A Study of the Differences between Consecutive Prime Numbers

Abstract

This paper will present heuristic arguments concerning the distribution of prime numbers and the spacings between consecutive primes. So that the reader will be familiar with some of the background material for this paper, a summary of "Mathematical Sieves" by David Hawkins is given in Appendix I. The important results of this paper are the "random number sieve" and the "proof" of the prime number theorem.