Question

I was trying to create this helper function in C# that returns the first n prime numbers. I decided to store the numbers in a dictionary in the <int,bool> format. The key is the number in question and the bool represents whether the int is a prime or not. There are a ton of resources out there calculating/generating the prime numbers(SO included), so I thought of joining the masses by crafting another trivial prime number generator.

My logic goes as follows:

public static Dictionary<int,bool> GetAllPrimes(int number)
    {
        Dictionary<int, bool> numberArray = new Dictionary<int, bool>();


        int current = 2;
        while (current <= number)
        {
            //If current has not been marked as prime in previous iterations,mark it as prime
            if (!numberArray.ContainsKey(current))
                numberArray.Add(current, true);

            int i = 2;
            while (current * i <= number)
            {
                if (!numberArray.ContainsKey(current * i))
                    numberArray.Add(current * i, false);
                else if (numberArray[current * i])//current*i cannot be a prime
                    numberArray[current * i] = false;
                i++;

            }
            current++;
        }
        return numberArray;
    }

It will be great if the wise provide me with suggestions,optimizations, with possible refactorings. I was also wondering if the inclusion of the Dictionary helps with the run-time of this snippet.

Answer 1

Storing integers explicitly needs at least 32 bits per prime number, with some overhead for the container structure.

At around 2³¹, the maximal value a signed 32 bit integer can take, about every 21.5th number is prime. Smaller primes are more dense, about 1 in ln(n) numbers is prime around n.

This means it is more memory efficient to use an array of bits than to store numbers explicitly. It will also be much faster to look up if a number is prime, and reasonably fast to iterate through the primes.

It seems this is called a BitArray in C# (in Java it is BitSet).