M000278

$$\pi=12621778600\arctan\left(\frac{2}{10355370165}\right)-4365018708\arctan\left(\frac{1}{32863722478}\right)+14921040158\arctan\left(\frac{1}{42354792693}\right)+20637624054\arctan\left(\frac{2}{86479075199}\right)+1993293966\arctan\left(\frac{2}{112899039159}\right)-8798592338\arctan\left(\frac{1}{71617196968}\right)+13193091290\arctan\left(\frac{1}{78535779057}\right)-13557828534\arctan\left(\frac{1}{102428655030}\right)+9939054248\arctan\left(\frac{1}{197877956739}\right)-9680764036\arctan\left(\frac{1}{225891903693}\right)+11766561494\arctan\left(\frac{1}{283378114193}\right)-6453334162\arctan\left(\frac{1}{324363564309}\right)+10347120916\arctan\left(\frac{1}{469027618483}\right)+2998083138\arctan\left(\frac{1}{492806748932}\right)+1925900920\arctan\left(\frac{1}{821345641657}\right)+1745608104\arctan\left(\frac{1}{3737240479718}\right)-14921040158\arctan\left(\frac{1}{11830545643782}\right)+7814457342\arctan\left(\frac{1}{28148191112477}\right)+3319338608\arctan\left(\frac{1}{55707370528529}\right)+8241098802\arctan\left(\frac{1}{69971515635443}\right)-12601817848\arctan\left(\frac{1}{109805699900318}\right)+3959621036\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula12621778600[10355370165/2] - 4365018708[32863722478] + 14921040158[42354792693] + 20637624054[86479075199/2] + 1993293966[112899039159/2] - 8798592338[71617196968] + 13193091290[78535779057] - 13557828534[102428655030] + 9939054248[197877956739] - 9680764036[225891903693] + 11766561494[283378114193] - 6453334162[324363564309] + 10347120916[469027618483] + 2998083138[492806748932] + 1925900920[821345641657] + 1745608104[3737240479718] - 14921040158[11830545643782] + 7814457342[28148191112477] + 3319338608[55707370528529] + 8241098802[69971515635443] - 12601817848[109805699900318] + 3959621036[7474541196075273]
Lehmer's measure1.86939
References
MRW (9Aug06) (full reference coming soon)