This is false. $-2$ is prime. One of the two following statements (depends a bit on context) is the definition of primarily.
Indivisibility: A number $p$ is prime if it doesn’t have any factors other than itself and $1$, up to unit multiples.
Note: “up to unit multiples” allows us to ignore the fact that $-1|7$ or $i|3i$
Primality: A number $p$ is prime if whenever $p|ab$ ether $p|a$ or $p|b$.
In the integers these definitions are equivalent, but for other sets they might not be. In other sets, we call the second the definition of primality usually. However, $-7$ is a prime integer according to both of these definitions. Although lay people might claim that there aren’t any negative primes, but there’s no mathematical basis for this claim.