I am working with recursive prime sequences of the form
Unfortunately, the values get large fast, and the Prime[n] function tops out at around Prime[8trillion].
Is there a way to get more primes, such as a Mathematica package or? I haven't been able to find any complete lists of primes larger than this. Ideally, I need a complete list of primes up to Prime[10^100] or so.
I suppose I could let a Sieve of Eratosthenes run, and dump primes to a text file, but I'm guessing that would take... months or years to get to Prime[10^100]? Any advice is appreciated.
Your guess is off by a bit...
Use the Prime Number Theorem to estimate how many primes are in the set of integers up to 10^100. Then do any of the following.
(1) Estimate how long to store that sequence, assuming you can store one per chip cycle, using say 10^5 chips each operating at 10^12 cycles per second.
(2) Compare the number to estimated atoms in the universe.
(3) Rethink the computation you are doing to see if there is a variant that is computationally feasible. The one stated is not.
Thanks Daniel. Kind of a silly question in retrospect. I will use an estimating function for the time being, such as (DasGupta 2005)
If anyone has a more accurate one, I'm all ears.