M000274

$$\pi=35859521929\arctan\left(\frac{2}{24138356789}\right)+6250946021\arctan\left(\frac{1}{32863722478}\right)-17521159433\arctan\left(\frac{2}{86479075199}\right)+8304183266\arctan\left(\frac{2}{112899039159}\right)+20750040291\arctan\left(\frac{1}{71617196968}\right)-14349727468\arctan\left(\frac{1}{78535779057}\right)+62466290753\arctan\left(\frac{1}{102428655030}\right)-38542246281\arctan\left(\frac{1}{197877956739}\right)-11686577907\arctan\left(\frac{1}{225891903693}\right)-15776257264\arctan\left(\frac{1}{283378114193}\right)-25386002062\arctan\left(\frac{1}{324363564309}\right)-48481300529\arctan\left(\frac{1}{373247513933}\right)-23506587142\arctan\left(\frac{1}{469027618483}\right)-1306992291\arctan\left(\frac{1}{492806748932}\right)+23237743329\arctan\left(\frac{1}{560867262457}\right)+27169458120\arctan\left(\frac{1}{821345641657}\right)+37605130033\arctan\left(\frac{1}{3737240479718}\right)-9112396687\arctan\left(\frac{1}{28148191112477}\right)-9302439992\arctan\left(\frac{1}{55707370528529}\right)+3936023373\arctan\left(\frac{1}{69971515635443}\right)+46495447410\arctan\left(\frac{1}{109805699900318}\right)-8662157564\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula35859521929[24138356789/2] + 6250946021[32863722478] - 17521159433[86479075199/2] + 8304183266[112899039159/2] + 20750040291[71617196968] - 14349727468[78535779057] + 62466290753[102428655030] - 38542246281[197877956739] - 11686577907[225891903693] - 15776257264[283378114193] - 25386002062[324363564309] - 48481300529[373247513933] - 23506587142[469027618483] - 1306992291[492806748932] + 23237743329[560867262457] + 27169458120[821345641657] + 37605130033[3737240479718] - 9112396687[28148191112477] - 9302439992[55707370528529] + 3936023373[69971515635443] + 46495447410[109805699900318] - 8662157564[7474541196075273]
Lehmer's measure1.86658
References
MRW (9Aug06) (full reference coming soon)