I found the following claim here:
Chebyshev's theorem gives the lower bound $2^{(n/2)}$.
Is this correct?
If $n\#$ is the primorial of $n$, does it follow that:
$$n\# \ge 2^{(n/2)}$$
As I understand it, from this answer, Chebyshev's thereom establishes that: $$\pi(2n) \ge \frac{n\log 2}{\log(2n)} $$
Are these two estimates related as the poster claims? I have worked on it but am not able to derive the given lower bound of the primorial from the Chebyshev estimate.
Can someone help me to understand if the poster is correct?
