That random number thing is interesting, cause I don't understand how

can be in this kind of discrete probability, if I may say so. I guess that two randomly chosen positive numbers a and b both in the interval

has this chance of not sharing any prime factor:

because the chance is

for a to be divisible by p and hence have prime factor p, and the same is for b. For both a and b to have prime factor p the chance is

. For a and b to not share prime factor p the chance is

. And for a and b to not share any of the primes as a prime factor the chance is

. Though I have no idea how to connect that formula with

.