Difference between revisions of "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. | 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. | ||
| − | 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 | + | 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). |
Revision as of 16:38, March 18, 2007
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.
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.
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).