M000350

$$\pi=13786448189028\arctan\left(\frac{2}{17183229925989}\right)+6823574864300\arctan\left(\frac{1}{10546511281730}\right)+12929849850028\arctan\left(\frac{1}{11244667034168}\right)-2508850296128\arctan\left(\frac{2}{23780027088431}\right)+6576582455046\arctan\left(\frac{1}{13502703082318}\right)-1262083928172\arctan\left(\frac{1}{15420002333757}\right)-4863784252872\arctan\left(\frac{1}{15962244871097}\right)+460553845570\arctan\left(\frac{1}{16904505028627}\right)+7933341153970\arctan\left(\frac{1}{24405694099301}\right)-140768585516\arctan\left(\frac{1}{33308851938318}\right)-14288182891022\arctan\left(\frac{1}{35799989948887}\right)-2814739685430\arctan\left(\frac{1}{41887379804066}\right)+2140285046394\arctan\left(\frac{1}{42859110883727}\right)+909816387054\arctan\left(\frac{1}{62174834977445}\right)+1471430327066\arctan\left(\frac{1}{68965373220440}\right)+1183652406494\arctan\left(\frac{1}{69971515635443}\right)-10161797458260\arctan\left(\frac{1}{74230400727943}\right)+3854231404012\arctan\left(\frac{1}{94465125845354}\right)+1400744325434\arctan\left(\frac{1}{211773236092865}\right)+5857776706922\arctan\left(\frac{1}{240926005152903}\right)-4989077745018\arctan\left(\frac{1}{258213230677943}\right)-2750206269076\arctan\left(\frac{1}{320714306992682}\right)-15934231047738\arctan\left(\frac{1}{370392816588001}\right)-3029585092880\arctan\left(\frac{1}{581164002419357}\right)-12232747070208\arctan\left(\frac{1}{758341235653128}\right)+9821219927188\arctan\left(\frac{1}{830202489183166}\right)+6308319836712\arctan\left(\frac{1}{961550693718259}\right)+4171791446848\arctan\left(\frac{1}{1421149505569643}\right)+2994657070372\arctan\left(\frac{1}{1427056404016693}\right)$$
Compact formula13786448189028[17183229925989/2] + 6823574864300[10546511281730] + 12929849850028[11244667034168] - 2508850296128[23780027088431/2] + 6576582455046[13502703082318] - 1262083928172[15420002333757] - 4863784252872[15962244871097] + 460553845570[16904505028627] + 7933341153970[24405694099301] - 140768585516[33308851938318] - 14288182891022[35799989948887] - 2814739685430[41887379804066] + 2140285046394[42859110883727] + 909816387054[62174834977445] + 1471430327066[68965373220440] + 1183652406494[69971515635443] - 10161797458260[74230400727943] + 3854231404012[94465125845354] + 1400744325434[211773236092865] + 5857776706922[240926005152903] - 4989077745018[258213230677943] - 2750206269076[320714306992682] - 15934231047738[370392816588001] - 3029585092880[581164002419357] - 12232747070208[758341235653128] + 9821219927188[830202489183166] + 6308319836712[961550693718259] + 4171791446848[1421149505569643] + 2994657070372[1427056404016693]
Lehmer's measure2.08734
References
MRW (4Aug06) (full reference coming soon)