Prime number determinatorer!

Suppose the mod function is defined as $\text{mod}(x,y) = x- y \left\lfloor \dfrac{x}{y} \right\rfloor$ . Then define $\large f(x) = \text{mod}((x-(\text{mod}((x-1)!,x)),x)$ for all positive integers $x$ . Then $f(x)$ is a function which returns 1 if $x$ is prime , 0 if not.