#### Faster Perfect Numbers

S
```use super::{mersenne_primes::is_mersenne_prime, prime_numbers::prime_numbers};
use std::convert::TryInto;

/*
Generates a list of perfect numbers till `num` using the Lucas Lehmer test algorithm.
url : https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
*/
pub fn generate_perfect_numbers(num: usize) -> Vec<usize> {
let mut results = Vec::new();
let prime_limit = get_prime_limit(num);

for i in prime_numbers(prime_limit).iter() {
let prime = *i;
if is_mersenne_prime(prime) {
results.push(
(2_usize.pow(prime.try_into().unwrap()) - 1)
* (2_usize.pow((prime - 1).try_into().unwrap())),
);
}
}
results.into_iter().filter(|x| *x <= num).collect()
}

// Gets an approximate limit for the generate_perfect_numbers function
fn get_prime_limit(num: usize) -> usize {
(((num * 8 + 1) as f64).log2() as usize) / 2_usize
}

#[cfg(test)]
mod tests {
use super::*;

#[test]
fn perfect_numbers_till_n() {
let n = 335564540;
assert_eq!(generate_perfect_numbers(n), [6, 28, 496, 8128, 33550336]);
assert_eq!(generate_perfect_numbers(40), [6, 28]);
assert_eq!(generate_perfect_numbers(0), []);
}
}
```