---
id: 5900f39c1000cf542c50feae
challengeType: 5
title: 'Problem 47: Distinct primes factors'
forumTopicId: 302145
---
## Description
The first two consecutive numbers to have two distinct prime factors are:
14 = 2 × 7
15 = 3 × 5
The first three consecutive numbers to have three distinct prime factors are:
644 = 2² × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19
Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
## Instructions
## Tests
```yml
tests:
- text: distinctPrimeFactors(2, 2) should return 14.
testString: assert.strictEqual(distinctPrimeFactors(2, 2), 14);
- text: distinctPrimeFactors(3, 3) should return 644.
testString: assert.strictEqual(distinctPrimeFactors(3, 3), 644);
- text: distinctPrimeFactors(4, 4) should return 134043.
testString: assert.strictEqual(distinctPrimeFactors(4, 4), 134043);
```
## Challenge Seed
```js
function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
// Good luck!
return true;
}
distinctPrimeFactors(4, 4);
```
## Solution
```js
function distinctPrimeFactors(targetNumPrimes, targetConsecutive) {
function numberOfPrimeFactors(n) {
let factors = 0;
// Considering 2 as a special case
let firstFactor = true;
while (n % 2 == 0) {
n = n / 2;
if (firstFactor) {
factors++;
firstFactor = false;
}
}
// Adding other factors
for (let i = 3; i < Math.sqrt(n); i += 2) {
firstFactor = true;
while (n % i == 0) {
n = n / i;
if (firstFactor) {
factors++;
firstFactor = false;
}
}
}
if (n > 1) { factors++; }
return factors;
}
let number = 0;
let consecutive = 0;
while (consecutive < targetConsecutive) {
number++;
if (numberOfPrimeFactors(number) >= targetNumPrimes) {
consecutive++;
} else {
consecutive = 0;
}
}
return number - targetConsecutive + 1;
}
```