One final example

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...