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

If you can figure out which ones are Mersenne or other easily represented prime numbers, you might be able to save a few bits by using that representation with a flag for applicable numbers.

Also, how about storing the numbers as the difference from the previous number? Then the size shouldn't rise quite as fast (but lookup would be slow). Combining with the approach above, you could store Mersenne primes and the difference from the last Mersenne prime.