# Prime Numbers and Applications

May 5th, 2015
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A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6.

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Prime Numbers and Applications-------------------------------------------------Prime numberAprime number(or aprime) is anatural numbergreater than 1 that has no positivedivisorsother than 1 and itself. A natural number greater than 1 that is not a prime number is called acomposite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6. Thefundamental theorem of arithmeticestablishes the central role of primes innumber theory: any integer greater than 1 can be expressed as a product of primes that is uniqueup toordering. This theoremrequires excluding1 as a prime. -------------------------------------------------Number theoryNumber theoryis a branch ofpure mathematicsdevoted primarily to the study of theintegers. Number theorists studyprime numbers(which, wh

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