# Definition:Chebyshev-Sylvester Constant

## Definition

The Chebyshev-Sylvester constant is a mathematical constant $\alpha$ which was shown by Pafnuty Lvovich Chebyshev and James Joseph Sylvester that for sufficiently large $x$, there exists at least one prime number $p$ satisfying:

$x < p < \paren {1 + \alpha} x$

The number $\alpha$ was demonstrated to be $0 \cdotp 092 \ldots$

In $1896$, Jacques Salomon Hadamard and Charles de la Vallée Poussin independently proved the Prime Number Theorem.

This demonstrated that the above inequality is true for all $\alpha > 0$ for sufficiently large $x$,.

Hence this constant is now only of historical interest.

## Source of Name

This entry was named for Pafnuty Lvovich Chebyshev and James Joseph Sylvester.