Efficient storage of prime numbers

Question

For a library, I need to store the first primes numbers up to a limit L. This collection must have a O(1) lookup time (to check whether a number is prime or not) and it must

Answer 1

At the moment you are treating 2 as special case and then having an array where every odd number is mapped to an element in the array (with some odd numbers being prime). You could improve on this by treating 2 and 3 as special cases recognising that the rest of the prime numbers are in the form 6n+1 or 6n-1 (that is for all primes p where p > 3, p mod 6 = 1 or 5). This can be further generalised - see Wikipedia. For all primes p > 5, p mod 30 = 1, 7, 11, 13, 17, 19, 23 or 29. You could keep going with this and reduce the memory needed at the expense of processing time (although it will still be O(1), just a slower O(1)).