M000291

$$\pi=242723982216\arctan\left(\frac{1}{120563046313}\right)+163683700424\arctan\left(\frac{2}{258565442223}\right)-185622435552\arctan\left(\frac{1}{146235453343}\right)-141953024052\arctan\left(\frac{1}{157245105893}\right)+259862953880\arctan\left(\frac{1}{191092631540}\right)+117033645000\arctan\left(\frac{1}{378137211957}\right)+58955716200\arctan\left(\frac{1}{529611885793}\right)+149867648260\arctan\left(\frac{2}{1097963074309}\right)+285415575852\arctan\left(\frac{1}{798587208809}\right)-70896871472\arctan\left(\frac{1}{810494143407}\right)-116132884352\arctan\left(\frac{1}{1029114662298}\right)-116628051108\arctan\left(\frac{1}{2196973730667}\right)-167576472740\arctan\left(\frac{1}{2267426627682}\right)-147049303700\arctan\left(\frac{1}{3037967579288}\right)-78295896292\arctan\left(\frac{1}{3737240479718}\right)-31908792724\arctan\left(\frac{1}{10463035477341}\right)+143262480128\arctan\left(\frac{1}{14113057272907}\right)+131173415472\arctan\left(\frac{1}{15962244871097}\right)+80891076476\arctan\left(\frac{2}{53518224361625}\right)-13705899640\arctan\left(\frac{1}{42205358676970}\right)+79954850700\arctan\left(\frac{1}{69971515635443}\right)+73542185920\arctan\left(\frac{1}{96648634011432}\right)-648362708\arctan\left(\frac{1}{150361024828932}\right)-276269169736\arctan\left(\frac{1}{74295753693510382}\right)$$
Compact formula242723982216[120563046313] + 163683700424[258565442223/2] - 185622435552[146235453343] - 141953024052[157245105893] + 259862953880[191092631540] + 117033645000[378137211957] + 58955716200[529611885793] + 149867648260[1097963074309/2] + 285415575852[798587208809] - 70896871472[810494143407] - 116132884352[1029114662298] - 116628051108[2196973730667] - 167576472740[2267426627682] - 147049303700[3037967579288] - 78295896292[3737240479718] - 31908792724[10463035477341] + 143262480128[14113057272907] + 131173415472[15962244871097] + 80891076476[53518224361625/2] - 13705899640[42205358676970] + 79954850700[69971515635443] + 73542185920[96648634011432] - 648362708[150361024828932] - 276269169736[74295753693510382]
Lehmer's measure1.92746
References
MRW (8Aug06) (full reference coming soon)