---
id: 5900f39c1000cf542c50feae
challengeType: 5
title: 'Problem 47: Distinct primes factors'
---

## Description
<section id='description'>
The first two consecutive numbers to have two distinct prime factors are:
<div style='padding-left: 4em;'>14 = 2 × 7</div>
<div style='padding-left: 4em;'>15 = 3 × 5</div>
The first three consecutive numbers to have three distinct prime factors are:
<div style='padding-left: 4em;'>644 = 2² × 7 × 23</div>
<div style='padding-left: 4em;'>645 = 3 × 5 × 43</div>
<div style='padding-left: 4em;'>646 = 2 × 17 × 19</div>
Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: '<code>distinctPrimeFactors(2, 2)</code> should return 14.'
    testString: 'assert.strictEqual(distinctPrimeFactors(2, 2), 14, "<code>distinctPrimeFactors(2, 2)</code> should return 14.");'
  - text: '<code>distinctPrimeFactors(3, 3)</code> should return 644.'
    testString: 'assert.strictEqual(distinctPrimeFactors(3, 3), 644, "<code>distinctPrimeFactors(3, 3)</code> should return 644.");'
  - text: '<code>distinctPrimeFactors(4, 4)</code> should return 134043.'
    testString: 'assert.strictEqual(distinctPrimeFactors(4, 4), 134043, "<code>distinctPrimeFactors(4, 4)</code> should return 134043.");'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
  // Good luck!
  return true;
}

distinctPrimeFactors(4, 4);
```

</div>



</section>

## Solution
<section id='solution'>


```js
function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {

  function isPrime(num) {
    for (let i = 2, s = Math.sqrt(num); i <= s; i++) {
      if (num % i === 0) {
        return false;
      }
    }
    return num !== 1;
  }

  function getPrimeFactors(num) {
    const factors = [];
    for (let i = 2; i <= Math.sqrt(num); i++) {
      if (num % i === 0) {
        // found a factor
        if (isPrime(i)) {
          factors.push(i);
        }
        if (isPrime(num / i) && i !== Math.sqrt(num)) {
          factors.push(num / i);
        }
      }
    }
    return factors;
  }

  function findConsecutiveNumbers() {
    let number = 0;
    let consecutive = 0;
    while (consecutive < targetConsecutive) {
      number++;
      if (getPrimeFactors(number).length >= targetNumPrimes) {
        consecutive++;
    } else {
        consecutive = 0;
      }
    }
    return (number - targetConsecutive) + 1;
  }

  return findConsecutiveNumbers();
  }
```

</section>