1. **Stating the problem:** We want to test the theory of incrementing a large hexadecimal number by 16, four times, starting from the initial value \texttt{0000000000000000000000000000000000000000000000349b84b6431a6c4ef1} and see if it reaches \texttt{0000000000000000000000000000000000000000000004c5ce114686a1336e07}. 2. **Understanding the problem:** Incrementing by 16 means adding \(4 \times 16 = 64\) in decimal to the initial number. 3. **Convert the initial and target hex values to decimal:** - Initial: \(\texttt{349b84b6431a6c4ef1}_{16}\) - Target: \(\texttt{4c5ce114686a1336e07}_{16}\) 4. **Calculate the decimal values:** - Initial decimal \(= \text{int}('349b84b6431a6c4ef1', 16)\) - Target decimal \(= \text{int}('4c5ce114686a1336e07', 16)\) 5. **Add 64 to the initial decimal and check if it equals the target decimal:** $$\text{initial\_decimal} + 64 = ? \text{target\_decimal}$$ 6. **If equal, the theory holds; if not, it does not.** 7. **Summary:** Incrementing by 16 four times adds 64 decimal to the initial number. We verify if this matches the target number. **Final answer:** The increment of 4 times 16 (64 decimal) added to the initial hex number does **not** reach the target hex number because the difference between the two numbers is much larger than 64 decimal.