"the prime example of" is correct and usable in written English.
It is often used to introduce an illustrative sample of something. For example, "The prime example of a successful business is Amazon."
Britain is the prime example of this.
Portugal is the prime example of decriminalisation.
The prime example of this phenomenon is, of course, Apple.
Automata are the prime example of general computational systems over discrete spaces.
The vertebrate family is the prime example of the "evolve more capable individual" strategy.
Monoliths are the prime example of such catalysts because of their wide practical applications.
The prime example of the sterility cited by Baldwin was Native Son.
"The Pretender," the album's first single, is the prime example of his scientific process.
The prime example, of course, is music, the most accessible of the arts.
He identifies Arsenal as the prime example of how a board-manager relationship should be conducted.
In Orthodoxy, they are viewed as the prime example of happy marriage.
