On the probability of co-primality of two natural numbers chosen at   random (Who was the first to pose and solve this problem?)
  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. 
Sergei Abramovich, Yakov Yu. Nikitin
math.HO math.PR