Mills' Constant Unpublished Extras The brown paper used in the making of Numberphile's video on Mills' Constant was recently sold on eBay. Here is an image of it, from the eBay listing, !Image of Brown Paper used in the making of Mill's Constant The bottom two lines appear on the brown paper, but were not written in the video, > $\lfloor {2 \omega n} \rfloor \hspace{10 mm} \omega = 1.9287800...$ > > $2, \hspace{1 mm} 11, \hspace{1 mm} 1361, \hspace{1 mm} \text{[sic]} \hspace{1 mm} 252100887, \dots $ It is clear that the bottom line are the first Mill's Primes. However, I cannot figure out what the second to bottom line is? * **What is $\omega \approx 1.929$?** * **What is $\lfloor {2 \omega n} \rfloor$?**

This value is cited in Mathematical Constants by Stephen Finch on page 131 but called $c$. It is another prime representing function giving primes for the floors of $2^c,2^{2^c},2^{2^{2^c}},\dots$. It appears $2\omega n$ is the $n^{\text{th}}$ number of this series and the typography is not clear to me.