Sharper Bounds for the Chebyshev function $θ(x)$

In this article, we provide explicit bounds for the prime counting function $θ(x)$ in all ranges of $x$. The bounds for the error term for $θ(x)- x$ are of the shape $εx$ and $\frac{c_k x}{(\log x)^k}$, for $k=1,\ldots,5$. Tables of values for $ε$ and $c_k$ are provided.

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