on blackboard

Numbers and Mathematics