M000297

$$\pi=-1950085840\arctan\left(\frac{2}{112899039159}\right)-51792427044\arctan\left(\frac{1}{120563046313}\right)+34351141236\arctan\left(\frac{1}{121409547033}\right)+55957203804\arctan\left(\frac{1}{138873731225}\right)+114504878624\arctan\left(\frac{1}{202954204459}\right)+255203095592\arctan\left(\frac{1}{261002206018}\right)+85193553324\arctan\left(\frac{1}{269007136889}\right)+52414315512\arctan\left(\frac{1}{343123176943}\right)+230757150944\arctan\left(\frac{1}{548275361132}\right)+192611683116\arctan\left(\frac{1}{656902304557}\right)+81204271916\arctan\left(\frac{1}{1372432573478}\right)+92839355812\arctan\left(\frac{1}{1374662101743}\right)+75298999828\arctan\left(\frac{1}{1622274975907}\right)+20004336152\arctan\left(\frac{1}{2710120765097}\right)-18030930624\arctan\left(\frac{1}{3761284561432}\right)+20033332988\arctan\left(\frac{2}{13078246979509}\right)+148083505588\arctan\left(\frac{1}{10892900268195}\right)-9874911316\arctan\left(\frac{1}{17780261434697}\right)+20573038596\arctan\left(\frac{1}{38759264489343}\right)+130701657644\arctan\left(\frac{1}{69971515635443}\right)+54986941560\arctan\left(\frac{1}{169838669284032}\right)-123466500504\arctan\left(\frac{1}{772654028018543}\right)-27571639548\arctan\left(\frac{1}{1948025182233307}\right)-145253671324\arctan\left(\frac{1}{7411710404595173}\right)$$
Compact formula- 1950085840[112899039159/2] - 51792427044[120563046313] + 34351141236[121409547033] + 55957203804[138873731225] + 114504878624[202954204459] + 255203095592[261002206018] + 85193553324[269007136889] + 52414315512[343123176943] + 230757150944[548275361132] + 192611683116[656902304557] + 81204271916[1372432573478] + 92839355812[1374662101743] + 75298999828[1622274975907] + 20004336152[2710120765097] - 18030930624[3761284561432] + 20033332988[13078246979509/2] + 148083505588[10892900268195] - 9874911316[17780261434697] + 20573038596[38759264489343] + 130701657644[69971515635443] + 54986941560[169838669284032] - 123466500504[772654028018543] - 27571639548[1948025182233307] - 145253671324[7411710404595173]
Lehmer's measure1.93174
References
MRW (8Aug06) (full reference coming soon)