The main module you'll interact with.

This module provides two functions, generate/1 and test/1, where the former essentially depends on the latter. That is, generate/1 generates a prime by means of yielding a random number using Enum.random/1 and, if the number gained is proven by test/1 to be a prime, it returns the prime, and if not it recursively invokes generate/1 until Enum.random/1 successfully returns a prime.

Prime number theorem asserts that there are approximately n/ln(n) prime numbers between 1 and n. Therefore we can assume the probability for the randomly chosen number between 1 and n to be the prime number is 1/ln(n).

ln(2^128) approximately equals to 89. This means you'll only need less than 100 attempts to find a prime number between 1 and 2^128. That's why it's just ok to make a recursion with no apparent base case. Note, however, that the probablistic nature again reside in the test/1, hence there is actually a little more than 1/ln(n) steps to generate a prime. See the doc of Prime.Fermat for details.