In which story we can find information about the Plant of Everlasting Youth and what kind of plant it was?
Did it give immortality or something else?
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The information about the Plant of Everlasting Youth form the Sumerian mythos can be found on the second half of The Epic of Gilgamesh.
In the Tablet eleven Utnapishtim's wife asks her husband to offer a parting gift to Gilgamesh, so he learns that
at the bottom of the sea there lives a boxthorn-like plant that will make him young again
(Note: there is already a related question with an answer that states that this plant was most probably a species of Rhamnus).
The Tablen eleven states that
if you can possess this plant, you'll be again as you were in your youth [...] with it a man can regain his vigour
and that Gilgamesh was planing to test this plant on a man of old age to see it the plan would rejuvenate him.
The epic explains how Gilgamesh loses the plant, so he can never make use of it. It is not described if it rejuvenating effects ara permanent or just a work-only-once-per-take property.