M000003588
$$\pi=8\arctan\left(\frac{1}{3}\right)+4\arctan\left(\frac{1}{5}\right)-4\arctan\left(\frac{1}{18}\right)+4\arctan\left(\frac{1}{21}\right)-4\arctan\left(\frac{1}{27}\right)-4\arctan\left(\frac{1}{86}\right)+4\arctan\left(\frac{1}{939}\right)-4\arctan\left(\frac{1}{1764383}\right)$$