Difference between revisions of "Prime Number"

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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.
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#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.
 

Latest revision as of 19:30, April 15, 2007

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