M000139

$$\pi=5773276\arctan\left(\frac{1}{1637147}\right)-2210720\arctan\left(\frac{1}{3014557}\right)+2632856\arctan\left(\frac{1}{9165843}\right)+2398552\arctan\left(\frac{1}{82189674}\right)-804432\arctan\left(\frac{1}{133311327}\right)+5582712\arctan\left(\frac{1}{227661182}\right)+2321828\arctan\left(\frac{1}{244653118}\right)-651840\arctan\left(\frac{1}{284862638}\right)-2025068\arctan\left(\frac{1}{403478642}\right)+4419196\arctan\left(\frac{1}{403916362}\right)+266596\arctan\left(\frac{1}{727507932}\right)+3579780\arctan\left(\frac{2}{74522099649}\right)+334076\arctan\left(\frac{1}{106334643058}\right)+1213312\arctan\left(\frac{1}{134520516108}\right)$$
Compact formula5773276[1637147] - 2210720[3014557] + 2632856[9165843] + 2398552[82189674] - 804432[133311327] + 5582712[227661182] + 2321828[244653118] - 651840[284862638] - 2025068[403478642] + 4419196[403916362] + 266596[727507932] + 3579780[74522099649/2] + 334076[106334643058] + 1213312[134520516108]
Lehmer's measure1.68584
References
MRW (14Dec03)(ΒΆΒΆ1.87611) (full reference coming soon)