Show logical notation for being prime

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The discussion focuses on expressing the logical notation for a number being prime, specifically for N = (P1, P2,...Pn) + 1. It presents a trial division approach, stating that if there exists a divisor M greater than 1 and less than the square root of Pn + 1, then Pn + 1 is not prime. The condition for a number to be prime is that its only divisors are 1 and itself. The notation implies that for all integers n, if n does not divide P, then n must be either 1 or P. Overall, the thread explores the logical framework for defining prime numbers through mathematical notation.
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Homework Statement


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

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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=((Pn+1)/((M>1)\wedge(M\leq√(Pn+1))))\inN) => (Pn+1 \neg=Prime number)

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

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