Any word which has no known rhyme (in the same language). A portmanteau of “prime” and “rhyme”.A “prime number” is a number whose only divisors are 1 and the number itself: 2, 3, 5, 7, 11, 23, 101, etc.
Thus, a “prhyme” is a word whose only rhyme is the word itself. (Maybe there should be a word-equivalent of the number 1, which rhymes with everything? I guess it would be <whitespace>.)
(Looks like Prhyme is also the name of a metal/ska band and a rap/hip-hop artist.)