M000246

$$\pi=4911441524\arctan\left(\frac{1}{1454097393}\right)+1018370564\arctan\left(\frac{2}{3340159163}\right)-1353718212\arctan\left(\frac{1}{2189376182}\right)-874998960\arctan\left(\frac{2}{7650575553}\right)+1078102032\arctan\left(\frac{2}{7850392761}\right)+2782708308\arctan\left(\frac{1}{3985944689}\right)-2610473480\arctan\left(\frac{1}{4038832337}\right)-1817188576\arctan\left(\frac{1}{6608082112}\right)+496910824\arctan\left(\frac{1}{9392165427}\right)+1194273564\arctan\left(\frac{1}{12957904393}\right)-1863979928\arctan\left(\frac{1}{18710140581}\right)-2769314416\arctan\left(\frac{1}{29546599818}\right)+929047344\arctan\left(\frac{2}{112899039159}\right)-4136372300\arctan\left(\frac{1}{225891903693}\right)-2527180184\arctan\left(\frac{1}{265542904947}\right)+3273708076\arctan\left(\frac{1}{378137211957}\right)+2339099180\arctan\left(\frac{1}{3737240479718}\right)+1756962860\arctan\left(\frac{1}{11830545643782}\right)-599437000\arctan\left(\frac{1}{28148191112477}\right)$$
Compact formula4911441524[1454097393] + 1018370564[3340159163/2] - 1353718212[2189376182] - 874998960[7650575553/2] + 1078102032[7850392761/2] + 2782708308[3985944689] - 2610473480[4038832337] - 1817188576[6608082112] + 496910824[9392165427] + 1194273564[12957904393] - 1863979928[18710140581] - 2769314416[29546599818] + 929047344[112899039159/2] - 4136372300[225891903693] - 2527180184[265542904947] + 3273708076[378137211957] + 2339099180[3737240479718] + 1756962860[11830545643782] - 599437000[28148191112477]
Lehmer's measure1.82070
References
MRW (10Aug06) (full reference coming soon)