M000191

$$\pi=383917720\arctan\left(\frac{1}{112519818}\right)-60253300\arctan\left(\frac{1}{194195097}\right)-45811372\arctan\left(\frac{1}{295806685}\right)+21950424\arctan\left(\frac{1}{1432278547}\right)+23670412\arctan\left(\frac{1}{1849507057}\right)+12571172\arctan\left(\frac{1}{2309197818}\right)-28792152\arctan\left(\frac{1}{2674664693}\right)+319511872\arctan\left(\frac{1}{2701984943}\right)+195503704\arctan\left(\frac{1}{4117799011}\right)+300531100\arctan\left(\frac{1}{8818809606}\right)-26630896\arctan\left(\frac{1}{8964659780}\right)-202862340\arctan\left(\frac{2}{19255151581}\right)-58914608\arctan\left(\frac{1}{14722389557}\right)-20003196\arctan\left(\frac{1}{48794637562}\right)+140253860\arctan\left(\frac{1}{219231737743}\right)-301511080\arctan\left(\frac{2}{10162014009261}\right)-297325012\arctan\left(\frac{1}{74796038391693}\right)$$
Compact formula383917720[112519818] - 60253300[194195097] - 45811372[295806685] + 21950424[1432278547] + 23670412[1849507057] + 12571172[2309197818] - 28792152[2674664693] + 319511872[2701984943] + 195503704[4117799011] + 300531100[8818809606] - 26630896[8964659780] - 202862340[19255151581/2] - 58914608[14722389557] - 20003196[48794637562] + 140253860[219231737743] - 301511080[10162014009261/2] - 297325012[74796038391693]
Lehmer's measure1.73499
References
MRW (19Oct04) (full reference coming soon)