---
id: 5900f4791000cf542c50ff8b
title: >-
  Problem 268: Counting numbers with at least four distinct prime factors less than 100
challengeType: 1
forumTopicId: 301917
dashedName: >-
  problem-268-counting-numbers-with-at-least-four-distinct-prime-factors-less-than-100
---

# --description--

It can be verified that there are 23 positive integers less than 1000 that are divisible by at least four distinct primes less than 100.

Find how many positive integers less than ${10}^{16}$ are divisible by at least four distinct primes less than 100.

# --hints--

`fourDistinctPrimeFactors()` should return `785478606870985`.

```js
assert.strictEqual(fourDistinctPrimeFactors(), 785478606870985);
```

# --seed--

## --seed-contents--

```js
function fourDistinctPrimeFactors() {

  return true;
}

fourDistinctPrimeFactors();
```

# --solutions--

```js
// solution required
```
