M000280

$$\pi=12621778600\arctan\left(\frac{2}{10355370165}\right)-4365018708\arctan\left(\frac{1}{32863722478}\right)+5716583896\arctan\left(\frac{2}{86479075199}\right)+29842080316\arctan\left(\frac{1}{53601936432}\right)+16914334124\arctan\left(\frac{2}{112899039159}\right)+6122447820\arctan\left(\frac{1}{71617196968}\right)-1727948868\arctan\left(\frac{1}{78535779057}\right)+1363211624\arctan\left(\frac{1}{102428655030}\right)+9939054248\arctan\left(\frac{1}{197877956739}\right)-9680764036\arctan\left(\frac{1}{225891903693}\right)-3154478664\arctan\left(\frac{1}{283378114193}\right)-21374374320\arctan\left(\frac{1}{324363564309}\right)+10347120916\arctan\left(\frac{1}{469027618483}\right)-41765037336\arctan\left(\frac{1}{492806748932}\right)-29842080316\arctan\left(\frac{1}{548275361132}\right)-27916179396\arctan\left(\frac{1}{821345641657}\right)-28096472212\arctan\left(\frac{1}{3737240479718}\right)-7106582816\arctan\left(\frac{1}{28148191112477}\right)+3319338608\arctan\left(\frac{1}{55707370528529}\right)-6679941356\arctan\left(\frac{1}{69971515635443}\right)-12601817848\arctan\left(\frac{1}{109805699900318}\right)-25882459280\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula12621778600[10355370165/2] - 4365018708[32863722478] + 5716583896[86479075199/2] + 29842080316[53601936432] + 16914334124[112899039159/2] + 6122447820[71617196968] - 1727948868[78535779057] + 1363211624[102428655030] + 9939054248[197877956739] - 9680764036[225891903693] - 3154478664[283378114193] - 21374374320[324363564309] + 10347120916[469027618483] - 41765037336[492806748932] - 29842080316[548275361132] - 27916179396[821345641657] - 28096472212[3737240479718] - 7106582816[28148191112477] + 3319338608[55707370528529] - 6679941356[69971515635443] - 12601817848[109805699900318] - 25882459280[7474541196075273]
Lehmer's measure1.87719
References
ASN (18Jan10) (full reference coming soon)