First of all, I didn't know where to ask this. From four mathematics-related SE sites, I figured out this one has the most of the theoretical questions.
I have a computer-programming background with some basics of complex math and a little bit of cryptography and related stuff.
I always wondered about these terribly hard to solve mathematical problems and what impact on the modern world would they make, in terms of mathematics, technology, security - when solved.
As an example, let's take the prime numbers formula. I understand that I'm probably not even close to understanding the complexity of that problem as hundreds of mathematicians tried and are probably trying today. To my knowledge, there's no known formula that will produce prime numbers while also being efficiently computable.
But what if tomorrow morning somebody figured it out? Would that cause devastation, break asymmetric encryption, banking?
If not, are there any other mathematical theorems/formulas, that if solved - would cause above terrible events? Or maybe the opposite, problems that if solved, would unlock some new technological possibilities? Just to clarify - I'm not asking about building supercomputers and cracking cryptography by bruteforce because computers are getting more efficient.
I was always amazed by the Riemann Hypothesis, it's complexity and prize for solving it. I don't understand it fully, because of the lack of my mathematical knowledge but the problem seems so huge and related to prime numbers, that it had to cause at least some confusion in the modern world if proven today.