One is not Prime/Proof 2

Proof
From Divisor Sum of Prime Number, the sum $\map {\sigma_1} p$ of all the positive integer divisors of a prime number $p$ is $p + 1$.

But from Divisor Sum of 1, $\map {\sigma_1} 1 = 1$.

If $1$ were to be classified as prime, then $\map {\sigma_1} 1$ would be an exception to the rule that $\map {\sigma_1} p = p + 1$.