M000206

$$\pi=166406742\arctan\left(\frac{1}{152087733}\right)+31013246\arctan\left(\frac{2}{322564791}\right)+53564820\arctan\left(\frac{1}{168623905}\right)+171972550\arctan\left(\frac{1}{201229582}\right)+100382192\arctan\left(\frac{1}{284862638}\right)+108821360\arctan\left(\frac{2}{604534317}\right)-19196406\arctan\left(\frac{1}{546365045}\right)-29427040\arctan\left(\frac{1}{2189376182}\right)+71579408\arctan\left(\frac{1}{3261365450}\right)+96486624\arctan\left(\frac{2}{11352069609}\right)-122211084\arctan\left(\frac{1}{7427844818}\right)+42576636\arctan\left(\frac{1}{27354282288}\right)-205420822\arctan\left(\frac{2}{108928448489}\right)-31064620\arctan\left(\frac{1}{71617196968}\right)-129909656\arctan\left(\frac{1}{164432798314}\right)+3695322\arctan\left(\frac{1}{4963640229982}\right)-118648528\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula166406742[152087733] + 31013246[322564791/2] + 53564820[168623905] + 171972550[201229582] + 100382192[284862638] + 108821360[604534317/2] - 19196406[546365045] - 29427040[2189376182] + 71579408[3261365450] + 96486624[11352069609/2] - 122211084[7427844818] + 42576636[27354282288] - 205420822[108928448489/2] - 31064620[71617196968] - 129909656[164432798314] + 3695322[4963640229982] - 118648528[169838669284032]
Lehmer's measure1.77196
References
MRW (11Aug06) (full reference coming soon)