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Barban's Constant


Barban's constant is defined as

C_(Barban)=product_(p)[1+(3p^2-1)/(p(p+1)(p^2-1))]
(1)
=2.596536...
(2)

(OEIS A175640), where the product is over the primes p.


See also

Artin's Constant, Feller-Tornier Constant, Heath-Brown-Moroz Constant, Murata's Constant, Prime Products, Quadratic Class Number Constant, Sarnak's Constant, Taniguchi's Constant, Twin Primes Constant

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References

Barban, M. B. "The Large Sieve Method and Its Application to Number Theory." Uspehi Mat. Nauk 21, 51-102, 1966.Finch, S. "Class Number Theory." http://algo.inria.fr/csolve/clss.pdf. May 6, 2005.Sloane, N. J. A. Sequence A175640 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Barban's Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BarbansConstant.html

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