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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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