M000242

$$\pi=874998960\arctan\left(\frac{1}{1304967682}\right)+742808604\arctan\left(\frac{2}{3340159163}\right)+2682724352\arctan\left(\frac{1}{2264712991}\right)+654136174\arctan\left(\frac{2}{4532659739}\right)+1047394870\arctan\left(\frac{1}{4038832337}\right)+790048590\arctan\left(\frac{1}{6608082112}\right)+478665032\arctan\left(\frac{1}{7220509743}\right)+672381966\arctan\left(\frac{1}{9392165427}\right)+540137390\arctan\left(\frac{1}{12957904393}\right)+143820238\arctan\left(\frac{1}{18710140581}\right)+113484710\arctan\left(\frac{1}{29546599818}\right)-1024053648\arctan\left(\frac{2}{112899039159}\right)+553991136\arctan\left(\frac{1}{65815220307}\right)+599437000\arctan\left(\frac{2}{520629831511}\right)-1697572868\arctan\left(\frac{1}{265542904947}\right)-163136406\arctan\left(\frac{1}{378137211957}\right)-2028642398\arctan\left(\frac{1}{693709623807}\right)+985435188\arctan\left(\frac{1}{3737240479718}\right)+227827726\arctan\left(\frac{1}{11830545643782}\right)$$
Compact formula874998960[1304967682] + 742808604[3340159163/2] + 2682724352[2264712991] + 654136174[4532659739/2] + 1047394870[4038832337] + 790048590[6608082112] + 478665032[7220509743] + 672381966[9392165427] + 540137390[12957904393] + 143820238[18710140581] + 113484710[29546599818] - 1024053648[112899039159/2] + 553991136[65815220307] + 599437000[520629831511/2] - 1697572868[265542904947] - 163136406[378137211957] - 2028642398[693709623807] + 985435188[3737240479718] + 227827726[11830545643782]
Lehmer's measure1.81873
References
MRW (10Aug06) (full reference coming soon)