Furstenberg's proof of the infinitude of primes

Furstenberg's proof of the infinitude of primes is a beautiful and elegant argument that uses topology and the theory of sequences. Unlike the traditional proofs, such as Euclid's, which rely on simple divisibility arguments, Furstenberg's proof employs an elegant structure found in the space of sequences. ### Outline of Furstenberg's Proof The key idea is to use the notion of a compact topological space and sequences to show that there are infinitely many primes.