Define a number $n$ to be composite if it can be written as $a\cdot b$ for some $a,b$ where $a,b\neq 1$.

Define $p$ to be prime if $p=a\cdot b$ implies $a=1$ or $b=1$.

The theorem that every composite number has a prime factor seems to require a bit more induction than just everything is either 0 or a successor. So what is a model of Robinson Arithmetic where that theorem fails?