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| − | A '''prime number''' is a number that is evenly divisible by no other number except for itself and 1. A number which is not prime is called a [[composite number]]. The classifications ''prime'' and ''composite'' apply to positive integers greater than 1, though there are related concepts in other fields of mathematics. Note that 1 is neither prime nor composite.
| + | #REDIRECT [[Prime number]] |
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| − | The smallest prime numbers are 2, 3, 5, 7, 11, 13... . An exmple of a composite number is 6, which is evenly divisible by both 2 and 3.
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| − | It is easy to prove that there are an infinite number of primes. If there were a finite number of primes, you could multiply them all together and add 1. The resulting number would show the existence of a new prime, since it would not be divisible by any smaller prime (it would always have a remainder of 1).
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| − | To construct a table of prime numbers, you would use a method called the '''Sieve of Eratosthenes'''. Simply write down an ordered list of all counting numbers greater than 1. Beginning with 2*2 = 4, cross out every second number:
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| − | :2 3 <s>4</s> 5 <s>6</s> 7 <s>8</s> 9 <s>10</s> 11 ...
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| − | then beginning with 3*3 = 9 cross out every third number:
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| − | :2 3 <s>4</s> 5 <s>6</s> 7 <s>8 9 10</s> 11 ...
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| − | Beginning with 5*5 = 25, cross out every fifth number, then repeat for the primes 7, 11, 13, etc. The result will be a table of primes which is accurate up to ''n''-squared, where ''n'' is the largest number you sieved for.
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