Like for $\pi$, we have an algorithm/infinite series that can give us the first 50 decimal places in about 3 terms. So if I wasn't to calculate like $ln(25551879...)$ (a really huge integer, most likely a prime), upto 100 decimal places, what will be the algorithm I should use or is used worldwide and how efficient is it? I know that the Taylor series is rather slow in its work, so any other algorithm in which this is computed?

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