M000186

$$\pi=30640352\arctan\left(\frac{1}{27872057}\right)+82773056\arctan\left(\frac{1}{82189674}\right)+29835920\arctan\left(\frac{1}{133311327}\right)+135691368\arctan\left(\frac{1}{227661182}\right)+104000852\arctan\left(\frac{1}{244653118}\right)-52596712\arctan\left(\frac{1}{284862638}\right)-17556312\arctan\left(\frac{1}{403478642}\right)+54153348\arctan\left(\frac{1}{403916362}\right)-72982796\arctan\left(\frac{1}{727507932}\right)+24867076\arctan\left(\frac{1}{1365179943}\right)-86147780\arctan\left(\frac{1}{2132621070}\right)+27077796\arctan\left(\frac{1}{4193879974}\right)+22673580\arctan\left(\frac{2}{74522099649}\right)-45837520\arctan\left(\frac{1}{106334643058}\right)+26080388\arctan\left(\frac{1}{134520516108}\right)-27077796\arctan\left(\frac{1}{70354516949466842682}\right)$$
Compact formula30640352[27872057] + 82773056[82189674] + 29835920[133311327] + 135691368[227661182] + 104000852[244653118] - 52596712[284862638] - 17556312[403478642] + 54153348[403916362] - 72982796[727507932] + 24867076[1365179943] - 86147780[2132621070] + 27077796[4193879974] + 22673580[74522099649/2] - 45837520[106334643058] + 26080388[134520516108] - 27077796[70354516949466842682]
Lehmer's measure1.73223
References
ASN (6Jul12)(*1.84553) (full reference coming soon)