291600). If there were to be middle 3 digits, that would leave 6 − 3 = 3 digits to be distributed to the left and right of the middle. It is impossible to evenly distribute these digits equally on both sides of the middle number, and therefore there are no "middle digits". It is acceptable to pad the seeds with zeros to the left in order to create an even valued n-digit number (e.g. 540 → 0540). For a generator of n-digit numbers, the period can be no longer than 8n. If the middle n digits are all zeroes, the generator then outputs zeroes forever. If the first half of a number in the sequence is zeroes, the subsequent numbers will be decreasing to zero. While these runs of zero are easy to detect, they occur too frequently for this method to be of practical use. The middle-squared method can also get stuck on a number other than zero. For n = 4, this occurs with the values 0100, 2500, 3792, and 7600. Other seed values form very short repeating cycles, e.g., 0540 → 2916 → 5030 → 3009. These phenomena are even more obvious when n = 2, as none of the 100 possible seeds generates more than 14 iterations without reverting to 0, 10, 50, 60, or a 24 ↔ 57 loop. Example implementation Here, the algorithm is rendered in Python 3. seed_number = int(input("Please enter a four-digit number:\n[####] ")) number = seed_number already_seen = set() counter = 0 while number not in already_seen: counter += 1 already_seen.add(number) number = int(str(number * number).zfill(8)[2:6]) # zfill adds padding of zeroes print(f"#{counter}: {number}") print(f"We began with {seed_number} and" f" have repeated ourselves after {counter} steps" f" with {number}.") References See also Linear congruential generator Blum Blum Shub Pseudorandom number generators Articles with example C code Articles with example Python (programming language) code John von Neumann