M000141

$$\pi=3948772\arctan\left(\frac{1}{2789116}\right)+8805204\arctan\left(\frac{1}{3549443}\right)-4349676\arctan\left(\frac{1}{5033696}\right)+1385052\arctan\left(\frac{1}{6826318}\right)-2038484\arctan\left(\frac{1}{36313568}\right)-3531984\arctan\left(\frac{1}{152087733}\right)-3682000\arctan\left(\frac{1}{213255960}\right)+1634748\arctan\left(\frac{2}{437556239}\right)-1108192\arctan\left(\frac{1}{284862638}\right)-1599988\arctan\left(\frac{1}{1125440538}\right)+1564116\arctan\left(\frac{1}{2123253543}\right)+705728\arctan\left(\frac{1}{66492889557}\right)+2109116\arctan\left(\frac{1}{138873731225}\right)+3044660\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula3948772[2789116] + 8805204[3549443] - 4349676[5033696] + 1385052[6826318] - 2038484[36313568] - 3531984[152087733] - 3682000[213255960] + 1634748[437556239/2] - 1108192[284862638] - 1599988[1125440538] + 1564116[2123253543] + 705728[66492889557] + 2109116[138873731225] + 3044660[169838669284032]
Lehmer's measure1.68620
References
MRW (15Dec00)(ΒΆΒΆ1.87196) (full reference coming soon)