1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook