A covering system whose smallest modulus is 40 (Q1011684)

A set of congruence classes with distinct moduli, each greater than 1, such that each integer satisfies at least one of the congruences, is said to be a covering system. An old still open Erdős' conjecture from 1950 states that the least modulus \(N\) of a covering system can be arbitrarily large. Improving previous best known result with modulus \(N=25\) constructed recently by \textit{D. J. Gibson} [Math. Comput. 78, No. 266, 1127--1146 (2009; Zbl 1208.11019)] the author describes his construction of a covering system with \(N=40\). Difficulties connected with the presented construction lead the author to believe that Erdős' problem could have a negative solution