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every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes

But clearly, this statement does not reveal the structure of the statement in the formal language the first order theory. Can you re-state this theorem by only using the first order language elements such as "for all" "there exists" and variable and so on? You can obviously use sets.

I'm having trouble especially on stating the concepts of "a product" and "rearrangement" in the formal language.