Proofs in Discrete Math

$\mathrm{\forall}n\in N+$, n composite $\to \mathrm{\exists}p\in N+$, p is prime and $p\le \sqrt{n}$ and p|n.

Am I supposed to prove that $p\le \sqrt{n}$ and p|n when n is composite and p is prime? Could someone fix my translation if I'm wrong?

$\mathrm{\forall}n\in N+$, n composite $\to \mathrm{\exists}p\in N+$, p is prime and $p\le \sqrt{n}$ and p|n.

Am I supposed to prove that $p\le \sqrt{n}$ and p|n when n is composite and p is prime? Could someone fix my translation if I'm wrong?