Exercise in FOL Section 4.1, ex. $3.(2)$ of Introduction to mathematical Logic by Richard Hodel.
Express the following statements:

(2) For every natural number $a$ greater than 1, there is a prime $p$ that divides $a$.

Is the following, in language of FOL, correct:
$\forall a\in \Bbb N \left[a>1\Rightarrow\left(\exists p\in \Bbb N(\forall b\in \Bbb N \lnot(b \vert p)\; \land\; p \vert a\right) \right].$
Edit
Reply to @Bram28:
Writing instead of $(\forall b\in \Bbb N \lnot(b \vert p))$ this:
$(\forall b\in \Bbb N(b>1\; \land b\neq p))$
would work?

No.
You always have that $p|p$, as well as $1|p$, whether $p$ is prime or not.
Hence, the $\forall b\in \Bbb N \lnot(b \vert p)$ part will always be false.
It'll take a bit more work to express that $p$ is a prime ... but take into consideration what I just said, and try again!
Also, the rest of the expression has the right format, good job!
