Show logical notation for being prime

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SUMMARY

The discussion focuses on expressing the logical notation for determining if a number is prime, specifically for the number Pn+1 derived from a sequence of prime numbers (P1, P2,..., Pn). The proposed logical notation states that if there exists a divisor M, where M is greater than 1 and less than or equal to the square root of Pn+1, then Pn+1 is not a prime number. The condition for a number to be prime is defined as having only two integer divisors: 1 and itself, represented as ∀ n ∈ ℕ : n ⊥ P ⇒ n ∈ {1, P}.

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  • Understanding of prime numbers and their properties
  • Familiarity with logical notation and quantifiers
  • Basic knowledge of trial division as a method for primality testing
  • Concept of square roots in relation to integer sets
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  • Study the principles of number theory related to prime numbers
  • Learn about logical quantifiers and their applications in mathematics
  • Explore advanced primality testing algorithms beyond trial division
  • Investigate the implications of the Fundamental Theorem of Arithmetic
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Homework Statement


Show logical notation for being prime given N=(P1, P2,...Pn) +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)
([itex]\exists[/itex]x=((Pn+1)/((M>1)[itex]\wedge[/itex](M[itex]\leq[/itex]√(Pn+1))))[itex]\in[/itex][itex]N[/itex]) => (Pn+1 [itex]\neg[/itex]=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 [itex]P[/itex] being prime is that its only integer divisors are 1 and [itex]P[/itex]. This is [tex] \forall n \in \mathbb{N} : n \perp P \Rightarrow n \in \{1, P\}.[/tex]
 

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