M000296

$$\pi=76051360238\arctan\left(\frac{1}{104279454193}\right)+136439800674\arctan\left(\frac{1}{108813338187}\right)+80541880244\arctan\left(\frac{1}{157245105893}\right)+72624714760\arctan\left(\frac{1}{195681621507}\right)+55856052494\arctan\left(\frac{1}{432529546649}\right)+28184017084\arctan\left(\frac{1}{501226901209}\right)-15228272240\arctan\left(\frac{1}{539080504531}\right)+28055785558\arctan\left(\frac{1}{751830514193}\right)-47209713158\arctan\left(\frac{1}{807477925657}\right)+30892228138\arctan\left(\frac{2}{1771130530361}\right)+33546602988\arctan\left(\frac{1}{1107182624153}\right)+118029499066\arctan\left(\frac{1}{1921044951457}\right)+27434027440\arctan\left(\frac{1}{2359916741811}\right)-15461334416\arctan\left(\frac{1}{2723656442157}\right)+69826860766\arctan\left(\frac{2}{8914226121489}\right)+4670011640\arctan\left(\frac{1}{5688475754312}\right)-52562548988\arctan\left(\frac{1}{7078665458307}\right)-8856608522\arctan\left(\frac{1}{8885683084543}\right)+10131007010\arctan\left(\frac{1}{15962244871097}\right)-41902126764\arctan\left(\frac{1}{22486542112682}\right)-38615537750\arctan\left(\frac{2}{195894972911511}\right)-13505985384\arctan\left(\frac{1}{159162340999667}\right)+64077341620\arctan\left(\frac{1}{389928169608307}\right)-28465335576\arctan\left(\frac{1}{4439568777547493}\right)$$
Compact formula76051360238[104279454193] + 136439800674[108813338187] + 80541880244[157245105893] + 72624714760[195681621507] + 55856052494[432529546649] + 28184017084[501226901209] - 15228272240[539080504531] + 28055785558[751830514193] - 47209713158[807477925657] + 30892228138[1771130530361/2] + 33546602988[1107182624153] + 118029499066[1921044951457] + 27434027440[2359916741811] - 15461334416[2723656442157] + 69826860766[8914226121489/2] + 4670011640[5688475754312] - 52562548988[7078665458307] - 8856608522[8885683084543] + 10131007010[15962244871097] - 41902126764[22486542112682] - 38615537750[195894972911511/2] - 13505985384[159162340999667] + 64077341620[389928169608307] - 28465335576[4439568777547493]
Lehmer's measure1.93092
References
MRW (13Apr07) (full reference coming soon)