Number of Primes and Probability Considerations

Abstract

IN the first sentence of Lord Cherwell's communication¹ occurs the phrase “a number chosen at random”; and the applicability of the theory of probability surely depends on the possibility of random choice. Now an integer can be chosen at random from any finite set, but there is no way of choosing one at random from the infinite set of all positive integers. Thus if Lord Cherwell chooses an integer “at random” it will certainly be less than ${10}^{{10}^{10}}$ as otherwise he will not live long enough to write it down. But the probability that an integer chosen at random is less than ${10}^{{10}^{10}}$ is zero.