M000033

$$\pi=2690\arctan\left(\frac{1}{1023}\right)+3022\arctan\left(\frac{1}{5832}\right)+366\arctan\left(\frac{2}{97059}\right)-1416\arctan\left(\frac{2}{226043}\right)-1464\arctan\left(\frac{2}{2513489}\right)+332\arctan\left(\frac{1}{6826318}\right)-366\arctan\left(\frac{1}{14130722757}\right)-1416\arctan\left(\frac{1}{109027476193}\right)+1416\arctan\left(\frac{2}{3375905320682366575989}\right)$$
Compact formula2690[1023] + 3022[5832] + 366[97059/2] - 1416[226043/2] - 1464[2513489/2] + 332[6826318] - 366[14130722757] - 1416[109027476193] + 1416[3375905320682366575989/2]
Lehmer's measure1.55559
References
MRW (23Sep09)(*1.65692, ΒΆΒΆ1.97604) (full reference coming soon)