# Obtain more primes than Prime[n] offers?

Posted 1 year ago
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 I am working with recursive prime sequences of the form Prime[Prime[Prime[Prime[n]]]] 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.
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Posted 1 year ago
 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.