Prime Number Checker

This challenge asks you to implement a function that determines whether a given integer is a prime number. Prime numbers are fundamental in number theory and cryptography, making this a foundational problem for many advanced algorithms.

Problem Description

You need to create a JavaScript function named isPrime that accepts a single integer argument, num. The function should return true if num is a prime number, and false otherwise.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Key Requirements:

• The function must correctly identify prime numbers.
• The function should handle various input values, including edge cases.

Expected Behavior:

• For any input num that is prime, isPrime(num) should return true.
• For any input num that is not prime, isPrime(num) should return false.

Edge Cases to Consider:

• Numbers less than or equal to 1.
• The number 2.
• Even numbers greater than 2.
• Large numbers.

Examples

Example 1:

Input: 7
Output: true
Explanation: 7 is a prime number because its only positive divisors are 1 and 7.

Example 2:

Input: 10
Output: false
Explanation: 10 is not a prime number because it is divisible by 2 and 5 (in addition to 1 and 10).

Example 3:

Input: 1
Output: false
Explanation: By definition, prime numbers must be greater than 1.

Example 4:

Input: 2
Output: true
Explanation: 2 is the smallest prime number and the only even prime number.

Constraints

• The input num will be an integer.
• num will be within the range of typical JavaScript number representation (e.g., -Number.MAX_SAFE_INTEGER to Number.MAX_SAFE_INTEGER).
• Your solution should aim for reasonable performance, especially for larger inputs. A naive approach iterating up to num might be too slow for very large numbers.

Notes

• Remember the definition of a prime number: a natural number greater than 1 that has no positive divisors other than 1 and itself.
• Consider how you can optimize your checks. For instance, do you need to check every number up to num as a potential divisor?
• Think about the properties of even numbers and their divisibility.