Hi,

This was supposed to be a comment to Mariano's answer, but it seems too long for a comment.

Somebody gave me that clock for Christmas and all along I thought $B_L'=1$ was some silly Physics constant... but it seems Mariano is right, and this refers to Legendre's constant (at least, that's the case according to this other site).

I was terribly curious, though, to find out where this notation came from and decided to go right to the source, "Essai sur la Theorie des Nombres", by Legendre. Amazingly, our friends at Google have scanned the whole book, and the whole volume is freely available here. It is a large volume, however! So it was not easy to locate the exact place where Legendre talks about the prime counting function. A nice paper by Goldstein in the American Math Monthly, "A history of the prime number theorem"" was very helpful to locate the exact reference: **p. 394-398 in the second edition** of the "Essai sur..." by Legendre.

In p. 395, Legendre explains that $\pi(x)$, the number of primes $\leq x$, seems to grow like
$$\frac{x}{A\log x + B}$$
and conjectures that $A=1$ and $B=-1.08366\ldots$ (now a famous mistake, since later on the proofs of the prime number theorem would show that $B=1$). But, in any case, Legendre himself called this constant $B$ and I suppose somebody added the subscript $L$, to $B_L$, to remind us of Legendre's name.

However, I am still puzzled by the apostrophe, $B_L'$.