Python nested for-loops & break statement

Question

I'm working my way through an official Python tutorial and I can't for the life of me figure out how the nested for loops work in example 4.4 :

for n in range(2, 10):
    for x in range(2, n):
        if n % x == 0:
            print n, '==', x, '*', n/x
            break
    else:
        # loop fell through w/o finding a factor
        print n, 'is a prime number'

range(2, 10) produces: n = [2, 3, 4, 5, 6, 7, 8, 9] ,so the way I understand it the inner for loop: for x in range(2, n): should produce (x, n-1) and thus the following pairs of x, n with each iteration: (2, 1), (3, 2), (4, 3), (5, 4), (6, 5), (7, 6), (8, 7), (9, 8) . Now, obviously that would never produce n % x == 0 but that's the only way I can think about it. When I print this piece of code:

for n in range(2, 10):
    for x in range(2, n):
        print x, n

to check what numbers will be generated, it returns (the first 6 pairs):

2 3
2 4
3 4
2 5
3 5
4 5

How can the first pair x, n be 2, 3 if the first n is 2 - 1 since the last position of range() will be excluded. I'm utterly and miserably lost.

Answer 1

The reason is that range(x,x) returns an empty list. In the first iteration you call for x in range(2, n) with n=2 . This loop is completely skipped and Python continues with the next iteration of the outer-loop.

Answer 2

Using the second code snippet for example:

for n in range(2, 10):

n doesn't start from 2 - 1 , it starts with 2 , then 3 , 4 , until 9 .

In the nested loop:

    for x in range(2, n):

When n is 2 , for x in range(2, 2) is an empty range. When n is 3 , x could be 2 , generating the first valid pair 2 3 . When n is 4 , x could be 2 and 3 , generating the second the third pair 2 4 and 3 4 . The rest is similar.