feat: 27 - quadratic primes

readme.md

@@ -16,7 +16,7 @@ All of the solutions here are written in rust. [main.rs](src/main.rs) is the hom
 
 ## Challenge Completion
 
-### <!-- completed -->21<!-- completed --> out of 100 public challenges completed.
+### <!-- completed -->22<!-- completed --> out of 100 public challenges completed.
 
 - [x] 1 - [Multiples of 3 or 5](src/bin/1.rs)
 - [x] 2 - [Even Fibonacci numbers](src/bin/2.rs)
@@ -44,7 +44,7 @@ All of the solutions here are written in rust. [main.rs](src/main.rs) is the hom
 - [ ] 24 - Lexicographic permutations
 - [ ] 25 - 1000-digit Fibonacci number
 - [ ] 26 - Reciprocal cycles
-- [ ] 27 - Quadratic primes
+- [x] 27 - [Quadratic primes](src/bin/27.rs)
 - [ ] 28 - Number spiral diagonals
 - [ ] 29 - Distinct powers
 - [ ] 30 - Digit fifth powers
@@ -119,4 +119,4 @@ All of the solutions here are written in rust. [main.rs](src/main.rs) is the hom
 - [ ] 99 - Largest exponential
 - [ ] 100 - Arranged probability
 
-<sub>Check out Project Euler <a href="https://projecteuler.net">here</a>.</sub>
+<sub>Check out Project Euler <a href="https://projecteuler.net">here</a>.</sub>

src/bin/27.rs

@@ -0,0 +1,72 @@
+/*
+Problem 27 - Quadratic primes
+
+Euler discovered the remarkable quadratic formula:
+$n^2 + n + 41$
+It turns out that the formula will produce 40 primes for the consecutive integer values $0 \le n \le 39$. However, when $n = 40, 40^2 + 40 + 41 = 40(40 + 1) + 41$ is divisible by 41, and certainly when $n = 41, 41^2 + 41 + 41$ is clearly divisible by 41.
+The incredible formula $n^2 - 79n + 1601$ was discovered, which produces 80 primes for the consecutive values $0 \le n \le 79$. The product of the coefficients, −79 and 1601, is −126479.
+Considering quadratics of the form:
+$n^2 + an + b$, where $|a| < 1000$ and $|b| \le 1000$   where $|n|$ is the modulus/absolute value of $n$ e.g. $|11| = 11$ and $|-4| = 4$
+Find the product of the coefficients, $a$ and $b$, for the quadratic expression that produces the maximum number of primes for consecutive values of $n$, starting with $n = 0$.
+*/
+
+use std::ops::Mul;
+
+const PRIMES: [i32; 168] = [
+    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
+    101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
+    197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307,
+    311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
+    431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
+    557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
+    661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
+    809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
+    937, 941, 947, 953, 967, 971, 977, 983, 991, 997,
+];
+
+fn is_prime(n: i32) -> bool {
+    if n <= 1 {
+        return false;
+    }
+
+    for a in 2..n {
+        if n % a == 0 {
+            return false;
+        }
+    }
+
+    true
+}
+
+fn consecutive_primes(a: i32, b: i32) -> i32 {
+    let mut n = 0;
+
+    loop {
+        let t = (n + a).mul(n) + b;
+
+        if !is_prime(t) {
+            return n;
+        }
+
+        n += 1;
+    }
+}
+
+pub fn main() {
+    let mut max_c = 0;
+    let mut max_ab = 0;
+
+    for a in (-999..=1001i32).step_by(2) {
+        for i in 0..PRIMES.len() {
+            let b = PRIMES[i];
+            let c = consecutive_primes(a - (if i == 0 { 1 } else { 0 }), b);
+
+            if c > max_c {
+                max_c = c;
+                max_ab = a * b;
+            }
+        }
+    }
+
+    println!("{:?}", max_ab);
+}

src/commands/run.rs

@@ -52,8 +52,8 @@ mod twenty_two;
 // mod twenty_five;
 // #[path = "../bin/26.rs"]
 // mod twenty_six;
-// #[path = "../bin/27.rs"]
-// mod twenty_seven;
+#[path = "../bin/27.rs"]
+mod twenty_seven;
 // #[path = "../bin/28.rs"]
 // mod twenty_eight;
 // #[path = "../bin/29.rs"]
@@ -240,7 +240,7 @@ pub async fn execute(
         // 24 => twenty_four::main(),
         // 25 => twenty_five::main(),
         // 26 => twenty_six::main(),
-        // 27 => twenty_seven::main(),
+        27 => twenty_seven::main(),
         // 28 => twenty_eight::main(),
         // 29 => twenty_nine::main(),
         // 30 => thirty::main(),