How the Riemann zeta function reveals the hidden distribution of prime numbers

What does the Riemann zeta function have to do with the distribution of primes?

I explore how Euler connected the infinite sum of prime reciprocals to the Riemann zeta function using the Euler product formula. By bridging number theory and calculus, I demonstrate that the divergence of the harmonic series proves there are infinitely many primes, revealing a profound link between simple arithmetic and complex analysis.

"The Euler product formula is a way of encoding unique prime factorization in calculus, serving as a vital bridge between number theory and the study of infinite series."