On the nth composite number

Abstract

An asymptotic formula for the nth composite number C _n , with an error term O(n/log ^m n) for any fixed m, is given. Exact calculations for C _n with various n ≤ 10¹³ are also given, showing that approximations to C _n by the asymptotic formula have errors less than 35000 for such n.

Keywords:

• Prime number theorem
• logarithmic integral
• fixed point iterations

C.R. CATEGORIES::

• G.1.2