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Homework Help: Primes and their powers

  1. Feb 14, 2010 #1
    1. The problem statement, all variables and given/known data
    I am proving something different and need this to be true.

    choose prime p > 11. then p^2 is less than the product of all primes that came before it.

    2. Relevant equations
    U(n)= {1, a_1, ... a_k} this is the ring of numbers co prime to n.

    ex: let p=13. 13^2 = 169<3*5*7*11

    3. The attempt at a solution

    I am using 11 because it's not generally true for primes less than 11 and I have dealt with those cases in my proof.

    is this generally correct? is there a simple proof I should show? or take it as general knowledge.
  2. jcsd
  3. Feb 14, 2010 #2


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    Staff Emeritus
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    Gold Member

    The "product of the first N primes" function grows so ridiculously fast as compared to the "square of the N-th prime" function, that pretty much any approximation at all should be usable to prove the inequality.
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