M000187

$$\pi=29427040\arctan\left(\frac{1}{27872057}\right)+29002772\arctan\left(\frac{1}{39451318}\right)+35072334\arctan\left(\frac{1}{42443947}\right)+38065980\arctan\left(\frac{1}{144235918}\right)+2322866\arctan\left(\frac{2}{322564791}\right)+46903316\arctan\left(\frac{1}{201229582}\right)+1468944\arctan\left(\frac{1}{284862638}\right)-14261956\arctan\left(\frac{1}{1514342682}\right)+27789460\arctan\left(\frac{2}{4204410541}\right)-8154604\arctan\left(\frac{1}{7427844818}\right)+34734946\arctan\left(\frac{1}{7959681215}\right)+25150576\arctan\left(\frac{2}{75525552427}\right)-12100544\arctan\left(\frac{2}{127939586297}\right)+16902228\arctan\left(\frac{1}{77000574832}\right)+3752632\arctan\left(\frac{2}{1087840667761}\right)-9024030\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula29427040[27872057] + 29002772[39451318] + 35072334[42443947] + 38065980[144235918] + 2322866[322564791/2] + 46903316[201229582] + 1468944[284862638] - 14261956[1514342682] + 27789460[4204410541/2] - 8154604[7427844818] + 34734946[7959681215] + 25150576[75525552427/2] - 12100544[127939586297/2] + 16902228[77000574832] + 3752632[1087840667761/2] - 9024030[169838669284032]
Lehmer's measure1.73310
References
MRW (12Aug06) (full reference coming soon)