[math-fun] 3+2i and Catalan's constant

I finally got my hands on a paper recommended to me by W. Edwin Clark. George Collins (the author) got it right, but could have simplified more. If b and c are two random integers, then P[GCD[b,c]=1] = (6/Pi^2) If b and c are two random Gaussian integers, then P[GCD[b,c]=1] = (6/Pi^2)/Catalan I think that's a gorgeous result. --Ed Pegg Jr, www.mathpuzzle.com 90m:11165 Collins, George E.(1-OHS-C); Johnson, Jeremy R.(1-OHS-C) The probability of relative primality of Gaussian integers. Symbolic and algebraic computation (Rome, 1988), 252--258, Lecture Notes in Comput. Sci., 358, Springer, Berlin, 1989. 11R27 (11Y40)