I'm trying to prove $f(n) = 2n$ is primitive recursive. I understand that for something to be primitive recursive it must have the following properties:

$0(x)=x$ the zero function

$s(x)= x+1$ the successor

$p^i (x1,...x2,x3)= xi =$ projection

So would the primitive recursive definition of $f(n)=2n$:

$f(2,n)$

$s(2\*f(x))$

$p^i (2)$

Is this correct? If not could someone give me an intuitive explanation? I'm really struggling to understand this!

Thank you in advance!

**----EDIT: 
Ive now got a different answer: 
$f(0,m)$
$f(2,n)=f(mult(2,n))$**