Title:  Strings of composite numbers

Abstract:  Given d and e in {1,...,9} we consider the set of positive integers k that have the following property: k with d appended on the right n times is composite for all positive integers n. We also consider the set of positive integers k that have the following property: k with d and e appended alternately on the left and right (i.e. k,kd,ekd,ekdd...) is always composite regardless of the number of appended digits. We will discuss methods for finding elements in these sets and also consider finding their minimum elements.