Where can I get a list of prime numbers up to 10^617?

Question

I'm not sure how many there are... enough though to discourage me from finding them all myself :-)

But ya, just a list.

I think 10,000 is about 1/1000000000000000000000000000000000000 what I need... Try harder please :-)

I can't load your pages for some reason...

I don't care how big it is, I can wait a month.

And buy some extra hard drives.

And some RAM.

Maybe a new processor too.

Answer 1

You will have to be realistic. A character file containing all the primes up to only 10^12 would occupy about 400 gigabytes. Compare that with your broadband download ration, and see how many more powers of 10 you could manage even if the files existed.

There are world-class researchers exploring the density of primes. They make use of refined approximation formulae, instead of an actual list of primes, once they get up towards 10^20.

Answer 2

The approximate number of primes less than some number x, denoted π(x), is approximately equal to x/ln x (see http://en.wikipedia.org/wiki/Prime_number_theorem). This means that the number of prime numbers that would be on your supposed list is approximately:

10^617/(617 ln 10) ≈ 7.0388 * 10^613. Conversely the number of atoms in the universe is less than 10^100. The corollary is that there cannot possibly be a list of all the prime numbers up to 10^617, since such a list would be entirely too large to fit in the universe.

Answer 3

It gives 10,000 prime numbers

Answer 4

err, you are asking for all primes with less than 617 digits... Wikipedia had some big ones, however none were *that* big!!!

Answer 5

Same site has the first 15 million primes:
http://primes.utm.edu/lists/small/millions/

But, that's still a long ways off from where you want to be.

Answer 6

This may not answer your question, but it's certainly worth looking at.