def is_prime(n):
    if n == 2:
        return True
    if n%2:
        return False
    k = 3
    while k*k <= n:
        if n%k == 0:
            return False
        k += 2
    return True
def smallest_factor(n):
    """ n is an integer n >= 2
    returns smallest factor of n that is >= 2.
"""
    if n% 2 == 0:
        return 2
    k = 3
    while k*k <= n:
        if n%k == 0:
            return k
        k += 2
    return n
def prime_factors(n):
    """ n is an integer, n >= 2
    returns a list of all of the prime factors of n
    prime_factors(100) -> [2, 2, 5, 5]
    prime_factors(1003) -> [17, 59]
    prime_factors(997) -> [997]
    prime_factors(16777216)
    
    """
    out = []
    k = 2
    while n > 1:
        d = smallest_factor(n)
        n //= d
        out.append(d)
    return out

def prime_factors(n):
    if n == 1:
        return []
    d = smallest_factor(n)
    return [d] + prime_factors(n//d)
print(prime_factors(105))
print(prime_factors(16777216))
print(prime_factors(1003))
print(prime_factors(997))
print(smallest_factor(100) ==2)
print(smallest_factor(1003) ==17)
print(smallest_factor(1000000007) ==1000000007)
#for k in range(2,101):
    #print(f"{k} -> {smallest_factor(k)}")