[seqfan] "Euler-Mertens" constant
Tomasz Ordowski
tomaszordowski at gmail.com
Sat Feb 25 20:21:15 CET 2023
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
More information about the SeqFan
mailing list