Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Someone asked me, and I told them I would try to find out... what is the meaning of this symbol:

B'L     or     BL'

(I'm not sure if the tick comes before or after the L. It was found on a "nerd clock". The value of this symbol, by the way, is 1.

share|improve this question
add comment

closed as off topic by Felipe Voloch, Alain Valette, Gerald Edgar, j.c., Andy Putman Feb 19 '13 at 22:19

Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

2 Answers

up vote 11 down vote accepted

Apparently, it is supposed to be Legendre's constant, also known as $1$.

share|improve this answer
4  
This is the clock: photodump.com/wp-content/uploads/2009/09/geek-clock.jpg –  Dan Piponi Apr 22 '10 at 22:24
2  
That makes me flash on a dialogue from my youth: Professor (slow Texas drawl): That's almost as useful as knowing Bieberbach's constant. Student (the stooge): What's Bieberbach's constant? Professor: One-fourth. –  Carl Weisman Apr 22 '10 at 23:26
1  
Isn't there a similar story (with Edmund Landau) concerning the "Caratheodory constant"? –  Yemon Choi Apr 22 '10 at 23:33
2  
Can someone please post a link where we can buy the clock? –  Joel David Hamkins Apr 23 '10 at 0:43
    
A clock set in Computer Modern is somewhat cute :) –  Mariano Suárez-Alvarez Apr 23 '10 at 1:02
show 1 more comment

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, $B_L'$.

share|improve this answer
add comment

Not the answer you're looking for? Browse other questions tagged or ask your own question.