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The article attempts to demonstrate the rich history of one truly remarkableproblem situated at the confluence of probability theory and theory of numbers- finding the probability of co-primality of two randomly selected naturalnumbers. The goal of the article is to reveal the genesis of the problem andunderstand the role of mathematicians of the past in solving this problem andusing it as a background for advancing mathematical ideas. The articledescribes different approaches to the solution of the problem, reviews itsvarious generalizations, examines similar problems, and offers diversehistorical perspectives.

On the probability of co-primality of two natural numbers chosen at random (Who was the first to pose and solve this problem?)