92 lines
1.9 KiB
Markdown
92 lines
1.9 KiB
Markdown
---
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id: 5900f39c1000cf542c50feae
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title: 'Problem 47: Distinct primes factors'
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challengeType: 5
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forumTopicId: 302145
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dashedName: problem-47-distinct-primes-factors
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---
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# --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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# --hints--
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`distinctPrimeFactors(2, 2)` should return a number.
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```js
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assert(typeof distinctPrimeFactors(2, 2) === 'number');
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```
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`distinctPrimeFactors(2, 2)` should return 14.
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```js
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assert.strictEqual(distinctPrimeFactors(2, 2), 14);
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```
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`distinctPrimeFactors(3, 3)` should return 644.
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```js
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assert.strictEqual(distinctPrimeFactors(3, 3), 644);
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```
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`distinctPrimeFactors(4, 4)` should return 134043.
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```js
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assert.strictEqual(distinctPrimeFactors(4, 4), 134043);
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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 distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
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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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# --solutions--
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```js
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// Initalize factor count with seive
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const NUMFACTORS = Array(135000).fill(0);
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(function initFactors(num) {
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for (let i = 2; i < num; i++)
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if (NUMFACTORS[i] === 0)
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for (let j = i; j < num; j += i)
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NUMFACTORS[j]++;
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})(135000);
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function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
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let numConsecutive = 0;
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let currNumber = 10;
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while (numConsecutive < targetConsecutive) {
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if (NUMFACTORS[currNumber] === targetNumPrimes)
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numConsecutive++;
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else
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numConsecutive = 0;
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currNumber++;
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}
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return currNumber - targetConsecutive;
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}
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```
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