The Riemann Hypothesis has many important consequences in number theory, including a better understanding of the distribution of prime numbers, and has far-reaching implications in other fields such as physics, cryptography, and computer science

The Riemann zeta function is defined as:

ζ(s) = 1 + 1/2^s + 1/3^s + 1/4^s + ...

where s is a complex number with real part greater than 1. The series on the right-hand side of the equation is called the zeta series and it converges for the specified values of s.

The Riemann zeta function is intimately connected to the distribution of prime numbers. In particular, it is related to the prime-counting function π(x), which counts the number of prime numbers less than or equal to x. More precisely, the Riemann Hypothesis, one of the most important unsolved problems in mathematics, states that all non-trivial zeros of the Riemann zeta function lie on the so-called critical line, which is a vertical line in the complex plane where the real part of the input is equal to 1/2