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PRIME NUMBERS

Prime numbers are positive integers which have only two divisors:  one and itself.  For example, 23 is a prime number because its only divisors are 1 and 23.  Based on this definition, one is not a prime number because it has only one divisor.  Some of the small prime numbers include:

   2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, .....

There are an infinite number of prime numbers.  Neither is there a largest prime number.

Any natural number which is a multiple of a smaller integer other than one is not a prime number.  These numbers are called composite numbers.  Because all even numbers greater than two are multiples of two, all even numbers except two are not prime numbers.  In other words, two is the only even prime number.

Prime numbers have captured the hearts of many mathematicians for centuries.  Euclid proved that there is no largest prime number.  During 18th century, mathematician Christian Goldbach (1690-1764) wrote to Leonhard Euler that he believed it could be shown that every even integer greater than 2 is the sum of 2 primes.  For example, 30 = 23+7 and  36 = 13+23.  Until now, this conjecture has neither been proved or disproved.

In the present age of information technology where we find vital information being transmitted via the internet, prime numbers found its usefulness in information security, message encoding, and crytography.

 

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