M000285

$$\pi=8877823344\arctan\left(\frac{2}{112899039159}\right)+65600588352\arctan\left(\frac{2}{115004793075}\right)+7061027488\arctan\left(\frac{1}{102428655030}\right)-51894688712\arctan\left(\frac{1}{113044448178}\right)+22621131648\arctan\left(\frac{1}{120563046313}\right)+267125922332\arctan\left(\frac{2}{258565442223}\right)-92193892584\arctan\left(\frac{1}{146235453343}\right)-54937145864\arctan\left(\frac{1}{157245105893}\right)-18547250180\arctan\left(\frac{1}{191092631540}\right)+37078794300\arctan\left(\frac{1}{378137211957}\right)+245080409532\arctan\left(\frac{2}{1097963074309}\right)+221835017384\arctan\left(\frac{1}{810494143407}\right)+192537855336\arctan\left(\frac{1}{1029114662298}\right)-7666771340\arctan\left(\frac{1}{2267426627682}\right)-845501940\arctan\left(\frac{1}{3037967579288}\right)+169533331520\arctan\left(\frac{1}{3737240479718}\right)+109567023620\arctan\left(\frac{1}{5489234813093}\right)-15290488124\arctan\left(\frac{1}{5506897705002}\right)-201367758320\arctan\left(\frac{1}{10463035477341}\right)+54662013456\arctan\left(\frac{1}{14113057272907}\right)+176752200456\arctan\left(\frac{2}{30586892281911}\right)-58996821556\arctan\left(\frac{1}{15962244871097}\right)+1853171256\arctan\left(\frac{1}{74295753693510382}\right)$$
Compact formula8877823344[112899039159/2] + 65600588352[115004793075/2] + 7061027488[102428655030] - 51894688712[113044448178] + 22621131648[120563046313] + 267125922332[258565442223/2] - 92193892584[146235453343] - 54937145864[157245105893] - 18547250180[191092631540] + 37078794300[378137211957] + 245080409532[1097963074309/2] + 221835017384[810494143407] + 192537855336[1029114662298] - 7666771340[2267426627682] - 845501940[3037967579288] + 169533331520[3737240479718] + 109567023620[5489234813093] - 15290488124[5506897705002] - 201367758320[10463035477341] + 54662013456[14113057272907] + 176752200456[30586892281911/2] - 58996821556[15962244871097] + 1853171256[74295753693510382]
Lehmer's measure1.91506
References
MRW (21Jul11) (full reference coming soon)