Question

So I’m trying to learn Python using some tutorials, and I decided to create my own exercise. I wanted to create a script that figures out how many prime numbers there are between 1 and 1000, as well as printing the prime numbers. This is what I have so far:

numberlist = []
a = 1
prime = True
while a < 1000:
    a = a + 1
    for divisor in range(2,a):
        if a/divisor==int(a/divisor):
            prime=False
        if prime == True:
            print a
            numberlist.append(a)

print "Number of prime numbers between 1 and 1000:", len(numberlist)

However, when I start the application, it returns

“Number of prime numbers between 1 and 1000: 0”

I don’t know what I’ve done wrong. Can someone please clarify what I screwed up on?

Thank you for your help.

Edit: So now the code looks like this, but the same problem is occurring:

numberlist = []

a = 1

for a in xrange(1, 1000):
    for divisor in range(2,a):
        if a % divisor == 0:
           prime=False
        else:
           prime=True
if prime == True:
    print a
    numberlist.append(a)

print "Number of prime numbers between 1 and 1000:", len(numberlist)

Answer 1

There are a number of problems with this code. First, a/divisor == int(a/divisor) is always True, because division in Python is integral (you will always get an integer result). Use a % divisor == 0 instead.

Another problem is that prime = True is outside the loop, meaning that as soon as one value is declared not prime, no more values can be prime! (prime will never get set back to True anywhere.)

A third issue, more of style, is that it is preferred to use a for ... in loop in python, eg

for a in xrange(1, 1000):
    for divisor in xrange(2, a): ...

Edit: Regarding your modified code: your if statement at the very end is not indented, and therefore not part of the for loop. It is only being executed once, after the loop ends, meaning prime will be the last value set (where a is 999, not a prime). You want to indent the entire if statement to be in your inner for loop. You could condense this, though:

for a in xrange(1, 1000):
    for divisor in xrange(2, a):
        if a % divisor == 0:
            break
    else:
        print a
        numberlist.append(a)

Note that this uses the for ... else clause. Putting else at the end of a for loop will cause that else block to run only if the loop is not broken by break.

As a further comment, starting the whole loop at 1 will have 1 in the list, but 1 is not a prime.