If a number is not divisible by 2, 3 and 5, is enough to say that number is prime?

Question

I'm Computer Science student. Last day, my teacher say this to the class room: "If a number is not divisible by 2, 3, and 5, mean that number is prime. This because odd numbers are divisible by 3 or 5, and even numbers by 2".

That can be true? If it's or not, why?

Edit: I'm not an mathemathician. I necer belive the words of my teacher. I just want an professional clarify.

Answer 1

$49$ is not divisible by any of those number but it is not a prime.

In general, take a prime number that is not $2,3,$ or $5$, consider $p^n$ where $n \ge 2$ works as a counter example.