Two by Two
Since all primes except 2 are odd and in our case 2 is not a factor of 600851475143, we can start with 3 and iterate two by two, which is not a great improvement, but this problem has no interesting solution anyway.
From solution2.py:
def largest_prime_factor(n=600851475143):
res = 3
while n != 1:
if n % res == 0:
n //= res
else:
res += 2
return res