TOPICS
Search

Murata's Constant


Murata's constant is defined as

C_(Murata)=product_(p)[1+1/((p-1)^2)]
(1)
=2.82641999...
(2)

(OEIS A065485), where the product is over the primes p. It can also be written as the sum

C_(Murata)=exp[-sum_(n=2)^(infty)((1+i)^n+(1-i)^n-2)/nP(n)]
(3)
=exp[sum_(n=2)^(infty)(2-2^(n/2+1)cos(1/4npi))/nP(n)],
(4)

where P(n) is the prime zeta function.


See also

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

Explore with Wolfram|Alpha

References

Finch, S. R. "Artin's Constant." §2.4 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 104-106, 2003.Murata, L. "On the Magnitude of the Least Prime Primitive Root." J. Number Th. 37, 47-66, 1991.Niklasch, G. "Some Number-Theoretical Constants." http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml.Sloane, N. J. A. Sequence A065485 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Murata's Constant

Cite this as:

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

Subject classifications