Suppose that Riemann Hypothesis is Correct
Reading some facts on books and the internet is interesting but most of the time, you don’t see exact examples. I’ve read several times that Riemann Hypothesis is important and many theorems are based on the fact that RH is correct, but I had never found an example. And, out of nowhere, in one of my Cryptography classes I just heard it.
The Miller-Rabin primality test is a probabilistic algorithm that determines whether a given number is likely to be a prime.
Miller’s version of the test is deterministic but here is the catch, it relies on the unproven Riemann Hypothesis.
The point of the article is not to explain and talk about the Miller-Rabin primality test. I’m not the appropriate person to explain it here. I would suggest the interested reader do his own research about the topic.
What I want to highlight here is how theoretical mathematics can be behind many different areas of math in mysterious ways and this is something that excites me every day. How the roots of a function can lead to many results about prime numbers and a completely theoretic concept can help create tests about if a number is prime, leading to many applied results in Computer Science.
But after all, this is the beauty of science. It is everywhere, and any researcher can get help from previous giants in order to make a small step forward of their research.
If you know any more theorems that require the RH to be correct, don’t hesitate to write it on the comments.
