A natural number that may be expressed as the sum of two prime numbers is called a semiprime. Examined is the asymptotic behavior of the function π2(x), which returns the number of semiprimes that are equal to or less than x. The asymptotic series of π2(x) is found using a combinatorial argument, where each term is explicitly presented. The constants involved in the asymptotic series are calculated to 20 significant digits and a technique for doing so is described. We look at the partial sum mistakes of the asymptotic series. For k ≥ 3, an extension of this method to products of k primes is also suggested.

A natural number that may be expressed as the sum of two prime numbers is called a semiprime.