M000273

$$\pi=\frac{118194530516}{7}\arctan\left(\frac{2}{10355370165}\right)\frac{-713050640}{7}\arctan\left(\frac{1}{32863722478}\right)+\frac{10174006956}{7}\arctan\left(\frac{2}{86479075199}\right)\frac{-967982396}{7}\arctan\left(\frac{2}{112899039159}\right)\frac{-46669106208}{7}\arctan\left(\frac{1}{71617196968}\right)-1727948868\arctan\left(\frac{1}{78535779057}\right)\frac{-20299598948}{7}\arctan\left(\frac{1}{102428655030}\right)+9939054248\arctan\left(\frac{1}{197877956739}\right)\frac{-37923267936}{7}\arctan\left(\frac{1}{225891903693}\right)\frac{-29842080316}{7}\arctan\left(\frac{1}{277386771993}\right)+\frac{7760729668}{7}\arctan\left(\frac{1}{283378114193}\right)\frac{-30252298976}{7}\arctan\left(\frac{1}{324363564309}\right)+\frac{12745685780}{7}\arctan\left(\frac{1}{469027618483}\right)\frac{-23776538508}{7}\arctan\left(\frac{1}{492806748932}\right)\frac{-16360773876}{7}\arctan\left(\frac{1}{821345641657}\right)\frac{-29842080316}{7}\arctan\left(\frac{1}{2961447369272}\right)+\frac{42061337044}{7}\arctan\left(\frac{1}{3737240479718}\right)+\frac{9938080920}{7}\arctan\left(\frac{1}{28148191112477}\right)+3319338608\arctan\left(\frac{1}{55707370528529}\right)+\frac{12924571140}{7}\arctan\left(\frac{1}{69971515635443}\right)\frac{-58370644620}{7}\arctan\left(\frac{1}{109805699900318}\right)+3959621036\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula118194530516/7[10355370165/2] - 713050640/7[32863722478] + 10174006956/7[86479075199/2] - 967982396/7[112899039159/2] - 46669106208/7[71617196968] - 1727948868[78535779057] - 20299598948/7[102428655030] + 9939054248[197877956739] - 37923267936/7[225891903693] - 29842080316/7[277386771993] + 7760729668/7[283378114193] - 30252298976/7[324363564309] + 12745685780/7[469027618483] - 23776538508/7[492806748932] - 16360773876/7[821345641657] - 29842080316/7[2961447369272] + 42061337044/7[3737240479718] + 9938080920/7[28148191112477] + 3319338608[55707370528529] + 12924571140/7[69971515635443] - 58370644620/7[109805699900318] + 3959621036[7474541196075273]
Lehmer's measure1.86637
References
MRW (9Aug06) (full reference coming soon)