Returning whether or not a number is prime as a Boolean in Python

Question

For context, I am trying to solve Project Euler problem 3 using Python:

What is the largest prime factor of the number 600851475143?

As a first step to this, I am trying to write a function that returns whether or not a number is prime as a Boolean. I made a first attempt, and checked out how this has been written previously. I have ended up with the following code:

def isprime(x):
    limit = x**0.5
    i = 2

    if x < 2:
        return False
    elif x == 2:
        return True
    else:
        while i <= limit:
            if x%i == 0:          
                return False
                i = i + 1       
            else:
                return True

For some reason, the code above does not work perfectly. For example, isprime(99) would return True.

Please, can someone help me understand why this isn't working? I am trying to avoid just copying and pasting someone else's code, as I want to understand exactly what is going on here.

To me, it looks like the issue is with the final else statement. I say this because the logic reads "in the event that x%i == 0 , this number is not prime" but it doesn't explicitly say what to do in the event that no x%i iterations == 0 .

Any help on this would be appreciated, I'm not necessarily looking for the cleanest, neatest way of doing this. but more just trying to first make this code work.

Answer 1

Try this:

def isprime(x):
    limit = x**0.5
    i = 2
    if x <= 2:
        return False

    while i <= limit:
        if x%i == 0:          
            return False      
        i = i + 1
    return True 

I've changed many things. have this point in your mind that there is no need to else clauses when you return at the end of if block.

Answer 2

you need to tell what happens when x%i==0 condition not met and the value of i remain constant and also need to see when all conditions not met, then it is a prime

# your code goes here
def isprime(x):
    limit = x**0.5
    i = 2

    if x < 2:
        return False
    elif x == 2:
        return True
    else:
        while i <= limit:
            if x%i == 0:         
                return False
            i+=1
    return True
print(isprime(144)) # false
print(isprime(99)) # false
print(isprime(131)) # true

Answer 3

Just to show an alternative, what you could do is checking from number 2 to your number if the operation (x % i) is equal to zero. If it never happend, it will be a prime.

def isprime(x):
   # check for factors
   for i in range(2,x):
       if (x % i) == 0:
           return False
   else:
       return True

print(isprime(99))