M000276

$$\pi=-29608575908\arctan\left(\frac{1}{32863722478}\right)+18338362496\arctan\left(\frac{2}{86479075199}\right)+12621778600\arctan\left(\frac{1}{50443911578}\right)-63414860592\arctan\left(\frac{2}{112899039159}\right)+43987783620\arctan\left(\frac{1}{71617196968}\right)+129088360248\arctan\left(\frac{1}{78535779057}\right)+130816309116\arctan\left(\frac{1}{97569070557}\right)+13984990224\arctan\left(\frac{1}{102428655030}\right)-146120812068\arctan\left(\frac{1}{197877956739}\right)-60167878436\arctan\left(\frac{1}{225891903693}\right)+156059866316\arctan\left(\frac{1}{250645741818}\right)+140283609052\arctan\left(\frac{1}{283378114193}\right)+58954820396\arctan\left(\frac{1}{324363564309}\right)-95225631000\arctan\left(\frac{1}{469027618483}\right)+262331439812\arctan\left(\frac{1}{492806748932}\right)+39791236720\arctan\left(\frac{1}{821345641657}\right)+301243562136\arctan\left(\frac{1}{3737240479718}\right)+98466169100\arctan\left(\frac{1}{28148191112477}\right)-152740527708\arctan\left(\frac{1}{55707370528529}\right)+111514589160\arctan\left(\frac{1}{69971515635443}\right)+118214491268\arctan\left(\frac{1}{109805699900318}\right)+147397708752\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula- 29608575908[32863722478] + 18338362496[86479075199/2] + 12621778600[50443911578] - 63414860592[112899039159/2] + 43987783620[71617196968] + 129088360248[78535779057] + 130816309116[97569070557] + 13984990224[102428655030] - 146120812068[197877956739] - 60167878436[225891903693] + 156059866316[250645741818] + 140283609052[283378114193] + 58954820396[324363564309] - 95225631000[469027618483] + 262331439812[492806748932] + 39791236720[821345641657] + 301243562136[3737240479718] + 98466169100[28148191112477] - 152740527708[55707370528529] + 111514589160[69971515635443] + 118214491268[109805699900318] + 147397708752[7474541196075273]
Lehmer's measure1.86801
References
MRW (9Aug06) (full reference coming soon)