OFFSET
0,1
COMMENTS
The negative first derivative of the prime zeta function at 2.
REFERENCES
Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
LINKS
Henri Cohen, High-precision computation of Hardy-Littlewood constants, preprint 1998.
Henri Cohen, High-precision computation of Hardy-Littlewood constants. [pdf copy, with permission]
Tengiz O. Gogoberidze, Baker's dozen digits of two sums involving reciprocal products of an integer and its greatest prime factor, arXiv:2407.12047 [math.GM], 2024. See p. 2.
R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], Table 2.
J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 64-94, Table IV
EXAMPLE
0.493091109368764462197826205056491258055588126346468290713327120321336...
MATHEMATICA
RealDigits[PrimeZetaP'[2], 10, 104] // First (* Jean-François Alcover, Sep 11 2015 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Mar 09 2008
EXTENSIONS
Removed 6 digits where preprints disagree. Added zero to an A-number in formula. Corrected Cohen preprint year. Added 2nd link. - R. J. Mathar, Nov 27 2008
More digits from Jean-François Alcover, Sep 11 2015
STATUS
approved