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Quite possibly the answer obtained by Alexander J Lee and Shigeru Kondo in October 2011. See link.

However, it is highly unlikely that you will be able to use it in any computer you can lay your hands on. Furthermore, it is claimed that the error in pi to 40 digits is smaller than the width of a hydrogen atom at the far end of the known universe. For most purposes that degree of accuracy is overkill!

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Q: Which is a closer approximation for pi?
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