One final example
Before we finish off this chapter, how about a final example? I was thinking we could write a function to generate a list of prime numbers up to a limit. We've already seen the code for this so let's make it a function and, to keep it interesting, let's optimize it a bit.
It turns out that you don't need to divide it by all numbers from 2 to N-1 to decide if a number N is prime. You can stop at 
. Moreover, you don't need to test the division for all numbers from 2 to , you can just use the primes in that range. I'll leave it to you to figure out why this works, if you're interested. Let's see how the code changes:
primes.py
from math import sqrt, ceil def get_primes(n): """Calculate a list of primes up to n (included). """ primelist = [] for candidate in range(2, n + 1): is_prime = True root = int(ceil(sqrt(candidate))) # division limit for prime in primelist: # we try only the primes if prime > root: # no need to check...