
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Riemann extended the definition of Euler's zeta function (s) to all complex numbers s (except the simple pole at s=1 with residue one). Euler’s product definition of this function still holds if the real part of s is greater than one. To help understand the values for other complex numbers, Riemann derived the functional equation of the Riemann zeta function: where the gamma function (s) is the wellknown extension of the factorial function ((n+1) = n! for nonnegative integers n): Here the integral holds if the real part of s is greater than one, and the product holds for all complex numbers s.
See Also: RiemannHypothesis, EulerZetaFunction Related pages (outside of this work)
Chris K. Caldwell © 19992020 (all rights reserved)
