M000269

$$\pi=\frac{52786375958}{3}\arctan\left(\frac{2}{10355370165}\right)-4365018708\arctan\left(\frac{1}{32863722478}\right)\frac{-12692328628}{3}\arctan\left(\frac{2}{86479075199}\right)\frac{-8941158260}{3}\arctan\left(\frac{2}{112899039159}\right)-8798592338\arctan\left(\frac{1}{71617196968}\right)+\frac{24658233712}{3}\arctan\left(\frac{1}{78535779057}\right)+1363211624\arctan\left(\frac{1}{102428655030}\right)+9939054248\arctan\left(\frac{1}{197877956739}\right)+\frac{14921040158}{3}\arctan\left(\frac{1}{208853282318}\right)\frac{-14121251950}{3}\arctan\left(\frac{1}{225891903693}\right)+\frac{5457604166}{3}\arctan\left(\frac{1}{283378114193}\right)-6453334162\arctan\left(\frac{1}{324363564309}\right)-4573919242\arctan\left(\frac{1}{469027618483}\right)\frac{-5926790744}{3}\arctan\left(\frac{1}{492806748932}\right)+1925900920\arctan\left(\frac{1}{821345641657}\right)+\frac{35078904628}{3}\arctan\left(\frac{1}{3737240479718}\right)+\frac{8522331868}{3}\arctan\left(\frac{1}{28148191112477}\right)+3319338608\arctan\left(\frac{1}{55707370528529}\right)\frac{-5118783910}{3}\arctan\left(\frac{1}{69971515635443}\right)+\frac{14921040158}{3}\arctan\left(\frac{1}{74541849600668}\right)\frac{-7963373228}{3}\arctan\left(\frac{1}{109805699900318}\right)\frac{-3042177050}{3}\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula52786375958/3[10355370165/2] - 4365018708[32863722478] - 12692328628/3[86479075199/2] - 8941158260/3[112899039159/2] - 8798592338[71617196968] + 24658233712/3[78535779057] + 1363211624[102428655030] + 9939054248[197877956739] + 14921040158/3[208853282318] - 14121251950/3[225891903693] + 5457604166/3[283378114193] - 6453334162[324363564309] - 4573919242[469027618483] - 5926790744/3[492806748932] + 1925900920[821345641657] + 35078904628/3[3737240479718] + 8522331868/3[28148191112477] + 3319338608[55707370528529] - 5118783910/3[69971515635443] + 14921040158/3[74541849600668] - 7963373228/3[109805699900318] - 3042177050/3[7474541196075273]
Lehmer's measure1.85923
References
MRW (9Aug06) (full reference coming soon)