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AI solution for JavaScript Coding Question on BFE.dev
120. create `isPrime()`

One possible implementation for isPrime() function in JavaScript is:

function isPrime(num) {
  if (num <= 1) {
    return false;
  }
  for (let i = 2; i <= Math.sqrt(num); i++) {
    if (num % i === 0) {
      return false;
    }
  }
  return true;
}

This function first checks if the number is less than or equal to 1, which is not prime by definition. It then loops from 2 up to the square root of the number and checks if the number is divisible by any of those values. If it is, then it returns false because the number is not prime. If the loop finishes without finding any divisors, then the number must be prime, so it returns true.

The time cost of this implementation is O(sqrt(n)), which is relatively efficient compared to checking every number up to n-1. However, we can further optimize this function by only checking odd divisors after checking for 2, and checking until the square root of the number OR the smallest prime factor found so far, whichever is smaller. This reduces the number of comparisons and makes the algorithm faster for large inputs.

Here is an example of an optimized isPrime() function:

function isPrime(num) {
  if (num <= 1) {
    return false;
  }
  if (num % 2 === 0) {
    return num === 2; // only 2 is even and prime
  }
  for (let i = 3, limit = Math.sqrt(num), factorFound = false; i <= limit && !factorFound; i += 2) {
    if (num % i === 0) {
      factorFound = true; // stop checking when smallest factor found
    }
  }
  return !factorFound;
}

This implementation checks if the number is even first, because all even numbers (except 2) are not prime. If the number is odd, it then loops through odd divisors starting from 3 and checks if they divide the number evenly until either the square root of the number is reached, or the smallest prime factor has been found (in which case, the loop is terminated early). If no factor was found, the number is prime and the function returns true.

The time cost of this optimized implementation is also O(sqrt(n)), but with a smaller constant factor due to the restricted loop conditions.