Python Prime Checker错误25？

Question

So I'm relatively new to Python and trying to define a function which will check to see if a number is prime or not. The code is as follows:

def prime(x):
    if x < 2:
        return False
    elif x == 2:
        return True
    else:
        for i in range(3, int((x**0.5)+1)):
            if x % i == 0:
                return False
            else:
                return True

This seems to work for most values however it fails on certain values such as 25, can anyone help to explain to me why? Thanks!

Answer 1

return leaves your function once it is reached. Let's look at the case of 25 .

• Is x<2 no, so continue.
• Is it x==2 no, so continue.
• Is x divisible by i(=3) ? No, so go to the else clause, return True leave the function.

See the issue?

To put it another way, for sufficiently large x , your function is equivalent to:

def prime_prime(x):
    if x < 2:
        return False
    elif x == 2:
        return True
    else:
        if x % 3 == 0:
            return False
        else:
            return True

Answer 2

It's the

else:

clause, the first i it checks will make it return true.

Instead, write

else:
    for i in range(3, int((x**0.5)+1)):
        if x % i == 0:
            return False
    return True

EDIT: And as @mata points out, you actually need to start at 2, so it should be for i in range(2, int((x**0.5)+1)):