When did the number got included in the list?

[deanhystad]

Anyway whats the point of having a function if you need an if statement to stop the generator.

First off, it is a generator, not a function. Functions return a value and they are done. Generators return a value and hold.

The point of a generator like this is you may not always know when a sequence should end. Lets say I want a sequence of prime numbers that add up to 100 or less. I don't know when my sequence should stop exactly. I can guess, but I don't know. I could write it like this:

primes = []
total = 0
for p in prime_numbers():
    if (total := total + p) > 100:
        break
    else:
        primes.append(p)
print(sum(primes), primes)

Output:
100 [2, 3, 5, 7, 11, 13, 17, 19, 23]

Or if you prefer a while loop.

primes = []
total = 0
prime_gen = prime_numbers()
while total < 100:
    p = next(prime_gen)
    if (total := total + p) <= 100:
        primes.append(p)
print(sum(primes), primes)

My example is a bit hokey, but so is the prime_numbers() generator in your example. I think this code is supposed to demonstrate using a generator and is not meant to be used as a prime number generator.

I agree that there is probably a little language barrier here. Some of your questions are a bit awkward, but I am only proficient in one language, so you are way ahead of me. This is far from "conversational English" and many native English speakers have trouble asking questions on this forum.