Show logical notation for being prime

[Painguy]

Homework Statement

Show logical notation for being prime given N=(P₁, P₂,...P_n) +1

Homework Equations

The Attempt at a Solution

I came up with the following, but I am not sure if it makes sense (I used trial division)
($\exists$x=((P_n+1)/((M>1)$\wedge$(M$\leq$√(P_n+1))))$\in$$N$) => (P_n+1 $\neg$=Prime number)

If there exists a number P_n+1 divided by a number M greater than 1 and less than the squareroot of P_n plus 1 contained in a set of integers then P_n +1 is not a prime number.

 

[pasmith]

The condition for $P$ being prime is that its only integer divisors are 1 and $P$. This is $$\forall n \in \mathbb{N} : n \perp P \Rightarrow n \in \{1, P\}.$$