// Public domain / CC0. Use freely for any purpose. RoyR 2026
// primes.cm - Prime number calculator
// Demonstrates: algorithms, loops, mathematical operations

void printf(uint8 *fmt);

int32 is_prime(int32 n) {
    if (n <= 1) return 0;
    if (n <= 3) return 1;
    if (n % 2 == 0 || n % 3 == 0) return 0;
    
    int32 i = 5;
    while (i * i <= n) {
        if (n % i == 0 || n % (i + 2) == 0) {
            return 0;
        }
        i = i + 6;
    }
    return 1;
}

int32 nth_prime(int32 n) {
    if (n == 1) return 2;
    
    int32 count = 1;
    int32 candidate = 3;
    
    while (count < n) {
        if (is_prime(candidate)) {
            count = count + 1;
        }
        candidate = candidate + 2;
    }
    
    return candidate - 2;
}

int32 count_primes_under(int32 limit) {
    int32 count = 0;
    for (int32 i = 2; i < limit; i = i + 1) {
        if (is_prime(i)) {
            count = count + 1;
        }
    }
    return count;
}

int32 main(void) {
    printf("First 20 prime numbers:\n");
    for (int32 i = 1; i <= 20; i = i + 1) {
        printf("%d ", nth_prime(i));
        if (i % 10 == 0) printf("\n");
    }
    printf("\n");
    
    int32 limit = 100;
    int32 count = count_primes_under(limit);
    printf("\nThere are %d primes less than %d\n", count, limit);
    
    printf("\nPrime check:\n");
    int32 test_nums[8] = { 1, 2, 15, 17, 97, 100, 101, 121 };
    for (int32 i = 0; i < 8; i = i + 1) {
        int32 num = test_nums[i];
        printf("  %d is %s\n", num, is_prime(num) ? "prime" : "not prime");
    }
    
    return 0;
}