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Prime numbers
Topic Started: Jan 19 2013, 02:11 AM (283 Views)
CJ
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A very minor case of serious brain damage

So, I remove the Maths & Philosophy forum because it's hardly used....and then I go and start a maths topic :P .

A prime number is a natural number ('natural numbers' are the ordinary numbers used for counting) greater than 1, whose only factors are 1 and itself. The first 20 prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, ....

In some ways, prime numbers are the basic 'building blocks' of the rest of the natural numbers, because all of the natural numbers can be formed by multiplying prime numbers. Here are a few examples:

1 = No primes multiplied together at all ( :P )
2 = 2 (It's already prime!)
30 = 2 x 3 x 5
126 = 2 x 7 x 9
2520 = 2 x 2 x 2 x 3 x 3 x 5 x 7 (usually written as 23 x 32 x 5 x 7)

(Also, for each natural number, there's only one way to break it down into primes like this. This is called the Fundamental Theorem of Arithmetic)

There are infinitely many of them. Here's a proof of this fact, as given by Euclid around 300BC:
Proof that there are infinitely many prime numbers


So, do you have any questions?
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