Returning comparison in Python

Question

I have this code:

def isPrime(nr):
    """
    Verify if a number is prime
    nr - integer number, nr>1
    return True if nr is prime, False otherwise
    """
    div = 2 #search for divider starting from 2
    while div<nr and nr % div>0:
        div=div+1
    #if the first divider is the number itself 
    #then the number is prime
    return div>=nr

It's not written by me, so I'm trying to understand how the algorithm works, apparently it is using a form of divide & conquer.

What I don't understand is what the last line does:

return div>=nr

Answer 1

return div>=nr

...is equivalent to...

if div >= nr:
    return True
else:
    return False

That is, it is not "returning a comparison" but returning the result of a comparison.

Answer 2

The algorithm is just testing every number from 2 up to nr to test if nr is divisible by the number. If at any point it is (nr % div is equal to 0), the loop breaks. This will return False if div < nr. If the loop gets to nr, then we know there is no number between 2 and nr that divides the nr and so it is prime, returning True. The other answer explains how the return works.

Definitely not using divide & conquer.

Answer 3

Python comes with an interactive environment where you can experiment with simple scripts like the one you posted.

$ python                           # From the command line just run 'python'.

>>> nr = 13                        # Type in some code.
>>> div = 2
>>> while div<nr and nr % div>0:
...   div=div+1
...                                # Press 'Enter' here to end the indentation.
>>> div                            # Type a variable to see what it equals.
13
>>> nr                             # Again.
13
>>> div>=nr                        # Ahhh, the answer to your question.
True
>>>