Dexter's Lab

Dr. Dexter is a mad-scientist, who has made 'weird' rules to be followed in his lab.

There are $3$ bulbs in his lab, say $A$ , $B$ and $C$ .

$A$ emits $4W$ of power, $B$ emits $2W$ , and $C$ , $1W$ .

Now, whenever the bulbs are switched on, in such a way that the total power emitted $($ in watts $)$ is a 'prime', a buzzer starts buzzing, prompting the user, to switch them otherwise. $($ Dr. Dexter's hatred for primes $!$ $)$

It is known that, the switches are connected to the buzzer, via a 'logic' circuit, with the use of $'N'$ number of one particular universal gate. What is the minimum value of $'N'$ $?$

$($ Assuming no electrical interaction 'between' the circuits. $)$