# Homework Help: Product of primes less than or equal to n

1. Sep 16, 2011

### R.P.F.

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. Sep 16, 2011

### ArcanaNoir

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?

3. Sep 16, 2011

### Petek

I corrected your tex. There was an extra space between the final "/" and "tex".

4. Sep 16, 2011

### ArcanaNoir

And I fail to see the obvious.... :( I guess it's bed time. Really cool problem though! (not that I can solve it)

5. Sep 17, 2011

### ArcanaNoir

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.