Editorial Board

JMI2009A-6 On asymptotic behavior of composite integers $n = pq$ (pp.45-49)

Author(s): Yasufumi Hashimoto

J. Math-for-Ind. 1A (2009) 45-49.

In this paper, we study the asymptotic behavior of the number of composite integers written by products of two primes. Such integers are sometimes called by the RSA integers, because these are used in the RSA cryptosystems. The number of all such integers has been already studied by Landau, Sathe, Selberg etc. Furthermore, the number of integers with $n = pq$ and $p < q < cp$ for a fixed $c > 1$ was recently studied by Decker and Moree. The aim of this paper is to extend Decker-Moree's result, and the main theorem describes the asymptotic formula of the number of integers with $p < q < f(p)$ for a fixed increasing function $f$.

Keyword(s).  composite integer $n = pq$, prime number theorem, RSA cryptosystem