M000224

$$\pi=3319338608\arctan\left(\frac{1}{2112819717}\right)+2410596180\arctan\left(\frac{1}{2189376182}\right)+2142127108\arctan\left(\frac{1}{2420845318}\right)-1364916080\arctan\left(\frac{1}{3985944689}\right)-1757429112\arctan\left(\frac{1}{6608082112}\right)+905334488\arctan\left(\frac{1}{15480069807}\right)+60067392\arctan\left(\frac{2}{112899039159}\right)+3905914920\arctan\left(\frac{1}{62143967598}\right)+2387777232\arctan\left(\frac{2}{130869454251}\right)+5775913856\arctan\left(\frac{1}{142140039332}\right)+226473660\arctan\left(\frac{1}{208666916697}\right)+1191400488\arctan\left(\frac{1}{225891903693}\right)-3414055396\arctan\left(\frac{1}{283378114193}\right)+1439923688\arctan\left(\frac{1}{324363564309}\right)-3921560532\arctan\left(\frac{1}{821345641657}\right)-1393686396\arctan\left(\frac{1}{3737240479718}\right)+351300840\arctan\left(\frac{1}{28148191112477}\right)-3578915340\arctan\left(\frac{1}{29676519680807}\right)-218450052\arctan\left(\frac{1}{69971515635443}\right)+2782158376\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula3319338608[2112819717] + 2410596180[2189376182] + 2142127108[2420845318] - 1364916080[3985944689] - 1757429112[6608082112] + 905334488[15480069807] + 60067392[112899039159/2] + 3905914920[62143967598] + 2387777232[130869454251/2] + 5775913856[142140039332] + 226473660[208666916697] + 1191400488[225891903693] - 3414055396[283378114193] + 1439923688[324363564309] - 3921560532[821345641657] - 1393686396[3737240479718] + 351300840[28148191112477] - 3578915340[29676519680807] - 218450052[69971515635443] + 2782158376[7474541196075273]
Lehmer's measure1.79066
References
MRW (28Mar04)(ΒΆΒΆ1.91882) (full reference coming soon)