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


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    $\begingroup$ This is a very nice clock. I recall a question about this on MathOverflow. mathoverflow.net/questions/22266/… $\endgroup$ – Asaf Karagila Aug 14 '11 at 20:38
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    $\begingroup$ I don't know, I got the digital one. $\endgroup$ – gary Aug 14 '11 at 20:40
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    $\begingroup$ 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? $\endgroup$ – André Nicolas Aug 14 '11 at 20:44
  • $\begingroup$ 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. $\endgroup$ – Lee Feb 14 '18 at 18:51

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 $n$.

  • $\begingroup$ You may be right, but this one seems to be the odd one out among the very basic writings of the other numbers... $\endgroup$ – t.b. Aug 14 '11 at 20:55
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    $\begingroup$ 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. $\endgroup$ – Jonas Meyer Aug 14 '11 at 21:15

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