M000175

$$\pi=46329268\arctan\left(\frac{1}{27872057}\right)+18157246\arctan\left(\frac{1}{44203064}\right)+50179384\arctan\left(\frac{1}{144235918}\right)+20480112\arctan\left(\frac{2}{322564791}\right)+63818404\arctan\left(\frac{1}{201229582}\right)+59500208\arctan\left(\frac{1}{284862638}\right)+41116176\arctan\left(\frac{1}{778401733}\right)+3895290\arctan\left(\frac{1}{1514342682}\right)+15688916\arctan\left(\frac{2}{4204410541}\right)+1267878\arctan\left(\frac{1}{3866973557}\right)+16059344\arctan\left(\frac{1}{7427844818}\right)+10520998\arctan\left(\frac{1}{7959681215}\right)+42052804\arctan\left(\frac{2}{75525552427}\right)-6056702\arctan\left(\frac{1}{118034929852}\right)-8360772\arctan\left(\frac{2}{1087840667761}\right)-9024030\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula46329268[27872057] + 18157246[44203064] + 50179384[144235918] + 20480112[322564791/2] + 63818404[201229582] + 59500208[284862638] + 41116176[778401733] + 3895290[1514342682] + 15688916[4204410541/2] + 1267878[3866973557] + 16059344[7427844818] + 10520998[7959681215] + 42052804[75525552427/2] - 6056702[118034929852] - 8360772[1087840667761/2] - 9024030[169838669284032]
Lehmer's measure1.72384
References
MRW (12Aug06) (full reference coming soon)