#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>

uint32_t rand32() { return (rand() << 16) | (rand() & 0xFFFF) | 1; }

void print_uint128(unsigned __int128 n) {
    if (n == 0) {
        printf("0\n");
        return;
    }

    // A 128-bit number can have up to 39 decimal digits
    char buffer[40];
    int i = 0;

    // Extract digits from right to left
    while (n > 0) {
        buffer[i++] = (n % 10) + '0'; // Convert math digit to character
        n /= 10;
    }

    // Print them in reverse order (left to right)
    while (i > 0) {
        putchar(buffer[--i]);
    }
    putchar('\n');
}

uint64_t rand64() {
    uint64_t r = 0;
    for (int i = 0; i < 4; i++) {
        r = (r << 16) | (rand() & 0xFFFF);
    }

    // Force the bottom bit to 1, this will make all generated primes odd
    r = r | 1;
    return r;
}

// Stitch two 64-bit random numbers into a 128-bit number
unsigned __int128 generate_stitched_128() {
    uint64_t top_half = rand64();
    uint64_t bottom_half = rand64();

    // Cast the top half to 128-bit, shift it over by 64 bits, and attach the bottom
    unsigned __int128 full_number = ((unsigned __int128)top_half << 64) | bottom_half;

    return full_number;
}

unsigned __int128 generate_prime_candidate() {
    unsigned __int128 candidate = generate_stitched_128();

    // Force the bottom bit to 1, this will make all generated primes odd
    candidate = candidate | 1;

    // 3. Force the top bit to 1 (Ensures it is a full 128-bit number)
    candidate = candidate | ((unsigned __int128)1 << 127);

    return candidate;
}