Has Prudentius mistaken Cyprian of Carthage for Cyprian of Antioch?

In his Peristephano (a collection of confessional poems on various martyrs), Prudentius asserts that prior to conversion Cyprian of Carthage practiced the dark arts: > He was pre-eminent among young men for skill in perverse arts, would > violate [a woman's] modesty by a trick, count nothing holy, and often > practice a magic spell amid the tombs to raise passion in a wife and > break the law of wedlock. The whole Peristaphano here: https://archive.org/details/prudentius00pruduoft/page/328/mode/2up Yet according to the basic recount of his early life in the wiki page on [Cyprian of Carthage](https://en.wikipedia.org/wiki/Cyprian) , it makes no mention of this. It was well documented that another Cyprian, the veritable Cyprian of Antioch, *did* practice such devious acts. Compared to the Cyprian of Antioch, the early life of Cyprian of Cartage seems uneventful: an unassuming rhetorician/lawyer. Later on in Cyprian of Carthage's wiki, it in fact points out that he is often conflated with Cyprian of Antioch. All this leads me to believe that Prudentius is one of those authors who mistaken the identity of these two early church figures that share the name Cyprian. That said, I cannot prove it, it's all still circumstantial evidence.

Question

Do we have any "hard" textual evidence or authoritative testimony that can assure us that Prudentius has indeed mistaken Cyprian of Carthage for Cyprian of Antioch?