TheAlgorithms/Python · error · ValueError

is_prime() only accepts positive integers

Error message

is_prime() only accepts positive integers

What it means

is_prime() in maths/prime_check.py uses 6k+/-1 trial division and requires its argument to be a non-negative Python int: if not isinstance(number, int) or not number >= 0 it raises ValueError('is_prime() only accepts positive integers'). Both wrong type (floats like 16.1, strings) and negatives (-4) hit the same guard. The message says 'positive' but 0 and 1 are accepted (they return False), so the real contract is 'non-negative integer'.

Source

Thrown at maths/prime_check.py:44

    >>> is_prime(563)
    True
    >>> is_prime(2999)
    True
    >>> is_prime(67483)
    False
    >>> is_prime(16.1)
    Traceback (most recent call last):
        ...
    ValueError: is_prime() only accepts positive integers
    >>> is_prime(-4)
    Traceback (most recent call last):
        ...
    ValueError: is_prime() only accepts positive integers
    """

    # precondition
    if not isinstance(number, int) or not number >= 0:
        raise ValueError("is_prime() only accepts positive integers")

    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5, int(math.sqrt(number) + 1), 6):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True


class Test(unittest.TestCase):
    def test_primes(self):
        assert is_prime(2)

View on GitHub (pinned to f5988cc097)

Solutions

1. Convert with int() when the value is integral: is_prime(int(number)) or use is_prime(number // divisor) style integer ops.
2. Validate at the data boundary so only ints reach primality code.
3. Catch ValueError if bad input is a runtime possibility in your pipeline.

Example fix

# before
is_prime(n / 2)  # float argument -> ValueError

# after
is_prime(n // 2)  # true division yields float; floor division yields int

if not isinstance(number, int) or number < 0:
    number = int(number)
is_prime(number)

def is_prime_input(v) -> bool:
    return isinstance(v, int) and not isinstance(v, bool) and v >= 0

try:
    is_prime(n)
except ValueError:
    n = int(n)  # last resort for numeric strings/floats

When it happens

Trigger: Calling is_prime(16.1), is_prime(-4), is_prime('7'), or is_prime(7.0). Values read from JSON ('7' or 7.0) or division results (10/2 == 5.0) commonly produce floats.

Common situations: Python 3 division always yielding floats (n / 2 passed onward); JSON/deserialized data; code ported from Python 2 where 5/2 was int; catching TypeError instead of ValueError around the call.

Related errors

• number must be an integer
• multiplicative_persistence() only accepts integral values
• multiplicative_persistence() does not accept negative values
• additive_persistence() only accepts integral values
• additive_persistence() does not accept negative values

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/324844b8b96a1dbc. Report an issue: GitHub.