Yes, showing factorization into primes is a paradigmatic example of the use of strong induction.

oldguynewstudent: I believe your solution is correct. Whether to put the five initial cases into the base case or into the induction step is a matter of preference. You could prove

as the base case. Then, in the induction step while proving

from

you could say this: "If

or

, then we give an explicit representation. Otherwise (

) [

*the following you already have*],

, so we apply

and add a 5-cent stamp".

I personally think those initial five statements belong to the base case.

One small remark.

I would explicitly say that the first sentence is the induction hypothesis. Then there would be no ambiguity about the status of the sentence: whether it is the hypothesis or the whole statement that has to be proved in the induction step.

By the way, did you know that strong induction is not really stronger than regular one? Every proof that uses strong induction can be rewritten so that it uses only regular induction. One only has to find the appropriate induction statement

.