M000229

$$\pi=499507264\arctan\left(\frac{1}{1454097393}\right)+2926025692\arctan\left(\frac{1}{1479406293}\right)-856753168\arctan\left(\frac{1}{3739944528}\right)+1353663992\arctan\left(\frac{1}{3816349818}\right)-106194348\arctan\left(\frac{1}{4038832337}\right)+4880488948\arctan\left(\frac{1}{6608082112}\right)-4700847112\arctan\left(\frac{1}{18710140581}\right)+5517049316\arctan\left(\frac{1}{20875536277}\right)+599437000\arctan\left(\frac{1}{24858161060}\right)+1642619844\arctan\left(\frac{1}{29546599818}\right)-1907655128\arctan\left(\frac{1}{44356375201}\right)-149054688\arctan\left(\frac{2}{112899039159}\right)-1731752128\arctan\left(\frac{1}{102416588812}\right)-3612207184\arctan\left(\frac{1}{113201494333}\right)-4534494272\arctan\left(\frac{1}{265542904947}\right)+1365998728\arctan\left(\frac{1}{378137211957}\right)-4466147356\arctan\left(\frac{1}{1628612367538}\right)+385998188\arctan\left(\frac{1}{3737240479718}\right)+2032524820\arctan\left(\frac{1}{11830545643782}\right)$$
Compact formula499507264[1454097393] + 2926025692[1479406293] - 856753168[3739944528] + 1353663992[3816349818] - 106194348[4038832337] + 4880488948[6608082112] - 4700847112[18710140581] + 5517049316[20875536277] + 599437000[24858161060] + 1642619844[29546599818] - 1907655128[44356375201] - 149054688[112899039159/2] - 1731752128[102416588812] - 3612207184[113201494333] - 4534494272[265542904947] + 1365998728[378137211957] - 4466147356[1628612367538] + 385998188[3737240479718] + 2032524820[11830545643782]
Lehmer's measure1.79895
References
HCL (22Feb04) (full reference coming soon)