Finding a function whose value at $n$ is the $n^{th}$ prime

Finding a function whose value at $n$ is the $n^{th}$ prime

For positive integers $a$ and $b$, evaluate:
$$f\left ( a,b \right )=\frac{1}{a}\sum_{j=1}^{a}cos\left ( \frac{2\pi
jb}{a} \right )$$
Hence, find a function $g\left ( n \right )$, $n \in \mathbb{Z}$, such
that $g(n)=1$ if $n$ is prime and $g(n)=0$ if $n$ is composite.
Use $g(n)$ to construct a function $p\left ( n \right )$ whose value at
$n$ is the $n^{th}$ prime number.