M000295

$$\pi=143303585484\arctan\left(\frac{1}{102428655030}\right)+177654726720\arctan\left(\frac{1}{121409547033}\right)-20156995508\arctan\left(\frac{1}{138873731225}\right)-71666320764\arctan\left(\frac{1}{202954204459}\right)+197046098368\arctan\left(\frac{1}{218123852367}\right)-118981813216\arctan\left(\frac{1}{250645741818}\right)-23807459608\arctan\left(\frac{1}{261002206018}\right)+7129268172\arctan\left(\frac{1}{269007136889}\right)+85503479620\arctan\left(\frac{1}{548275361132}\right)+99772327304\arctan\left(\frac{1}{656902304557}\right)+134946784800\arctan\left(\frac{1}{1372432573478}\right)+10681587964\arctan\left(\frac{1}{1622274975907}\right)+18054250312\arctan\left(\frac{1}{2710120765097}\right)-73723529348\arctan\left(\frac{1}{3761284561432}\right)-43255881504\arctan\left(\frac{2}{13078246979509}\right)+117031727376\arctan\left(\frac{1}{8589803519307}\right)+27151606532\arctan\left(\frac{1}{10892900268195}\right)+6850245184\arctan\left(\frac{1}{17780261434697}\right)+72987354108\arctan\left(\frac{1}{38759264489343}\right)+117876672824\arctan\left(\frac{1}{69971515635443}\right)+54986941560\arctan\left(\frac{1}{169838669284032}\right)-38967442224\arctan\left(\frac{1}{342036110675693}\right)+86404582684\arctan\left(\frac{1}{772654028018543}\right)-12796568888\arctan\left(\frac{1}{1948025182233307}\right)$$
Compact formula143303585484[102428655030] + 177654726720[121409547033] - 20156995508[138873731225] - 71666320764[202954204459] + 197046098368[218123852367] - 118981813216[250645741818] - 23807459608[261002206018] + 7129268172[269007136889] + 85503479620[548275361132] + 99772327304[656902304557] + 134946784800[1372432573478] + 10681587964[1622274975907] + 18054250312[2710120765097] - 73723529348[3761284561432] - 43255881504[13078246979509/2] + 117031727376[8589803519307] + 27151606532[10892900268195] + 6850245184[17780261434697] + 72987354108[38759264489343] + 117876672824[69971515635443] + 54986941560[169838669284032] - 38967442224[342036110675693] + 86404582684[772654028018543] - 12796568888[1948025182233307]
Lehmer's measure1.92926
References
MRW (18Sep04) (full reference coming soon)