6cfd0fc503
* fix: improve Project Euler descriptions and test case Improve formatting of Project Euler test descriptions. Also add poker hands array and new test case for problem 54 * feat: add typeof tests and gave functions proper names for first 100 challenges * fix: continue fixing test descriptions and adding "before test" sections * fix: address review comments * fix: adjust grids in 18 and 67 and fix some text that reference files rather than the given arrays * fix: implement bug fixes and improvements from review * fix: remove console.log statements from seed and solution
121 lines
2.5 KiB
Markdown
121 lines
2.5 KiB
Markdown
---
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id: 5900f39c1000cf542c50feae
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challengeType: 5
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title: 'Problem 47: Distinct primes factors'
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forumTopicId: 302145
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---
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## Description
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<section id='description'>
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The first two consecutive numbers to have two distinct prime factors are:
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<div style='padding-left: 4em;'>
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14 = 2 × 7<br>
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15 = 3 × 5
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</div>
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The first three consecutive numbers to have three distinct prime factors are:
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<div style='padding-left: 4em;'>
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644 = 2<sup>2</sup> × 7 × 23<br>
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645 = 3 × 5 × 43<br>
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646 = 2 × 17 × 19
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</div>
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Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>distinctPrimeFactors(2, 2)</code> should return a number.
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testString: assert(typeof distinctPrimeFactors(2, 2) === 'number');
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- text: <code>distinctPrimeFactors(2, 2)</code> should return 14.
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testString: assert.strictEqual(distinctPrimeFactors(2, 2), 14);
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- text: <code>distinctPrimeFactors(3, 3)</code> should return 644.
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testString: assert.strictEqual(distinctPrimeFactors(3, 3), 644);
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- text: <code>distinctPrimeFactors(4, 4)</code> should return 134043.
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testString: assert.strictEqual(distinctPrimeFactors(4, 4), 134043);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
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// Good luck!
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return true;
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}
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distinctPrimeFactors(4, 4);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
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function numberOfPrimeFactors(n) {
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let factors = 0;
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// Considering 2 as a special case
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let firstFactor = true;
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while (n % 2 == 0) {
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n = n / 2;
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if (firstFactor) {
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factors++;
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firstFactor = false;
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}
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}
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// Adding other factors
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for (let i = 3; i < Math.sqrt(n); i += 2) {
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firstFactor = true;
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while (n % i == 0) {
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n = n / i;
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if (firstFactor) {
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factors++;
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firstFactor = false;
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}
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}
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}
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if (n > 1) { factors++; }
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return factors;
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}
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let number = 0;
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let consecutive = 0;
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while (consecutive < targetConsecutive) {
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number++;
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if (numberOfPrimeFactors(number) >= targetNumPrimes) {
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consecutive++;
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} else {
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consecutive = 0;
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}
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}
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return number - targetConsecutive + 1;
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}
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```
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</section>
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