M000258

$$\pi=-16986797308\arctan\left(\frac{1}{32863722478}\right)+18338362496\arctan\left(\frac{2}{86479075199}\right)+65408154558\arctan\left(\frac{1}{49476317237}\right)+14615072566\arctan\left(\frac{2}{112899039159}\right)+43987783620\arctan\left(\frac{1}{71617196968}\right)+38436648490\arctan\left(\frac{1}{78535779057}\right)+79393144782\arctan\left(\frac{1}{102428655030}\right)-55469100310\arctan\left(\frac{1}{197877956739}\right)-34924321236\arctan\left(\frac{1}{225891903693}\right)+49631897294\arctan\left(\frac{1}{283378114193}\right)-6453334162\arctan\left(\frac{1}{324363564309}\right)-17195697842\arctan\left(\frac{1}{469027618483}\right)+28241640338\arctan\left(\frac{1}{492806748932}\right)+14547679520\arctan\left(\frac{1}{821345641657}\right)+12621778600\arctan\left(\frac{1}{1682005443607}\right)+54531984062\arctan\left(\frac{1}{3737240479718}\right)-52786375958\arctan\left(\frac{1}{8256835333313}\right)+20436235942\arctan\left(\frac{1}{28148191112477}\right)-62088815950\arctan\left(\frac{1}{55707370528529}\right)+33484656002\arctan\left(\frac{1}{69971515635443}\right)+27562779510\arctan\left(\frac{1}{109805699900318}\right)+3959621036\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula- 16986797308[32863722478] + 18338362496[86479075199/2] + 65408154558[49476317237] + 14615072566[112899039159/2] + 43987783620[71617196968] + 38436648490[78535779057] + 79393144782[102428655030] - 55469100310[197877956739] - 34924321236[225891903693] + 49631897294[283378114193] - 6453334162[324363564309] - 17195697842[469027618483] + 28241640338[492806748932] + 14547679520[821345641657] + 12621778600[1682005443607] + 54531984062[3737240479718] - 52786375958[8256835333313] + 20436235942[28148191112477] - 62088815950[55707370528529] + 33484656002[69971515635443] + 27562779510[109805699900318] + 3959621036[7474541196075273]
Lehmer's measure1.84858
References
MRW (26Mar04)(ΒΆΒΆ1.95515) (full reference coming soon)