On the prime example of programming

Abstract

The problem of finding prime numbers has been much favoured by expositors of modern programming methodology. In this paper the problem is tackled once more, but from a broader view of the programming process than has previously been taken. The initial steps toward a solution parallel those in the well-known presentations of Dijkstra and Wirth. However a general program transformation is shown to capture the clever "inventive step" in Dijkstra's solution, and another is employed to lead naturally to an alternative program. Complexity analyses of the two programs show that the latter is significantly more efficient.