Python Prime Testing
Congratulations, you just came up with a prime sieve! And indeed, it's faster than always considering all the multiples of 2 of 3. But why do you stop at multiples of 2 and 3? What about 5? And 7? But why stop somewhere?

Let's be more ambitious. What about skipping all the multiples of all the primes encountered so far? This is called the sieve of Eratosthenes. It uses more memory (if you double the maximum number you're interested in, you need twice the memory), but it will be faster and will tell you if any number below your maximum number is prime.

If you want more improvements, note that other prime sieves exist: both the sieve of Sundaram and the sieve of Atkin improve over the sieve of Eratosthenes. And of course, if you're interested in raw speed, use numpy or even a language like C.