Hence the probability that s numbers are all divisible by this prime is 1/p^s, and the probability that at least one of them is not is 1 − 1/p^s. Now, for distinct primes, these divisibility events are mutually independent because the candidate divisors are coprime (a number is divisible by coprime divisors n and m if and only if it is divisible by nm, an event which occurs with probability 1/(nm).)
Thus the asymptotic probability that s numbers are coprime is given by a product over all primes,
