Powers of two wouldn't actually work there. Using primes lets you use division as a test for presence in the original set. The task is 'detect presence in the

Powers of two wouldn't actually work there. Using primes lets you use division as a test for presence in the original set. The task is 'detect presence in the set', and integers are uniquely identified by their prime factorization. Powers of two would just give you another power of two. That wouldn't actually preserve the information you're looking for. Consider an original string 'bb', and a test string 'c'. With powers of two, you'd have 2*2, and your test would be a division by 4, which would be successful by having no remainder, indicating that 'c' is a subset of 'bb'.