M000243

$$\pi=2946789812\arctan\left(\frac{1}{1085592682}\right)-733776212\arctan\left(\frac{1}{1454097393}\right)-877517288\arctan\left(\frac{1}{1479406293}\right)-553991136\arctan\left(\frac{1}{3816349818}\right)+1983842296\arctan\left(\frac{1}{4038832337}\right)+3997691772\arctan\left(\frac{1}{5760773543}\right)+3361131404\arctan\left(\frac{1}{6608082112}\right)-2142354884\arctan\left(\frac{1}{18710140581}\right)+2507092128\arctan\left(\frac{1}{24858161060}\right)-265035284\arctan\left(\frac{1}{29546599818}\right)+1952749232\arctan\left(\frac{2}{112899039159}\right)-1907655128\arctan\left(\frac{2}{113079487129}\right)+3140938604\arctan\left(\frac{1}{94111829193}\right)-1925900920\arctan\left(\frac{1}{102416588812}\right)-1898700848\arctan\left(\frac{1}{113201494333}\right)+2215838520\arctan\left(\frac{1}{265542904947}\right)-2631693044\arctan\left(\frac{1}{378137211957}\right)-3611693584\arctan\left(\frac{1}{3737240479718}\right)-1771018160\arctan\left(\frac{1}{11830545643782}\right)$$
Compact formula2946789812[1085592682] - 733776212[1454097393] - 877517288[1479406293] - 553991136[3816349818] + 1983842296[4038832337] + 3997691772[5760773543] + 3361131404[6608082112] - 2142354884[18710140581] + 2507092128[24858161060] - 265035284[29546599818] + 1952749232[112899039159/2] - 1907655128[113079487129/2] + 3140938604[94111829193] - 1925900920[102416588812] - 1898700848[113201494333] + 2215838520[265542904947] - 2631693044[378137211957] - 3611693584[3737240479718] - 1771018160[11830545643782]
Lehmer's measure1.81903
References
ASN (21Dec10) (full reference coming soon)