Any integer bigger than 1 is the multiple of a prime

Any integer bigger than 1 is the multiple of a prime is a basic result in number theory, which can be proved by Reductio ad absurdum.

Assume there are integers bigger than 1 that are not the multiple of a prime, and let a be the smallest of them. Therefore every integer between 1 and a is the multiple of a prime. If a was a multiple of any number between 1 and a it would therefore also be a multiple of a prime, contradictory to our assumption. But a can neither be a multiple of an integer bigger than itself. So a is only divisible by itself and 1, making it prime, again in contradiction to the assumption. So the assumption has to be false.

Claim

Statement of the claim	Any integer bigger than 1 is the multiple of a prime
Level of certainty	Proven
Nature	Theoretical
Counterclaim
Dependent on	A positive integer bigger than 1 must be a prime or a multiple of smaller primes
Dependency of	There are infinitely many primes