by Asahatter

Created on: April 25, 2007   Last Updated: May 13, 2008

Natural numbers are the whole numbers that we use when counting items. So, 1, 2, 42, 69, 3,256 and 9 billion are all examples of natural numbers.

Some mathematicians consider zero to be a natural number, but the distinction is hardly important. To get yourself a list of natural numbers, just start at either 0 or 1 and repeatedly add 1 - all the way up to infinity.

A number of important properties exist for natural numbers, many of which are to do with their "factors". If one natural number can be exactly divided by a second then the second number is said to be a factor of the first. Thus 3 is a factor of 12, but 9 is not, because 12/3 = 4 whereas 12/7 = 1 and a bit.

If a natural number can be exactly divided by 2 (ie. 2 is a factor of the number), then that number is said the be "even". If not, it is "odd".

If a natural number has no factors other than itself and 1, then this number is said to be "prime". For example, 13 is a prime number as it cannot be exactly divided by any other natural numbers apart from 1 and 13. The sequence of prime numbers starts at 2 (1 is generally not considered to be a prime number) and continues 3,5,7,11,13,17,19 and so on, again all the way up to infinity.

Natural numbers, factors and prime numbers are central to "number theory", a branch of mathematics which is the foundation of modern cryptography and at the heart of every secure banking and Internet shopping site. Natural numbers and number theory are considered so important that there are large cash prizes available to anyone who can crack some of the theory's secrets - see for example http://mathworld.wolfram.com/RSANumber.html.

British publishing company Faber and Faber have offered $1 million to anyone who can solve another problem involving natural numbers, the so-called Goldbach Conjecture.

So - natural numbers are easy to understand as a concept, but if you ever get yourself a full understanding, you could be a millionaire

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