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Math Help - Odds and Primes

  1. #1
    Newbie euler42's Avatar
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    Odds and Primes

    I just wanted to know if there was a proof that every prime number greater than 2 was odd. Thanks.
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  2. #2
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    Quote Originally Posted by euler42 View Post
    I just wanted to know if there was a proof that every prime number greater than 2 was odd. Thanks.
    Surely! This is quite a simple one, as well - simply note that any even (not odd) number can be written as 2n for some n\in \mathbb{N}. But then 2 divides that number, thus it is not prime.
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    Quote Originally Posted by euler42 View Post
    I just wanted to know if there was a proof that every prime number greater than 2 was odd. Thanks.
    Prove by contradiction.

    Suppose there was a prime number greater than two that wasn't odd. Then it must be even, and therefore it must have two as a factor and hence is not prime. This contradicts our assumption and so we conclude that all primes greater than 2 are odd.
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