The prime numbers are those positive integers that are divisible by only 1 and themselves (for example,

Question:

The prime numbers are those positive integers that are divisible by only 1 and themselves (for example, 2, 3, 5, 7, 11, 13, . . ). A celebrated theorem states that the sequence of prime numbers {p_k} satisfies lim pr/(k In k) = 1. Show that k=2 k In k diverges, which implies that the series diverges.