M000362

$$\pi=-5445042390284\arctan\left(\frac{1}{11244667034168}\right)+3571325365352\arctan\left(\frac{1}{15962244871097}\right)+48159709961976\arctan\left(\frac{1}{20293776947868}\right)+1050709890136\arctan\left(\frac{2}{53518224361625}\right)+4951614234936\arctan\left(\frac{1}{33308851938318}\right)+14871088490480\arctan\left(\frac{1}{41887379804066}\right)-9588257242184\arctan\left(\frac{1}{53453286489686}\right)+17025924962384\arctan\left(\frac{1}{58705151760538}\right)-1125703157800\arctan\left(\frac{1}{69971515635443}\right)-24332130318488\arctan\left(\frac{1}{74285407663082}\right)+27629679331972\arctan\left(\frac{1}{83979525486773}\right)-11870694330484\arctan\left(\frac{1}{127528611030443}\right)+11988304005360\arctan\left(\frac{1}{131001068999312}\right)+31054435639616\arctan\left(\frac{1}{158682175700807}\right)+23165598591024\arctan\left(\frac{2}{351408485766961}\right)+12291362112724\arctan\left(\frac{1}{187458398552950}\right)+2967621927012\arctan\left(\frac{1}{211773236092865}\right)-22929615338336\arctan\left(\frac{1}{240926005152903}\right)+7599684952412\arctan\left(\frac{1}{258213230677943}\right)+6417753699136\arctan\left(\frac{1}{317335434728073}\right)+4912623992588\arctan\left(\frac{1}{370392816588001}\right)+25184099732840\arctan\left(\frac{1}{758341235653128}\right)-21584249661808\arctan\left(\frac{1}{830202489183166}\right)-11866598412016\arctan\left(\frac{1}{1086889881361383}\right)+37624116416980\arctan\left(\frac{1}{1143900177872158}\right)-1950950403804\arctan\left(\frac{1}{1427056404016693}\right)-23595226734360\arctan\left(\frac{1}{2270451385422943}\right)+11624904640852\arctan\left(\frac{1}{4204987898062723}\right)-22000466710316\arctan\left(\frac{1}{6805164953551432}\right)-14388350768536\arctan\left(\frac{1}{54969362078559518}\right)$$
Compact formula- 5445042390284[11244667034168] + 3571325365352[15962244871097] + 48159709961976[20293776947868] + 1050709890136[53518224361625/2] + 4951614234936[33308851938318] + 14871088490480[41887379804066] - 9588257242184[53453286489686] + 17025924962384[58705151760538] - 1125703157800[69971515635443] - 24332130318488[74285407663082] + 27629679331972[83979525486773] - 11870694330484[127528611030443] + 11988304005360[131001068999312] + 31054435639616[158682175700807] + 23165598591024[351408485766961/2] + 12291362112724[187458398552950] + 2967621927012[211773236092865] - 22929615338336[240926005152903] + 7599684952412[258213230677943] + 6417753699136[317335434728073] + 4912623992588[370392816588001] + 25184099732840[758341235653128] - 21584249661808[830202489183166] - 11866598412016[1086889881361383] + 37624116416980[1143900177872158] - 1950950403804[1427056404016693] - 23595226734360[2270451385422943] + 11624904640852[4204987898062723] - 22000466710316[6805164953551432] - 14388350768536[54969362078559518]
Lehmer's measure2.09484
References
MRW (19Aug11) (full reference coming soon)