For example, up to 10⁹, every positive integer which is a multiple of a primorial and is less than the following primorial satisfies the given inequality. There has also been little discussion on which primorials qualify in the different situations when RH fails.
Source: wiktionary
2020, Rong Pan, Qinheping Hu, Rishabh Singh, Loris D'Antoni, Solving Problem Sketches with Large Integer Values, Peter Müller (editor), Programming Languages and Systems: 29th European Symposium, Proceedings, Springer, LNCS 12075, page 587,
The following number theory result relates the primorial to the Chebyshev function.
θ(n)= log (n#)= log 2⁽¹⁺ᵒ⁽ⁿ⁾⁾ⁿ=(1+o(n))n
Source: wiktionary