  The article attempts to demonstrate the rich history of one truly remarkable
problem situated at the confluence of probability theory and theory of numbers
- finding the probability of co-primality of two randomly selected natural
numbers. The goal of the article is to reveal the genesis of the problem and
understand the role of mathematicians of the past in solving this problem and
using it as a background for advancing mathematical ideas. The article
describes different approaches to the solution of the problem, reviews its
various generalizations, examines similar problems, and offers diverse
historical perspectives.
