Talk:Meissel–Mertens constant

B3

Why not A083343?

A077761 Decimal expansion of Mertens' constant, which is the limit of Sum{1/p(i), i=1..k } - log(log(p(k))) as k goes to infinity, where p(i) is the i-th prime number.

$M:=\lim _{n\to \infty }\left\{\left(\sum _{p\leq n}{\frac {1}{p}}\right)-\log \log n\right\}=-\lim _{n\to \infty }\left\{\log \log n-\sum _{p\leq n}{\frac {1}{p}}\right\}.\,$

A083343 Decimal expansion of constant B3 (or B_3) related to the Mertens constant. B_3 = lim_{x to infty} ( log x - sum_{p <= x} log p / p ).

$B_{3}=\lim _{n\to \infty }\left\{\log n-\sum _{p\leq n}{\frac {\log p}{p}}\right\}.\,$

I'm trying to figure out how exactly does $B_{3}$ relates to $M$. — Daniel Forgues 05:52, 30 October 2012 (UTC)