$b$ is a real number, but not necessarily an integer.

For example, $\zeta (\frac{1}{2}+14.134i)=0$ (Here, $b=\mathrm{14.134...}$)

The relationship to prime numbers is more complicated, and not easy to visualize in an intuitive manner. Essentially, the prime counting function (how many primes are there up to some number $x$), can be expressed as a sum over functions of the non-trivial zeros of the zeta function