In Python, write a script that determines whether or not a user-inputted number is a prime number

Question

Write a script that determines whether or not a user-inputted number is a prime number and prints "The number that you inputted is a prime number" or "The number that you inputted is not a prime number" depending on what your script finds.

I have code that is failing some of the test cases and I'm not sure why. I see some answers on here that involve calculate the sqrt, but I don't understand why that'd be beneficial.

num= int(input())

if num == 0 or num ==1:
    print('The number you inputted is not a prime number.')
while num < 0:
    break
if num > 0:
    for i in range(2,num):
        if num%i==0:
            print('The number you inputted is not a prime number.')
            break
        else:
            print('The number you inputted is a prime number.')
            break

The code is always right when I try it with a few test cases, but it isn't passing my homework assignment.

Answer 1

Your logic is wrong; you should break only if the condition evaluates to True , since you need to test all numbers up to num ** 0.5 ( num in your code). 9 is an example of a non-prime number that your code evaluates as prime.

You want something like this:

prime = True
if num > 0:
    for i in range(2,num):
        if num % i == 0:
            prime = False
            break

    if prime:
        print(f'{num} is a prime number.')

    else:
        print(f'{num} is not a prime number.')

By setting prime to True at the start and changing it to False only if a factor is found, we can tell, after evaluation of the condition for all the values of i , if the number is prime.

Answer 2

The problem occurs in the logic below:

for i in range(2,num):
    if num%i==0:
        print('The number you inputted is not a prime number.')
        break
    else:
        print('The number you inputted is a prime number.')
        break

To see where the issue occurs, try using your code to check if 9 is prime. Your for loop does the following:

1. i = 2
2. if num % i == 0 , not prime, break.
3. else , prime, break.

This means that your for loop is guaranteed to stop at i==2 . In other words, your definition for a prime number, according to this algorithm is 'any odd number'.

To fix this, you need to find a way to allow the loop to iterate between all the remaining possible divisors, without breaking after the first iteration.

I'm going to stop there, to give you a chance to see if you can figure the rest out yourself. If you can't make any progress, let me know, and I'll give another hint.