The unique prime factorization of 15 is 3⋅5. Let's call a number an Igelau prime if it is the number 1 or a prime number. Then an Igelau prime factorization of

The unique prime factorization of 15 is 3⋅5. Let's call a number an Igelau prime if it is the number 1 or a prime number. Then an Igelau prime factorization of 15 is 3⋅5. Another Igelau prime factorization of 15 is 1⋅3⋅5. Another Igelau prime factorization of 15 is 1²⋅3⋅5. And so on. There are infinitely many Igelau prime factorizations of 15, thus there is no uniqueness. Edit: Clarifying what Igelau primes are.