出版社：Vilnius University, University of Latvia, Latvia University of Agriculture, Institute of Mathematics and Informatics of University of Latvia
摘要：We consider representing of natural numbers by arithmetical expressions using ones, addition, multiplication and parentheses. The (integer) complexity of n – denoted by n – is defined as the number of ones in the shortest expressions representing n. We arrive here very soon at the problems that are easy to formulate, but (it seems) extremely hard to solve. In this paper we represent our attempts to explore the field by means of experimental mathematics. Having computed the values of n up to 1012 we present our observations. One of them (if true) implies that there is an infinite number of Sophie Germain primes, and even that there is an infinite number of Cunningham chains of length 4 (at least). We prove also some analytical results about integer complexity.
