Another algebra problem about prime and induction

[kntsy]

Homework Statement

prove by induction that the n^{\text th} prime is less than 2^{2^{\text n}}

Homework Equations

hint:assume it is correct for all n \leq k, and then compare p_{k+1} with p_{1}p_{2}...p_{k}+1

The Attempt at a Solution

is p_{k+1} smaller/greater than p_{1}p_{2}...p_{k}+1 so that i can extend the use of inequality?
I attempt to use euclidean algorithm but do not know where to use.
Thank you.

 

[Office_Shredder]

If p_{k+1} is larger than the suggested number, you should be able to prove that it has no prime divisors which is a contradiction