Zeta Function -1 1/2 and prime numbers

[Niaboc67]

I talked with an old friend of mine. We discussed prime numbers and Ulams Spiral, and the mathematical patterns that surround us all. He brought up something called the Zeta-Function and something about -1 1/2 and how this all related to prime numbers. I did a google search and found some interesting results but didn't quite find enough on the purpose of -1 1/2, guess I should have dug a little deeper. Anyways could someone please explain the Zeta Function and why it is important and purposeful, as well as it's correlation to prime numbers and -1 1/2.

Thank You

 

[mathman]

I don't know where -1 1/2 comes from. There is a famous open question in mathematics (called the Riemann hypothesis) which says that in the strip in the complex plane (0<x<1, where x is the real part of z) the only zeroes of the zeta function are along the line x = 1/2.

Start here:
http://en.wikipedia.org/wiki/Riemann_zeta_function