# Probability, Primes, and Pi

What is the probability that two randomly chosen integers have no prime factors in common?  In honor of Pi Day, I’d like to explain the surprising answer: $6/\pi^2$.

The hero of this story is Leonhard Euler, who worked out this astonishing connection between prime numbers and $\pi$ through a series of brilliant insights.  In the spirit of Euler, I will be rather cavalier about issues of convergence and rigor here, focusing on the key underlying ideas.