M000252

$$\pi=4751996876\arctan\left(\frac{1}{2406126693}\right)-1798771112\arctan\left(\frac{1}{3024600267}\right)+5993108680\arctan\left(\frac{1}{4038832337}\right)+117720844\arctan\left(\frac{1}{6608082112}\right)+599437000\arctan\left(\frac{1}{12139595709}\right)+1811902136\arctan\left(\frac{1}{20112174818}\right)+889068008\arctan\left(\frac{2}{47029703269}\right)-1112834172\arctan\left(\frac{1}{29546599818}\right)-3454533200\arctan\left(\frac{2}{63770783801}\right)+7593742184\arctan\left(\frac{1}{35217386577}\right)+1752906536\arctan\left(\frac{2}{112899039159}\right)-1050901960\arctan\left(\frac{1}{120563046313}\right)+2145262564\arctan\left(\frac{1}{215644443543}\right)-5836117916\arctan\left(\frac{1}{265542904947}\right)+1495301284\arctan\left(\frac{1}{378137211957}\right)-3860797520\arctan\left(\frac{1}{3737240479718}\right)-1825971184\arctan\left(\frac{1}{6494737887682}\right)-3530523240\arctan\left(\frac{2}{16784619514521}\right)+2969427996\arctan\left(\frac{1}{11830545643782}\right)-2069272524\arctan\left(\frac{1}{210894042529419}\right)$$
Compact formula4751996876[2406126693] - 1798771112[3024600267] + 5993108680[4038832337] + 117720844[6608082112] + 599437000[12139595709] + 1811902136[20112174818] + 889068008[47029703269/2] - 1112834172[29546599818] - 3454533200[63770783801/2] + 7593742184[35217386577] + 1752906536[112899039159/2] - 1050901960[120563046313] + 2145262564[215644443543] - 5836117916[265542904947] + 1495301284[378137211957] - 3860797520[3737240479718] - 1825971184[6494737887682] - 3530523240[16784619514521/2] + 2969427996[11830545643782] - 2069272524[210894042529419]
Lehmer's measure1.82283
References
MRW (10Aug06) (full reference coming soon)