Recursions to produce the prime numbers in Python 2

Question

I was trying to use a recursion to produce the prime numbers in python (because I found that an iterative approach would take too much time, especially if say one wants to find all the prime numbers up to a number like 1 million or so). This is my code:

def primes(n): #to produce prime numbers less than or equal to n
    if n <= 1:
        return "No primes that satisfy"
    elif n == 2:
        return [2]
    else:
        if all(n%a != 0 for a in primes(n-1)): #A number, n, must not be divisible by any of the prime numbers contained in the list primes(n-1)
          k = primes(n-1).append(n)
          return k
        else:
          S = primes(n-1)
          S = primes(n)
          return S
print primes(5)

I am getting the following error- TypeError:'NoneType' object is not iterable. I am only a beginner in Python and I am not sure what this means. I would greatly appreciate it if anyone could point out why this error originates and what improvements I may be able to make to the program to avoid this error. Thank you

Answer 1

Consider this program fragment:

k = primes(n-1).append(n)
return k

The return value from list.append() is None, so k = None, and you effectively perform return None.

Try this:

k = primes(n-1) + [n]

Aside: OP has at least one other bug. They need to delete the line S = primes(n)