Before we finish off this chapter, how about one last 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 whether a number, N, is prime. You can stop at √N. Moreover, you don't need to test the division for all numbers from 2 to √N, 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 = ceil(sqrt(candidate)) # division limit
for prime in primelist: # we try only the primes
if prime > root: # no need...