Yes, there are a few additional optimizations you can add to further improve the performance of this algorithm:

    Check for divisibility by smaller primes: Before checking for divisibility by 6k ± 1, you can check for divisibility by smaller primes, such as 2, 3, 5, 7, 11, etc. This will save time as the smaller primes will divide many numbers before 6k ± 1 has a chance.

    Check only odd numbers: Since all even numbers are not prime, you can skip checking them and only check odd numbers. This will reduce the number of checks required by half.

    Use an optimized method for finding the square root: Instead of using the sqrt function from the math.h library, you can use an optimized method for finding the square root, such as the Newton-Raphson method or the Binary Search method. These methods are faster than the standard sqrt function and can improve the performance of the algorithm.

Here's an updated implementation incorporating these optimizations:

#include <stdbool.h>

bool is_prime(int num) {
    if (num <= 1) return false;
    if (num <= 3) return true;
    if (num % 2 == 0 || num % 3 == 0) return false;
    if (num % 5 == 0 || num % 7 == 0 || num % 11 == 0) return false;

    int i;
    for (i = 13; i * i <= num; i += 2) {
        if (num % i == 0) return false;
    }
    return true;
}
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