神奇的圆周率

APPSYZY

Given any pair of whole numbers chosen from a large, random collection of numbers, the probability that the two numbers have no common factor other than one (1) is
$$
\frac{6}{\pi^2}
$$
For example, using the small collection of numbers: $2,3,4,5,6$; there are 10 pairs that can be formed: $(2,3),(2,4)$, etc. Six of the 10 pairs: $(2,3),(2,5),(3,4),(3,5),(4,5)$ and $(5,6)$ have no common factor other than one. Using the ratio of the counts as the probability we have:
$$
\begin{aligned}
\frac{6}{\pi^2} & \approx \frac{6}{10} \\
\pi & \approx 3.162
\end{aligned}
$$

orzweb111

回复 1# APPSYZY
You were asking the Probability of coprimality. Here is an answer en.wikipedia.org/wiki/Coprime_integers#Probability_of_coprimality