The Number of Primes

The number of primes is infinite

Explanation

It is proved that the number of primes is infinite. The proof uses an indirect (contradiction) approach: assume there is a finite largest prime \(P\), form \(N = 2 \cdot 3 \cdot 5 \cdots P\), and show that \(N + 1\) must itself be prime — contradicting the assumption. There is, however, no known formula that generates all primes.