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From Latin priapismus, from Priapus (“the god of procreation, the penis”)

In Greek mythology, Priapus is a minor rustic fertility god, protector of livestock, fruit plants, gardens and male genitalia. Priapus is marked by his oversized, permanent erection, which gave rise to the medical term priapism. He became a popular figure in Roman erotic art and Latin literature, and is the subject of the often humorously obscene collection of verse called the Priapeia.