M000347

$$\pi=\frac{22885620989420}{3}\arctan\left(\frac{1}{12502765871656}\right)+17060523154052\arctan\left(\frac{1}{13502703082318}\right)+\frac{1112648249698}{3}\arctan\left(\frac{1}{15962244871097}\right)+\frac{27668040153896}{3}\arctan\left(\frac{1}{20293776947868}\right)+6950683048336\arctan\left(\frac{2}{56823139867939}\right)+6129614043410\arctan\left(\frac{1}{33308851938318}\right)+\frac{11491686434362}{3}\arctan\left(\frac{1}{41887379804066}\right)+3420607540852\arctan\left(\frac{1}{42512655792373}\right)+\frac{13896675754880}{3}\arctan\left(\frac{1}{69971515635443}\right)+\frac{39561672581402}{3}\arctan\left(\frac{1}{83979525486773}\right)-2114856084530\arctan\left(\frac{1}{109386512159826}\right)-1669605560076\arctan\left(\frac{1}{127528611030443}\right)+3053010084786\arctan\left(\frac{1}{158682175700807}\right)-8146548865546\arctan\left(\frac{1}{187458398552950}\right)+10531136503572\arctan\left(\frac{1}{211773236092865}\right)-3669704168540\arctan\left(\frac{1}{240926005152903}\right)\frac{-14343856967318}{3}\arctan\left(\frac{1}{258213230677943}\right)+\frac{8822225790010}{3}\arctan\left(\frac{1}{317335434728073}\right)-1061853240492\arctan\left(\frac{1}{370392816588001}\right)+\frac{43059374235382}{3}\arctan\left(\frac{1}{758341235653128}\right)-572856694514\arctan\left(\frac{1}{830202489183166}\right)+1220285407704\arctan\left(\frac{1}{1143900177872158}\right)\frac{-41678722212872}{3}\arctan\left(\frac{1}{1427056404016693}\right)-4165113745784\arctan\left(\frac{1}{2270451385422943}\right)-363399364508\arctan\left(\frac{1}{4204987898062723}\right)\frac{-40809976137236}{3}\arctan\left(\frac{1}{4475336554336643}\right)\frac{-31120771343500}{3}\arctan\left(\frac{1}{5364838594036907}\right)+\frac{19219480125314}{3}\arctan\left(\frac{1}{5407789116841693}\right)-13166303813834\arctan\left(\frac{1}{6559960445784918}\right)\frac{-23139452232892}{3}\arctan\left(\frac{1}{6805164953551432}\right)$$
Compact formula22885620989420/3[12502765871656] + 17060523154052[13502703082318] + 1112648249698/3[15962244871097] + 27668040153896/3[20293776947868] + 6950683048336[56823139867939/2] + 6129614043410[33308851938318] + 11491686434362/3[41887379804066] + 3420607540852[42512655792373] + 13896675754880/3[69971515635443] + 39561672581402/3[83979525486773] - 2114856084530[109386512159826] - 1669605560076[127528611030443] + 3053010084786[158682175700807] - 8146548865546[187458398552950] + 10531136503572[211773236092865] - 3669704168540[240926005152903] - 14343856967318/3[258213230677943] + 8822225790010/3[317335434728073] - 1061853240492[370392816588001] + 43059374235382/3[758341235653128] - 572856694514[830202489183166] + 1220285407704[1143900177872158] - 41678722212872/3[1427056404016693] - 4165113745784[2270451385422943] - 363399364508[4204987898062723] - 40809976137236/3[4475336554336643] - 31120771343500/3[5364838594036907] + 19219480125314/3[5407789116841693] - 13166303813834[6559960445784918] - 23139452232892/3[6805164953551432]
Lehmer's measure2.08460
References
MRW (4Aug06) (full reference coming soon)