M000284

$$\pi=-58307353492\arctan\left(\frac{2}{112899039159}\right)+50187311156\arctan\left(\frac{2}{115004793075}\right)+147331816428\arctan\left(\frac{1}{102428655030}\right)+214663820228\arctan\left(\frac{1}{120563046313}\right)-86378478580\arctan\left(\frac{2}{258565442223}\right)-76780615388\arctan\left(\frac{1}{146235453343}\right)+85333643076\arctan\left(\frac{1}{157245105893}\right)+137014026884\arctan\left(\frac{1}{191092631540}\right)+88973483012\arctan\left(\frac{1}{378137211957}\right)+47137285684\arctan\left(\frac{2}{1097963074309}\right)-152860306920\arctan\left(\frac{1}{810494143407}\right)-197447957092\arctan\left(\frac{1}{1029114662298}\right)+30703765320\arctan\left(\frac{1}{1131133876777}\right)+80709328888\arctan\left(\frac{1}{2267426627682}\right)-15290488124\arctan\left(\frac{1}{2554104718836}\right)+35635909576\arctan\left(\frac{1}{3037967579288}\right)+8071619188\arctan\left(\frac{1}{3737240479718}\right)-36481411516\arctan\left(\frac{1}{3931260155877}\right)+63760542364\arctan\left(\frac{1}{10463035477341}\right)+33471090064\arctan\left(\frac{1}{14113057272907}\right)+102464890776\arctan\left(\frac{1}{15962244871097}\right)-88376100228\arctan\left(\frac{1}{143321763441087}\right)-86522928972\arctan\left(\frac{1}{74295753693510382}\right)$$
Compact formula- 58307353492[112899039159/2] + 50187311156[115004793075/2] + 147331816428[102428655030] + 214663820228[120563046313] - 86378478580[258565442223/2] - 76780615388[146235453343] + 85333643076[157245105893] + 137014026884[191092631540] + 88973483012[378137211957] + 47137285684[1097963074309/2] - 152860306920[810494143407] - 197447957092[1029114662298] + 30703765320[1131133876777] + 80709328888[2267426627682] - 15290488124[2554104718836] + 35635909576[3037967579288] + 8071619188[3737240479718] - 36481411516[3931260155877] + 63760542364[10463035477341] + 33471090064[14113057272907] + 102464890776[15962244871097] - 88376100228[143321763441087] - 86522928972[74295753693510382]
Lehmer's measure1.90536
References
MRW (21Jul11) (full reference coming soon)