Some operations preserving primitivity of words

We investigate some operations where essentially, from a given word w , the word w w ′ is constructed where w ′ is a modified copy of w or a modified mirror image of w . We study whether w w ′ is a primitive word provided that w is primitive. For instance, we determine all cases with an edit distance of w and w ′ at most 2 such that the primitivity of w implies the primitivity of w w ′ . The operations are chosen in such a way that in the case of a two-letter alphabet, all primitive words of length ≤ 11 can be obtained from single letters.