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