"morbidly persistent erection of the penis," 1620s, from Late Latin priapismus, from Greek priapismos (also "lewdness"), from priapizein "to be lewd," from Priapos, the name of the god of male reproductive power. See priapic + -ism.
"phallic; of or relating to the cult and myths of Priapus," 1786, with -ic + Priapus (Greek Priapos), son of Dionysus and Aphrodite, the god who personified male reproductive power. His name is of unknown origin. Earlier was Priapean (1690s).
word-forming element making nouns implying a practice, system, doctrine, etc., from French -isme or directly from Latin -isma, -ismus (source also of Italian, Spanish -ismo, Dutch, German -ismus), from Greek -ismos, noun ending signifying the practice or teaching of a thing, from the stem of verbs in -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached. For distinction of use, see -ity. The related Greek suffix -isma(t)- affects some forms.
"excessive and unrestrainable venereal desire in the male," 1650s, medical Latin, from Greek satyriasis, from satyros (see satyr). Also in the same sense was satyromania (1889 as a dictionary word; 1759 in Modern Latin), and compare priapism.
<a href="https://www.etymonline.com/word/priapism">Etymology of priapism by etymonline</a>
Harper, D. (n.d.). Etymology of priapism. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/priapism