M000174

$$\pi=9709316\arctan\left(\frac{2}{16859469}\right)+17556312\arctan\left(\frac{1}{13522943}\right)+9669908\arctan\left(\frac{1}{31030563}\right)+7127356\arctan\left(\frac{1}{36313568}\right)-1054128\arctan\left(\frac{1}{162166243}\right)+44964584\arctan\left(\frac{1}{284862638}\right)-14823684\arctan\left(\frac{1}{657922943}\right)+18344448\arctan\left(\frac{1}{727507932}\right)+27717968\arctan\left(\frac{2}{1498434239}\right)-1591220\arctan\left(\frac{1}{2111380107}\right)-20037732\arctan\left(\frac{2}{4417955351}\right)+14229872\arctan\left(\frac{1}{5606994804}\right)+11779024\arctan\left(\frac{2}{74522099649}\right)-21738368\arctan\left(\frac{1}{66492889557}\right)-13044632\arctan\left(\frac{2}{292685901589}\right)$$
Compact formula9709316[16859469/2] + 17556312[13522943] + 9669908[31030563] + 7127356[36313568] - 1054128[162166243] + 44964584[284862638] - 14823684[657922943] + 18344448[727507932] + 27717968[1498434239/2] - 1591220[2111380107] - 20037732[4417955351/2] + 14229872[5606994804] + 11779024[74522099649/2] - 21738368[66492889557] - 13044632[292685901589/2]
Lehmer's measure1.72277
References
MRW (12Aug06) (full reference coming soon)