  In this article, we derive a Euler prime product formula for the magnitude of
the Riemann zeta function $\zeta(s)$ valid for $\Re(s)>1$, as well as similar
formulas for $\zeta(s)$ valid for an even and odd $k$th positive integer
argument. We shall further give a set of generated formulas for $\zeta(k)$ up
to $11$th order, including Ap\'ery's constant, and also construct formulas for
$\zeta(3/2)$. We'll also validate these formulas numerically.
