2855649748
501359906929152571833851080212811049755339847366927914398892041851355831303575
673710465224807454744982583885183287167357146092090743402851746571565499082292
999884612996137479952358336507860770516087879631202738350102895965881076822440
14681214726789035888008851819053742866660552775722734105313225337

Taken from
The Favorite mathematical constants of Steven Finch, Mathsoft Inc.

The constant is given by this (see z below)...

124 1/3
a := - --- 11
363

2501 1/2
b := ----- 33
11979

/ 31 1/3 // 2501 1/2 \1/3 / 2501 1/2 \1/3\\1/3
c := |1/4 - --- 11 ||----- 33 + 1| - |----- 33 - 1| ||
\ 242 \\11979 / \11979 / //

1/4 7/12
3 11
z1 := 3/44 ------------------------------------------------------------------
/ 31 1/3 // 2501 1/2 \1/3 / 2501 1/2 \1/3\\2/3
|1/4 - --- 11 ||----- 33 + 1| - |----- 33 - 1| ||
\ 242 \\11979 / \11979 / //

1/3 1/2 1/3 1/3 2/3 1/2 1/2 2
z2 := (1 - (1 - %1 ) + (2 + %1 + 2 (1 + %1 + %1 ) ) )

31 1/3 // 2501 1/2 \1/3 / 2501 1/2 \1/3\
%1 := 1/4 - --- 11 ||----- 33 + 1| - |----- 33 - 1| |
242 \\11979 / \11979 / /

1/3 1/2 1/3 1/3 2/3 1/2 1/2 2
z3 := (- 1 - (1 - %1 ) + (2 + %1 + 2 (1 + %1 + %1 ) ) )

31 1/3 // 2501 1/2 \1/3 / 2501 1/2 \1/3\
%1 := 1/4 - --- 11 ||----- 33 + 1| - |----- 33 - 1| |
242 \\11979 / \11979 / /

1/3 1/2
z4 := 1/(1/33 (1089 + 372 11 )

/ 124 1/3 / 124 1/3 15376 2/3\1/2\1/2
+ |2 - --- 11 + 2 |1 - --- 11 + ------ 11 | | )^1/2
\ 363 \ 363 131769 / /

1/4 7/12
z := 3/44 3 11

1/3 1/2