[08_revisit_everything] add solution

Luckily M[30] is easily factorable as it is almost a perfect square.

src/bin/08_revisit_everything.rs

@@ -1,10 +1,9 @@
 #![allow(dead_code)]
-use std::str::FromStr;
 use std::sync::LazyLock;
+use lib::submit_with_name;
+use rug::ops::DivRounding;
 use rug::Integer;
-use rug::ops::{DivRounding, Pow};
-use lib::compute_async;
-
+use std::str::FromStr;
 
 // You can change the color of your name without changing your name.
 static M: LazyLock<Vec<Integer>> = LazyLock::new(|| vec![
@@ -53,31 +52,35 @@ static M: LazyLock<Vec<Integer>> = LazyLock::new(|| vec![
 ]);
 
 static E: LazyLock<Integer> = LazyLock::new(|| Integer::from(65537));
-static E_100: LazyLock<Integer> = LazyLock::new(|| Integer::from(65537).pow(100));
 
-const N: u128 = 1000000000073185001u128;
-const X: LazyLock<Integer> = LazyLock::new(|| Integer::from_str("674404660282415099554286008259705897519728869877764551165256987500863620745793154396934476537394982658025146065927801862469915739446118680825670854157276563716625217760696826462684682154873582522786834148305185591910769146737370100544900325").unwrap());
+/// the first prime factor of [`M[30]`](M)
+static P: LazyLock<Integer> = LazyLock::new(|| Integer::from_str("2134638905903015345595412931439525422327695207079839833349799642610037970639957457078422305821013930668706217301787851463").unwrap());
+/// the second prime factor of [`M[30]`](M)
+static Q: LazyLock<Integer> = LazyLock::new(|| Integer::from_str("2134638905903015345595412931439525422327695207079839833349799642610037970639957457078422305821013930668706217301787851473").unwrap());
+/// [`φ(M[30])`](M) where `φ` is Euler's totient function
+static PHI: LazyLock<Integer> = LazyLock::new(|| Integer::from_str("4556683258594822402855414380362620295231673046713752880933967889771646856051745784462468117575177892006513392693685616565666555545842363207724851343853529903674824524238732001458342230627654145983386115997227846421784693186847971068054052064").unwrap());
+
+const LIMIT: u128 = 100_000_000_000_000_000_000;
+const NAME: &str = "           Jonah";
+const N: u128 = 1000000000000000000;
+const X: &str = "3595876711108608978";
 
 fn main() {
+    debug_assert_eq!(M[30].clone(), P.clone() * Q.clone());
+    debug_assert_eq!(PHI.clone(), (P.clone() - 1) * (Q.clone() - 1));
+
     let truth = Integer::from(42);
-    let w: usize = X.clone().modulo(&truth).try_into().unwrap();
-    println!("w = {w}");
+    let k = Integer::from(LIMIT - N) * 100;
+    let e = E.clone().pow_mod(&k, &PHI).unwrap();
 
-    compute_async(move |tx| {
-        let mut n = N;
-        let y = X.clone().div_floor(&truth);
+    let x = Integer::from_str(X).unwrap();
+    let w: usize = x.clone().modulo(&truth).try_into().unwrap();
+    assert_eq!(w, 30);
 
-        let mut temp = y.clone();
-        loop {
-            for _ in 0..10_000 {
-                n += 1;
-                temp = temp.pow_mod(&E_100, &M[w]).unwrap();
-            }
+    let mut y = x.clone().div_floor(&truth);
+    y = y.pow_mod(&e, &M[30]).unwrap();
 
-            let mut res = temp.clone();
-            res *= &truth;
-            res += w;
-            tx.send((n, res)).unwrap();
-        }
-    });
+    let x: Integer = y * 42 + w;
+    println!("x = {x}\nn = {LIMIT}");
+    submit_with_name(NAME, LIMIT, x).unwrap();
 }