Disproving using a Constructive Proof

Question

I cannot find the n to prove the negation for the following:

Disprove (Prove the negation) of:

For every positive integer n, $3^n + 2$ is prime

The way in which I have written the negation is:

There exists a positive integer n, such that $3^n + 2$ is not prime

But I have not been able to find such n.

Answer 1

$3^5+2=243+2=245$ which is not prime since it is divisible by $5$ and $7^2$