Henry Iwaniec

The Distribution of Prime Numbers

June 11, 2024

Source: Rutgers Current Trends in Mathematics

Divergence of $\sum \frac{1}{p}$

$$ \sum \dfrac{1}{p} = \prod \dfrac{1}{1-\frac{1}{p}} \to \infty $$

Prime Number Theorem

$$ \pi(x) \sim \dfrac{x}{\log x} $$

Polymath8

There are infinitely many primes that differ by at most 246.