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primes

is_prime(number)

States if a number is prime.

Parameters:

Name Type Description Default
number int

A number

 required

Returns:

Type Description
bool

Whether or not the number is prime

Examples:

>>> is_prime(31)
True

>>> is_prime(42)
False
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/primes.py 
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def is_prime(number: int) -> bool:
    """States if a number is prime.

    Parameters:
        number: A number

    Returns:
        Whether or not the number is prime

    Examples:
        >>> is_prime(31)
        True

        >>> is_prime(42)
        False
    """
    for factor in range(2, number):
        if not number % factor:
            return False
    return True

generate_primes(limit)

Generates primes up to a given limit.

Parameters:

Name Type Description Default
limit int

The limit.

 required

Returns:

Type Description
List[int]

Primes

Examples:

>>> generate_primes(31)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/primes.py 
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def generate_primes(limit: int) -> List[int]:
    """Generates primes up to a given limit.

    Parameters:
        limit: The limit.

    Returns:
        Primes

    Examples:
        >>> generate_primes(31)
        [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
    """
    return [n for n in range(2, limit + 1) if is_prime(n)]

prime_factors(number)

Finds prime factors of an integer (by trial-division).

Parameters:

Name Type Description Default
number int

The integer to factor

 required

Returns:

Type Description
List[int]

Prime factors

Examples:

>>> prime_factors(314)
[2, 157]

>>> prime_factors(31)
[31]
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/primes.py 
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def prime_factors(number: int) -> List[int]:
    """Finds prime factors of an integer (by trial-division).

    Parameters:
        number: The integer to factor

    Returns:
        Prime factors

    Examples:
        >>> prime_factors(314)
        [2, 157]

        >>> prime_factors(31)
        [31]
    """
    factor = 2
    factors = []
    while factor * factor <= number:
        if number % factor:
            factor += 1
        else:
            number //= factor
            factors.append(factor)
    if number > 1:
        factors.append(number)

    return factors

lcm(numbers)

Least common multiple of a list of integers.

Parameters:

Name Type Description Default
numbers List[int]

List of integers

 required

Returns:

Type Description
int

Least common multiple

Examples:

>>> lcm([15, 3, 5])
15

>>> lcm([21, 6, 7])
42
Source code in /opt/hostedtoolcache/Python/3.11.3/x64/lib/python3.11/site-packages/jintonic/primes.py 
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def lcm(numbers: List[int]) -> int:
    """Least common multiple of a list of integers.

    Parameters:
        numbers: List of integers

    Returns:
        Least common multiple

    Examples:
        >>> lcm([15, 3, 5])
        15

        >>> lcm([21, 6, 7])
        42
    """
    return reduce(lambda x, y: x * y // gcd(x, y), numbers)