Computational Logics

General Purpose Algorithm Collections

Prime Number

def is_prime(n):
    """
    Function to check if a number is prime or not
    :param n: the input number, can expect integer
    :return: boolean. True - input is prime number, False - not a prime number
    """
    if n <= 1:
        return False
    if n <= 3:
        return True
    if n % 2 == 0 or n % 3 == 0:
        return False
    i = 5
    while i * i <= n:
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i += 6
    return True

Sieve of Eratosthenes

def sieve_eratosthenes(limit):
    """
    Function to create a black box of primes. i.e. a box of all primes till the given limit.
    :param limit: int - the number up to which the blackbox should be created
    :return: list - the list containing indicator for all primes till the limit
    Function will create a list of boolean indicating True for prime index and False for composite index
    """
    sieve = [True] * limit
    sieve[0] = sieve[1] = False
    for current in range(2, int(limit ** 0.5) + 1):
        if sieve[current]:
            for multiple in range(current * current, limit, current):
                sieve[multiple] = False
    # primes = [num for num, is_prime in enumerate(sieve) if is_prime]
    return sieve