2020/06/30 by Dragos Crisan, Radek Erban, Crisan, Dragos +1 · 2 citations
Mathematics · #11K65 #11N37 (primary) #11Y60 (secondary) #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2006.16491
openalex publication_date 2020/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A semiprime is a natural number which can be written as the product of two primes. The asymptotic behaviour of the function π2(x), the number of semiprimes less than or equal to x, is studied. Using a combinatorial argument, asymptotic series of π2(x) is determined, with all the terms explicitly given. An algorithm for the calculation of the constants involved in the asymptotic series is presented and the constants are computed to 20 significant digits. The errors of the partial sums of the asymptotic series are investigated. A generalization of this approach to products of k primes, for k≥ 3, is also proposed.