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id	challengeType	title
5900f39c1000cf542c50feae	5	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?

Instructions

Tests

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.');

Challenge Seed

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

distinctPrimeFactors(4, 4);

Solution

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();
  }

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