In the Wikipedia article on primorial, in the Characteristics Section, it is stated:
$$\lim\limits_{n \rightarrow \infty} \sqrt[n]{n\#} = e$$
This sounds reasonable to me. There is a footnote that references an article in French. I read through the article but could not find the argument establishing the above result. I am not fluent in French.
Is this claim correct? If so, does it follow from the Prime Number Theorem? Does it follow from the article referenced?
I would be very interested in understanding the outline of the proof.