Quickly determine if a number is prime in Python for numbers < 1 billion

Question

My current algorithm to check the primality of numbers in python is way to slow for numbers between 10 million and 1 billion. I want it to be improved knowing that I will never

Answer 1

For numbers as large as 10^9, one approach can be to generate all primes up to sqrt(10^9) and then simply check the divisibility of the input number against the numbers in that list. If a number isn't divisible by any other prime less than or equal to its square root, it must itself be a prime (it must have at least one factor <=sqrt and another >= sqrt to not be prime). Notice how you do not need to test divisibility for all numbers, just up to the square root (which is around 32,000 - quite manageable I think). You can generate the list of primes using a sieve.

You could also go for a probabilistic prime test. But they can be harder to understand, and for this problem simply using a generated list of primes should suffice.