TITLE: Asymptotics of Product of consecutive primes
QUESTION [5 upvotes]: I am looking for the asymptotic growth of product of consecutive primes. Is there anything that is known about this growth?

REPLY [5 votes]: You can also prove that $$\displaystyle\lim_n\left(\prod_1^n p_i\right)^{1/p_n} = e$$
(where $p_i$ is the $i$-th prime number and $e$ is Euler's exponential number)