M000218

$$\pi=228560924\arctan\left(\frac{1}{168623905}\right)+599708304\arctan\left(\frac{1}{284862638}\right)+297454688\arctan\left(\frac{1}{325248932}\right)-494596888\arctan\left(\frac{1}{599832943}\right)-408524164\arctan\left(\frac{1}{1012047353}\right)-58377516\arctan\left(\frac{1}{1125440538}\right)-135715016\arctan\left(\frac{1}{1962455907}\right)+253034304\arctan\left(\frac{1}{2315430018}\right)+137352596\arctan\left(\frac{1}{6746573033}\right)-448946964\arctan\left(\frac{1}{41253530807}\right)+118697436\arctan\left(\frac{1}{54863117693}\right)-80313772\arctan\left(\frac{1}{57821838732}\right)-475823876\arctan\left(\frac{1}{65553787597}\right)+196034936\arctan\left(\frac{1}{66492889557}\right)+72368168\arctan\left(\frac{1}{186498738693}\right)-105470284\arctan\left(\frac{1}{13688849577057}\right)-333082708\arctan\left(\frac{1}{30038155625330}\right)-73969680\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula228560924[168623905] + 599708304[284862638] + 297454688[325248932] - 494596888[599832943] - 408524164[1012047353] - 58377516[1125440538] - 135715016[1962455907] + 253034304[2315430018] + 137352596[6746573033] - 448946964[41253530807] + 118697436[54863117693] - 80313772[57821838732] - 475823876[65553787597] + 196034936[66492889557] + 72368168[186498738693] - 105470284[13688849577057] - 333082708[30038155625330] - 73969680[169838669284032]
Lehmer's measure1.78329
References
MRW (12Dec00) (full reference coming soon)