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The Giant Pacific Octopus is the longest lived octopus in captivity with records of them living 6 years, but they might be able to live longer. It's hard to say which octopus is the most impressive, everyone will have a different answer. Some of the most interesting ones aren't found in the pet trade.
of the ones commonly kept by TONMO folks, bimacs and briareus tend to last the longest. vulgaris can live for quite a while, too, but needs a larger tank than most people are inclined to have at home... also, a lot of short-lived dwarf species are sold as "baby vulgaris" so it's pretty common to get a dwarf that will den up and lay eggs less than a month after it's bought, even if you think you're buying a vulgaris.
The bigger the octopus is supposed to get full grown, the longer it will live. In home aquaria, you can prolong their life by cooling down the tank and by feeding infrequently (don't starve your octo though!). The giant pacific octopus is (I believe) the biggest of all octopuses so far discovered; they can live much longer than smaller octopuses.