Geminis answer: LLMs cannot perform the computations needed to find a SHA-512 hash with specific characteristics. This requires specialized hardware and software designed for brute-force calculations.

ChatGPT: Yes, getting an AI to solve a problem like finding a SHA-512 hash with 12 leading zeros would indeed take a significant amount of computational time and resources. This is because it would require brute-forcing through a vast number of inputs to find one that produces the desired hash, which is a computationally intensive task.

Finding a SHA-512 hash with 12 leading zeros involves iterating through possible inputs and hashing each one until you find a hash that starts with 12 zeros. This is a classic example of a proof-of-work problem, similar to what is used in cryptocurrency mining.

Here’s a Python script that demonstrates how one might go about attempting this task:

import hashlib

def find_hash_with_leading_zeros(target_zeros):
    target = '0' * target_zeros
    nonce = 0
    
    while True:
        input_str = f'{nonce}'
        hash_result = hashlib.sha512(input_str.encode()).hexdigest()
        
        if hash_result.startswith(target):
            return nonce, hash_result
        
        nonce += 1

# Example: Find a SHA-512 hash with 12 leading zeros
target_zeros = 12
nonce, hash_result = find_hash_with_leading_zeros(target_zeros)

print(f'Nonce: {nonce}')
print(f'Hash: {hash_result}')

Running this script can take a very long time, especially as the number of leading zeros increases. The number of possible combinations grows exponentially, making it a time-consuming process.

To actually implement this in a controlled and efficient manner, specialized hardware (like ASIC miners used in cryptocurrency mining) would be required. This is beyond the capabilities of typical general-purpose CPUs and would indeed tie up computational resources for a significant amount of time.