M000299

$$\pi=141102100880\arctan\left(\frac{1}{104279454193}\right)+127399961116\arctan\left(\frac{1}{108813338187}\right)-33024050288\arctan\left(\frac{1}{113201494333}\right)-241091212\arctan\left(\frac{1}{157245105893}\right)+42329196788\arctan\left(\frac{1}{166846193428}\right)+38242514920\arctan\left(\frac{1}{195681621507}\right)+49849123712\arctan\left(\frac{2}{393707737329}\right)+35747263884\arctan\left(\frac{1}{432529546649}\right)+1748814192\arctan\left(\frac{1}{501226901209}\right)+24465143824\arctan\left(\frac{2}{1771130530361}\right)-4159323188\arctan\left(\frac{1}{1273911086135}\right)+122570693772\arctan\left(\frac{1}{1921044951457}\right)+50182226604\arctan\left(\frac{1}{2359916741811}\right)+3793263216\arctan\left(\frac{1}{2723656442157}\right)+22617147608\arctan\left(\frac{2}{8914226121489}\right)+124211740732\arctan\left(\frac{1}{5688475754312}\right)-49422053688\arctan\left(\frac{2}{14158549277239}\right)-59981805880\arctan\left(\frac{1}{12083508387829}\right)-48757956260\arctan\left(\frac{1}{15962244871097}\right)+1960938488\arctan\left(\frac{1}{159162340999667}\right)-51103729404\arctan\left(\frac{1}{180481359172943}\right)-7400483336\arctan\left(\frac{1}{389928169608307}\right)-3732253164\arctan\left(\frac{1}{4204987898062723}\right)-66635209176\arctan\left(\frac{1}{4439568777547493}\right)$$
Compact formula141102100880[104279454193] + 127399961116[108813338187] - 33024050288[113201494333] - 241091212[157245105893] + 42329196788[166846193428] + 38242514920[195681621507] + 49849123712[393707737329/2] + 35747263884[432529546649] + 1748814192[501226901209] + 24465143824[1771130530361/2] - 4159323188[1273911086135] + 122570693772[1921044951457] + 50182226604[2359916741811] + 3793263216[2723656442157] + 22617147608[8914226121489/2] + 124211740732[5688475754312] - 49422053688[14158549277239/2] - 59981805880[12083508387829] - 48757956260[15962244871097] + 1960938488[159162340999667] - 51103729404[180481359172943] - 7400483336[389928169608307] - 3732253164[4204987898062723] - 66635209176[4439568777547493]
Lehmer's measure1.93219
References
MRW (8Aug06) (full reference coming soon)