What percent of numbers are primes?

Question

I understand that there are infinitely many primes and (obviously) infinitely many integers, but is there any way to calculate the total percentage of integers that are primes? Thanks

Answer 1

The function $\pi(n)$ tells us the amount of primes lower or equal to $n$. It is known that $\pi(n) \sim \frac{n}{\ln n}$ so the proportion as $n$ grows is about:

$$\frac{n}{\ln n}·\frac{1}{n} = \frac{1}{\ln n}$$

This means that as $n$ grows, the proportion tends to zero.