94 lines
2.1 KiB
Markdown
94 lines
2.1 KiB
Markdown
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---
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id: 5900f39d1000cf542c50feb0
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title: 'Problem 49: Prime permutations'
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challengeType: 5
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forumTopicId: 302159
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dashedName: problem-49-prime-permutations
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---
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# --description--
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The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
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There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
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What 12-digit number do you form by concatenating the three terms in this sequence?
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# --hints--
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`primePermutations()` should return a number.
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```js
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assert(typeof primePermutations() === 'number');
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```
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`primePermutations()` should return 296962999629.
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```js
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assert.strictEqual(primePermutations(), 296962999629);
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```
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# --seed--
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## --seed-contents--
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```js
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function primePermutations() {
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return true;
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}
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primePermutations();
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```
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# --solutions--
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```js
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function primePermutations() {
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function arePermutations(num1, num2) {
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const numStr1 = num1.toString();
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let numStr2 = num2.toString();
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if (numStr1.length !== numStr2.length) {
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return false;
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}
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for (let i = 0; i < numStr1.length; i++) {
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const index = numStr2.indexOf(numStr1[i]);
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if (index === -1) {
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return false;
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}
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numStr2 = numStr2.slice(0, index) + numStr2.slice(index + 1);
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}
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return true;
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}
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function isPrime(num) {
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if (num < 2) {
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return false;
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} else if (num === 2) {
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return true;
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}
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const sqrtOfNum = Math.floor(num ** 0.5);
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for (let i = 2; i <= sqrtOfNum + 1; i++) {
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if (num % i === 0) {
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return false;
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}
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}
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return true;
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}
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for (let num1 = 1000; num1 <= 9999; num1++) {
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const num2 = num1 + 3330;
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const num3 = num2 + 3330;
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if (isPrime(num1) && isPrime(num2) && isPrime(num3)) {
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if (arePermutations(num1, num2) && arePermutations(num1, num3)
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&& num1 !== 1487) {
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// concatenate and return numbers
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return (num1 * 100000000) + (num2 * 10000) + num3;
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}
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}
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}
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return 0;
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}
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```
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