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'''Prime numbers''' are those [[natural number]]s that are divisible by only 1 and itself. The only even prime number is 2. There is no upper limit to the quantity of primes, but there is no known formula for deriving the nth prime. [[Leonhard Euler]] once commented: <blockquote>
'''Prime number''' is a [[natural number]] that is divisible by only 1 and itself. The only even prime number is 2. There is no upper limit to the quantity of primes, but there is no known formula for deriving the nth prime. [[Leonhard Euler]] once commented: <blockquote>
''Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate.''
''Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate.''
</blockquote>
</blockquote>
==The Prime Numbers==
==The Prime Numbers==
The smallest prime numbers are 2, 3, 5, 7, 11, 13... . An example 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 example of a [[composite number]] is 6, which is evenly divisible by both 2 and 3, in addition to 1 and itself.
It is easy to prove that there are an infinite number of primes using [[Euclid's second theorem]]. 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).
It is easy to prove that there are an infinite number of primes using [[Euclid's second theorem]]. 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).