Chebyshev-Sylvester Constant

In 1891, Chebyshev and Sylvester showed that for sufficiently large x, there exists at least one prime number p satisfying


where alpha=0.092.... Since the prime number theorem shows the above inequality is true for all alpha>0 for sufficiently large x, this constant is only of historical interest.

Explore with Wolfram|Alpha


Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 22, 1983.

Referenced on Wolfram|Alpha

Chebyshev-Sylvester Constant

Cite this as:

Weisstein, Eric W. "Chebyshev-Sylvester Constant." From MathWorld--A Wolfram Web Resource.

Subject classifications