What is the Riemann Hypothesis, and why is it considered one of the most important unsolved problems in mathematics? Furthermore, what are some of the implications of proving or disproving the Riemann Hypothesis for number theory and cryptography?

The Riemann Hypothesis posits that all nontrivial zeros of the Riemann zeta function have a real part equal to 1/2. It is a central conjecture in number theory with profound implications for the distribution of prime numbers. Its resolution could lead to advances in areas such as cryptography, where prime numbers play a crucial role in encryption algorithms.