Is the value of $c$ in $\prod_{i=1}^{n}\frac{p_i}{p_i-1}<e^c \cdot (\log p_n) \cdot(1+\frac{1}{\log_2p_n})$ known?

Question

I Recently read this paper by Rosser and Schoenfeld (http://projecteuclid.org/download/pdf_1/euclid.ijm/1255631807)

In Theorem 8, corollary 1, they state: $$\prod_{i=1}^{n}\frac{p_i}{p_i-1}<e^c \cdot (\log(p_n)) \cdot (1+\frac{1}{\log_2(p_n)})$$ I was wondering whether the value of the constant $c$ is known. I know that by Mertens' 3d theorem: $$\lim_{n\to\infty}{\frac{1}{\log(p_n)} \cdot \prod_{i=1}^{n}\frac{p_i}{p_i-1}}=e^{\gamma}$$ but I don't know if this means that $c=\gamma$.

Answer 1

Yes, although it is a capital letter $C.$ Back on page 65, formula (2.9) is followed by

where $C$ is Euler's constant.

The same is used in the integral table book of Gradshteyn and Ryzhik, especially in section 8.36, pages 952-956 in the fifth edition