Riemann Zeta Explorer
Explore the fascinating Riemann zeta function, fundamental to understanding prime number distributions and one of mathematics' greatest unsolved problems.
ζRiemann Zeta Explorer
MathematicsOverview
Explore the fascinating Riemann zeta function, fundamental to understanding prime number distributions
🚀 Intermediate
Key Facts About the Riemann Zeta Function
The Critical Strip
The most interesting behavior occurs in the "critical strip" where the real part is between 0 and 1, particularly on the "critical line" where Re(s) = 1/2.
Prime Number Connection
The Riemann zeta function has a deep connection to prime numbers through the Euler product formula: ζ(s) = ∏p prime 1/(1-p-s).
Million Dollar Problem
The Riemann Hypothesis is one of the Clay Mathematics Institute's Millennium Prize Problems, with a $1,000,000 reward for a solution.