M000266

$$\pi=12621778600\arctan\left(\frac{2}{10355370165}\right)+10081602604\arctan\left(\frac{2}{86479075199}\right)+8184296708\arctan\left(\frac{2}{112899039159}\right)+21112042900\arctan\left(\frac{1}{65815220307}\right)+1757429112\arctan\left(\frac{1}{71617196968}\right)+2637069840\arctan\left(\frac{1}{78535779057}\right)-3001807084\arctan\left(\frac{1}{102428655030}\right)+9939054248\arctan\left(\frac{1}{197877956739}\right)-950726620\arctan\left(\frac{1}{225891903693}\right)+4365018708\arctan\left(\frac{2}{520629831511}\right)-3154478664\arctan\left(\frac{1}{283378114193}\right)-12644336904\arctan\left(\frac{1}{324363564309}\right)-7557938312\arctan\left(\frac{1}{492806748932}\right)-10764921984\arctan\left(\frac{2}{1057852873951}\right)-2439117788\arctan\left(\frac{1}{821345641657}\right)+7727710312\arctan\left(\frac{1}{3737240479718}\right)+1623454600\arctan\left(\frac{1}{28148191112477}\right)-5982102208\arctan\left(\frac{2}{76154600377261}\right)+3319338608\arctan\left(\frac{1}{55707370528529}\right)+14432101544\arctan\left(\frac{1}{69971515635443}\right)-12601817848\arctan\left(\frac{1}{109805699900318}\right)+14306741952\arctan\left(\frac{1}{7474541196075273}\right)$$
Compact formula12621778600[10355370165/2] + 10081602604[86479075199/2] + 8184296708[112899039159/2] + 21112042900[65815220307] + 1757429112[71617196968] + 2637069840[78535779057] - 3001807084[102428655030] + 9939054248[197877956739] - 950726620[225891903693] + 4365018708[520629831511/2] - 3154478664[283378114193] - 12644336904[324363564309] - 7557938312[492806748932] - 10764921984[1057852873951/2] - 2439117788[821345641657] + 7727710312[3737240479718] + 1623454600[28148191112477] - 5982102208[76154600377261/2] + 3319338608[55707370528529] + 14432101544[69971515635443] - 12601817848[109805699900318] + 14306741952[7474541196075273]
Lehmer's measure1.85700
References
MRW (9Aug06) (full reference coming soon)