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I do not think that any one particular species is longest lived. Most parrots of this species can live well into their 60's and 70's and some even longer. In captivity all species can have a rather lesser of a life than they can in the wild while trying to replicate their natural environment when it comes to foods, vitamins, minerals and a healthy life with flight (which is incredibly important to any bird)
If you are asking to due wanting to know just how long your feathered Friend may be around, expect most of the duration within your lifetime possibly. It is a very looooooong committment both emotionally, physically and financially to own such a long lived bird.
Here is a good reference that I have seen before. It suggest captive birds, hence living alot shorter than that could in the wild.