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**Prime Numbers**

One of the fascinations of mathematics is the discovery of patterns. One of
the simplest patterns to discover is that of prime numbers. Prime numbers begin
with **2**. Starting at 2 is, in itself, a problem since it
usually occurs to people that the first prime number is 1. Why is 2 the first
prime number?

- Suggested reason:

Look at the numbers 1,2,3,... These are called the Counting Numbers (we use them to do our counting of sheep and things like that).

A *definition* of prime numbers:

- A prime number is the
**first**number of a list of multiples.

(For example, 5 is the first number of the list 5, 10, 15, 20, ...)

- The prime numbers are all of these 'first' numbers on lists which still remain when previous lists have been removed from the Counting Numbers.

**Argument**: Suppose that **1** was allowed to be
the first number of a list of multiples of 1. The list would be as follows:
1,2,3,4,...

In this case there would be only one prime number, the number 1. There could be no other lists since the multiples of 1 contain all other numbers and this list is removed from the Counting Numbers.

So, if we want to have more than one prime number it is not a good idea to have 1 as a prime number using this meaning of 'prime'.

It has been agreed by mathematicians (don't ask me where!) that 1 is not a prime number.

Some lists of multiples:

**2**, 4, 6, 8, 10, ...

**3**, 6, 9, 12, 15, ...

**5**, 10, 15, 20, ...

**7**, 14, 21, 28, ...

The prime number list begins as follows: **2**, **3**,
**5**, **7**, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, ...

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