If a number N has a prime factor larger than the square root of N, then it also has a prime factor smaller than square root of N.

The seventh Project Euler problem - 10001st prime - is stated as follows. By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number?

```
#![feature(iterator_step_by)]
fn is_prime(n: u64) -> bool {
if n == 2 || n == 3 {
return true;
} else if (n < 2) || (n % 2 == 0) {
return false;
}
let upper_limit = (n as f64).sqrt() as u64;
(3..upper_limit + 1)
.step_by(2)
.find(|i| n % i == 0)
.is_none()
}
fn main() {
let n = 10_001;
let mut primes = 0u64;
let mut i = 0u64;
while primes < n {
i += 1;
if is_prime(i) {
primes += 1;
}
}
println!("{} is prime number {}.", i, n);
}
```

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