Inverse of prime counting function The prime counting function $ \pi (x) \approx \dfrac {x} {\ln(x-1)} $.
This function returns the number of primes less than $x$.

Note: $x-1$ gives a better estimate than $x$.

How to find $x$ given $ \pi(x) $ ?
Instead of an analytical Expression or 1-Step Approximation use a Fixed Point Iteration that converges relatively fast to the Inverse of x/ln(x). 

8 Iterations yield the Result e.g. x = 4_210_563_857 for y = 190_000_000: 

    public static double PI_INVERSE(double y) {
        double xOld = 0;
        double x = y*Math.Log(y);
        const double maxDiff = 0.5;
        for (; x - xOld &gt; maxDiff;) { //strictly monotonous
            xOld = x;
            x = y*Math.Log(x);
        }
        return x;
    }
Look up
Meissel's prime-counting function.

One reference is here:

https://en.wikipedia.org/wiki/Prime-counting_function