  Motivated by a conjecture of Frid, Puzynina, and Zamboni, we investigate
infinite words with the property that for infinitely many n, every length-n
factor is a product of two palindromes. We show that every Sturmian word has
this property, but this does not characterize the class of Sturmian words. We
also show that the Thue-Morse word does not have this property. We investigate
finite words with the maximal number of distinct palindrome pair factors and
characterize the binary words that are not palindrome pairs but have the
property that every proper factor is a palindrome pair.
