M000271

$$\pi=\frac{67707416116}{3}\arctan\left(\frac{2}{10355370165}\right)\frac{-29842080316}{3}\arctan\left(\frac{1}{27354282288}\right)\frac{-42937136440}{3}\arctan\left(\frac{1}{32863722478}\right)\frac{-42534408944}{3}\arctan\left(\frac{2}{86479075199}\right)\frac{-8941158260}{3}\arctan\left(\frac{2}{112899039159}\right)\frac{-11474736856}{3}\arctan\left(\frac{1}{71617196968}\right)-1727948868\arctan\left(\frac{1}{78535779057}\right)+\frac{33931715188}{3}\arctan\left(\frac{1}{102428655030}\right)+9939054248\arctan\left(\frac{1}{197877956739}\right)-9680764036\arctan\left(\frac{1}{225891903693}\right)-3154478664\arctan\left(\frac{1}{283378114193}\right)\frac{-34281042644}{3}\arctan\left(\frac{1}{324363564309}\right)\frac{-28642797884}{3}\arctan\left(\frac{1}{469027618483}\right)\frac{-5926790744}{3}\arctan\left(\frac{1}{492806748932}\right)\frac{-24064377556}{3}\arctan\left(\frac{1}{821345641657}\right)+1745608104\arctan\left(\frac{1}{3737240479718}\right)+\frac{8522331868}{3}\arctan\left(\frac{1}{28148191112477}\right)+3319338608\arctan\left(\frac{1}{55707370528529}\right)+\frac{9802256248}{3}\arctan\left(\frac{1}{69971515635443}\right)\frac{-7963373228}{3}\arctan\left(\frac{1}{109805699900318}\right)\frac{-29842080316}{3}\arctan\left(\frac{1}{399267828838807}\right)\frac{-17963217208}{3}\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula67707416116/3[10355370165/2] - 29842080316/3[27354282288] - 42937136440/3[32863722478] - 42534408944/3[86479075199/2] - 8941158260/3[112899039159/2] - 11474736856/3[71617196968] - 1727948868[78535779057] + 33931715188/3[102428655030] + 9939054248[197877956739] - 9680764036[225891903693] - 3154478664[283378114193] - 34281042644/3[324363564309] - 28642797884/3[469027618483] - 5926790744/3[492806748932] - 24064377556/3[821345641657] + 1745608104[3737240479718] + 8522331868/3[28148191112477] + 3319338608[55707370528529] + 9802256248/3[69971515635443] - 7963373228/3[109805699900318] - 29842080316/3[399267828838807] - 17963217208/3[7474541196075273]
Lehmer's measure1.86310
References
MRW (9Aug06) (full reference coming soon)