7
$\begingroup$

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

image

  • 1
    This is a very nice clock. I recall a question about this on MathOverflow. http://mathoverflow.net/questions/22266/what-is-the-mathematical-meaning-of-this-symbol2011-08-14
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    I don't know, I got the digital one.2011-08-14
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    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?2011-08-14
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    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.2018-02-14

1 Answers 1

9

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 $n$.

  • 0
    You may be right, but this one seems to be the odd one out among the very basic writings of the other numbers...2011-08-14
  • 3
    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.2011-08-14