# Math Help - prime numbers

1. ## prime numbers

In proving that there are infinitely many primes, one could define a function $f: \mathbb{N} \to \mathbb{N}$ by $f(n) = n!+1$ and show that (1) $f(n) > n$ for all $n \in \mathbb{N}$, (2) $f(n)$ is either prime or composite and (3) $f(n)$ has prime factors greater than $n$ if $f(n)$ is composite.

So in general can we find a function $f: \mathbb{N} \to \mathbb{N}$ defined by $f(n) = n! + a$ and choose $a$ accordingly to satisfy the above conditions? Could we define a function $f: \mathbb{N} \to \mathbb{N}$ in another way that satisfies the above condtions?

2. keep in mind that n! +a where a is between 2 and n
are always composite numbers

3. Uggg, just never mind. No helpful thoughts... I'm thinking some more.