Improve Rust example program

binaries/rust/src/main.rs

@@ -1,7 +1,48 @@
+// https://play.rust-lang.org/?gist=4d6abc78a8c0d205da57a17c02201d7c&version=stable&mode=release&edition=2015
+
+/// Returns the nth prime.
+///
+/// It uses a sieve internally, with a size of roughly
+/// `n * (n.ln() + n.ln().ln()` bytes. As a result, its
+/// runtime is also bound loglinear by the upper term.
+///
+pub fn nth_prime(n: u32) -> Option<u64> {
+    if n < 1 {
+        return None;
+    }
+
+    // The prime counting function is pi(x) which is approximately x/ln(x)
+    // A good upper bound for the nth prime is ceil(x * ln(x * ln(x)))
+    let x = if n <= 10 { 10.0 } else { n as f64 };
+    let limit: usize = (x * (x * (x).ln()).ln()).ceil() as usize;
+    let mut sieve = vec![true; limit];
+    let mut count = 0;
+
+    // Exceptional case for 0 and 1
+    sieve[0] = false;
+    sieve[1] = false;
+
+    for prime in 2..limit {
+        if !sieve[prime] {
+            continue;
+        }
+        count += 1;
+        if count == n {
+            return Some(prime as u64);
+        }
+
+        for multiple in ((prime * prime)..limit).step_by(prime) {
+            sieve[multiple] = false;
+        }
+    }
+    None
+}
 
 fn main() {
-    // Statements here are executed when the compiled binary is called
+	assert_eq!(nth_prime(0), None);
+	assert_eq!(nth_prime(1), Some(2));
+	assert_eq!(nth_prime(2), Some(3));
+	assert_eq!(nth_prime(3), Some(5));
 
-    // Print text to the console
-    println!("Hello World!");
+	println!("Sieve(256000) == {}\n", nth_prime(256000).unwrap());
 }