1. When n = 2, the proposition obviously holds.

2. Suppose that when n

Then when n = k+ 1, if n is a prime number, the proposition holds.

If n is not a prime number, then n = st, where s and t are natural numbers greater than 1.

Obviously, both S and T are less than N. According to the inductive hypothesis, S and T can be expressed as the product of prime numbers.

Or s and t are prime numbers themselves,

Therefore, n = ST is the product of prime numbers.

That is, when n = k+ 1, the proposition also holds.

To sum up, the proposition holds for natural numbers greater than 2.