Thread: Storing a "large" number of prime numbers

I have been writing some c code to investigate the properties of prime numbers. Currently I have a function getPrimes(int primemax) which dynamically allocates memory for an array of the primes, so that primes[0]=2 , primes[1]=3 .... This has been working well, but I am going to need a more permanent and scalable way to store them as primemax grows large. I am not opposed to using some service (if such a service exists) or to writing my own code to possibly store them as a csv list.
My future algorithm will constantly be needing to find primes[bignumber] where bignumber is the index of the primes array. The actual prime stored in that index will be even larger.
Any thoughts appreciated. Thanks.

I will need go beyond 64 bit unsigned integers, so I will need to use some sort of additional library at the least. I am beginning to think python might be an easier road, i've read that the int datatype has an arbitrary size. I've just started to get dialed into c and feel that under the hood it will be better to do it with c though.
And yes I am aware there are infinite primes, in fact it's one of my favorite proofs. (And possibly the only proof I have memorized)
And so "large" will mean 50-100+ decimal digits (for the prime values) dwarfing the default data size for ints-- the indexes on the other hand should be ~2% of the largest prime I'll need.

I am trying to factor large semi-prime numbers (prime multiplied by a prime.) You can probably do the math, and I realize that this may all be in vain, but it's a lot of fun and I'm learning a ton about other things I would never come across. And for the record I am doing it as a purely academic pursuit (though not for credit) in the sense that I am not trying to factor any one particular number to crack it, but to look at properties of all semi primes. I realize there is a >99% chance I will not find an algorithm better than current sieves. But that doesn't mean you can't try.

Thanks