Prime Number has 4 Integral Divisors

Theorem
Every prime number $p$ has exactly four integral divisors: $1, -1, p, -p$.

Proof

 * From the definition of a prime number, $1$ and $p$ divide $p$.

Also, we have $-1 \backslash p$ and $-p \backslash p$ from One Divides All Integers and Every Integer Divides Its Negative.


 * Now suppose $x < 0: x \backslash p$ where $x \ne -1$ and $x \ne -p$.

Then $\left|{x}\right| \backslash x \backslash p$ and $\left|{x}\right|$ is therefore a positive integer other than $1$ and $p$ that divides $p$, which is a contradiction of the conditions of $p$ being a prime.

So $-1$ and $-p$ are the only negative integers that divide $p$, and the result follows.