\begin{definition}[Definition:Chebyshev-Sylvester Constant]
The '''Chebyshev-Sylvester constant''' is a mathematical constant $\alpha$ which was shown by {{AuthorRef|Pafnuty Lvovich Chebyshev}} and {{AuthorRef|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 $1896$, {{AuthorRef|Jacques Salomon Hadamard}} and {{AuthorRef|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.
{{NamedforDef|Pafnuty Lvovich Chebyshev|name2 = James Joseph Sylvester|cat = Chebyshev|cat2 = Sylvester}}
\end{definition}