python - Whats the difference between those two prime number checking algorithms

Question

so recently I've been trying to figure out algorithm which is supposed to check whether the number is prime or not. So I came up with an idea and made the code look like this:

def if_prime(num):
   
    for divisor in range(2,num):
        if (num % divisor) == 0:
            return f"{num} is not prime"
        else:
            return f"{num} is prime"
print(if_prime(9))

So basically this code returns the wrong value, it says that 9 is a prime number and obviously it is not, however the following code seems to work, and I have no idea what's the difference.

def if_prime(num):
    for divisor in range(2,num):
        if (num % divisor) == 0:
            return f"{num} is not prime"                                      
    return f"{num} is prime"

print(if_prime(9))

question from:https://stackoverflow.com/questions/65833150/whats-the-difference-between-those-two-prime-number-checking-algorithms

Answer 1

There is a lot difference!

The first one is wrong!:

def if_prime(num):
   
    for divisor in range(2,num):
        if (num % divisor) == 0:
            return f"{num} is not prime"
        else:
            return f"{num} is prime"

This checks whether a number has any factor between 0 and num and if it finds a factor it returns saying that the number is not prime.

But the mistake is that if it does not find a factor then it returns true at once and does not check for other divisors:

For example this will say that 9 is a prime number is it is not divisible by 2 and the if condition becomes false!

On the other hand the second one is correct! :

def if_prime(num):
    for divisor in range(2,num):
        if (num % divisor) == 0:
            return f"{num} is not prime"                                      
    return f"{num} is prime"

In this one too we loop through all the divisors from 2 to num but in this case we do not return anything if one number is not a divisor( we check through all the possible divisors ) thus if the loop ends and we find no divisor then it means it is a prime number!

But this too has a small bug as it will say 1 is a prime number!

Here is a proper and efficient version of the if_prime function:

def if_prime(num):
    for divisor in range(2, num/2):
        if (num % divisor) == 0:
            return f"{num} is not prime"                                      
    if num == 1:
        return f"{num} is not prime"
    else:
        return f"{num} is prime"