Prime numbers within a range in JavaScript

We are required to write a JavaScript function that takes in two numbers, say, a and b and returns the total number of prime numbers between a and b (including a and b, if they are prime).

For example: If a = 21, and b = 38.

• The prime numbers between them are 23, 29, 31, 37

• And their count is 4

• Our function should return 4

Understanding Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Numbers like 2, 3, 5, 7, 11 are prime, while 4, 6, 8, 9 are not.

Solution Approach

We'll create two functions:

• isPrime() - checks if a single number is prime
• primeBetween() - counts primes in a range using isPrime()

Example

const isPrime = num => {
    if (num <= 1) return false;
    if (num <= 3) return true;
    if (num % 2 === 0 || num % 3 === 0) return false;
    
    let count = 5;
    while (count * count <= num) {
        if (num % count === 0 || num % (count + 2) === 0) {
            return false;
        }
        count += 6;
    }
    return true;
};

const primeBetween = (a, b) => {
    let count = 0;
    for (let i = Math.min(a, b); i <= Math.max(a, b); i++) {
        if (isPrime(i)) {
            count++;
        }
    }
    return count;
};

console.log(primeBetween(21, 38));
console.log(primeBetween(10, 20));
console.log(primeBetween(2, 10));

4
4
4

How It Works

The isPrime() function uses an optimized algorithm:

• Numbers ? 1 are not prime
• 2 and 3 are prime
• Numbers divisible by 2 or 3 are not prime
• Check divisors of form 6k±1 up to ?num for efficiency

Alternative: Simple Approach

Here's a simpler but less efficient version for educational purposes:

const isPrimeSimple = num => {
    if (num <= 1) return false;
    if (num === 2) return true;
    if (num % 2 === 0) return false;
    
    for (let i = 3; i <= Math.sqrt(num); i += 2) {
        if (num % i === 0) return false;
    }
    return true;
};

const primeBetweenSimple = (a, b) => {
    let count = 0;
    let primes = [];
    
    for (let i = Math.min(a, b); i <= Math.max(a, b); i++) {
        if (isPrimeSimple(i)) {
            count++;
            primes.push(i);
        }
    }
    
    console.log("Prime numbers found:", primes);
    return count;
};

console.log("Count:", primeBetweenSimple(21, 38));

Prime numbers found: [ 23, 29, 31, 37 ]
Count: 4

Performance Comparison

Conclusion

This solution efficiently counts prime numbers in any range by combining a prime-checking function with range iteration. The optimized version handles larger numbers more efficiently by reducing the number of divisibility checks.