How to create the most compact mapping n → isprime(n) up to a limit N?

Question

Naturally, for bool isprime(number) there would be a data structure I could query.
I define the best algorithm, to be the algorithm that pr

Answer 1

According to wikipedia, the Sieve of Eratosthenes has complexity O(n * (log n) * (log log n)) and requires O(n) memory - so it's a pretty good place to start if you aren't testing for especially large numbers.