Happy Pi day everyone!!

[ttw]

Sum of reciprocals of integers (limit of course) from One to Infinity (not starring Deborah Kerr and Frank Sinatra) is Pi^2/6.

Probability that two random (will define below) integers are co-prime is 6/Pi^2.

How to uniformly choose an integer at random.
1. Choose a large (not necessarily specified) integer: X.
2. Choose an integer within 1 to X with probability 1/X (using come criterion).
3. If the density of integers satisfy that criterion has a limit as X goes to infinity, the will choose an integer with the proper density.

Example: Choose even integer within 1-x. Probability is either 1/2 or 2X/(2*X+1) which has a limit 1/2 so we can meaningfully say that half of all integers are even.