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)
(\existsx=((P_n+1)/((M>1)\wedge(M\leq√(P_n+1))))\inN) => (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 <br /> \forall n \in \mathbb{N} : n \perp P \Rightarrow n \in \{1, P\}.