**23**

The sequence of prime numbers

To conclude this book we now spend some time exploring the theory of prime numbers, one of the most fascinating and oldest areas of number theory and one in which some apparently very simple questions still remain unanswered. It is a branch of mathematics which until recently seemed remote from any applications but this has now changed. In this chapter we consider the sequence of prime numbers and factorization into primes.

**Definition 23.1.1** *A positive integer n is said to be* *when n* 1 *and the only positive divisors of n are* 1 *and n. If an integer n* 1 *is not prime then it ...*

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