M000208

$$\pi=1777667516\arctan\left(\frac{1}{657922943}\right)-387683036\arctan\left(\frac{1}{727507932}\right)+223433268\arctan\left(\frac{2}{1498434239}\right)-597802408\arctan\left(\frac{1}{934981432}\right)+2660821080\arctan\left(\frac{1}{1711814953}\right)+1383292768\arctan\left(\frac{2}{4417955351}\right)-1898018204\arctan\left(\frac{1}{5606994804}\right)-1177206100\arctan\left(\frac{1}{7804016832}\right)-2384989164\arctan\left(\frac{1}{9398109378}\right)-2036595448\arctan\left(\frac{2}{27894683333}\right)+457215076\arctan\left(\frac{2}{74522099649}\right)+3300214208\arctan\left(\frac{1}{66492889557}\right)-1242176048\arctan\left(\frac{1}{68844144046}\right)-3259392272\arctan\left(\frac{1}{106334643058}\right)+475611908\arctan\left(\frac{1}{134520516108}\right)+57905980\arctan\left(\frac{1}{190122366697}\right)+1522225092\arctan\left(\frac{1}{293153860797}\right)+914713368\arctan\left(\frac{1}{169838669284032}\right)$$
Compact formula1777667516[657922943] - 387683036[727507932] + 223433268[1498434239/2] - 597802408[934981432] + 2660821080[1711814953] + 1383292768[4417955351/2] - 1898018204[5606994804] - 1177206100[7804016832] - 2384989164[9398109378] - 2036595448[27894683333/2] + 457215076[74522099649/2] + 3300214208[66492889557] - 1242176048[68844144046] - 3259392272[106334643058] + 475611908[134520516108] + 57905980[190122366697] + 1522225092[293153860797] + 914713368[169838669284032]
Lehmer's measure1.77418
References
ASN (7Jun10)(ΒΆΒΆ1.90053) (full reference coming soon)