Consider the following integral:
$$π(n)=\frac{1}{(2πi)}\oint_{C_n}\frac{f'(x)}{f(x)}dx$$
Where , $$f(x)=\sin^2(πx)+\sin^2(π(1+\Gamma(x))/x)$$
The integral extends over a closed contour $C_n$ enclosing a segment $x$- axis from $1$ to $n$ and narrow enough to contain no complex zero.
We can clearly see that $f(x)$ has real zeroes only at primes .
This integral is considered by S.Wigert.
Question: Is this analysis "resurrectable"? By resurrectable I mean can this be modified such that it may be workable?
