Whilst I'm not sure about the longest symphonies in existence, Cage's 'As Slow as Possible' and Jem Finer's 'Longplayer' are sure contenders to the title of longest composition. 'Longplayer' is an algorithm-based composition (muddying the issue slightly) which is intended to last
a thousand years, whilst 'As Slow as Possible' is a notated work, a current performance of which is scheduled to end after
639 years.
"A 1997 conference of musicians and philosophers discussed the implications of his instruction to play the piece "as slow as possible", given that an organ imposes virtually no time limits. A project emerged to perform the piece so that it would take a total of 639 years to play. This length was decided based on the estimated lifespan of the organ. The origin of this number is as follows: the piece was to be performed in the St. Burchardi church in Halberstadt, Germany, beginning in the year 2000; 639 years earlier, in the year 1361, the first big organ had been constructed in that church."
As Slow As Possible - Wikipedia, the free encyclopedia