Question

def all_primes(start,end):
    list_nonprimes = []
    list_primes = []

    for i in range(start,end):
        for a in range(2,i):
            if i % a == 1 and i not in list_nonprimes:
                if i not in list_primes:
                    list_primes.append(i)
            else:
                list_nonprimes.append(i)

    return list_primes

Why is this giving me an an incorrect output?

>>> all_primes(1,10)
[3,5,7,9]

How do I eliminate the 9?

Answer 1

There’s a more straightforward way to do this, since you’re already inherently generating the list of primes less than the number you’re currently checking:

def all_primes(start,end):
    list_primes = []

    for i in range(2,end):
        for a in list_primes:
            if i % a == 0:
                break
        else:
            list_primes.append(i)

    return [x for x in list_primes if x >= start]

Key to understanding this is knowing how the for...else construct works in Python. Essentially, a for loop can have an else statement, which is only executed if no break statement was run during the evaluation of the loop.