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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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This is a very nice clock. I recall a question about this on MathOverflow.… – 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
up vote 7 down vote accepted

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 $n$.

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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

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