M000302

$$\pi=\frac{-406893117716}{3}\arctan\left(\frac{2}{181932669739}\right)+311931187048\arctan\left(\frac{1}{121409547033}\right)+\frac{2718889568}{3}\arctan\left(\frac{1}{138873731225}\right)+\frac{979498667080}{3}\arctan\left(\frac{1}{202954204459}\right)\frac{-544233194908}{3}\arctan\left(\frac{1}{218123852367}\right)-9027125156\arctan\left(\frac{1}{239811563516}\right)-4414066008\arctan\left(\frac{1}{250645741818}\right)+214355159964\arctan\left(\frac{1}{261002206018}\right)+\frac{57496305140}{3}\arctan\left(\frac{1}{269007136889}\right)+103557729932\arctan\left(\frac{1}{548275361132}\right)+\frac{334525830844}{3}\arctan\left(\frac{1}{656902304557}\right)+\frac{79191363088}{3}\arctan\left(\frac{1}{1372432573478}\right)+\frac{484290145516}{3}\arctan\left(\frac{1}{3761284561432}\right)+107420366328\arctan\left(\frac{2}{13078246979509}\right)-15590270144\arctan\left(\frac{1}{8589803519307}\right)+141719353740\arctan\left(\frac{1}{10892900268195}\right)-125249335172\arctan\left(\frac{1}{16081448958596}\right)-107717502024\arctan\left(\frac{1}{17780261434697}\right)+143303585484\arctan\left(\frac{2}{61788694303449}\right)+\frac{223025799056}{3}\arctan\left(\frac{1}{38759264489343}\right)+\frac{598935317864}{3}\arctan\left(\frac{1}{169838669284032}\right)+\frac{647684546248}{3}\arctan\left(\frac{1}{342036110675693}\right)\frac{-948374743208}{3}\arctan\left(\frac{1}{772654028018543}\right)\frac{-29362581508}{3}\arctan\left(\frac{1}{1948025182233307}\right)$$
Compact formula- 406893117716/3[181932669739/2] + 311931187048[121409547033] + 2718889568/3[138873731225] + 979498667080/3[202954204459] - 544233194908/3[218123852367] - 9027125156[239811563516] - 4414066008[250645741818] + 214355159964[261002206018] + 57496305140/3[269007136889] + 103557729932[548275361132] + 334525830844/3[656902304557] + 79191363088/3[1372432573478] + 484290145516/3[3761284561432] + 107420366328[13078246979509/2] - 15590270144[8589803519307] + 141719353740[10892900268195] - 125249335172[16081448958596] - 107717502024[17780261434697] + 143303585484[61788694303449/2] + 223025799056/3[38759264489343] + 598935317864/3[169838669284032] + 647684546248/3[342036110675693] - 948374743208/3[772654028018543] - 29362581508/3[1948025182233307]
Lehmer's measure1.93285
References
MRW (8Aug06) (full reference coming soon)