---
id: 5900f39c1000cf542c50feae
title: 问题47：不同的素数因素
challengeType: 5
videoUrl: ''
dashedName: problem-47-distinct-primes-factors
---

# --description--

前两个连续数字有两个不同的素数因子是：

14 = 2×7

15 = 3×5

前三个连续数字有三个不同的素因子：

644 =2²×7×23

645 = 3×5×43

646 = 2×17×19

找到前四个连续的整数，每个整数有四个不同的素数因子。这些数字中的第一个是什么？

# --hints--

`distinctPrimeFactors(2, 2)`应该返回14。

```js
assert.strictEqual(distinctPrimeFactors(2, 2), 14);
```

`distinctPrimeFactors(3, 3)`应该返回644。

```js
assert.strictEqual(distinctPrimeFactors(3, 3), 644);
```

`distinctPrimeFactors(4, 4)`应该返回134043。

```js
assert.strictEqual(distinctPrimeFactors(4, 4), 134043);
```

# --seed--

## --seed-contents--

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

  return true;
}

distinctPrimeFactors(4, 4);
```

# --solutions--

```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;
}
```