Definition:Chebyshev-Sylvester Constant/Historical Note
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Historical Note on Chebyshev-Sylvester Constant
In $1896$, Jacques Salomon Hadamard and Charles de la Vallée Poussin independently proved the Prime Number Theorem.
This demonstrated that the inequality defining this constant is true for all $\alpha > 0$ for sufficiently large $x$,.
Hence the Chebyshev-Sylvester constant is now only of historical interest.