M000304

$$\pi=-92839355812\arctan\left(\frac{1}{102428655030}\right)+39096842928\arctan\left(\frac{1}{120563046313}\right)+175704640880\arctan\left(\frac{1}{121409547033}\right)+55957203804\arctan\left(\frac{1}{138873731225}\right)+207344234436\arctan\left(\frac{1}{202954204459}\right)+19060154296\arctan\left(\frac{1}{261002206018}\right)-148999302132\arctan\left(\frac{1}{269007136889}\right)+236142941296\arctan\left(\frac{1}{391410916593}\right)+87453565460\arctan\left(\frac{1}{548275361132}\right)+333965182760\arctan\left(\frac{1}{656902304557}\right)-64049399408\arctan\left(\frac{1}{1372432573478}\right)+127713315340\arctan\left(\frac{1}{1622274975907}\right)+1950085840\arctan\left(\frac{1}{2639669568570}\right)+18054250312\arctan\left(\frac{1}{2710120765097}\right)+123322569020\arctan\left(\frac{1}{3761284561432}\right)-123270252496\arctan\left(\frac{2}{13078246979509}\right)+146133419748\arctan\left(\frac{1}{10892900268195}\right)-153178496800\arctan\left(\frac{1}{17780261434697}\right)+71037268268\arctan\left(\frac{1}{38759264489343}\right)+37862301832\arctan\left(\frac{1}{69971515635443}\right)+54986941560\arctan\left(\frac{1}{169838669284032}\right)+234192855456\arctan\left(\frac{1}{292512967855698}\right)-32577230532\arctan\left(\frac{1}{772654028018543}\right)-170875225032\arctan\left(\frac{1}{1948025182233307}\right)$$
Compact formula- 92839355812[102428655030] + 39096842928[120563046313] + 175704640880[121409547033] + 55957203804[138873731225] + 207344234436[202954204459] + 19060154296[261002206018] - 148999302132[269007136889] + 236142941296[391410916593] + 87453565460[548275361132] + 333965182760[656902304557] - 64049399408[1372432573478] + 127713315340[1622274975907] + 1950085840[2639669568570] + 18054250312[2710120765097] + 123322569020[3761284561432] - 123270252496[13078246979509/2] + 146133419748[10892900268195] - 153178496800[17780261434697] + 71037268268[38759264489343] + 37862301832[69971515635443] + 54986941560[169838669284032] + 234192855456[292512967855698] - 32577230532[772654028018543] - 170875225032[1948025182233307]
Lehmer's measure1.93336
References
MRW (23Jan05 - corrected 5Aug13) (full reference coming soon)