Listing all the prime numbers upto a specific number in JavaScript

We are required to write a JavaScript function that takes in a number, say n, and returns an array containing all the prime numbers up to n.

For example: If the number n is 24.

Then the output should be ?

const output = [2, 3, 5, 7, 11, 13, 17, 19, 23];

Therefore, let's write the code for this function ?

Method 1: Using Helper Function for Prime Check

This approach uses a helper function to check if a number is prime, then iterates through numbers up to n:

const num = 24;

const isPrime = num => {
    let count = 2;
    while(count  {
    if(num 

[
    2, 3, 5, 7, 11,
    13, 17, 19, 23
]


Method 2: Optimized Prime Check Using Square Root

This version improves efficiency by only checking divisors up to the square root of the number:

const primeUptoOptimized = num => {
    if(num  {
        if(n 

[
    2,  3,  5,  7, 11,
   13, 17, 19, 23, 29
]


How It Works

The first method checks each number by testing divisibility from 2 to half the number. The second method uses mathematical optimization:

• Numbers divisible by 2 or 3 (except 2 and 3 themselves) are not prime
• All primes greater than 3 can be written as 6k ± 1
• Only check divisors up to ?n since larger factors would have corresponding smaller factors

Comparison

Conclusion

Both methods successfully find all prime numbers up to a given limit. The optimized version using square root checking is more efficient for larger numbers and follows mathematical principles for prime detection.