prime in python

eratosthenes.py

def eratoshenes_effective(num):
    numbers = list(range(num + 1))
    numbers[0] = numbers[1] = False
    for i in range(2, num):
        if numbers[i]:
            for j in range(i * i, num + 1, i):
                numbers[j] = False
    return numbers

python _is_prime_O(N).py

def is_prime(num: int):
    
    if num == 1:
        return False
    
    count = 2
    
    while count < num:
        if num % count == 0:
            return False
            
        count += 1
    
    return True
            

python _is_prime_O(sq(n)).py

def is_prime(num):

    if num == 1:
        return False
    
    count = 2
    
    while count * count <= num:
    
        if num % count == 0:
            return False
            
        count += 1
        
    return True