M000247

$$\pi=2265623728\arctan\left(\frac{1}{1426584882}\right)+\frac{8175664252}{3}\arctan\left(\frac{2}{5493779561}\right)+1542215492\arctan\left(\frac{2}{10355370165}\right)\frac{-3352615820}{3}\arctan\left(\frac{1}{8634733487}\right)+\frac{8025027340}{3}\arctan\left(\frac{1}{8895085098}\right)+1811401504\arctan\left(\frac{1}{12957904393}\right)\frac{-2657413876}{3}\arctan\left(\frac{1}{38185029043}\right)\frac{-5864148436}{3}\arctan\left(\frac{2}{112899039159}\right)+\frac{9217837112}{3}\arctan\left(\frac{1}{66492889557}\right)-1702255108\arctan\left(\frac{1}{82926000318}\right)+\frac{4075495876}{3}\arctan\left(\frac{1}{102428655030}\right)\frac{-10846424536}{3}\arctan\left(\frac{1}{120563046313}\right)\frac{-220914544}{3}\arctan\left(\frac{1}{250645741818}\right)\frac{-243643328}{3}\arctan\left(\frac{2}{672369361511}\right)+717073488\arctan\left(\frac{1}{548275361132}\right)\frac{-2402110076}{3}\arctan\left(\frac{1}{579766497643}\right)+\frac{5037854564}{3}\arctan\left(\frac{1}{838010977198}\right)\frac{-5835777928}{3}\arctan\left(\frac{1}{13474294213307}\right)\frac{-3821152972}{3}\arctan\left(\frac{1}{46150510628682}\right)+\frac{5558982064}{3}\arctan\left(\frac{1}{69971515635443}\right)$$
Compact formula2265623728[1426584882] + 8175664252/3[5493779561/2] + 1542215492[10355370165/2] - 3352615820/3[8634733487] + 8025027340/3[8895085098] + 1811401504[12957904393] - 2657413876/3[38185029043] - 5864148436/3[112899039159/2] + 9217837112/3[66492889557] - 1702255108[82926000318] + 4075495876/3[102428655030] - 10846424536/3[120563046313] - 220914544/3[250645741818] - 243643328/3[672369361511/2] + 717073488[548275361132] - 2402110076/3[579766497643] + 5037854564/3[838010977198] - 5835777928/3[13474294213307] - 3821152972/3[46150510628682] + 5558982064/3[69971515635443]
Lehmer's measure1.82085
References
MRW (10Aug06) (full reference coming soon)