Question

I’m trying to do a simple primality test in Python.

Accoding to Wikipedia, a primality test is the following:

Given an input number n, check whether any integer m from 2 to n − 1 divides n. If n is divisible by any m then n is composite, otherwise it is prime.

I started with ruling out the even numbers – with the exception of 2 – as candidates to prime

def prime_candidates(x):
    odd = range(1, x, 2)
    odd.insert(0, 2)
    odd.remove(1)
    return odd

Then writing a function to check for primes, according to the rules above.

def isprime(x):
    for i in range(2, x-1):
            if x % i == 0:
                    return False
            else:
                    return True

And this is the main function, which iterates over a list of 8000 prime candidates and tests their primality

def main():
    end = 8000
    candidates = prime_candidates(end)
    for i in candidates:
            if isprime(i) and i < end:
                    print 'prime found ' + str(i)

The problem is that the isprime function returns True for numbers that aren’t primes.

Answer 1

In brief, your isprime(x) checks whether the number is odd, exiting right after if x % 2 == 0.

Try a small change so that you would actually iterate:

def isprime(x):
    for i in range(2, x-1):
        if x % i == 0:
            return False
    else:
        return True

Note that else: is now part of the for loop rather than if statement.