Basic implementation of Sieve of Eratosthenes

sieve.rs

/// Find all prime numbers less than `n`.
/// For example, `sieve(7)` should return `[2, 3, 5]`
pub fn sieve(n: usize) -> Vec<usize> {
    let mut p:usize = 2;
    let range =  p..n;
    let mut list:Vec<usize> = vec![];

    //build list
    for x in range {
        list.push(x);
    }

    // go through the list
        // check multiples of P are less then n and not in list
        // if in list remove them
        // reassign the next element in the iteration as p

    for i in p..list.len() {
        for j in p..list.len() {
            let multiple_of_p = p * j;

            let multiple_of_p_in_list = list.contains(&multiple_of_p);

            if multiple_of_p < n && multiple_of_p_in_list {
                let index = list.iter().position(|x| *x == multiple_of_p).unwrap();
                list.remove(index);
            }
        }

        p = i;
    }

    list
}