M000233

$$\pi=3530523240\arctan\left(\frac{1}{1454097393}\right)+2069272524\arctan\left(\frac{1}{1479406293}\right)-847798888\arctan\left(\frac{1}{2406126693}\right)+1731752128\arctan\left(\frac{1}{3024600267}\right)-3137210324\arctan\left(\frac{1}{4038832337}\right)+117720844\arctan\left(\frac{1}{6608082112}\right)+599437000\arctan\left(\frac{1}{12139595709}\right)-1385260676\arctan\left(\frac{1}{18710140581}\right)-257370388\arctan\left(\frac{1}{20112174818}\right)-572182708\arctan\left(\frac{2}{47029703269}\right)-1112834172\arctan\left(\frac{1}{29546599818}\right)-75326104\arctan\left(\frac{1}{35217386577}\right)-1853606744\arctan\left(\frac{2}{112899039159}\right)-1050901960\arctan\left(\frac{1}{120563046313}\right)-1697572868\arctan\left(\frac{1}{265542904947}\right)+887279476\arctan\left(\frac{1}{378137211957}\right)+1814988284\arctan\left(\frac{1}{3737240479718}\right)+1704552056\arctan\left(\frac{1}{6494737887682}\right)+900155472\arctan\left(\frac{1}{11830545643782}\right)$$
Compact formula3530523240[1454097393] + 2069272524[1479406293] - 847798888[2406126693] + 1731752128[3024600267] - 3137210324[4038832337] + 117720844[6608082112] + 599437000[12139595709] - 1385260676[18710140581] - 257370388[20112174818] - 572182708[47029703269/2] - 1112834172[29546599818] - 75326104[35217386577] - 1853606744[112899039159/2] - 1050901960[120563046313] - 1697572868[265542904947] + 887279476[378137211957] + 1814988284[3737240479718] + 1704552056[6494737887682] + 900155472[11830545643782]
Lehmer's measure1.80774
References
MRW (30Mar04) (full reference coming soon)