diff --git a/readme.md b/readme.md index 3db2113..2661a4a 100644 --- a/readme.md +++ b/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 -### 21 out of 100 public challenges completed. +### 22 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 -Check out Project Euler here. +Check out Project Euler here. \ No newline at end of file diff --git a/src/bin/27.rs b/src/bin/27.rs new file mode 100644 index 0000000..c961408 --- /dev/null +++ b/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); +} diff --git a/src/commands/run.rs b/src/commands/run.rs index 0171793..4e158ac 100644 --- a/src/commands/run.rs +++ b/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(),