Computational methods in number theory

This paper presents a number of methods for testing the primality of any given number N. A brief history of number theory is introduced in Chapter I. The main task of this paper is to test the primality of any given number. However, if the test shows a negative result, or that the given number is not a prime but a composite, then the task is extended to the next step - factoring the given number. Several methods for factorization of a given number N are discussed in Chapter III. In addition, a representive example for both tasks as carried out by a computer program written in the Fortran IV language is presented.