Oh No$!$ Grace was studying CIS $1600$ in Van Pelt when a terrifying snow storm prevents her

from leaving the library! Now that Grace has endless time on her hands, she decides to come up

with a new mathematical term: A Grace Number. A number n in N is called a Grace Number if

the sum of all of n$$s factors other than n itself is equal to n$.$ For example, $6$ is a Grace Number

because its factors are $1,2,3,$ and $6,$ and $1+2+3=6.$ Help Grace prove that there are no

prime numbers that are Grace Numbers.

Note: Grace Number is not a formal mathematical term. It was defined for the context of this

problem only.