# Thread: The natural number p is prime

1. ## The natural number p is prime

Question: Using quantifiers, give a formal expression for the following statement:

"The natural number p is prime"

Thanks all

2. A prime $p$ is a natural number whose unique positive divisors are $1$ and $p.$

So we can write for $F(p)$: "the natural number $p$ is a prime"

$F(p)$: $p\in\mathbb{N}\wedge\forall k(k\in\mathbb{N}\Rightarrow(k|p\Rightarrow (k=1\vee k=p)))$

What you call formal may depend on what symbols you can use. If only a symbol $\times$ for multiplication is allowed (and the division one $|$ isn't), it becomes:

$F(p)$: $p\in\mathbb{N}\wedge\forall k(k\in\mathbb{N}\Rightarrow(\exists n(n\in\mathbb{N}\wedge n\times k=p)\Rightarrow (k=1\vee k=p)))$