Can the Product of All Primes Before p Be Greater Than p^2?

[cap.r]

Homework Statement

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.

Homework 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

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.

 

[Hurkyl]

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.