Euler's Product Formula

Euler's Product Formula states that the sum of the reciprocals of all natural numbers raised to a power \(s\) (the Riemann zeta function) can be expressed as an infinite product over all prime numbers. In essence, it reveals that primes are the building blocks of all natural numbers. This formula links the additive world of number sums to the multiplicative nature of primes, showing that understanding primes is key to understanding overall number behavior. It highlights the deep connection between prime distribution and properties of numbers, fundamental in analytic number theory.