# What is $B'_L$ and why is it equal to 1?

I understand all the other ones, but the $B'_L$ has me stumped. What does it mean and why is it equal to 1?

• This is a very nice clock. I recall a question about this on MathOverflow. mathoverflow.net/questions/22266/… – Asaf Karagila Aug 14 '11 at 20:38
• I don't know, I got the digital one. – gary Aug 14 '11 at 20:40
• If it is a mathematical clock, shouldn't it be $0$ at the extreme right ($\theta=0$)? And shouldn't the hands move "counterclockwise" with appropriate renumbering? – André Nicolas Aug 14 '11 at 20:44
• I have a watch with that symbol and, like the original poster, it was the only one I couldn't figure out. I agree that it appears to be Legendre's constant. – Lee Feb 14 '18 at 18:51

$$B^\prime_L = \lim_{n \to \infty}\left ( \log n - \frac{n}{\pi(n)} \right)$$
where $\pi(n)$ stands the number of primes not exceeding $n$.
• Álvaro Lozano-Robledo says in his MO answer that $B$ comes from Legendre, speculates that the subscript $L$ was added as a tribute to Legendre, and expresses puzzlement on the source of the apostrophe. – Jonas Meyer Aug 14 '11 at 21:15