There was not much time to think, since he still had classes to teach. Xiao Yi quickly stopped pondering and turned to the students present. "All right, everyone. Next, let's continue discussing how to use analytic continuation to obtain further results on the distribution of prime numbers."
"First, we need to explain what the Riemann zeta function is."
Xiao Yi then began writing on the blackboard.
By combining the Riemann zeta function with the Prime Number Theorem, he ultimately laid out the form of the Riemann Hypothesis, then explained just how closely the Riemann Hypothesis was related to the distribution of primes.
"Some of you may think that once the Riemann Hypothesis is proven, we'll be able to find a general formula for prime numbers. That's incorrect."
"Although the distribution of primes displays certain patterns, such as the Ulam spiral, it also exhibits a degree of randomness within those patterns. Therefore, finding a general formula for prime numbers is completely impossible—at least for now."
"The main use of proving the Riemann Hypothesis lies in helping us make better estimates of the distribution of primes based on the Prime Number Theorem."
"If the Riemann Hypothesis holds, we can give a more precise upper-bound estimate for the difference between π(x) and x/ln(x)."
"That would make it easier for us to identify which regions among the infinite natural numbers are highly likely to contain a prime."
"As for whether the Riemann Hypothesis can be used to crack RSA encryption, that's nonsense. We can simply assume the Riemann Hypothesis is true and use it directly; this is quite common in related fields. Mathematicians have already discovered more than a thousand propositions that rely on the Riemann Hypothesis being true."
"So if the Riemann Hypothesis could help crack RSA encryption, it would have been used