Here is a simple algorithm for checking if a number is prime in C. This implementation uses two optimizations to determine if a number is prime. First, if the number is divisible by 2 or 3, it is not considered prime. Second, the fact that all primes can be expressed as 6k ± 1 is utilized, allowing for faster processing by checking multiples of 6:

#include <math.h>
#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;

    int i;
    for (i = 5; i <= sqrt(num); i += 6) {
        if (num % i == 0 || num % (i + 2) == 0) return false;
    }
    return true;
}
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