M000225

$$\pi=540597244\arctan\left(\frac{2}{1244961989}\right)+1528675280\arctan\left(\frac{1}{1479406293}\right)+2476528824\arctan\left(\frac{2}{3472598789}\right)-1006833592\arctan\left(\frac{2}{7850392761}\right)-1767059984\arctan\left(\frac{1}{4038832337}\right)+1002448200\arctan\left(\frac{1}{5959574158}\right)+1129775552\arctan\left(\frac{2}{12800795261}\right)+2168491456\arctan\left(\frac{1}{6608082112}\right)-1942853520\arctan\left(\frac{1}{18710140581}\right)-1034033664\arctan\left(\frac{1}{24139206772}\right)-26112728\arctan\left(\frac{2}{112899039159}\right)-1260163208\arctan\left(\frac{1}{71354040503}\right)+1103041988\arctan\left(\frac{1}{225891903693}\right)-1979100104\arctan\left(\frac{1}{378137211957}\right)+327972764\arctan\left(\frac{1}{1053586529897}\right)-553991136\arctan\left(\frac{1}{2554104718836}\right)-1005999652\arctan\left(\frac{1}{3737240479718}\right)-168938060\arctan\left(\frac{1}{3931260155877}\right)+457893912\arctan\left(\frac{1}{28148191112477}\right)$$
Compact formula540597244[1244961989/2] + 1528675280[1479406293] + 2476528824[3472598789/2] - 1006833592[7850392761/2] - 1767059984[4038832337] + 1002448200[5959574158] + 1129775552[12800795261/2] + 2168491456[6608082112] - 1942853520[18710140581] - 1034033664[24139206772] - 26112728[112899039159/2] - 1260163208[71354040503] + 1103041988[225891903693] - 1979100104[378137211957] + 327972764[1053586529897] - 553991136[2554104718836] - 1005999652[3737240479718] - 168938060[3931260155877] + 457893912[28148191112477]
Lehmer's measure1.79575
References
MRW (9Aug06) (full reference coming soon)