Prime Number Theorem/Interpretation

Interpretation of Prime Number Theorem

The Prime Number Theorem can also be rendered as:

$\ds \lim_{x \mathop \to \infty} \dfrac {\map \pi x / x} {1 / \ln x} = 1$

where $\dfrac {\map \pi n} n$ 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 $\dfrac 1 {\ln n}$.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.16$: The Sequence of Primes