I would like to make an iterator that generates a stream of prime numbers. My general thought process was to wrap an iterator with successive filters so for example you start with

```
let mut n = (2..N)
```

Then for each prime number you mutate the iterator and add on a filter

```
let p1 = n.next()
n = n.filter(|&x| x%p1 !=0)
let p2 = n.next()
n = n.filter(|&x| x%p2 !=0)
```

I am trying to use the following code, but I can not seem to get it to work

```
struct Primes {
base: Iterator<Item = u64>,
}
impl<'a> Iterator for Primes<'a> {
type Item = u64;
fn next(&mut self) -> Option<u64> {
let p = self.base.next();
match p {
Some(n) => {
let prime = n.clone();
let step = self.base.filter(move |&: &x| {x%prime!=0});
self.base = &step as &Iterator<Item = u64>;
Some(n)
},
_ => None
}
}
}
```

I have toyed with variations of this, but I can't seem to get lifetimes and types to match up. Right now the compiler is telling me

- I can't mutate self.base
- the variable prime doesn't live long enough

Here is the error I am getting

```
solution.rs:16:17: 16:26 error: cannot borrow immutable borrowed content `*self.base` as mutable
solution.rs:16 let p = self.base.next();
^~~~~~~~~
solution.rs:20:28: 20:37 error: cannot borrow immutable borrowed content `*self.base` as mutable
solution.rs:20 let step = self.base.filter(move |&: &x| {x%prime!=0});
^~~~~~~~~
solution.rs:21:30: 21:34 error: `step` does not live long enough
solution.rs:21 self.base = &step as &Iterator<Item = u64>;
^~~~
solution.rs:15:39: 26:6 note: reference must be valid for the lifetime 'a as defined on the block at 15:38...
solution.rs:15 fn next(&mut self) -> Option<u64> {
solution.rs:16 let p = self.base.next();
solution.rs:17 match p {
solution.rs:18 Some(n) => {
solution.rs:19 let prime = n.clone();
solution.rs:20 let step = self.base.filter(move |&: &x| {x%prime!=0});
...
solution.rs:20:71: 23:14 note: ...but borrowed value is only valid for the block suffix following statement 1 at 20:70
solution.rs:20 let step = self.base.filter(move |&: &x| {x%prime!=0});
solution.rs:21 self.base = &step as &Iterator<Item = u64>;
solution.rs:22 Some(n)
solution.rs:23 },
error: aborting due to 3 previous errors
```

Why won't Rust let me do this?