M000263

$$\pi=12621778600\arctan\left(\frac{2}{10355370165}\right)+35558664212\arctan\left(\frac{2}{86479075199}\right)-17292764900\arctan\left(\frac{2}{112899039159}\right)-23719632496\arctan\left(\frac{1}{71617196968}\right)+25477061608\arctan\left(\frac{1}{73052066693}\right)+28114131448\arctan\left(\frac{1}{78535779057}\right)-28478868692\arctan\left(\frac{1}{102428655030}\right)+9939054248\arctan\left(\frac{1}{197877956739}\right)-5315745328\arctan\left(\frac{1}{225891903693}\right)-3154478664\arctan\left(\frac{1}{283378114193}\right)+8467705996\arctan\left(\frac{1}{324363564309}\right)+35824182524\arctan\left(\frac{1}{469027618483}\right)-11922957020\arctan\left(\frac{1}{492806748932}\right)-4365018708\arctan\left(\frac{1}{757744781467}\right)+1925900920\arctan\left(\frac{1}{821345641657}\right)+1745608104\arctan\left(\frac{1}{3737240479718}\right)-29842080316\arctan\left(\frac{1}{24527847221977}\right)+22735497500\arctan\left(\frac{1}{28148191112477}\right)+3319338608\arctan\left(\frac{1}{55707370528529}\right)-6679941356\arctan\left(\frac{1}{69971515635443}\right)-12601817848\arctan\left(\frac{1}{109805699900318}\right)+3959621036\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula12621778600[10355370165/2] + 35558664212[86479075199/2] - 17292764900[112899039159/2] - 23719632496[71617196968] + 25477061608[73052066693] + 28114131448[78535779057] - 28478868692[102428655030] + 9939054248[197877956739] - 5315745328[225891903693] - 3154478664[283378114193] + 8467705996[324363564309] + 35824182524[469027618483] - 11922957020[492806748932] - 4365018708[757744781467] + 1925900920[821345641657] + 1745608104[3737240479718] - 29842080316[24527847221977] + 22735497500[28148191112477] + 3319338608[55707370528529] - 6679941356[69971515635443] - 12601817848[109805699900318] + 3959621036[7474541196075273]
Lehmer's measure1.85463
References
MRW (9Aug06) (full reference coming soon)