M000000108

$$\pi=6348\arctan\left(\frac{1}{2852}\right)+1180\arctan\left(\frac{1}{4193}\right)+2372\arctan\left(\frac{1}{4246}\right)+1436\arctan\left(\frac{1}{39307}\right)+1924\arctan\left(\frac{1}{55603}\right)+2500\arctan\left(\frac{1}{211050}\right)-2832\arctan\left(\frac{1}{390112}\right)$$

Compact formula	`6348[2852] + 1180[4193] + 2372[4246] + 1436[39307] + 1924[55603] + 2500[211050] - 2832[390112]`
Lehmer's measure	1.63617
Notes	This formula was used in 2024 by Matt Parker and a large group of volunteers to compute 139 digits of π.
References	Arndt, Jörg. Remarks on arithmetical algorithms and the computation of π, 1993. [www.jjj.de/joerg.html] Arndt, Jörg and Harnel, Christoph. Pi - Unleashed, Springer, 1998. [DOI: 10.1007/978-3-642-56735-3] Download references as BibTeΧ