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Product of primes less than or equal to n

  1. Sep 16, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm working on a problem and as long as I can show that
    [tex] \prod_{p\leq n}p \leq \prod_{n<p\leq 2n}p [/ tex]
    then I'm done. But I'm having trouble with this..Can someone help? :tongue:
    2. Relevant equations



    3. The attempt at a solution

    I tried to use PNT but could not solve it..
    EDIT: and maybe someone could also tell why my tex commands did not work out..?
     
  2. jcsd
  3. Sep 16, 2011 #2
    I can't really tell what you were going for with the tex. can you try to write it out with regular text and maybe then I can straighten out the tex?
     
  4. Sep 16, 2011 #3
    I corrected your tex. There was an extra space between the final "/" and "tex".
     
  5. Sep 16, 2011 #4
    And I fail to see the obvious.... :( I guess it's bed time. Really cool problem though! (not that I can solve it)
     
  6. Sep 17, 2011 #5
    So, it's not always true. Not true for n less than 8, and not true again for n=18 (510,510 and 392,863). I'm supposing it's not true for other values of n, but I think this is sufficient counter-example to rethink the situation.
     
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