This notebook was prepared by [Thunder Shiviah](https://github.com/ThunderShiviah). Source and license info is on [GitHub](https://github.com/ThunderShiviah/code_guild).

Solution Notebook

Problem: Implement list_primes(n), which returns a list of primes up to n (inclusive).

Constraints
Test Cases
Algorithm
Code
Unit Test

Constraints

Does list_primes do anything else?
- No

Test Cases

list_primes(1) -> [] # 1 is not prime.
list_primes(2) -> [2]
list_primes(12) -> [2, 3, 5, 7 , 11]

Algorithm

Primes are numbers which are only divisible by 1 and themselves.

5 is a prime since it can only be divided by itself and 1. 9 is not a prime since it can be divided by 3 (3*3 = 9). 1 is not a prime for reasons that only mathematicians care about.

To check if a number is prime, we can implement a basic algorithm, namely: check if a given number can be divided by any numbers smaller than the given number (note: you really only need to test numbers up to the square root of a given number, but it doesn't really matter for this assignment).

Code



In [98]:

    
def list_primes(n):
    primes = []
    for p in range(2, n + 1): # we add a '+ 1' to be inclusive.
        for num in range(2, p):
            if p % num == 0:
                break
        else:
            primes.append(p)
    return primes

Unit Test



In [100]:









    



Overwriting test_list_primes.py



In [101]:

    
%run -i test_list_primes.py









    



Success: test_list_primes



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