(related to Proposition: Natural Numbers and Products of Prime Numbers)
We prove it by induction. Base case $n=2$ * Since $2$ is a prime number, it is a product of prime numbers (consisting of only one factor).
Induction step $n-1\to n$ * Let $n > 2$ and the proposition be proven for $2,3,\ldots,n-1.$ * If $n$ is a prime number, then $n$ is a product of prime numbers (consisting of only one factor). * Otherwise $n$ can be written as a product $n=n_1n_2$ with $1 < n_1 < n$ and $1 < n_2 < n.$ * By hypothesis, $n_1$ and $n_2$ are products of prime numbers. * Thus, $n$ is a product of prime numbers.
