TheAlgorithms/Python · critical · ValueError

Parameter n must be greater than or equal to one.

Error message

Parameter n must be greater than or equal to one.

What it means

Documented ValueError from project_euler/problem_003/sol2.py:solution when n <= 0 after int(n) succeeds; the trial-division factorization loop requires a positive integer. CAVEAT: the module is unparseable under Python 3 ('except TypeError, ValueError:' at line 48), so it raises SyntaxError at import and this ValueError is unreachable until the syntax is repaired.

Source

Thrown at project_euler/problem_003/sol2.py:50

    Traceback (most recent call last):
        ...
    ValueError: Parameter n must be greater than or equal to one.
    >>> solution([])
    Traceback (most recent call last):
        ...
    TypeError: Parameter n must be int or castable to int.
    >>> solution("asd")
    Traceback (most recent call last):
        ...
    TypeError: Parameter n must be int or castable to int.
    """

    try:
        n = int(n)
    except TypeError, ValueError:
        raise TypeError("Parameter n must be int or castable to int.")
    if n <= 0:
        raise ValueError("Parameter n must be greater than or equal to one.")
    prime = 1
    i = 2
    while i * i <= n:
        while n % i == 0:
            prime = i
            n //= i
        i += 1
    if n > 1:
        prime = n
    return int(prime)


if __name__ == "__main__":
    print(f"{solution() = }")

View on GitHub (pinned to f5988cc097)

Solutions

1. Repair the except clause at project_euler/problem_003/sol2.py:48 to parenthesized form so the module loads.
2. Pass n >= 1.
3. Validate bounds before calling: if not isinstance(n, int) or n < 1: reject.
4. Catch ValueError when iterating over externally supplied bounds.

Example fix

# before
solution(0)

# after
n = max(int(user_input), 1) if str(user_input).strip().isdigit() else None
if n is None:
    raise ValueError('n must be a positive integer')
solution(n)

n = int(n)
if n <= 0:
    raise ValueError(f'n must be >= 1, got {n}')
solution(n)

def is_valid_factorization_input(n) -> bool:
    return isinstance(n, int) and n >= 1

try:
    solution(n)
except ValueError:
    ...

When it happens

Trigger: After the fix: solution(0) or solution(-1). Today: any import of project_euler/problem_003/sol2.py under Python 3 raises SyntaxError('multiple exception types must be parenthesized') instead.

Common situations: Calling the legacy solution from a py3 driver or doctest; batch scripts enumerating n from a range that includes 0; input parsing that yields 0 for empty strings (int('') raises TypeError instead - a related trap).

Related errors

• Parameter n must be greater than or equal to one.
• Parameter n must be greater than or equal to one.
• Parameter n must be greater than or equal to one.
• Parameter n must be int or castable to int.
• Parameter n must be int or castable to int.

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/66218fe516305aee. Report an issue: GitHub.