TheAlgorithms/Python · error · ValueError

'base' must be between 2 and 36 inclusive

Error message

'base' must be between 2 and 36 inclusive

What it means

Raised by int_to_base() in maths/special_numbers/harshad_numbers.py when the base argument is outside [2, 36]. The function converts a positive integer to its string representation in the given base using the digit alphabet '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ', which only defines 36 digits, so bases below 2 (no positional radix) or above 36 (no digit symbols) are meaningless.

Source

Thrown at maths/special_numbers/harshad_numbers.py:38

    >>> int_to_base(167, 16)
    'A7'
    >>> # bases below 2 and beyond 36 will error
    >>> int_to_base(98, 1)
    Traceback (most recent call last):
        ...
    ValueError: 'base' must be between 2 and 36 inclusive
    >>> int_to_base(98, 37)
    Traceback (most recent call last):
        ...
    ValueError: 'base' must be between 2 and 36 inclusive
    >>> int_to_base(-99, 16)
    Traceback (most recent call last):
        ...
    ValueError: number must be a positive integer
    """

    if base < 2 or base > 36:
        raise ValueError("'base' must be between 2 and 36 inclusive")

    digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
    result = ""

    if number < 0:
        raise ValueError("number must be a positive integer")

    while number > 0:
        number, remainder = divmod(number, base)
        result = digits[remainder] + result

    if result == "":
        result = "0"

    return result


def sum_of_digits(num: int, base: int) -> str:

View on GitHub (pinned to f5988cc097)

Solutions

1. Clamp or reject the base before calling: only call when 2 <= base <= 36
2. If you need base-2-only logic, hard-code base=2 instead of parameterizing
3. Validate user input for base at the API boundary with a clear error of your own

Example fix

// before
s = int_to_base(98, 37)  # ValueError

// after
base = 37
if not 2 <= base <= 36:
    raise ValueError(f"unsupported base {base}")
s = int_to_base(98, base)

def safe_int_to_base(number: int, base: int) -> str:
    if not 2 <= base <= 36:
        raise ValueError(f"base {base} out of range 2-36")
    return int_to_base(number, base)

try:
    s = int_to_base(n, base)
except ValueError as e:
    if 'base' in str(e):
        s = int_to_base(n, 10)  # fall back to decimal
    else:
        raise

When it happens

Trigger: Calling int_to_base(number, base) with base < 2 (e.g. base=1 or base=0) or base > 36 (e.g. base=37). The check runs before any conversion, so even valid numbers like int_to_base(98, 37) fail immediately.

Common situations: Passing a user-supplied radix without clamping, off-by-one loops like `for b in range(2, 37)` miswritten as `range(2, 38)`, or assuming the function supports arbitrary bases like base64.

Related errors

• surface_area_cube() only accepts non-negative values
• surface_area_cuboid() only accepts non-negative values
• surface_area_sphere() only accepts non-negative values
• surface_area_hemisphere() only accepts non-negative values
• surface_area_cone() only accepts non-negative values

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/b1ff12d90ff6ba18. Report an issue: GitHub.