M000277

$$\pi=25590231200\arctan\left(\frac{1}{11566119443}\right)-4567298808\arctan\left(\frac{1}{20825269187}\right)+4523978404\arctan\left(\frac{1}{38185029043}\right)+6651965832\arctan\left(\frac{1}{48389473527}\right)+11378123004\arctan\left(\frac{2}{112899039159}\right)+7453828572\arctan\left(\frac{2}{115004793075}\right)+21634626368\arctan\left(\frac{1}{66492889557}\right)+6424129528\arctan\left(\frac{1}{111110023057}\right)+19164980192\arctan\left(\frac{1}{120563046313}\right)+15850138824\arctan\left(\frac{1}{313329771682}\right)-5881245824\arctan\left(\frac{1}{425963011457}\right)-17583294896\arctan\left(\frac{1}{501226901209}\right)+16110420776\arctan\left(\frac{1}{828289603318}\right)+959829168\arctan\left(\frac{2}{2136194739989}\right)-6929641936\arctan\left(\frac{1}{1130041002202}\right)-6536088716\arctan\left(\frac{1}{1921044951457}\right)+11530766064\arctan\left(\frac{1}{2184851093363}\right)+11134262116\arctan\left(\frac{1}{15962244871097}\right)+18183786884\arctan\left(\frac{1}{46150510628682}\right)+15000977420\arctan\left(\frac{1}{69971515635443}\right)+3141968176\arctan\left(\frac{1}{222158954830457}\right)+6663771404\arctan\left(\frac{1}{4439568777547493}\right)$$
Compact formula25590231200[11566119443] - 4567298808[20825269187] + 4523978404[38185029043] + 6651965832[48389473527] + 11378123004[112899039159/2] + 7453828572[115004793075/2] + 21634626368[66492889557] + 6424129528[111110023057] + 19164980192[120563046313] + 15850138824[313329771682] - 5881245824[425963011457] - 17583294896[501226901209] + 16110420776[828289603318] + 959829168[2136194739989/2] - 6929641936[1130041002202] - 6536088716[1921044951457] + 11530766064[2184851093363] + 11134262116[15962244871097] + 18183786884[46150510628682] + 15000977420[69971515635443] + 3141968176[222158954830457] + 6663771404[4439568777547493]
Lehmer's measure1.86916
References
MRW (9Aug06) (full reference coming soon)