[seqfan] "Euler-Mertens" constant

[Tomasz Ordowski]

Dear readers,

I have something interesting:

C = lim_{n->oo} (log p(n) - Sum_{k=1..n} g(k)/p(k)),
where p(n) = prime(n) and g(k) = p(k+1) - p(k).

Amiram Eldar calculated that C = 0.0477967...

Since g(k)/p(k) = p(k+1)/p(k) - 1 and log p(n) - p(n)/n ~ 1, so
C = lim_{n->oo} (n + p(n)/n + 1 - Sum_{k=1..n} p(k+1)/p(k)).

Is this a new math constant?

Best regards,

Thomas Ordowski