Any integer bigger than 1 is the multiple of a prime
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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.
| Statement of the claim | Any integer bigger than 1 is the multiple of a prime |
| Level of certainty | Proven |
| Nature | Theoretical |
| Counterclaim | There are integers bigger than 1 that are not multiples of primes |
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