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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,60 +1,61 @@ | ||
| /** | ||
| * Project Euler Problem 60 | ||
| * | ||
| * Problem: | ||
| * | ||
| * The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the | ||
| * result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, | ||
| * 792, represents the lowest sum for a set of four primes with this property. | ||
| * | ||
| * Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime. | ||
| * | ||
| * @return {number} | ||
| */ | ||
| exports.p0060 = function() { | ||
| const iterator = primes.primes(); | ||
| const cached_primes = [3]; | ||
| iterator.next(); // 2 is excluded because higher even numbers can't be prime | ||
| iterator.next(); | ||
| iterator.next(); // 5 is excluded because if a number ends with 5, it's divisible by 5 | ||
| const compat = new Map(); | ||
| for (const x of iterator) { | ||
| for (const y of cached_primes) { | ||
| if (is_concat_prime(x, y)) { | ||
| for (const [a, b, c] of iters.combinations(compat.get(y) || new Set(), 3)) { | ||
| if (compat.get(b).has(a) && compat.get(c).has(a) && compat.get(c).has(b)) { // remember these are commutative | ||
| if (is_concat_prime(a, x) && is_concat_prime(b, x) && is_concat_prime(c, x)) { | ||
| return x + y + a + b + c; | ||
| } | ||
| } | ||
| } | ||
| if (!compat.has(x)) { | ||
| compat.set(x, new Set()); | ||
| } | ||
| compat.get(x).add(y); | ||
| if (!compat.has(y)) { | ||
| compat.set(y, new Set()); | ||
| } | ||
| compat.get(y).add(x); | ||
| } | ||
| } | ||
| cached_primes.push(x); | ||
| } | ||
| return -1; | ||
| }; | ||
|
|
||
| /** | ||
| * Tests if a pair of numbers generates a prime if concatenated in both orders. | ||
| * | ||
| * @param {number} x | ||
| * @param {number} y | ||
| * @return {number} | ||
| */ | ||
| const is_concat_prime = function(x, y) { | ||
| const sx = x.toString(); | ||
| const sy = y.toString(); | ||
| return primes.isPrime(parseInt(sx + sy)) && primes.isPrime(parseInt(sy + sx)); | ||
| }; | ||
|
|
||
| const iters = require('./lib/iters.js'); | ||
| const primes = require('./lib/primes.js'); | ||
| /** | ||
| * Project Euler Problem 60 | ||
| * | ||
| * Problem: | ||
| * | ||
| * The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the | ||
| * result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four | ||
| * primes, 792, represents the lowest sum for a set of four primes with this property. | ||
| * | ||
| * Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime. | ||
| * | ||
| * @return {number} | ||
| */ | ||
| exports.p0060 = function() { | ||
| const iterator = primes.primes(); | ||
| const cachedPrimes = [3]; | ||
| iterator.next(); // 2 is excluded because higher even numbers can't be prime | ||
| iterator.next(); | ||
| iterator.next(); // 5 is excluded because if a number ends with 5, it's divisible by 5 | ||
| const compat = new Map(); | ||
| for (const x of iterator) { | ||
| for (const y of cachedPrimes) { | ||
| if (isConcatPrime(x, y)) { | ||
| for (const [a, b, c] of iters.combinations(compat.get(y) || new Set(), 3)) { | ||
| // remember these checks are commutative | ||
| if (compat.get(b).has(a) && compat.get(c).has(a) && compat.get(c).has(b)) { | ||
| if (isConcatPrime(a, x) && isConcatPrime(b, x) && isConcatPrime(c, x)) { | ||
| return x + y + a + b + c; | ||
| } | ||
| } | ||
| } | ||
| if (!compat.has(x)) { | ||
| compat.set(x, new Set()); | ||
| } | ||
| compat.get(x).add(y); | ||
| if (!compat.has(y)) { | ||
| compat.set(y, new Set()); | ||
| } | ||
| compat.get(y).add(x); | ||
| } | ||
| } | ||
| cachedPrimes.push(x); | ||
| } | ||
| return -1; | ||
| }; | ||
|
|
||
| /** | ||
| * Tests if a pair of numbers generates a prime if concatenated in both orders. | ||
| * | ||
| * @param {number} x | ||
| * @param {number} y | ||
| * @return {number} | ||
| */ | ||
| const isConcatPrime = function(x, y) { | ||
| const sx = x.toString(); | ||
| const sy = y.toString(); | ||
| return primes.isPrime(parseInt(sx + sy)) && primes.isPrime(parseInt(sy + sx)); | ||
| }; | ||
|
|
||
| const iters = require('./lib/iters.js'); | ||
| const primes = require('./lib/primes.js'); |