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kimwalisch avatar kimwalisch commented on August 15, 2024

I am asked about supporting primes > 2^64 about once a year and I have thought about whether or not to implement this quite extensively.

Here are the reasons why I will not implement this:

  • Most libprimesieve use cases require generating small primes.
  • The segmented sieve of Eratosthenes uses O(sqrt(n)) memory which becomes an issue above 2^64. E.g. primesieve would require > 1 terabyte of RAM for sieving near 10^25.
  • The initialization time of the segmented sieve of Eratosthenes becomes a bottleneck past 2^64. The initialization could takes hours for large numbers even if sieving a tiny interval.
  • libprimesieve should be extremely portable without any external dependencies.
  • boost::multiprecision is not an option because it is so slow it is not even funny.

My main design goals for primesieve are: it should be self contained (no external dependencies), it should use only standard C++ and it should be extremely portable.

Sorry, I know supporting arbitrarily large primes would be cool but it won't happen.

from primesieve.

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