@kruoli: As of now, the program uses a bit array for the primes, which it iterates. The parallelized algorithm relies on some way to store the primes, and then it chops the list of primes into about equal pieces (whether by the length of the range, or prime count in that range  about the same for these quantities of primes), saves the actual value of the last prime in each range (one range per worker), and when the actual values are needed in the computation, it calculates the from the position in the range, range number (used for finding the last prime in previous range) and if running from a savefile, also the last prime used in the computation of the savefile.
BTW, I forgot to mention, that I need a way to efficiently sieve them, too. Sieving is done quite easily in RAM, but sieving on disk is a bit more complicated, albeit not too complicated. To be clear, I am not thinking about using other methods than Eratosthenes (unless they are more efficient), but the storage of bits representing the integers is the tricky part when you need a lot of them.
Storing only the prime gaps seems to be a lot better, but is there a better way to store the sieving data?
@Batalov: As kruoli kindly explained, I am calculating the Prime representing constant, which can only generate (thus my confusion in the name) primes which were used in its computation, using the recursive formula. So 1 billion digits of the constant only suffice for primes under about 2 302 586 000.
Using the formula to generate the primes back is perhaps the only way to confirm the correctness of the digits, apart from computing them with some different method (there is another formula, but it is equivalent to the one mentioned in the paper  it is basically the same, only the one in the paper has its terms grouped, thus has fewer terms for the same amount of digits, but the terms take longer to compute, so it equals out).
