# 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

## 1 Answer

It seems this is Legendre's constant

$$B^\prime_L = \lim_{n \to \infty}\left ( \log n - \frac{n}{\pi(n)} \right)$$

where $\pi(n)$ stands the number of primes not exceeding $n$.

-
You may be right, but this one seems to be the odd one out among the very basic writings of the other numbers... –  t.b. Aug 14 '11 at 20:55
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