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What it the fastest/most efficient algorithm for estimating Euler's Constant $\gamma$?

What it the fastest algorithm for estimating Euler's Constant $\gamma \approx0.57721$? Using the definition: $$\lim_{n\rightarrow\infty} \sum_{x=1}^{n}\frac{1}{x}-\log n=\gamma$$ I finally get 2 ...