The distribution and density of these zeros affect the error term in the Prime Number Theorem. If the Riemann Hypothesis holds, it implies a tighter error bound in the Prime Number Theorem.

The Riemann Hypothesis proposes a specific location (the critical line) for the non-trivial zeros of the Riemann zeta function. This paper argues that the aperiodicity observed in the distribution of these non-trivial zeros and the distribution of primes numbers is a fundamental property. A periodic zeta function would significantly alter