Prime Number Theorem/Interpretation

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Interpretation of Prime Number Theorem

The Prime Number Theorem can also be rendered as:

$\displaystyle \lim_{x \mathop \to \infty} \dfrac {\pi \left({x}\right) / x} {1 / \ln x} = 1$

where it can be interpreted as the probability that a number chosen at random will be prime.

Thus, for large $n$, that probability is approximately equal to $\dfrac 1 {\ln n}$.