Prime Implicants in Boolean Function
An implicant of $F$ is a partial assignment to the variables of $F$ which guarantees that $F$ is satisfied. A prime implicant is a minimal implicant, that is, an implicant that is no longer an implicant if we remove any single variable.

Let us start by finding all the implicants of $F$. Let $\alpha$ be any partial assignment to the variables of $F$, and suppose that $\alpha$ assigns $k$ variables to true. We can complete $\alpha$ to an assignment by assigning the rest of the variables to false, in which case we get an assignment containing $k$ true variables. Hence $\alpha$ can only be an implicant if $k \geq 3$. Conversely, it is not hard to check that if $\alpha$ assigns at least 3 variables to true then it is an implicant of $F$.

When is an implicant a prime implicant? It must be a partial assignment with at least 3 true variables, such that if we remove any single variable, there are at most 2 true variables. Can you figure out how all such implicants look like? Give it a try.

As an aside, your function is monotone, and so its prime implicants are also known as minterms. Minterms have a special structure – they cannot be arbitrary partial assignments. I'll let you figure out the special property that minterms have.