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Math Help - Prime numbers.

  1. #1
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    Prime numbers.

    Let n be an integer n > or equal to 2. Suppose that for every prime p < or equal to sqrt(n), p does not divide n. Prove that n is prime.

    Is 221 prime? Is 223 prime?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Say a>1 is natural co-prime, hence a=b*c, when 1<b,c<a. Suppose that b<=c ==> b^2<=bc=a or b<=sqrt(a). b>1 therefor b have at least one prime factor, say p; hence p<=b<=sqrt(a), moreover p|b. and b|a, hence p|a...

    So we can conclude that for co-prime a, must to be prime factor p, when p<=sqrt(a)
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